CA1157917A - Fast learn digital adaptive equalizer - Google Patents

Abstract

Abstract of the Disclosure An automatic adaptive equalizer operative on a test pattern including a carrier-only period, clock-only period and a single test impulse. The equalizer employs a transversal filter under control of a microprocessor. Samples of in-phase and quadrature phase components of the received impulse response are cross correlated and autocorrelated to form elements of a complex matrix equation describing the optimum equalizer tap settings. The microprocessor performs a special iterative operation utilizing elements of this equation to rapidly and exactly calculate the optimum initial settings for the tap constants. The clock-only portion of the test pattern is analyzed to accurately set a sampling clock to properly sample the received impulse so that the matrix formation can be carried out during the duration of the received impulse. Initial equalization can be achieved in a time on the order of 30 milliseconds at a data rate of 9600 bits per second.

Description

FAST LEARN DIGITAL ADAPTIVE EQUALIZER

Background of the Invention The subject invention relates to data communication equalizers and more particularly to automatic adaptive equalizers utilized in high speed data modems. The equalization scheme of the subject invention is parti.cularly adapted to implementation under microprocessor control and provides a ~B

l 1~7917 1 method and apparatus for performing highly accurate, ultra-ast

2 equalization by operation on the channel respons~ to only a

3 single transmittea test impulse.

4 The equalizer of the invention is particularly ~uited to high speed polling applications. In such applications, it is 6 customary to rapidly successively address a nwmber of remote 7 stations, for example in different cities, from a ce~ 21 site.
Tran~ssion frcm each remote station involv~ a n~w transmission 9 line such that equalization must be re-established each time a new remo~e site is polled. Therefore, it is highly desirahle 11 to shorten the equalization time as much as possibl e in order 12 to increase data throughputO
13 Many prior art equalizers have been relatively slo~
14 to equalize when first connected to a new transmission line and have thus wasted valuable data throughput time. Typically, 16 ~.any time consuming incremental adjustments of the equalizer 17 taps are required during analysis of a relatively long period of 18 ranaom data or a training pattern containing numerous test p~1lses.

2 One prior art system proposes to equalize on ~ ~inc,le 0 transmitted test pulse bu~ actually requires a multiplicity o~
21 test pulses. This system is disclàsed in-the Bell System 23 Technical Journalr Vol~ 50, NoO 6 pp~ 1969-2041~ in an article .
by Robert W. Chang titled "A New Equalizer Structure for Fas~
24 Start Up Digital Communications~ n Ano~her prior art system, disclosed i~ U.S~ Patent No.
26 3,962,637 issued to David Motley et al9 achieves e~ualization 27 during the duration of the response to two transmitted impulses utilizing a technique which approxi~ates the well-known zero-29 forcing scheme and does not ~mploy ~orrelation of signal samples.

~2 -2-",, ., 11579t7 l Equaliz~tion in this system requires an extra impulse to adjust 21 the phase of the line signal so that proper sampling will occur.
31 Because this system uses a zero-forcing scheme and then only an 41 approximation thereto, it will not work on a highly distorted line or-when high precision is neceæsary While the Motley ¦ system suggests itself for operation at 4800 bps~ it is not 71 suitable for operation at the much higher data rate of 9600 bps ~¦ at which the equalizer of the subject invention ~an operate.
91 I~ IEEE Transactions On Communications, Vol. Çom-23, 10¦ No. 6, June 1975, P. Butler et al disclose a method permitting 11¦ a direct solution of a matrix equation in real variables 12¦ describing the s~ttings o~ equalizer tap eonstants in a single 13¦ ~ideband system. Thi~ technique requires a much longer training 14 ¦ ~equence to reach an estimation of reasonable accuracy than 15 ¦ that proposed by the subject invention~ Moreover, the method 16 ¦ will not 801ve a complex variable matrix equation. Accordingly 17 ¦ the approach ~annot be used ~o.achieve equalization in a double :
18 I ~deband ~ystem as will the subject in~ention.

20 ¦ UMMA~Y_OF THE INVENTqON
21 ¦ It ~8 therefore an object of the invention to provide 22 a fa ter operating and more accurate equalizer for data trans-23 mission systems.
24 It is another object of ~he invention to provide a practical equali~er w~ich reguire~ a~alysi~ of only a single 27 transmitted i~pulse to ini~ially set the equalizer t~ps for a wide range of varying line distortions and data rates.

It is another object of the invention to provide an equalizer wherein the equalizer tap constants are calculated exactly, rather than by using approximations.
It is another object of the invention to achieve such an exact calculation by an iterative technique which is performed during the time when a transmitted impulse response is being r~ceived such that the equalizer tap constants are calculated and set during the interval between the end of the impulse t~me and the time when the first received data reaches the major tap of the equalizer.
It is another object of the invention to provide an equalizer which can achieve a precise initial setting within a very fast time, such as 30 milliseconds for a data rate of 9600 bps and 15-20 milliseconds for a data rate of 4800 bps.
In accordance with the present invention there is provided in combination with an equalizer means adapted to receive a first signal transmitted across a distorting medium said equalizer means having a plurality of taps settable for compensating for distortion in said first signal induced by said medium, the 20 apparatus comprising: -means for generating a plurality of second signals representing samples of in-phase and quadrature-phase impulse response signals, said impulse response representing that of said distorting medium; and means operative upon said second signals to auto-correlate and cross-correlate said second signals, form elements of a matrix equation from the auto-correlated and cross-correlated ~ 157917 said second signals, said elements including complex constants and complex variables, said variables def ining the optimum initial setting for said taps, for iteratively calculating the exact values of said optimum initial settings utilizing said constants and for

5 setting said taps to said exact values to produce a substantially distortion free signal.
Also in accordance with the invention there is provided an apparatus adapted for use as an equalizer comprising:
first means for connection to a communi.cat~on channel 10 said first means including a plurality of taps settable fox compensating for distortion in said channel; and second means for producing a plurality of successive .
samples of signals representing in-phase and quadrature-phase components of the impulse response of sa.id channel and for operating 15 upon said samples to form elements of a matrix equation from said samples, to iteratively calculate the exact values of the optimum settings for said taps utilizing said elements, and to set said taps to said optimum values, wherein said samples are both auto-correlated and cross-correlated and wherein said matrix equation 20 includes complex constants and complex variables. :
. .
Further in accordance with the invention there is provided apparatus adapted for use as an equalizer comprising:
a first means for connecting to a communication channel, said first means including a plurality of taps settable for compensating for distortions in said channel; and ;

-- 4a ~ 1 5 `~
second means for producing a plurality of successive samples of first and second signals representing the impulse response of said channel and for operating upon said samples to form elements of a matrix equation from said samples, to iteratively 5 calculate the exact values of the optimum settings for said taps utilizing said elements, and to set said taps to said optimum values, wherein said successive samples are derived from a received test impulse and wherein said exact values are calculated in a time less than the duration of said received test impulse.
Further in accordance with the invention there is provided an equalizer for equalizing to a training waveform and received impulse response comprising:
means for connecting to a communication channel and having a plurality of taps settable for compensating for distortion in said channel;
means for detecting the presence of said training waveform and for initiating a sampling count;
means for adjusting said sampling count in response to said training waveform;
means for forming in-phase and quadrature-phase impluse response signals from said received impulse response;
means for sampling said in-phase and quadrature-phase signals in accordance with the adjusted sampling count to produce a plurality of samples;
means for storing said samples;
means for correlating said samples;

- 4b , ~ t5791~

means for utilizing said correlated samples in a set of iterative calculations to obtain the exact values of the optimum setting for said taps; and means for setting said taps to said optimum values.
Further in accordance with the invention there is provided an equalization apparatus comprising:
means for receiving signals transmitted across a distort-ing medium and having a plurali.ty of tap coefficients settable for compensating for distortion in said signals induced by said medium;
means responsive to a training signal containing therein the response of said medium to only one transmitted impulse for sampling said response to produce a plurality of impulse response samples;
means operative upon said impulse response samples to auto-correlate and cross-correlate said samples, form elements of a matrix equation from the auto-correlated and cross-correlated samples, said elements including complex constants and complex variables, said variables defining the optimum initial settings for said tap coefficients, for iteratively calculating the exact values of said optimum initial settings utilizing said constants, and for setting said tap coefficients to said exact values to substantially remove said distortion.
Further in accordance with the invention there is provided in a data communication system, the process for achieving initial adjustment of an equalizer in a receiver adapted to receive a signal containing distortion comprising:
providing said receiver with an initial training waveform including the response to only one transmitted impulse;
sampling the impulse response to produce a plurality of impulse response samples;

-- ~c 1 1~7917 deriving the exact initial settings for the tap coefficient~
of said equalizer from said samples; and setting the coefficients of said equalizer to said values to substantially eliminate said distortion.
Further in accordance with the invention there is provided in combination with an equalizer means adapted to receive a first signal transmitted across a distorting medium, said equalizer means having a plurality of taps settable for compensating for sittortion in said first signal induced by 0 said medium, the apparatus comprising:
means for generating a-plurality of second 3ignals representing samples of in-phase and quadrature-phase impluse response signals, said impulse response representing that of said distorting medium; and means operative uponsaid second signals to auto~correlate and cross-correlate said second signals, form elements of a matrix equation from the auto-correlated and cross-correlated said second signals, said elements including complex constants and complex variables, said variables defining the optimum initial settings 20 for said taps, for iteratively calculating the exact values of said optimum initial settings utilizing said constants in N iterations for an NxN matrix and for setting said taps to said exact values to produce a substantially distortion free signal.

Further in accordance with the invention there is 25 provided in combination with an equalizer means adapted to receive a first signal transmitted across a distorting medium, said equalizer means having a plurality of taps settable for compensating for distortion in said first signal induced by said medium, the apparatus comprising:
- ~d - .

1 15791~
means for generating a plurality of second signals representing samples of in-phase and quadrature-phase impulse response signals, said impulse response representing that of said distorting medium; and means operative upon said second signals to auto-correlate and cross-corr~late said second signals, form el~ments of a matrix equation from the auto-correlated and cross-correlated said second signals, said elements including complex constants and complex variables, said variables defining the optimum initial settings 10 for said taps, for iteratively and nonconvergently calculating the exact values of said optimum initial settings utilizing said constants and for setting said taps to said exact values to produce a substantially distortion free signal.
Further in accordance witn the invention there is provided a data receiver apparatus adapted to receive a training pattern and impulse response, the apparatus comprising:
means adapted for connection to a communication channel and having a plurality of coefficients settable for compensating for distortion in the channel;
a sampling clock; ;:
means for detecting the presence of the training pattern and for initiating counting by the sampling clock;
means for adjusting the sampling clock in response to the training pattern;

means for forming in-phase and quadrature-phase impulse response samples from the received impulse response and utilizing the adjusted sampling clock;

_ 4e i 1~791~
means for storing the samples;
means for correlating the samples;
means for utilizing the correlated samples in a set of iterative calculations to obtain the exact values of the 5 optimum settings for the coefficients; and means for setting the coefficients to the optimum values.

The apparatus of the invention has the major advantage of enabling precise equalization constant calculations from the samples in alminimal amount of time despite wide variations in the distortion induced by the medium over which the received impulse is transmitted.
Utilizing the invention, an equalizer has been constructed which can achieve initial equalization in a time on the order of 30 milliseconds at a data rate of 9600 bits per second. This is nearly five times faster than equalization can be achieved by presently commercially available systems. In the preferred embodiment of the invention, equalization is performed in response to a single received impulse,~and an important feature of the preferred apparatus is provision of a means to determine the Z~ optimum points at which to sample.the impulse response prior to : receiving t. While equalization is performed using in-phase and quadrature phase impulse response signals at baseband frequencies in the preferred embodiment, such signals may be derived at passband or other translated frequencies.
2~

BRIEF DESCRIPTION OF THE DRAWINGS
-The preferred embodiment and best mode presently contemplated for implementing the just summarized invention will now be described in detail in conjunction withthe drawings of which:

" ~ 1157917 1 Fig. lA illustrates the received signal utilized by 2 the equalizer of the preferred embodiment.
3 Fig. lB and lC illustrate two phase componen~s in 4 ~elative quadrature produced from the received signal on the same S time scale as Fig. lA.

6 Fig. 2 is a schematic diagra~ useful in illustrating

7 the structure and operation of the equalizer of the preferred

8 embodiment.

9 Fig. 3 is a schematic diagram illustrating the digital processor utilized in the preferred embodimen~ of the invention.
11 . .

6~1 .

~9!
201 . .
21l 221 . ' . I
231 . I

31 I .

32 I -6- .

I ~ 57gl7 1 Fig. 4 is a flow diagram illustrating the overall 2 structure and operation utilized to properly time the sampling 3 of the received ~gnal in the preferred embodiment.
4 Fig. 5 is a detailed flow diagram illustrating the 5 method and apparatus utilized to detect the presence of the 6 received signal in the preferred embodiment.
7 Fig. 6 is a detailed flow diagram illustratinq the 8 method and apparatus employed in the preferred embodiment 9 to proper.ly set the points for sampling the received signal.
Fig. 7 is a detailed flow diagram illustrating the 11 method and apparatus employe~ in the preferred embodiment 12 to determine the equalizer tap constant settings from the samples 13 of the received signal.
14 Fig. 8 is a continuation of the flow of FigO 7.
.Fig. 9 illustrates one technique suitable for 16 generàting phase quadrature signals for use i~ the subject 17 invention.
18 Fig. 10 illustrates an alternative technique ~or 1g generating phase quadrature signals for use in the subject in~ention.
21 Fig. ll illustrate~ an alternative technique for 22 generating phase quadrature signals for use in the subject 23 invention.
24 DETAI1ED DESCRXPTION OF THE PREFERRED EMBODIMæN~
The automatic adaptive equalizer of the invention 26 may be conveniently introduced in conjunction with the training 27 ¦ pattern waveform utilized to set uP automatic aain co~tr~l~timina and 29 equalizationO as shown in Fig. l. Tha training pattern of Fig. 1 32 . o7_ l 15~917 1 i5 the analog demodulated pattern at the receiver after t-ans-2 mission. The system of the preferred embodiment is particularly 3 directed to the quadrature amplitude modulation (QAM) technique.
4 The training pattern includes in succession a number of bauds of carrier-only 11~ a number of bauds of clock-only 13, 6 a quiet or squelch period 15, a received impulse 17, and another 7 squelch period 19. The training pattern may also include an 8 optional fine tuning sequence before the transmission of 9 customer data 20.
In the preferred embodiment, eight bauds of carrier-11 only 11 and seventeen bauds of clock-only 13 are sent. The 12 squelch periods 15f 19 are twenty-seven and twenty-one bauds long, 13 respectively, and the impulse period is one baud long. Each 14 baud period is 416.7 miliseconds. Of course~ other baud periods could be utilized~ Also, the length of the periods 11, 17~ 15 16 and 19 depend on the maximum distortion. Wher. the line distor-17 tion is less,.fe~r bauds are required for each one of them, 18 especially for periods 179 15 and 19 9 and the total time fsr 19 tuning will be shoxter~ When the line distortion is se~ere, more bauds are required for each period, and the total tuning 21 tLme will be longer~
22 During the carrier-only period 13 in Fig. 1, the 23 initial incidence of carrier energy on the line is detected 24 ~carrier detect) 9 starting system operation. When carrier detect occurs; a rough tLming counter KSTMX is started, which ultimately .
26 anticipates the occurrence of the impulse response 17. KSTMX
27 count~ once per baudO
28~ ~u omatic gain control i~ then perfocmed on the carrier~

~2 .~ .`

~ ` 1~917 1 only signal 11. After a fixed number of bauds of carrier-only 2 11 are detected, the system knows it is actually receiving a 3 training pattern and can then expect the clock-only signal 13.
4 During the clock-only pattern 13, the apparatus 5 examines the transmitted pattern to determine the optimum 6 points to sample the forthcoming impulse response 17. The 7 apparatus then sets up for the impulse response sampling 8 procedure. The first step is to use the sampling point prev-9 iously calculated to jump or preset the sampling clock to the

10 optimum sampling position. I~ may thus be ~een that the

11 preferred embodiment actually samples the response to a

12 transmitted impulse although other means for generating signals

13 representative of such samples could be employed. .

14 During the squelch period 15, the rough timing counter RSTMX, which was ~et~up-upon detection of carrier-only, continues 16 to count to subsequently indicate to the apparatus the point i~
17 time at which to start to sample the in-phase and quadrature 18 phase impulse responses 17 (Fig. lB, lC~. The samples are then 19 taken, stored and correlated for forming a matrix. Ater the 20 matrix is formed a special iterative technique is utilized to 21 determine the precise initial equalizer tap settings, as dis-22 cussed further below. .
23 The apparatus employed to perform these operations 24 is illustrated conceptually in block form in Fig. 2. The apparatus includes an analog to digital ~A/D) converter an 26 aut~matic gain control (AGC) section 21, a digital processor 27 23, and a transversal equalizer 28. The equalizer ~8 is shown 28 conceptually for purpo~e~.of illustra~ion and is-preferably 29 implemented digitally, in which case it could also be shown as 32 _9_ ~

11~7917 1 part of the digital processor 23.
2 Digital demodulation of the QAM signal into in-phase 3 (X) and quadrature phase (Y) base band components, is preferably 4 accomplished in the digital processor 23. The analog form 5 of the demodulated in-phase and quadrature phase baseband 6 components is illustrated in Figures l~ and lC, respectively.
7 Demodulation again may be performed by well-known techniques 8 and may optionally ~e performed ~y dedicated apparatus outside 9 the digital processor 23~ Neither the AGC or demodulation 10 technique used form a part of the subject invention.
11 The X and Y phase components produced by demodulation 12 represent samples in digital form of the baseband signal9 the 13 Y compunent sample being demodulated by a carrier 90 out of 14 phase ~rom the carrier demodulating the X component sample. In

15 order to calculate the proper sampling time during the clock-

16 ¦only period9 two samples per baud are taken in the preferred

17 ¦embodiment~ After the optimum clock phase is s~t~ the system

18 ¦takes one sample per baud.

19 ¦ These samples X, Y are sent to separate channels 25,-

20 27 of the transversal equalizer 28. Each channel 25, 27 includes

21¦ equally spaced digital delay elements 29~ 31 and digital multi-

22 pliers 30, 32~ 33, 35 as known in ~he prior art. The multi-

23 pliers 32~ 33 multiply the delayed samples X~ by constants

24 CPi and cqi while the multipliers 30~ 35 multiply the delayed samples Ym by constants CPi and cqi. The i'constants'l just 26 referred to are also called "coefficients" by some persons in the 27 art. The outputs of each multipliers 30, 32~ 33~ 35 are summed 28 by respective summers 40, 42~ 44~ 46 and fed to an adder 36.
29 The output of one summer 46 is subtrac~ed from that of the other 30 ¦42 in a summer 32 ~lO-. 11579~

1 37 to give the output data signal EQX. The outputs of the other 2 two summers 40, 44 are su~med by a summer 36 to give the output 3 data signal EQY.
4 As shown in more detail in Fig. 3, the preferred 5 embodime.nt of the invention includes a programmed microprocessor 6 structure and an equalizer unit. The equalizer unit 34 includes 7 the functions of the e~ualizer 28 of Fig. 2 and performs steady 8 state adaptive equalization, for example as taught in U.S. Patent 9 4,035,625 issued on July 12, 1977 and assigned to the present 10 assignee, In the preferred 11 structure of the present invention, the equalizer unit 34 also 12 contains some circuitry for accomplishing the initial equalizer 13 setting, as will be further detailed below.
14 The microprocessor ~tructure of Fig. 3 is conventional, 15 and includes a program store 16, a program counter 18, for 16 addressing the program store 16, a command decoder 14 for 17 decoding instructions from the program store 16 to produce 18 control signals and an arithmetic unit 22 for performing the 19 instructions in response to the control signals from the decoder 14. The microprocessor structure also includes a data storage 21 memory 26 and an address decoder 24 for-addressing the memory.
22 The program store 16 is a conventional read only memory (ROM) 23 of sufficient capacity to store the i.nstructions for performing 24 the equali~er operations to be described below and may be constructed fro~ four AMD 9216 ROM chips. The program counter 26 18 is a conventional counter which can be loaded or jumped 27 as necessary in response to control signals from the command 28~ decoder 200 The arithmetic unit 22 is also conventional in .:,' 57~17 1 structure and of sufficient power to carry out necessary 2 operation`s as hereafter described. The data storage memory 3 26 includes storage for constants and 256 words of random 4 access memory and may be configured from three AM91~12ADC
5 R~M chips and one General Instrument R03-5120 chip. The random 6 access storage is used to store incoming samples of the impulse 7 response 17 and subsequent data 20 while calculations are 8 underway.
9 The apparatus of Fig. 3 just described performs rapid 10 initial equalization by calculating the initial equalizer tap 11 multiplier constants in very rapid fashion. The manner of this 12 calculation and the function and structure of the apparatus 13 of Fig. 3 will now be explained in detail.
14 The multiplier constants to be calculated are labeled 15 c c c .O. c i and cql~ Cq2v Cq3 Cqi ( 16 In complex form the equalizer tap constants may be expressed as:
17 ~i=Cpi~jCqi ~ ~i=l, 2~ 3,...~
1 To calculate the equalizer constants ci from the pair of demodu-19 ¦lated impulse responses as shown in Fig. lB and lC, the following 20 ¦definitions are adopted.

22 ¦ rTO = ~(X2 + ~,2 23 l 24 ¦ 1 (Xm Xm+l ~ Y~ Ym+l) + j ~M l(X~Ym+1 _ y X ~ (2)

25 ¦ m-l m=l

26 ~ rT2 = ~ (xmxm+2 + YmYm+2) + j ~1(XmYm+2 YmXm+2~

29 ~ rTn-l m= (Xm m+n-l mYm+n-l)~j=l (XmYm+n 1 YmXm+n-1)(4) 1 15791~

1 The following elements are defined:
2 ~ = Xn-q~k _ jYn-q-k k=1,2 .. n (5) 3 rT0 4 rTi r - i=1,2 ~.n-l (6) 6 r~0 7 In the above equations (1) - (6)l Xm and Ym are the m th 8 sample of thein phase and quadrature phase of the impulse response used for calculating the autocorrelation and cross 10 correlation. Equation~ (2), (3), (4) represent the auto-11 correlation and cross-correlation of the samples ~ and Ym.
12 In the above equations 1-6, M is the total number 13 of samples used for calculating the auto-correlation and cross-14 correlation and n is equal to the number of taps, twenty for 15 M and sixteen for n in the preferred embodimentp and q equals 16 the subscript of the first sample actually used to cal~ulate 17 hk. The variable q accounts for the fact that in the preferred 18 embodiment not all samples taken are used, in other words n is 19 less than M as later explained in detail. If n equals M, q=l.
~Q With these definitions~ the equationS defining the 21 optimum tap constants cl~ c2, ~ n for an equalizer of n taps 22 is written follow~ in matrix form:

~7 ~21 -13-~P~ I . ..

1 rl r2 ............................ r* 1 ~ cl ~
2 r 1 rl* .......................... rn-2 C2 h2 3 r2 rl 1 r*l................... ~... r*n 3 .: .

6 ; ~ -r~

8 r 1' ' ' ~ . r 1 1 cn = h In equation (7), rl...ri and hl...hn are complex constants while 11 cl...cn are complex variables. The asterisk (*~ indicates the 12 complex conjugate form.
13 According to the invention, a special solution of this 14 equation (7).permits a precise iterative c~lculation o~ the tap constants cl...ci within the time interval required by the 16 training scheme of Fig. 1 plus the time delay ~equired for 17 data to propagate between the input and outpu~ of the equalizer.
1 According to this solution, the following definitions are made:
19 1 1 ~ Irl¦ ~ (8) 20 ¦ ~here ¦rl¦ represents the magnitude of the complex quantity rl; !
21 ¦ s ~1~ = r (9) I Where superscript ~(l)W indicates the first iteration i=l; and 23 ¦ cl~ ) = hl ~10) 25 ¦ Adapting these definitions, the exact iterative solution for 26 ¦ the tap constants is as follows: i

27 I .

28 I .
2g ~ . I

1i1579 c l 1l) = (hi+l ~ m~l cm ri m+
2 ~i+l = ~(ri+l +m~l Sm j -ri-m~l) (Zi) (12) 4 ~ i+l = c(i) + ~ 1+l 5i*(+) 1 < j < i (13) 6 5j i~l = s~i) + s i+l Si(~ j < i (14) 8~ ei+l 5 e~ +1) ¦ 2) (15) Zi 1 11 The superscripts again indicate the value of the variable ~or 12 a particular iteration. These equations 7-16 provide a simple 13 means for rapidly and exactly~calculating the tap cons~ants c 14 in the complex matrix equation (7). This iterative technique enables the apparatus of the invention to calculate the constants¦
16 ci and set the equalizer to achieve initial equalization during a 17 total training time of approximately 30 milliseconds from the 18 beginning of carrier only ~o the first bit of customer data in 19 a 2400 baud machine. Variations of the matrix equation (7) may be 20¦ written and solved by the technique illustra~ed above without 21j departing from the scope of this invention.
2Z¦ The structure and operation of the apparatus of Fig~ 3, 231 as it relates to the preferred embodiment ofthe invention~ will now ~

24 ¦ described in further detail in conj~nction with Figs. 4-8~ j 25 ¦ After the carrier is de~ected and the clock KS~MX is 26¦ started~ the system operates according to the 1OW illustrated 271 in the flow chart of Fi~. 4. The flow of Fig. 4 illustra~es

29 3~ I 15-~ 11S7917 1 ¦ accomplishment of the automatic gain control function, filter, 2 ¦ demodulation, the detecting of the training pattern present (TPP) 3 ¦ and calculation of the optimum sampling point to be used in the ¦ subsequent operations of Fig. 7. Two samples of the carrier-only 5 ¦ signal are processed each baud for the eight bauds of carrier-6 ¦ only 11. A counter N is set up at -8 to direct operation.
7 ¦ As long as N iS less than zero, the left branch 43 8 of the flow is followed and each sample is subjected to an auto-9 matic gain control operat;on 47, a filter and demodulation opera-PO tion 49 and the test pattern present detection 51~ The test 11 pattern detectiGn checks six successive bauds of carrier~only 12 signal and thereafter sets a flag indicating that a test pattern 13 is in fact being received. Each baud, the counter N is incre-14 mented by one, as is the counter RSTMX.
When N equals zero, the clock-only signal 13 begins.
6 ¦ AGC is frozen and the right hand branch ~3 of the flow of Fig. 4 i5 entered. In this branch 53, a filter and demodulation opera-8 tion 55 is performed and a test 57 of the TPP flag is made.
20 ! Assuming TPP has been detected and the TPP flag setp the fast 211 learn clock operation 59 is performed~ During this operation, 2 1 denoted FLCLK, the apparatus calculates the optimum sampling 21 point for the forthcoming impulse based on the demodulated clock- ¦
231 only information~ After each two samples per baud have been 241 demodulated and u~ed in the FLCLR proces~, the counter XSTMX
251 // . ' , ,. 261 //
27 ~
,, 281 , I
29 I !

32 I -16- i '';, I
~- I , I

~ ~57917 1 i~ incremented by one, as is the N counter. When FLCLK is done, 2 the flow proceeds to Fig. 7.
3 The manner in which the training pattern detection is 4 performed is illustrated in more detail in Fig. 5. Referring S to Fig. 5, X and Y samples of the demodulated baseband signal 6 are supplied to respecti~e inpu~sat the rate of two samples 7 per baud.
8 The samples presented to the X input are operated upon 9 as followsu Each sample is first squared by a multiplier 63 and the output of the multiplier 63 is stored for one sample time 11 in a delay element 65~ The current output of the multiplier 63 12 is added to the negative value of the previous output of the 13 multiplier 63 in an adder 67~ The output of the adder 67 is 14 supplied as one input to a second adder 69. The X input is also supplied to a second one sample time d~lay element 71. The 16 output ~f the second one-sample delay element 71 is supplied to 17 a second multiplier 73, alsv supplied with the X input, such that 18 the current X input sample is multiplied by the immediately 19 preceding X sample~ The output of t~e second multiplier 73 is fed to one input of a third summer 75.
21 The Y input is similarly operated on. A delay element 22 77 delays the first sample of the Y input and a multiplier 79 .
23 multiplies the firs~ sample of the Y input by the delayed sample 24 for supply to the third summer 75. The Y input is also squared and the squaredY input value i5 supplied to a delay element 81 261 me delayed squared sample is subtracted from a present squared 271 sample by a summer 83 whose output is supplied to the second 28¦ summer 69~ .
29 The output of the third summer -15 is multiplied by two ~2 ~17-1 1~7917 l .~t n n~ultiplier 85 to form ~n output denoted aq ACK. The output 2 of the second summer 69 is denoted BCK. The arc tangent of 3 ACK/BCK is then taken to determine the sampling angle Q .
4 The current value of ~ lS stored by a delay element 87. The stored value of ~ is used in the clock preset to be subsequently 6 discussed.
7 It is then determined whether ~n is within bounds for 8 each of a number of counts NTPP. ~hen NTPP is greater than l0, 9 five bauds of samples have been examined. Thus, if¦~ -90¦is less than 15 continuously for greater than l0 NTPP counts it is con-11 firmed that carrier has been received for 5 bauds, and the TPP
12 flag is therefore set equal to l. ~hi; operation is illustrated 13 in Fig. 5 by proceeding through blocks 9l, ~2, 93, to bl~ck 94, 14 TPP equals l. Once¦~ -go¦is greater than 15 al1d TPP equals l, the clock preset routine is entered.
16 In the event however, that¦~n~9~¦is greater than l~ on 17 any of the carrier-only sa~ples operated on~ the test block 95~
18 TPP=l, will not be satisfied, and NTPP will be reset to zero. In 19 such event~ if KSTMX is greater than l9~ indicating nineteen bauds have occurred without detecting TPP, TPP not present is 21 indicated. Failure to detect TPP normally indicates line dropou~
22 Once the training pattern is detec~ed~ it is necessary 23 to properly align the timing of the sampling of the received 24 impulse response 17. The sampling points are calculated sucb that the equalizer can best minimize the output error. The 26 struc~ure and technique used in the preferred embodiment for 271 performing the presetting of the sampling clock ~LCLK) is 28¦ lllustrated in detail in Flg. 6.

1l Assuming no distortion or noise, the difference between 21 successi~e angles ~ should be 180~ Therefore, if the 31 magnitude 41 ~ n 1~ ~ 1 s¦ is less than 12 for several successive samples, the clock is 6 in good r~nge~ Assuming that ~ is in good range over several 7 sampling intervals of the clock-only pattern~ the loop including 8 blocks 101, 102, 103, 104, 105, 106, and 107 in Fig. 6 is 9 operative. Initially, three counters NCNT, NSAMP~ and NAV are set to zexo. When the ~irst sample is tested, the sampling 11 counter NSAMP is incremented by 1 as indicated by the block 101.
12 The angle ~ is then tested; and if it is within range~ the .
13 counter NCNT is incremented by 1. After four consecutive good 14 samples, the test, NCNT greater than or equal to four (Block 104), is satisfied, and NAV = 0 is satisfied. In this event, the test 16 indicated by block 106 is performed to ascertain whether the 17 magnitude of ~ is less than 90. If so, a counter NR is set 18 -equal to 1. The counter NAV, representing he number to be 19 averaged, is set equal to 1 and TAGL (total angle) is defined as equal to ~ at this moment~ The next time around the loop, 21 the test NAV = 0 is not true~ and NR is incremented by one at 22 block 108. NR + 1 is then equal to two. NR is then not odd, 23 and another sample is taken~ After this sample, assuming ~
24 is still in boundsJ NR is odd ~equal to 3). Therefore the num-ber averaged NAV ~ 2 and TAGL is equal to the previous ~
26 value plus the new ~n value~ Thus there are two angles to be 27 averaged. ~ssuming that ~ continues to be within bounds, the 28 number of ~n samples averaged is incremented to 4 and then the angle P~ is de~ermined a~ block 109 by calculating the ~uotient 32 _~9_ 1 15791~

1 of TAGL and NAV. P~ indicates the number of degrees from which 2 the sampling point being used diverges from the optimum sampling 3 point. Thus, it takes lO angle differences within bounds to 4 reach the block P~ = TAGL/NAV.
In the event, however, that distortion is occurring, 6 other provisions are made for calculating 7 P~ . For example, if it occurs that ~ is greater 8 than 12~ satisfying block 102, a test llO if made to determine is 9 the number of good samples counted NCNT is greater ~han or equal to 4, i.e. whether four inbounds angle tests have occurred. If 11 so, a test lll is made of the NAV counter to determine whether 12 any samples TAGL have been stored for averaging. I~ any samples 13 have been stored, the average ~av = TAGL/NAVL is computed as 14 indicated by the four blocks 112~ 113~ 114, 115. These four blocks indicate that P~ is taken as equal to ~av if NR is even, .
16 whereas P~ is taken as equal to 78 ~GN (a av)¦ [180 ¦~av¦]

19 if NR is odd. If~ however, at the test lll~ NAV is found to be equal to zero, indicating no samples ~ have been accumulated, 21 P~ is ~aken to be the current sample ~n.
22 If the NCNT ~ 4 test llO is not satisfied, a test 117 23 of the number of samples~ indicated by counter NSAMR is made.
24 If that number NSAMP is greater than 2g (~ 14 bauds), P~ is again taken to be ~ . If NCNT > 4 is not satisfied and NSAMP
26 29 is not satisfied; NCNT is set to zero and another sample is 27 examined. This procedure assures that if the angle determination 28 is initally or occasionally out of bounds~ subsequent angles can 29 be examined to average the clock according to the previously discussed procedures~

~2 -20~
,,,~,~,"

P~ t~en det~rmines the pha3e shift of the impulse 2 ~ampling clock to be u~ed in the ~atrix ~ampling operation 3 illustrated in ~ig. 7.
4 ~n Fig. 7, the first time through, the new program (NP) test 121 i~ po~itive and the left branch 123 of the flow is 6 followed. Here the equalizer random access memory (RAM) 26 i~
7 reset. Also the optimum sampling point determined by FLCLK is 8 used to jump the sampling clock to the optimum sampling position 9 within each baud. The clock rate is reduced in half to 2400 Hz such ~hat one sample per baud of the impulse response i8 11 taken from each of the X and Y channels. .
12 The second time through the flow of Fig. 7, a ~econd ~3 branch 1~5 is followed. Detected samples are demodulated (block 14 127), and then a tes~ 9 is performed on KSTMX to see if it i~ ¦
greater ~han 45. If it is not, RSTMX is incremented (block 131).
16 As soon a~ RSTMX is greater than 45, matrix formation 133 from 17 the sampled impulse 17 begins.
18 Th~ branch followed when XSTMX < 45 includes a demodu-19 lated output energy test which assures that the system i5 ~0 ¦ receiving the equalizer tes~ pattern and not customer dataO
21 ¦ After ~STMX i~ greater than i8 the energy i~ determined as denoted 22 ¦ by blocks 134, 138. If the energy ~8 below a ~et level Eref~ the ¦
23 ¦ squelch period is as~umed to have been detec~ed and the ~ystem 25 ¦ knows a training pattern is present. ~f the energy is greater than Eref, training pattern TPP not pre~ent is ~ndicated. This 26 ¦ provide~ a doubl~ check on the presence of a training pattern.
271 . . I
281 ' ' . ' I
291 .
301 .

321 -2~-1 Sampling of the impulse wave form 17 is illustrated by 2 the vertical lines in Fig. lB and lC. The number of samples is 3 counted by a counter K, started when KSTMX = 45. Each sample 4 produces an X component xi and a Y component Yi. As the samples xi, Yi are successively takenl formation of the matrix equation 6 (7) according to the definitional equations (1)~ (2), (3)~ (4) begins. For e~ample, during the ~first baud, xl and Yl are t~ken 8 and stored in the RAM 25 and may then be used to calculate xl + Yl , the first iter~ ion of rT0, equation (1). During the second and successive samples, iterations of rT0 and the corre-11 lating equations rTl, rT2... are calculated.
As the second sample x2, Y2 is taken, it is stored in 13 the RAM 26~ and the square of its magnitude, X2 + Y2 is com-14 pared to the square of the first sample magnitude xl + Yl~ to determine which is larger. The larger is retained and compared tc , 16 the square of the magnitude of the next sample to determine the lr ¦ largest sample and hence ~he peak 180 of the sampled impulse 18 response 17. The baud KP during which the peak 180 occurs is ! stored to be used in subsequent operations. All ~amples ~i~ Yi 20¦ are also stored.
21 Sampling is terminated upon one of two conditions as 22 indicated by a test 137 (Fig. 7). For the applicat~on of the preferred embodiment~ it is advantageous to use eight samples 24 before t~e peak and eleven after the peak. If eleven samples have occurred after the peak, K= KP + 11, and matrix formation 27 is terminated. If ~ ~8, KP is set equal to eight (blocks 135, 136) so that at least nineteen samples must he taken before for~

mation can be terminated upon K = KP ~ Otherwise~ once ~1 . I
32 ! -22-~157~17 1 twenty-four total samples have been taken, matrix formation is 2 terminated and a flag is set.
3 Once the matrix flag is set, the next time through 4 the flow, a branch 132 occurs to the test 141, K > 20 (Fig. 8).
If greater than 20 samples have been taken, the test 141 is 6 satisfied, and the processor 23 proceeds to correct the effect 7 on the matrix of taking too many samples.
8 Thus, K > 20 indicates that, because of the rough 9 alignment of the counter KSTMX, too many samples before the occurrence of the peak 18 have been taken. These samples will 11 likely contribute to inaccuracies and their effect is subtracted 12 by an operation 1~3 denoted SUB 1. This subtraction is accom-13 plished by taking the first samples xli Yl from memory, calcu-14 lating their impact upon the values for the equations (1), (2), (3) for rTO, rTl, rT2~ etc. and subtracting that impact. After 16 the effect of the first sample xl~ Yl is subtracted the sample 17 counter R is decremented by one (block 145) and the K > 20 test-18 141 is ayain performedO If the test 14~ is satisfied, the 191 effect of the second sample pair x2~ Y2 is calcula~ed and sub-20¦ tracted, etc. until X < 200 Once R < 20, the values determined 21 by the remaining sampleS xi~ Yi are utilized in the subsequent 22 matrix calculations.
23 Once K is reduced to 20, a br~nch 147 occurs to the 24 tap constant calculation process, equations (5) - (6) and (8~ ~
(16), first passing through a test 149 to determine if the calcu-26 laton has already been done. At the beginning of the calcula-27 tion process, a c~ounter N is set to zeroO A test 151 of the 28 value of N is then madeO

1 The first step 153 in the calculation process, with N
2 equal to zero, is a normalization process. During this step, 3 the ri's and hk's of equations (4) and ~5) are calculated by the microprocessor structure of Fig. 3.
The next time through branch 147, with N equal to 1 6 (block 155), the microprocessor develops the equali ~tion con-7 stants ci by calculating successive iterations of the equations 8 (11) (12) (13) (14) ~15~ (16), pre~iously discussed.
9 With N - 2, the microprocessor structure of Fig. 3 begins to interact with the equalizer unit 34 in ~he following 11 manner. The microprocessor calculates equations (11) and tl2) 12 and then transfer the "r'~ matrix (equation 7) and other inter-13 mediate calculation results to the equalizer unit 34. In this 14 manner, the microprocessor shifts part of the calculation respon-~
sibility to the equalizer unit 34 in order to free the processor 16¦ to handle other operations on the incoming d~ta. The equalizer 17~ unit 34 contains hard wired logic which performs or calculates 18 I the subsequent iterations of equations (11) through (14~ For I N = 2, the ~lizer only calculates equations (13~ and (14)~ At 20 ~ the end of each calculation of an iteration of equations 21 through (14) in the ~qualizer unit 34, (13 and 14 only for N = 2) the processor calculates the quantity Zitl equations ~15~ and 23 (16), and returns that value to the equalizer 34 for performance 24 of the next-iteration of equations (11) through (14)~ This allocation of calculation between microprocessor and equalizer 26 unit is merely due to a desire to efficiently utilize the appara-27 tus. As is apparent, the assignment of the calculations of ~2 -24-,,, ? 157917 1 equations (11) through (14) to circuitry associated ~chematically 2 with the equalizer unit 34 i3 one approach to calculating the 3 instant equalizer settings. Other approaches such as utilization of a more powerful microprocessor to do all calculations ~ould be implemente~ according to the su~ject invention.
6 When N is equal to 15, the matrix has been solved for 7 the ~ap constants ck and the iteration done flag is set. When 8 the final tap constants are calculated, the hk's are stored and 9 the final equalizer constantæ ci determined according to the just described procedure are set~
11 The just discussed operation is sufficient to set 16 12 taps. I~ the line signal is of such a poor quality that addi-13 tional taps are needed, a fine tuning procedure may be performed 14 in which additional bauds of known two pha~e data are ~ent and the error difference detected and used to adjust the additional 16 taps according to conventional procedures.
17 A~ is indicated in the above discu~sion, many modifica-18 tions and adaptationQ of the preferred embodiment are possible 1~ without departing from ~he scope and spirit of the invention.
20¦ For example, as illustrated in Fig. 9, 10, and 11 the I in-phase and quadrature-phase signals used by the equalizer of the 22 ¦ invention may be derived other than at baseband and in systems 23 ¦ using various demodulation schemes~
l Fig~ 9 illustrates a simple quadrature demodulation 25 ¦ technique wherein baseband signals x(t) and y(t) constitute the 26 ¦ in-phase and quadrature-pha e signals. In Fig. 9, the received 27 ¦ 8~ gnal on an input line 201 i8 fed to first and second mixers ~ i 29¦
311 . ' .
.1 1 15791~

1 203, 205 wherein the line signal is mixed with respective signals 2 cos~ct and - sin~ct where ~c is the carrier frequency. The com-3 ponents are then filtered by respective baseband filters 207, 209 4 to yield the baseband quadrature components x~t) and y(t).
In ~ig. 10, the received signal is fed to a first pas-~-band filter 211 having an impulse response h(t) and to a second 7 passband filter 213 having an impulse response h(t), which is 8 the ~ilbert transform of the impu7se response h(t~ of the first 9 filter 2Il. The respective outputs h(t), h(t~ of the filters 211, 213 are at passband frequency and constitute in-phase and quadrature-phase signals which could be sampled by the equalizer 12 of the subject invention.
13 In Fig. 11, an output h(t) of the ilter 211 is fed to 14 a first mixer 215 and to a fourth mixer æl. The output h(t) of the filter 213 is fed to a second mixer 217 and to a third 16 mixer 219. The four mixers 2i5, 217, 219, 221 receive respec- !
~7 iive second inputs of cos~ct9 sin~ct~ cos~ct, C08~t~ where ~c 18¦ is the carrier frequency~ ~he outputs of ~he first and second 1~¦ mixers 215~ 217 are the~ summed by a summer 218 to give ~he ~emo-20¦ dulated baseband signal x(t~. The output of the rourth mixer 21 221 is subtracted from the ou~put of the third mixer 219 at a 22 summer 220 to give the demodulated baseband signal y(t). I~
23 Fig. 11, x(t~ and y(t). are.in-phase and quadrature-phase signals 24 which can also be samplèd according to the invention to accomplis~
initial setting of ~he equalizer taps~ ' 26 Therefore, it is to be understood that~ within the ., ;
27 scope of the appended claims~ the invention may be practiced otheJ
28 than as specifically described herein. ¦

.
31 . .

~2~1 -26-~ I

Claims (44)

The embodiments of the invention in which an exclusive property or privilege is claimed are defined as follows:

1. In combination with an equalizer means adapted to receive a first signal transmitted across a distorting medium said equalizer means having a plurality of taps settable for compensating for distortion in said first signal induced by said medium, the apparatus comprising:
means for generating a plurality of second signals representing samples of in-phase and quadrature-phase impulse response signals, said impulse response representing that of said distorting medium; and means operative upon said second signals to auto-correlate and cross-correlate said second signals, form elements of a matrix equation from the auto-correlated and cross-correlated said second signals, said elements including complex constants and complex variables, said variables defining the optimum initial setting for said taps, for iteratively calculating the exact values of said optimum initial settings utilizing said constants and for setting said taps to said exact values to produce a substantially distortion free signal.

2. The apparatus of Claim 1 wherein said means for generating produces said second signals from the received first signal.

3. The apparatus of claim 1 wherein said received signal in-cludes a training pattern waveform and wherein said means for generating includes:
means for forming said in-phase and quadrature-phase impulse response signals from said received signal and for sampling the in-phase and quadrature-phase impulse response signals at successive points to produce said second signals; and means for setting the successive points at which to sample the received first signal in response to said training pattern waveform.

4. The apparatus of claim 3 wherein the portion of the received first signal utilized to produce said second signals in a single received impulse response.

5. The apparatus of claim 4 wherein said received signal is quadrature amplitude modulated.

6. The apparatus of claim 1 wherein the received signal includes the response to a single transmitted impulse and said second signals are produced by sampling in-phase and quadrature-phase components of said response.

7. The apparatus of claim 6 wherein said exact values are calculated in a time less than the duration of said received impulse.

8. The apparatus of claim 6 further including means for detecting the said second signal closest to the peak of said impulse response and for subtracting the effect of particular said second signals on said elements based upon said location.

9. The apparatus of claim 6 wherein said received signal further includes a training waveform and wherein said apparatus further includes:
means for detecting the presence of said training waveform;
and means responsive upon detection of said training waveform to control the sampling points of said impulse response.

10. The apparatus of claim 9 wherein said detecting means comprise:
means for forming an arc tangent from the samples produced by said sampling during transmission of said training waveform; and means for testing successive values of said arc tangent to confirm that said training waveform is present.

11. The apparatus of claim 10 wherein said training waveform includes a carrier-only period and wherein said arc tangent forming means operates on samples taken during said carrier-only period.

12. The apparatus of claim 9 wherein said sampling control means comprises:
a sampling clock;
means for determining the phase angle error of said clock from the samples produced by said sampling during transmission of said training waveform; and means for adjusting the phase of said clock to compensate for said error.

13. The apparatus of claim 12 wherein said means for determining said phase angle error tests successive arc tangents generated from successive samples produced by said sampling.

14. The apparatus of claim 13 wherein said testing determines whether said arc tangent is in a defined range for a plurality of intervals of a clock-only signal.

15. The apparatus of claim 14 wherein successive arc tangents are averaged to determine said phase angle error if said arc tangent is determined to be within said defined range for said plurality of intervals.

16. The apparatus of claim 14 further including means for determining the phase angle error if said arc tangent is not within said defined range for said plurality of intervals.

17. Apparatus adapted for use as an equalizer comprising:
first means for connection to a communication channel said first means including a plurality of taps settable for compensating for distortion in said channel; and second means for producing a plurality of successive samples of signals representing in-phase and quadrature-phase components of the impulse response of said channel and for operating upon said samples to form elements of a matrix equation from said samples, to iteratively calculate the exact values of the optimum settings for said taps utilizing said elements, and to set said taps to said optimum values, wherein said samples are both auto-correlated and cross-correlated and wherein said matrix equation includes complex constants and complex variables.

18. Apparatus adapted for use as an equalizer comprising:
a first means for connecting to a communication channel, said first means including a plurality of taps settable for compensating for distortions in said channel; and second means for producing a plurality of successive samples of first and second signals representing the impulse response of said channel and for operating upon said samples to form elements of a matrix equation from said samples, to iteratively calculate the exact values of the optimum settings for said taps utilizing said elements, and to set said taps to said optimum values, wherein said successive samples are derived from a received test impulse and wherein said exact values are calculated in a time less than the duration of said received test impulse.

19. An equalizer for equalizing to a training waveform and received impulse response comprising:
means for connecting to a communication channel and having a plurality of taps settable for compensating for distortion in said channel;
means for detecting the presence of said training waveform and for initiating a sampling count;
means for adjusting said sampling count in response to said training waveform;
means for forming in-phase and quadrature-phase impluse response signals from said received impulse response;
means for sampling said in-phase and quadrature-phase signals in accordance with the adjusted sampling count to produce a plurality of samples;
means for storing said samples;
means for correlating said samples;
means for utilizing said correlated samples in a set of iterative calculations to obtain the exact values of the optimum setting for said taps; and means for setting said taps to said optimum values.

20. The equalization apparatus comprising:
means for receiving signals transmitted across a distorting medium and having a plurality of tap coefficients settable for compensating for distortion in said signals inducea by said medium;
means responsive to a training signal containing therein the response of said medium to only one transmitted impulse for sampling said response to produce a plurality of impulse response samples;
means operative upon said impulse response samples to auto-correlate and cross-correlate said samples, form elements of a matrix equation from the auto-correlated and cross-correlated samples, said elements including complex constants and complex variables, said variables defining the optimum initial settings for said tap coefficients, for iteratively calculating the exact values of said optimum initial settings utilizing said constants, and for setting said tap coefficients to said exact values to substantially remove said distortion.

In a data communication system, the process for achieving initial adjustment of an equalizer in a receiver adapted to receive a signal containing distortion comprising:
providing said receiver with an initial training waveform including the response to only one transmitted impulse;
sampling the impulse response to produce a plurality of impulse response samples;
deriving the exact initial settings for the tap coefficients of said equalizer from said samples; and setting the coefficients of said equalizer to said values to substantially eliminate said distortion.

22. In combination with an equalizer means adapted to receive a first signal transmitted across a distorting medium, said equalizer means having a plurality of taps settable for compensating for distortion in said first signal induced by said medium, the apparatus comprising:
means for generating a plurality of second signals representing samples of in-phase and quadrature-phase impluse response signals, said impulse response representing that of said distorting medium; and means operative upon said second signals to auto-correlate and cross-correlate said second signals, form elements of a matrix equation from the auto-correlated and cross-correlated said second signals, said elements including complex constants and complex variables, said variables defining the optimum initial settings for said taps, for iteratively calculating the exact values of said optimum initial settings utilizing said constants in N iterations for an NxN matrix and for setting said taps to said exact values to produce a substantially distortion free signal.

In combination with an equalizer means adapted to receive a first signal transmitted across a distorting medium, said equalizer means having a plurality of taps settable for compensating for distortion in said first signal induced by said medium, the apparatus comprising:
means for generating a plurality of second signals representing samples of in-phase and quadrature-phase impulse response signals, said impulse response representing that of said distorting medium; and means operative upon said second signals to auto-correlate and cross-correlate said second signals, form elements of a matrix equation from the auto-correlated and cross-correlated said second signals, said elements including complex constants and complex variables, said variables defining the optimum initial settings for said taps, for iteratively and nonconvergently calculating the exact values of said optimum initial settings utilizing said constants and for setting said taps to said exact values to produce a substantially distortion free signal.

24. Data receiver apparatus adapted to receive a training pattern and impulse response, the apparatus comprising:
means adapted for connection to a communication channel and having a plurality of coefficients settable for compensating for distortion in the channel;
a sampling clock;
means for detecting the presence of the training pattern and for initiating counting by the sampling clock;
means for adjusting the sampling clock in response to the training pattern;
means for forming in-phase and quadrature-phase impulse response samples from the received impulse response and utilizing the adjusted sampling clock;
means for storing the samples;
means for correlating the samples;
means for utilizing the correlated samples in a set of iterative calculations to obtain the exact values of the optimum settings for the coefficients; and means for setting the coefficients to the optimum values.

25. The data receiver apparatus of claim 24 wherein said training pattern includes a carrier-only signal and said means for detecting the presence of the training pattern comprises:
means for deriving a series of angles from the received signal;
means for forming a plurality of difference values from a series of angles derived from the carrier-only signal by said means for deriving; and means for testing said difference values to determine whether a plurality of said difference values are within a selected first range and for producing a signal indicating said carrier signal is present upon detection of a selected number of said difference values being in range.

26. The apparatus of claim 25 wherein said difference values are formed by subtracting each angle derived from the carrier-only signal from 90°.

27. The apparatus of claim 26 wherein said first range is 0. to 15°.

28. The apparatus of claim 24 wherein said testing means is further operative to detect the number of angles outside of said first range and, after a first selected number of angles have been tested and a second selected number are detected outside of said-first range, to produce a signal indicating carrier-only is not present.

29. The apparatus of claim 24 or 25 wherein said training pattern includes a clock-only signal and wherein said means for adjusting the sampling count comprises:
means for deriving a series of angles from clock-only signal;
means for forming the difference between a plurality of pairs of said angles; and means for testing a plurality of said differences to ascertain whether each tested difference is within a selected second range and responsive to said testing to produce a correction value for adjusting the timing of said sampling signal.

30. The apparatus of claim 24 or 25 wherein said training pattern includes a clock-only signal and wherein said means for adjusting the sampling count comprises:
means for deriving a series of angles from clock-only signal;
means for forming the difference between a plurality of pairs of said angles; and means for testing a plurality of said differences to ascertain whether each tested difference is within a selected second range and responsive to said testing to produce a correction value for adjusting the timing of said sampling signal, said correction value being produced by averaging said selected differences by the testing means.

31. The apparatus of claim 24 or 25 wherein said training pattern includes a clock-only signal and wherein said means for adjusting the sampling count comprises:
means for deriving a series of angles from clock-only signal;
means for forming the difference between a plurality of pairs of said angles; and means for testing a plurality of said differences to ascertain whether each tested difference is within a selected second range and responsive to said testing to produce a correction value for adjusting the timing of said sampling signal, said correction value being produced by averaging said selected differences by the testing means wherein, if testing of said differences indicates the sampling signal is not within the selected second range, said testing means performs a plurality of further tests to establish said correction value.

32. The apparatus of claim 24 or 25 wherein said training pattern includes a clock-only signal and wherein said means for adjusting the sampling count comprises:
means for deriving a series of angles from clock-only signal;
means for forming the difference between a plurality of pairs of said angles; and means for testing a plurality of said differences to ascertain whether each tested difference is within a selected second range and responsive to said testing to produce a correction value for adjusting the timing of said sampling signal;
said correction value being produced by averaging said selected differences by the testing means wherein, if testing of said differences indicates the sampling signal is not within the selected second range, said testing means performs a plurality of further tests to establish said correction value, and if said testing means detects a first condition wherein a first selected number of differences lies within said second range and at least one lies outside of said second range, said correction value is set equal to a first average of a second selected number of differences within said second range.

33. The apparatus of claim 24 wherein said training pattern includes a clock-only signal and wherein said means for adjusting the sampling count comprises:
means for deriving a series of angles from clock-only signal;
means for forming the difference between a plurality of pairs of said angles; and means for testing a plurality of said differences to ascertain whether each tested difference is within a selected second range and responsive to said testing to produce a correction value for adjusting the timing of said sampling signal;
said correction value being produced by averaging said selected differences by the testing means wherein, if testing of said differences indicates the sampling signal is not within the selected second range, said testing means performs a plurality of further tests to establish said correction value, and if said testing means detects a first condition wherein a first selected number of differences lies within said second range and at least one lies outside of said second range, said correction value is set equal to a first average of a second selected number of differences within said second range, and wherein under said first condition, said testing means alternatively may set said correction value to the value of the sign of a second average of a number of said differences within range multiplied by the difference between a constant and the magnitude of said second average.

34. The apparatus of claim 33 wherein said testing means is responsive to a second condition to set said correction value equal to the most recently determined said difference.

35. The apparatus of claim 24 wherein said set of iterative calculations is non-convergent.

36. The apparatus of claim 24 or 35 wherein said samples are used by said means for utilizing to form elements of an N X
N matrix and said calculations are performed by said means for utilizing in N iterations.

37. The apparatus of claim 25 wherein said means for detecting the presence of a training pattern utilizes two in-phase samples and two quadrature-phase samples per baud to derive said angles from the carrier-only signal.

38. The apparatus of claim 37 wherein said means for detecting the presence of a training pattern derives said angle by evaluating the inverse trigonometric function of an argument which is the quotient of two quantities formed from samples.

39. The apparatus of claim 38 wherein the inverse trigonometric function is the arc tangent function.

40. The apparatus of claim 38 wherein the inverse trigonometric function is:
On=tan-l where On is the derived angle, Xn is an in-phase sample taken at sample time "n", Yn is an quadrature phase sample taken at the sample time "n" and "n-l" indicates a sample taken at the sample time immediately preceding sampling time "n".

41. The apparatus of claim 24 or 25 wherein said training pattern includes a clock-only signal and wherein said means for adjusting the sampling count comprises:
means for deriving a series of angles from clock-only signal;
means for forming the difference between a plurality of pairs of said angles; and means for testing a plurality of said differences to ascertain whether each tested difference is within a selected second range and responsive to said testing to produce a correction value for adjusting the timing of said sampling signal, said angles being derived from the clock only signal by said means for adjusting the sampling count using two in-phase samples and two quadrature-phase samples per baud.

42. The apparatus of claim 24 or 25 wherein said training pattern includes a clock-only signal and wherein said means for adjusting the sampling count comprises:
means for deriving a series of angles from clock-only signal;
means for forming the difference between a plurality of pairs of said angles; and means for testing a plurality of said differences to ascertain whether each tested difference is within a selected second range and responsive to said testing to produce a correction value for adjusting the timing of said sampling signal, said angles being derived from the clock only signal by said means for adjusting the sampling count using two in-phase samples and two quadrature-phase samples per baud, wherein said means for adjusting the sampling count derives said angles by evaluating the inverse triogonometric function of an argument which is the quotient of two quantities formed from said samples.

43. The apparatus of claim 24 or 25 wherein said training pattern includes a clock-only signal and wherein said means for adjusting the sampling count comprises:
means for deriving a series of angles from clock-only signal;
means for forming the difference between a plurality of pairs of said angles; and means for testing a plurality of said differences to ascertain whether each tested difference is within a selected second range and responsive to said testing to produce a correction value for adjusting the timing of said sampling signal, said angles being derived from the clock only signal by said means for adjusting the sampling count using two in-phase samples and two quadrature-phase samples per baud, wherein said means for adjusting the sampling count derives said angles by evaluating the arc tangent function of an argument which is the quotient of two quantities formed from said samples.

44. The apparatus of claim 24 or 25 wherein said training pattern includes a clock-only signal and wherein said means for adjusting the sampling count comprises:
means for deriving a series of angles from clock-only signal;
means for forming the difference between a plurality of pairs of said angles; and means for testing a plurality of said differences to ascertain whether each tested difference is within a selected second range and responsive to said testing to produce a correction value for adjusting the timing of said sampling signal, said angles being derived from the clock only signal by said means for adjusting the sampling count using two in-phase samples and two quadrature-phase samples per baud, wherein said means for adjusting the sampling count derives said angles by evaluating the arc tangent function of an argument which is the quotient of two quantities formed from said samples, wherein the said arc tangent function is On=tan-l where On is the derived angle, Xn is an in-phase sample taken at sample time "n", Yn is an quadrature-phase sample taken at the sample time "n" and "n-l" indicates a sample taken at the sample time immediately preceding sampling time "n".