CA2158014C - Adaptive noise-predictive partial-response equalization for channels with spectral nulls - Google Patents

Abstract

The present application makes use of a novel adaptive noise-predictive parti al-response equalization scheme for channels (30) exhibiting spectral nulls and/or near nulls. The noise-predictive partial re sponse (PR) equalizer employed in the different embodime nts of the present invention consists of a linear PR equalizer (32) which shapes the channel response to a predetermined partial-respons e function, followed by a linear predictor. This scheme modifies the output se quence of said linear partial-response equalizer (32) by whitening the total distortion, i.e. by whitening the noise components and t he residual interference components at said linear PR eq ualizer output, thereby achieving the best possible signal-to-noise ratio (SNR) befo re detection.

Description

WO 94/29989 ~15 8 0 14 PCT/EP93/01500 DESCRIPTION

Adaptive Noise-Predictive Partial-Response ~qualization for Channels with Spectral Nulls TECHNICAL FIELD

The present invention concerns a method and apparatus for digital information transmission over channels with spectral nulls or near nulls, making use of a novel adaptive noise-predictive partial-response equalization scheme. Typic~l channels exhibiting spectral nulls or near nulls are wire transmission an~ magn~tic recording channels.

BACKGROUND OF THE INVENTION

In many practical digital information transmission systems including magnetic recording systems, the frequency response of the channel exhibits spectral nulls and/or near nulls. For example, wire pair or twisted-pair subscriber loops terminated by transformers exhibit a spectral null at dc and strong attenuation at high frequencies, i.e. the corresponding frequency response 10 has a null at dc (f = 0) and a near null at high frequencies, as shown in Figure 1. The ftequency response of the magnetic recording channel has similar characteristics due to the magnetic head. It is known in the art, that receivers which employ nonlinear decision-feedback equalizers (DFE) cope more effectively with channels having spectral nulls than receivers employing linear transversal Nyquist equalizers. Furthermore, a decision-feedbaclc equalizer ccmpensates more easily for the postcursor intersymbol-interference (ISI~ such as the one caused by the presence of bridged taps in the subscriber loop plant. Examples of test loops with bridged taps can be found in the American National Standard for Telecommunications "Integrated Services Digital ~letwork (ISDN) - Basic ~ccess Interface for Use CO~lrlR~.lAtlON COP~

WO 94/29989 . PCT/EP93/01500 215~01~ 2 on Metallic Loops for Application on the Network Side of the NT (Layer 1 Specification)", ANSI Document T1.601, 19~8.

A multiplication-free compromise decision-feedback equalizer with fixed forward and adaptive feedback sections has been described in "Full-Duplex Data Over Local Loops", N.-S. Lin et al., IEEE Communications Magazine, Vol.
26, No. 2, pp. 31 - 42, 1988. Another decision-feedback equalizer whose coefficients are updated by the sign algorithm has been proposed in "A Long Reach Digital Subscriber Loop Transceiver", P.F. Adams et al., Br.
Telecommunications Journal, Vol. 5, No. 1, pp. 2~ - 31, 1987.

The application of adaptive decision-feedback equalization in the magnetic recording channel has been discussed in the tutorial article "Adaptive Equalization in Magnetic-Disk Storage Channels", J.M. Cioffi et al., IEEF
Commmunications Magazine, Vol. 28, No. 2, pp. 14 - 29, 1990.

Linear partial response tPR) equalization followed by Viterbi detection is an alternative to I~FE and symbol-by-symbol detection. A partial response maximum likelihood (PRML) system for the magnetic recording channel has been described in "A PRMI System for Digital Magnetic Recording", R.D.
Cideciyan et al., IEEE Journal on Selected Ar~as in Communications, Vol. 10, Nc. 1, pp. 38 - 56, January 1992.
In US Patent 4 571 734 with title "Method and Apparatus for Decoding the Output of a Partial-Response Signal of a Partial-Response Class-lV
Communication or Recording Device Channel", issued 18 February 1986, the implementation of PR Viterbi detectors for partial response systems is described .

In US patent ~ 031 195, with title "Fully Adaptive Modem Receiver Using Whitening Matched Filtering", issued 9 July 1991, a modem (modulator-demodulator) receiver is disclosed which comprises a whitened-matched filter (WMF) 20, a Viterbi decoder Z1, and an intersymbol interference (ISI) coefficient estimator 22, as illustrated in Figure 2. Some 2 ~ 5 8 ~ ~ ~ PCT/EP93/01500 details of the operation of said modem receiver when receiving TCM (Trellis Coded Modulation) signals are described below with reference to Figure 2.

An analytic passband signal Yk, which is sampled with a sample rate s/T, is fed into said WMF 20. The WMF 20 mainly consists of a minimum mean-squared error linear equalizer 23, with fractional-T spaced coefficients {c,}, whose output signal Zk iS input to multiplication means 26 for the correction of the carrier phase offset. The signal Zk' after carrier phase offset correction is fed into a linear predictor Z4. This linear predictor 24 is operated as a whitening filter by adding the predictor's output 25 signal Zk'' to Zk' Theresulting signal vk is fed to a Viterbi decoder 21 to determine the TCM
encoded sequence {ak~ and to make it available, after some delay ~s at the output 27. The linear equalizer 23 first eliminates the ISI in a mean-squared error sense and the predictor 24 subsequently whitens the noise and the residual ISI components of the equalized output signal Zk~- It is mentioned in this US patent that the WMF 20 can be made adaptive by updating the equalizer coefficients {ci} and predictor coefficients {p,~ using the error si~nals ek' and ek, respectively, as indicated by the dashed lines in Figure 2. Both error signals are formed by using zero-delay tentative decisions âk released by the Viterbi detector 21 at the output line 28. The prediction error ek is obtained using the ISI coefficient estimator 2Z receiving said zero-delay tentative decisions âk-This fully adaptive modem receiver is not suited for use in channels exhibitingspectral nulls or near nulls. The reason is that the linear equalizer 23 in Figure 2 in its attempt to invert the channel frequency response, would lead to severe noise enhancement. Note that for channels with spectral nulls a linear equalizer optimized under a zero-forcing criterion cannot be defined, since inversion of a spectral null leads to an undefined operation.

Linear PR equalizers such as the ones described in the article "A PRML
System for Digital Magnetic Recording", R.D. Cideciyan et al., IEEE Journal on Selected Areas in Communications, Vol. 10. No. 1, pp. 38 - 56, January 1992.

WO 94/29989 PCT/EP~3101500 21~14 alleviate the problem of invelting a spectral null. However, linear equalizationleads to substantial noise-enhancement due to the mismatch between the actual channel frequency response characteristics 10 and the desired PR
shape 11, in Figure 1.

It is an object of the present invention to provide a method and apparatus for improving the performance of PR systems such as PR data transmission systems or PR magnetic recording systems.

It is an object o~ the present invention to provide a method and apparatus for improved and reliable transmission and detection of data over a channel exhibiting spectral nulls and/or near nulls.

It is another object of the present invention to provide a method and apparatus which can be employed in a conventional transmission system comprising a linear partial-response equalizer and a PR Viterbi detector to enhance performance.

SUMMARY OF THE INVENTION

The above objects have been accomplished by making use of a novel adaptive noise-predictive partial-response equalization scheme for channels exhibiting spectral nulls and near nulls. The noise-predictive partial-response (PR~
equalizer employed in the different embodiments of the present invention consists of a linear PR equalizer which shapes the channel response to a predetermined partial-response function, followed by a linear predictor. In systems employing a PR Viterbi detector reliable operation is achieved by using decisions from the path memory of the VTterbi detector, i.e. by imbedding the prediction process into the Viterbi detector, thus obtaining a modified sequence estimator with PR Viterbi detector. This scheme modifies the output sequence of said linear PR equalizer by whitening the total distortion, i.e. by whitening the noise components and the residual Wo 94/29g89 21 S 8 014 5 PCT/EP93/01500 interference components at said linear PR equalizer output, thereby achieving the best possible signal-to-noise ratio (SNR) before detection. The performance of conven~tional partial-response systems, e.g. of the magnetic recording system claimed in US patent 4 571 734, can always be substantially improved by attaching said linear predictor.

Some conceptuai aspects of the present invention, i.e. of the adaptive noise-predictive partial-response equalization scheme, have been published by the inventors themselves at the IEEE International Conference on Communications (ICC), 14 June 1992 till 18 June 1992, Chicago, IL. The presentation took place on 15 June 1992. A reprint of this presentation has been published by the IEEE Communications Society, 345 East 47th Street, New York, NY 10017, U.S.A entitled "Noise-Predictive Partial-Response Equalizers and Applications", P.P~. Chevillat, E. Eleffheriou, and D. Maiwald.
With regard to this publication, claims 1 through 15 are enclosed for the United States Gf America, and a second set of claims, in particular claims 2 through 15, for all other countries than the United States of America. The firstset of claims is deemed to be allowable in the United States of America since the present application has been filed within the 12 months grace period after the date of publication.

At this conference a receiver in a data transmission system for the reception of uncoded data sequences has been published, said receiver comprising the inventive noise-predictive partial-response equalizer. Said disclosed receiver consists of a PR shaping linear equaiizer and a noise-whitening predictor.
Reliable operation of this receiver is achieved by using in the predictor decisions from the path memory of a PR Viterbi detector. The text of the presentation, as it has been reprinted in "Noise-Predictive Partial-Response Equalizers and ApplicatTons", P.R. Chevillat, E. Eleftheriou, and D. Maiwald., by IEEE Communications Society, 34~ East 47th Street, New York, NY 10017, U.S.A., is made part of the detailed description.

, DESCRIPTION OF THE DRAWINGS
AND NOTATIONS USED

The invention is described in detail below with reference to the following drawings:

FIG. 1 shovils the frequency response of a channel exhibiting a spectral null and a partial-response class-lV transfer function.

FIG. 2 shows a schematic block diagram of a fully adaptive modem receiver (Prior Art).

FIG. 3 shows a schematic block diagram of a data transmission system, in accordance with the first embodiment of the present invention, which has been derived from the data transmission system presented at the 1992 IEEE International Conference on Communications.

FIG. 4 shows a schematic block diagram of a partial-response Viterbi detector employed in the first embodiment.

FIG~ 5 shows an adaptive modem receiver based on the first embodiment FIG. 6 shows an example of a 4-s~ate subset trellis for a quaternary alphabet on which the PR Vilerbi detector of the first embodiment operates.
-FIG. 7 shows a schematic block diagram of a data transmission system, in accordance with the second embodiment of the present invention.

WO 94/29989 ~ l ~3 8 ~ 1 ~ PCT/EP93/01500 FIG. 8 shows an adaptive modem receiver based on the second embodiment FIG. 9 shows a schematic diagram of a magnetic recording system.

xk information or data symbol {xk} discrete time digital information sequence x(D) D-transform representing {xk~

xk(,uk) data symbol estimate taken from the path memory associated with state ~Ik GENERAL DESCRIPTION

The first embodiment of the present invention which is based on the data transmission system disclosed at the 1992 IEEE International Conference on Communications is described in greater detail below, with reference to Figures 3 - 6. The relevant sections of the article "Noise-Predictive Partial-Response Equalizers and Applications", of P.R. Chevillat, E. Eleftheriou.
and D. Maiwald.. reprinted by IEEE Communications Society, 345 East 47th Street, New York, NY 10017, IJ.S.A., have been incorporated, accordingly. The inventive noise-predictive partial-response equalizer, as part of a receiver of a digital information transmission system, is illustrated in Figure 3.

Let the data symbol Xk take on values from an equally spaced M-level alphabet as for example: + 1, + 3, + (M--1) if M is an even number, and WO 94/29g89 PCT/EPS3tO1500 O, + 2, + (M--1) if M is an odd number. The M-ary digital information sequence {Xk~ transmitted via the channel 30 is represented by the D-transform x(D) = ~;kxkDk- The transmitted digital information sequence is assumed to be uncorrelated with average symbol energy ~Jx and symbol rate 1/T. The inventive receiver obser~.~es a signal emerging from a linear dispersive channel which adds white Gaussian noise. The discrete-time channel autocorrelation coefficients are denoted by R"(k), and the power spectral density of the additive noise is N~. After symbol-rate sampling (sample rate 1/T) at the output of a matched filter 31, the digital information sequence {Yk~ with D-transform y(D) enters a PR linear equalizer 32 with transfer function d(D) . The coefficients ~d,} of the PR equalizer 32 are optimized such that the overall transfer function, including channel 30 and matched filter 31, closely matches a desired PR transfer function f(D) having appropriate nulls where the channel has spectral nulls and/or near nulls, i.e.

f(D) = ~ fj Di . (1) i=o In the correlative coding literature the coeflicients {f~} are usually restricted to integers with a greatest common divisor equal to one. Here we assume that the {fj} can take on any real value as is the case in generalized PR systems.
The discrete time output sequence of the PR equalizer 3Z is given by z(D) = x(D~f(D) J.- n(D), (2) where n(D) represents the total distortion, i.e. the noise and residual interference components. The predictor 35, operating as a whitening filter, subsequently whitens and reduces the total distortion, and the resulting sequence, w(D) = x(D)f(D) -~ e~D), (3) WO 94/29989 ~ 1 ~i g 0 14 PCT/EP93/01500 hereinafter referred to as modified discrete time sequence, enters the partial-response Viterbi detector 33 which estimates the original, i.e. the transmitted digital information sequence x(D). The combination of the linear PR equalizer 32 with the noise predictor 35 is called a noise-predictive PR
equalizer. Note that the sequence e(D) in (3), although white, is not necessarily Gaussian. In the following sections the zero-forcing and minimum mean square error (MMSE) noise-predictive partial-response equalization are described .

Zero-Forcing Formulation The coefficients of an infinitely long linear equalizer can be selected such that the overall impulse response at the output of this equalizer satisfies exactly the PR transfer function in (~). In other words the intersymbol interference (ISI) is restricted to a known amount that spans L symbol intervals and is zero elsewhere. The zero-forcing PR equalizer transfer function will then be d(D! = S (D) ' (4) where Sh(D) is the D-transform of Rh(k). The existence of nulls and/or near nulls in the channel frequency response (see curve 10 in Figure 1 ) will be reflected in the PR transfer function (curve 11 in Figure 1 ) by placing appropriate zeros in f(D). Equation t4) is still well defined by simply transferring the zeros from the matched filter 31, in Figure 3, into the transfer function d(D) of the PR equalizer 32. For example, if the channel frequency response has an l-th order null at dc and an m-th order null at half the symbol frequency, then an appropriate selection is f(D) = (1--D)'(1 + DJm. The cases I = m = 1 and I = 1, m = 2 are of practical significance in wire transmission and magnetic recording. The first case is known in the technical literature as partial-response class-lV (PR-IV), whereas the latter case is known as extended partial-response class-lV (EPR-IV). In a zero-forcing formulation the WO 94/29g89 , PCT/EP93/01~;00 sequence n(D) is a filtered version of the additive white Gaussian noise sequence. The autocorrelation function of n(D) is Sn(D) = ( ) (D) ) No (5) The power of the noise sequence n(D) can be reduced by linear prediction.
A linear predictor 35 with coefficients {qj~ operating on the noise sequence n(D) will produce the estimate R(D), where the prediction-error sequence is given by e(D) = n(D) + n(D) = n(D)(1 + q(D)) (6) The optimum predictor q(D) = q, D + q2D2+ ..., which minimizes the mean-square error ~ = E{ ¦ ek¦ 2} iS given by q(D) = b(D)/bo --1, where b(D) is the minimum phase causal factor of 1/Sn(D). Assuming that f(D) is minimum phase, one readily finds that the minimum achievable mean-square error min is given by { 27r J ~ Sh(ei) }

For PR functions with fO= 1 which includes the impor~ant class (1--D)'(1 + D)m, equation (7) reduces to an expression which is identical to the minimum mean-square error (MMSE) of a known infinitely long zero-forcing decision-feedback equalizer (DFE~, as for example described in "Adaptive equalization", S.U.H. Qureshi, Proceedings of the IEEF, Vol. 73, No.
9, pp. 1 349 -1 387 , Sept. 1 985 .

WO 94/29g8g 213 ~ 014 PCT/EP93/01500 Minimum Mean-Square Error (MMSE) Formuiation The transfer function of an infinitely long PR linear equalizer based on the MMSE criterion is d(D) = ~2 f(D) (8) ~x Sh(D) -~ No The sequence n(D) now represents the total distortion at the output of the PR
equalizer 32. It consists of a filtered noise component and a residual interference component. It can be shown that the autocorrelation function of n(D) in the MMSE case is given by Sn(D) = 2 S (D) N No (9) Therefore, the MMSE predictor for the total distortion sequence n(D) is given by q(D)= b(D)/bo --1, where b(D)b~ ')= 1/Sn(D). Assuming now that f(D) is minimum phase, one finds = Ifol exp{ 2~ n ~2Sh(ei~')+No }

Clearly, for fO = 1 the expression for n,jn of an MMSE noise-predictive PR
equalizer is identical to the MMSE of an inflnitely long MMSE DFE, as for example described in the above mentioned article of S.U.H. Qureshi.

Note that in the MMSE formulation of the noise-predictive PR equalizer, selecting f(D) to have roots on the unit circle may yield a q(D) which is not realizable, i.e. its coefficients are not square-summable. This could occur WO 94129989 PCT/EP93/01500 ~
2 ~ 12 even if the zeros of the PR transfer function f(D) are located at those frequencies where the channel has spectral nulls and/or near nulls. The non-square-summable condition can be eliminated by moving the zeros infinitely close to the unit circle.

Modified Sequence Estimator It is clear from the discussion in the previous sections that an ideal noise-predictive PR equalizer (using perfect past decisions in the noise predictor) can decorrelate and significantly reduce the total distortion power at the input of the partial-response Viterbi detector 33. Unfortunately, zero-delay tentative decisions x(D) from the PR Viterbi detector 33, furnished at output 38, are usually unreliable in practical applications. Reliable operation of the noise-predictive PR equalizer is achieved by using decisions from the path memory of the PR Viterbi detector 33, i.e. by imbedding the prediction process into the PR Viterbi detector. The combination of the PR
Viterbi detector 33, the partial response filter 34 with coefficients {f,}, and the imbedded predictor 35 with coefficients ~qj~ is hereinafter called modified sequence estimator with PR Viterbi detector 36, as shown in Figure 3.

Let ~Ik = (Xk-~ Xk-2~ ..., Xk-L) at tlme k denote one of the M' possible states of the PR Viterbi detector 33. The modified sequence estimator with PR Viterbi detector 36 will then use the following branch metric associated with state ~Lk k(~k) = I Zk + ~ q; (Zk_; ~ fJxk_j_j(,uk)) ~ fjxk--j ¦ (11) j=o j=o where xk ~ uk) denotes data symbol decisions taken from the path memory associated with state ~Ik- The second term on the right hand side of equation (11) is indicative of the prediction process imbedded into the PR Viterbi detector 33. Equivalently, the branch metric in (11) can be written as WO 94/29989 ~15 8 014 PCT/EP93/UI500 k(~k) = I Wk(~k)--~ fjxk--; ¦ . (1Z) j=O

For notational simplicity, the sequences ~xk(,uk)} and {wk~,uk)} are representedin Figure 3 by x(D? and w(D), respectively. In Figure 3, the dependency of the digital sequences {Xk} (or x(D)) and ~Wk~ (or w(D)) on the path memory associated with state ,Uk is indicated by thick solid lines.

Having specified the new branch metric in (11) or (12), the modified sequence estimator with PR Viterbi detector 36 proceeds recursively as is described in the US patent 5 031 195, with titie "Fully Adaptive Modem Receiver Using Whitening Matched Filtering", issued 9 July 1991.

A schematic diagram of the partial-response Viterbi detector 33 is shown in Figure 4. This PR detector 33 comprises a subset decoder 40, a branch metric computation and decision uni~ 41, a survivor path memory 42, and a path decoder unit 43. These four units of the PR Viterbi detector 33 reflect that thedetection process can, in general, be decomposed into ~our parts. For the magnetic recording channel where the signalling alphabet is restricted to be +1, the subset decoder unit 40 can be omitted. In data transmission applications over wires where a multilevel signal alphabet is used, the subset decoder 10 offers a trade-off between performance and PR Viterbi detector state complexity.

For example, in quaternary 2~ (two binary, one quaternary). i.e. +1, +3, transmission over wires and PR class-lV (f(D) = 1--D2) shaping at the receiver a 16-state PR Viterbi detector is required. The PR Viterbi detector state complexity can be reduced by usin~ the subset state concept as is described in US patent 5 031 195. In this case. the PR Viterbi detector 33 operates on the 4-state subset trellis for a quaternary alphabet, shown in Figure 6. The newbranch metric for the modified sequence estimator with PR Viterbi detector 36 will then become 'lk(~Uk) = I Z~C + ~ qi (Zk--i Xk~ Uk) + Xk--i--2(~Uk)) Xk(~lk) + Xk--2(~k) ~ 3) Implementation of Adaptive Receiver In practical applications, the PR linear equalizer and noise predictor have finite lengths. For known channel characteristics the coefficients of a finite-length noise-predictive PR equalizer can be obtained by solving two sets of equations separately. In a first step the optimum coefficients of a finite-length PR linear equalizer are obtained. The predictor coefficients are then the solution of the well-known normal equations. The PR linear equalizer can be implemented as a T-spaced or fractionally-spaced equalizer. If the transmitter puls shaping filter has excess bandwidth then a fractionally-spaced equalizer makes the receiver insensitive to the sampling phase. For unknown and slowly time-varying channels standard adaptation algorithms can be applied. The adaptation algorithms can operate in reference-directed or decision-directed mode.

An adaptive modem receiver based on the first embodiment is shown in Figure 5. It consists of an MMSE linear partial-response equalizer 32 with T-spaced coefficients {d,} of plurality N, ~- 1, a predictor-coefficient estimator 50, a partial-response filter 39 with coefficients {fj} of plurality L+1, and a modified sequence estimator with PR Viterbi detector 36. After rate-1/T
sampling at the output of the matched filter 31. see Figure 3, the sequence of samples {Yk}. with D-transfonn y(D), enters the equalizer 3Z. The partial-response equalized samples Zk are then fed into the modified sequence estimator with PR Viterbi detector 36. The predictor-coefficient estimator 50 provides the set of predictor coefficients ~q,} of plurality N2 which will be used in the branch metric computation of the modified sequence estimator with PR
Viterbi detector 36.

WO 94/29989 ~ 1 ~ 8 ~ ~ ~ PCT/EP93/01~00 1~

The partial-response equalizer 32 and the predictor-coefficient estimator 50 can be made adaptive using the error signal ek -- Zk rk = Zk ~ fjxk_j (14) i=o for adjusting the PR equalizer coefficients ~d,~, and the prediction error ek = ek + ~ qje k--i (15) i=, for updating the predictor coefficients ~q,~. As indicated by the dashed lines in Figure ~, the error signals ek and ek' are furnished to 3Z and 50 for updating the coefficients. The symbols xk are either known reference symbols used during the training mode, or tentative decisions obtained from the modified sequence estimator with PR Viterbi detector 36 during the data transmission mode. Note that (1~) describes the predictor operation as that of a whitening filter operating on the equalizer-error sequence {ek'~ . Thus, the PR equalizer 32 and predictor coefficient estimator ~0 of the noise predictive PR equalizer in the first embodiment are adjusted according to the following gradient algorithms dj(k + 1) = dj(k)--Uek'Yk~ = 0,1, -, N1 (16) qj(k + 1) = qj(k)--~ek(zk_;--rk_j), i = 1, 2, ~ N2' (17) where a and ~ are adaptation parameters, and rk is defined in (14).

WO 94/29989 PCT/EP93/01500 ~
~1~8~ ~ 16 SECOND EMBODIMENT

In the following, a second embodiment of the present invention is described with respect to Figures 7 and 8. This embodiment is herein referred to as adaptive partial-response whitened matched filter (PR WMF) receiver. This receiver consists of a PR-WMF 82 followed by a modified sequence estimator with Viterbi detector 76. After matched ~TItering in 71 and sampling, a sequence of samples ~Yk}. or equivalently in the D-trans~orm domain y(D), enters the linear PR equalizer 72 at a rate 1/T. The discrete time PR equalized sequence z(D) is given by z(D) = x(D)f(D) + n(D), (18) where as before n(D) represents the total distortion. The predictor 81, operating as a whitening filter, subsequently whitens the noise and the residual ISI components of the PR equalized sequence z(D). In view of (6), (18) and the configuration in Figure 7, the output sequence v(D) can be written as v(D) = [x(D)f(D) + n(D)] [1 + q(D)] = x(D)f(D) + x(D)f(D)q(D) + e(D), (19) where e(D) is a white szquence. It can be seen that v(D) consists primarily of three components. A partial response component, an ISI component dependent on the predictor coe~ficients ~qj} and finally, a white total distortion component. The ISI component is causal provided that the PR function f(D) is causal. The combination of the rnatched filter 71, PR equalizer 72, and the predictor 81 has been called PR-WI\/IF 82. The PR-WMF output sequence v(D) enters into the modified sequence estimator with PR Viterbi detector 76. The PR Viterbi detector 73 operates on the PR trellis using the following branch metric 1~ WO 94129989 2 ~ 58 ~14 PCT/EP93tOl~OO

k(Jlk) = I Vk ~ qi~ fjXk~ k) ~ fiXk--J I (20) j=o j=o where xk ~ k) denotes data symbol estimates taken from the path memory associated with state ~lk. Equivalently, the branch metric in (20) can be written as Ak(~k) = ¦ wk(yk)--~ fjxk_; I (21 j=~

For notational simplicity, the signals {X(~k)} and {wk(,uk)} are represented in Figure 7 by x(~) and w(D), respectively. In Figure 7, the depen~ency of the digital sequences ~Xk} (or x(D~) and {Wk} (or w(D)~ on the path memory associatecl with state ,Uk is in~iicated by thick solid lines. Having specified the branch metric in (20) or (21), the modified sequence estimator with PR Viterbi detector 76 operates as has been described in the first em~odiment.

An adaptive modem receiver based on the second embodiment is shown in Figure 8 It consists of an MMSE linear partial-response equalizer 72 with T-spaced coefficients ~di} of plurality N, ~1, a predictor filter 81 with coefficients {qi~ of plurality N2, a predictor-coefficient estimator 80 with coefficients ~q,~ of plurality N2, a paltial-response filter 7~ with coefficients {f,}
of plurality L+ ~, and a modified sequence estimator with PR Viterbi detector 76.

Once per symb~l interval, the output value~ of equalizer 72 and predictor 81 are added, which yields the output sequence Vk = Zk + ~ qi Zk~ dj Yk_; + ~ qi Zk--i (2 i--~ i=O i=l WO 94/29989 PCTtEP93/01500 2~5~014 18 The output of the PR filter 79 is given by rk =
i=o and the output of the predictor 80 by uk = ~ q; rk--i (24) If the transmission channel is unknown and slowly time varying, then standard adaptation algorithms can be applied. The PR-WMF receiver of the second embodiment can be made adaptive, e.g., by adjusting the coefficients {d,} of the equalizer 72 and the coefficients ~ql} of the predictors 80 and 81 with the following gradient algorithms dj(k + 1) = dj(k)--aek'Yk~ = 0, 1, ........... , N1 (25) qj(k + 1) = qj(k!--~ek(zk_;--rk_j), i = 1, 2, .. .~ N2' (26) where ~ and ,B are adaptation parameters, and rk is given by (23). The corresponding error signals are ek = Zk--rk (27) for updating the coefficients {d~} of the equalizer 72, and ek = vk--uk rk (28) Wo 94/29989 ~ Q ~ ~ PCT/EP93/01500 for adjusting the coefficients ~q,} of the predictors 80 and 81.

Using the above embodiments in wire transmission applications the whitening of the total distortion and the improved signal-to-noise ratio (SNR) lead to an increase in distance over which reliable transmission can be achieved andlor an increase in data transmission speed. In particular, for ISDN basic rate transmission the present scheme offers the following benefits:

-- improved robustness in the presence of noise and near-end crossfalk interference.

-- more reliable operation on subscriber lines with bridged taps, and -- increased percentage of coverage in the subscriber loop plant The present adaptive noise--predictive partial-response equalization scheme can also be used in magnetic recording systems. This further embodiment of the present invention is schematically illustrated in Figure 9. The present noise predictive partial response receiver with PR Viterbi detector, depicted by reference number 94, is made part of a magnetic recording system. When employing the receiver of the first embodiment, box 94 comprises the matched filter 31, the partial-response equalizer 32, and the modified sequence estimator with PR Viterbi detector 36. In case that the receiver of the second embodiment is used, box 94 comprises the modified se~uence estimator with PR Viterbi detector 76 3nd the PR-WMF 82. Note that due to the fact that the signalling alphabçt of the magnetic recording channel is restricted to be ~1, the subset decoder unit 70, shown in Figure 4, is not needed. This system further comprises a magnetic medium 90. for example a magnetic disk, a read/write magnetic head 91, switching means 9Z for switching from the write mode to the read mode and vice versa, and a amplifying means 93. The frequency response of this magnetic recording system is similar to the frequency response 10 shown in Figure 1. The magnetic head 91 transmits no dc, and the channel has a near null at high frequencies. When employing the WO 94/29g8g ~158 0 ~ ~ I PCT/EP93/01500 t inventive equalization scheme in the receiver 94, the areal storage density can be increased.

A further advantage of the present scheme is that the noise predictor, imbedded in the PR Viterbi detector, can be piggybacked on existing PR
systems to enhance performance such that no further hardware changes are necessary .

When the present invention is employed in a system where encoded digital information sequences are transmitted via the channel, then the PR Viterbi detector 33 in the first embodimenl or 73 in the second embodiment operates on a trellis which encompasses in addition the state space defined by the encoder. Combined PR and code trellis examples can be found in the article "Trellis Coding for Partial-Response Channels~, J.K. Wolf et al., IEEE
Transactions on Communications, Vol. 39, No. 8, pp. 76~ - 773, August 1986.

Claims (9)

1

1. Apparatus for detecting a digital information sequence x(D) transmitted via a channel exhibiting spectral nulls and/or near nulls. said apparatus comprising .cndot. a partial-response linear equalizer (32: 72) having a transfer function d(D) for shaping said channel to a desired partial-response transfer function such that the discrete time output sequence z(D), at an output of said partial-response linear equalizer (32: 72), has spectral nulls approximately where the channel response has spectral nulls and/or near nulls.
.cndot. a modified sequence estimator (36: 76) with partial-response Viterbi detector which provides zero-delay tentative decisions X(D) at an output line (38; 78), and which comprises - a partial-response Viterbi detector (33: 73) estimating said transmitted digital information sequence x(D), and - a partial-response filter (34; 74) followed by a noise predictor (35; 75) being connected to said partial-response Viterbi detector (33; 73) to isolate noise components and residual interference components of said discrete time output sequence z(D) and to predict future noise components and residual interference components, said apparatus being characterized in that it is made adaptive by means of a second partial-response filter (39; 79) and a predictor-coefficient estimator (50: 80), said second partial-response filter operating on said zero-delay tentative decisions ~(D) to provide a shaped output sequence {r k} which is subtracted from said discrete time output sequence z(D) to obtain an error sequence {e'k} used for updating the coefficients {d i} of said partial-response linear equalizer (32; 72).

2. The apparatus of claim 1. wherein said shaped output sequence {r k} is subtracted from said discrete time output sequence z(D) prior to being used as input to said predictor-coefficient estimator (50) which provides an output sequence {~k} which is used for the generation of an error sequence {e k} by subtracting said error sequence {e'k} from said output sequence {~k}, said error sequence {e k} being employed for updating the coefficients {q i} of said predictor-coefficient estimator (50).

3. The apparatus of claim 1, wherein the coefficients {d k} of said partial-response linear equalizer (32: 72) are optimized such that the overall transfer function including said channel closely matches a desired partial-response transfer function.

4. The apparatus of claim 1, wherein the coefficients {f i} of said second partial-response filter (39; 79) can take on any real values.

5. The apparatus of claim 1, comprising a predictor filter (81) operating as a whitening filter coupled to the output of said partial-response linear equalizer (72) such that said discrete time output sequence z(D) of said partial-response linear equalizer (72) and the output sequence of said predictor filter (81) are added to form a whitened sequence v(D) being forwarded to said modified sequence estimator with partial-response Viterbi detector (76).

6. The apparatus of claim 1, wherein said shaped output sequence {r k} is further used as input to said predictor-coefficient estimator (80) which provides an output sequence ~k} which is used for the generation of an error sequence {e k} by subtracting ~k} and {r k} from {v k}. said error sequence {e k} being employed for updating the coefficients {q k} of said predictor-coefficient estimator (80).

7. The apparatus of claim 6, wherein said error sequence {e k} is employed for updating the coefficients {q l} of said predictor filter (81).

8. The apparatus of claim 1, wherein said transmitted digital information sequence x(D) is redundantly encoded and said partial-response Viterbi detector comprises means, for exploiting that redundancy at the Viterbi detector.

9. A data transmission system or magnetic recording system comprising the apparatus of claim 1.