CA2315196A1 - Spectral optimization and joint signaling techniques for communication in the presence of cross talk - Google Patents

Abstract

A system and method for determining transmission characteristics for a communications channel and for transmitting data on the communications channel. This method may be used in communicating data when the channel is subject to interference from one or more other communications channels, including near-end cross talk (NEXT) and far-end cross talk (FEXT) from other channels carrying the same service and/or different services. The present ivention may be used in digital subscriber-line (xDSL) communications or in a variety of other applications, such as in well-logging and in systems involving multiple interfering radio transmitters. In a preferred embodiment, the invention comprises a method of determining an optimal transmit mask or power spectral density (PSD) function for use on the communications channel. The transmit function is preferably determined in response to the channel transfer function and the amounts of self-NEXT interference, self-FEXT interference, and uncorrelated interference such as AGN and interference from different-service communications channels.

Description

SPECTRAL Ol'I'1M1ZATION AND JOINT SIGNALING TECHNIQUES FOR COMMUNICATION IN
THE PRESENCE OF
CROSS TALK
s FIELD OF THE INVENTION
to The invention relates to electronic communication and, more particularly, to techniques for commutucating on communications channels subject to interference such as cross talk and noise.
OUTLINE
is Description of the Related Art 1 Communications Background 1.1 Twisted pairs 1.2 Overview of services 1.3 Crosstalx interference 20 1.3.1 1VEXT and FEXT
I.3.2 Notation for self NEXT and self FEXT
1.4 Ca~pacit;y and performance margin 2 Problem Statement 2.1 General statement 2s 2.2 Particular statement for DSLs 2.2.1 1HDSL2 service 2.2.2 "GDSL" service WO 99/33215 PCT/US98l27154 2.2.3 "VDSL2" service 3 Previous Work -3.1 Static PSD Masks and transmit spectra 3.2 Joint signaling techniques 3.3 Multit~one modulation 3.4 Summary of previous work Summary of the Invention t o Brief Description of the Drawings Detailed Description ~of the Preferred Embodiments 4 New, Optimized Signaling Techniques 4.1 Assumptions, Notation, and Background 4.2 Interference models and simulation conditions 4.3 Signaling schemes 4.4 Optimization: Interference from other services (DSIN-NEXT and DSIN-FEXT) - Solution: E(>PSD signaling 4.4.1 Problem statement 20 4.4.2. Additional assumption 4.4.3 Solution 4.4.4 Examples 4.5 Optimization: Interference from other services (DSIN-NEXT and DSIN
FEXT) plus self interference (self NEXT and low self FEXT) - Solution: EQPSD
and 2_<<~ FDS signaling 4.5.1 Self NEXT and self FEXT rejection using orthogonal signaling 4.5.2. Problem statement 4.5.3 Additional assumptions 4.5.4. Signaling scheme 4.5.5 Solution: One frequency bin 5 PCT/US98lZ7154 4.5.6 Solution: All frequency bins 4.5.7 Algorithm for optimizing the overall transmit spectrum 4.5.8 Fast, suboptimal solution for the EQPSD to FDS switch-over bin 4.5.9 Flow of the scheme 4.5.10 Grouping of bins and wider subchannels 4.5.11 Examples and results 4.5.12 Spectral compatibility 4.6 Optimization: Interference from other services (DSIN-NEXT and DSIN-FEXT) plus self interference (self NEXT and high self FEXT) - Solution: EQPSD, FDS
and mufti-line FDS signaling 4.6.1 Self FEXT and self NEXT rejection using mufti-line FDS
4.6.2 Problem statement 4.6.3 Additional assumptions 4.6.4 Signaling scheme is 4.6.5 Solution using EQPSD and FDS signaling: All frequency bins 4.6.6 Switch to mufti-line FDS: One frequency bin 4.6.7 Switch to mufti-line FDS: All frequency bins.
4.6.8 Special case: Performance of 2 lines 4.6.9 Flow of the scheme 20 4.6.1 ~0 Examples and results 4.7 Joint signaling for lines differing in channel, noise, and interference characteristics 4.7.1 Solution for 2 lines: EQPSD and FDS signaling 4.7.2 Solution for M lines: EQPSD and FDS signaling 2s 4.7.3 Solution for 2 lines: EQPSD and mufti-line FDS signaling 4.8 Optimizing under a PSD mask constraint: No self interference 4.8.1 Problem statement 4.8.2 Solution 4.8.3 Examples 30 4.9 Optimizing under a PSD mask constraint: With self interference WO 99/33215 PCTNS9t3/Z7154 4.9.1 Problem statement 4.9.2 Solution 4.9.3 Algorithm for constrained optimization of the transmit spectra 4.9.4 Examples and results , s 4.10 Bridged taps 4.10:1 Optimal transmit spectra 4.1 ~D.2 Suboptimal transmit spectra 4.1 ~D.3 Examples and discussion 4.11 Optimization: Asymmetrical data-rate channels t o 4.12 ExtE;nsions 4.12.1 More general signaling techniques 4.12.2 More general interferes models 4.1:2.3 Channel variations 4.12.4 Broadband modulation schemes t s 4.12.5 Linear power constraints in frequency 4.1:2.6 CDS signaling under a peak power constraint in frequency 4.1:2.7 Multi-user detector at central office Optimal signaling techniques for asymmetrical data-rate channels 5.1 Asymmetric data-rate optimization: Interference from other services zo (DSIN-NEXT and DSIN-FEXT) - Solution: SPSD Signaling 5.1..1 Problem Statement 5.1.2 Additional assumptions 5.1.3 Solution 5.1.4 Examples zs 5.2 Asymmetric data-rate optimization: Interference from other services (DSIN-NEXT and I>SIN-FEXT) plus self interference (self NEXT and low self FEXT) -Solution: SPDS and FDS Signaling 5.2.1 Problem Statement 5.2.2 Additional assumptions 30 5.2.3 Signaling scheme 5.2.4 Solution: One frequency bin 5.2.5 Solution: All frequency bins 5.2.6 Examples and results 5.2.7 Extensions 6 Summary of Contributions References Glossary Notation ~ o Appendix DESCRIPTION OF THE RELATED ART
1 Communications Background 1.1 Twisted pair' telephone lines s Telephone service is provided to most businesses and homes via a pair of copper wires (a "twisted pair"). A telephone cable contains many twisted pairs: 25 twisted pairs are grouped in close proximity into 2 "binder groups," and several binder groups are packed together to form a cable. The two terminations of a telephone cable are at the user (subscriber) end and at the telephone company (central office, CO) end. We will use the to terms "twisted pair," "line," and "subscriber loop" interchangeably herein as one example of a communications channel.
Voice telephony uses only the first 4 kHz of bandwidth available on the lines.
However, one can modulate data to over 1 MHz with significant bit rates. Only recently have schemes been developed to exploit the additional bandwidth of the telephone is channel. A plot of tile frequency response of a typical telephone channel is given in FIG.
1.
1.2 Overview of services In the past fe;w years, a number of services have begun to crowd the bandwidth of zo the telephone channel. Some of the important services are:
POTS - KPlain Old Telephone Service." This is the basic telephone service carrying voice traffic in the 0 - 4 kHz bandwidth. Conventional analog modems also use the same bandwidth.
ISDN - Integrated Services Digital Network. This service allows end-to-end digital zs connectivity at bit rates of up to 128 kbps (kilo-bits-per-second).

Tl - Transmission 1. This is a physical transmission standard for twisted pairs that uses 24 multiplexed channels (each at 64 kbps) to give a total bit rate of 1.544 Mbps (Mega-bits-per-second). It uses costly repeaters.
HDSL - High hit-rate Digital Subscriber Line. This is a full-duplex (two-way) s like (1.544 rrlbps) signal transmission service using only two twisted pairs and no repeaters.
ADSL - Asymmetric Digital Subscriber Line. Over one twisted pair, this service provides a high-speed (on the order of 6 Mbps) downstream (from central office (CO) to subscriber) channel to each user and a low-speed (on the order of 640 ~o kbps) upstrc;am (from subscriber to the central office) channel. This service preserves thE; POTS service over a single twisted pair.
VDSL - Very high bit-rate DSL. This yet-to-be-standardized service will provide a very high speed (on the order of 25 Mbps) downstream channel to subscribers and a lower speed upstream channel to the central office over a single twisted pair less ~ s than 3 to 6 kft long. Further, it will preserve the POTS service.
HDSL2 - High bit-rate Digital Subscriber Line 2. This soon-to-be-standardized service will provide full-duplex 1.544 Mbps signal transmission service in both directions (fill duplex) over a single twisted pair (<18 kft long) without repeaters.
"GDSL" - General Digital Subscriber Line. This hypothetical service would (for 2o illustration purposes) carry 25 Mbps full-duplex data rate over a single twisted pair (see Sections 2.2.2 and 4.6.10).
"VDSL2" - Very high bit-rate DSL Line 2. This hypothetical service would (for illustration purposes) carry 12.4 Mbps full-duplex data rate over a single twisted pair less thm 3 to 6 kft long (see Sections 2.2.3 and 4.6.10).
2s Currently, all the above mentioned services have an ANSI standard except for VDSL, HDSL2, "C~DSL" and "VDSL2". The various DSL standards (such as generic DSLs, ADSL, VDSL, HDSL2, and others) are collectively referred to as xDSL.

1.3 Crosstalk interference 1.3.1 NEXT and F»:XT
Due to the close proximity of the lines within a binder, there is considerable s amount of crosstalk interference between different neighboring telephone lines.
Physically, there are two types of interference (see in FIG. 2):
Near-end crosstalk (NEXT): Interference between neighboring lines that arises when signals are transmitted in opposite directions. If the neighboring lines carry the same type of service then the interference is called self NEXT; otherwise, we ao will refer to it as different-service NEXT.
Far-end crossta.lk (FEXT): Interference between neighboring lines that arises when signals are transmitted in the same direction. If the neighboring lines carry the same type of'service then the interference is called self FEXT; otherwise, we will refer to it as different-service FEXT.
os FIG. 3 shows that crosstalk interference can be modeled as additive interference.
Since neighboring limes may carry either the same or a different flavor of service, there are three categories of interference (see FIG. 3):
1. Self interferfnce (self NEXT and self FEXT) between lines carrying the same seance.
ao 2. Interference into a channel carrying service A from other lines carrying services other than A (DSIN-NEXT and DSIN-FEXT).
3. Interference from a channel carrying service A into other lines carrying services other than A (DSOUT-NEXT and DSOUT-FEXT).
Channel noise will be modeled as additive Gaussian noise (AGN).
zs s 1.3.2 Notation for self NEXT and self FEXT
Here is some notation to keep things clear. Number the M twisted pairs (lines) in the cable with index iE {1, . . . , M}, and denote the direction of transmission with index o E {u, d}, with a = upstream (to the central offce) and d = downstream (from the central s office). All the twisted pairs in the cable bundle are assumed to carry the same service.
Let o be the complement direction of o: a = d , d = a . Denote the transmitters and receivers on line i as:
T,.° : transmitter f Tx) on twisted pair i in direction o.
R,.° : receiver (Rx;) on twisted pair i in direction o.
~ o Ideally, T,.° intends to transmit information only to R,.° .
In a real system, however, T,.° 's signal leaks into the receivers R j and R~ . Using our notation, this self interference corresponds to:
Self NEXT: Crosstalk from T,.° into R~ for all j ~ i, o E {u, d}, and Self FEXT: Cros;stalk from T,.° into RJ for all j ~ i, o a {u, d}.
is In a full-duplex xDSL service, each twisted pair i supports transmission and reception in both directions (using echo cancelers), so each line i has a full set of transmitters and receivers: { T" , R; , T,.° , Rd }. With perfect echo cancellation, there is no crosstalk from T° into R° . We will assume this for the balance of this document, although this crosstalk could be dealt with in a fashion similar to self NEXT
and self 2o FEXT.
1.4 Capacity and performance margin The Channel capacity C is defined as the maximum number of bits per second that can be transmittmi over a channel with an arbitrarily small bit error probability. The ' achievable rate RA for a channel is any transmission rate below or equal to capacity, i.e., R~ <_ C. Another channel performance metric is performance margin (or margin).-It is defined (in dB) as SNR"
margin =1 Olog,o SNR""
s where SNR,,~ is the received signal-to-noise ratio (SNR) and SNRm;n is the minimum received SNR required to achieve a fixed bit error probability (BER) at a given transmission rate. The performance margin of a channel for a fixed bit en:or probability measures the maximum degradation (from noise and interference) in achievable bit rate that a channel can sustain before being unable to transmit at that bit rate for a fixed BER
(see [ 12)). The higher the performance margin of a channel at a given transmission rate and fixed BER, the more robust it is to noise and interference, i.e., the better is its performance.
2 Problem Statement ~s 2.1 General statement Given an ai~britrary communications channel with:
1. Self interference (self NEXT and self FEXT) between users of service A, 2. Interference fc~om users of different services with users of service A
(DSIN-NEXT
and DSIN-FI?XT), ~:0 3. Interference from users of service A into users of different services (DSOUT-NEXT and D~SOUT-FEXT), and 4. Other interference (including noise), maximize the capacity of each user of service A without significant performance (capacity or margin) degradation of the other services.
~o Here services could refer to different possible signaling schemes. Users refer to the generic Tx-ltx pars. -2.2 Particular statement for DSLs s 2.2.1 HDSL2 service As a special case of the general problem, we will look into a particular problem of subscriber loops. In particular, we can phrase our statement in the language of HDSL2 [2). Here, the communications channel is the collection of twisted pairs in the telephone cable, interference is caused by:
to 1. Self NEXT .and self FEXT between neighboring HDSL2 lines (self NEXT
dominates over self FEXT [8]), 2. DSIN-NEXT quid DS1N-FEXT from Tl, ISDN, HDSL and ADSL, 3. Interference fn~m HDSL2 into other services, such as T 1, ISDN, HDSL and ADSL, and is 4. Channel noise;, which we will model as AGN.
We wish to 'maximize the capacity of the HDSL2 service in presence of other HDSL2, T1, ISDN, IaDSL, ADSL, VDSL lines and even services not yet imagined while maintaining spectral; compatibility with them. We will consider HDSL2 service in Sections 4.4 to 4.7.
2o The HDSL2 service is intended to fill a key need for fast (1.544 Mbps) yet affordable full duplex service over a single twisted pair. Efforts to define the standard are being mounted by several companies and the T1E1 standards committee. The two key issues facing HDSL~. standards committee are:
Spectral optimization. All previously proposed schemes for HDSL2 achieve the zs required data rates with satisfactory margins only in complete isolation.
i~

wo ~r~32is rcTius9snms4 However, due to the proximity of the lines in a cable, there is considerable DSINNEXT. DSIN-FEXT, self NEXT and self FEXT interference from T1, ISDN, HDS1L, ADSL and HDSL2 into HDSL2 - this interference reduces the capacity of the HDSL2 service.
s Simultaneow~ly, there is considerable DSOUT-NEXT and DSOUT-FEXT
interference .from HDSL2 into T1, ISDN, HDSL and ADSL. This problem is known as spectral compatibility. The scheme ultimately adopted for HDSL2 must not interfere overly with other DSL services like Tl, ISDN, HDSL, and ADSL.
Modulation scheme. No prior system has been developed that systematically n o optimizes the HDSL2 spectrum and reduces interference effects both from and into HDSL2. Further, a modulation scheme for HDSL2 has not been decided upon at this time.
2.2.2 "GDSL" service is Consider the hypothetical DSL service "GDSL" described above. The "GDSL"
service will enable very high bit-rate full-duplex, symmetric traffic over a single twisted pair. We assume that the lines carrying GDSL service have good shielding against self NEXT. In this case, iinterference is caused by:
1. Self NEXT .and self FEXT between neighboring "GDSL" lines (self-FEXT
::o dominates over self NF.~1CT~, 2. DSIN-NEXT quid DSIN-FEXT from T1, ISDN, HDSL, HDSL2 and ADSL, 3. Interference from "GDSL" into other services, such as T1, ISDN, HDSL, HDSL2 and ADSL, and 4. Channel noise., which we will model as AGN.
:a We wish to maximize the capacity of the "GDSL" service in presence of other "GDSL", Tl, ISDN, HDSL, ADSL, HDSL2 lines and even services not yet imagined while maintaining spectral compatibility with them. The spectral optimization issue is similar to the one discussed for HDSL2 case, and we need to find an optimal transmit spectrum for "GL)SL". Further, a good modulation scheme needs to be selected.
s 2.2.3 "VDSL2" service Consider the hypothetical DSL service "VDSL2" described above. Optical fiber lines having very high channel capacity and virtually no crosstalk will be installed in the future up to the curb of each neighborhood (FT'TC). The final few thousand feet up to the customer premises could be covered by twisted pairs. In such a scenario, high bit-rate ro asymmetric-traffic services (like VDSL) and symmetric-traffic services (like "VDSL2") over short length twisted pairs would become important. For illustration of such a potential future service we propose a hypothetical "VDSL2" service that would cant' very high bit-rate symmetric tragic over short distance loops on a single twisted pair. In the "VDSL2" case, the interference will be caused by:
~s Z. Self NEXT' and self FEXT between neighboring "VDSL2" lines (both self-NEXT
and self F.EXT are dominant), 2. DSIN-NExT and DSIN-FEXT from Tl, ISDN, HDSL, HDSL2, VDSL and ADSL, 3. Interference from "VDSL2" into other services, such as T1, ISDN, HDSL, HDSL2, VDSL and ADSL, and 20 4. Channel noise, which we will model as AGN.
Again, we wish to maximize the capacity of "VDSL2" in presence of all the other interferers. To achieve this we need to find optimal transmit spectra and a good modulation scheme.

3 Previous VWork Here we discuss prior work pertaining to HDSL2 service.
3.1 Static PSD masks and transmit spectra s The distribution of signal energy over frequency is known as the power spectral density (PSD). A F'SD mask defines the maximum allowable PSD for a service in presence of any interference combination. The transmit spectrum for a service refers to the PSD of the transmitted signal. Attempts have been made by several groups to come up with PSD masks for HDSL2 that are robust to both self interference and interference to from other lines. One way of evaluating channel performance is by fixing the bit rate and measuring the performance margins [12]: The higher the performance margin for a given disturber combination, the more robust the HDSL2 service to that interference.
The term crosstalk here implies self interference plus interference from other lines.
To the best a~f our knowledge, no one has optimized the PSD of HDSL2 lines in ~s presence of crosstalk: and AGN. The significant contributions in this area, MONET-PAM
and OPTIS, [1, 2, 4, 5] suggest a static asymmetrical (in input power) PSD
mask in order to attempt to suppress different interferers. The PSD masks suggested in [1, 2, 4, 5] have a different mask for each direction of transmission. Furthermore, the techniques in [l, 4]
use different upstream and downstream average powers for signal transmission.
However, 2;o the mask is static, implying it does not change for differing combinations of interferers.
Optis [5] is currently the performance standard for HDSL2 service.
When a constraining PSD mask is imposed, the transmit spectrum lies below the constraining mask. .Specifying a constraining PSD mask only limits the peak transmit spectrum. We do PSDs (transmit spectra) and not masks in this document unless stated :a otherwise. In Section 4.11 we indicate ideas to get PSD masks.

3.2 Joint signaling techniques Self NEXT is the dominant self interference component in symmetric-data-rate, full-duplex, long-length line xDSL service (e.g., HDSL2). One simple way of completely suppressing self NF?XT is to use orthogonal signaling (for example, time division s signaling (TDS), frequency division signaling (FDS), or code division signaling (CDS)).
In TDS, we assign different services to different time slots. In FDS, we separate in frequency the services that could interfere with each other. In CDS, a unique code or signature is used in each direction of service. Further, in CDS each service occupies the entire available bandwidth for all of the time. CDS is similar to code division multiple access (CDMA), but here instead of providing multiple access, CDS separates the upstream and downstream transmit spectra using different codes.
The choice of orthogonal signaling scheme depends on the intent. We will see that FDS is in a sense optimal under an average power constraint (see Section 4.5.12).
To eliminate self NEXT using FDS, we would force the upstream transmitters is {T" , i = 1, . . . , M'},and the downstream transmitters {Td , i = 1, . . .
, M} to use disjoint frequency bands. Thus, in FDS signaling, the upstream and downstream transmissions are orthogonal and hence can be easily separated by the corresponding receivers.
Since in a typical system FDS cuts the bandwidth available to each transmitter' to %2 the overall channel bandwidth, we have an engineering tradeoff FDS eliminates se f NEXT
and 2o therefore increas~c system capacity; however, FDS also reduces the bandwidth available to each transmittErrlreceiver pair and therefore decreases system capacity.
When self NEXT is not severe enough to warrant FDS, both upstream and downstream transmitters occupy the entire bandwidth. In this case, the upstream and downstream directions have the same transmit spectrum; we refer to this as equal PSD (EQPSD) signaling.
2s On a typical telephone channel, the severity of self NEXT varies with frequency.
Therefore, to maximize capacity, we may wish to switch between FDS and EQPSD
depending on the severity of self NEXT. Such a joint signaling strategy for optimizing the performance in the presence of self NEXT and white AGN was introduced in j3].

The scheme in [3] is optimized, but only for an over simplified scenario (and therefore not useful in practice). In particular, [3] does not address self FEX'I' and interference from other lines as considered in this work. Further, [3] does not address spectral compatibility issue.
s All other schemes for joint signaling employ ad-hoc techniques for interference suppression [ 1, 2, 4~, 5].
3.3 Multitone modulation Multicarrier or discrete multitone (DMT) modulation [6] can be readily used to io implement a communication system using a wide variety of PSDs. Multitone modulation modulates data over multiple carriers and adjusts the bit rate carried over each Garner according to the signal to noise ratio (SNR) for that carrier so as to achieve equal bit error probability (BER) for each carrier (see in FIG. 4).
Orthogonal FDS signaling is easily implemented using the DMT: we simply is assign transmitter/receiver pairs to distinct sets of carriers. Note, however, that multitone modulation is definitely not the only modulation scheme that can be used to implement (optimal) transmit spectra. We can just as well use other techniques, such as CAP, QAM, mufti-level PAM, etc.
zo 3.4 Summary of previous work The current state of the art of DSL technology in general and HDSL2 in particular can be described as follows:
Ad-hoc schemes (sometimes referred to as "optimized' have been developed that attempt to deal with self interference and DS1N-NEXT and DS1N-FEXT as well 2s as spectral compatibility of the designed service with other services.
However, these schemes by no means optimize the capacity of the services considered.

An optimal signaling scheme has been developed in [3] for the case of self NEXT
and white additive Gaussian noise only. The development of [3] does not address crosstalk from other sources, such as DSIN-NEXT and DSIN-FEXT, or self FEXT, or other types of additive Gaussian noise. The development of [3] also s does not address spectral compatibility of the designed service with respect to other service:~.
SUMMARY OF THE INVENTION
One embodiment of the present invention comprises a method for determining a to transmit spectrum for use in communicating data on a communications channel. This method may be used in communicating data when the channel is subject to interference from one or more otlher communications channels. The first steps in this method comprise determining a cha~.el transfer function of the communications channel and an amount of self interference into the communications channel from the other communications is channels that carry the same type of service. The transfer function and the amount of self interference are examined, and a transmit spectrum for the channel is determined based on the examining. The transfer function and the amount of interference may be determined by measurement or they may be received from a remote or local analyzer or memory storage. Determining the transmit spectrum preferably comprises determining an zo EQPSD/FDS/MFD:i transmit spectrum.
The method further preferably comprises a further step of determining an amount of uncorrelated interference into the communications channel, such as additive Gaussian noise (AGN) and different-service interference from one or more of the other communications channels that may carry a different type of service than the service on 2s the communications channel. Determining the transmit spectrum is then performed in response to the amount of uncorrelated interference.
i~

WO 99/33215 PCTlUS98/27154 In another embodiment, the present invention comprises a method for transmitting data on a communications channel that is subject to interference from one or more other communications channels. The method comprises the steps of determining a channel transfer function of the communications channel, initiating a data transfer on the s communications channel, and transferring the data on the communications channel using the transmit spectrum. The step of initiating the transfer comprises determining interference characteristics of the interfering communications channels, and determining a transmit spectrum in response to the channel transfer function and the interference characteristics. The transmit spectrum is preferably determined to substantially maximize to the data transmission rate for the communications channel, in such a manner that the communications channel has equal upstream and downstream capacities, and that the transmit spectrum is spectrally compatible with the one or more other communications channels.
Another embodiment of the present invention comprises a method for determining is a transmit spectrums for use in communicating data on a communications channel, preferably by deternnining signaling techniques in one or more frequency bins in the available frequency lband of the communications channel. The first steps in this method comprise determining a channel transfer function of the communications channel. An amount of self interference into the communications channel from the other 2o communications channels carrying the same type of service is determined, preferably along with an amount of uncorrelated interference. The transfer function and the amount of self interference are examined, preferably along with the amount of uncorrelated interference. A transmit spectrum for the channel is then determined based on the examining. If a partiicular signaling technique is employed in one or more neighboring 2s frequency bins, the transmit mask may be either a discrete transmit mask or a contiguous transmit mask over the range of the neighboring bins. If the channel transfer function and the interference characteristics are substantially monotonic over the frequency band of the communications channel, then determining which frequency bins use a particular ~s WO 99/33215 PCTNS98lZ7154 technique may comprise a binary search for transition bins in which appropriate characteristic quantities cross particular threshold values.
BRIEF DESCRIPTION OF THE DRAWINGS
s Other objects and advantages of the invention will become apparent upon reading the following detaled description and upon reference to the accompanying drawings in which:
FIG. 1 is an e~;ample of the frequency-response for a twisted pair telephone channel;
FIG. 2 shows NEXT and FEXT between neighboring lines in a telephone cable, with to "Tx" and "Rx" indicating transmitters and receivers, respectively;
FIG. 3 shows how NEXT (DSIN-NEXT and self NEXT) and FEXT (DSIN-FEXT
and self FEXT) are modeled as additive interference sources, with DSOUT-NEXT and DSOUT-FEXT representing the interference leaking out into other neighboriyig services;
~ s FIG. 4 illustrates how multicarrier, or discrete multitone (DMT) modulation multiplexes the data onto multiple orthogonal carrier waves;
FIG. 5 and FIG. SA are representative views of a subscriber-line communications system anal a well-logging system that use the present invention;
FIG. 6 is a representative view of a home system using the present invention for DSL
2o commuIllcatioriS;
FIG. 7 is a block diagram of one embodiment of the computer from FIG. 6;
FIG. 8 is a block diagram of one embodiment of the DSL card from FIG. 7;
FIG. 9 is a flowchart for determining transmission characteristics for a communications system in one embodiment of the invention;

FIG. 10 is a flowchart for determining a transmit spectrum with preliminary analyses of self interfesrence and FEXT levels;
FIG. 11 is a floarchart for determining a transmit spectrum with preliminary analyses of self interfE;rence levels;
s FIG. 12 is a flowchart for determining a transmit spectrum;
FIG. 13 is a flowchart for method for transmitting data on a communications channel;
FIG. 14 is a flovrchart for initiating a data transfer on the communications channel;
FIG. 15 is a flowchart for determining transmission characteristics for a communications system in one embodiment of the invention;
FIG. 16 is a frequency-response graph showing the channel sub-division into K
narrow bins (subchannels), each of width W (Hz);
FIG. 17 shows the magnitude squared transfer function of the channel (CSA loop 6), with 39 self=NEXT interferers, and 39 self FEXT interferers (see (1)-(3));
FIG. 18 shows transmit spectra for EQPSD, FDS and mufti-line FDS signaling is schemes in a single frequency bin k for the case where the number of lines is 3 (this also works for any number of lines);
FIG. 19 is a model for combined additive interference from other services (DSIN-NEXT and DSIN-FEXT) plus channel noise (AGN);
FIG. 20 is a flowchart of a method for determining an optimal transmit spectrum 2o using only EQPSD signaling;
FIG. 21 is a graph of an optimal transmit spectrum of HDSL2 (on CSA loop 6) with 49 HDSL DSIN-NEXT interferers and AGN of -140 dBm/Hz;
FIG. 22 is a gxaph of an optimal transmit spectrum of HDSL2 (on CSA loop 6) with 25 T1 DSIN-NEXT interferers and AGN of -140 dBm/Hz;

WO 99!33215 PCT/US98/27154 FIG. 23 shows upstream and downstream transmit spectia in a single frequency bin (a = 0.5 ~ F;QPSD signaling and a = 1 ~ FDS signaling);
FIG. 24 is a graph demonstrating that R,~ is monotonic in the interval aE
(0.5, 1];
FIG. 25 shows E;QPSD and FDS signaling in a single frequency bin;
s FIG. 26 shows upstream and downstream transmit spectra with regions employing EQPSD signaling (in bins [1, ME2F]) and FDS signaling (in bins [ME2F+ 1, K]);
FIG. 27 is a flowchart of the optimal and suboptimal schemes to determine the transmit spectrum using EQPSD and FDS signaling (and EQPSD/FDS transmit spectrum);
to FIG. 28 shows joint EQPSD/FDS signaling for a channel with "discrete" and "contiguous" transmit spectra for upstream (top graphs) and downstream (bottom graphs) signaling;
FIG. 29 is a graph of an optimal upstream transmit spectrum for CSA Loop 6 using HDSL2 with 39 self NEXT and 39 self FEXT interferers, with EQPSD signaling is taking place to the left of bin 9 (indicated by solid line) and FDS
signaling taking place to the :right (indicated by dashed line);
FIG. 30 shows graphs of optimal "contiguous" upstream and downstream transmit spectra for CSA Loop 6 using HDSL2 with 39 self NEXT and 39 self FEXT
interferers (l3QPSD signaling taking place to the left of bin 9);
2o FIG. 31 shows graphs of another set of optimal "contiguous" upstream and downstream transmit spectra for CSA Loop 6 using HDSL2 with 39 self NEXT
and 39 self=FEXT interferers, with the property that these spectra yield equal performancc; margins (equal capacities) and equal average powers in both directions of transmission (EQPSD signaling taking place to the left of bin 9);
2s FIG. 32 shows transmit spectra of signaling line (S~, interfering line (Y
and ~, and lumped channel noise (11~ for two cases: the FDS scheme (Case 2) for interfering WO 99!33215 PGT/US98lZ7154 line yields rugher capacity for signaling line (S) than other schemes like CDS
(Case 1 );
FIG. 33 shows 1~QPSD and mufti-line FDS signaling in a single frequency bin k for the M = 3 line case;
s FIG. 34 shows FDS and mufti-line FDS signaling in a single frequency bin k for the M = 3 line c~~se;
FIG. 35 is an ex,nnple of an upstream transmit spectrum of line 1 ( S; ( f ) ) employing EQPSD, FDS and mufti-line FDS signaling schemes for the M = 3 line case, in which bins [l, ME2MFDS~ ~PIOy EQPSD, bins [MEZMFDS '+ I, MMFDS2FDS~
to employ mufti-line FDS, bins [MMFDS2FDS + 1, MFDS1MFDS~ Ploy FDS, and bins [MFDS2MFDS + l, K] employ mufti-line FDS; The downstream spectrum of line 1 ( S° ( f ) )is similar to S; ( f ) except for putting power in the complementary halves of FL>S bins; The upstream spectra of lines 2 and 3 are similar to S; ( f ) except for putting power in complementary thirds of mufti-line FDS bins; The t s downstream spectra for lines 2 and 3 are similar to S; ( f ) except for putting power in the; complementary halves of the FDS bins and in the complementary thirds of mufti-line FDS bins;
FIG. 36 illustrates practical observation 1, a case of an EQPSD/FDS/MFDS
hansmit spectrum in which there is no FDS spectral region; bins [1, ME2MFDS~ Ploy 2o EQPSD, and. bins [ME2MFDS + 1, K] employ mufti-line FDS;
FIG. 37 illustrates practical observation 2, a case of an EQPSD/FDS/1V)FDS
transmit spectrum in which there is no mufti-line FDS spectral portion within the EQPSD
region; bins [1, MMFDS2FDS~ ~PlOy EQPSD, blnS [MMFDS2FDS + 1, MFDS2MFDS~
employ FDS., and bins [MFDS2MFDS'~' 1, KJ ploy mufti-line FDS;
2s FIG. 38 shows upstream and downstream transmit spectra in a single frequency bin (a = 0.5 ~ I~QPSD signaling and a = 1 ~ mufti-line FDS signaling);

FIG. 39 shows EQPSD and mufti-line FDS signaling in a single frequency bin;
FIG. 40 is a flowchart of a scheme for determining an optimal transmit spectrum using EQF'SD, FDS, and mufti-line FDS signaling (an EQPSD/FDS/NIFDS
transmit spectrum);
s FIG. 41 shows, for the case vsrhere the lines have different line characteristics, upstream and downstream transmit spectra in a single frequency bin (a = 0.5 ~
EQPSD si~~aling and a = 1 ~ mufti-line FDS signaling);
FIG. 42 shows, for the case where the lines have different line characteristics, upstream and downstream transmit spectra in a single frequency bin (a = 0.5 ~
to EQPSD si~~aling and a =1 ~ mufti-line FDS signaling);
FIG. 43 is a graph of an optimal downstream transriiit spectrum for HDSL2 (on CSA
loop 6) ur.~der an OPTIS downstream constraining PSD mask with 49 HDSL
DSIN-NEXT interferers and AGN of -140 dBm/Hz (the 'o-~' line shows the peak-constrained optimal transmit spectrum and the '-' line shows the t s constraining OPTIS PSD mask);
FIG. 44 is a gxaph of an optimal upstream transmit spectrum for HDSL2 (on CSA
loop 6) under an OPTIS upstream constraining PSD mask with 25 T1 DSIN-NEXT interferers and AGN of -140 dBm/Hz (the 'o-o' line shows the peak-constrained optimal transmit spectrum and the '-' line shows the constraining 20 OPTIS PS:D mask);
FIG. 45 shows graphs of optimal upstream and downstream transmit spectra for HDSL2 (on CSA loop 6) under the OPTIS upstream and downstream constraining PSD masks with 39 HDSL2 self NEXT and self FEXT interferers and AGN of -140 dBm/1Hz (the 'o-o' lines show the peak-constrained optimal transmit spectra 2s and the '--' lines show the constraining OPTIS PSD masks);
FIG. 46 shov~rs graphs of optimal upstream and downstream transmit spectra for HDSL2 (on CSA loop 6) under the OPTIS upstream and downstream constraining PSD masks with 24 HDSL2 self NEXT and self FEXT interferers, 24 T1 interferers, and AGN of -140 dBm/Hz (the 'o-o' lines show the peak-constrained optimal transmit spectra and the '--' lines show the constraining OPTIS PSD
masks);
s FIG. 47 shows graphs of optimal "contiguous" upstream and downstream transmit spectra for HDSL2 (on CSA loop 4, with a non-monotonic channel function due to bridged taps) with 39 HDSL2 self NEXT and self FEXT interferers; these transmit spectra yield equal performance margins (equal capacities) and equal average powers in both directions of transmission (note that there is only one ~o transition region from EQPSD to FDS signaling);
FIG. 48 shows (in the top graph) the channel transfer function, self NEXT, and self FEXT transfer functions for a short loop with bridged taps employing "GDSL"
service (note that self NEXT is very low for this hypothetical service), and shows (in the bottom graph) the distributed EQPSD and FDS spectral regions for the ~ s upstream and downstream transmit spec~a, with a 0 indicating EQPSD
signaling, a 1 indicating FDS, and a 0.5 indicating EQPSD or FDS signaling (note that in this case the non-monotonicity of the channel transfer function leads to several distributed signaling regions);
FIG. 49 shows an alternative signaling scheme: in the presence of high degrees of 20 self NEXT and self FEXT between group of lines 1 and 2 and lines 3 and 4, we employ mufti-line FDS; there is EQPSD signaling within each group of lines (1 and 2 employ EQPSD as do 3 and 4) that have low self interference; .
FIG. 50 shows optimal transmit spectra (upstream and downstream) of ADSL (on CSA loop 6) with 49 HDSL DSIN-NEXT interferers and an AGN of -140 25 dBm/Hz;
FIG. S 1 shows optimal transmit spectra (upstream and downstream) of ADSL (on CSA loop ti) with 25 T1 DSIN-NEXT interferers and an AGN of -140 dBm/Hz;
and FIG. 52 shows upstream and downstream transmit spectra in a single frequency bin (a = 0.5 => SPSD signaling and a = 1 ~ FDS signaling).
While the invention is susceptible to various modifications and alternative forms;
s specific embodiments thereof are shown by way of example in the drawings and will herein be described in detail. It should be understood, however, that the drawings and detailed description thereto are not intended to limit the invention to the particular form disclosed, but on the contrary, the intention is to cover all modifications, equivalents and alternatives falling within the spirit and scope of the present invention as defined by the t o appended claims.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
The present invention comprises an improved system and method for communicating information such as voice, images, video, data, or other information on a i s transmission medium. The present invention provides improved communications on the transmission medium in the presence of interference. More specifically, the present invention operates to model and then minimize the effects of interference on the transmission medium. The interference may take the form of similar services being transmitted on neighboring transmission mediums and/or may take the form of 2o uncorrelated interference fibm different services on neighboring transmission mediums and or interference from various noise sources which affect the transmission medium.
FIG. 5- Subscriber Line Embodiment FIG. 5 illustrates a preferred embodiment for use of the present invention.
FIG. S
25 illustrates a first location, e.g., a home 10 that is coupled through a subscriber line 12 to a second location, e.g. a telephone company central office (CO) 14. It is noted that the first and second locations may be any of various types of sites, such as a home, an office, business, an office lbuilding, or a CO.
In this embodiment of the invention, the communication system and method is comprised in a digital subscriber line (DSL) device that operates to perform xDSL
s communications o:n subscriber line 12. Thus, this figure shows a configuration that includes subscriber line 12; e.g., a twisted-pair copper line, that is coupled between home and CO 14. The present invention is comprised in each of home 10 and CO 14.
As discussexi in the background section, subscriber lines are generally included in a cable that has a lplurality of closely positioned. transmission mediums, including other ~o subscriber lines. Due to the close proximity of the transmission mediums comprised in a subscriber cable, a given subscriber line is subject to interference firm neighboring transmission mediums, including self NEXT and self FEXT interference, and different service interference (DSII~. Some of the transmit spectra discussed herein are substantially optinuzed to maximize performance margins and avoid the effects of this t s interference, thereby providing improved communication.
By design" an optimal transmit spectra give increased perfon~nance margins (increased immunity against noise) and spectral compatibility margins as compared to one fixed transmit spectrum. The optimal transmit spectra described herein are typically obtained by fixing the average input power and choosing the best signaling strategies and optimal power distribution to maximize the bit rate or performance margin. The transmit spectra may also be used to minimize the required average input power where the desired performance margins or bit rates are fixed.
FIG. SA - Well Logging Embodiment 2s FIG. SA illustrates an alternate scenario for use of the communication system and method of the present invention. FIG. SA illustrates a drill hole and/or well-logging scenario which utilizes the communication system of the present invention. As an example, in FIG. SA communication equipment 16 on the surface communicates through a communication medium 12A to instrumentation 18 comprised in the bore-hole underground. The communication system and method operates to reduce the effects of interference in the vvell hole and to provide improved communications.
s Although FIfG. 5 and FIG. SA illustrate two embodiments for use of the system and method of the present invention, it is noted that the present invention may be used in any of various typea of systems or scenarios which involve communication of data on a transmission medium that is subject to noise or other interference. The present invention is particularly useful in scenarios where the transmission medium is in close proximity to ~o various sources of interference that can be ascertained, identified, and modeled. In general, the present invention is applicable to reduce the effects of interference on transmission media that are subject to interference from known or unknown sources where the spectral characteristics of the interference can be modeled.
In the analyses presented herein, we use a generic DSL (xDSL) model. For t s concreteness, we present results optimizing DSL services such as HDSL2, "GDSL", and "VDSL2" in the face of noise and interference from neighboring services. The invention is not, however, limited to these services, but can be applied to any communications channel that exhibits crosstalk interference.
Although F'IG. 5 illustrates a subscriber line embodiment, it is noted that the 2o present invention may be used for any of various types of transmission media, e.g., copper wire, fiber .optic, lines, co-axial cable, wave guides, etc. For example, the present invention is well suited for use in local and wide-area networks to minimize noise interference on networks, e.g., Ethernet, token ring, and wide area networks such as frame relay, Switched 5~6, ATM (asynchronous transfer mode), etc. Also, although FIG. 5 2s illustrates use of the present invention between a home 10 and a central office 14 over a subscriber loop or subscriber line 12, it is noted that the present invention may also be used for the various trunks comprised in the PSTN. The present invention is also useful in the various backba~nes or lines used for the Internet.
z~

WO 99/33215 PCTNS98l27154 The present invention is also useful for wireless transmission applications, e.g., cellular telephones, cordless telephones, short wave radio, etc. as well as the various broadcast media such as the various digital satellite services providing television, Internet, data or voice services. In short, the present invention is applicable to any of s various types of systems which involve the transmission of data over a wired or wireless medium. The present invention is also applicable to any of the various types of signaling protocols such as frequency division multiple access (FDMA), time division multiple access (TDMA} and code division multiple access (CDMA) as well as hybrids of these, among others.
~o Therefore, t;he present invention is applicable to a variety of communications channels in a number of communication scenarios. In the description that follows, the present invention i;c described with respect to the preferred embodiment, the preferred embodiment being a digital subscriber line application between a first location, e.g., a home or business 10, and a telephone company central office 14.
~s FIG. 6 - Home DS:L System FIG. 6 illustrates a system 100 comprised in location 10, i.e., in the home or business 10 which performs digital subscriber line (DSL) communication operations over subscriber line 12. In a preferred embodiment, the DSL circuitry of the present invention 2o is comprised in a computer system 102 coupled to subscriber line 12 through an xDSL
port 106. In one embodiment, computer system 102 is also coupled to a telephone system 104. However, it is noted that the DSL system of the present invention may be comprised in any of various types of systems including computer systems, Internet appliances, televisions or dedicated boxes. In the preferred embodiment, the DSL system of the 2s present invention i" comprised in a DSL device on an add-in card to the general purpose computer system 102. In the preferred embodiment, the DSL card includes a port for coupling to a standard telephone jack, or "splitter," which in turn couples to the subscriber line 12. In this embodiment, the computer system 102 may be utilized as a WO 99/33215 PG"T/US9ti/Z7154 virtual telephone v~ihich operates through the DSL device for voice communications over the subscriber line 12. In another embodiment, a separate telephone system 104 is coupled to a second. port of the DSL card, as shown in FIG. 6.
s FIG. 7 - Computer System Block Diagram Turning now to FIG. 7, a block diagram of one embodiment of computer system 102 is shown. Other embodiments are possible and contemplated. The depicted system includes a microprocessor or CPU 110 coupled to a variety of system components through a bus bridle 114 . In the depicted system, a main memory 112 is also coupled to to bus bridge 114. Finally, a plurality of PCI devices are coupled to bus bridge I14 through a PCI bus 116. In the depicted embodiment, the PCI devices include a video card 118 and a add-in card for tle DSL device 120.
Bus bridge 114 provides an interface between microprocessor 1 I0, main memory 112, and the devices attached to PCI bus 116. When an operation is received from one of is the devices connected to bus bridge 114, bus bridge 114 identifies the target of the operation (e.g. a particular device or, in the case of PCI bus 116, that the target is on PCI
bus 116). Bus bridge 114 routes the operation to the targeted device. Bus bridge 114 generally translates an operation from the protocol used by the source device or bus to the protocol used by floe target device or bus.
2o Main memory 112 is a memory in which application programs are stored and from which microprocessor 110 primarily executes. A suitable main memory 112 comprises DRAM (Dynamic Random Access Memory), and preferably a plurality of banks of SDRAM (Synchronous DRAM).
2s FIG. 8 - DSL Device FIG. 8 is ,~ block diagram illustrating DSL device 120 comprised in the computer 102 of FIG. 6. As noted above, although in the preferred embodiment the DSL
device is compnised as a computer add-in card, DSL device 120 may take any of various types of forms including being comprised in a television system, Internet appliance, or dedicated device, among others systems. As shown, the DSL device or add-in card 120 comprises a first port 160 for coupling to an expansion bus of the computer system, preferably a PCI
s expansion bus port as shown. DSL device 120 also includes at least one subscriber line port 170 for coupling to the digital subscriber line 12. DSL device 120 may include any of various hardware elements for performing the communication operations of the present invention. For example, in one embodiment, the DSL communication~device includes one or more programmable processing units which implement instructions from a memory.
to For example, the DSL communication device may include a progt~ammable digital signal processor (DSP) 152, a general purpose processor, or other processors that execute instructions from a memory 156 to implement the communication operations of the present invention. Alternatively, or in addition, the DSL communication device includes one or more application specific integrated circuits (ASICs) 154 and 158 or t s programmable logic: devices such as FPGAs etc. that implement a portion or all of the present invention. In short, the communication system and method of the present invention may be implemented in any of various types of ways including programmable devices such as processing units, CPUs, DSPs, microcontrollers, etc., dedicated hardware such as ASICs, programmable logic devices such as FPGAs, or combinations of the 2o above.
FIG. 9 - FIG.12 -'.Method for Determining Transmission Characteristics FIG. 9 is a flowchart for determining a transmit spectrum for use in communicating data on a communications channel according to one embodiment of the 2s present invention. This method may be used in communicating data on the communications channel when the communications channel is subject to interference from one or more other communications channels. The communications channel of interest and one or more of the other communications channels carry a particular type of service, such as xDSL, ISDN, T1, or spread-spectrum, for example. The first steps in this wo ~r~3Zis rcrius9sm~s4 method comprise determining a channel transfer function of the communications channel 210 and an amount of self interference 220 into the communications channel from the other communications channels that carry the same type of service. In step 230, the transfer function and the amount of self interference are examined, and in step 240 a s transmit spectrum for the channel is determined based on the examining.
Determining the channel transfer function in step 210 of FIG. 9 may be done by directly measuring it. For example, a transmitter on one end of the communications channel, such as at C:O 12 (in FIG. 1 ) or in well-logging instrumentation 18 {in FIG. 1 A), may be directed to send a signal or a series of signals with predetermined intensities as a io function of frequency, with which the a receiver at the other end of the channel may measure the attenuation, and perhaps also the phase shim., as a function of frequency. The measurement may be extended to determine nonlinear responses of the channel by repeating the measurement with varying source strengths. Alternately, the channel characteristics may be determined in advance of the communication and stored, for is example in a database at the CO or in a memory on a DSL card. Determining the channel transfer function could then entail receiving it from the CO, the local memory storage, or other storage locations. In the case where the invention is used in a subscriber line system, receiving the channel transfer function from the CO is particularly useful since the CO may rapidly look up pre-stored information on the particular physical line being 2o used for the communications channel.
Similarly, the amount of self interference may be determined in step 220 of FIG. 9 by receiving it or, if transmitter/receiver pairs are accessible on the other same-service channels, by measuring it. Determining the amount of self interference in step 220 may comprise determining a total self interference power, or a power distribution, or a 2s coupling coefficient from the other same-service channels into the channel of interest, or a coupling coefficient with frequency dependence (such as a self interference transfer function) from the; other same-service channels into the channel of interest, or a combination of these characteristics, among others. The amount of self interference may also include a chac~acterization of the self interference in terms of self NEXT and self WO 99/33215 p~NSg~~I~
FEXT interference. In a preferred embodiment of the invention, step 220 includes determining a self hIEXT transfer function and a self FEXT transfer function from the other same-service c;hannels into the channel of interest.
FIG. 10 - F'.fG. 12 show various embodiments 240a-c of step 240, in which the s transmit spectrum i.; determined.
In one embodiment of the invention, as shown in steps 241 and 245 of FIG. 10, determining the trar.~smit spectrum in step 240 comprises determining an EQPSD
transmit spectrum if the amount of self interference is substantially low or negligible. An EQPSD
transmit spectrum is a transmit spectrum in which EQPSD signaling is used on at least ~o one portion of the available spectrum of communication frequencies.
The method: may also include steps 242 and 247, in which an EQPSD/FDS
transmit spectrum is found if the amount of self interference is substantially high or non-negligible.
In general, am EQPSD/FDS transmit spectrum has a number of frequency regions ~ s in which EQPSD signaling is used, and a number of frequency regions in which FDS
signaling is used. The locations of these regions in the available spectrum of communication fraluencies and the transmission power as a function of frequency are preferably determi3~:ed so that the data transmission rate on the channel is substantially maximized. An EQ~PSD/FDS transmit spectrum preferably includes at least one portion 2o using FDS signaling and one portion using FDS signaling, but in a degenerate case, the maximization may be achieved by using only EQPSD or only FDS signaling. An EQPSD/FDS transmit spectrum is thus a transmit spectrum in which the available spectrum of comrrmnication frequencies includes at least one portion using EQPSD
signaling or FDS signaling.
2s Still furthc;r, the method may also include step 249, in which an EQPSD/FDS/MFDS transmit spectrum is found if the amount of self interference is substantially high or non-negligible and if the amount of self FEXT
interference is substantially high. In multi-line FDS (MFDS) signaling, different channels carrying the same or similar services are orthogonally separated to reduce crosstalk interference. -In general, an EQPSD/FDS/MFDS transmit spectrum has a number of frequency regions in which EQPSD signaling is used, a number of frequency regions in which FDS
s signaling is used, and a number of frequency regions in which MFDS signaling is used.
Again, the locations of these regions in the available spectrum of communication frequencies and the transmission power as a function of frequency are preferably determined so that the data transmission rate on the channel is substantially maximized.
An EQPSD/FDS/MFDS transmit spectrum preferably includes at least one portion using io FDS signaling, one portion using FDS signaling, and one portion using MFDS
signaling, but in a degenerate case, the maximization may be achieved by using only EQPSD
or only FDS or only MFDS signaling. An EQPSD/FDS/MFDS transmit spectrum is thus a transmit spectrum in which the available spectrum of communication frequencies includes at least one portion using EQPSD signaling or FDS signaling or MFDS
o s signaling.
In another embodiment of the invention, as shown in FIG. 11, determining the transmit spectrum in step 240 comprises determining an EQPSD transmit spectrum (in step 245) if the amount of self interference is substantially low or negligible (according to step 241), and determining an EQPSD/FDS/MFDS transmit spectrum (in step 249) if the 2;o amount of self interference is substantially high or non-negligible.
In yet another embodiment of the invention, as shown in FIG. 12, determining the transmit spectrum in step 240 comprises determining an EQPSD/FDS/lviFDS
transmit spectrum (in step 249). For the degenerate cases in which only one or two of the EQPSD, FDS, and MFDS signaling techniques are needed for maximizing the data transmission 2s rate, the EQPSD/FDS/MFDS transmit spectrum will reduce to the appropriate signaling techniques.
In a preferred embodiment of the invention, the method further comprises a step of determining an amount of uncorrelated interference, such as additive Gaussian noise (AGN), into the communications channel. If one or more of the other communications channels carry a different type of service~than the service on the communications channel, then the uncorrelated interference may include different-service interference (DSIN) from the other communications channels carrying the different service. Thus, the uncorrelated s interference includes a total noise interference that preferably comprises AGN, DSIN, and other noise and interference whose spectral characteristics are not controlled by the user.
Determining the transmit spectrum in step 240 is then performed in response to the amount of uncorrelated interference.
to FIG.13 - FIG.14 - Method for Transmitting Data FIG. 13 is a flowchart of a method for transmitting data according to one embodiment of the present invention. This method may be used in communicating data on a communications channel when the communications channel is subject to interference from one or more other communications channels. The other is communications channels may be located proximate to the communications channel, for example, in the case of multiple subscriber lines in a binder group of a telephone cable, or in the case of multiple radio transmission systems with closely located transmitters or overlapping coverage regions. The communications channel of interest carries a particular type of service, such as xDSL, ISDN, T1, or spread-spectrum, for example. The method 2o comprises the steps of determining a channel transfer function of the communications channel in step 310, initiating a data transfer on the communications channel in step 320, and transferring the data on the communications channel using the transmit spectrum in step 330. As shown in FIG. 14, the step 320 of initiating the transfer comprises determining interference characteristics of the interfering communications channels in 2s step 322, and determining a transmit spectrum in response to the channel transfer function and the interference characteristics in step 324.
As discussed earlier, step 310 of determining the channel transfer function may comprise measuring the channel transfer function, receiving the channel transfer function, or determining the channel transfer function through other means. The channel transfer function may be determined at power-up of a transmission system, or at regular intervals in time, or in response to temperature changes, or at other appropriate times.
The transmit spectrum is preferably determined in step 324 to substantially s maximize the data transmission rate for the communications channel, so that the maximum information may be communicated per unit time on the communications channel in light of the various sources of noise and interference. The transmit spectrum is also preferably determined in such a manner that the communications channel has equal upstream and downstream capacities, and that the transmit spectrum is spectrally io compatible (that is, determined with regard to spectral compatibility) with the one or more other communications channels.
In one embodiment of the present invention, the transmit spectrum is preferably determined so that it satisfies a predetermined average power constraint for the ' communications channel. Note that if the channel capacities depend on the transmit ~s spectra of other :Lines carrying the same service, for example in the case of self interference, then the water filling technique may be carried out as described in reference [16]. If the cha~mel capacity depends on channel noise andlor different-service interference, then the classical water-filling technique is used, as described in [14). The transmit spectrum is preferably determined dynamically so that it may be optimized in 2o response to changing interference conditions or a changing channel transfer function.
In another embodiment of the invention, the transmit spectrum is determined so that it satisfies both a predetermined average power constraint and a predetermined peak power constraint for the communications channel, and may be determined using a peak constrained water-filling technique. Note that i f the channel capacities depend on the 2s transmit spectra o:f other lines carrying the same service, for example in the case of self interference, then the peak constrained water filling technique may be earned out as described in section 4.8.3 (which presents a modification of the technique discussed in [16]). If the channel capacity depends on channel noise and/or different-service interference, then the peak constrained water-filling technique is used, as described in section 4.$.2. The transmit spectrum is preferably determined dynamically so that it may be optimized in response to changing interference conditions or a changing chaimel transfer function.
In another embodiment of the invention, the transmit spectrum is determined so s that it satisfies only a predetermined peak power constraint for the communications channel, and may be determined using a peak constrained water-filling technique.
Dynamical determination of transmit masks In a preferred embodiment of the invention, steps 322 and 324 of determining the ~ o interference characteristics and of determining the transmit spectrum are performed more than once so that the transmit spectrum is modified appropriately as the interference characteristics change in time. These steps 322 and 324 may be performed each time a data transfer is initiated. Or, if step 330 of transferring data occurs repeatedly at regular or irregular intervals in time, then steps 322 and 324 of determining the interference ~ s characteristics and of determining the transmit spectrum are preferably performed prior to each occurrence of transferring data in step 330. In one embodiment of the invention, a new transfer function or a new set of interference characteristics may be determined during a data transfer and used to calculate a new transmit spectrum. The new transmit spectrum may then be used in a subsequent portion of the data transfer. These measures ::o of dynamically determining the transfer function enhance the data transfer by allowing the transfer function to adapt as the characteristics of the communications channel change in time.
Orthogonality for upstreamldownstream separation and multi-line separation :a In one embodiment of the present invention, the transmit spectrum is determined so that it specifies a pair of complementary spectra: one for transmission in each of the two directions on the communications channel. These two spectra may be called the PCT/US9ti/27154 "upstream transmit spectrum" and the "downstream transmit spectrum." For example, in the case where the channel provides communication between home l0 and CO 14, the transmit spectrum used in transmission from home 10 may be designated the upstream transmit spectrum, while the transmit spectrum used in transmission from CO 14 may be s designated the downstream transmit spectrum. Similarly, in other cases, such as a well-logging or a multiple-radio-transmitter embodiment, "upstream" and "downstream"
indicate opposite directions of transmission as desired.
The upstream and downstream transmit spectra may include one or more regions of the spectrum that use FDS signaling. In these regions, the upstream and downstream to transmit spectra are orthogonal with respect to each other. In a preferred embodiment of the present invention, this duplexing orthogonality is achieved by choosing two non-overlapping frequency subregions in the FDS region, using one of the subregions for upstream signaling, and using the other subregion for downstream signaling.
More generally, the FDS region may be constructed by choosing two non-overlapping sets of ~s frequency subregion.s in the FDS region, using one of the sets for upstream signaling, and using the other set far downstream signaling. In another embodiment of the invention the duplexing orthogonality is achieved by using code division signaling (CDS) to separate the upstream and downstream signals in the "FDS" region. In this embodiment, one access code is used :in upstream signaling, and a second, orthogonal, access code is used in downstream signaling.
It is noted that there is an additional benefit to these transmit spectra with one or more regions of FDS signaling: as would be appreciated by one skilled in the art of communications electronics, using regions of arthogonally separated upstream and downstream signaling may reduce the overhead of echo cancellation.
2.s The method indicated in FIG. 13 and FIG. 14 may be used in communicating data on a communicatians channel in a situation where one or more of the other communications channels carries the same type of service as the communications channel. Under such a condition, step 322 of determining interference characteristics preferably includes determining an amount of self interference into the communications WO 99/33215 PCT/US9t3/27154 from the other same-service communications channels. Step 324 of determining the transmit spectrum may then include eXamining the channel transfer function and the amount of self interference. The transmit spectrum is then preferably determined in step 324 in response to the channel transfer function and the amount of self interference.
s In another embodiment of the present invention, the transmit spectrum is determined so that it specifies a number M of complementary spectra: one for transmission on each of M channels in a subset of the one or more of the other communications channels that carry the same type of service. These M transmit spectra may include one or more regions of the spectrum that use MFDS signaling. In these ~ o regions, the M transmit spectra are orthogonal with respect to each other.
In one embodiment of the present invention, this mufti-line orthogonality is achieved by choosing M non-overlapping frequency subregions in the MFDS region, and using one of the subregions for transmission on each of the M lines. More generally, the MFDS region may be constructed by choosing M non-overlapping sets of frequency subregions in the ~s MFDS region, and using one of the sets for transmission on each of the M
channels. In another embodiment of the invention, the mufti-line orthogonality is achieved by using mufti-line code division signaling (mufti-line CDS) in the "MFDS" region. In this embodiment, different orthogonal access codes are used on each of the M
channels.
In another embodiment of the present invention; the transmit spectrum is 2o determined so that: it specifies a number M' (>M) of complementary spectra:
one for transmission on each of M channels in the subset of same-service channels, and additional spectra to provide orthogonal duplex separation on one or more of the M
channels. These M' transmit spectra may include one or more regions of the spectrum that use FDS
signaling as well as one or more regions of the spectrum that use MFDS
signaling.
2s In a preferred embodiment of the invention, determining the amount of self interference comprises determining (1) a self NEXT transfer function and (2) a self FEXT transfer function that describe the coupling from near-end and far-end transmitters, respectively, on the other same-service communications channels. In this preferred embodiment determining the interference characteristics in step 322 further comprises wo ~r~aais Pc~r~s9smis4 determining an amount of uncorrelated interference arising from factors such as additive Gaussian noise (A(iN) and crosstalk from one or more different-service channels, which carry a type of service different than the service on the channel of interest, among the one or more other channels. The transmit spectrum is then determined in response to the s channel transfer fiutction, an average power constraint or requirement for the channel, the self NEXT and the self FEXT transfer functions, and the amount of uncorrelated interference. In regions of the communications spectrum where the self interference is substantially low, the transmit spectrum is determined to be an EQPSD transmit spectrum. In regions where the self NEXT interference is substantially high and the self to FEXT interference is not substantially high, the transmit spectrum is determined to be an FDS transmit spectrum. And in regions where the self FEXT interference is substantially high, the transmit spectrum is determined to be an MFDS transmit spectrum.
Some specific examples of techniques for determining regions of EQPSD, FDS, and MFDS
signaling are presented below.
is In other embodiments of the invention, determining the interference characteristics in step 322 includes determining some but not all of the self NEXT and the self FEXT transfer functions, and the amount of uncorrelated interference and the average power constraint or requirement for the channel may or may not be determined.
The transmit spectrum is then determined in response to the channel transfer function and 2o the determined quantities, and is preferably optimized in response to these quantities.
In one embodiment of the present invention, the transmit spectrum is determined in response to one or more characteristics of the communications channel and the sources of noise or crosstalk. Determining these characteristics comprises steps such as determining the channel transfer function, determining the self NEXT transfer function, 2s and determining t:he self FEXT transfer function. In one preferred embodiment, the transmit spectrum is determined in response to the power-transfer characteristics of the communications channel, so determining these characteristics preferably comprises determining only the squared modulus of the mathematical transfer functions.
Thus, in this preferred embodiment, determining the channel transfer function means determining WO 99/33215 PCTNS9t3lZ7154 the function H{~") --- I H~ ( f ~ Z , determining the self NEXT transfer function means determining the function X ( f ) = I HN ( f ~ Z , and determining the self FEXT transfer function means determining the function F( f ) --_ I HF ( f ~Z . In this preferred embodiment, the phases of the transfer functions H~(f ), HN tf ~, and HF (f ) may or may not be s determined in addition to their squared modulii. In the case where a distinction is to be made between the various functions for different lines, the subscript i is used to indicate the different lines {as in H; ( f ) , X J ( f ), and F,. ~ f ')) with channel number i=1 being the channel for which the transmit spectrum is being determined.
Another characteristic of the communications channel and the sources of noise or to crosstalk is the signal to noise ratio G;~f ). In the case where a distinction is to be made between different lines, G; ( f ~ indicates, at a frequency f, the ratio of the signal (specifically, the signal power spectral density at n in channel number i to the noise (specifically, the noise spectral density at ~ in channel number 1. Here, channel number i=1 is the channel for which the transmit spechum is being determined, and channel is number i (for i > 1) is another channel that carries the same type of service as channel number 1, and which may provide interference into channel number 1.
Method for Determining Transmission Characteristics with Frequency Binning Another embodiment of the present invention comprises a method for determining 2o a transmit spectrum for use in communicating data on a communications channel, preferably by determining signaling techniques in one or more frequency bins in the available frequency band of the communications channel. This method is outlined in the flowchart of FICi. 15. This method may be used in communicating data on a communications channel when the communications channel is subject to interference 2s from one or more other communications channels, some of which carry the same type of service as the communications channel of interest. Additionally, some of the other ao communications channels may carry different types of service than the communications channel of interest.
The first steps in this method comprise determining a channel transfer function of the communications channel 410. An amount of self interference 420 into the s communications channel from the other communications channels carrying the same type of service is determined in step 420. An additional amount of uncorrelated interference is preferably determined in step 425. In step 430, the transfer function and the amount of self interference ~~re examined, preferably along with the amount of uncorrelated interference. In step 440 a transmit spectrum for the channel is determined based on the ~ o examining.
In a preferred embodiment of the method, the transmit spectrum is determined in step 440 so that different signaling techniques may be used in different frequency ranges in the communications band. These frequency ranges, or frequency bins, are non-overlapping ranges of the frequency spectrum, preferably with uniform frequency widths, y s and preferably chosen so that they cover the communications band. In other embodiments of the present invention, the frequency bins have non-uniform widths or do not cover the entire communications band.
In this embodiment of the invention, the transmit spectrum operates to specify an amount of transmission power used in each frequency bin for at least one direction of 2o communication on at least one communications channel. The amount of transmission power in each bin is preferably determined by a water-filling technique or a peak constrained water-filling technique.
In one embodiment of the invention, in a given frequency bin the transmit spectrum specifies EQPSD signaling if the amount of self interference is substantially 2s low in that bin; and FDS signaling if the amount of self interference is substantially high in that bin.
In one embodiment of the invention, in a given frequency bin the transmit spectrum specifies MFDS signaling if the amount of self FEXT interference is WO 99/33215 PCTNS9$/27154 substantially high in that bin. Otherwise, the transmit spectrum specifies EQPSD
signaling if the amount of self NEXT interference is substantially low in that biri, and FDS signaling if the amount of self NEXT interference is substantially high in that bin.
Under certain conditions, this method of the present invention may determine a s transmit spectrum that includes one or more regions of neighboring bins using FDS
signaling. In one embodiment of the present invention, the step of determining a transmit spectrum comprises determining a discrete FDS transmit spectrum in such regions of neighboring FDS bins. In the discrete FDS transmit spectrum, each bin has two subregions; one is used for transmission in the upstream direction, and one for to transmission in the downstream direction. In another embodiment of the present invention, the step of determining a transmit spectrum comprises determining a contiguous FDS transmit spectrum in such regions of neighboring FDS bins. In the contiguous FDS transmit spectrum, the neighboring frequency bins are grouped into two sets of neighboring bins, one of the sets is used for transmission in the upstream direction, ~s and the other set is used for transmission in the downstream direction. In one embodiment of the invention, the two sets of neighboring bins are chosen so that the contiguous FDS
transmit spectrum provides equal upstream and downstream signaling capacities.
Alternatively, the two sets of neighboring bins may be chosen so that the contiguous FDS
transmit spectrum provides equal upstream and downstream average power. In a 2o preferred embodiment, the two sets of neighboring bins are chosen so that the contiguous FDS transmit spectrum provides equal upstream and downstream signaling capacities and equal upstream anal downstream average powers.
Similarly, under certain conditions, this method of the present invention may determine a transmit spectrum that includes one or more regions of neighboring bins 2s using MFDS signaling. In one embodiment of the present invention, the step of determining a transmit spectrum comprises determining a discrete MFDS transmit spectrum in such regions of neighboring MFDS bins. In the discrete MFDS
transmit spectrum, each bin has M subregions. Each of the M subregions is used for bi-directional transmission on one of the M same-service channels. In another embodiment of the WO 99133215 t'CT/US98/27154 present invention, the step of determining a transmit spectrum comprises determining a contiguous MFDS transmit spectrum in such regions of neighboring MFDS bins. In the contiguous MFDS txamsmit spectrum, the neighboring bins are grouped into M
sets of neighboring bins. Each of the M sets of frequency bins is used for bi-directional s transmission on one of the M same-service channels. The M sets of neighboring bins are preferably chosen so that the contiguous MFDS transmit spectrum provides equal signaling capacities on the M channels.
If the channel transfer function and the interference characteristics are substantially monotonic in frequency, the determination of which frequency bins use a particular type of signaling may be simplified by determining frequency values at which the different types of interference become substantially large or substantially small. Thus, in one embodiment of the present invention, determining the transmit spectrum in step 440 includes one or more steps of identifying "transition bins" that mark the endpoints (in the frequency spectrum) of different types of signaling techniques. These transitions bins ~ s may be rapidly identified by searching for bins in which certain characteristic quantifies meet particular predetermined criteria. These searches, which axe preferably implemented as binary searches, may be carried out in the step 430 of examining the channel transfer function and interfi:rence. The following list is a sample of transition bins that may be identified.
2o ME: for bins with center frequencies < or < the center frequency of ME, EQPSD
signaling is used.
MF: for bins with center frequencies > or z the center frequency of MF, FDS
signaling is used.
ME2F~ for bins with center frequencies < or <_ the center frequency Of ME2F, EQPSD
2s signaling is used, and FDS signaling is used in higher-frequency bins. In other words, MEl~: indicates a transition from EQPSD signaling to FDS signaling.
ME2MFDS~ indicates a transition from EQPSD signaling to MFDS signaling.

MMFDS1PDS~ indicates a transition from MFDS signaling to FDS signaling.
ME2MFDS~ indicates a transition from EQPSD signaling to FDS signaling.
Similarly, transition frequencies may be defined for particular frequencies that s mark transitions from one form of signaling to another. For example, fE2F
represents a transition frequency where EQPSD is used in a region with frequency less than fEZF, and, and FDS signaling is used in a region with frequency less than fE2F

wo ~r~3zis pcT~s9smis4 4 New, Optimized Signaling Techniques The proposed techniques combine a number of ideas into one signaling system that optimizes its performance given many different possible combinations of interferers. These ideas include:
1. Given expressions for the crosstallc from other services (DSIN-NEXT and DSIN-FEXT) into an xDSL channel and channel noise (AGN), our scheme computes the optimal distribution of power ac~nss frequency that maximizes the capacity (see Section 4.4). This distribution uses the same transmit spectrum (EQPSD signaling) in both upstream and downstream directions.
2. Given expressions for the self NEXT and self FEXT crosstalk in an xDSL
channel along with interference from other services (DSIN-NEXT and DSIN-FEXT) and channel noise (AGN), our scheme computes the optimal distribution of power across frequency that max-imizes the capacity. This distribution involves equal PSD (EQPSD) signaling in frequency bands with low self interference, orthogonal signaling (FDS) in frequency bands where self NEXT dominates other interference sources (Section 4.5), and orthogonal signaling (multi-line FDS introduced in Section 4.3) in frequency bands where self FEXT is high (Section 4.6).
3. Given different channel, noise, and interference characteristics between lines, our scheme chooses the optimal signaling strategy (EQPSD, FDS or multi-line FDS) in each frequency bin (see Section 4.7) to maximize the channel capacity.
4. Given an additional peak-power constraint in frequency, our scheme computes the optimal transmit spectra that maximize the capacity and choose the optimal joint signaling strategy (EQPSD, FDS and multi-line FDS) for a given channel, noise and interference characteristics (see Sections 4.8 and 4.9).
5. We present optimal and near-optimal signaling strategies in case of non-monotonic channel, self NEXT and self-FEXT transfer functions (see Section 4.10 on bridged taps).
We will present the above ideas in the following sections in the context of a generic xDSL line carrying symmetric-data rate services like HDSL2, "GDSL", and "VDSL2"
services. Note that the techniques developed here can be applied to a more general communications channel with inter-ference characteristics characterized by self interference and different-service interference models.
Further, we can extend this work to apply to channels that support asymmetric data rates (different in each direction) (see Scxtion 5), for e.g., ADSL, and VDSL. We can follow a similar approach of binning in frequency and then analyzing the signaling strategy in each bin.
In the asymmetrical data-rate case, the ratio of the average power between upstream and downstream directions needs to be known. ' We will present background material and our assumptions in Section 4.1. In Section 4.2 we give details about the interference models and the simulation conditions.
Section 4.3 looks at the various signaling schemes we will employ. We will present the optimal transmit spectrum using EQPSD signaling in Section 4.4 in the presence of only different-service interference and AGN.
Sections 4.5 and 4.6 detail the new signaling strategies to obtain an optimal and/or suboptimal transmit spectrum in the presence of self interference, different-service interference and AGN.
Section 4.7 derives some results applicable when neighboring lines vary in channel, noise and interference characteristics. Sections 4.8, and 4.9 present optimal transmit spectra under additional peak-power constraint in frequency. We present optimal and near-optimal signaling schemes for non-monotonic channel, self NEXT, and self FEXT transfer functions in Section 4.10. We discuss optimal signaling for asymmetrical data-rate channels in Section 5. Finally, Section 4.12 presents several new ideas, extending the results presented here.
Note: All the transmit spectra are optimal (i.e., yield the maximum possible bit rates or per-forniartce margins) given the assumptions in Section 4.1 (see Sections 4.4.2, 4.5.3, and 4.6.3 for additional assumptions) and that one of the specific joint signaling strategies is employed over the channel (see Sections 4.4, 4.5, and 4.6).
4.1 Assumptions, Notation, and Background We present background material and some of the standard assumptions made for simulations.
These assumptions apply throughout the document unless noted otherwise.
1. Channel noise can be modeled as additive Gaussian noise (AGN) [13].

2. Interference from other services (DSIN-NEXT and DSIN-FEXT) can be modeled as additive colored Gaussian noise [ 13].
3. We assume the channel can be characterized as a LTI (linear time invariant) system. We divide the transmission bandwidth B of the channel into narrow frequency bins of width W (Hz) each and we assume that the channel, noise and the crosstalk characteristics vary slowly enough with frequency that they can be approximated to be constant over each bin (For a given degree of approximation, the faster these characteristics vary, the more narrow the bins must be. By letting the number of bins K -~ oo, we can approximate any frequency characteristic with arbitrary precision).t We use the following notation for line i on the channel transfer function [ 10]
Hs,x if ~f -.fx~ ~ 2 ~ (1) ~Hc~.f)~2 -0 otherwise, self NEXT transfer function [8]
HN (f ) 12 - Xs~ if ( f - .fx ~ <_ 2 (2) 0 otherwise, and self FEXT transfer function [9]
Fi~~ if ~ f - fk ~ ~ i ~ (3) IHF(f)12 -0 otherwise.
Here fk are the center frequencies (see Figures 16 and 17) of the K
subchannels (bins) with index k E {1, . . . , K}. We will employ these assumptions in Sections 4.5.4, 4.6.6, 4.6.8 and 4.7.1. The DSIN-NEXT and DSIN-FEXT transfer functions are also assumed to vary slowly enough that they can be similarly approximated by a constant value in each frequency bin.
Note that the concept of dividing a transfer function in frequency bins is very general and can include nonuniform bins of varying widths or all bins of arbitrary width (i.e., the bins need not be necessarily narrow).
~ We divide the channel into narrow frequency bins (or subchannels) for ow analysis only. This does not necessarily mean that we need to use DMT as the modulation scheme.

4. Echo cancellation is good enough that we can ignore crosstalk from T° into 1~. We can relax this assumption in some cases where spectral regions employ FDS signaling (see Sections 4.5, 4.6, 4.7, 4.9, and 4.10).
S. All sources of DSIN-NEXT can be lumped into one PSD DSN ( f ) and all sources of DSIN-FEXT can be lumped into one PSD DSF( f ).
6. All sources of self NEXT can be added to form one overall self NEXT source.

7. All sources of self h~XT can be added to form one overall self FF.XT
source.

8. Spectral optimizatian is done under the average input power constraint, i.e., the average input power is limited to ,P~,~ (Watts) in each direction of transmission in the symmetric data-rate case . In the asymmetric data-rate case the average input power in upstream and downstream directions is limited to PUP (Watts)and PDN (Watts) (see Section 5).

9. The PSDs of the upstream and downstream transmission directions can be written using the notation introduced in Section 1.3.2. There are M interfering lines carrying the same service with index i E {1, . . . , M}. Denote the direction of transmission with index o E {u, d}, with a = upstream (to CO) and d = downstream (from CO). Denote the upstream and downstream PSDs on line i as:
S; ( f ): PSD on twisted pair i in upstream direction u.
Sd( f ): PSD on twisted pair i in downstream direction d.
Further, we denote the upstream and downstream. PSD on line i in a generic frequency bin (or subchannel) k as:
s; ( f ): PSD on twisted pair i in upstream direction u.
sd ( f ) : PSD on twisted pair i in downstream direction d.
Note: When we refer to s= ( f ) we mean PSD on twisted pair i in a generic bin, demodulated to baseband ( f E (~- W, WJ) for ease of notation. When we refer to s°
( f ) we mean PSD on a generic twisted pair in a generic bin, demodulated to baseband (f E (-W, WJ) for ease of notation.

10. We assume a monotone decreasing channel transfer function. However, in case the chan-nel transfer function is non-monotonic (e.g., in the case of bridged taps on the linej, our optimization techniques can be applied in each individual bin independently.
This scenario makes the power distribution problem more difficult however (see Section 4.10).

11. We assume we desire equal channel capacities in upstream and downstream directions (ex-cept when the channel, noise, and interference characteristics between lines vary as in Sec-tion 4.7 and when we desire asymmetric data rates from both directions of transmission as in Section 5).
4.2 Interference models and simulation conditions The interference models for different services have been obtained from Annex B
of T1.413-1995 ([9], the ADSL standard), with exceptions as in T1E1.4/97-237 [7]. The NEXT
coupling model is 2-piece Unger model as in T1E1.4/95-127 [8]. BER was fixed at 10-7. Our optimal case re-sults were simulated using Discrete Multitone Technology (DMT) and were compared with that of MONET PAM [1]. MONET PAM uses Decision Feedback Equalizers (DFE) [20] in the receivers along with mufti-level pulse amplitude modulation (PAM) scheme. The margin calculations for DFE margins were done per T1E1.4/97-18081 [11], Section 5.4.2.2.1.1. AGN of power -140 dBm/Hz was assumed in both cases. MONET PAM uses PAM with 3 bits/symbol and a baud rate of fbaud = 517.33 ksymbols/s. The actual upstream and downstream power spectra can be ob-tained from [1]. MONl; f PAM spectra is linearly interpolated from 2x 1552/3 Hz sampled data.
The PAM line-transformer hpf corner, that is, the start frequency is assumed to be at 1 kHz. A 500 Hz rectangular-rule integration is carried out to compute margins. The required DFE SNR margin for 10-7 BER is 27.? dB..
To implement our optimal signaling scheme, we used DMT with start frequency 1 kHz and sampling frequency of 1 MHz. This gives us a bandwidth of 500 kHz and 250 carriers with carrier spacing of 2 kHz. No cyclic prefix (used to combat intersymbol interference (ISI)) was assumed, so the DMT symbol rate is same as the carrier spacing equal to 2 kHz. However, the scheme can easily be implemented by accounting for an appropriate cyclic prefix. The addition of cyclic prefix lowers the symbol. rate and hence lowers the transmission rate. No limit was imposed on the maximum number of bits per carrier (this is often done for simulations). Even with a 15 bits/carrier limit, the results should not change very much, as some of the test runs show.
4.3 Signaling schemes The joint signaling techniques used in the overall optimized signaling schemes use one of the basic signaling schemes (see Figure 18) in different frequency bins depending on the crosstalk and noise combination in those bins.
Figure 18 illustrates the three signaling schemes: EQPSD, FDS and mufti-line FDS (in the case of three lines).2 The Figure shows in frequency bin k the PSDs for each case (recall the notation introduced in Section 4.1., Item 9):
~ When crosstalk and noise are not significant in a frequency bin, EQPSD
signaling is pre-ferred as it achieves higher bit rate than the other two orthogonal signaling schemes (see Section 4.5.5). In EQPSD signaling, the upstream and downstream PSDs are the same (s~ (f) = s~(.f)).
~ When self NEXT is high and self FEXT is low in a bin and there are a large number of neighboring lines carrying the same service together, FDS signaling yields the highest bit rates by eliminating self NEXT (we prove this in Section 4.5.5). In FDS
signaling, each frequency bin is further divided into two halves, with all the upstream PSDs being same for all the lines and all the downstream PSDs being same for all the lines (s; ( f ) 1 sd( f )).
This type of orthogonal signaling completely eliminates self NEXT but does not combat self FEXT.
~ In frequency bins where self FEXT is high, using FDS is not sufficient since self FEXT still exists. In this case, doing mufti-line FDS eliminates self FEXT as well as self NEXT and this achieves the highest bit rates when there are ony a few lines and self FEXT is high and dominant over self NEXT (we prove this in Section 4.6). In mufti-line FDS
signaling each ZThe signaling schemes EQPSD, FDS, and mufti-line FDS work in general for M
lines.

WO 99133215 PCT/US98n'f154 line gets a separate frequency slot (W/M for M lines carrying the same service) in each bin and the upstream and downstream PSDs for each line are the same (ss ( f ) 1 s~
( f ) b'j ~
i, o E {u, d}).
We will see in future sections the exact relationships that allow us to determine which scheme is optimal given an interference and noise combination.
4.4 Optimization: Interference from other services (DSIN-NEXT and DSIN-FEXT) - Solution: EQPSD signaling In this scenario, each xDSL line experiences no self-interference (Figure 19 with neither self NEXT nor self-FEXT). There is only DSIN-NEXT and DSIN-FEXT from other neighboring ser-vices such as Tl, ADSL, IaDSL, etc., in addition to AGN. The solution is well known, but will be useful later in the development of the subsequent novel (Sections 4.5, 4.6, 4.7, and 4.12) signaling schemes.
4.4.1 Prnblem statement Maximize the capacity of an xDSL line in the presence of AGN and interference (DSIN-NEXT
and DSIN-FEXT) from other services under two constraints:
1. The average xDSL input power in one direction of transmission must be linuted to P~
(Watts).
2. Equal capacity in both directions (upstream and downstream) for xDSL.
Do this by designing the distribution of energy over frequency (the transmit spectrum) of the xDSL
transmission.
4.4.2 Additional assumption We add the following assumption to the ones in Section 4.1 for this case:

12. Both directions (upstream and downstream) of transmission experience the same channel noise (AGN) and different service interference (DSIN-NEXT and DSIN-F~XT').
4.4.3 Solution Consider a line (line 1) carrying xDSL service. Line 1 experiences interference from other neigh-boring services (DSIN-NEXT and DSIN-FEXT) and channel noise No ( f ) (AGN) but no self NEXT or self FEXT (see Figure 19).
The DSIN-NEXT and DS1N-FEXT interference can be modeled as colored Gaussian noise for calculating capacity [13]. Recall that DSnr(f) is the PSD of the combined DSIN-NEXT and let DSF ( f ) is the PSD of the combined DS1N-FEXT. Let S" ( f ) and Sd ( f ) denote the PSDs of line 1 upstream (u) direction and downstream (c~ direction transmitted signals respectively. Further, let C" and Cd denote the upstream and downstream direction capacities of line 1 respectively. Let H~ ( f ) denote the channel transfer function ~of line 1. The twisted pair channel is treated as a Gaussian channel with colored Gaussian noise. In this case the channel capacity (in bps) is given by [ 14]

C"= sup J~loga 1+ ~H~(f)~ S"(f) df (4) o No(f) +DSN(f)+DSF(f), (f) and ~Hc(f)~Z Sd(f) Cd = sup ~ log2 1 + df . (5) s~(f) ~ Na(f)) + DSN(f) + DSF(f) The supremum is taken over all possible S" ( f ) and Sd ( f ) satisfying S"(f) >_ 0 bf, Sd(f) >_ 0 df~
and the average power constraints for the two directions 2 ~~ S"'(f)df <_ ~'max~ and 2 ~~ Sd(f)df <_ Pmax. (6) It is sufficient to find the optimal S" ( f ) which gives C", since setting Sd ( f ) = S" ( f ) 'd f , gives the capacity Cd = C" as seen from (4) and (5). Thus, the optimal upstream and downstream channel capacities are equal (C" = Cd).

The optimal power distribution in this case is obtained by the classical "water-filling" tech-nique [ 14]. The optimal Su ( f ) is given by ~ - No(f)+DSN(f)+DSF(~ for f E E
Sopt(f) = IHc(f)I (7) 0 otherwise, with a a Lagrange multiplier and E the spectral region where S" ( f ) >_ 0. We vary the value of a such that Supt ( f ) satisfies with equality the average power constraint in (6). The equality is satisfied for a single value of a giving us a unique optimal PSD Supt ( f ).
Plugging the optimal PSD
Supt ( f ) in (4) yields the capacity C" under the average power constraint.
This procedure yields a unique optimal transmit spectrum Supt ( f ) [ 14].
Keynote: Sd ( f ) = S" ( f ) d f - EQPSD signaling.
Figure 20 gives a flowchart to obtain the optimal transmit spectrum using only EQPSD sig-naling in the presence of DSIN-NEXT, DSIN-FEXT and AGN. It uses the classic water-filling solution to obtain the transmit spectrum. The novelty is in applying this to xDSL scenario to achieve a dynamic transmit spectrum (different for each interference type).
The channel capacities can be calculated separately for each direction of transmission in case of nonuniform interference between the two directions, i.e., when the additional assumption in Section 4.4.2 does not hold. The transmit spectra in general will be different (Sd( f ) ~ S"( f )) for this case, but will still occupy the same bandwidth.
4.4.4 Examples In this Section, we present some examples for the HDSL2 service. An average input power (Pme,,~) of 20 dBm and a fixed bit rate of 1.5b2 Mbps was used for all simulations. The performance margin was measured in each simulation and the comparison with other static transmit spectra (obtained from static PSD masks) proposed is presented in Section 4.5.11. Figure 21 shows the optimal upstream and downstream transmit spectrum for HDSL2 in the presence of DSIN-NEXT from 49 HDSL interferers and AGN (-140 dBm/Hz). Note the deep null in the transmit spectrum from approximately 80 to 2S5 kHz. This results from "water-filling" - the peak of the first main lobe of HDSL lies in the vicinity of 80 to 255 kHz.

Figure 22 shows the optimal upstream and downstream transmit spectrum for HDSL2 in the presence of DSIN-NEXT' :from 25 Tl interferers and AGN (-140 dBm/Hz).
The optimal transmit spectra for the two cases are significantly different, evidence of the fact that the optimal transmit spectra will change depending on the nature of the interfer-ence.
Summary: Recall the discussion on static PSD masks of Section 3.1. We have seen that the optimal transmit spectrum varies significantly with the interference combination. The water-filling solution yields a unique transmit spectrum for each interference combination [14]. The optimal transmit spectrum adapts to minimize the effect of the interference combination. The optimal transnut spectra for upstream and downstream direction are the same (EQPSD
signaling) and thus, employ the same average power in each direction.
4.5 Optimization: Interference from other services (DSIN-NEXT and DSIN-FEXT) plus self interference (self-NEXT and low self FEXT) - Solution:
EQPSD and FDS signaling In this scenario each xDSL line experiences self interference (high self NEXT
and low self FEXT) in addition to AGN and.DSIN-NEXT and DS1N-FEXT from other services (see Figure 3) in a generic xDSL service. This is the case of interest for HI)SL2 service.
45.1 Self NEXT and self FEXT rejection using orthogonal signaling As we saw in Section 3.2, orthogonal signaling can completely reject self NEXT. In addition, FDS
gives better spectral compatibility with other services than other orthogonal schemes like CDS or TDS (see Section 4.5.12 for a proof). Therefore, we choose to use the FDS
scheme for orthogonal signaling. Recall the FDS signaling tradeoff: FDS eliminates self NEXT and therefore increases system capacity; however, FDS also reduces the bandwidth available to each transmitter/receiver pair and therefore decreases. system capacity.
To eliminate self FEXT using orthogonal signaling, we would force each upstream transmitter wo 99/3321s PCT/US98/Z7154 T;' to be orthogonal to all other transmitters ~, j ~ a. Using mufti-Iine FDS, we would separate each T~' into different frequency bands. Unfortunately, this would reduce the bandwidth available to each transmitter to 1/M the overall channel bandwidth. In a typical implementation of HDSL2, M will lie between 1 and 49; hence orthogonal signaling (mufti-line FDS) for eliminating self FEXT is worth the decrease in capacity only when self FEXT is very high. We will show later in Section 4.6 that mufti-line FDS gives gains in capacity when there are only a few number of interfering lines carrying the same service (M = 2 to 4) In this scenario, we assume self NEXT dominates self FEXT and self FEXT is not very high (see Figure 17 and [8]), so we will design a system here with only self-NEXT suppression capability. However, self=FEXT still factors into our design in an important way. This is a new, non-trivial extension of the work of [3].
4.5.2 Problem statement Maximize the capacity o:P an xDSL line in the presence of AGN, interference (DSIN-NEXT and DSIN-FEXT) from other services, and self-NEXT and self FEXT under two constraints:
1. The average xDSL input power in each direction of transmission must be limited to Pm~
(Watts), and 2. Equal capacity in both directions (upstream and downstream) for xDSL.
Do this by designing the distribution of energy over frequency (the transmit spectrum) of the up-stream and downstream xDSL transnussions.
4.5.3 Additional assumptions We add the following assumptions to the ones in Section 4.1 for this case:
12. The level of self-FEXT is low enough in all bins that it is not necessary to use orthogonal signaling between different transmitter/receiver pairs operating in the same direction (see Section 4.5.1 ).

PCT/US9ti/Z7154 13. All the M lines considered are assumed to have the same channel and noise characteristics and face the same interference combination (interference combination refers to combination of different interfering services) in both transmission directions (upstream and downstream).
We will develop some results in Section 4.7 for when this does not hold true.
Thus, we assume that the upstream PSDs of all lines are the same (S"( f )) and the downstream PSDs of all lines are the same (Sd ( f )). That is, S"(f) - S; (f), i E {1,...,M}
Sd(f) - Sd(f), i E {1,..., M}. (g) 14. The coupling transfer functions of NEXT and FEXT interference are symmetrical between neighboring services. For example, each line has the same self-NEXT transfer function HN ( f ) and self-FEXT transfer function HF ( f ) for computing coupling of interference power with any other line. However, we develop some results in Section 4.7 when there are different NEXT and FEXT coupling transfer functions between lines.
4.5.4 Signaling scheme Since the level of self NEXT will vary with frequency (recall Figure 17), it is clear that in high self NEXT regions of the spectrum, orthogonal signaling (FDS, for example) might be of use in order to reject self NEXT. However, in low self NEXT regions, the loss of transmission bandwidth of FDS may outweigh any gain in capacity due to self NEXT rejection.
Therefore, we would like our signaling scheme to be general enough to encompass both FDS signaling, EQPSD signaling, and the spectrum of choices in between. Our approach is related to that of [3).
Key to our scheme is that the upstream and downstream transmissions use di,~'erent transmit spectra. All upstream (to CO) transmitters Tu transmit with the spectrum S" ( f ) All downsixeam (from CO) transmitters T a transmit with the spectrum Sd( f ) Implicit in our scheme is the fact that in this case, self NEXT dominates self FEXT and self FEXT is small. If not, it would not be wise to constrain all Tt ' to the same transmit PSD.
Our goal is to maximize the upstream capacity (C'~) and the downstream capacity (Cd) given an average total power constraint of P~ and the equal capacity constraint Cu = Cd.

Consider the case of two lines with the same service. Line 1 upstream capacity is C" and line 2 downstream capacity is Cd. Under the Gaussian channel assumption, we can write these capacities (in bps) as 00 - ~HC(f)~2 S"(f) sup ~ 1°g2 1 + No(f) + DSN(f) + DSF(f) + ~HN(.f)j Sd(f) + ~HF(.f)~ S
(f) s~(r)~s~(r) (g) and Cd =
~Hc(f)~2Sd(.f) d .
$us ~ logs 1 + Na(f) + DSN(f) + DSF(f) + I HN(f)12 S"(.f) + ~HF(f)~2 Sd(f) f s (f)~ (r) (10) The supremum is taken over all possible S" ( f ) and Sd ( f ) satisfying S,r,(f) >_ 0 df, Sd(.f) >_ 0 tJf~
and the average power constraints for the two directions °° (11) 2 ~ °° Su (.f ) df ~ Pmax ~ ~d 2 J Sd (.f ) df ~ Pm~' We can solve for the capacities C" and Cd using "water-filling" if we impose the restriction of EQPSD, that is S"(f ) = Sd(f) df ~ However, this gives low capacities.
Therefore, we employ ~S ('S'~ ( f ) orthogonal to Sd( f )) in spectral regions where self NEXT is large enough to limit our capacity and EQPSD in the remaining spectrum. This gives much improved performance.
To ease our analysis, we divide the channel into several equal bandwidth subchannels (bins) (see Figure 16) and continue our design and analysis on one frequency bin k assuming the subchan-nel frequency responses (,1~(3). Recall that Figure 17 shows that the channel and self interference frequency responses are smooth and justifies our assuming them flat over narrow subchannels. For ease of notation, in this Section set X-X~ F=Fik H = Ht k~ , ,x~ , in (1~(3)~ (12) and PCT/US98lZ7154 N = No( fk) + DSN( f~) + DSF(fk), - (13) the noise PSD in bin k. Nate that N consists of both AGN plus any interference (DSIN NEXT and DSIN FEXT) from other services. Let s" ( f ) denote the PSD in bin k of line 1 upstream direction and sd ( f ) denote the PSD in bin k of line 2 downstream direction (recall the notation introduced in Section 4.1, Item 9). The corresponding capacities of the subchannel k are denoted by cu and ca.
We desire a signaling scheme that includes FDS, EQPSD and all combinations in between in each frequency bin. Therefore we divide each bin in half and define the upstream and downstream transmit spectra as follows (see Figure 23):
aaw if ~f ~ S ~ , s"(f) _ (1- a)2W if 2 < (f~ ~ W, (14) 0 otherwise and (1-a)Zyp~y ~~f~ < a, sd(f) = a2w if 2 < ~f) < W, (15) 0 otherwise.
Here Pm is the average dower over frequency range (0, WJ in bin k and 0.5 < a < 1. When a = 0.5, s"( f ) = sd( f ) d f E (0, WJ (EQPSD signaling); when a = 1, su( f ) and sd ( f ) are disjoint (FDS signaling). These two extreme transmit spectra along with other possible spectra (for different values of a) are illustrated in Figure 23. The PSDs su( f ) and sd( f ) are "symmetrical" or power complementary to each other. This ensures that the upstream and downstream capacities are equal (c" = cd). The factor cx controls the power distribution in the bin, and W is the bandwidth of the bin.
Next, we show that given this setup, the optimal signaling strategy uses only FDS or EQPSD
in each subchannel.
3The power split-up in a bin does not necessarily have to be 5096 to the left side of the bin and 5096 to the right side of the bin as shown in Figun: 23. In general any 50% - 50% power-complementary split-up between opposite direction bins will work.

PC'T/US98/27154 4.5.5 Solution: One frequency bin If we define the achievable rate as then RA(s"(f):~ sd(f)) _ ~W log2 1 + N + s su(X)Hs F ~~ (16) d(f) a f Cu = O,m81~1 .RA(su(f)~ sd(f)) ~d Cd = omaxl RA(sd(f)~ sa(f))~ (17) Due to the power complementarity of s" ( f ) and sd ( f ), the channel capacities c" and cd are equal.
Therefore, we will only consider the upstream capacity cu expression. Further, we will use RA for RA(su( f ), sd( f )) in the remainder of this Section. Substituting for the PSDs from (14) and (15) into (16) and using (17) we get the following expression for the upstream capacity c"
a2P",H 1-a 2P",H
W
2 omy , log2 1 + N + 1-a 2P",X a2P",F + lOg2 1 -~- a2P.,.XW 1-a 2P",F .
W + W N+ W + W
(18) Let G = N denote the SNR in the bin. Then, we can rewrite (18) as Cu =
W aGH (1- a)GH
o.~ «< i 2 ~ log2 1 + 1 + 1- a GX + aGF ~' log2 1-f- 1 .
( aGX
+ + 1-a GF
( (19) Note from (17) and (19;) that the expression after the max in (19) is the achievable rate RA.
Differentiating the achievable rate (RA) expression in (19) with respect to a gives us BR,, W 1 ~- (1 - a)GX + aGF
8a 2 In 2 ~ [ 1 + ( 1- a GX + aGF + aGH x GH(l. + (1 - a)GX + aGF) - aGH(-GX + GF) +
(Z + (1- a)GX + aGF)Z
1 + aGX -i- (1 - a)GF
1 + crGX + (1 - a)GF + (1 - a)GH x -GH(1 + aGX + (1 - a)GF) - (1 - a)GH(GX - GF)1 ~ (20) (1 + aGX + (1 - a)GF)2 J -- G(2a - 1) ~2(X - F) + G(XZ - F2) - H(1 + GF)~ L, (21) ~~rith L > 0 da E (O,1J. Setting the derivative to zero gives us the single stationary point a = 0.5.
'I7ie achievable rate RA is manotonic in the interval a E (0.5,1J (see Figure 24). If the value a = 0.5 corresponds to a maximum, then it is optimal to perform EQPSD
signaling in this bin. If the value a = 0.5 corresponds to a minimum, then the maximum is achieved by the value a = 1, meaning it is optimal to perform FDS signaling in this bin. No other values of a are an optimal nption. See Figure 25.
The quantity a = 0.5 corresponds to a maximum of R,, (EQPSD) if and only if g~
< 0 'da E (0.5,1). For all a E (0.5,1J, the quantity (2a -1) is positive and 88 is negative if and only iif (see (21 )) 'This implies that 2(X - F) + G(X2 - F2} - H(1 + GF) < 0.
(a(X2 - F'z - HF) < H - 2(X - F).
'Thus, the achievable rate RA is maximum at a = 0.5 (EQPSD) ~or if X2 -- F2 - HF < 0 and G > H - 2(X - F) (22) if X2 -- F2 - HF > 0 and G < H - 2(X - F) (23) Xa-F2-HF' In a similar fashion a = 0.5 corresponds to a minimum of RA if and only if 88 > 0 'da E
(0.5,1J. This implies that a = 1 corresponds to a maximum of RA (FDS) since there is only one stationary point in the interval a E (0.5,1J (see Figure 24). For all a E
(0.5,1J, 88 is positive if and only if This implies that 2(X -F)+G(X2-F2}-H(1+GF) > 0.
G(X2 - F2 - HF) > H - 2(X - F).

Thus, the achievable rate RA is maximum at a = 1 (FDS) if X 2 - F2 - HF < 0 and G < XZ - F~ HF _ (~) or if .X 2 - F2 - HF > 0 and G > X - FX HF . (25) Thus, we can determine whether the value a = 0.5 maximizes or minimizes the achievable rate by evaluating the above inequalities. If a = 0.5 corresponds to a maximum of RA, then we achieve capacity c" by doing EQPSD signaling. If a = 0.5 corresponds to a minimum of RA, then we achieve capacity cu by doing FDS signaling. This can be summed in test conditions to determine the signaling nature (F'DS or EQPSD) in a given bin. Using (22) and (24) we can write If X 2 - F2 - HF < 0 then G - ZPm EQPSD H - 2~X - F) 26 NW FDS X - F2 - HF' { ) Also, using (23) and (25) we can write If X 2 - F2 - HF > 0 then G - 2Pm EQPSD H - 2(X - F) 27 NW FDS X 2 - FZ - HF ( ) Thus, we can write the upstream capacity cu in a frequency bin k as W logs ~1 + nrw+P", X+F), ~ if a = 0.5, eu ;_ {28) 2' loge f l + N ~~~ , if a = 1.
Note: Its always optimal to do either FDS or EQPSD signaling; that is, a = 0.5 or 1 only.
FDS signaling scheme is a subset of the more general orthogonal signaling concept. However, of all orthogonal signaling schemes, FDS signaling gives the best results in terms of spectral compatibility under an average power constraint and hence is used here (see proof in Section 4.5.12). In the case of a peak power constraint in frequency, other orthogonal schemes, such as CDS, could be more appropriate (see Section 4.12.6).

wo ~r~szis 45.6 Solution: All frequency bins rcrius9smis4 We saw in Section 4.5.5 how to determine the optimal signaling scheme (FDS or EQPSD) in one frequency bin for the upstream and downstream directions. In this Section we will apply the test conditions in (26) and (27) to all the frequency bins to determine the overall optimal signaling scheme. Further, using "water-filling" (this comprises of the classical water-filling solution [14]
and an optimization technique to compute capacity in the presence of self interference [16]) opti-mize the power distribution over the bins given the average input power (Pm~).
We divide the channel into K narrow subchannels of bandwidth W (I-iz) each (see Figure 16). For each subchannel k, we compute the respective channel transfer function (H~( fk), self ~ (HN(fk))~ self FEXT (HF( fk)), DSIN-NEXT (DSN( f,~)), DSIN-FEXT (DSF( fk)) and AGN (No( fk)). Then, by applying (26) and (27) to each bin k in the generic xDSL scenario (with the usual monotonicity assumptions as outlined in Section 4.1),4 we can divide the frequency axis (K bins) into 3 major regions:
1. The right side of (26) < 0 for bins (1, MEJ. These bins employ EQPSD
signaling (since power in every bin is > 0).
2. The right side of (27) < 0 for bins [MF, K). These bins employ FDS
signaling (since power in every bin is > 0) and ME < MF.
3. The signaling scheme switches from EQPSD to FDS signaling at some bin MEaF, which lies in the range of bins (ME, MF).
Figure 26 illustrates the situation of the 3 bins ME, MF and M~F. In the next Section we develop an algorithm to find the optimal bin MEaF and the optimal power distribution.
4When the channel transfer function is non-monotonic (as in the case of bridged taps) a bin-by-bin approach may be required to achieve the optimal power distribution (see Section 4.10).

WO 99/33215 PCTNS98l27154 4.5.7 Algorithm for optimizing the overall transmit spectrum To find the optimal EQPSD to FDS switch-over bin MEaF and the optimal power distribution over all bins:
1. Set up equispaced frequency bins of width W (Hz) over the transmission bandwidth B of the channel. The bins should be narrow enough for the assumptions (1~(3) of Section 4.1 to hold.
2. Estimate the interference (DSIN-NEXT, DSIN-FEXT, self NEXT and self FEXT) and noise (AGN) PSDs. Lump the corresponding interference PSDs together into one PSD.
3. Compute the bins MF and MF using (26) and (27) as outlined in Section 4.5.6.
4. Choose an initial estimate of M~~r. (s'~fE :~ a great start).
5. Choose an initial distribution of how much proportion of the total power (P~) should go in the spectrum to the left of MEaF and how much should go to the right. Denote these powers by PE and PF = Pm$X - PE respectively.
6. Use water-filling to distribute these powers (PE and PF) optimally over frequency [14, 16]
with EQPSD signaling in bins [1, MEaFJ and FDS signaling in bins [MEaF + 1, KJ. Compute the subchannel capacity c" in each bin using (28). Calculate the channel capacity C" by summing all subchannel capacities.
7. Re-estimate the powers PE and PF.
8. Repeat steps 6 to 7 for a range of powers PE and PF in search of the maximum channel capacity Cu. This search is guaranteed to converge [3].
9. Re-estimate the optimal EQPSD to FDS switch-over bin MEaF~
10. Repeat steps 5 to 9 for a range of bin values for ME2F
11. Choose the bin number which yields the highest channel capacity C" as the true optimal bin MEar after which the signaling switches from EQPSD to FDS.

WO 99133215 PCTI(J898/Z7154 Notes:
1. Standard minimization/maximizadon routines (like fmin in the software package MATLAB) can be used to search for the optimal powers PE and PF.
2. We can use fast algorithms like the Golden Section Search [ 19] to find the optimal bin M~F.
This routine tries to bracket the minimum/maximum of the objective function (in this case capacity) using four function-evaluation points. We start with a triplet (g~, q, r) that brackets the minimum/rnaximum. We evaluate the function at a new point x E (q, r) and compare this value with that at the two extremities to form a new bracketing triplet (1n, q, x) or (q, x, r) for the minimum/maxirnum point. We repeat this bracketing procedure till the distance between the outer points is tolerably small.
4.5.8 Fast, suboptimal solution for the EQPSD to FDS switch-over bin In the estimation of the optimal bin M~F we have observed in practice that M~, ,a M~, typi-cally within 1 or 2 bins especially when self interference dominates the total crosstalk (see Section 4.5.11). In the case of low AGN and different-service interference the suboptimal solution is a sub-stantially optimized solution. Thus, with significantly less computational e, f,~ort than the algorithm described in Section 4.5.7, a near-optimal solution can be obtained Even if a search is mounted for MaF, we suggest that the search should start at ME (and move to the right).
Algorithm to implement the suboptimal solution:
1. Perform Steps 1 and 2 of the algorithm of Section 4.5.7.
2. Compute the bin MF using (26) as outlined in Section 4.5.6.
3. Set the EQPSD to FDS switch-over bin ME2F equal to ME.
4. Obtain the optimal power distribution and the channel capacity C" by performing Steps 5 through 8 of the algorithm in Section 4.5.7.

4.5.9 Flow of the scheme Consider a line carrying an xDSL service satisfying the assumptions of Sections 4.1 and 4.5.3.
Lines carrying the same xDSL service and different xDSL services interfere with the line under consideration. We wish to hnd the optimal transmit spectrum for the xDSL line under consideration (see problem statement in Section 4.5.2).
1. Determine the self NEXT and self FEXT levels due to other xDSL lines, bin by bin. These can be determined either through:
(a) a worst-case bound of their levels determined by how many lines of that xDSL service could be at what proximity to the xDSL line of interest; or (b) an adaptive estimation (training) procedure run when the modem "turns on:' In this process the CO will evaluate the actual number of active self interfering xDSL
lines and the proximity of those lines with the line of interest.
2. Detenrune DSIN-NEXT and DSIN-FEXT levels, bin by bin. These can be determined either through:
(a) a worst-case bound of their levels determined by how many lines of which kinds of service could be at what proximity to the xDSL line of interest; or (b) an adaptive estimation (training) procedure run when the modem "turns on".
In this procedure no signal transmission is done but we only measure the interference level on the xDSL line at the receiver. Finally, the combined DSIN-NEXT and DSIN-FEXT
can be estimated by subtracting the self interference level from the level measured at the receiver.
3. an adaptive estimation (training) procedure nxn when the modem "turns on".
4. Optimize the spectrum of transmission using the algorithms of Section 4.5.7 or 4.5.8.
5. Transmit and receive data.

6. Optional: Periodically update noise and crosstalk estimates and transmit spectrum from Steps 1-3.
Figure 27 illustrates a flowchart showing the steps for the optimal and the suboptimal solution.
4.5.10 Grnuping of bins and wider subchannels The optimal and near-optimal solutions of Sections 4.5.7 and 4.5.8 divide the channel into narrow subchannels (bins) and employ the assumptions as discussed in Sections 4.1 and 4.5.3. In the case of self interference, the resulting optimal transmit spectrum uses FDS and is "discrete" (a "line spectrum"). Such a transmit spectrum is easily implemented via a DMT
modulation scheme, but is not easy to implement 'with other modulation schemes like PAM, mufti-level PAM, or QAM
[20]. In addition, the DM'T scheme can introduce high latency which may be a problem in some applications. Thus, one may want to use other low-latency modulation schemes.
In such a scenario, we can combine or group FDS bins to form wider subchannels and then employ other broadband modulation schemes. This may result in different perfarmance margins but we believe that the change in margins would not be significant. An alternative broadband modulation scheme like mufti-level PAM or QAM would use a decision feedback equalizer (DFE) [20] at the receiver to compensate for the channel attenuation characteristic (see Section 4.12.4 for further discussion).
Figure 28 shows one possible way of grouping the bins. The left-hand-side figures show the optimal upstream and downstream "discrete" transmit spectra S" ( f ) and Sd( f ) as obtained by the algorithm of Section 4,5.7. The right-hand-side figures show the same optimal transmit spectra after appropriate grouping of bins resulting in "contiguous" transmit spectra.
While grouping, only the bins employing FDS signaling are grouped together and the leftmost bins employing EQPSD
signaling are retained as they are. In this particular case, we have grouped the bins such that the upstream and downstream capacities are equal (C" = Cd). The upstream transmit spectrum is completely "contiguous" while the downstream spectrum is "contiguous" except for one "hole" as shown in Figure 28.
Note: This is not tk~ only way that the bins can be grouped. The bins can be grouped in a variety of different ways giving many different optimal transmit spectra.
Particular modula-WO 99/33215 PCT/US98lZ7154 lion schemes and spectral compatibility with neighboring services may influence the way bins are grouped. Further, grouping of bins may lead to different input powers for opposite directions of transmission.
We look at another possible way of grouping bins such that we achieve equal performance margins and equal upstream and downstream average powers. This could be a preferred grouping for symmetric data-rate services.
Algorithm for "contiguous" optimal transmit spectra: Equal margins and equal average powers in both directions»
1. Solve for the optimal transmit spectrum S" ( f ) according to the algorithms in Sections 4.5.7, 4.5.$, or 4.6, where S'"( f ) is the water-filling solution (refer to [14, 16]
if the spectral region employs EQPSD or mufti-line FDS signaling and to [16] if the spectral region employs FDS
signaling) (see Sections 4.5 and 4.6). This gives a discrete transmit spectrum S"(f ).
2. Denote the spectral region employing FDS signaling as EMS and the spectral region em-ploying EQPSD signaling as EaqPSD.
Obtain Sd ( f ) from S" ( f ) by symmetry, i.e., Sd { f ) = S" ( f ) in EQPSD
and mufti-line FDS
regions and Sd ( f ) J- S" ( f ) in FDS spectral regions. Merge Sd ( f ) and S" ( f ) to form S ( f ) as S(f) - '~(f) - Sd{f) df In ~PSD~
S (f ) - 5"' {f ) U Sd (f ) df in ErDS ~ (29) where U represents the union of the two transmit spectra.
3. Estimate bins M~ E (ME2r, K~, and Mc E {M~, K~. Group the bins of S( f ) to obtain upstream and downstream transmit spectra as S (f ) df in EEQpSD ~ and S ~ ( f ) = d f in bins (Mc, Mc], (30) p otherwise, wo 99r~3ms PCTNS98/271s4 f ( f ) b' f in EE~psD, and Sd f f in bins (ME2s, Mc], and _ o~c(f) _ (gl) 'd f in bins (M~, K), 0 otherwise.
4. Iterate previous step for various choices of Mc and M~. The bin Mc is chosen such that we get equal performance margins in both directions of transmission and the bin M~ is chosen such that upstream and downstream directions have equal average powers.
The resulting transmit spectra Soy ( f ) and S pt ( f ) are another manifestation of the grouping of bins and yield equal performance margins (equal capacities) and equal average powers in both directions of transmission.
4.5.11 Examples and results In this Section, we present some examples and results for the HDSL2 service.
AGN of -140 dBm/Hz was added to the interference combination in all simulations. Table 1 lists our simulation results performance margins and compares them with results from [1]. The simulations were done for the Carrier Serving Area (CSA) loop number 6, which is a 26 AWG, 9 kft line with no bridged taps. The column "Our-PAM" refers to our implementation using T1E1.4/97-18081 [11]
of the PAM scheme (MONI:'T PAM) suggested by the authors in [1] using their transmit spectra.
We believe the slight differences in margins between MONET PAM and "Our-PAM"
exist due to slight differences in our channel, self-NEXT and self FEXT models. The use of "Our-PAM"
margins allows us a fair comparison of our optimal results with other proposed transmit spectra.
The columns Up and Dn refer to the upstream and downstream performance margins respectively.
The column Optimal refers to the performance margins obtained using the optimal transmit spectra.
The column Diff shows the difference between the performance margins for the optimal transmit spectrum and the MONET PAM transmit spectrum (using "Our-PAM" margins). A full-duplex bit rate of 1.552 Mbps and a BER of 10'~ was fixed in order to get the performance margins. The HDSL2 standards committee desires a high uncoded margin (preferably more than 6 dB). Table 1 shows that we achieve very high uncoded margins far exceeding current schemes.

Table 1: Uncoiled performance margins (in dB) for CSA No. 6: MONET PAM vs.
Optimal.
MONET "Our-PAM"
PAM

Crosstalk xDSL serviceUp Dn Up Dn OptimalDiff source 49 HDSL HDSL2 9.38 3.14 10.053.08 18.75 15.67 39 self HDSL2 10.3 6.03 11.186.00 18.39 12.39 25 Tl HDSL2 19.8 20.3 I 20.29 I 21.54I 7.31 ~ 14.23~ I
I

Bit rate fixed at 1.552 Mbps.
Diff = Difference between Optimal and worst-case "Our-PAM".
Table 2 shows the difference between the optimal solution of the signaling scheme (using the optimal M~F) and the fast approximate suboptimal solution (using ME2F = ME) for a variety of interfering lines. The column Diff (in dB) notes the difference in performance margins between the optimal scheme and the suboptimal scheme. Note that there is hardly any difference between the two when self interference dominates the total crosstalk. This is a very significant result from an implementation view point for it shows that near-optimal signaling can be obtained with very little computational effoc~t. The optimal solution requires a somewhat complicated optimization over the bins starting from ME and moving towards the right. Our results clearly indicate that the near-optimal solution can give extremely attractive results with no search for the optimal bin.
Further, this suggests that the optimal bin MEaF is closer to ME than MF and so one should search for it to the immediate right of ME.
An optimal upstream transmit spectrum in the case of self interference is illustrated in Figure 29. The Figure shows the optimal upstream transmit spectrum for HDSL2 service in the presence of self NEXT and self Ff:XT from 39 HDSL2 disturbers and AGN of -140 dBmlHz.
The down-stream transmit spectra for the HDSL2 service are symmetric with the upstream transmit spectra as discussed earlier.
Figure 30 illustrates optimal "contiguous" transmit spectra for the same case of 39 self NEXT
and self FEXT disturbers with AGN of -140 dBm/Hz. The "contiguous" transmit spectra were obtained by grouping the: bins as outlined in Section 4.5.10 (C" = Cd). The upstream and down-Table 2: Uncoded performance margins (in dB) for CSA No. 6: Optimal vs.
Suboptimal.
Crosstalk sourcexDSL Optimal M~F Fast, suboptimalME Diff servicescheme scheme (dB) (dB) 1 self HDSL2 27.68 11 27.68 10 0 self HDSL2 21.94 10 21.94 10 0 19 self HDSL2 20.22 8 20.22 8 0 29 self HDSL2 19.13 8 19.13 8 0 39 self HDSL2 18.39 9 18.39 9 0 10 self + 10 :HDSL2 12.11 60 11.46 19 0.65 HDSL

10 self + 10 HDSL2 7.92 27 7.90 23 0.02 Tl Bit rate fixed at 1.552 Mbps.
Diff = Difference between <~timal and suboptimal scheme.
stream directions exhibit the same performance margins and use different powers.
Figure 31 illustrates another set of optimal "contiguous" transmit spectra for the same case of 39 self NEXT and self FEX'T disturbers with AGN of -140 dBm/Hz. These "contiguous" transmit spectra were obtained by grouping the bins as outlined in the algorithm of Section 4.5.10 such that now we have both equal performance margins (equal capacities) and equal average powers in both directions of transmission.
4.5.12 Spectral compatibility When we optimize the capacity of an xDSL service in the presence of interferers, we must ensure that the optimized xDSL service is not spectrally incompatible with other services. That is, the performance margins of other services must not significantly degrade due to the presence of that xDSL. Our optimal xDSL transmit spectra involve water-filling (after choosing the appropriate joint signaling strategy). To maximize xDSL capacity we distribute more power in regions of less interference and vice versa. This implies the services which interfere with xDSL see less interference in spectral regions where they have more power and vice versa.
This suggests that the PC."IYUS98J27154 spectral compatibility margins for other services in the presence of optimized xDSL PSD should be high.
Table 3 lists our simulation results for HDSL2 service and compares them with results from [ 1 ].
The simulations were done for the CSA loop number 6 (26 AWG, 9 kft, no bridged taps) and CSA
loop number 4 (26 AWG, bridged taps). The column "Our-PAM" refers to our implementation using T1E1.4/97-18081 [11] of the PAM scheme (MONET PAM) suggested by the authors in [1]
using their transmit spectra. We believe the slight differences in margins between MONET PAM
and "Our-PAM" exist due to the differences in our channel, self NEXT and self FEXT models.
The column Optimal lists the performance margins of the xDSL service under consideration using the optimal transmit spectrum only when HDSL2 is a crosstalk source. The use of "Our-PAM"
margins allows us a fair comparison of our optimal margins with the other proposed ~transnut spectra. From Table 3, we can clearly see that the optimal transmit spectrum has a high degree of spectral compatibility with the surrounding interfering lines.
Our optimal results in case of self NEXT and self FEXT give rise to FDS
signaling, which has a peaky PSD in bins employing FDS. All orthogonal schemes like FDS, TDS, and CDS give self NEXT rejection and can transnut at the same bit rate. But, using FDS is better than CDS since there is a gain in the performance margin of the interfering line. We now prove that FDS signaling gives higher spectral compatibility margins than other orthogonal schemes like CDS.
Theorem: Let the line under consideration be the signaling line (with PSD S in a single bin) and the line that interferes with this line be the interfering line (with PSD
a" ( f ) and sd ( f ) in a single bin). Then, using an FDS scheme instead of CDS scheme for the interfering line results in higher capacity for the signaling line under an average power constraint and a Gaussian channel model.
Proof Consider, as usual the scenario of one single frequency bin of width W
(Hz) as illustrated in Figure 32. In this Figure, S is the transmit spectrum of the signaling line under consideration (for example Tl, HDSL, ADSL, etc.), Y and Z represent the different service interference powers from a neighboring interfering line (for example HDSL2) and N represents the lumped channel noise (AGN) and other different-service interference. There are two cases of interest:

Table 3: Spectral-compatibility margins: MONET PAM vs. Optimal MONET "Our-PAM" Optimal PAM
Dn C:rosstalk xDSL SrvcCSA CSA 4 CSA CSA CSA CSA
Src 6 6 4 6 4 4.9 HDSL HDSL 8.53 8.09 8.09 7.78 39 HDSL2 HDSL 10.1 10.9 9.74 10.53 15.44 15.60 Up 39 HDSL2 HDSL 8.28 7.99 7.74 7.53 Dn 39 HDSL EC ADSL 8.43 9.55 7.84 9.02 39 HDSL2 EC ADSL 9.70 11.7 8.17 10.00 6.93 9.10 49 HDSL EC ADSL 8.12 9.24 7.52 8.7 49 HDSL2 HDSL 7.10 6.91 14.95 15.12 Case 1: 'Che interfering line uses a CDS signaling scheme. In this case the power in a single bin k (Pm) is uniformly distributed throughout the bin resulting in a flat PSD, i.e., s"(f) = sd(f) = a.
~~Ve assume the subchannel frequency responses (1~(3) and the notation introduced in (12) fmd (13). We assume here that the NEXT and FEXT coupling transfer functions between different service lines are the same as that for same-service lines. Thus, we can write the different service interference power in signaling line bin k as DSN(f)+DSF(f) - su(f)X +sd(f)F
- aX + aF. (32) ~JVe define Y and Z as Y - a(X - F) Z - 2aF. (33) l:Jsing (33) we can write the interference power in (32) as DSN(f)+DSF(f)=Y+Z.

Case 2: The interfering line uses an FDS signaling scheme. In this case the power in a single bin k (P",) is distributed in only half the bin, resulting in a peaky PSD, i.e., 2a, if If I ~ 2 0, ifs'<IfI<_W, and, 0, if I f I <_ z , 2a, if 2 < I f I <_ W .
We assume the subchannei frequency responses (1~(3) and the notation introduced in (12) and (13). We assume here that the NEXT and FEXT coupling transfer functions between different service lines are the same as that for same-service lines. Thus, we can write the different se:e~ice interi~:e~ce YoWer in signaling line bin k as DSnr(.f) + DSF(f) - s"(,f)X + sd(f)F
2aX, if I f ~ < 2 , - ( 2aF, if 2 < I f I <_ W.
Using (33) we can write the interference power in (34) as 2Y+Z, if If) < 2, DSN(f) + DSF(f) = Z~ if 2 < I f I <_ W.
Getting back to the problem, we consider a single signaling line (line 1). We divide the signal-ing line channel into narrow subchannels (or bins) and we analyze a narrow subchannel k. We use the standard assumptions of Section 4.1. We can write the upstream subchannel capacity of bin k of the signaling line in Case 1 as ci (Case 1 ) - 2W 2 {ln [1 + ~, + Z + N, '~ In [1 + ~, + Z + NJ ~ ' (35) and in Case 2 as ci (Casf; 2) = 2 n 2 { In [1 + 2Y + 2 + N J '+' In [1 + Z + N, } ' (36) Compute the capacity riifferences in the two cases as D = ci (Case 2) - ci (Case 1) = W In ~1 + 2Y+z+nr) ~1 ~' z+N) . (37) 21n2 (1 + y+2+N) Taking the partial derivative of D with respect to Y we get 8D _ W 1 1 8Y ln2S (Y-~-Z+N)(Y+Z-f-N-f-S) (2Y-~Z+N)(2Y-~Z+N+S),' Let U - Y+Z+N, V - Y+Z+N+S.
Note that U, V > 0 and that we can rewrite the partial derivative of D with respect to Y as 8D _ _W 1 _ 1 _ W Y2 + (U + Y)Y (3g) aY In 2 S U'Y ( Lt -;- Y) (V + Y) ~ In 2 S UV U + Y V + y ( )( ) Further, eY I Y-o - 0. The slope of D with respect to Y is always positive and hence, ci (Case 2) -ci (Case 1) is always increasing with Y, which implies that ci (Case 2) - ci (Case 1) b'Y > 0.
When Y < 0, i.e., when FEXT is higher than NEXT in a bin (F > X ), we can redefine Y and Z
as Z = 2aX, and, Y = a(F - X).
We can then follow the same analysis and show that the capacity ci (Case 2) is greater than ci (Case 1 ).
Thus, we have proven that FDS scheme rather than CDS scheme for interfering lines, results in higher capacities for signaling lines under an average power constraint.
Q.E.D.
Interestingly, the power-peaky FDS transmit spectra should be very compatible with the ADSL
standard, since ADSL can balance how many bits it places in each of its DMT
subchannels using a bit loading algorithm [17).
Note: FDS beats CDS in terms of spectral compatibility margins only in the case of an average power constraint. In the case of a peak power constraint in frequency, we may not be able to use a power-peaky scheme like FDS in some spectral regions. Here, we may find that other orthogonal signaling schemes like CDS offer better spectral compatibility margins.

4.6 Optimization: Interference from other services (DSIN-NEXT and DSIN-FEXT) plus self interference (self NEXT and high self FEXT) - Solu-tion: EQPSD, FDS and multi~line FDS signaling In this scenario we have self interference (self NEXT and high self FEXT) in addition to AGN and DSIN-NEXT and DSIN-FEXT from other services (see Figure 3) in a generic xDSL
service. This is the case of interest for °'GDSL", "VDSL2", and HDSL2 (with a small number of lines).
4.6.1 Self FEXT and self NEXT rejection using mufti-line FDS
To reject sei~ FEXT and self-NEXT, we use mufti-line FDS (see Section 4.3 and Figure 18). In mufti-line FDS we separate ea;,~:1?ne by transmitting on each in different frequency bands. This reduces the transmission bandwidth to 1/M the total ci~annel ~~.:dwidth, with M the number of lines carrying the service under consideration. Thus, mull-line FDS signaling can increase the capacity only when there are a few number of lines.
We will design a system here that has both self NEXT and self FEXT rejection capability.
Thus, this serves as the complete solution under the assumptions in Section 4.1 and the constraints of limited average input power (Pm~) and equal capacity in both directions.
4.6.2 Problem statement Maximize the capacity of an xDSL line in the presence of AGN, interference (DSIN-NEXT and DS1N-from other services, and self NEXT and self FEXT under two constraints:
1. The average xDSL input power in each direction of transmission must be limited to P~
(Watts), and 2. Equal capacity in both directions (upstream and downstream) for xDSL.
Do this by designing the distribution of energy over firquency (the transmit spectrum) of the up-stream and downstream xDSL transmissions.

4.6.3 Additional assumptions We add the following assumptions to the ones in Section 4.1:
12. All the M lines carrying the xDSL service are assumed to have the same channel and noise characteristics and face the same interference combination in both transmission directions (upstream and downstream). Refer to Section 4.7 for results when this does not hold true.
13. The coupling transfer functions of NEXT and FEXT interference are symmetrical between neighboring services. For example, each line has the same self NEXT transfer function HN ( f ) and self-FEXT transfer function HF ( f ) for computing coupling of interference power with any other line. However, we develop some results in Section 4.7 when there are different NEXT and FEXT coupling transfer functions between lines.
4.6.4 Signaling scheme The level of self NEXT and self FEXT varies over frequency (recall Figure 17).
In regions of low self NEXT and low self FEXT, EQPSD signaling is the best choice. In spectral regions of high self NEXT but low self FEXT, orthogonal signaling scheme like FDS is preferred (due to its self NEXT rejection, as we saw in Section 4.5). But, in regions of high self FEXT, multi-line FDS
signaling might be rcquired for gaining capacity.
Key to our scheme is that the upstream and downstream transmissions of each of the M lines use di,~''erent transmit spectra.
4.6.5 Solution using EQPSD and FDS signaling: All frequency bins First, we assume that self FEXT is small and then, using EQPSD or FDS
signaling in each bin, we find the solution. for all frequency bins as outlined in Sections 4.5.4 -4.5.8. Thus, we ob-tain the optimal (or suboptimal) EQPSD to FDS switch-over bin M~F under the low self-FEXT
assumption.
Next, we relax the self-FEXT assumption and open the possibility of multi-line FDS. We search each bin to see if we need to switch from EQPSD to mufti-line FDS or FDS to mufti-line FDS. This may not necessarily yield the optimal solution for the transmit spectrum given that we use a joint signaling scheme comprising of the three signaling schemes (EQPSD, FDS and multi-line FDS). But, this analysis is tractable and gives significant gains in channel capacity and is presented next.
4.6.6 Switch to mufti-line FDS: One frequency bin Consider the case of M lines with significant self FEXT interference between them. We divide the channel into several equal bandwidth (W Hz) bins (see Figure 16) and perform our analysis on one frequency bin k assuming subchannel frequency responses (1}-(3). We employ the notation introduced in (12) and (13). Let si ( f ) denote the PSD in bin k of line 1 upstream direction and si ( f ) denote the PSI) in bin k of line 1 downstream direction (recall the notation introduced in Section 4.1, Item 9). Let Pm be the average power over the frequency range (0, W~.
Next, we determine when we need to switch to mufti-line FDS in a given bin to completely reject self FEXT:
IEQPSD to mufti-line FDS: Figure 33 illustrates the two possible signaling schemes EQPSD
and mufti-line FDS in bin k of each line for the case of M = 3 lines . We will consider line 1 for our capacity calculations. Line 1 upstream and downstream capacities for EQPSD signaling are denoted by ci~EQPSD ~d ~,EQPSD reSp~aVCIy. Similarly, line 1 upstream and downstream capacities for mufti-line FDS signaling are denoted by ci~,DS and ~~~5 respectively. Since the upstream and downstream transmit spectra of line 1 in bin k for EQPSD and mufti-line FDS are the same, we have:
a d a d ~1,EQPSD = ~1,EQPSD ~ ~1,MFDS = ~1,MFDS
Thus, we will consider only the upstream capacities in our future discussion.
Under the Gaussian channel assumption, we can define the EQPSD upstream capacity (in bps) as WO 99/33215 PG"T/US98l27154 su ( H - (39) cI,EQPSD = W logs 1~ + N + sdX)+ si F, ' where si (,f) = si(f) = W' if ~.f ~ E [O~ W]~
0 otherwise.
Let G = W denote the SNR in the bin. Then we can rewrite ci~~psD as GH
cI~,EQPSD = W loge [1 + 2 + GX + GFJ ' Similarly, we can define the mufti-line FDS upstream capacity (in bps) as a W si(f)H (41) cI,MFDS = M loge I + N , where mtpm ~ if ~f ~ E ~0~ M]
si(f) = w 0, otherwise, and G = w is the SNR in the bin. Then we can rewrite ci~~DS as ci,MFDS = M logs [1 + 2 GHJ , (42) Define the difference between the two capacities as D = ci,MFDS - ci,F,c~sn. (43) We wish to determine when it is better to do mufti-line FDS than EQPSD, i.e., when is the capacity ci,MFDS ~a~r than ci,F,QPSD~ This means we need a condition for when D > 0.
Substituting from (40) and (42) into (43) we get D > 0 iff F > ~2 + G(X + H)] - (1 + 2 GH) ~ (2 + GX ) . ( ) GC~1+ 2GH)~~-1, Similarly, EQPSD is better (gives higher capacity) than mufti-line FDS when D
< 0, i.e., iff F < .[2 + G(X + H)] - ~1 + 2 GH~'a (2 + GX ) . (45) GCti+ 2GH~"' -1) We can combine (44) and (45) into one test condition that tells us the signaling scheme to use in a single frequency bin F mufti --j ne FDS ~2 + G(X + H)~ - ~ 1 + a GH) ~ (2 + GX ) . (~) E(,~PSD G ~ (1 + Z GH) ~ -1 ) FDS to musti-line FDS: Figure 34 illustrates the two possible signaling schemes FDS and multi-line FDS in bin k of each line for the case of M = 3 lines. We will consider line 1 for our capacity calculations. Line 1 upstream and downstream capacities for FDS signaling are denoted by ci,FDs and ~~~S respectively. Similarly, line 1 upstream and downstream capacities for mufti-line FDS
signaling are denoted by ci~,~FDS ~d ~,MFDS re~avely. Since the upstream and downstream transmit spectra of line 1 in bin k for EQPSD a~~ mufti-line FDS are the same, we have:
~1,FDS = ~,FDS ~ ~1,MFDS = ~,MFDS
Thus, we will consider only the upstream capacities in our future discussion.
Under the Gaussian channel assumption we c;an define the FDS upstream capacity (in bps) as si (.f )H 47 ~1,FDS = 2 loge 1 + N + auF ' ( ) i where si(f) = aw ' if ~f ~ E (0~ Z ~~
0, OtherWlSe.
Let G = y N denote the SNR in the bin. Then we can rewrite ci,FDS as ci~~s = ~ loga [1 + 1 + GF, .
Similarly, we can define the mufti-line FDS upstream capacity (in bps) as W s"( H (49) ~L,MFDS = M logs 1 + 1 N) ' where si(f) = H' ' if ~f~ E ~0~ M
0, otherwise, and G = N is the SNR in the bin. Then we can rewrite ci,MFns ~
PCTNS98lZ7154 ci,~ns = M toga [; + 2 GH, , (50) Define the difference between the two capacities as D = ci,~,,n, ns - ci,Fns ~ (51 ) We wish to find out when.it is more appropriate to perform mufti-line FDS than FDS, i.e., when the capacity Ci~MFDS iS greater than ci~DS. For this, we need a condition for when D > 0. Substituting from (48) and (50) into (51;1 we get D > 0 iii F > (1 +' GH) - ~1 ~- z GH) ~
G,rl+ 2GH)~-1' .
(52) Similarly, FDS is better (gives higher capacity) than mufti-line FDS when D <
0, i.e., iff F < (1 + GH) - (~ + ~ GH) (53) G~~1+ 2GH)~-11 .
We can combine (52) and (~3) into one test condition which tells us the signaling scheme to use mufti -C ne FDS (1 + GH) - (1 + a GH) ~ .
F ( ) FDS G C (1 + 2 GH) ~ -11 Thus, we can write the generic upstream capacity ci for bin k of line 1 as W logs ~1 + Nw+p,~x + ~ , if EQPSD, ci = ~ z logs [1 + N--~-F, , if FDS, 'M toga ~1 + MyPN J , if mufti-line FDS.
4.6.7 Switch to multi.line FDS: All frequency bins We saw in the previous Section how to determine if we need to switch to mufti-line FDS from EQPSD or FDS in a given bin. We already have the optimal solution assunung EQPSD and FDS

signaling scheme (from Section 4.5). Now, we apply the conditions (46) and (54) to each bin k. Interestingly, due to the assumed monotonicity of self FEXT, self NEXT and channel transfer function, we can divide the frequency axis (all K bins) into 4 major regions:
1. Using test condition (4fi), we find that bins [1, MEZMFDSJ employ EQPSD
signaling.
2. Using test condition (46), we find that bins [MEZMFDS + 1, M~,.DgzFDSJ
employ mufti-line FDS signaling. Note that MMFDSZFDS = MEZF obtained from optimization procedure of Section 4.6.5.
3. Using test condition (S~), we find that bins [M~DSZFDS + 1, MFDSZMFDSJ
employ FDS sig-naling.
4. Using test condition (54), we find that bins [MFDSZMFDS + 1, KJ employ mufti-line FDS
signaling.
Figure 35 illustrates the 3 bins M~MFDS ~ MMFDSZFDS ~d MFDSZMFDS ~d ~e EQPSD, FDS
and mufti-line FDS regions. In practice we mainly see 2 scenarios:
1. If MEZMFDS < MMFDS2FDS den MFDS2MFDS = MMFDS2FDS~ ~d we get only 2 distinct spectral regions as shown in Figure 36:
(a) Bins [l, M~MFDgJ employ EQPSD signaling.
(b) Bins [MEZMFDS + 1, KJ employ mufti-line FDS signaling.
FDS signaling is not employed in this case.
2. If M~M~S = M~Dg2FDS = MEZF then we get 3 distinct spectral regions as shown in Figure 37:
(a) Bins [l, M1,,~DSZFDSJ employ EQPSD signaling.
(b) Bins ~MMFDS2FDS + 1, MFDS2MFDSJ employ FDS signaling.
(c) Bins [MFDSZMFDS -+-1, KJ employ mufti-line FDS signaling.

There is no switch to multi-line FDS signaling within the EQPSD signaling region (bins (1.~ MEaF~).
Note that the bin MM~rDggFDS = ME2F 1S fixed from the optimization procedure from Section 4.6.5.
X4.6.8 Special case: Performance of 2 lines (ten in practice we may have only two twisted pair lines carrying the same service and interfering with each other. It is important to derive the optimal transmit spectrum for such a scenario. In this ;>ecdon we focus on this special case of only 2 lines. We will see that in this case it is optimal to perform either multi-line FDS or EQPSD signaling in each bin. In this scenario with arbitrary self F'EXT and self-NEXT wE; easily see that there is no need to perform FDS
signaling (reject .elf NEXT only) as multi-line FDS rejects both self-NEXT and self FEXT while achieving the same capacity as FDS. Thus, we choose between EQPSD and mufti-line FDS
signaling schemes for each bin to achieve the optimal transmit spectrum.
Let Si ( f ) and Si ( f ) denote the upstream and downstream transmit spectra of line 1 and S2 ( f ) and Sa ( f ) denote the upstream and downstream transmit spectra of line 2 respectively. Let the line 7l upstream capacity be Ci and let the line 2 downstream capacity be C2. Under the Gaussian channel assumption, we can write these capacities (in bps) as Ci - gup o0 Si (~~~(f)~ss (~
IHe(f)laSi(f) loge 1 + No(f) + DsN(f) + DSF(f) + ~HN(f)~ Sz(f) + ~HF(f)~ ~'(f ~tnd C2 - sup o0 ss (f)~s~ (f),s~ (f) IHC(f)IZS2(f) loge 1 + No(f) + DSN(f) + DSF(f) + I HN(f)I2 Sl (f) + ~HF(f)~2 S~(f) '~~ (s~) 'The supremum is taken over all possible Si ( f ), S2 ( f ), Sd ( f ) and SZ ( f ) satisfying ~(f) :? ~~ Si(f) ? fi~ ~(.f) »~ SZ(f) > U,'df and the average power constraints for the two directions 'Z J~ Si (f )df ~ Pmax, ~d 2 J~ S2 (f )df < Pma~~ (58) We employ mufti-line FDS (Si ( f ) and Si ( f ) orthogonal to 52 ( f ) and SZ
( f )) in spectral rf;gions where the self FEXT is large enough and EQPSD in the remaining spectrum. This gives optimal performance.
To ease our analysis, as usual, we divide the channel into several equal bandwidth subchannels (bins) (see Figure 16) and continue our design and analysis on one frequency bin k assuming subchannel frequency responses (1~(3). We use notation introduced in (12) and (I3). Let si ( f ) and si ( f ) denote the PSDs in bin k of line l upstream and downstream directions and sa ( f ) and s:; ( f ) denote the PSDs in bin k of line 2 upstream and downstream directions. The corresponding capacities of the subchannel k are denoted by ci , ~, c2 and ~.
We desire a signaling scheme that can have mufti-line FDS, EQPSD and all combinations in between in each frequency bin. Therefore we divide each bin in halfs and define the upstream and downstream transmit spectra as follows (see Figure 38):
and a ayP--~-y if ~ f I ~
si(f)=sa(f)= (1-a)2W if a < ~f~ ~W~
0 otherwise, (1 - a)aw if ~.f ~ ~ a sa (f ) = sa (f ) = a 2W if 2 < ~ f ~ < W, (60) 0 otherwise.
Here, Pm is the average power over frequency range ~0, W) in bin k and 0.5 < a < 1. In this discussion we will only use the PSDs si ( f ) and sa ( f ). When a = 0.5, si ( f ) = sa ( f ) d f E ~0, W~
(I:QPSD signaling); when a == 1, si ( f ) and s2( f ) are disjoint (mufti-line FDS signaling). The P;SDs si ( f ) and sa( f ) are "symmetrical" or power complementary to each other. This ensures the sThe power split-up in a bin does not necessarily have to be 50~ to the left side of the bin and 5086 to the right side of the bin as shown in Figure 38. In general any 50% - 50% power complementary split-up between different-line bins will work.

capacities of the two lines are equal (ci = cz). The factor a controls the power distribution in the lbin and W is the bandwidth o:f the bin.
Next, we show that the optimal signaling strategy uses only mufti-line FDS or EQPSD in each subchannel.
The achievable rate for one frequency bin can be written as R~(si(f)~s2(f)~sz(f))=~W loga 1+N+s~tf)X)Hs2(f)F df~ (61) then ci =o_~~iRA(si(f)'~sa(f)~s~(f)) ~d cz=om~lRA(sa(.f)~si(f)~s2(f))~ (62) lDue to the power complementarity of si ( f ) and s2 ( f ), the channel capacities are equal (ci = ,c~.l).
'Therefore, we will only consider the upstream capacity ci expression.
Further, we will use RA for .RA (si ( f ), s2 ( f ), sa ( f )) in thc; remainder of this Section.
Substituting for the PSDs from (59) and (60) into (61) and using (62) we get the following expression for the upstream capacity ci W a2P,.. A 1-a 2P", X
2 oma~l loge 1 + N + tl-aW mX + 1- W mF + loge 1 ~- 1V + «~~ -E- °~zPmF
W W
(63) iLet G = W denote the SNR in the bin. Then, we can rewrite (63) as ci =
W max Toga ~1-~ - aGH ~ + loge ~1 + (1- a)GH
2 o.s<«<1 1 + (1 - a)GX + (1- a)GF 1 + aGX + aGF
( Using (62) and differentiating the achievable rate (RA) expression in (64) with respect to a ;gives us A =~ (2a -1) (2(X + F) + G(X + F)2 - H] L, (65) with L > 0 da E (0,1]. Setting the derivative to zero gives us the single stationary point a = 0.5.
'Thus, the achievable rate RA is monotonic in the interval a E (0.5,1] (see Figure 24). If the value a = 0.5 corresponds to a maximum of RA, then it is optimal to perform EQPSD
signaling in this lbin. If the value a = 0.5 corresponds to a minimum of RA, then the maximum of R,a is achieved 'by the value a = 1, meaning it is optimal to perform mufti-line FDS signaling in this bin. No other values of a are an optimal option (see Figure 39).
The quantity a = 0.5 corresponds to a maximum of RA (EQPSD) if and only if ge < 0 da E (0.5,1]. For all a E (0.5,1], the quantity (2a - 1) is positive and g is negative iff (see (65)) 2(X + F) + G(X + F)2 - H < 0.
This implies that G < H - 2 (X + F) , (66) (X + F)2 In a similar fashion a = 0.5 corresponds to a mi.~.imum of RA if and only if a > 0 ba E
(0.5,1]. This implies that a = 1 corresponds to a maximum (multi-line FDS) since there is only one stationary point in the interval a E (0.5,1] (see Figure 24). For all a E
(0.5,1], 88 is positive iff 2(X + F) + G(X + F)2 - H > 0.
This implies that G> H-2(X+F), (67) (X + F)2 The above statements can be summed in a test condition to determine the signaling nature (mufti-line FDS or EQPSD) in a given bin. Using (66) and (67) we can write G - 2F,m mufti -Cne FDS H - 2(X 2F) .
(68) NW E(1PSD (X + F) Thus, we can write the upstream capacity ci in a frequency bin k as W loge ~1 + NW+p~»~X.~F)~ ~ if a = 0.5, (69) ci -2 logs ~1 + 2Nw ~ if a = 1.
Note: It is globally optimal to employ either mufti-line FDS or EQPSD
signaling; that is, a = 0.5 or 1, only in the case of 2 lines.

WO 99!33215 PCT/US98/Z7154 ~~.6.9 Flow of the scheme 1. Perform steps 1-3 of Section 4.5.9.
2. Compute bins M~~ns, MMFDS2FDS ~d MFDS2MFDS ~d employ signaling schemes in bins as described in Section 4.6.5.
3. Transmit and receive data.
4. Optional: Periodically update noise and crosstalk estimates and transmit spectrum from Steps 1-3 of Section 4.5.9. Repeat Step 2 from above.
Figure 40 gives a flowchart to obtain the optimal transmit spectrum using EQPSD, FDS, and mufti-line FDS (MFRS) signaling !~ the presence of self interference (self NEXT and self FEXT), DSIN-NEXT, DSIN-FEXT and AGN.
4.6.10 Examples and results Optimal transmit spectra were used in all examples to compute performance margins and channel capacities.
HDSL2 service: Table 4 lists our simulation results performance margins and channel capacities using the EQPSD, FDS and mufti-line FDS signaling schemes.
Notes:
1. Sampling frequency f s =1000 kHz, Bin width W = 2 kHz and number of subchannels K = 250. Average input power of 20 dBm in each transmission direction.
2. Cs denotes the upstream capacity of line i using EQPSD and FDS signaling only and C; (MFRS) denates the upstream capacity of line i using EQPSD, FDS and mufti-line FDS signaling schemes. All the rates are in Mbps.
3. The column Margin lists the performance margin when the bit rate is fixed at 1.552 Mbps. In each :row in the top half the capacity is fixed at C= = 1.5520 and in the bottom half the capacity is fixed at C~ (MFDS) = L5520.

'Cable 4: Uncoded performance margins (in dB) and channel capacities (in Mbps) using EQPSD, FDS and mufti-line FDS for HDSL2 (CSA No. 6).
Xtalk M~~DS
Src MIuIFDS2FDSMFDS2MFDSCf Ci ~~$) ~~n Dlff 1 HDSL2 8 11 11 1.55202.3763 27.682 9.852 1 HDSL2 0 0 0 0.80271.5520 37.534 2 HDSL2 9 9 30 1.55201.8293 25.934 4.543 2 HDSL2 4 4 19 1.18611.5520 30.477 3 HDSL2 8 8 112 1.55201.6067 24.910 0.985 3 HDSL2 7 7 100 1.47921.5520 25.791 4 HDSL2 8 8 246 1.5520I 1.5520 I 24.186I 0 Diff = Difference between bottom half and top half of each row of Margin.
4. The column Diff denotes the gain in performance margins between using EQPSD
and FDS versus EQPSD, FDS and mufti-line FDS signaling, i.e., the difference in margins between the bottom half and top half of each row.
5. Each HDSL2 line contributes NEXT and FEXT calculated using 2-piece Unger model f8).
6. These runs were done with no different service (DS) interferers. The results would vary depending on the particular DS interferer(s) present.
Conclusions:
1. Significant gains in margin for small number of lines. The gains decrease with increase in number of lines.
2. There is no gain in margin using mufti-line FDS for 5 or more lines (4 Crosstalk dis-turbers) for these line and interference models.
"GDSL" service: Table 5 lists our simulation results performance margins and channel capacities using the EQPSD, FDS and mufti-line FDS signaling schemes in the case of "GDSL".
Notes:

'.Cable 5: Uncoded performance margins (in dB) and channel capacities (in Mbps) using EQPSD, FDS and mufti-line FDS for "GDSL"
(3 kft line).

Xtalk ME2MFDS ~MFDS2FDS MFDS2MFDSCi SrC

1 GDSL 505 1253 1253 25.004631.6188 8.21 8.49 1 GDSL 245 981 981 16.514125.0007 16.70 2 GDSL 952 1214 1214 25.000727.3923 6.13 2.91 2 GDSL 825 1116 1116 22.007625.0030 9.04 3 GDSL i 186 1212 1212 25.000425.6686 5.05 0.75 3 GDSL 1145 1186 1186 24.217225.0008 5.80 4 GDSL 1222 1222 2000 25.001825.0018 4.37 0 Diff - Difference between bottom half and top half of each row of Margin.
1. Sampling frequency f, = 8000 kHz, Bin width W = 2 ~z and number of subchannels K = 2000. Average input power of 20 dBm in each transmission direction.
2. C; denotes the upstream capacity of line a using EQPSD and FDS signaling only and C; (MFDS) denotes the upstream capacity of line i using EQPSD, FDS and mufti-line FDS signaling schemes. All the rates are in Mbps.
3. The column Margin lists the performance margin when the bit rate is fixed at 25 Mbps.
In each row in the top half the capacity is fixed at C; = 25 and in the bottom half the capacity is fixed at C~'(MFDS) = 25.
4. The column Diff denotes the gain in performance margins between using EQPSD
and FDS versus EQPSD, FDS and mufti-line FDS signaling, i.e., the difference in margins between the bottom half and top half of each row.
5. Each "GDSL" 'line contributes self NEXT and self FEXT calculated using 2-piece Unger model [8]. In "GDSL" case the self FEXT level is more dominant than self NEXT. To model this we take only 1% of the self NEXT power calculated using 2-piece Unger model in our simulations.
6. These runs were done with no different service (DS) interferers. The results would vary 'Table 6: Uncoded performance margins (in dB) and channel capacities (in Mbps) using EQPSD, FDS and mufti-Line FDS for "VDSL2" (3 kft Iine).
Xtalk M~~DS M~S2FDS M~sa~ns C; Ci (M~3S)Margin Diff Src 1 VDSL2 58 236 236 12.4011 24.8234 16.022 18.913 1 VDSL2 8 50 50 2.5552 12.4001 34.935 2 VDSL2 160 219 219 12.4003 18.8073 14.074 13.476 2 VDSL2 46 78 78 4.4478 12.4036 27.550 3 VDSL2 217 217 217 12.4028 15.6002 12.985 7.765 3 VDSL2 127 127 127 7.3365 12.4002 20.750 4 VDSL2 219 219 553 12.4016 13.7787 12.250 3.275 4 VDSL2 179 179 359 10.1474 12.4012 15.525 S VDSL2 224 224 1014 12.4014 12.9039 11.705 1.005 VDSL2 211 211 878 11.6945 12.4014 12.710 6 VDSL2 231 231 1455 12.4025 12.5278 11.280 0.212 6 VDSL2 229 229 1412 12.2521 12.4018 11.492 7 VDSL2 240 240 1880 12.4004 12.4049 10.945 0.007 7 VDSL2 240 240 1878 12.3954 12.4001 10.952 Diff = Difference between bottom half and top half of each row of Margin.
depending on the particular DS interferer(s) present.
Conclusions:
1. Significant gains in margin for small number of lines. The gains decrease with increase in number of lines.
2. There is no gain in margin using mufti-line FDS for 5 or more lines (4 Crosstalk dis-turbers) for these 'line and interference models.
"VDSL2" service: Table 6 lists our simulation results performance margins and channel capaci-ties using the EQPSD, :FDS and mufti-line FDS signaling schemes in the case of "VDSL2".

wo ~r~3ms pcr~s98nns4 Notes:
1. Sampling frequency fa = 8000 kHz, Bin width W = 2 kHz and number of subchannels K = 2000. Average input power of 20 dBm in each transmission direction.
2. C; denotes the upstream capacity of line i using EQPSD and FDS signaling only and C; (MFRS) denotes the upstream capacity of line $ using EQPSD, FDS and mufti-line FDS signaling schemes. All the rates are in Mbps.
3. The column Margin lists the performance margin when the bit rate is fixed at 12.4 Mbps. In each row in the top half the capacity is fixed at C; = 12.4 and in the bottom half the capacity is fixed at C; (MFDS) = 12.4.
4. The column Diff denotes the gain in perf~rr3ance margins be~Neen using EQPSD and FDS versus EQPSD, FDS and mufti-line FDS signaling, i.e., the difference in margins between the bottom half and top half of each row.
5. Each VDSL2 line contributes self NEXT and self FEXT calculated using 2-piece Unger model [8]. In VDSL2 case self NEXT and self FEXT both are high but self NEXT
dominates self FEXT.

Conclusions:
1. Significant gains in margin for small number of lines. The gains decrease with increase in number of lines.
2. There is no gain in margin using mufti-line FDS for 9 or more lines (8 crosstalk dis-turbers). These runs were done with no different service (DS) interferers. The results would vary depending on the particular DS interferer present.
4.7 Joint signaling for lines differing in channel, noise and interference char-acteristics We have so far looked at a scenario where all the lines in a binder have the same channel charac-teristics and experience similar noise and interference characteristics in both directions of trans-mission. These assumptions made the signaling scheme solutions more tractable.
We also need to look at a scenario between neighboring lines in binder groups where the channel characteristics vary (e.g., different length and different gauge lines) and we have different noise and interference characteristics between upstream and downstream transmission (e.g., asymmetrical services like ADSL and VDSL; different coupling transfer function in different directions).
In this Section, we derive results for neighboring lines carrying the same service when they differ in channel, noise and interference characteristics. Specifically, we develop test conditions to determine the signaling nature in a given bin k.
4.7.1 Solution for 2 lines: EQPSD and FDS signaling Consider the case of 2 lines with different channel, noise and interference characteristics. We again divide the channel into several equal bandwidth bins (see Figure 16) and continue our design and analysis on one frequency bin k assuming the subchannel frequency responses (1~(3). For ease of notation in this Section, for line 1 we set hTl = Ht,,~, .Xl = X~,k~ Fl = F't,~ as in (1~(3)~ (70) and let Nl = No(fi~) + DSN(fk) + DSF(fk)> - (71) be the lumped noise PSD in line 1 bin k. Further, let Pml and P",2 be the average powers over range (0, W~ Hz in bin k of line 1 and 2 respectively. Let si ( f ) and si ( f ) denote the PSDs in bin k of line 1 upstream and <iownstream directions and s~ ( f ) and sa ( f ) denote the PSDs in bin k of line 2 upstream and downstream directions (recall the notation introduced in Section 4.1, Item 9).
The corresponding capacities of the subchannel k are denoted by ci , ~, c2 and ~.
We desire a signaling scheme that can have FDS, EQPSD and all combinations in between in a frequency bin. Therefore we divide each bin in half and define the upstream and downstream transnut spectra as follows (see Figure 41):
aaw if ~.f~ 5 2, si (f ) _ (1 - a) ZW if z < ~f ( ~ W ~ (~2) 0 otherwise, (1 -a)~W
sa(f) = a W if 2 < ~f ~ ~ W~ (73) 0 otherwise, aa-per, if~f~ < z, sa(f) _ (1 -a)aw if Z < ~f~ <_ W, (74) 0 otherwise, and (1-a)2Py--~v if~f~~ ~~
si(f) = aaw if 2 < ~f~ ~ W~ (75) 0 otherwise, where 0.5 < a < 1. We assume that the upstream and downstream transmit spectra obey power complementarity, i.e. line 1 puts less power where line 2 puts more and vice versa. When a = 0.5, si (f ) = si(f )~ sz (f ) _ s~(f ) d.f E (0, W~ (EQPSD signaling); when a = l, si ( f ) and s2 ( f ) are disjoint (FDS signaling). '.Che capacities of opposite directions are equal for each line:
ci = ca and c2 = ~.

The factor a controls the power distribution in the bin, and W is the bandwidth of the bin.
Next, we show that the optimal signaling strategy uses only FDS or EQPSD in each subchan-nel. We also derive a test condition to determine the optimal signaling scheme to use.
The achievable rate for one frequency bin can be written as RA(si (f)~ s~(~)~ s2(f)) _ ~W loga 1 + Nl + s2(f)X)~+1 sz(f)Fl df ~ (76) Thus, ci = max RA(si (.f)~ s~(.f)~ si(f))~ (77) O.b<a<1 We will consider the upstream capacity ci expression for our analysis.
Further, we will use RA
for RA(si ( f ), sa( f ), s2 ( f )) in the remainder of this Section.
Substituting for the PSDs from (72), (73) and (74) into (76) and using (77) we get the following expression for the upstream capacity ci _ W max 2 0.8<a< 1 a2P t8t (1-«)'ZPmiHI
logs 1 + Nl + ~1_«J~W~ Xl + ~ w Fl + loge 1.'f' Ni + «ap;y x +
(1-a)2P",sFi (78) Let Gi = W , and G2 = W denote the SNRs in the bin due to line 1 and line 2 respectively.
Then, we can rewrite (78) as ci _ max W
o.b<«<i 2 l0 1 + aGlH1 + l0 1-.~ (1- a)G1H1 8Z 1 + 1- a)GaXI + aG~Fi ga [ 1 + aG2X1 + (1 - a)GZFi ( (79) Using (77) and differentiating the achievable rate (RA) expression in (79) with respect to a gives us aRA = (2a - 1) (Gi(Xi - Fi ) + 2G~(Xl - Fl) - G1H1(G2F1 + 1)) L, (g~) 8a with L > 0 da E (O,1J. Setting the derivative to zero gives us the single stationary point a = 0.5.
Thus, the achievable rate RA is monotonic in the interval a E (0.5,1] (see Figure 24). If the value a = 0.5 corresponds to a maximum of RA, then it is optimal to perform EQPSD
signaling in this bin. If the value a = 0.5 cairesponds to a minimum of RA, then the maximum is achieved by the value a = 1, meaning it is optimal to perform FDS signaling in this bin. No other values of a are an optimal option.
The quantity a = 0.5 corresponds to a maximum of RA (EQPSD) if and only if 88 < 0 da E (0.5,1). For all a E (0.5,1), 88 is negative if and only if (see (80)) Ga(Xi - Fi ) + 2G2(Xl - Fl) - GiHi(GaFI + 1) < 0.
This implies that Gl > Ga(Xi - ~) + 2Ga(Xl - Fl) (81) GaFiHi + Hl In a similar fashion a = 0.5 corresponds to a minimum of RA if and only if e~
> 0 b'a E (0.5,1J. This implies that a = 1 corresponds to a maximum (FDS) since there is only one stationary point in the interval a E (0.5,1) (see Figure 24). For all a E
(0.5,1, 88 is positive if and only if (see (80)) This implies that G2(Xi - Fi ) + 2G2(Xl - Fl) - G1H1 (G2Fi + 1) > 0.
Gl < G~(Xi - ~) + 2Ga(Xl - Fl). (82) G2FiH1 + H~
The above statements can be summed in a test condition to determine the signaling nature (FDS or EQPSD) in a given bin. Using (81) and (82) we can write G1 - '.2P",i F'QPSD ~(Xl - ~) + 2Ga(Xi - Fl) , (83) N1W FDS G2F1H1 + Hl Thus, we can write the upstream capacity ci of line 1 in bin k as W loge ~1 + N,w+ ,~ HXl+F,)~ ~ if a = 0.5, ci - (84) 2 lOg~ ~1 + N~ w+2 ~lzF~ ~ , if a = 1.

4.7.2 Solution for M lines: EQPSD and FDS signaling It is straightforward to generalize the result in the previous Section to M
lines where each line i has parameters H~, G~, Pte, X= and F; for i E { 1, . . . , M}. Further, we assume that the self NEXT
and self FEXT coupling transfer functions between lines 2, ~ ~ ~ , M and line 1 are all the same. The test condition to determine signaling nature (EQPSD or FDS) in bin k of line 1 for M line case can be written as EQPSD M a 2 M
Gl = 2Pm1 ~ (E;-2 G=) (Xi M ~) + 2(~f-z Gi)(Xl - Fl) , (85) N1W FDS (E;-2 Gs)~'~H~ + H~
We can write the upstream capacity of line 1 in bin k as W logs' 1 + Nln,+(~p z m:)(X,+F,l, ~ if a = 0.5, ci = (86) -a loge [1 + N1 W+~(~s~mi~r'1 ~ ' if a = 1.
4.7.3 Solution for 2 tines: EQPSD and multi-line FDS signaling We saw in Section 4.6.8 that in the case of two lines it is optimal to use mufti-line FDS instead of FDS signaling. In this Section we will derive a test condition to determine the signaling nature in a given bin. We use the notation as introduced in Section 4.7.1.
We desire a signaling scheme that supports mufti-line FDS, EQPSD, and all combinations in between in a frequency bin. Therefore we divide each bin in half and define the upstream and downstream transmit spectra as follows (see Figure 42):
if If~ ~ 2 r 8i (f) = si(f) _ (1 - a)2w if 2 < (.f~ ~ Wr (87) 0 otherwise, ( 1 - a) aPy~y if ~ f ~ <_ 2 , sa(f) =sa(f) _ ~x2w if 2 < ~f~ ~ Wr (88) 0 otherwise, WO 99/33215 PCTNS98l27154 where 0.5 < a < 1. We assume that the upstream and downstream transmit spectra obey power complementarity, i.e., line 1 puts less power where line 2 puts more and vice versa. In further dis-cussion we will use transmit spectra si ( f ) and s2 ( f ). When a = 0.5, si ( f ) = sa ( f ), 'd f E (0, W J
(EQPSD signaling); when a. = 1, si ( f ) and sa ( f ) are disjoint (FDS
signaling). The capacities of opposite directions are equal for each line:
ci = cd and c2 = ca.
The factor a controls the power distribution in the bin and W is the bandwidth of the bin.
Next, we show that the optimal signaling strategy uses only EQPSD or mufti-line FDS in each subchannel and derive a test. condition to determine the signaling scheme to use.
The achievable rate for one frequency bin can be written as RA(si(f)~sa(f)~sa(f)) _ ~wlogZ LI+ Nl +s2(f)X)Hls~(f)F'1 df~ (89) then ci = meat RA(si(f)~sa(f)~8z(f))~
0.5<a< 1 We will consider the upstream capacity ci expression for our analysis.
Further, we will use RA for RA(si (f ) ~ s2 (f ) ~ sa (f )) in the remainder of this Section. Substituting for the PSDs from (72) and (73) into (89) and using (90;1 we get the following expression for the upstream capacity ci - W max 2 0.5<«<i a2P,..iH~ ~1-a)zP",~ Hl logz I + Nl + ~_« aP,~zx + (i-a)2P~,sF, + logs I ~- Ni + as ,~~W ~" a .~s a w w w w (91 ) Let Gl = W , and G2 = w denote the SNRs in the bin due to line 1 and line 2 respectively.
Then, we can rewrite (91 ) as ci - max W
0.5<a<1 2 l0 1 + aGlH1 + l0 I + (I - a)G1H1 1 + 1 - a)GZXl + (I - a)G2F1 g2 1 + aG2X1 + aG2FlJ
( (92) Using (90) and differentiating the achievable rate (RA) expression in (92) with respect to a gives us aRA = (2a - 1) ~GZ(Xl + Fl)a + 2Ga(Xl + Fl} - GIHiJ L, (93) as with L > 0 da E (O,1J. Setting the derivative to zero gives us the single stationary point a = 0.5.
Thus, the achievable rate R~, is monotonic in the interval a E (0.5,1J (see Figure 24). If the value a = 0.5 corresponds to a maximum of RA, then it is optimal to perform EQPSD
signaling in this bin. If the value a = 0.5 corresponds to a minimum of RA, then the maximum is achieved by the value a = 1, meaning it is optimal to perform mufti-line FDS signaling in this bin. No other values of a are an optimal option.
The quantity a = 0.5 corresponds to a maximum of RA (EQPSD) if and only if 88 < 0 b'a E (0.5,1J. For all a E (0.5,1J, 88 is negative if and only if (see (93)) Ga(Xl + Fi)2 + 2G2(Xi + Fl) - G1H1 < 0.
This implies that Gl > ~(Xi + Fi)2 + 2G~(Xi + Fl) . (94) In a similar fashion a =: 0.5 corresponds to a minimum of RA if and only if 88 > 0 da E
(0.5,1J. This implies that a - 1 corresponds to a maximum of RA (mufti-line FDS) since there is only one stationary point in the interval a E (0.5,1J (see Figure 24). For all a E (0.5,1J, 88 is positive if and only if (see (93)) This implies that G2(Xl + Fl)2 + 2GZ(Xl + Fi} - GiHl > 0.
Gl < G2(X 1 + Fi}Z + ZGZ(Xl + Fl} .
H (95) The above statements can be summed in a test condition to determine the signaling nature (EQPSD or mufti-line FDS) in a given bin. Using (94) and (95) we can write G - ZPmI EQPSD ~(Xi + Fl)2 + 2G2(Xl + Fi) . (96) N1W mufti - lineFDS Hi WO 99/33115 PCTNS98l17154 Thus, we can write the upstream capacity ci of line 1 in bin k as ., W logz ~1 + N, w+ ,n~~XW-F~ ), ~ if a = 0 5 ci = (97) Z logeh+ZN,w'~, ifa=1.
4.8 Optimizing under a PSD mask constraint: No self interference In this Section we will impose an additional peak power constraint in frequency, i.e., a limiting static PSD mask constraint. This implies that no transmit spectrum can lie above the PSD mask constraint. This constraint is in addition to the average power constraint. We shall obtain optimal transmit spectra for an xDSl:, line under these constraints, in the absence of self interference.
4.8.1 Problem statement Maximize the capacity of an xDSL line in the presence of AGN and interference (DSIN-NEXT
and DSIN-FEXT) from other services under two constraints:
1. The xDSL transmit spectra are limited by constraining static PSD~masks; ~"
( f ) for upstream and Qd ( f ) for downstream.
2. The average xDSL input power in each direction of transmission must be limited to P~
(Watts).
Do this by designing the distribution of energy over frequency (the transmit spectrum) of the xDSL
transmission.
4.8.2 Solution Consider a line (line 1) carrying an xDSL service. Line 1 experiences interference from other neighboring services (DSIN-NEXT and DSIN-FEXT) and channel noise Na( f ) (AGN) but no self NEXT or self FEXT (see Figure 19).

The twisted pair channel can be treated as a Gaussian channel with colored Gaussian noise [13]. Recall that DSN ( f ) is the PSD of the combined DSIN-NEXT and DSF( f }
is the PSD of the combined DSIN-FEX7 : Let Su ( f } and Sd( f ) denote the PSDs of line 1 upstream (u) direction and downstream (c~ direction transmitted signals, respectively. Further, let C" and Cd denote the upstream and downstream direction capacities of line 1 respectively. Let He ( f ) denote the channel transfer function of line 1.
The channel capacities (in bps) are given by [ 14]
a =
C su ~ l0 1 + ~Hc(f )~Z ~(f ) d S~tPI ~ g2 No(f) + DSN(f) + DSF(f) f (98) and Cd= sup °°log~ 1+ ~Hc(f)~2Sd(f) df.
No(f )) + DSN(f ) + DSF(f ) The supremum is taken ovc;r all possible Su( f ) and Sd ( f } satisfying the average power constraints for the two directions Z ~~ ~(f)df < pmax &nd 2 ~~ Sd(f)df ~ Pmax~ (1~) and the positivity and new peak power constraints 0 < Su(.f} ~ ~"(f) df and 0 <_ Sd(f) ~ ~(f) df~ (101) Note that these equations are the same as (4~(6) except for the additional peak power constraint in frequency. For discussion purposes, we will focus on the upstream transmission. The same analysis can be applied to the downstream channel.
We wish to maximize (98) subject to the constraints (100), (101). The constraints (100), (101) are differentiable and concave. Further, the objective function to be maximized (98) is also con-cave (the log function is concave). Any solution to this problem must satisfy the necessary KKT
(Karush-Kuhn-Tucker) [22) conditions for optimality. For a concave objective function and con-cave, differentiable constraints, any solution that satisfies the necessary KKT conditions is a unique globally optimal solution [:!2]. Thus, we seek any solution that satisfies the KKT conditions, since it is automatically the unique optimal solution.

The optimal solution to (98), (99), (100), (101) is basically a "peak-constrained water-filling' :6 The optimal transmit spectrum is given by -~ _ NoU))+nsNU)+n~ for f E Ep~, IXa(f)I
'~~ (f ) ' ~~' (f ) for f E E~, ( 102) 0 otherwise, with a a Lagrange multiplier. The spectral regions Ep~, and E~ are specified by - f .f : 0 < S"(f) ~ Q"(f)}s and - ~. f : 5"' (.f ) > ~" (f ) ~ ~ ( 103) We vary the value of a to achieve the optimal transmit spectrum Soy ( f ) that satisfies the average and peak power constraints (100), (101). It can be easily shown that this solution satisfies the KKT
conditions for optimality. Substituting the optimal PSD ,Soy ( f ) into (98) yields the capacity C"
under the average an<i peak power constraints.
Note that if the maximum allowed, average power (Pm~) exceeds the power under the con-straining mask then the optimal transmit spectrum is the constraining PSD mask itself. In the absence of an average power constraint (but with a peak power constraint) the optimal transmit spectrum is again the constraining PSD mask.
4.8.3 Examples In this Section we consider a line carrying HDSL2 service under the OPTIS [5]
constraining PSD
mask and input power specifications. An average input power (Pm~) of 19.78 dBm and a fixed bit rate of 1.552 Mbps was used for all simulations.
Figure 43 shows the optimal downstream transmit spectrum for HDSL2 with OPTIS
down-stream constraining mask in the presence of DSFIV-NEXT from 49 HDSL
interferers and AGN
(-140 dBm/Hz). The key features in the case of HDSL interferers are:
6Peak-constrained water-filling can be likened to filling water in a closed vessel with uneven top and bottom surfaces.

WO 99/33215 PCT/IlS9ti/Z7154 1. Comparing the peak-constrained transmit spectrum in Figure 43 with the unconstrained in peak power one in Figure 21 indicates that the peak-constrained optimal solution tries to follow the unconstrained in peak power optimal solution. The peak-constrained optimal solution has a null in the spectrum around 150 kHz similar to the one in the unconstrained in peak power spectrum. The null in the transmit spectra occurs in order to avoid the interfering HDSL transmit spectrum.
2. An OPTIS transmit spectrum, achieved by tracking I dBm/Hz below the OPTIS
PSD mask throughout, does not yield good performance margins (see Table 7). The OPTIS
transmit spectrum looks different from the peak-constrained optimal spectrum (see Figure 43). The null in the peak-constrained optimal spectrum (which is not seen in the OPTIS
transmit spectrum) indicates tlhat it is suboptimal to distribute power according to the OPTIS transmit spectrum.
Figure 44 shows the optimal upstream transmit spectrum for HDSL2 with OPTIS
upstream constraining mask in the pr<;sence of DSIN-NEXT from 25 Tl interferers and AGN
(-140 dBm/Hz).
Again, we compare the peak-constrained transmit spectrum in Figure 44 with the unconstrained in peak power one in Figure 22. Note that the peak-constrained optimal transmit spectrum puts no power in the high-frequency spectrum (to avoid Tl interference) as opposed to an OPTIS transmit spectrum.
4.9 Optimizing under a PSD mask constraint: With self interference The solution outlined in the previous Section applies only in the absence of self interference. In this Section we will find an optimal transmit spectrum in the presence of additional self NEXT
and self FEXT. We will impose a peak power constraint in frequency, i.e., a limiting static PSD
mask constraint, in addition to the average power and symmetric bit-rate constraints. We will obtain the optimal transmit spectra for an xDSL line under these constraints in the presence of self interference.

Table 7: Uncoiled performance margins (in dB) for CSA No. 6: OPTIS vs. Peak-constrained Optimal "under OPTIS"
OPTIS Optimal Diff Crosstalk :xDSL serviceDn Up Dn Up Dn Up Src 49 HDSL :HDSL2 12.242.7 13.743.74 1.54 1.03 25 Tl :HDSL2 17.5 19.9 18.8120.43 1.31 0.53 39 self :HDSL2 9.0 2.1 15.5117.58 6.51 15.48 24 self+24 :HDSL2 1.7 4.3 4.74 4.52 3.04 0.22 Tl Bit rate fixed at 1.552 Mbps.
Average Input power =19. 78 dBm.
Diff (Dn) = Difference in Downstream margins (Optimal - OPTIS) Diff (Up) = Difference in Upstream margins (Optimal - OPTIS) 49.1 Problem statement Maximize the capacity of an xDSL line in the presence of AGN, interference (DSIN-NEXT and DSIN-FEXT) from other services, and self interference (self NEXT and self FEXT) under three constraints:
1. The xDSL transmit spectra are limited by constraining static PSD masks; Q"
( f ) for upstream and Qd ( f ) for downstream.
2. The average xDSL input power in each direction of transmission must be limited to Pm~
(watts).
3. Equal capacity in both directions (upstream and downstream) for xDSL.
Do this by designing the distribution of energy over frequency (the transmit spectra) of the xDSL
transmissions.
Additional assumptions are made in this case as given in Section 4.5.3 or 4.6.3 depending on the signaling scheme used.

WO 99/33215 p~,~s9~'1~
49.2 Solution Consider a line (line 1 ) carrying xDSL service. Line 1 experiences interference from other neigh-boring services (DSIN-NEXT and DSIN-FEXT), channel noise No( f ) (AGN), and self interference (self NEXT and self FEXT) (see Figure 3).
We need to find peak-constrained optimal transmit spectra for upstream and downstream trans-mission. We let the constraining PSD mask Q( f ) be the maximum of the two upstream and down-stream constraining masks (Q" ( f ) and ~d( f )). We then employ the solutions as described in Sections 4.5 or 4.6 but limit the peak power to the constraining mask Q( f ).
Thus, we obtain a peak-constrained transmit spectrum Supt ( f ). Using this mask, we optimally group the bins (see Section 4.5.10) to obtain optimal upstream ~:.~ downstream transmit spectra (Si ( f ) and Sd( f )).
49.3 Algorithm for peak-constrained optimization of the transmit spectra 1. Choose the constraining PSD mask as ~(f)=max(Qu(f)~Rd(f)) df~
2. Solve for the optimal transmit spectrum opt ( f ) according to the algorithms in Sections 4.5.7, 4.5.8, or 4.6 with the following added constraint:
Sopt(f) = Q(f ) df where Su(f) > Q(.f)~ (l~) Su ( f ) otherwise, where S" ( f ) is the water-filling solution (refer to [14, 16] if the spectral region employs EQPSD or mufti-line, FDS signaling and to (16] if the spectral region employs FDS signaling) (see Sections 4.5 and 4.6). This is the peak-constrained water-filling solution in the presence of self interference. As argued in the previous Section, this solution satisfies the necessary KKT conditions for optimality and therefore is the unique optimal solution.
3. Denote the spectral :region employing FDS signaling as EFns and the spectral region em-ploying EQPSD signaling as EEQpsD~

WO 99/33215 PCT/US9t3l17154 Obtain S ~ ( f ) from Soy ( f ) by symmetry, i.e., Sit ( f ) = Soy ( f ) in EQPSD and mufti-line FDS regions and S pt ( f ) 1 Soy ( f ) in FDS spectral regions. Merge S ~ ( f ) and ,Soy ( f ) to form Sit ( f ) as Soy (f ) - ops (f ) = o~ (f ) df in EEQpSD ~
S~(f) - o'~c(f) U S~t(f) bf in EgDS~ (105) where U represents the union of the two transmit spectra.
Group the bins to obtain upstream and downstream masks as Si (f ) - Sod (f ) 'df in EFDS ~d where Q" (f ) ~ ~d (f ) Si (f) - Sorn(f) df in EFDS ~d where Q"(f) < Qd(f) (106) in EFns and ~(f ) = Si (f ) = Sopt (f ) df in E~PSD~ (107) 4. Check if the average power constraint is violated for upstream or downstream transmission.
5. If the average power constraint is violated for direction o (i.e., the total transmit power in the direction o is more tb.an Pm~)~ then transfer power from Si ( f ) to Si ( f ).
Transfer power first from spectral regions of Si ( f ) to Sa( f ) with the least Si ( f ) - Si ( f ) digerence. Repeat this successively in spectral regions with increasing Si ( f ) - Si ( f ) difference until the average power in both directions is the same.s We transfer power from one direction o to the other direction a in spectrtl regions where the difference in power between the two transmission directions is the least: until the power between the two directions becomes equal. This power transfer scheme is in a sense optimal as it tries to even out the powers between the two directions, with the least loss in the total sum of the transmit powers of the two directions.
Note that if the total transmiit power in direction o is more than Pm~ then the transmit power in direction o is less than Pm~.
aThis approach of transferring power from direction o to direction o can be likened to "stealing from the rich and giving to the poor."

WO 99/33215 Ptr"f/US98lZ7154 If the difference S~ ( f ) -S$( f ) is the same (or marginally varying) for a range of frequencies, then transfer power from direction o to direction o in those spectral regions that give the maximum gain in bit rates for direction o.
4.9.4 Examples and results In this Section we consider a line carrying HDSL2 service under the OPTIS [5]
constraining PSD
mask and input power specifications. An average input power (Pm~) of 19.78 dBm and a fixed bit rate of 1.552 Mbps was used for all simulations.
Figure 45 shows the optimal upstream and downstream transmit spectra for HDSL2 with OP-TIS constraining masks in; the presence of self NEXT and self FEXT from 39 HDSL2 interferers and AGN (-140 dBrn/Hz). Note that the optimal upstream and downstream transmit spectra are separated in frequency (u.sing FDS signaling) in a large spectral region in order to avoid high self NEXT. On the other hand, OPTIS transmit spectra have a large spectral overlap at lower fre-quencies (self NEXT is high here) that significantly reduces its performance margins (see Table 7).
Figure 46 shows the optimal upstream and downstream transmit spectra for HDSL2 with OP-TIS constraining masks in the presence of self-NEXT and self FEXT from 24 HDSL2 interferers, DSIN-NEXT from 24 Tl anterferers, and AGN (-140 dBm/Hz). Again, we see that the upstream and downstream optimal ;spectra are separated in frequency (using FDS
signaling) over a large spectral region. However" the EQPSD spectral region towards the beginning of the spectrum is larger here than in the previous example, since we have more DSIN-NEXT from Tl.
Key here is that optimal transmit spectra employ optimal separation in frequency of upstream and downstream services in the presence of interference. The "1 dB below OPTIS" transmit spectra do not do this, and so have inferior performance.
Table 7 compares the performance margins of the OPTIS transmit spectra (obtained from the OPTIS PSD mask by uniformly subtracting 1 dBm/Hz over the entire frequency range as in [S]) with the optimal transnut spectra under the OPTIS PSD mask constraints. Table 7 shows that the optimal scheme significantly outperforms OP'TIS in the case of self-interference. In cases involving different service interferers (HDSL and Tl) the optimal scheme consistently outperforms OP'TIS
by 1 dB or more. Further, comparing these results with those in Table 1 suggests that the OPTIS
PSD mask is not a good constraining PSD mask, since the unconstrained in peak power margins in Table 1 are significantly higher than the ones in Table 7. Comparing 'Fables 1 and 7 suggests that optimal signaling with no peak power constraint (static PSD mask) gives high performance margin gains.
4.10 Bridged taps Bridged taps (BTs) are short segments of twisted pairs that attach to another twisted pair that carries data between the subscriber and the CO. BTs are terminated at the other end with some characteristic impedance. BTs reflect the signals on the data-carrying line.
These reflections de-structively interfere with the transmitted signal over certain frequencies.
This leads to nulls in the channel transfer function and the self FBX'T transfer function at these frequencies (see Figure 48).
These nulls in the channel transfer function significantly reduce the data transmission rate. Thus, bridged taps pose an important problem in achieving high bit rates over xDSL
lines.9 Bridged taps presence, location, and length vary according to each loop setup.
Thus, the effect of BTs on the transmission signals is different for each loop. This means that the channel transfer function nulls (in frequency) vary for each separate line. We need to adapt the transmit spectrum to the channel conditions in .order to achieve high bit-rates. We need the optimal power distribution that maximizes the bit-rates in the presence of bridged taps and interference.
This further enforces the need for optimal dynamic transmit spectra and indicates that static transmit spectra are not a good idea. In this Section, we present optimal and near-optimal solutions to find the transmit spectra in the presence of BTs.
4.10.1 Optimal transmit spectra Optimal signaling is more computationally expensive to implement in the presence of bridged taps [3], as the channel tra»tfer function has nulls and thus loses its monotonicity. In this scenario, 9Bridged taps can be removed from xDSL lines, but this is an expensive (labor-intensive) procedure.

even the self FEXT transfer function has nulls. In spite of this, the overall optimal solution can be obtained by a bin by bin analysis:
1. Divide the frequency axis into narrow bins or subchannels. Compute channel transfer func-tion, various interference transfer functions, and AGN.
2. Choose an initial power distribution of Pm~ over all bins.
3. Given the powers in each bin decide the optimal signaling scheme in each bin. Compute capacities for each bin and hence compute channel capacity.
4. Re-distribute the powers in each bin by water-filling [ 14], [ 16), decide the optimal signaling scheme in each bin, and re-calculate the channel capacity. Repeat this step until we find the maximum possible channel capacity. It can be exceedingly computationally intensive to find the optimal power distribution over all bins. There can be several local maxima for the channel capacity curve, and there is no guarantee that a search algorithm will converge to the global maximum.
The optimal power distribution algorithm suggests that EQPSD, FDS, and mufti-line FDS bins could be randomly distributed throughout the transmission bandwidth. The search for the optimal switchover bins from one signaling scheme to the other could be exceedingly expensive (involving a mufti-dimensional search).
4.10.2 Suboptimat transmit spech~a We saw in the previous Section that the optimal transmit spectrum could be very expensive to obtain. However, we can always get a good suboptimal solution for line i as follows:
1. Divide the frequency axis into narrow bins or subchannels as in Section 4.1. Compute chan-nel transfer function (H~( f )), the various interference transfer functions (HN( f ), HF( f ), DSN( f ), and DfF( f )), and AGN (No( f )). Obtain subchannel values (H;,k, Xs,~, Ft,k) for each bin using (1)-(3) and (13). Let k denote the bin number.

WO 99/33215 PCT/US98~17154 2. Use the condition c;valuations in (26) and (27) to determine the signaling scheme (EQPSD
or FDS) in each bin. For each bin:
~ If (X~~ - F~ - H;,kF;~k < 0) and the right side of (26) < 0, then employ EQPSD
signaling in that bin (since power in every bin >- 0).
~ If (X; k - F;l~ ~- H~,,~ F;,~ > 0) and the right side of (27) < 0, then employ FDS signaling in that bin (since power in every bin > 0).
~ Employ FDS signaling if both the above conditions are not satisfied.
3. Perform the optimal power distribution under average power constraint of Pm~ using water-filling technique [ 14], [ 16].
4. Use condition evaluations in (46) and (54) to determine bins employing mufti-line FDS. Re-distribute power optimally using water-filling technique. This step is optional and indicates which bins employ mufti-line FDS signaling.
The suboptimal solution determines the signaling strategy in each bin by simple, fast comparisons involving transfer functions and SNRs. This is followed by a simple optimal power distribution scheme using the water-filling technique.
Note that the optimal and suboptimal algorithms can be implemented under a peak frequency-domain power constraint (static PSD mask). This is achieved by using peak-constrained water-filling technique (instead of just water-filling) for optimal power distribution (see Sections 4.8 and 4.9) in the algorithms given in Sections 4.10.1 and 4.10.2.
4.10.3 Examples and discussion Optimal transmit spectra: Theoretically, the optimal transmit spectrum in the presence of BTs can have several switchover bins from one signaling scheme to the other (for e.g., EQPSD to FDS and FDS to EQPSD switchover bins). However, we argue that in most of the symmet-rical data-rate services (like HDSL2 and "VDSL2") there is only one switchover bin from EQPSD to FDS inspite of bridged taps.

WO 99/33215 PCT/US98lZ7154 As frequency increases, the self NEXT transfer function rapidly increases but the self FEXT
and the channel transfer functions generally decrease even for bridged taps case (see Figures 17 and 48). Thus, the quantity X; x - F,. k - Hi,~F;,k tends to be an increasing function of frequency or bin number k, and stays positive once it becomes positive.
Similarly, the quantity H=,k - 2(;X;,k - F;,~) tends to decrease with frequency or bin number k and stays negative once it becomes negative. Using the condition evaluations (26) and (27) for all the frequency bins indicate that there is only one EQPSD to FDS switchover bin.
Our studies indicate that is indeed true for a wide range of loops having bridged taps and employing HDSL2, "VDSL2" or similar symmetric services. The optimal switchover bin along with the optimal transmit spectrum can be determined using the algorithm in Section 4.5.7.
Figure 47 illustrates a case of "contiguous" optimal transmit spectra in case of a loop with bridged taps (CSA loop 4). We can clearly see that the optimal transmit spectra have only one transition region from EQPSD to FDS signaling. The transmit spectra were obtained such that we have equal performance margins and equal average powers in both directions of transmission.
Suboptimal transmit spectra: We presented strong arguments in support of only one EQPSD to FDS switchover bin in the previous paragraph. However, there can be exceptions when the arguments do not hold, and we have multiple EQPSD and FDS regions (see Figure 48).
Consider a hypothetical case of a short loop (1.4 kft with 3 bridged taps) carrying the "GDSL" service. 7'he channel transfer function, self NEXT, and self FEXT
transfer func-tions are illustratef. at the top of Figure 48. Note that for "GDSL" service the self NEXT
is assumed very low. Since the self NEXT is low, the non-monotonicity of the self-FEXT
and the channel transfer function lead to distributed EQPSD and FDS regions across the transmission bandwidth as illustrated in the bottom of Figure 48. In such a scenario, the optimal power distribution algorithm of Section 4.10.1 is exceedingly difficult to implement.
However we can easily implement the suboptimal solution as given in Section 4.10.2 4.11 Optimization: Asymmetrical data-rate channels Please refer to Section 5.
4.12 Extensions 4.12.1 More general signaling techniques PCT/US98/Z~154 The signaling techniques outlined earlier are not the only techniques that can give us improved capacity results. One possible scheme is illustrated in Figure 49. In this Figure, UP; and DOW N;
refer to line i, upstream and downstream direction PSDs respectively. In this scheme, we use multi-line FDS between group of lines (1 and 2) having high self NEXT and high self FEXT with other group of lines (3 and 4). However, there is EQPSD among group of lines (1 and 2 employ EQPSD
as do 3 and 4) that have low self-NEXT and low self-FEXT within the group.
This scheme can be extended for M self interfering lines (with different self NEXT and self FEXT combinations between them) using combination of EQPSD, FDS, and multi-line FDS signaling schemes between different lines and frequency bins.
The above scheme can be applied in the case of groups of lines with different self interference (self NEXT and self FEXT) characteristics between different set of lines.
4.12.2 More general interferer models If the self NEXT and self :FEXT interferer model cannot be easily characterized by monotonicity in regions, (that is, if they vary rapidly and non-monotonously from one subchannel to the other), then we must search for the overall optimal solution on a bin by bin basis.
This search is outlined in the Section 4.10 on bridged taps.
4.12.3 Channel variations ' Some channels (e.g., the geophysical well-logging wireline channel) undergo a significant change in channel transfer function Hue( f ) as a function of temperature.
Temperature variations are a part of nature and hence we need to continuously update our channel transfer functions. Changes in channel characteristics can change the channel capacity. We can develop an adaptive optimal transmit spectrum to adjust to these as well as any other variations.
4.12.4 Broadband modulation schemes We saw in Section 4.5.10 that we can easily group the bins of the optimal transmit spectrum to make it smoother (with fewer discontinuities), so that we could apply different broadband modulation schemes. One can apply different broadband modulation schemes (like mufti-level PAM, QAM, CAP, etc.) over large spectral regions to the optimal transmit spectrum obtained after grouping the bins and determine the performance margins. In this case, we need to use a DFE
at the receiver to compensate for the severe channel attenuation characteristics. All these broadband modulation schemes do not suffer from latency as DMT does, but the DFE structure is complex. It is worth-while to compare the margins obtained with broadband modulation schemes with those obtained using DMT as well as compare the complexity and implementation issues involved.
4.12.5 Linear power constraints in frequency We saw in earlier Sections 4.4 - 4.10, optimal power distribution using water-filling technique un-der an average power constraint, and peak-constrained water-filling technique under a peak power constraint in frequency or average plus peak power constraint in frequency. In general, we can determine the optimal power distribution under any set of general linear power constraints in fre-quency. Further, we can employ one of the joint signaling techniques discussed in this document under these new constrainks using similar analysis.
4.12.6 CDS signaling under a peak power constraint in frequency In case of a limiting static PSD mask, (see Sections 4.8 and 4.9), or otherwise, one rnay be required to limit the peak power in one or all the frequency bins. In this case a power-peaky signaling scheme like FDS or mufti-line FDS will no longer be optimal as now we have a peak power constraint instead of the average power constraint. For this case, CDS or mufti-line CDS signaling WO 99/33215 PCT/(JS98/27154 [20] would be a better orthogonal signaling technique and would give increased capacity benefits without compromising spectral compatibility.
Recall, that in frequency bins where self NEXT is high and self-FEXT is low, we need orthog-onal signaling (FDS, TDS, or CDS) between upstream and downstream transmissions, i.e., si (f) ~- s~(f)~ dz # 3. (108) Under an average power constraint, FDS signaling is the optimal signaling strategy (see Section 4.5.12). In FDS signaling s~ ( f ) and s~ ( f ) occupy distinct separate frequency bands that are twice as higher than those using EQPSD signaling (see Figure 25). In CDS signaling the transmit spectra ss ( f ) and s~ ( f ) look similar to EQPSD signaling but the upstream and downstream spectra are separated using two orthogonal codes. Under a peak power constraint in frequency CDS signaling is preferred. Towards this end, we can group together bins using FDS into one spectral region ENDS. We can implement spread spectrum CDS (SS-CDS) over this spectral region EFns such that S;'(f) 1 S~(f)~ d$ ~.9~ df E E~s~ (1~) Further, recall that in frequency bins where self-FEXT is high, we need to use orthogonal sig naling (mufti-line FDS, TDS, or mufti-line CDS) between upstream and downstream transmissions of all the M lines, i.e., ss(f) ~- s~(f)~ di ~ 9~ o E {u~d~~ (110) Mufti-Iine CDS separates the M interfering lines using M orthogonal codes and is Iess power-peaky in frequency than mufti-line FDS. Under an average power constraint, mufti-line FDS sig-naling strategy is preferred. In mufti-line FDS each line gets a separate frequency slot within each bin for transmission. The PSD ss ( f ) in each bin is M times higher (or taller) than the corre-sponding PSD using EQPSD signaling (see Figure 18). Clearly, under a peak power constraint an alternative orthogonal signaling scheme like mull-line CDS is preferred. We can group together bins using mufti-line FDS into one spectral region E~,c~'DS. We can implement SS-CDS over this spectral region EMFns such that Ss (.f) -1- s,(.f)~ da ~ ~~ o E ~u~d}~ ~d 'df E EH(FDS~ (111) Note that implementation of SS-CDS cannot give perfectly orthogonal codes;
instead we have only codes with very low cross-correlation. However, use of CDS or mufti-line CDS signaling yields similar capacity (in the limit as cross-correlation between codes -~ 0) as FDS or mufti-line FDS schemes.
4.12.7 Mufti-user detector at central office We have seen that self interference is a major limiter in achieving higher channel capacity. We can extend the work in previous Sections and construct a mufti-user detector [21] at the central office that uses the self interference for joint detection of each user (or line). In this sense the self interference is not treated as only noise but can be used as information to achieve further significant gains in capacity of twisted pair lines.
Optimized Signaling techniques for Asymmetrical data-rate channels Section 4 developed optimal signaling techniques for symmetric data-rate channels. In this Section, we will generalize the results in the previous Sections to general asymmetric data-rate channels.
Asymmetrical data-rate channels have different upstream and downstream transmission rates, for e.g., ADSL and VDSL services. These channels also employ different average powers in the two transmission directions. We find joint signaling strategies and optimal power distribution for these channels using similar approaches as described in previous Sections (see Sections 4.5, and 4.6). In this case we assume the knowledge of the ratio of average powers between upstream and downstream directions.
We will employ similar assumptions as in Section 4.1 with additional assumptions noted in particular cases. Further, we again employ joint signaling techniques comprised of one or more of the signaling schemes discussed in Section 4.3 with scaled-PSD (SPSD) signaling replacing EQPSD. SPSD is similar to EQPSD in that both upstream and downstream occupy the same band-width but we relax the constraint that both have to have the same PSD, instead one is a scaled version of another in each. narrow bin.
5.1 Asymmetric data-rate optimization: Interference from other services (DSIN-NEXT and DSIN-FEXT) - Solution: SPSD Signaling In this scenario, each xDSL line experiences no self interference (Figure 19 with neither self NEXT nor self-. There is only DSIN-NEXT and DSIN-FEXT from other neighboring ser-vices such as T1, ADSL, HDSL, etc., in addition to AGN. The solution is well known (classical water-filling [14]), but the idea is to optimally distribute power in a dynamic fashion.
5.1.1 Problem statement Maximize the upstream and the downstream capacity of an xDSL line in the presence of AGN and interference (DSIN-NEXT and DSIN-FEXT) from other services under the constraint:
1. The average xDSL input power in the upstream and downstream directions of transmission must be limited to ~°~ (Watts) and PDN (Watts).
Do this by optimally designing the distribution of energy over frequency (the transmit spectrum) of the xDSL transmission.
5.1.2 Additional assumption We add the following assumption to the ones in Section 4.1 for this case:
12. Both directions (upstream and downstream) of transmission experience the same channel noise (AGN) and different service interference (DSIN-NEXT and DSIN-FEXT).
5.1.3 Solution Consider a line (line 1) carrying xDSL service. Line 1 experiences interference in both directions from other neighboring services (DSIN-NEXT and DSIN-FEXT) and channel noise No( f ) (AGN) but no self NEXT or self-FEXT (see Figure 19).
The DSIN-NEXT and DSIN-FEXT interference can be modeled as colored Gaussian noise for calculating capacity [13]. Recall that DSN ( f ) is the PSD of the combined DSIN-NEXT and let DSF( f ) is the PSD of the combined DSIN-FEXT. Let S"( f ) and Sd( f ) denote the PSDs of line 1 upstream (u) direction and downstream (d) direction transmitted signals respectively. Further, let C" and Cd denote the upstream and downstream direction capacities of line 1 respectively. Let H~ ( f ) denote the channel transfer function of line 1. The twisted pair channel is treated as a Gaussian channel with colored Gaussian noise. In this case the channel capacity (in bps) is given by [ 14]
C"= sup J~log2 1-f- ~H~(.f)E2S"(f) ldf (112) s°(f ~ No(f) + DSN(f) + DSF(f)J
and Cd = sup J~loga 1 + ~H~(f)IaSd(f) df, (113) sd o L 1Vo(f)) + DSN(f) + DSF(f) (f) The supremum is taken over all possible S" ( f ) and Sd( f ) satisfying S"(f) >_ 0 df, Sd(f) >_ 0 df~
and the average power constraints for the two directions 2~~5"(f)df ~ pvP~ ~d 2~Sd(f)df <_ ~'nrr. (114) Note that in general botix directions experience di; fj'erent AGN, DSIN-NEXT
and DSIN-FEXT
interference. The upstream and downstream capacities can be independently calculated by sepa-rately maximizing (1 I2) and (113). For illustration purposes we optimize the upstream transmit PSD 5'"( f ).
The optimal power distribution in this case is obtained by the classical "water-filling" tech-nique [ 14] . The optimal f a ( f ) is given by ~ _ 1Vo(f)+DSN(f)-I-D~ for f E E
(115) Sopt(f) = IHa(I)I
0 otherwise, with a a Lagrange multiplier and E the spectral region where S" ( f ) >_ 0. We vary the value of a such that Sops ( f ) satisfies with equality the average power constraint in (114). The equality is satisfied for a single value of a giving us a unique optimal PSD So'pt ( f ).
Plugging the optimal PSD
Supt ( f ) in ( 112) yields the capacity C" under the average power constraint. This procedure yields a unique optimal upstream transmit spectrum Supt ( f ) [ 14]. Similarly we can find the optimal downstream transmit spectrum S pt ( f ). The transmit spectra in general are different (Sd ( f ) ~
Su( f )) for the opposite directions of transmission.
Figure 20 gives a flowchart to obtain the optimal transmit spectrum in each direction using only SPSD signaling in the presence of DSIN-NEXT, DSIN-FEXT and AGN. It uses the classic water-filling solution to obtain the transmit spectrum. The novelty is in applying this to xDSL
scenario to achieve a dynamic transmit spectrum (different for each interference type) in the two directions of transmission.
5.1.4 Examples In this Section, we present come examples for the ADSL service [9]. We used an upstream average input power (over positive frequency) (0.5 * PUp) of 13 dBm and a downstream input power (over positive frequency) (0.5*PnN) of 20.4 dBm. An uncoded performance margin of 6 dB was fixed for both upstream and downstream. We measured the achievable rates for the two directions. Figure 50 shows the optimal upstream and downstream transmit spectrum for ADSL in the presence of DSIN-NEXT from 49 HDSL interferers and AGN (-140 dBm/Hz). Note the deep null in the upstream transmit spectrum from approximately 110 to 220 kHz. This results from "water-filling"
- the peak of the first main lobe of HDSL lies in the vicinity of 80 to 255 kHz.
Figure 51 shows the optimal upstream and downstream transmit spectra for ADSL
in the pres-ence of DSIN-NEXT from 25 Tl interferers and AGN (-140 dBm/Hz).
The optimal transmit spectra for the two (HDSL and Tl interferers) cases are signift-cantly different, evidence of the fact that the optimal transmit spectra will change depending on the nature of the interference.
Table 8 lists achievable bit rates (in Mbps) for ADSL service in presence of DSIN-NEXT from HDSL and Tl interferers. Note that a desired ratio (r) between the upstream and downstream rates can be achieved by appropriately changing the input powers PUp and PDN.

Table ~: Achievable bit rates (in Mbps) using SPSD signaling Bit Ratio of rates rates Crosstalk xDSL serviceC" Cd I C" r = Cu source I I ~ +Cd I

49 HDSL ADSL 4.396.61 11.00 1.51 25 Tl ADSL 2.252.95 5.20 1.31 Uncoded performance margin fixed at 6 dB.
Summary: We have seen that the optimal transmit spectra vary signi, f cantly with the interfer-ence combination. The water-filling solution yields unique transmit spectra for each interference combination [14]. The transmit spectra adapt to minimize the effects of the interference combina-tion. The optimal transmit spectra for upstream and downstream direction are scaled replicas of each other in narrow bins, i.e. they employ SPSD signaling.
5.2 Asymmetric data-rate optimization: Interference from other services (DSIN-NEXT and DSIN-FEXT) plus self interference (self NEXT and low self FEXT) - Solution: SPSD and FDS Signaling In this scenario each asymmetric data-rate xDSL line experiences self interference (high self NEXT and low self FEXT) in addition to AGN and DS1N-NEXT and DS1N-FEXT from other services (see Figure 3) in a generic xDSL service. This is the case of interest for the ADSI.
service.
We assume self NEXT dominates self FEXT and self-FEXT is not very high. So, we will design a system that rejects self-NEXT using orthogonal signaling as described in Section 4.5.1.
5.2.1 Problem statement Maximize the surn of the: upstream and the downstream capacity of an xDSL line in the presence of AGN, interference (DSIN-NEXT and DSIN-FEXT) from other services, and self-NEXT and self FEXT under the constraints:
1. The average xDSL input power in the upstream and downstream directions of transmission must be limited to Pig (Watts) and PDN (Watts).
Do this by designing the distribution of energy over frequency (the transmit spectrum) of the up-stream and downstream xDSL transmissions.
We can also add an additional constraint of having the upstream and downstream powers in the SPSD region have the same ratio as the input powers.
5.2.2 Additional assumptions We add the assumptions mentioned in Section 4.5.3 to the ones in Section 4.1 for this case.
5.2.3 Signaling scheme Since the level of self-NE~,XT will vary with frequency (recall Figure 17), it is clear that in high self NEXT regions of the spectrum, orthogonal signaling (FDS, for example) might be of use in order to reject self-NEXT. However, in low self NEXT regions, the loss of transmission bandwidth of FDS may outweigh any gain in capacity due to self NEXT rejection.
'Therefore, we would like our signaling scheme to be general enough to encompass both FDS signaling, SPSD signaling, and the spectrum of choices in between. Our approach is similar to that in Section 4.5.4.
Key to our scheme is; that the upstream and downstream transmissions use different transmit spectra. All upstream (to CO) transmitters T" transmit with the spectrum S" ( f ) All downstream (from CO) transmitters T d transmit with the spectrum Sd ( f ) Implicit in our scheme is the fact that in this case, self NEXT dominates self FEXT and self FEXT is small. If not, it would not be wise to constrain all Tf ' to the same transmit PSD.
Our goad is to maximize the sum of the upstream capacity (C") and the downstmam capacity (Cd) given an average upstream and downstream total power constraint of P~ and P,~N respectively WO 99/33215 PCTNS98lZ7154 Consider the case of two lines with the same service. Line 1 upstream capacity is C" and line 2 downstream capacity is C'i. Under the Gaussian channel assumption, we can write these capacities (in bps) as su ~l0 1+- ~Hc(f)I2S"(f) a df ~'V + DS + DS + H Sd + HF f S" f , ' s ~f),S ~f) o(f) 1V f F(f) I N(f)I (f (116) and °° IHc(f)I2 Sd(f) ~ df.
S~SUS o loge[1+.lVa(f)+DSN(f)+D5F(f)+IHN(f)I Su(f)+IHF(f)I Sd(f) (f)~ (f) (117) The supremum is taken over all possible S" ( f ) and Sd ( f ) satisfying S"(f) >_ ~ 'df, Sd(f) ? U 'df~
and the average power constraints for the two directions 2~°°S"(f)df ~ FcrP~ ~d 2 J~Sd(,f)df ~ F'nN. (118) We can solve for the capacities C" and Cd using "water-filling" if we impose the restriction of SPSD. However, this gives low capacities. Therefore, we employ FDS (S" ( f ) orthogonal to Sd( f )) in spectral regions where self NEXT is large enough to limit our capacity and SPSD in the remaining spectrum. This gives much improved performance.
We assume the subchannel frequency responses (1}-(3) and the notation introduced in (12) and ( i 3). Let s" ( f ) denote the PSD in bin k of line 1 upstream direction and sd ( f ) denote the PSD
in bin k of line 2 downstream direction (recall the notation introduced in Section 4.1, Item 9). The corresponding capacities of the subchannel k are denoted by c" and cd.
We desire a signaling scheme that includes FDS, SPSD and all combinations in between in WO 99/33215 PCTNS9$/27154 each frequency bin. We divide each bin of width W in two partst° : ~ 1 and h W and define the upstream and downstream transmit spectra as follows (see Figure 52):
ahWP", iflfl<h tt~
yqu(f) _ (' ah~ yyl~P"' if h l1 < ~f ~ ~ W~ (119) 0 otherwise and g( 1-a) (h+t)P,n W
w if ~.f ~ ~ h+t sd(f) = g*a(h+i)Pm if w < ~f) ~ W~ (120) h*W h-Hl 0 Otherwise.
Here Pm and g * Pm are the average upstream and downstream powers over frequency range (0, WJ
in bin k and 0.5 < a < 1 (Note that . When a = 0.5, s"( f ) and sd( f ) occupy the entire bin 'd f E ~0, WJ (SPSD signaling); when a = 1, su( f ) and sd( f ) are disjoint (FDS signaling).
These two extreme transmit spectra along with other possible spectra (for different values of a) are illustrated in Figure 52. T'he PSDs s" ( f ) and sd( f ) are "symmetrical" or power complementary to each other. This tries to ensure the the upstream and downstream capacities scale according to some desired ratio.
Next, we show that given this setup, the optimal signaling strategy uses only FDS or SPSD in each subchannel under some additional constraints.
5.2.4 Solution: One frequency bin Recall the definition of the achievable rate from (16) and that of c" and cd from (17). Substituting for the PSDs from (119) and (120) into (16) and using (17) we get the following expressions for the upstream and downstream capacities W a(h+t)P", H
o.s<~ i h + 1 loge 1 + N + (t_a)g(hv+t) mx ,~ a(h+wP,~F ~ +
( 1-a) (h+1)P", H
8z hw (121) h ~~ 10 1 -~' N + a9(h+1)PMX + (t-a)(h+1)Pml'' hw hw ~°The bin split-up does not necessarily have to be g96 to the left side of the bin and 1 - g9'o to the right side of the bin as shown in Figure 52. In general any g% - (1 - g)% power-complementary (using a and(1 - a) ) split-up between opposite direction bins will work.

~1-a)g(h+1)P", H
1 h + 1 lUg2 1 + N + a(h+~ mX + (1-a)9(hy+1)P.nF +
a h+I P", H
h Wl 1°g2 1 '~ N + ~1-a)(h+1)PnsX ,+ a9(h+1)PmF ~ (I22) hW hW
Let G = hwN'" denote the SNR in the bin. Then, we can write the sum of the capacities (c,~~ = c" + cd) using ( 121 ) and ( 122) as - h~ 10.~~ 15 logs 1 + 1 + g(1 - a)G + aGF +
' (1 - a}GH
h loge 1 + h + gaGX + (1 - a)GF +
g(1- a)GH
loge 1 + 1 + aGX + g(1- a)GF +
gaGH 123 h loge 1 + h + (1- a)GX + gaGF ~ ' ( ) Note: To get a truly global maximum for cwt we need to jointly maximize (123) over a, h, and g. This is a hard problem. to solve analytically. But we could numerically solve it for the range of bins by using constrained maximization routines over several variables if computational resources are available. We note this but take the alternative approach of finding some sort of analytical relationship between the variables to decide the signaling scheme in each bin.
We found that the problem can be solved if we assume that the power scaling factor between upstream and downstream (g), is equal to the scaling factor between the bin widths (h), i.e., g = h.
This is a reasonable approach since in FDS regions this would give us the same scaling of g = h between the upstream and downstream rates. Substituting for g in (123) we get coot - h~ 1 o.s«'~1 loge 1 + 1 + h(1 a)GX + aGF +
(1- a)GH
h loge 1 + h + haGX + (1- a)GF +
h(1- a)GH
loge 1 + 1 + aGX + h(1- a)GF +
haGH 1 ~
h loge 1 + h + 1- a)GX + haGF] } ' ( ) {

We define the quantity after max in the above equation as RAtot, i.e., the total achievable rate between the upstream and downstream directions. We search for the maxima of RAt~ in the above problem by treating it first as an unconstrainted optimization problem. We follow similar steps as described in Section 4.:5.5, i.e., we differentiate RAt~ with respect to a and equate it to zero.
Still, we are unable to solve the problem analytically. But, numerical studies show that we have a maximum of RA~t at either a = 0.5 or a = 1. Thus, we study the behavior of the derivative at a = 1, i.e., e~ la=a Wf' determine whether this derivative is positive (a =
0.5 is the maximum point) or negative (a = 1 i.s the maximum point).
Interestingly the signaling scheme-deciding conditions that we get are similar to the ones in (26) and (27) and can be stated as If X 2 - FZ -HF < 0 then (h + 1)P"a SP$D H - 2(X - F,,~

G, _ ( ) FDS

If X 2 - F2 -HF > 0 then (h+1)P", SP;D H-2(X -F) G,- ( ) FDS

Thus, we can write the upstream and downstream capacities cu and cd in a frequency bin k as W logs ~1 + NW~,9pmX-~'PmF~~ ~ if a = 0.5, a =-(127) h i loga ~1 + 1V P P,hF] ~ if a = 1.
Wlo ~1+ gp'"H ~ ifa=0.5 g2 NW+P,nX-E9P.nf'') ~
~ _ (128) hW log2 Ll + N + +9 mF~ , if a = 1.
5.2.5 Solution: All frequency bins We can extend this joint signaling technique to all frequency bins similar to that described in Section 4.5.6. The algorithm for doing so is similar to the one described in Section 4.5.7 with the following exceptions:

1. We maximize the joint capacity of the lines, i.e., C" + Cd.
2. Note that the ratio between upstream and downstream powers can vary with each bin. In the SPSD signaling region we can additionally impose the restriction that each bin should have the same ratio between upstream and downstream powers equal to gsPSn why 9SPSD
=
gt~ _ ~, where c~~ is the ratio between the upstream and downstream input powers.
A fast, subopdmal solution can be obtained by using ME as the SPSD to FDS
swith-over bin as described in Section 4.5.8. Further, we can obtain contiguous spectra by using the grouping ideas discussed in Section 4.5.10.
5.2.6 Examples and results In this Section, we present some examples and results for the ADSL service.
AGN of -140 dBm/Hz was added to the interference combination in all simulations. We present results for joint capacity maximization under the following two scenarios:
Fixed power ratio in SPSD bins: We constrain the SPSD bins to have the same downstream to upstream power ratio (9gpgD) as the ratio between the total downstream and upstream powers IySPSD = 9coc = '~). Table 9 lists achievable rates (in Mbps) obtained from our simula-tions for CSA loop number 6. We used an upstream average input power (over positive frequency) (0.5 * PUp) of 13 dBm and a downstream input power (over positive frequency) (0.5 * PDN) of 20.4 dBm. A fixed 6 dB of encoded performance margin was used for all simulations along with a BER of 10-7. The last column lists the ratio of rates (r) between the downstream anal upstream rates. We see significantly higher joint capacities than 6 Mbps in presence of most interference combinations.
'Izable 10 shows the difference between the optimal solution (using the optimal M~F) and the fast approximate suboptimal solution (using M~F = ME) for a variety of interfering lines.
The column Diff (in Mbps) shows the difference in achievable rates between the optimal and the subopdmal scheme. We make a similar note as in Section 4.5.11 that the suboptimal scheme gives near-optimal results that requires very little computational effort.

Table 9: Achievable bit rates (in Mbps) using SPSD and FDS signaling for CSA
No. 6 Bit Ratio of rates rates Crosstalk sourcexDSL serviceC" Cd C" +Cd r = ~4 1 self ADSL 1.99 8.4010.39 4.22 self ADSL 1.65 7.348.99 4.46 19 self ADSL 1.54 6.988.52 4.53 29 self ADSL 1.48 6.728.20 4.54 39 self ADSL 1.43 6.557.98 4.58 10 self+ 10 ADSL 1.41 5.657.06 400 HDSL

10 self+ 10 ADSL 0.74 2.373.11 3.19 Tl.

Uncoded performance margin fixed at 6 dB.
Table 10: Achievable bit rates (in Mbps) for CSA No. 6: Optimal vs.
Suboptimal.
Crosstalk sourcexDSL DptlZnal ME2F F~~ suboptimalME Diff service scheme scheme (Mbps) (Mbps) 1 self ADSL 10.39 16 10.39 16 0 10 self ADSL 8.99 12 8.99 12 0 19 self ADSL 8.52 11 8.52 11 0 29 self ADSL 8.20 11 8.20 11 0 39 self ADSL 7.98 10 7.98 10 0 10 self + 10 ADSL 7.06 30 6.98 12 0.08 HDSL

10 self + 10 ADSL 3.11 12 3.11 12 0 Uncoded performance margin fixed at 6 dB.

Table 11: Achievable bit rates (in Mbps) using SPSD and FDS signaling for CSA
No. 6: Variable power ratio in SPSD bins Bit Ratio of Diff rates rates Crosstalk xDSL serviceCu Cd Cu +Cd r =
source 1 self ADSL 5.01 5.7210.74 1.42 0.35 self ADSL 4.36 5.6710.02 0.77 1.03 19 self ADSL 5.83 3.959.78 0.68 1.26 29 self ADSL 5.84 3.759.60 0.64 1.40 39 self ADSL 5.88 3.579.45 0.61 1.47 10 self+ 10 LADSL I I 1.76I 3.20 I.22 I 0.09 Tl 1.45 ( I I
I

Uncoded performance margin fixed at 6 dB.
Variable power ratio in SPSD bins: We relax the constraint of fixed ratio of powers in SPSD
bins in our optimization process. In this case, see better performance but the elegance of uniform complementarity of powers in each bin amongst SPSD or FDS bins is lost.
Table 11 Iists achievable rates (in Mbps) obtained from our simulations for CSA loop number 6. We used similar simulation conditions as in the case for fixed power ratio case. The last column lists the difference (Diff) between the variable power ratio and fixed power ratio cases. We note that variable power ratio case always performs better than the fixed ratio case. In the variable power ratio we mostly observe that the upstream and downstream power spectra employ FDS and occupy two distinct contiguous bandwidths.
All the transmit spectra are spectrally compatible with existing services by design. This is true again, due to water-filling techniques that optinuze power-distribution without causing significant interference in existing neighboring services.

5.2.7 Extensions Based on the work described in earlier Sections we can easily write the following extensions for the asymmetrical data-rate :>ignaiing scheme:
1. In case of significant self-FEXT we can apply signaling techniques incorporating multi-line FDS as described in Section 4.6.
2. The ideas on joint signaling in presence of differing channel, noise and interference char-acteristics as described in Section 4.7 can also be easily extended to asymmetrical data-rate lines.
3. The optimization can also be easily done under a PSD mask constraint as described in Sec-tions 4.8 and 4.9.
4. The results on bridged taps (see Section 4.10) and the extensions in Section 4.12 hold for asymmetrical data-rate lines.
6 Summary of Contributions The key differences from the prior art are:
1. Increased capacity far xDSL lines using optimal and suboptimal transmit spectra involving joint signaling schemes.
2. "Symmetrical " (or power complementary) upstreamldownstream optimal transmit spectrum for a xDSL line in presence of self NEXT, self FEXT, AGN, and other interfering lines like Tl, HDSL, and ADSL using EQPSD and FDS signaling.
3. Fast near-optimal solution for the transmit spectrum which is computationally very attractive and very easy to implement for xDSL lines.
4. Spectral optimizatian gives good spectral compatibility with other services (FDS better than CDS for spectral compatibility under an average power constraint).

5. Dynamic transmit spectrum that adjusts automatically according to the interference type.
6. Mufti-line FDS signaling technique to combat self FEXT.
7. Increased capacity for HDSL2; "GDSL", and "VDSL2" lines using mufti-line FDS signaling when appropriate.
8. Increased capacity in generic xDSL lines when neighboring lines have different channel, noise and interferencx characteristics.
9. Concept of static estimation of interference values by reading look-up table of the topology of the cables (which self interfering lines are where) at powerup. The self-interference values can be estimated in this manner. Dynamic measurement of interference values is done by "listening" to the interference during powerup. (Subtract the estimated self-interference from this measured interference to get the different service interference.) 10. We can also interpret our results as capacity estimates given a fixed margin in the presence of fixed interferers.
11. Extension of above points to asymmetrical data-rate channels like ADSL and VDSL.
Final notes:
1. We have framed our work within the context of the HDSL2, "GDSL", and "VDSL2" trans-mission formats. However, our results are more general, and apply to all channels that exhibit crosstalk interference from neighboring channels. We summarize a few channels where this technique could be potentially applied:
(a) Twisted pair lines (standard telephone lines) (b) Untwisted pairs of copper lines (c) Unpaired cables (d) Coaxial cables (e) Power lines (f) Geophysical well-logging telemetry cables (g) Wireless channels.
2. If a static mask is desired (e.g., for ease of implementation), we propose that a thorough study be made of the optimal solutions in different interference and noise scenarios as proposed in this document and then a best static compromising PSD mask be chosen.

References [1) S. McCaslin, "Performance and Spectral Compatibility of MONET PAM HDSL2 with Ideal Transmit Spectra-Preliminary Results," TI E1.4/97 307.
[2) M. Rude, M. Sorbara, H. Takatori and G. Zimmerman, "A Proposal for HDSL2 Transmission:
OPTIS," Tl E1.4~97-2 38.
[3] A. Sendonaris, V Veeravalli and B. Aazhang, "Joint Signaling Strategies for Approaching the Capacity of Twisted Pair Channels;' IEEE Trans. Common., vol. 46, no. 5, May 1998.
[4] S. McCaslin and N. V Bavel, "Performance and Spectral Compatibility of MONET(Rl) HDSL2 with Ideal Transmit Spectra-Preliminary Results;' Tl E1.4/97-412.
[5] J. Girardeau, M. Rude, H. Takatori and G. Zimmerman, "Updated OPTIS PSD
Mask and Power Specification for HDSL2," Tl E1.4/97-435.
[6) J.A.C. Bingham, "Muldcarrier Modulation for Data Transmission: An Idea Whose Time has Come;' IEEE Common. Magazine, May 1990.
[7] G. Zimmerman, "Performance and Spectral Compatibility of OPTIS HDSL2," Tl E1.4/97-237.
[8) K. Kerpez, "Full-duplex 2B 1 Q Single-pair HDSL Performance and Spectral Compatibility,"
Tl E1.4/95-127.
[9] American National Standard for Telecommunications, "Network and Customer Installation Interfaces-Asymmetric Digital Subscriber Line (ADSL) Metallic Interface,"
T1.413-1995, Annex B.
[10] American National Standard for Telecommunications, "Network and Customer Installation Interfaces-Asymmetric Digital Subscriber Line (ADSL) Metallic Interface,"
T1.413-1995, Annex E.
[11] G. Zimmerman, "Nonnative Text for Spectral Compatibility Evaluations;' Tl E1.4/97-18081.

WO 99/33215 PCT/US981~7154 [12] M. Barton and M.L. Honig, "Optimization of Discrete Multitone to Maintain Spectrum Com-patibility with Other Transmission Systems on Twisted Copper Pairs;' IEEE J.
Select. Areas Common., vol. 13, na. 9, pp. 1558-1563, Dec. 1995.
[13] K.J. Kerpez, "Near-End Crosstalk is almost Gaussian;' IEEE Traps.
Common., vol. 41, no. 1, Jan.1993.
(14] R.G. Gallager, "Information Theory and Reliable Communication;' New York:
~ley, 1968.
[15] I. Kalet, "'The Multitone Channel;' IEEE Traps. Common., vol. 37, no. 2, Feb. 1989.
[16] J.T. Aslanis and J.M. Cioffi, "Achievable Information Rates on Digital Subscriber Loops:
Limiting Information Rates with Crosstalk Noise;' IEEE Traps. Common., vol.
40, no. 2, Feb. 1992.
[17] PS. Chow, J.M. Cioffi and J.A.C. Bingham, "A Practical Discrete Multitone Transceiver Loading Algorithm for Data Transmission over Spectrally Shaped Channels;' IEEE
Traps.
Common., vol. 43, nos. 2/3/4, FeblMarJApril 1995.

[18] I. Kalet and S. Shamai (Shitz), "On the Capacity of a Twisted-Wire Pair.
Gaussian Model;' IEEE Traps. Common., vol. 38, no. 3, Mar. 1990.

[19] W.H. Press, S.A. Teukolsky, W.T. Vellerling and B.P Flannery, "Numerical recipes in C-The Art of Scientific Computing;' Cambridge University Press, 2nd edition, 1997.

[20] J.G. Proakis, "Digital Communications;' McGraw Hill, 3rd edition, 1995 [21] S. Verdu, "Recent-Progress in Multiuser Detection" in "Multiple Access Communications;' Edited by N. Abramson IEEE press, 1993 [22] , R. Horst, P M. Pardalos and N. V Thoai, "Introduction to Global Optimization;' Kluwer Academic Publishers, 1995 Glossary ADSL: Asymmetrical digital subscriber line AGN: Additive Gaussian noise BER: Bit error rate (or probability) BT: Bridged tap CAP: Carrierless arnplitude/pulse modulation CDMA: Code-division multiple access CDS: Code-division signaling CO: Central office CSA: Carrier serving area DFE: Decision feedback equalization DMT: Discrete rnultitone technology DSL: Digital subscriber line EQPSD: Equal power spectral density signaling FDS: Frequency division signaling FEXT: Far-end crosstalk ~~GDSL": General digital subscriber line HDSL: High bit-rate digital subscriber line HDSL2: High bit-rate digital subscriber line 2 ISDN: Integrated services digital network ISI: Intersymbol interference MFDS: Mufti-line Frequency division signaling _ NEXT: Near-end crosstalk PAM; pulse amplitude modulation POTS: Plain old telephone services PSD: Power spectral density QAM: Quadrature amplitude modulation SNR: Signal to noise ratio SPSD: Scaled power spectral density signaling ~_~: Spread spectrum code-division signaling Tl: Transmission 1 standard ~S: Time division signaling VDSL: Very high bit-rate DSL
~~VDSL2": Very high bit-rate DSL 2 ~L; pny generic DSL service WO 99/33215 PGTNS98n7154 Notation 1: Orthogonal U: Union A: Kind of service, such as ADSL, HDSL, HDSL2, VDSL, etc.
B: Channel transmission bandwidth C: Channel capacity or line capacity D: Difference between two capacities E: Spectral region F: Magnitude squared Far-end crosstalk (self FEXT) transfer function in a single bin G: Signal to noise ratio (SNR) in a single bin H: Magnitude squared channel transfer function in a single bin J: Kind of signaling scheme, such as EQPSD, FDS, multi-line FDS, etc.
K: Total number of bins within channel transmission bandwidth L: Function of line parameters (G, F, X, H) in a single bin; it is always a positive quantity M: Number of interfering lines carrying the same service N: Total additive Gaussian noise (AGN) power plus total different service interference P: Power ~: Constraining PSD mask R: Receiver S: Power spectral density (PSD) WO 99133215 PCTNS9t3/27154 T: Transmitter U: Positive quantity equal to Y + Z + N
V: Positive quantity equal to Y + Z + N + S
W: Bandwidth of a bin or a subchannel X: Magnitude squared Neax end crosstalk (self NEXT) transfer function in a single bin Y; Part of crosstalk power that couples into another service line Z: Part of crosstalk power that couples into another service line a: An amplitude level of a transmit spectrum b; An amplitude level of a transmit spectrum c: Capacity of a bin or a subchannel d: Downstream direction f : Frequency g~ Ratio between downstream and upstream powers in a single bin (g = ~ ) h: Ratio between downstream and upstream bandwidths in a single bin employing FDS
i: Line number j : Line number k: Bin index n: Fraction to choose power distribution, 0 <_ 11 < 1 o: Direction index o E {u, d}
r: Ratio between downstream and upstream rates (r = ~~ ) u: Upstream direction C= : Capacity of line a in transmission direction o C°: Capacity of a line in direction o C;: Capacity of a line %
EFDS: Spectral region employing FDS signaling E~s: Spectral region employing mufti-line FDS signaling F;,k: Magnitude squared self FEXT transfer function on line i and bin k F;: Magnitude squared self-FEXT transfer function of line i in a single bin G;: Ratio of signal power in line i to noise power in line 1 in a single bin H;,~: Magnitude squared channel transfer function of line i and bin k H;: Magnitude squared channel transfer function of line a in a single bin N°( f ): Channel noise N=: AGN plus different service interference on line i P",f: Power in positive frequency range ((0, Wj) of a single bin of line i Pm: Power in positive frequency range ((0, W~) of a single bin Pm~: Total average power over the entire frequency range ((-B, B~) of the channel Q°( f ): Constraining PSD mask in direction o RA: Achievable rate in a single bin or subchannel R~ : Receiver on line i in direction o S~ ( f ): PSD of line i in direction o S° ( f ) : PSD of a line in direction o T°: Transnutter on line i in direction o WO 99/33215 PCT/US981~7154 X;,k: Magnitude squared self NEXT transfer function on line i and bin k X~: Magnitude squared self NEXT transfer function on line i in a single bin c= ,,: Capacity of a single bin of line i using signaling scheme J.
c= : Capacity of a single bin of line i in direction o c°: Capacity of a single bin in direction o s~ ( f ): PSD in a single bin of line i in direction o s°( f ): PSD in a single bin in direction o APPENDIX
Source code describing one preferred embodiment of the invention.
function [DsRbmax, Sfopt, fopt, UsRbmax] = psdestim(LoopNo, df, symrate,...
startf, Dsfs, Usfs, maxbits, margin, PdBmin, agn,...
ADSL, HDSLnext, ISDNnext, Tlnext, self, UporDn);
g __________________._______________________________________________________ $ The function 'psdestim' estimates the capacity (datarates) of an xDSL
$ loop given the average input power, performance margin, $ the channel noise .and the crosstalk sources.
$ Input:

$ LoopNo . ~CSA Loop Number $ df . Bandwidth (kHz) of each subchannel $ symrate . DMT symbol rate $ startf . Start frequency (kHz) of the channel $ Dsfs . Stop frequency (kHz) of the downstream channel $ Usfs . Stop frequency (kHz) of the upstream channel $ maxbits . Max.
number of bits per carrier (subchannel) $ margin . Performance or noise margin (dB) $ PdBmin . Total average Input Power (dHm) $ agn . Additive gaussian noise (dBm/Hz) $ ADSL . Number of interfering (NEXT+FEXT) ADSL
lines $ HDSLnext:
Number of interfering (NEXT) HDSL lines $ ISDNnext:
Number of interfering (NEXT) ISDN lines $ Tlnext . Number of interfering (NEXT) T1 lines $ self . Number of self-interfering (NEXT+FEXT) lines $ UporDn . Upstream =1, Downstream = 0 $ Output:

$ DsRbmax : Downstream maximum optimal bit rate $ Sfopt . Transmit spectrum of optimal scheme $ fopt . Frequency vector used by optimal scheme $ UsRbmax : Upstream maximum optimal bit rate Example:
psdestim(206,2,2,1,1000,1000,1e5,18.39,20,-140,0,0,0,0,39,2);
$ Rohit Gaikwad $ Rice University $ 2/2/98 $ __________________._______________________________________________________ $
$ __________________._______________________________________________________ $
8 Set Fontsize and l.inewidth fsize - 19;
lwidth = 1.5;
largefonts(fsize,lwi.dth);
$ ______________________________________________ __________________________ $
$ Nomenclature % DS: Different service % DSIN-NEXT : DS NEXT into line under consideration _ % DSIN-FEXT : DS FEXT into line under consideration % self-NEXT : NEXT from neighboring lines carrying same service % self-FEXT : FEXT from neighboring lines carrying same service % Mo . M_E2 F

% Ml . M_E

% E2MFDS
Mac . M

$ _ Mbc . M FDS~MFDS

% _____________-____________________________________________________________ %

% _________________.________________________________________________________ IS % _________________________________________________ _________________________ %

% Compute magnitude squared channel transfer function (~Hc(f)I~2) % Ref: ADSL standard T1.413-95, Annex E

T - 1/(symrate*:Le3): % DMT symbol period DsW
-Dsfs/2;
%
downstream bandwidth N - 1+floor((DsW-startf)/df): % number of subchannels [Hfsqr, freq, len]
_-cablemodel(LoopNo,N,startf,startf+(N-1)*df);

% compute the channel transfer function endf =
max(freq);
%
Last tone frequency P - 0.5*le-3*10"(PdBmin/10); % Input power (Watts) on pos freq.
range % _________________.________________________________________________________ %

% _________________.________________________________________________________ %

% __________________________________________________________________________ %

% Do DSIN-NEXT and DSIN-FEXT interference computations % Ref: ADSL standard T1.413-95, Annex B

% _________________.________________________________________________________ %

% Initialization Phdslnext =
0;
Pdslnext =
0:
Ptlnext =
0:
Padsl =
0;

% _________________.________________________________________________________ %

% DSIN-NEXT+DSIN-FEXT due to ADSL

if (ADSL
~=
0) (finkHzF, Padsl:Eext] = adslfextmain(ADSL,LoopNo);

[finkHzN, Padsl,,Padslnext] = adslUsnextmain(ADSL);

[fadslF, Padslfext] = resamp(finkHzF,Padslfext,df,startf,endf);

[fadslN, Padslnext] _ resamp(finkHzN,Pads.Lnext,df,finkHzN(1),max(finkHzN));

indlow - lengtJa(find(fadslF < fadslN(1)));

indup - length(find(fadslF > max(fadslN)));

Padslnext - (zeros(l,indlow-1) Padslnext zeros(l,indup)];

Padsl - Padslnext + Padslfext;
end % _________________________________________________________________________ %
% ____________________________________________ __________________________ %
% DSIN-NEXT due to HDSL
% 2B1Q signaling if (HDSLnext =- 49) load /home/rohitg/Research/Nortel/HDSL NEXT/hdslnext49.mat finkHz Phdslnext elseif (HDSLnext =- 20) load /home/rohitg/Research/Nortel/HDSL_NEXT/hdslnext20.mat finkHz Phdslnext elseif (HDSLnext =- 10) load /home/rohitg/Research/Nortel/HDSL_NEXT/hdslnextl0.mat finkHz Phdslnext elseif (HDSLnext =- 1) load /home/rohitg/Research/Nortel/HDSL NEXT/hdslnextl.mat finkHz Phdslnext end if (HDSLnext ~= 0) [fhdsl, Phdslnext] = resamp(finkliz, Phdslnext,df, startf, endf};
end ______________________________________________________________________ __________-___________________________________________________________ ~ DSIN-NEXT due to ISDN
$ 2B1Q signaling of basic access DSLs if (ISDNnext =- 49) load /home/rohitg/Research/Nortel/ISDN NEXT/isdnnext49.mat finkHz Pisdnnext elseif (ISDNnext == 24) load /home/rohitg/Research/Nortel/ISDN NEXT/isdnnext24.mat finkHz Pisdnnext elseif (ISDNnext =- 10) load /home/rohitg/Research/Nortel/ISDN NEXT/isdnnextl0.mat finkHz Pisdnnext end if (ISDNnext ~- 0) [fdsl, Pdslnext] = resamp(finkliz, Pisdnnext,df,startf, endf):
end ____________ ________________________________________________________ ______________________________________________________________________ ~ DSIN-NEXT due to T1 $ Same binder T1 if (Tlnext =- 49) load /home/rohitg/Research/Nortel/T1 NEXT/tlnext49.mat finkHz Ptlnext elseif (Tlnext == 25) load /home/rohitg/Research/Nortel/T1 NEXT/tlnext25.mat finkHz Ptlnext elseif (Tlnext =- 29) load /home/rohitg/Research/Nortel/T1'NEXT/tlnext29.mat finkHz Ptlnext elseif (Tlnext =- 10) load /home/rohitg/Research/Nortel/T1 NEXT/tlnextl0.mat finkHz Ptlnext end if (Tlnext ~= 0) [ftl, Ptlnext] = reaamp(finkHz, Ptlnext, df,startf, endf);
end _______________.________________________________________________________ ______________________________________________________________________ $ self-NEXT + self-F'EXT
if (self ~- 0) $keyboard;
$ Ref: 2-piece Unger model from T1E1.4/95-127 Ntr - [49 10 1] ;
chilr = [4.8e-9 7.1e-10 6.6e-11];
chihr = [2.4e-13 9.5e-19 8.9e-15];
explr = [0.9 0.5 0.6];
exphr = [1.4 1.4 1.5];
chil = interpl(Ntr, chilr, self, 'linear'):
chih = interpl(Ntr, chihr, self, 'linear'):
expl = interpl(Ntr, explr, self, 'linear');
exph = interpl(Ntr, exphr, self, 'linear');
Hnextsqr=(freq<=20)*chil.*((freq*le3).~expl)+...
(freq>20)*chih.*((freq*le3).~exph);
$ Reduce Hnextsqr to 1~ of its value in case of " GDSL "
Hnextsqr = 0.01.*Hnextsqr;
Hfextsqr -~ ...
(((3.083e-20)./(10~v.5;)*(°e'_i~(O.Ei))~ienw(lte3*freq).~2).*Hfsqr);
Hxfsqr = Hnextsqr + Hfextsqr;
else $ Zero self-interference if no self interfering lines Hxfsqr - zeros(size(Hfsqr));
Hnextsqr= zeros(size(Hfsqr)):
Hfextsqr= zeros(size(Hfsqr)):
Mo - 0; $ EQPSD is optimal, no FDS required end _______________._______________________________________________________ ~ __________________._______________________________________________________ _______________._______________________________________________________ $ Add-up DS-interference and channel noise (AGN) interf - Ptlne~a + Pdslnext + Phdslnext + Padsl; $ Total DS-interference No = 2*le-3*10~(agn/10); $ AWGN in W/Hz noisePSD= ((No/2)+interf)'; ~ in W/Hz noisePSD= noisePSD.*ones(size(freq)); $ convert into a vector df - (freq(2)-freq(1))*1e3; ~ convert df into Hz SNRgap - 9.8; ~ dB ~ factor which allows one to compute achievable bit rates instead of capacity gamma = 10~((margin + SNRgap)/10); $ Total performance margin (units) noisePSD = gamma*noisePSD; ~ weighted Noise PSD
Hxfsqr - gamma*Hxfsqr; $ weighted total self-interference Hnextsqr = gamma*Hnextsqr;
Hfextsqr = gamma*Hfe:xtsqr;
H = Hfsqr;
X = Hnextsqr;
F = Hfextsqr;
~ _________________._-______________________________________________________ % ______________________________-___ _______________________________________________________________________ %
% Initialization PdBm - [ J
Ceqpsd - [J; % Lagrange multiplier EQPSD soln. with self-interf.
Cwgn - (J; % Water-filling with no self-interference Cx - [J% ~'s self-interference limit when using EQPSD
Cfds - [l: 4s FDS signalling in all subchannels Pwgn - [J:
Bits - [l;
Bitsx = [J:
Bitsfds = [ J %
Bitseqpsd - [J:
DsRbmaxnoise = [l: % Bit rate doing EQPSD water-filling with no self-interference DsRbmaxx - (J% % Bit rate for self-interference limit % self-interference dominates AGN and DS-interference DsRbmaxeqpsd = [J: % Bit rate doing EQPSD with self-interference DsRbmaxfds - [J: % Bit rate doing FDS in all subchannels DsRbmaxopt - [J: % Bit rate doing EQPSD/FDS optimally SNR - ( J %
Mzeros - [ J %
Bracket - [J%
fMo [ J
w = noisePSD.'kdf; __-W - 2*(endf-s'tartf)_________________________________________________ % _____-______________ % _________________________________________________________________________ %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
% Lagrange multiplier solution for the transmit spectrum using EQPSD
% signaling in presence of self-NEXT+self-FEXT
%
X40 % Ref: 'Achievab:le Information Rates on Digital Subscriber Loops:
% Limiting information rates with crosstalk noise' - J.T. Aslanis and % J.M. Cioffi in IEEE Trans. on Commun., vol. 40, no. 2, Feb. 1992 %%%%%%%%%%%%%%%%'~%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
if (Hxfsqr) % Using bisection method to calculate the correct value of lamda lamdal - (8.06)*1e14%
lamdau - le-4;
a Hxfsqr.*(Hxfsqr + Hfsqr):
b = w,*(2*Hxfsqr + Hfsqr);
c = w,*(w - (W.*Hfsqr)./(lamdal*2*N));
Pestl - (-b + sqrt((b.~2) - 4*a.*c))./(2*a);
Pestl(find (Pestl<0)) = 0:
c = w.*(w _ (W.*Hfsqr)./(lamdau*2*N ));
Pestu - (-b + sqrt((b.~2) - 4*a.*c))./(2*a):
Pestu(find(Pestu<0)) = 0;
Pest = Pestl; _.
while ( (abs(sum(Pest) - P) > (le3*eps))& .

(abs(lamdal-lamdau) > le0*eps)) lamda - (lamdal+lamdau)/2; %Search at the midpoint c = w.*(w - (W.*Hfsqr)./(lamda*2*N ));
Pest - (-b + sqrt(b.~2 - 4.*a.*c))./(2.*a);
Pest(find(Pest<0).) = 0;
% Set the new boundaries for the bisection to work if (sum(Pest) > P) lamdau - lamda;
elseif (sum(Pest) <= P) lamdal - lamda;
end % end if end % end while % Bisection method converges to yield correct value of lamda %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
% Computation of capacity and achievable bit rate Ceqpsd - [Ceqpsd sum(df*log2(1+(Pest.*Hfsqr)./(w+ (Hxfsqr.*Pest))))];
Bitseqpsd = [Bitseqpsd min(maxbits,(log2(1+(Pest.*Hfsqr)./...
(w + (Hxfsqr.*Pest)))))];
DsRbmaxeqpsd = [DsRbmaxeqpsd (1/T)*sum(Bitseqpsd)];
else Pest - zeros (:size ( freq) ) ;
DsRbmaxeqpsd =- 0;
end % fi Hxfsqr %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
% Transmit spectrum calculation using FDS in all the bins %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
if (Hfextsqr) noisefds= noiaePSD;
[Rbmax, Sfds]
fdsxtalk(P,Hfsqr,no:isefds,Hfextsqr,N,maxbits,symrate*le3,df);
else noisefdsup = interpl(l:N,noisePSD,l:(N-1)/(2*N-1):N);
Hfsqrup = interpl(1:N,Hfsqr,l:(N-1)/(2*N-1):N);
% Using bisection method to calculate the correct value of lamdafds lamdafdsL - le-19;
lamdafdsU - 1e4;
SfdsL = lamdafdsL - ((noisefdsup)./Hfsqrup);
SfdsL(find(SfdsL<0)) - 0;
SfdsL = down(SfdsL,2,0);
SfdsU = lamdafdsU - ((noisefdsup)./Hfsqrup);
SfdsU(find(SfdsU<0)) - 0;
SfdsU = down(SfdsU,2,0);
Sfds = SfdsL;
while ( (abs((df/2)*sum(Sfds) - P) > (lel*eps))& ...
(abs(lamdafdsL-lamdafdsU) > le0*eps)) lamdafds - (lamda.fdsL+lamdafdsU)/2; %Search at the midpoint Sfds - lamdafds - ((noisefdsup)./Hfsqrup);

Sfds(find(Sfds<0)} - 0;
Sfds = down(Sfds,2,0):
% Set the new boundaries for the bisection to work if ( (df/2) *sum(Sfds) > P) lamdafdsU - lamdafds;
elseif ((df/2)*sum(Sfds) <= P) lamdafdsL - lamdafds;
end % end if end % end while % Bisection method converges to yield correct value of lamdawgn if(mod(length(Hfsqru;p),2)) Sfds = up (Sfds, 2, 0) ;
else Sfds = up (Sfds, 2, 1 ) :
end end % fi Hfextsqr %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$%%%%%%%%%%%%%%$%%%%%%%%
%%
%%%%%%%%%%%%%%%%%$%%%%$%$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$%%$
%%
% Transmit spectrum calculations for SUBOPTIMAL scheme with self-interference % Do EQPSD in bins [1, M1] and FDS in bins [M1,K] where M1 is obtained % by computing the inequalities as listed below %%%%%%$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
if(Hxfsqr) NumF = (H - 2*(X-F));
DenF - ((X.~2) - (F.~2) - (H.*F));
Fxt = NumF./DenF;
Fxtdec = 0.5*ones(size(freq));
Fxtindeqpsd = find((NumF> 0) & (DenF <0));
Fxtdec(Fxtindeqpsd) = zeros(size(Fxtindeqpsd)):
Fxtindfds - find( (NumF <0) & (DenF > 0}):
Fxtdec(Fxtindfds) = ones(size(Fxtindfds)};
if (isempty(Fxtindfds}) istar = length(Fxtdec):
else istar = min(Fxtindfds};
end M1 = max(Fxtindeqpsd):
if (isempty(M1)) M1 = 0;
end optIn = (0 le-12*P];
% Water-filling or peak-constrained water-filling to optimize % power distribution given the signaling strategy in each bin [P1 optOut]=fmin('rbmax',O,P,optIn,Ml,P,freq,...
Hfsqr,Hnextsqr,Hfextsqr,noisePSD,maxbits,T):
% Compute the achievable bit rate and the optimal transmit spectrum [DsRbmaxeqpsdfds, Sfeqpsdfds]= rbmaxpsd(P1,Ml,P,freq,...
Hfsqr,Hnextsqr,Hfextsqr,noisePSD,maxbits,T):
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%

%%%%$%%%%%%%%%%%$%%%%%%%%%%%%%%%%%%%$%%%%%$%%%%%%%%%%%%%%%%%%%%%%%~%$%%$%%%
%$ -% Transmit spectrum calculations using OPTIMAL scheme of % EQPSD in bins [l,:Mo] and % FDS in bin [Mo,K) %$$%$%%%%%%%%%%%%%~%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$%%%%%$%%%%$%%%%%
%%
% Using Golden Section Search in One dimension %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$%$%%%%%%%%$$%%%%%$%%$%%$%%%%%%
%%
Cap = [ ] ; Sfopt = [ ] ;
R - 0.61803399; % Golden Ratios C - 1-R;
MoL = M1; % make use of the new knowledge that % all bins [1, M1) do EQPSD
MoH - istar; % All bins [istar,K] do FDS
else istar = 0 end if (Hxfsqr) MoM - round((Mo:L+MoH)/2);
optIn - [0 le-12*IP) ;
% We use the four point method where the min is bracketed by % the three abscissas MoL< MoM < MoH and the capacity % CMoM > CMoL arid CMoM > CMoH, i.e. the oridnate of MoM is more than the other % two ordinates.
% Ref: 'Numerical Recipes in C'-Cambridge University Press, 2nd ed. pp.

x0 = MoL;
x3 = MoH:
if (abs(MoH-MoM) > abs(MoM-MoL)) xl = MoM;
x2 = round(MoM+C*(MoH-MoM));
else x2 = MoM; ' xl = round(MoM-C*(MoH-MoM));
end % Water-filling or peak-constrained water-filling to optimize % power distribution given the signaling strategy in each bin [P11 opt0utl]=fmin ('rbmax'., 0, P, optIn, xl, P, freq, . . .
H:Esqr,Hnextsqr,Hfextsqr,noisePSD,maxbits,T);
[P12 optOut2]=fmin('rbmax',O,P,optIn,x2,P,freq,...
H:fsqr,Hnextsqr,Hfextsqr,noisePSD,maxbits,T);
[x0 xl x2 x3];
while(abs(x3-x0)> 1) i f ( optOut 2 ( 8 ) < optOut l ( 8 ) ) [x0,x1] = shft2(x0,xl,x2);
x2 - floor(R*xl+C*x3);
[P1 opt0utN2J=fmin('rbmax',O,P,optIn,x2,P,freq,...
H:fsqr,Hnextsqr,Hfextsqr,noisePSD,maxbits,T);
[opt0utl,optOut2) = shft2(optOutl,optOut2,opt0utN2);
else t44 WO 99/33215 PCT/US98lZ7154 [x3,x2] = shft2(x3,x2,x1);
xl - floor(R*x2+C*x0); _ [P1 optOutNl] =fmin ('rbmax' , 0, P, optIn, xl, P, freq, . . .
Hfsqr,Hnextsqr,Hfextsqr,noisePSD,maxbits,T);
[optOut2,optOutl] = shft2(optOut2,opt0utl,optOutN1);
end [x0 xl x2 x3];
end % Output the best of the two current values between xl and x2 if (optOutl(8) < opt0ut2(8)) Mo = xl;
opt0ut = optOutl;
else IS Mo = x2;
optOut = opt0ut2;
end Bracket = [Bracket; x0 xl x2 x3];
Mzeros - [Mzeros Mo];
if (Mo}
fMo - [fMo .freq(Mo)];
end;
DsRbmaxopt - [DsRbrnaxopt -optOut(8)];
else DsRbmaxopt - 0;
DsRbmaxeqpsdfds = 0;
end % fi (Hxfsqr) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
%%%%%%%%%%%%%%%%$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$%%%%%%%%%%%%%%%%
%%
% Transmit spectrum calculations in presence of no self-NEXT or self-FEXT:
% EQPSD signaling % Ref: 'The Multitione channel'--Irving Kalet, IEEE trans on comm, % vol. 37, no. 2, Feb. 1989 %%%%%%%%%%%%%%%%%%%~;%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%~%%%%%
% %
% Using bisection meahod to calculate the correct value of lamdawgn lamdaL - le-14;
lamdaU - 1e4;
SfL - lamdaL - (noisePSD./Hfsqr);
SfL(find(SfL<0)) - 0;
SfU - lamdaU - (nc>isePSD./Hfsqr);
SfU(find(SfU<0) ) - 0;
Sf = SfL;
while ( abs(df*sum(Sf) - P) > (le2*eps) ) lamdawgn - (lamdah+lamdaU)/2; %Search at the midpoint Sf - lamdawgn - (noisePSD./Hfsqr);
Sf(find(Sf<0)) - 0;
fsubA = find(Sf > 0);
% Set the new boundaries for the bisection to work if (df*sum(Sf) > P) iamdaU - la.mdawgn;

elseif (df*sum(Sf) <= P) lamdaL - lamdawgn;
end % end if end % end while % Bisection method c:onverges to yield correct value of lamdawgn %%%%%%%%%%%%%%%%%%%~;%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
% Computation of capacity and achievable bit rate PdBm - [PdBm 10*7_ogl0(2*P/le-3)];
SNR - [SNR 10*log7_0(P./(noisePSD.*DsW))];
Cwgn - [Cwgn df*sum(log2(1 + (Sf.*Hfsqr)./(noisePSD)))]~
Pwgn - [Pwgn df*sum(Sf)'];
Bits - [Bits min(maxbits,(log2(1+(Sf.*Hfsqr)./noisePSD)))];
% Bits per transmission % in each subchannel or bits/symbol DsRbmaxnoise - [DsRbmaxnoise (1/T)*sum(Bits)];
% Total bit rate in bps % T is the DMT symbol period %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
% Peak PSD constraint in presence of AGN: EQPSD solution % 5/14/9$
[DsRbmaxnoiseP,SfP,SfOPTIS] = peakpsdwf(noisePSD,Hfsqr,P,df,maxbits,...
T,freq,UporDn);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
% Capacity crosstal:k limit if (Hxfsqr) Cx = sum((W/(2*N))*log2(1 + (Hfsqr./Hxfsqr)));
Bitsx = [Bitsx min(maxbits,(log2(1 + Hfsqr./Hxfsqr)))];
DsRbmaxx= [DsRbmaxx (1/T)*sum(Bitsx)];
end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
% Capacity of scheme using FDS through all the bins if (Hfextsqr) Cfds = [Cfds 0.5*df*sum(log2(1+(Sfds'.*Hfsqr)./(Sfds'.*Hfextsqr+noisefds)))];
Bitsfds - [Bitsfds min(maxbits,0.5*(log2(1+(Sfds'.*Hfsqr)./...
(Sfds'.*Hfextsqr + noisefds))))]:
% Bits per symbol DsRbmaxfds = [DsRbm.axfds (1/(T))*sum(Bitsfds)];
else Cfds - [Cfds (df/2)*sum~(log2(1 + (Sfds.*Hfsqrup)./(noisefdsup)))];
Bitsfds =[Bitsfds m,in(maxbits, 0.5*(log2(1 +
(Sfds.*Hfsqrup)./(n.oisefdsup))))];
% Bits per symbol DsRbmaxfds = [DsRbmaxfds (1/T)*sum(Bitsfds)]; % bit rate in bps Sfds = down(Sfds,2,0);
end %%%%%%%%%%%%%%%~%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% Upsample all the transfer functions WO 99/33215 PCT/US98/2~154 Hfsqrup - interpl(1:N,Hfsqr,l:(N-1)/(2*N-1):N);
Hxfsqrup - interpl(1:N,Hxfsqr,l:(N-1)/(2*N-1):N); _ Hnextsqrup - interpl(1:N,Hnextsqr,l:(N-1)/(2*N-1):N);
Hfextsqrup - interpl(1:N,Hfextsqr,l:(N-1)/(2*N-1):N);
noisePSDup - inter)?1(l:N,noisePSD,l:(N-1)/(2*N-1):N);
%%%%%%%%%%%%%%%%%%%'~%%$%%%$%%%%%%%%$%%%%%%%%%%%%%%%%%%%%%%%$%%%%%%%%%%$%%%$
$%
% Marshalling output arguments if (self) UsRbmax = 0;
(DsRbmax, Sfopt]= rbmaxpsd(Pl,Mo,P,freq,...
Hfsqr,Hnextsqr,Hfextsqr,noisePSD,maxbits,T);
fopt - freq;
fbit = DsRbmax; % Bit rate in bps %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
% Upsample the transmit spectra Sfupl = [Sfopt(l:Mo): Sfopt(l:Mo)]; % EQPSD region Sfupl = Sfupl(:);
Sfup2 - [Sfopt(Mo+l: end); zeros(1,N-Mo)]; % FDS region Sfup2 = Sfup2(:);
Sfoptup = (Sfupl; S:Eup2]; % Upsampled correct transmit spectra foptup - interpl(l:N,fopt,l:(N-1)/(2*N-1):N);
dfl = df/2;
fupl - foptup(l::Length(Sfupl));
fup2 - foptup(1+:Length(Sfupl):end);
SfoptupDn = [Sfupl:cshift(Sfup2',1)']; % Upsampled correct downstream % transmit spectra %%%%%%%%%%%%%%%%%%%$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
% Multi-line FDS signaling (Scheme C) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
G = [2*Sfopt(l:IKo)'./noisePSD(l:Mo): Sfopt(Mo+1:N)'./noisePSD(Mo+1:N)];
exprBC - ((1+G.*H) - ((1+((self+1)/2)*G.*H).~(2/(self+1))))./...
(G.*((1+((self+1)/2)*G.*H).~(2/(self+1))-1)):
indSchmBC = find(F<exprBC): % FDS (Scheme B) in these bins if (~isempty(indSchmBC)) Mbc = .rnax(max(indSchmBC),Mo);
else Mbc = Mo:
end % Lets keep the same G
exprAC - ( (2+G.*(X+H))-((1+((self+1)/2)*G.*H).~(1/(self+1)).*(2+G.*X) ))./...
(G.*((1+((self+1)/2)*G.*H).~(1/(self+1))-1));
indSchmAC = find(F<exprAC); % EQPSD (Scheme A) in these bins if (~isempty(indSchmAC)) Mac - :max(indSchmAC):
else Mac - 0:
end if (Mac > Mo) Mac = Mo;
end [DsRbmaxC,SfoptC] = rbmaxpsdC(Pl,Mo,P,freq,... .
Hfsqr,Hnextsqr,Hfextsqr,noisePSD,maxbits,T,Mac,Mbc,self):
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Grouping of bins: Contiguous spectra (several ways to optimally group) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$%%%%%%%%%%%%%%%%
% Optimal grouping: equal performance margins in both transmission % directions Sfdsupdn = [Sfopt(Mo+l:end); Sfopt(Mo+l:end)];
Sfdsupdn = Sfdsupdn(:);
Bitsopteqpsddn= [log2(1+(Sfopt(l:Mo)'.*Hfsqr(l:Mo)./...
(Sfopt(l:Mo)'.*Hxfsqr(l:Mo) + noisePSD(l:Mo) )))]:
Bitsopteqpsddn - [l3itsopteqpsddn'; Bitsopteqpsddn']:
Bitsopteqpsddn = Bit sopteqpsddn(:):
Bitsoptfds = [log2(1+(Sfdsupdn'.*Hfsqrup(2*Mo+1:2*N))./...
(Sfdsupdn'.*Hfextsqrup(2*Mo+1:2*N) + noisePSDup(2*Mo+1:2*N)))]:
Bitsopt - (Bits~opteqpsddn' Bitsoptfds]:
Bitsoptcum - cumsum(Bitsoptfds);
eqpsddn = sum(Bitso;pteqpsddn);
fds - sum(Bitsoptfds)./2;
fds+eqpsddn;
if(~isempty(Bitsoptcum)) Mg - 2*Mo + max(find(Bitsoptcum < (Bitsoptcum(end)/2)));
else Mg _ 2*Mo:
end sum(Bitsopt(2*Mo+l:Mg)):
sum(Bitsopt(Mg+1:2*N)):
SfoptUpDn - [Sfupl; Sfdsupdn];
SfoptsmthUp = [Sfupl' Sfdsupdn(l:Mg-2*Mo)' eps*ones(1,2*N-Mg)]':
SfoptsmthDn = [Sfupl' eps*ones(l,Mg-2*Mo) Sfdsupdn(Mg-2*Mo+l:end)']':
% Optimal grouping: equal performance margins and equal average powers in % both directions of transmission % Note that Mg = 2*Mo + Mc + somemore Mc - 114 % for 39 self-NEXT + 39 self-FEXT
% Mc - 60; % for 24 T1 NEXT + 24 HDSL2 NEXT
% Mc = 92 : '~ CSA 4: 39 self-NEXT + 39 self-FEXT
% Mc - 112 ; % fo:r 39 self-NEXT + 39 self-FEXT + 1 HDSL
% Mc - 113 : % :Eor 99 self-NEXT + 99 self-FEXT + 1 HDSL
Sfdscum = cumsum(Sfdsupdn(Mc+l: end));
Mg = 2*Mo + Mc + max(find(Sfdscum < (Sfdscum(end)+sum(Sfdsupdn(l:Mc)))/2 )):
SfoptUpDn - [Sfupl; Sfdsupdn];
SfoptsmthUp = [Sfupl' eps*ones(l,Mc) Sfdsupdn(Mc+l:Mg-2*Mo)' ...
eps*ones(1,2*N-Mg)]':
SfoptsmthDn = [Sfupl' Sfdsupdn(l:Mc)' eps*ones(l,Mg-2*Mo-Mc) ...
Sfdsupdn(Mg-2*Mo+l:end)']';
PDn = 10*1og10(lea*2*sum(SfoptsmthDn)*(df/2)) PUp = 10*1og10(lea*2*sum(SfoptsmthUp)*(df/2)) %%%%%%%%%%%%%%%%%$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
by % %

%%%%%%%%%%%%%%%%%%$%%%%%$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$%%%%%%%%
%%
% Broadband modulation schemes for the contiguous spectra (specifically % multi-level PAM u:;ing Decision Feedback Equalizers (DFE) at the receiver %%%%%%%%%%%%%%%%%%%'~%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
Sfdsupdncum = cumsum(Sfdsupdn);
if (~isempty(Sfdsupdncum)) dfeupdnbrk = 2*Mo +max(find(Sfdsupdncum < (Sfdsupdncum(end)/2)));
else dfeupdnbrk = 2*Mo;
end _ dfeupdnbrk = Mg;
dfeSfoptUp = [Sfopt:UpDn(l:dfeupdnbrk); zeros(2*N-dfeupdnbrk:l)];
dfeSfoptDn = [Sfopt:UpDn(1:2*Mo); zeros(dfeupdnbrk-2*Mo,l);
SfoptLJpDn(dfeupdnbrk+1:2*N)];
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%~~%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
20 % DFE margin estimation of the contiguous spectra baud - (1,*fhit)/(3*le3);
% baud - foptup(max(find(Sfoptsmthup>0)))/(df/2e3) reqdsnr = 2~~~%
% Check DFE margin of smooth PSD using marginest program 25 BWUp - 2*le3*foptup(dfeupdnbrk); % Upstream bandwidth BWDn - 2*le3*(1+foptup(end)-foptup(dfeupdnbrk)+foptup(2*Mo));
% BWDn = 2*1e:3*foptup(end);
bu - fbit/BWUp; % bits/symbol for Upstream bd - fbit/BWDn; % bits/symbol for Downstream 30 baudUp - fbit/(dfl*bu); % symbols/s baudDn = fbit/(dfl*bd);
reqdsnrUp = pamreqdsnr(2~bu, le-7);
reqdsnrDn = pamreqdsnr(2~bd, le-~): ~.
noisePSDdfeUp = noisePSDup+(Hfextsqrup.*(dfeSfoptUp')) +
3h (Hnextsqrup.*(dfeSfoptDn')); ~
dfeM smthL7p = dfemarginest(SfoptsmthUp,Hfsqrup,noisePSDdfeUp'./g~a.w baudUp, reqdsnrUp); ~, noisePSDdfeDn = noisePSDup+(Hfextsqrup.*dfeSfoptDn') +
(Hnextsqrup.*dfeSfoptUp'); ~~
40 dfeM smthDn = dfemarginest(SfoptsmthDn,Hfsqrup,noisePSDdfeDn'./gamma,.
baudDn, reqdsnrDn);
%%%%%%%%%%%%%%~%%%%%%%~%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
%%%%%%%%%%%%%%$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
a5 %%
% Check DMT margin of contiguous spectra using marginest program noisePSDUp = no.isePSDup+(Hfextsqrup.*SfoptsmthUp') + ~~~
SO Hnextsqrup.*SfoptsmthDn'; ~~
chkM smthUp - dmtmarginest(SfoptsmthUp',Hfsqrup,noisePSDUp./gamma,.
- SNRgap, maxbits, (2*DsRbmax)/(symrate*le3),0) noisePSDDn = noisePSDup+(Hfextsqrup.*SfoptsmthDn') + ~-Hnextsqrup.*SfoptsmthUp'; ~
55 chkM_smthDn = dmtmarginest(SfoptsmthDn',Hfsqrup,noisePSDDn./gamma,..
SNRgap, maxbits, (2*DsRbmax)/(symrate*le3),0) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$%%%%%%%%%%%%%%%$%%%%%%%%%%%%%
%%
60 %%%%%%%%%%%%%%%%%%%%%%%~%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%

% No self-interference else DsRbmax = DsRbmaxnoise;
Sfopt = Sf' fopt - freq;
fbit = DsRbmax; % Bit rate in bps foptup - interpl(l:N,fopt,l:(N-1)/(2*N-1):N);
dfl = df/2;
Sfoptup = interpl(1:N,Sfopt,l:(N-1)/(2*N-1}:N);
Sfoptup = Sfoptup(:);
chkM_disc=dmtmargineat(Sfopt',Hfsqr,noisePSD./gamma,SNRgap,maxbits,...
DsRbmax/(symrate*le3),0):
bsym = fbit/(2*le3*(fopt(length(find(Sfopt>eps)))));
baud - fbit/ (df*t>sym) reqdsnr = pamreqdsnr(2~bsym, le-7);
dfeM_disc = dfemargi.nest(Sfopt,Hfsqr,noisePSD'./gamma,...
baud, reqdsnr);
end %%%%%~%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%~%%%%%%%%%%%%%%%%%%%%%%%%
%%
%%$%%%%%%%%%%%%$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
% Check DMT margin of discrete PSD using marginest program noisePSDdmtup = noisePSDup+(Hfextsqrup.*Sfoptup') + ...
[Hnextsc;rup(1:2*Mo).*Sfoptup(1:2*Mo)' zeros(1,2*N-2*Mo));
%noisePSDdmtup - interpl(l:N,noisePSDdmt,l:(N-1)/(2*N-1):N);
chkM_disc=dmtmargine~st(Sfoptup',Hfsqrup,noisePSDdmtup./gamma,SNRgap,maxbits ,...
(2*DsRbmax)/(symrate*le3),0);
% baud - (1*1..°i520e3) /3;
% reqdsnr = 27.7;
if (self) bsym = fbit/(2*le3*(foptup(2*Mo) + (1+foptup(end)-foptup(2*Mo))/2}):
else bsym = fbit/(:?*le3*(foptup(length(find(Sfoptup>eps))))):
end baud - fbit/(dfl*bsym):
reqdsnr = pamreqdsnr(2~bsym, le-7};
dfeM_disc = dfemarginest(Sfoptup,Hfsqrup,noisePSDdmtup'./gamma,...
baud, reqdsnr);
baud = 2*baud:
%%%%%%%%%%%%%~%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% Print the various margins fprintf('\nCheck margins for various modulation techniques\n');
fprintf('DiscDMT
DiscDFE\tContDMTup\tContDFEup\tContDMTdn\tContDFEdn\n'):
fprintf('%2.2f %2.2f \t %2.2f \t %2.2f \t %2.2f \t %2.2f\n',...
chkM disc,dfeM disc,chkM smthUp,dfeM smthL7p,chkM smthDn,dfeM-smthDn);
fprintf('\n');
%%%%%%%%%%%%%%%%%%%~%$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
% Plot the different. PSDs if (self) plot(fup1,10*1og10(1.e3*Sfupi)); hold on;
Sfdsupdn(1) = Sfupl(end);
plot(fup2,10*1og10(1.e3*Sfdsupdn),'r--'); hold off;
legend('EQPSD signal.ing','FDS signaling',0);
else plot(foptup, 10*1og10(le3*Sfoptup));
end hold off; grid on; l.argefonts(fsize,lwidth);
axis([0 500 -54 -34]);
IS xlabel('Frequency (kHz)');
ylabel('Amplitude (dBm/Hz)');
if(HDSLnext) % title('Optimal HD:3L2 transmit spectrum with 99 HDSL DSIN-NEXT');
elseif(Tlnext) % title('Optimal HD;~L2 transmit spectrum with 2S T1 DSIN-NEXT');
elseif(self) title('Optimal HDSL.? transmit spectrum with 39 self-NEXT + 39 self-FEXT');
end orient tall;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
% Print the various Powers Qtmp - le-3*(:LO.~((SfOPTIS-1)./10));
Ptmp = df*sum(Qtmp);
PtmpdBm = 10*1og10 (:Le3*Ptmp) ;
fprintf('\n Powers (Positive freq. spectrum) for various tranmit spectra\n');
fprintf('OPTIS\t ContigUp\t ContigDn\t (in dBm)\n');
fprintf('%2.2f\t %2.2f\t %2.2f \t \n', PtmpdBm,...
10*1og10(lea*(df/2)'~sum(SfoptsmthUp)), 10*1og10(lea*(df/2)'"'sum(SfoptsmthDn)));
fprintf('\n');
%%%%%%%%%%%%%%%%%%%'l;%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
%%%%%%%%%%%%%%%%$%%$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
% SPECTRAL COMPATIBILITY
% Define optional parameters %%%%%%%%%%%%%%%%%%$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$%%%%%%
%%
srcno - self;
cdmaOrfds = 2; % 0 = water-filling, no self-NEXT or self-FEXT
% 1 = FDS in all bins % 2 = EQPSD in 1 to Mo bins and FDS from Mo+1 bin onward % 3 = EQPSD in 1 to Mo bins and CDS from Mo+1 bin onward %%%%~%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
freqH2 - freq;
dfH2 - freq(2) - freq(1);
if (Hnextsqr) switch cdma0rfd.s % 1 if next exists otherwise 0 case 0, 15l case 1, SfH2 - Sf;
SfH2 = Sf~ds;
case 2, SfH2 = Sf~optup;
freqH2 = foptup';
dfH2 - freqH2(2) - freqH2(1);
case 3, [CH2, SfH2]= rbmaxpsd(Pl,Mo,P,freqH2,...
Hfsqr,Hnextsqr,Hfextsqr,noisePSD,maxbits,T);
SfH2(Mo+1:N) _ (SfH2(Mo+1:N)./2);
SfH2(Mo+2:2:N) = SfH2(Mo+1:2:N-1);
otherwise, SfH2 - ;;f' ;
end % switch else SfH2 = Sf' ;
end % fi startf - 1;
%%%%%%%%%%%%%%%%%%%%'k%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Spectral compatibility with HDSL
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
[freqH, Phdsltx, Phdslnext] = hdslnextmain(49); % 99 HDSL DSIN-NEXT power baud = 392/dfH2;
wgn - le-3*10~(-140/10);
reqdsnrhdsl = 21.5;
freqH2 - freqH2";
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% HDSL2 into HDSL
% Computing NEXT of HDSL2 lines % Ref: 2-piece Unger model from T1E1.4/95-127 Ntr - (49 J.0 1]
chilr = [4.8e-9 7.1e-10 6.6e-11];
chihr = [2.4e~-13 9.5e-19 8.9e-15];
explr = [0.4 0.5 0.6];
exphr = [1.4 1.9 1.5];
chil = interpl(Ntr, chilr, srcno, 'linear');
chih = interpl(Ntr, chihr, srcno, 'linear');
expl = interpl(Ntr, explr, srcno, 'linear');
exph = interpl(Ntr, exphr, srcno, 'linear');
nextsqr=(freqH2<=20)*chil.*((freqH2*le3).~expl)+...
(freqH2>20)*chih.*((freqH2*le3).~exph);
[fH2, HfsqrH2] - resamp(fopt, Hfsqr, dfH2,startf,max(freqH2));
fextsqr - ...
(((3.083e-20)./(10~0.6))*(srcno~(0.6))*len*((le3*freqH2).~2).*HfsqrH2);
Phdsl2x = SfoptsmthUp'.*nextsqr + SfoptsmthDn'.*fextsqr;
% Check for contiguous spectra Phdsl2x = Phdsl2x.*(7../(1+(6500./(freqH2*le3))));
% LPF cutoff frequency = 6.5 kHz [HfsqrH,freqtH]=cablemodel(LoopNo,l+(max(freqH))/dfH2,freqH(1),...
max(freqH) );
[freqtH, PhdsltxH] = resamp(freqH, Phdsltx, dfH2,startf, max(freqtH));

Phdsl2xH = [Phdsl2x zeros(l,length(freqtH)-length(freqH2))];
hdsl2 in hdsl =dfemarginest(PhdsltxH,HfsqrH,Phdsl2xH+wgn,baud, reqdsnrhdsl) %%%%%%%%$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Spectral compatibility with echo-canceled ADSL (EC ADSL) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% HDSL2 into EC ADSI' dfadsl - 4..3125;
adslstartf = 25;
adslendf - 1:104;
[freqH2A, Phdsl2xA] = resamp(freqH2, Phdsl2x, dfH2, adslstartf, max(freqH2));
[freqadsl, PadsltxhF>, Padslnext] = adslnextmain(1);
% Note that we use adslnextmain, this does not include the sinc rolloff % as suggested by modifications in T1E1.4/95-127 [freqA, PadsltxhpA] = resamp(freqadsl, Padsltxhp,dfH2,adslstartf,adslendf);
N = 1+round((a.dslendf-startf)./dfH2);
[HfsqrA,f] = cablemodel(LoopNo, N, startf,adslendf);
[freqA, HfsqrA] = resamp(f, HfsqrA, dfH2,adslstartf, adslendf);
Phdsl2xA = [Phdsl2xA zeros(l,length(freqA)-length(freqH2A))];
hdsl2_in'ecadsl=dmtmarginest(PadsltxhpA,HfsqrA, Phdsl2xA+wgn,.
9.8,15,6.784e3/dfH2,0) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Claims (76)

WHAT IS CLAIMED:

1. A method for determining a transmit spectrum for use in communicating data on a communications channel, wherein the communications channel is subject to interference from one or more other communications channels, wherein the communications channel carries a first type of service, wherein the one or more other communications channels includes a first subset of communications channels that carry the first type of service, the method comprising:
determining a channel transfer function of the communications channel;
determining interference characteristics of the communications channel, wherein said determining interference characteristics includes one or more of:
a) determining an amount of self interference into the communications channel that results from interference from the first subset of communications channels that carry the first type of service, wherein the self interference includes self-FEXT, and b) determining an amount of uncorrelated interference into the communications channel, wherein the uncorrelated interference includes non-white noise;
examining the channel transfer function and the interference characteristics;
determining the transmit spectrum in response to said examining, wherein the transmit spectrum is useable in communicating data on the communications channel.

2. The method of Claim 1, further comprising:
transmitting data on the communications channel using the transmit spectrum.

3. The method of Claim 1, wherein said determining interference characteristics and said determining the transmit spectrum are dynamically performed each time a data transfer is initiated.

4. The method of Claim 1, wherein said determining interference characteristics and said transferring the data are performed a plurality of times;
wherein said determining interference characteristics and said determining the transmit spectrum are performed each time a data transfer is initiated.

5. The method of Claim 1, further comprising:
repeating said determining interference characteristics and said determining the transmit spectrum during the data transfer to produce a new transmit spectrum;
wherein the new transmit spectrum is used during a remainder of the data transfer.

6. The method of Claim 1, wherein said transferring the data includes:
performing a first portion of the data transfer;
repeating said determining interference characteristics and said determining the transmit spectrum during the data transfer to produce a new transmit spectrum after said performing the first portion of the data transfer; and performing a second portion of the data transfer using the new transmit spectrum after said repeating.

7. The method of any of Claims 1-6, wherein said determining the transmit spectrum further comprises:
determining an EQPSD transmit spectrum if said examining indicates that the amount of self interference is substantially low or absent.

8. The method of any of Claims 1-6, wherein said determining the transmit spectrum further comprises:
determining an EQPSD/FDS transmit spectrum if said examining indicates that the amount of self interference is substantially high.

9. The method of any of Claims 1-6, wherein said determining the transmit spectrum further comprises:
determining an EQPSD/FDS/MFDS transmit spectrum if said examining indicates that the amount of self interference is substantially high.

10. The method of any of Claims 1-9, wherein the uncorrelated interference includes additive Gaussian noise (AGN);
wherein the transmit spectrum is determined in response to the amount of AGN.

11. The method of any of Claims 1-10, wherein the uncorrelated interference includes different service interference (DSIN);
wherein the transmit spectrum is determined in response to the amount of DSIN.

12. The method of Claim 11, wherein the one or more other communications channels further includes a second subset of communications channels that carry a different type of service;
the method further comprising:

determining an amount of different-service interference into the communications channel that results from interference from the second subset of communications channels that carry the second type of service;
examining the amount of different-service interference;
wherein the transmit spectrum is determined in response to the amount of different-service interference.

13. The method of any of Claims 1-12, wherein said determining the channel transfer function comprises receiving the channel transfer function.

14. The method of any of Claims 1-12, wherein said determining the channel transfer function comprises measuring the channel transfer function.

15. The method of any of Claims 1-14, wherein said determining the channel transfer function is performed in response to a power-up, or at regular intervals in time, or in response to temperature changes.

16. The method of any of Claims 1-15, wherein the one or more other communications channels are located proximate to the communications channel.

17. The method of any of Claims 1-16, wherein the transmit spectrum is determined so that the communications channel has equal upstream and downstream capacities.

18. The method of any of Claims 1-16, wherein the transmit spectrum is determined so that the communications channel has equal upstream and downstream performance margins.

19. The method of any of Claims 1-18, wherein the transmit spectrum is determined in response to (1) a predetermined average power on the communications channel, or to (2) a predetermined peak power constraint in frequency, or to (3) a predetermined peak power constraint in frequency and a predetermined average power on the communications channel.

20. The method of any of Claims 1-19, wherein the transmit spectrum is spectrally compatible with the one or more other communications channels.

21. The method of any of Claims 1-20, wherein said determining the transmit spectrum comprises using a water-filling technique or a peak constrained water-filling technique to determine a power spectral density function.

22. The method of any of Claims 1-21, wherein said determining the transmit spectrum comprises determining a downstream transmit spectrum and an upstream transmit spectrum.

23. A method for determining a transmit spectrum for use in communicating data on a communications channel, wherein the communications channel is subject to interference from one or more other communications channels, wherein the communications channel carries a first type of service, wherein the one or more other communications channels includes a first subset of communications channels that carry the first type of service, the method comprising:
determining a channel transfer function of the communications channel;
determining interference characteristics of the communications channel, wherein said determining interference characteristics includes at least one of:
a) determining an amount of self interference into the communications channel that results from interference from the first subset of communications channels that carry the first type of service, wherein the self interference includes self-FEXT, and b) determining an amount of uncorrelated interference into the communications channel, wherein the uncorrelated interference includes non-white noise;
examining the channel transfer function and the interference characteristics;
determining the transmit spectrum in response to said examining, wherein the transmit spectrum is useable in communicating data on the communications channel, and wherein the transmit spectrum includes at least one of: (i) a portion using EQPSD signaling and (ii) a portion using FDS signaling.

24. The method of Claim 23, further comprising:
transmitting data on the communications channel using the transmit spectrum.

25. The method of Claim 23 or of Claim 24, wherein the transmit spectrum uses only EQPSD signaling if said examining indicates that the amount of self interference is substantially low or absent.

26. The method of any one of Claims 23-25, wherein the transmit spectrum includes at least one portion using FDS signaling if said examining indicates that the amount of self interference is substantially high.

27. The method of any one of Claims 23-26, wherein the uncorrelated interference includes additive Gaussian noise (AGN);
wherein the transmit spectrum is determined in response to the amount of AGN.

28. The method of any one of Claims 23-27, wherein said determining the channel transfer function comprises: (a) receiving the channel transfer function or (b) measuring the channel transfer function

29. The method of any one of Claims 23-28, wherein said determining interference characteristics includes:
determining an amount of self interference into the communications channel that results from interference from the first subset of communications channels that carry the first type of service;
wherein said determining the transmit spectrum includes determining a downstream transmit spectrum and an upstream transmit spectrum;
wherein said determining the transmit spectrum includes constructing at least a portion of the upstream and downstream transmit spectra to be orthogonal in response to said examining.

30. The method of Claim 29 wherein the at least a portion of the upstream and downstream transmit spectra is constructed to be orthogonal in response to said examining if said examining indicates a greater data transmission rate for the orthogonally constructed upstream and downstream transmit spectra than for non-orthogonally constructed upstream and downstream transmit spectra.

31. The method of Claim 29, wherein the transmit spectrum comprises a first portion using EQPSD signaling and a second portion using code-division duplex signaling.

32. The method of Claim 29, wherein the transmit spectrum comprises a first portion using EQPSD signaling and a second portion using FDS signaling.

33. The method of Claim 32, wherein the first portion covers a frequency range over which a first characteristic quantity is less than zero and a second characteristic quantity is less than zero;
wherein the second portion covers a frequency range over which the first characteristic quantity is greater than zero and the second characteristic quantity is less than zero;
and wherein the first and second characteristic quantities each depend on the channel transfer function and the amount of self interference.

34. The method of Claim 29, wherein said determining the amount of self interference includes:
determining a self-NEXT transfer function and determining a self-FEXT transfer function;
wherein the transmit spectrum is determined in response to the self-NEXT and self-FEXT transfer functions; and wherein the transmit spectrum includes a first portion using EQPSD signaling and a second portion using FDS signaling.

35. The method of Claim 34, wherein the first portion covers a frequency range over which a first characteristic quantity is less than zero and a second characteristic quantity is less than zero;
wherein the first and second characteristic quantities each depend on the channel transfer function, the self-NEXT transfer function, and the self-FEXT transfer function.

36. The method of Claim 34, wherein the second portion covers a frequency range over which a first characteristic quantity is greater than zero and a second characteristic quantity is less than zero;
wherein the first and second characteristic quantities each depend on the channel transfer function, the self-NEXT transfer function, and the self-FEXT transfer function.

37. The method of Claim 35 or of Claim 36, wherein the first characteristic quantity is given by the following expression, X(f)2 -F(f)2 -H(f)F(f);
wherein H(f)=)¦H c(f)¦2 is the channel transfer function, wherein X(f)=¦H
n(f)¦2 is the self-NEXT
transfer function, and wherein F(f)=¦H F(f)¦2 is the self-FEXT transfer function.

38. The method of Claim 35 or of Claim 36, wherein the second characteristic quantity is given by the following expression, wherein H(f) = ¦H c (f)¦2 is the channel transfer function, wherein X(f) = ¦H
N (f)¦2 is the self-NEXT transfer function, and wherein F(f)= ¦H F (f)¦2 = is the self-FEXT
transfer function.

39. The method of Claim 34, wherein the transmit spectrum includes a third portion using EQPSD signaling, wherein the third portion covers a frequency range between the first and second portions.

40. The method of Claim 34, wherein the transmit spectrum includes a third portion using FDS signaling, wherein the third portion covers a frequency range between the first and second portions.

41. The method of Claim 34, wherein the transmit spectrum includes a third portion, wherein the third portion covers a frequency range between the first and second portions, wherein the third portion includes a first set of one or more subportions using EQPSD signaling, and wherein the third portion includes a second set of one or more subportions using FDS signaling.

42. The method of Claim 34, wherein the transmit spectrum includes a third portion using CDS signaling, wherein the third portion covers a frequency range between the first and second portions.

43. A method for determining a transmit spectrum for use in communicating data on a communications channel, wherein the communications channel is subject to interference from one or more other communications channels, wherein the communications channel carries a first type of service, wherein the one or more other communications channels includes a first subset of communications channels that carry the first type of service, and wherein the communications channel is subject to self-NEXT and self-FEXT interference from the first subset of communications channels that carry the first type of service;
wherein the communications channel is subject to uncorrelated interference in addition to the self-NEXT and self-FEXT interference; and wherein the communications channel is constrained to carry a total average power P max;
the method comprising:
determining a self-NEXT transfer function and a self-FEXT transfer function for interference from the first subset of communications channels that carry the first type of service;
determining an amount of uncorrelated interference into the communications channel;
determining the transmit spectrum in response to the self-NEXT transfer function, the self-FEXT
transfer function, and the amount of uncorrelated interference, wherein the transmit spectrum is useable in communicating data on the communications channel, wherein said determining the transmit spectrum comprises:
dividing the channel into a plurality of frequency bins;
identifying frequency bins M E and M F in response to the self-NEXT transfer function and the self-FEXT transfer function, wherein EQPSD signaling leads to a greater channel capacity than FDS signaling for bins lower in frequency than M E, and wherein FDS signaling leads to a greater channel capacity than EQPSD signaling for bins greater in frequency than M F;
identifying a crossover frequency bin M E2F after said identifying frequency bins M E and M F, wherein M E ~ M E2F ~ M F;
calculating an amount of power transmitted in each of the plurality of frequency bins after said identifying the crossover bin M E2F. wherein said calculating the amount of power transmitted in each of the plurality of frequency bins is performed in response to the channel transfer function, the self-NEXT transfer function, the self-FEXT transfer function, and the amount of uncorrelated interference;
using EQPSD signaling in a first set of frequency bins, wherein each bin in the first set of frequency bins has a frequency less than or equal to the frequency of the crossover frequency bin M E2F, using FDS signaling in a second set of frequency bins, wherein each bin in the second set of bins has a frequency greater than or equal to the frequency of the crossover bin M E2F

44. The method of Claim 43, wherein said identifying the crossover bin ME2F using frequency bin M E as an initial estimate of the crossover bin M E2F; and wherein said calculating an amount of power transmitted in each of the plurality of frequency bins comprises:
(a) choosing a first amount of power P E for transmission in the first set of frequency bins and a second amount of power P F for transmission in the second set of frequency bins, wherein P E + P F =
P max;
(b) performing a first water-filling calculation for the first set of frequency bins with a constraining total power P E;
(c) performing a second water-filling calculation for the second set of frequency bins with a constraining total power P F;
(d) computing the channel capacity in response to the first and second water-filling calculations;
(e) modifying the values of P E and P F;
(f) repeating steps (b)-(e) until the channel capacity is substantially maximized;
(g) identifying a new crossover bin M E2F; and (f) repeating steps (a)-(g) until the channel capacity is substantially maximized.

45. The method of Claim 44, wherein said modifying the values of P E and P F
is performed such that the channel capacity is increased.

46. The method of Claim 44, wherein said identifying a new crossover bin M E2F
is performed such that the channel capacity is increased.

47. The method of Claim 43, wherein said identifying the crossover bin M E2F comprises using frequency bin M E as the crossover bin M E2F; and wherein said calculating an amount of power transmitted in each of the plurality of frequency bins comprises:
(a) choosing a first amount of power P E for transmission in the first set of frequency bins and a second amount of power P F for transmission in the second set of frequency bins, wherein P E + P F =
P max;
(b) performing a first water-filling calculation for the first set of frequency bins with a constraining total power P E;
(c) performing a second water-filling calculation for the second set of frequency bins with a constraining total power P F;
(d) computing the channel capacity in response to the first and second water-filling calculations;
(e) modifying the values of P E and P F;
(f) repeating steps (b)-(e) until the channel capacity is substantially maximized;

48. The method of Claim 47, wherein said modifying the values of P E and P F
is performed such that the channel capacity is increased.

49. A method for determining a transmit spectrum for use in communicating data on a communications channel, wherein the communications channel is subject to interference from one or more other communications channels;
wherein the communications channel carries a first type of service, wherein the one or more other communications channels includes a first subset of M-1 communications channels that carry the first type of service, wherein M is two or more;
the method comprising:
determining a channel transfer function H1 (f) of the communications channel;
determining a self-NEXT transfer function X1 (f) for self-NEXT interference into the communications channel from the first subset of communications channels that carry the first type of service;

determining a self-FEXT transfer function F1 (f) for self-FEXT interference into the communications channel from the first subset of communications channels that carry the first type of service;
determining a SNR G1 (f) of the communications channel;
determining other SNRs Gi(f) of the communications channels in the first subset of communications channels, wherein i ~ [2, M]; and examining the channel transfer function H1(f), the self-NEXT transfer function X1 (f), the self-FEXT transfer function F1(f), the SNR G1 (f), and the other SNRs Gi(f), determining the transmit spectrum in response to said examining, wherein the transmit spectrum is useable in communicating data on the communications channel.

50. The method of Claim 49, wherein said determining the transmit spectrum comprises determining an EQPSD transmit spectrum in a first frequency range of the communications channel;
wherein the SNR G1 (f) is greater than a SNR limit over the first frequency range; and wherein the SNR limit depends on at least two of the channel transfer function H1 (f), the self-NEXT transfer function X1 (f), the self-FEXT transfer function F1(f), and the other SNRs Gi(f).

51. The method of Claim 49, wherein said determining the transmit spectrum comprises determining an FDS transmit spectrum in a second frequency range of the communications channel;
wherein the SNR G1 (f) is less than a SNR limit over the second frequency range; and wherein the SNR limit depends on at least two of the channel transfer function H1 (f), the self-NEXT transfer function X1 (f), the self-FEXT transfer function F1(f), and the other SNRs Gi(f).

52. The method of Claim 50 or of Claim 51, wherein the SNR limit is given by the following expression,

53. A method for determining a transmit spectrum for use in communicating data on a communications channel, wherein the communications channel is subject to interference from one or more other communications channels, wherein the communications channel carries a first type of service, wherein the one or more other communications channels includes a first subset of communications channels that carry the first type of service, the method comprising:
determining a channel transfer function of the communications channel;

determining interference characteristics of the communications channel, wherein said determining interference characteristics includes:
determining an amount of self interference into the communications channel that results from interference from the first subset of communications channels that carry the first type of service, wherein the self interference includes self-FEXT, and determining an amount of uncorrelated interference into the communications channel;
examining the channel transfer function and the interference characteristics;
determining the transmit spectrum in response to said examining, wherein the transmit spectrum is constructed to orthogonally separate at least a subset of the first subset of communications channels that carry the first type of service in response to said examining.

54. The method of Claim 53, wherein the transmit spectrum comprises a first portion using EQPSD signaling and a second portion using one or more of (a) multi-line CDS
signaling and (b) multi-line FDS signaling.

55. The method of Claim 53, wherein said determining the amount of self interference includes:
determining a self-FEXT transfer function, determining a self-NEXT transfer function, and wherein said determining the amount of uncorrelated interference comprises:
determining a signal-to-noise ratio (SNR) for the communications channel;
wherein the transmit spectrum is determined in response to the self-FEXT
transfer function, the self-NEXT transfer function, and the SNR; and wherein the transmit spectrum includes a first portion using EQPSD signaling and a second portion using MFDS signaling.

56. The method of Claim 55, wherein the first portion covers a frequency range over which the self-FEXT
transfer function is less than a first self-FEXT limit.

57. The method of Claim 55, wherein the second portion covers a frequency range over which the self-FEXT
transfer function is greater than a first self-FEXT limit.

58. The method of Claim 55, wherein the first portion covers a frequency range over which the self-FEXT
transfer function is less than a first self-FEXT limit; and wherein the second portion covers a frequency range over which the self-FEXT
transfer function is greater than a first self-FEXT limit.

59. The method of Claim 56, or of Claim 57, or of Claim 58, wherein the first self-FEXT limit is given by the following expression, wherein H(f) ~¦H C(f)¦2 is the channel transfer function, wherein X(f)~ ¦H N
(f)¦2 is the self-NEXT transfer function, wherein G(f) is the SNR, and wherein M is the number of communications channels in the subset of the first subset of communications channels that carry the first type of service.

60. The method of Claim 53, wherein said determining the amount of self interference includes:
determining a self-FEXT transfer function, determining a self-NEXT transfer function, and wherein said determining the amount of uncorrelated interference comprises:
determining a signal-to-noise ratio (SNR) for the communications channel;
wherein the transmit spectrum is determined in response to the self-FEXT
transfer function, the self-NEXT transfer function, and the SNR; and wherein the transmit spectrum includes a first portion using FDS signaling and a second portion using MFDS signaling.

61. The method of Claim 60, wherein the first portion covers a frequency range over which the self-FEXT
transfer function is less than a second self-FEXT limit.

62. The method of Claim 60, wherein the second portion covers a frequency range over which the self-FEXT
transfer function is greater than a second self-FEXT limit.

63. The method of Claim 60, wherein the first portion covers a frequency range over which the self-FEXT
transfer function is less than a second self-FEXT limit; and wherein the second portion covers a frequency range over which the self-FEXT
transfer function is greater than the second self-FEXT limit.

64. The method of Claim 61, or of Claim 62, or of Claim 63, wherein the second self-FEXT limit is given by the following expression, wherein H(f) ~ ¦H c (f)¦2 is the channel transfer function, wherein X(f)~¦H N
(f)¦2 is the self-NEXT
transfer function, wherein G(f) is the SNR, and wherein M is the number of communications channels in the subset of the first subset of communications channels that carry the first type of service.

65. A method for determining a transmit spectrum for use in communicating data on a communications channel, wherein the communications channel is subject to interference from one or more other communications channels, wherein the communications channel carries a first type of service, wherein the one or more other communications channels includes a first subset of communications channels that carry the first type of service, the method comprising:
determining a channel transfer function of the communications channel;
determining interference characteristics of the communications channel, wherein said determining interference characteristics includes at least one of:
a) determining an amount of self interference into the communications channel that results from interference from the first subset of communications channels that carry the first type of service, wherein the self interference includes self-FEXT, and b) determining an amount of uncorrelated interference into the communications channel;
examining the channel transfer function and the interference characteristics;
determining the transmit spectrum in response to said examining, wherein the transmit spectrum is useable in communicating data on the communications channel, and wherein the transmit spectrum includes at least one portion using MFDS signaling;
wherein the communications channel is divisible into a plurality of frequency bins, wherein the transmit spectrum is operable to selectively allocate transmission power to different ones of the plurality of frequency bins.

66. A method for determining a transmit spectrum for use in communicating data on a communications channel, wherein the communications channel is subject to interference from one or more other communications channels;
wherein the communications channel carries a first type of service, wherein the one or more other communications channels includes a second communications channel that carry the first type of service;
the method comprising:
determining a channel transfer function X1(f) of the communications channel;
determining a self-NEXT transfer function X1(f) for self-NEXT interference into the communications channel from the first subset of communications channels that carry the first type of service;
determining a self-FEXT transfer function F1(f) for self-FEXT interference into the communications channel from the first subset of communications channels that carry the first type of service;
determining a SNR G1(f) of the communications channel;
determining a second SNR G2 (f) of the second communications channel; and examining the channel transfer function H1 (f), the self-NEXT transfer function X1 (f), the self-FEXT transfer function F1 (f), the SNR G1(f), and the second SNR G2(f);
determining the transmit spectrum in response to said examining, wherein the transmit spectrum is useable in communicating data on the communications channel.

67. The method of Claim 66, wherein said determining the transmit spectrum comprises determining an EQPSD transmit spectrum in a first frequency range of the communications channel;
wherein the SNR G1(f) is greater than an SNR limit over the first frequency range; and wherein the SNR limit depends on at least two of the channel transfer function H1 (f), the self-NEXT transfer function X1(f), the self-FEXT transfer function F1(f), and the second SNR G2(f).

68. The method of Claim 66, wherein said determining the transmit spectrum comprises determining an MFDS transmit spectrum in a second frequency range of the communications channel;
wherein the SNR G1(f) is less than an SNR limit over the second frequency range; and wherein the SNR limit depends on at least two of the channel transfer function H1(f), the self-NEXT transfer function X1(f), the self-FEXT transfer function F1(f), and the second SNR G2(f).

69. The method of Claim 67 or of Claim 68, wherein the SNR limit is given by the following expression,

70. A method for communicating data on a set of communications channels, wherein each communications channel in the set of communications channels carries a predetermined average power, and wherein each communications channel in the set of communications channels is subject to interference, the method comprising:
determining channel transfer functions of the set of communications channels;
determining interference characteristics of the set of communications channels;
determining transmit spectra for the set of communications channels in response to the channel transfer functions, the interference characteristics, and the predetermined average powers, wherein the transmit spectra include at least one of:
(a) a spectral region in which upstream and downstream transmissions are orthogonally separated for at least one communications channel in the set of communications channels;
(b) a spectral region in which the communications channels in the set of communications channels are orthogonally separated;
wherein the transmit spectra are substantially optimized in channel capacity;
distributing transmit portions of the transmit spectra so that spectral regions of orthogonal separation are contiguously grouped; and transmitting data on the set of communications channels with spectral power distributions given by the transmit spectra.

71. The method of Claim 70, wherein said distributing the transmit portions of the transmit spectra comprises distributing the transmit portions of the transmit spectra so that at least one communications channel in the set of communications channels has substantially equal channel capacities for upstream and downstream communication.

72. The method of Claim 70, wherein said distributing the transmit portions of the transmit spectra comprises distributing the transmit portions of the transmit spectra so that the communications channels in the set of communications channels have substantially equal channel capacities.

73. The method of Claim 70, wherein the transmit spectra include a first spectral region in which upstream and downstream transmissions are orthogonally separated for a first communications channel in the set of communications channels;
wherein said determining transmit spectra includes determining a first transmit spectrum for signaling in a first direction on the first communications channel;
wherein said distributing transmit portions of the transmit spectra includes:

contiguously grouping transmit portions in the first transmit spectrum, and determining a second transmit spectrum for signaling in a second direction on the first communications channel, wherein the second transmit spectrum is complementary to the first transmit spectrum in the first spectral region.

74. A method for communicating data on a set of communications channels, wherein transmit spectra for the set of communications channels include at least one of:
(a) a spectral region in which upstream and downstream transmissions are orthogonally separated for at least one communications channel in the set of communications channels;
(b) a spectral region in which the communications channels in the set of communications channels are orthogonally separated;
wherein the transmit spectra are substantially optimized in channel capacity;
the method comprising:
distributing transmit portions of the transmit spectra so that spectral regions of orthogonal separation are contiguously grouped; and transmitting data on the set of communications channels with spectral power distributions given by the transmit spectra.

75. The method of Claim 74, wherein said distributing the transmit portions of the transmit spectra comprises:
(a) dividing the spectral regions of orthogonal separation into a plurality of frequency ranges, wherein each frequency range is allocated to one or more of (i) a single communications channel in the set of communications channels and (ii) a single signaling direction;
(b) determining if the transmit spectra satisfy predetermined spectral criteria; and (c) if the transmit spectra do not satisfy predetermined spectral criteria, modifying boundaries between the frequency ranges and repeating said steps (a) - (b).

76. The method of Claim 75, wherein the predetermined spectral criteria include one or more of: a constraint of equal average power between upstream and downstream signaling, a constraint of equal channel capacity between upstream and downstream signaling, a constraint of equal performance margins between upstream and downstream signaling, a constraint of equal average power among the communications channels in said set of communications channels, a constraint of equal channel capacity among the communications channels in said set of communications channels, and a constraint of equal performance margins among the communications channels in said set of communications channels.