Classifications

• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04M—TELEPHONIC COMMUNICATION
  • H04M3/00—Automatic or semi-automatic exchanges
  • H04M3/08—Indicating faults in circuits or apparatus
  • H04M3/085—Fault locating arrangements
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04B—TRANSMISSION
  • H04B3/00—Line transmission systems
  • H04B3/02—Details
  • H04B3/20—Reducing echo effects or singing; Opening or closing transmitting path; Conditioning for transmission in one direction or the other
  • H04B3/23—Reducing echo effects or singing; Opening or closing transmitting path; Conditioning for transmission in one direction or the other using a replica of transmitted signal in the time domain, e.g. echo cancellers
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04B—TRANSMISSION
  • H04B3/00—Line transmission systems
  • H04B3/02—Details
  • H04B3/32—Reducing cross-talk, e.g. by compensating
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04B—TRANSMISSION
  • H04B3/00—Line transmission systems
  • H04B3/02—Details
  • H04B3/46—Monitoring; Testing
  • H04B3/487—Testing crosstalk effects
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L1/00—Arrangements for detecting or preventing errors in the information received
  • H04L1/24—Testing correct operation
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04M—TELEPHONIC COMMUNICATION
  • H04M11/00—Telephonic communication systems specially adapted for combination with other electrical systems
  • H04M11/06—Simultaneous speech and data transmission, e.g. telegraphic transmission over the same conductors
  • H04M11/062—Simultaneous speech and data transmission, e.g. telegraphic transmission over the same conductors using different frequency bands for speech and other data

Definitions

• This invention is related to the identification of crosstalk between subscriber loops transmitting high bandwidth telecommunication services through bundled telephone lines or cables, particularly to identification of crosstalk in digital subscriber line (“DSL”) service loops.
• Identification of the crosstalk enables minimization of its effect through crosstalk cancellation, and as part of the spectrum management of the local plant in a telecommunications system.
• Identification of the crosstalk disturbers is accomplished through a variety of methods including Multiple Regression (MR) analysis and an application of a Best Basis Set (BBS) problem with a sparse solution including use of a Matching Pursuit (MP) algorithm.
• MR Multiple Regression
• BSS Best Basis Set
• MP Matching Pursuit
• the mainstay of the telephone company local network is the local subscriber loop.
• the local subscriber loop is now being used to provide broadband digital telecommunication services such as DSL service.
• broadband DSL services include integrated services digital subscriber network ("ISDN”), high-rate digital subscriber line
• HDSL high rate digital subscriber lines
• ADSL asymmetrical digital subscriber lines
• VDSL very high rate digital l subscriber lines
• DSL technologies are engineered to operate over a class of subscriber loops, such as nonloaded loops (18 kft) or Carrier Serving Area (CSA) loops (9 to 12 kft).
• subscriber loops such as nonloaded loops (18 kft) or Carrier Serving Area (CSA) loops (9 to 12 kft).
• CSA Carrier Serving Area
• DSL Subscriber Line
• Twisted-pair cabling was designed and built to carry voice services, requiring only a very low probability of intelligible crosstalk at voice frequencies, generally up to a few kHz.
• Crosstalk generally increases, however, with increasing frequency, and because DSL frequencies extend into the MegaHertz ("MHz") range, crosstalk becomes the major limitation to high-speed DSL. Because a number of individual twisted pairs are wrapped together in a binder, and a number of binders are in each telephone cable (there are typically 12, 13, 25, 50 or 100 pairs in a binder) the crosstalk between pairs in the same binder is much higher than it is between pairs in different binders. Telephone cabling can be thought of as a multi-input, multi-output interference channel with crosstalk in-between from 12 to 100 channels, although there are typically a smaller number of high-power crosstalkers in each pair. DSL technology is still fairly new.
• FIG. 8 shows currently adopted power spectral density ("PSD") templates for each of these spectrum management classes except Class 6 with line 110 representing Class 1 and line 180 representing Class 9 with the others represented respectively in between.
• PSD power spectral density
• a method and system for the identification of crosstalk in high-bandwidth DSL systems are used to ensure spectral compatibility between a number of DSL lines/subscribers in a loop plant providing a means for spectrum management in a local loop plant.
• a novel method for crosstalk identification in the frequency domain computes the correlation coefficient between the measured spectrum and a set of pre-defined PSDs that may be viewed as a crosstalk basis set.
• the size of the basis set may be managed through the use of a singular value decomposition of the complete basis set in accordance with the type of crosstalk disturber.
• the measured power spectral density of a subscriber loop is correlated with a predetermined set of power spectral densities for a group of possible crosstalk disturbers and the crosstalk disturber having the most closely correlated power spectral density is selected as the identified disturber.
• the power spectral density for the selected crosstalk disturber is subtracted from the measured power spectral density of said subscriber loop using spectral subtraction and the resulting power spectral density is again correlated with the predetermined set of power spectral densities for the group of possible crosstalk disturbers to identify additional disturbers.
• the method may also employ Multiple Regression (MR) techniques or the Matching Pursuit (MP) algorithm for finding an optimal sparse representation of a vector from an overcomplete set of vectors.
• MR Multiple Regression
• MP Matching Pursuit
• the method may be applied to a DMT receiver capable of receiving a signal, ⁇ (k)
• a crosstalk PSD estimator estimates the power spectral density of the
• the channel estimates H( ⁇ ) and a crosstalk identifier identifies the type of the crosstalk
• crosstalk disturber by correlating the estimated power spectral density of the crosstalk disturber with a set of possible disturbers and selecting the disturber exhibiting the maximum correlation. Furthermore, a crosstalk predictor may be added to predict the p-th order linear MMSE prediction of the crosstalk disturber. The prediction may be used to cancel the effect of the crosstalk disturber in the DMT receiver. The identity of crosstalk disturbers can also be sent to an Operations Support
• OSS for the management of the broadband spectrum available for a plurality of subscriber loops.
• the information could also be used to cancel the effect of the crosstalk disturber in a DSL receiver.
• FIG. 1 depicts a DSL subscriber loop system having two DSL subscriber loops connecting to a central office;
• FIG. 2 depicts an illustrative embodiment of a crosstalk identification system according to the present invention
• FIG. 3 depicts a cable binder having N twisted pairs of copper wire
• FIG. 4 depicts the power sum of NEXT loss in dB for a binder having 25 twisted pairs of copper wire
• FIG. 5 depicts examples of measured pair-to-pair NEXT loss
• FIG. 6 depicts an example of a fourteen member canonical set of pair-to-pair NEXT couplings
• FIG. 7 depicts an example of a fourteen member basis set of T1 NEXT couplings
• FIG. 8 depicts the power spectral density ("PSD") templates for each of the spectrum management classes
• FIG. 9 depicts the NEXT PSD for a first unknown disturber
• FIG. 10 depicts the NEXT PSD for a second unknown disturber
• FIG. 11 is a flow diagram of the crosstalk identification and subtraction algorithms of the present invention.
• FIG. 12 is a diagram depicting measured mixed crosstalk containing a mixture of crosstalk from SDSL @1040 kbps and HDSL.
• FIG. 13 is a flow diagram of the crosstalk identification algorithm using Multiple
• FIG. 14 is a flow diagram of the crosstalk identification algorithm incorporating the use of Multiple Regression (MR) or the BBS sparse solution techniques such as Matching Pursuit.
• MR Multiple Regression
• BBS sparse solution techniques such as Matching Pursuit.
• FIG. 1 depicts crosstalk in an example of a local loop environment.
• DSL loops 18 comprising twisted pair copper wire connect two subscribers 20 to a central office (“CO") 12 or remote terminal (“RT").
• NXT Near-end crosstalk
• FEXT far-end crosstalk
• Twisted-pair wire 18 can be considered a multi-user channel by expressing the received signal vector as
• Y(f) R(f) + N(f) + H(f)D(f) (1 )
• R(f) is the received message vector
• N(f) is the vector of independent background noise
• D(f) is the vector of transmitted signals creating crosstalk on nearby pairs
• H(f) is the matrix of crosstalk couplings.
• N(f) is transmitted from one end of the cable and D(f) is transmitted from the other end.
• the received crosstalk H(f)D(f) can be canceled, minimized or otherwise treated so as to be less interfering than white noise.
• the twisted-pair multi-user channel is generally time invariant.
• Crosstalk couplings may vary as the temperature of the cable changes, but only very slightly.
• the crosstalk sources may turn on and off, but not very often because the main application of broadband service is "always on" Internet access.
• Time invariance allows the possibility of very accurate estimates of crosstalk coupling using large sample sizes.
• Joint statistics can be obtained by a "third-party" operating a third party system, which is connected to all lines through communications links to the modems, and the knowledge of all the transmitted data could be used to estimate the crosstalk couplings.
• a "third-party" or operations center having access to multi-user crosstalk statistics would be far more capable of diagnosing crosstalk problems than an uninformed technician.
• Received crosstalk can be measured by temporarily connecting measurement equipment to a single pair while crosstalk couplings could be measured by connecting measurement equipment to multiple pairs.
• the accuracy of estimates depends strongly on which elements of the multi-pair cable may be accessed, for example crosstalk couplings can be estimated accurately by accessing data from both transmitters and receivers.
• Crosstalk parameter estimation can be performed off-line using very many samples of data. Knowledge of crosstalk parameters can be useful for spectrum management and maintenance purposes and can also be used at run time to enhance modem performance. There are many vagaries in the telephone outside plant, some older cables have poor crosstalk performance. Unanticipated problems from crosstalk are likely to occur and may be extremely difficult to diagnose.
• the method of the present invention can be performed in any single receiver.
• the first step is identification of the type of DSL line that is generating the crosstalk.
• a receiver estimates which varieties of DSL are generating crosstalk. This can be accomplished because there is actually a small number of common crosstalker types at high frequencies: T1 lines, integrated services digital subscriber lines (ISDN), high bit-rate digital subscriber lines (HDSL), single-pair high bit-rate digital subscriber lines (HDSL2), asymmetric digital subscriber lines (ADSL), and symmetric digital subscriber lines (SDSL).
• ISDN integrated services digital subscriber lines
• HDSL high bit-rate digital subscriber lines
• HDSL2 single-pair high bit-rate digital subscriber lines
• ADSL asymmetric digital subscriber lines
• SDSL symmetric digital subscriber lines
• Single-pair high-speed digital subscriber lines (G.shdsl) and very-high rate digital subscriber lines (VDSL) are also likely to become possible sources of crosstalk soon. .
• Each of these crosstalker types has a unique crosstalk power spectral density (PSD), and this PSD is estimated with classic matched-filter correlation techniques.
• PSD power spectral density
• a crosstalk identification system provides for a computer 200 having a processor 210 in communication with a memory 220 (which can comprise either primary memory, such as RAM, or secondary memory, such as a magnetic disk drive or other storage media or a combination thereof) and input/output (I/O) unit 230.
• I/O unit 230 is adapted to receive data indicative of the power spectral density of one or more subscriber loops 18.
• Display 260 may be used to display graphical and/or textual information related to the PSD measurements and crosstalk identification.
• Other input/output devices may be used in conjunction with the computer 200 such as a keyboard, mouse, touchpad, trackball etc. in order to provide a user interface.
• Processor 210 executes the method steps described herein as stored in memory 220 in order to identify the crosstalk on one or more subscriber lines 18. Additional software may also be executed to generate the PSD from the measurements input through I/O unit 230. Alternatively, a separate test measurement device capable of measuring the PSD for the various subscriber loops may be attached to I/O unit 230.
• the identification algorithm is extended to the case of multiple crosstalkers by a process of successive estimation and cancellation using spectral subtraction described in greater detail below.
• FIG. 3 depicts a cable binder 100 having N twisted pairs of copper wire 18. Lines 40 of FIG. 3 represent the NEXT between the first two twisted pairs of copper wire 18 while lines 41 represent the NEXT between the first and last pairs of copper wire 18.
• Crosstalk can be characterized in terms of power-sums.
• the power-sum NEXT is formed from the sum of the pair-to-pair NEXT coupling powers of the other pairs in the binder group into this given pair.
• the 25 power sums are shown in FIG. 4.
• the power-sum is usually displayed as a power-sum "loss" and the lower the loss the higher the NEXT coupling.
• the NEXT power-sum loss is approximately linear with frequency on the log-log scale.
• the NEXT model often used for studies in the industry is stated as expected 1 % worst case power-sum crosstalk loss as a function of frequency.
• R k (f) is the received message signal
• N k (f) is independent background noise
• D t (f) is the signal transmitted on pair /
• H ik (f) is the crosstalk coupling between pair /and pair k
• the crosstalk received on pair k from a system transmitting on pair / is H ik (f)D t (/) .
• Crosstalk has a number of elements which may be identified or estimated: the crosstalk coupling H l (f) between each pair, the crosstalkers' transmitted spectrum D,(f), sequences of sampled received crosstalk, etc. DSL modems can measure crosstalk samples.
• crosstalk is measured while a DSL system is running, what is measured or estimated is the crosstalk in the bandwidth of the considered DSL system. For this reason, other DSL services running on adjacent pairs may not be detected if their bandwidth is not significantly overlapping, with the bandwidth of the disturbed system.
• a typical example would be ISDN crosstalk into non-overlapped downstream ADSL. If this is the case, there is little performance degradation for the considered DSL service but, from a spectrum management point of view, it may be important to have an accurate map of all the services that generate crosstalk into a given pair. Moreover, it may also be important to identify the services that are generating crosstalk on a pair that may not even be carrying DSL services.
• the correlation receiver is known to be an optimum detector in the case of equally likely transmitted signals with known waveforms transmitted over an AWGN channel. It is mathematically equivalent to the matched-filter receiver which can be shown to maximize the output signal to noise ratio by using Schwarz's inequality.
• the basic structure of a correlation receiver is used here, except that it is adapted with known transmitted signals but unknown crosstalk couplings
• the correlation coefficient is a measure of how well the two data sets move together (positive values) or move apart from one another (negative values).
• the data array Y ⁇ y l ,...., y N ⁇ is the measured crosstalk power spectrum density
• the data array X ⁇ x ⁇ ,...., x N ⁇ is a reference or
• Each basis set of crosstalk PSDs is generated from a single canonical set of measured strong pair-to-pair crosstalk couplings and a specific type of transmitted DSL PSD.
• Each type of transmitted DSL PSD is multiplied by all of the canonical crosstalk couplings to generate a basis set for that DSL.
• the assumption is that a member of this basis crosstalk set is highly correlated with any crosstalk that is strong enough to be troublesome or measurable.
• An example of a canonical set of pair-to-pair couplings is shown in FIG. 6. This canonical set comprises the fourteen out of 300 possible pair-to-pair NEXT couplings with the smallest crosstalk loss sum.
• the crosstalk loss sum is obtained by dB summing over 401 equally spaced frequency samples in the 10 kHz - 2 MHz band.
• the basis set of T1 disturber NEXT PSDs for this example is shown in FIG. 7.
• Basis sets for ISDN, HDSL, ADSL, 2B1Q SDSL and HDSL2 can be generated similarly. Increasing the number of members belonging to the canonical set of crosstalk transfer functions would increase the accuracy of the identification algorithm.
• Another example of a canonical set of pair-to-pair couplings could be all 300 measured independent pair-to-pair couplings.
• a particularly useful NEXT basis set is found to comprise the ISDN, HDSL, ADSL, 2B1 Q SDSL and HDSL2 NEXT sets that have power exceeding or equaling the 49 th disturber power for a given DSL type obtained from the ANSI 1% NEXT model as defined in the Spectrum Management Standard, T1.417.
• error vector E The presence of the error vector E is due to the fact that the measured crosstalk Y is due to a pair-to-pair coupling function that may be close, but not equal to, a coupling in the canonical basis.
• a canonical PSD basis set can be formed by using all the available measured pair-to-pair crosstalk couplings and combining them with all the DSL types under consideration. This approach, however, yields a very large basis set. To reduce the size of this large basis set, the crosstalk power within each DSL type can be ranked with only the first B vectors with the smallest crosstalk loss sum being chosen. The crosstalk loss sum is obtained by dB summing over the frequency samples in the band of interest.
• crosstalkers of the same type but different pair-to-pair couplings
• the similarity of crosstalkers of different types is much greater than the similarity of crosstalkers of different types.
• the present invention exploits this observation by applying the following method. For each type of crosstalkers, the dominant dimensions from the space spanned by all the PSD's for that type are extracted. Vectors corresponding to these dimensions are then used in lieu of the complete set of crosstalkers for that type. After the type of crosstalker is identified, the search for pair-to-pair couplings in the basis that is closed to the actual one is done within the subset of the original (and large) basis pertaining to the identified crosstalker type.
• the set or matrices of all possible PSD couplings ⁇ is partitioned into A sub-matrices pertaining to each type of crosstalker or disturber, j.
• This new and reduced-size basis enables us to identify efficiently which type(s) of crosstalk exist in the sample, but not which particular pair-to-pair couplings are associated with the crosstalk.
• we can rerun the analysis using the subset of the original crosstalk basis associated with that type of crosstalker. Practically, we have decomposed the original search problem among P A B vectors, into
• the measured crosstalk PSD is correlated as described in the last subsection with each of the basis PSDs, and the identification is simply the type of crosstalker which has the highest correlation.
• most common DSL types are simulated: ISDN Basic Rate Interface (BRI), HDSL, T1 , ADSL, 400 kbps SDSL, 1040 kbps SDSL, 1552 kbps SDSL, and HDSL2. All transmit system PSDs are as defined in the Spectrum Management Standard, T1.417. ADSL and HDSL2 have different PSDs upstream and downstream.
• An unknown disturber's NEXT PSD is shown in FIG. 9.
• the calculated correlation with each member of each DSL crosstalk basis set (for the example of a fourteen member canonical crosstalk coupling set ) is given in Table 2 set forth below.
• the DSL with the highest correlation and thus the identity of the unknown disturber is correctly identified as 1552 kbps SDSL.
• FIG. 10 Another unknown disturber's NEXT PSD is shown in FIG. 10.
• the calculated correlation with each member of each DSL crosstalk basis set (for the example of a fourteen member canonical crosstalk coupling set) is given in Table 3.
• the DSL with the highest correlation and thus the identity of this unknown disturber is correctly identified as downstream ADSL.
• the method of the present invention uses a frequency-domain onion peeling technique based on spectral subtraction methods as set forth in FIG. 11.
• Spectral subtraction is a method originally proposed in speech and music processing for the restoration of the power spectrum of a signal observed in additive noise through subtraction of an estimate of the average noise spectrum from the noisy signal spectrum.
• the iteration counter is set to zero 305 and at step
• a measurement of the PSD of a subscriber loop 18 is taken.
• the first estimated PSD is set to the measured PSD as set forth below:
• the iteration counter is set at one and the estimated PSD of the received crosstalk is correlated at step 330 with the basis set to identify the first source of crosstalk, i.e., the one having the highest correlation in accordance with the procedure described above.
• each crosstalk component h;(m)d;(m) so that the composite received
• c(m) c- ⁇ (m) + c 2 (m) be a composite crosstalk constituted of two crosstalk terms pertaining to two different DSL systems. Assuming that the identification algorithm (described above)identifies the strongest disturber that generated crosstalk c ⁇ m), an
• the maximum correlation is greater than a set threshold. If it is not, then the algorithm has identified all of the crosstalk components. If it is, the identified component must be subtracted for further processing. Basically, the composite crosstalk c(m) can be viewed as a noisy observation of the useful signal c 2 (m) embedded in the noise c- ⁇ (m). Because the output of the crosstalk identification algorithm is a true PSD obtained on the basis of a PSD mask and an estimated pair-to-pair coupling function, there is no need to perform an
• spectral subtraction can result in negative estimates of the power spectrum.
• Power spectra are non-negative functions of frequency, and any negative estimate of these variables should be mapped into a non-negative value.
• the power spectrum is post processed in steps 360 and 370 using a mapping function T[ ]of the form:
• Empirically a good value of ⁇ ranged from approximately 0.0 to approximately 0.1.
• the iteration ceases at step 380 when the maximum correlation is less than or equal to the threshold at step 340. It has been found by simulations that overall accuracy is enhanced by retaining and using identified crosstalkers only if the maximum crosstalk correlation is greater than a certain threshold that is empirically determined.
• the threshold is preferably between approximately 0.7 and 0.99 and is more preferably approximately 0.9.
• the crosstalk identification method of the present invention as set forth in FIG. 11 first identifies the strongest disturber as SDSL @1040 kbps. On the next iteration it identifies HDSL as the second strongest disturber. Finally on the third iteration, the maximum correlation of the remainder NEXT is less than 0.90, the set threshold.
• spectral subtraction may cause deterioration in the quality and the information content of the residual crosstalk PSD.
• the spectral subtraction equation can be expressed as the product of the noisy signal spectrum and the frequency response of a spectral subtraction filter as:
• the spectral subtraction filter H( ⁇ is a zero-phase filter, with its magnitude response in the range 0 ⁇ H(/) ⁇ 1.
• the filter acts as an SNR-dependent attenuator.
• each frequency increases with the decreasing SNR, and conversely decreases with increasing SNR.
• the least mean squared error linear filter for noise removal is the Wiener filter.
• the implementation of the Wiener filter requires the power spectra (or equivalent ⁇ the correlation functions) of the signal and the noise process.
• the Wiener filter is based on ensemble average spectra of the signal and the noise, and the averaging operations are taken across the ensemble of different realizations of the signal and noise processes.
• the spectral subtraction filter uses instantaneous spectra of the noisy observation and the time averaged spectra of the noise. This is necessary since in spectral subtraction only one realization of the noise process is available.
• Spectral subtraction is computationally efficient because it only requires an estimate of the noise power spectrum. Because it does not utilize the statistics of the signal process, however, it may use too little a priori information. However, for an ergodic process, the time-averaged spectrum approaches the ensemble averaged spectrum, so that the spectral subtraction filter asymptotically approaches the Wiener filter. This property does not hold when processing speech and music signals because they are intrinsically non-stationary (and, therefore, non-ergodic). When spectral subtraction is applied to the present case of crosstalk identification, however, the quantities involved are true PSDs and not instantaneous or time-averaged ones. Therefore, the implementation of spectral subtraction may be viewed as a sort of optimal Wiener filtering.
• regression coefficients a (fc) and b (k> are determined by the condition that the sum
• the linear multiple regression model is ( 1 ⁇ i ⁇ N , 1 ⁇ kj ⁇ P , 1 ⁇ j ⁇ M ):
• yi fl0 (* i --* if ) +fll (* ⁇ . ⁇ .* Jk )*(* ! > +... + a M ikl '-"' kM) x kM) +el kl ' " -' kM) , (13) where M is the hypothesized number of disturbing DSL types. Standard techniques are available to solve this problem.
• equation (14) Passing to a vector notation, equation (14) can be expressed as: P
• the problem of identification of multiple crosstalkers can be considered equivalent to the problem of finding an optimal sparse representation of a vector from an overcomplete set of vectors.
• the optimal solution to this problem is an NP-complete problem and requires a combinatorial search of prohibitive cost.
• more practical but suboptimal vector selection algorithms have been developed.
• those suitable for the problem of multiple crosstalker identification are the Matching Pursuit (MP) algorithm and its variations, and the FOCal Undetermined System Solver (FOCUSS). Given a signal vector Y and an overcomplete basis ⁇ , these algorithms solve the problem of finding the most compact representation of V within a given tolerance using the basis vectors in the dictionary ⁇ .
• FIG. 13 the use of the MR or BBS techniques in a method of identifying an crosstalk disturber is depicted.
• the power spectral density (PSD) for a given line is measured.
• the basis set of possible crosstalk disturbers is reduced using single value decomposition.
• the reduced crosstalk basis set is then used to identify, at step 430, the of the identity of the crosstalk disturbers using either the MR or BBS technique described above.
• the actual pair-to-pair coupling of the crosstalk disturber is then estimated using the MR or BBS techniques but utilizing the original complete basis set pertaining to the identified disturber.
• the estimated crosstalk is refined using the MR or BBS techniques.
• the stopping criterion is applied and is the identified crosstalk disturber falls within the stopping criterion then the method ends at step 580. If the stopping criterion has not been met the residual is computed using spectral subtraction at step 550 as described above and the iteration counter is increased by a count of one at step 525, The next most likely crosstalk disturber is then estimated in the next iteration which process continues until the stopping criterion is met.
• the measurement of the power spectral density on a subscriber line could either be a direct measurement taken through a network analyzer or other equivalent device but could also include estimated measurements based on information provided to the system from a modem.

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