CA2527685A1 - Vector equalizer and vector sequence estimator for block-coded modulation schemes - Google Patents

Abstract

A vector decision feedback equalizer (VDFE) device for the detection of codewords transmitted over a dispersive channel in systems employing a block code is disclosed. The VDFE device comprises a vector feedforward unit in which a received signal vector is processed to a feedforward-filtered vector; a vector feedback unit in which a delayed decision vector is processed to a feedback-filtered vector; a differential vector combiner which receives the feedforward-filtered vector and the feedback-filtered vector and delivers an estimated signal vector representing an estimate of a desired signal vector Di#191 = B0#191 Xi#191 . The device further comprises a Euclidean distance minimizer unit in which a set of metrics Mi,q#191 corresponding to squared Euclidean distances .DELTA.2i,q#191 is calculated between the estimated signal vector and a desired differential vector combiner output B0#191Cq#191 for each possible codeword Cq#191 being an element of the block code, and a decision index with a corresponding closest codeword Cqi#191 is selected such that the closest codeword Cqi#191 attains the minimum squared Euclidean distance in the set of metrics Mi,q#191. A codeword generator for selecting a delayed decision vector based on a delayed decision index that is derived from the decision index is further comprised in the device. Further is disclosed a reduced-state vector sequence estimator (RS-VSE) device for the detection of codewords transmitted over a dispersive channel. The RS-VSE device comprises a vector feedforward unit in which a received signal vector is processed to a feedforward-filtered vector; a plurality of state-metric processors each of which comprises a Euclidean distance minimizer unit outputting a set of metrics corresponding to smallest squared Euclidean distances and a vector feedback unit for computing a feedback-filtered vector based on a delayed decision vector that corresponds to a previous decided codeword Xi-1#191(k) ; and a Viterbi survivor metric selector which receives the sets of metrics from the plurality of state-metric processors and selects therefrom a final set of smallest metrics.

Description

VECTOR EQUALIZER AND VECTOR SEQUENCE ESTIMATOR FOR
BLOCK-CODED MODULATION SCHEMES
TECHNICAL FIELD
The invention is related to wireless or wired digital communication systems using block-coded modulation (BCM) over noisy communication channels subject to linear dispersion. The invention applies to wireless communication systems including, but not limited to wireless local area networks (WLANs), where the linear dispersion is primarily due to multipath propagation, as well as to wired communication systems. The invention relates to receivers based on a decision-feedback equalizer (DFE) or a near - maximum-likelihood sequence estimator (MLSE) for BCM schemes such as complementary code keying (CCK) employed in WLANs according to the IEEE 802.11 family of standards. More particularly, the invention relates to a vector decision feedback equalizer (VDFE) device and a reduced-state vector sequence estimator (RS-VSE) device for the detection of codewords transmitted over a dispersive channel in systems employing a block code.
BACKGROUND OF THE INVENTION
In digital communication systems, channels with linear dispersion such as multipath channels in wireless local area network (WLAN) systems cause a single transmitted data symbol to generate a receiver response extending over multiple data symbol periods. When block-coded modulation (BCM) is employed, transmitted codewords are often referred to as symbols and, particularly for direct-sequence spread spectrum (DSSS) based wireless systems, the elements of the transmitted codewords are known as chips. In systems using BCM with a block length of N
samples, the effect of linear dispersion may be conceptually divided into two components, namely inter-symbol interference (ISI) and inter-chip interference (ICI). In a given N sample interval associated with a current codeword, ISI is the component of the received signal contributed by adjacent codewords, while ICI is the component of a received sample due to adjacent chips of the current codeword.
A decision-feedback equalizer (DFE) is a well-known device for eliminating ISI
whenever a symbol comprises a single real-valued or complex-valued sample. In each iteration, such a scalar DFE estimates a single transmitted sample from received samples and past decisions (i.e., estimates of transmitted samples), obtains a new decision by selecting a signal point closest to the estimated single transmitted sample from the set of signal points known as the signal constellation, and immediately feeds back the new decision to a feedback section.
In systems using block-coded modulation (BCM), however, a symbol (also referred to as a codeword) comprises a block of N real-valued or complex-valued samples (also referred to as chips), where N is a fixed integer such as, for example, 4 or 8. Therefore, a symbol decision can only be made every N samples, which precludes the use of scalar DFE iterations with sample-by-sample decision feedback as described above.
There are known receiver techniques for BCM that are based on a scalar DFE, for example as described in US Patent No. 6,233,273 B 1, "RAKE Receiver with Embedded Decision Feedback Equalizer" and US Patent Application No. 2001/0036223 A1.
FIG. 1 shows a modified scalar DFE according to US Patent No. 6,233,273 B l, which differs from a scalar DFE in two respects. First, given that linear dispersion may be conceptually divided into ISI due to past codewords and ICI due to past chips of the current codeword, only an estimate 161 of the ISI is being subtracted from the output 111 of the feedforward section 110.
Second, the ISI-free signal at the output of the differential combiner 120, which is still distorted by ICI, is fed into a correlator bank 130. A maximum selector 140 is used every N samples to obtain a decision index 141 by picking the codeword index corresponding to the maximum correlation. The decision index 141 is presented both to a data decoder (not shown in FIG. 1) and to a codeword generator 150, which generates a BCM codeword 151 corresponding to the decision index 141 and used for estimating the ISI in feedback section 160.
It is known to those skilled in the art that, for BCM schemes such as CCK
having a generalized Reed-Muller (GRM) code structure as described in, for example, J.
A. Davis and J.
Jedwab, "Peak-to-Mean power control in OFDM, Golay complementary sequences, and Reed-Muller codes", IEEE Transactions on Information Theory, Vol. 45, No. 7, Nov. 1999, and in K. G. Paterson, "Generalized Reed-Muller codes and power control in OFDM
modulation", IEEE Transactions on Information Theory, Vol. 46, No. l, Jan. 2000, the correlator bank 130 may be implemented efficiently through a fast Walsh transform (FWT).

As mentioned in US Patent No. 6,233,273 B 1 and as described above, the performance of the modified scalar DFE shown in FIG. 1 is degraded by the residual ICI
distortion.
FIG. 2 shows a "RAKE receiver with embedded scalar DFEs" according to US
Patent No.
6,233,273 B 1, which was conceived for canceling both ISI and ICI. A
feedforward section 210 computes output signal 211 from received samples 200 according to ~Ni+n = ~ fm.YNi+n-m-8~ [Equ. 1]
m=-LF.+1 where 8 is a suitable delay parameter. For each of Q hypothetically transmitted current codewords indexed by q= 0 . . . Q-1, a separate receiver branch is provided comprising a feedback section 280.q, a differential combiner 220.q, and a codeword correlator 230.q. The feedback section 280.q computes output signal 281.q according to VNi+n, q- ~ .bm Cn-m, q + ~ bmXNi+n-m~ [Equ. 2~
m=1 m=n+1 where the term E bm Cn_m, q is an ICI estimate computed from the hypothetically transmitted current codeword and the term E bmXNi+n-m is an ISI estimate computed from previously m=n+1 decided codewords. The differential combiner 220.q computes a signal 221.q according to d ~z -v =z -Eb c E b ~ [ q Ni+n , q Ni+n Ni+n , q Ni+n ~1 m n-m, q ~n+1 m Ni+n-m ~ E Ll. 3 which represents an estimate of the transmitted signal element xNi+n under the assumption that aq is the current transmitted codeword. The signal 221.q is presented to codeword correlator 230.q. Finally, a maximum selector 240 determines from correlations 231.0 ...
231.Q-1 a decision index 241 corresponding to the codeword with maximum correlation, and the decision index 241 is presented to both the data decoder (not shown in FIG. 2) and the feedback path via a delay element 250.
As described in US Patent No. 6,233,273 B l, the codeword correlators 230.0 ... 230.Q-1 may be moved through the differential combiners 220.0 ... 220.Q-1 for efficiency. This results in the functionally equivalent but computationally more efficient receiver shown in FIG. 3, which features a correlator bank 320, i.e., a bank of codeword correlators operating on the same input signal 311, and a second set of codeword correlators that are combined with the feedback filter coefficients in feedback sections 370.0 ... 370.Q-l, e.g., by precomputing the convolutions of the feedback filter with the time-reversed and conjugated codewords and storing said convolutions in a look-up table accessible by feedback sections 380.0 ... 380.Q-1. As mentioned above, the correlator bank 320 may be implemented efficiently through an FWT for BCM
schemes having a GRM code structure. Despite the above simplifications, the receiver in FIG. 3 still has a high complexity because of the need for Q parallel feedback sections and differential combiners, since Q may be as high as 16, 64, or 256 in practice.
It will be apparent to those skilled in the art that ICI will be synthesized correctly in the feedback section of FIG. 2 or FIG. 3 corresponding to the actual transmitted codeword. On the other hand, the feedback of the hypothetical current codeword will cause additional distortion in the remaining feedback sections. Hence, the vectors T
d i , q - C dNi+0 , q ~ dNi+1, q ~ ~ ~ ~ i dNi+N-1, q formed by N subsequent outputs dNi+n, q of the differential combiners 220.0 ... 220.Q-1 in FIG. 2 often have substantially different energies. It is known that, under these circumstances, the decision device should minimize the squared Euclidean distance [Equ. 4]
Ei,qOI~di,q-cq~~
over the indices q= 0 ... ~-1, where cq= ~ co, q, cl, q, . . . , cal, q~ T
denotes the q-th codeword of the BCM code, rather than maximize the (real part of) correlation ~r [Equ. 5]
ri,cl~Cqdl,q- pCn,qai,q~
since Ei, q may be expanded as E'i,q=~~di-q~~~-2Re~ri,q~+~~cq~~2 [Equ.6]
wherein the energies II di, q II ~ may be substantially different as explained above. As a consequence, maximizing the suboptimal correlation metric instead of minimizing Euclidean distance may substantially degrade performance.
It should be noted that, for BCM schemes employing a constant-amplitude modulation such as QPSK (Quaternary Phase-Shift Keying) in case of CCK, the energies ~~
cq ~~ 2 of the transmitted codewords are identical.

A new approach attempting to take into account the variance of the energies II
di, q II ~ is to compute both the correlations ri, q and the energies II di, q I~ 2 for cr=
0 ... Q-1, and to combine these terms for minimizing the squared Euclidean distances shown in [Equ. 6].
Unfortunately, there is no fast algorithm for calculating the energies I I d i , q I I 2 for q= 0 . . . Q-1.

5 The fact that this energy calculation is computationally more expensive than-the FWT makes this approach impractical.
From the above it follows that there is a need in the art for an improved device suitable for the reception of BCM over dispersive channels which does not rely on maximization of the suboptimal correlation metric. Such a receiver device should provide fast and chip-area-efficient means for the calculation of the squared Euclidean distances.
Furthermore, there is a need for an enhanced receiver device counteracting the effects of error propagation that occur in DFE-based receivers.
SUMMARY AND ADVANTAGES OF THE INVENTION
In general, a vector decision feedback equalizer (VDFE) device is disclosed suitable for the reception of BCM codewords of length N transmitted over dispersive channels.
In contrast to conventional, scalar DFE-based receivers for single-input-single-output dispersive channels, the VDFE is based on interpreting the dispersive channel as a vector channel matched to the BCM
scheme and avoids the sample-by-sample decision feedback inherent in conventional DFE
structures. The VDFE can operate on length-N vectors and employ Nx N matrix-valued filter coefficients. Depending on the BCM scheme, VDFE devices may operate on real-valued or complex-valued vectors. The VDFE comprises a vector feedforward filter unit (or simply vector feedforward unit) and a vector feedback filter unit (or simply vector feedback unit), both coupled to a differential vector combines, whose output vector represents an estimate of an equalizer target vector. This output vector is optionally multiplied with a square matrix and then fed to a fast Euclidean distance minimizes for selecting the closest codeword in the sense of Euclidean distance. More particularly, the fast Euclidean distance minimizes performs a Euclidean distance minimization over the set of Euclidean distances between an estimated received vector and hypothetical received vectors derived from the set of transmitted codewords.
The VDFE cancels ISI due to previous codewords through vector decision feedback.
In accordance with a first aspect of the present invention, a vector decision feedback equalizer (VDFE) device for the detection of codewords transmitted over a dispersive channel in systems employing a block code is provided. The. device comprises a vector.
feedforward unit in which a received signal vector is processed to a feedforward-filtered vector; a vector feedback unit in which a delayed decision vector is processed to a feedback-filtered vector; a differential vector combines which receives the feedforward-filtered vector and the feedback-filtered vector and delivers an estimated signal vector representing an estimate of a desired signal vector Di = Bo Xi.
The device further comprises a Euclidean distance minimizes unit in which a set of metrics Mz,q is calculated corresponding to squared Euclidean distances ~Zq between the estimated signal vector and a desired differential vector combines output Bo Cq for each possible codeword Cq being an element of the block code, and a decision index with a corresponding closest codeword Cq~ is selected such that the closest codeword Cq~ attains the minimum squared Euclidean distance in the set of metrics Mi,q. A codeword generator for selecting a delayed decision vector based on a delayed decision index that is derived from the decision index is further comprised in the device.
The VDFE device allows to reduce error probability by computing Euclidean distances for codeword decisions rather than just correlations and provides a fast way for computing the set of Euclidean distances by taking advantage of a fast Walsh transform (FWT).
The desired signal vector Di =BoXi can comprise a matrix of filter coefficients Bo which are derived from a measured impulse response of the dispersive channel. This allows optimizing the filter coefficients Bo according to the minimum mean-squared error (MMSE) principle in order to reduce the distortion of the estimated signal vector relative to the desired signal vector.
The Euclidean distance minimizes unit can comprise a linear transform unit in which the estimated signal vector is multiplied with the complex-conjugate transpose of the matrix of filter coefficients Bo to derive a correlator-bank input vector. This allows to compute a correlation with the desired signal vector in two steps: first, correlate with the matrix of filter coefficients Bo, and second, correlate with each codeword.

A reduction of complexity can be achieved by performing the correlation with the matrix of filter coefficients B0 inside the vector feedforward unit and the vector feedback unit, thereby the correlator-bank input vector corresponds to the output of the differential vector combiner and multiplications with the complex-conjugate transpose of the matrix of filter coefficients Bo are performed by the vector feedforward unit and the vector feedback unit.
The Euclidean distance minimizer unit can compute the set of metrics Mi,q by subtracting a multiple of the real part of a correlation term pi, q from a precomputed energy term ~q. This is advantageous on a slowly varying or time-invariant channel, because the energy terms ~q can be precomputed during a channel estimation phase and used throughout the subsequent data reception phase.
Codeword correlations can be derived in parallel when each correlation term p;., q is computed by means of a correlator bank that correlates the correlator-bank input vector with each codeword Cq from the block code.
The correlator bank can be implemented as a fast transform unit to perform a Fast Walsh Transform (FWT), which results in a fast implementation of the Euclidean distance minimizer unit. This would exploit advantageously the GRM code structure to compute codeword correlations more efficiently.
The vector feedforward unit can use fractional tap spacing, which allows to improve the performance in systems using excess bandwidth, in addition to the minimum required Nyquist bandwidth.
The vector feedforward unit, the vector feedback unit, and the differential vector combiner can output decimated versions of the feedforward-filtered vector, the feedback, filtered vector, and the estimated signal vector, respectively, for eliminating a redundancy in codewords. Therewith, a lower complexity of the feedforward unit at lower data rates, e.g. for IEEE
802.11b at 5.5 Mb/s, can be realized.
In accordance with a second aspect of the present invention, there is provided a reduced-state vector sequence estimator (RS-VSE) device for the detection of codewords transmitted over a dispersive channel in systems employing a block code. The RS-VSE device allows to reduce error propagation of the VDFE device, retaining the efficient calculation of Euclidean distances.
The RS-VSE device comprises a vector feedforward unit in which a received signal vector is processed to a feedforward-filtered vector; a plurality of state-metric processors each of which comprises a Euclidean distance minimizer unit outputting a set of metrics corresponding to smallest squared Euclidean distances and a vector feedback unit for computing a feedback-filtered vector based on a delayed decision vector that corresponds to a previous decided codeword Xi-1(k); and a Viterbi survivor metric selector which receives the sets of metrics from the plurality of state-metric processors and selects therefrom a final set of smallest metrics.
The reduced-state vector sequence estimator (RS-VSE) device is suitable for the reception of BCM codewords of length N transmitted over dispersive channels. Similar to the VDFE, the RS-VSE is based on interpreting the dispersive channel as a vector channel matched to the BCM
scheme. The RS-VSE can operate on length-N vectors and employ Nx N matrix-valued filter coefficients. Depending on the BCM scheme, RS-VSE devices may operate on real-valued or complex-valued vectors. The RS-VSE device comprises the vector feedforward section or vector whitened matched filter and a reduced-state Viterbi algorithm designed to select a near -maximum-likelihood estimate of the transmitted sequence of codewords. The RS-VSE device provides a small number of states corresponding to a set of most likely past codewords and takes ISI due to previous codewords into account through a state-dependent fast branch metric calculation. Thereby, the RS-VSE device offers near-optimal receiver performance counteracting the well-known effects of error propagation at a modest increase in complexity. A branch in the RS-VSE Viterbi trellis corresponds to the transmission of an entire N chip codeword. Several branches may emanate from a single state in this trellis, each branch corresponding to the transmission of an N chip codeword. For efficiency, it will be desirable to limit the number of branches emanating from each state to a small number (for example, 2 or 4), corresponding to the (for example, 2 or 4) codewords at smallest Euclidean distance. The RS-VSE
device is particularly useful when the memory of the vector channel is 1.
Both VDFE and RS-VSE allow an optimization of the equalizer target vector, given an estimate of the dispersive channel and filter parameters. In particular, the equalizer target vector need not be equal to the transmitted codeword. Additional performance gains are obtainable by letting the equalizer target vector correspond to an optimized linear transformation of the transmitted codeword.

The matrix-valued filter coefficients for VDFE and RS-VSE may be computed and/or adapted using vectorized minimum-mean-squared-error (MMSE) or zero-forcing (ZF) estimation techniques, either based on channel estimates obtained during a preamble or startup sequence or through adaptive techniques.
For BCM schemes with the GRM code structure, both VDFE and RS-VSE permit a fast way to calculate the set of Euclidean distances required for distance minimization, taking advantage of a fast Walsh transform (FWT).
Receivers using the VDFE device improve performance compared to conventional receivers with embedded scalar DFEs that maximize the suboptimal correlation metric and fail to take into account the energy variance of codewords received over a multipath channel. At the same time, the presented VDFE device offers a reduced complexity by not requiring a set of Q parallel feedback sections.
The VDFE and/or the RS-VSE device may be implemented by dedicated or programmable hardware means, e.g. ASICs or FPGAs, or as a computer program, and may be provided as a computer program product stored on a computer usable medium.
BRIEF DESCRIPTION OF THE DRAWINGS
Preferred embodiments of the invention are described in detail below, by way of example only, with reference to the following schematic drawings.
FIG. 1 shows a DFE for BCM schemes according to prior art, characterized by a feedback section for canceling ISI due to past codewords (but not ICI due to past chips of the current codeword), and further characterized by the combination of a correlator bank and a maximum selector for selecting the codeword with largest correlation.
FIG. 2 shows a receiver with multiple parallel embedded feedback sections according to prior art, characterized by means for canceling both ISI and ICI and by the combination of correlators and a maximum selector for selecting the codeword with largest correlation.
FIG. 3 shows an optimized receiver with multiple parallel embedded feedback sections according to prior art, characterized by means for canceling both ISI and ICI
and by the combination of a correlator bank and a maximum selector for selecting the codeword with largest correlation.
FIG. 4 shows a block diagram of a vector decision-feedback equalizer (VDFE) with a fast Euclidean distance calculator according to the present invention.
5 FIG. 5 shbws a block diagram of a reduced-state vector sequence estimator (RS-VSE) with a fast Euclidean metric calculator, for an exemplary implementation with four reduced states corresponding to the four best previous codewords.
The drawings are provided for illustrative purposes only and do not necessarily represent practical examples of the present invention to scale.
DETAILED DESCRTPTION OF PREFERRED EMBODIMENTS
FIG. 4 shows a schematic block diagram of a vector decision feedback equalizer (VDFE) device 400 according to the present invention. The VDFE device 400, hereafter simply also referred to as VDFE, comprises a vector feedforward unit 410, a differential vector combiner 420, an optional matched filter 430, a Euclidean distance minimizer unit 440, also referred to as fast Euclidean distance minimizer 440, suitable for finding a closest codeword from a given block code, and a feedback path comprising a delay element 450, a codeword generator 460, and a vector feedback unit 470. For the subsequent detailed description, sample vectors 401, 411, 421, 461 and 471 of length N are introduced and defined as Yi ~ ~ ~Ni+N-1 i ~ ~ ~ i ~Ni+1 ~ .1' Ni+0 ~ T
T
Zi ~ ~ zNi+1~1 ~ ~ ~ ~ ~ ~Ni+1 i zNi+0 T
Di ~ C dNi+N-1 ~ ~ ~ ~ ~ dNi+1 ~ dNi+0 T
Xi ~ ~ XNi+1~1 i ~ ~ ~ ~ ~Ni+1 ~ ~Ni+0 and T
Yi 0 ~ VNi+1~1 ~ ~ ~ ~ i VNi+1 i VNi+0 ~ , respectively. The sample vectors 401, 411, 421, 461 and 471 are also referred to as received signal vector 401, feedforward-filtered vector 41 l, estimated signal vector 421, delayed decision vector 461, and feedback-filtered vector 471, respectively. While the received signal vector 401 has length N in what follows, it is in the scope of the invention to have longer input vectors for fractional tap spacing enhancements common in the art of equalization. The vector feedforward unit 410 uses NxN matrix-valued feedforward filter coefficients F~", m=-LF ...
0, while the vector feedback unit 470 uses Nx N matrix-valued feedback filter coefficients Bm, m =1 . . . MB.
The vector feedforward unit 410 computes the feedforward-filtered vector 411 from received vectors 401 according to Z.i = ~ Fm Yi_m-EF, [Equ. 7]
m=-LF.+1 where 8F is a suitable delay parameter, and the vector feedback unit 470 computes the feedback-filtered vector 471 from the delayed decision vector 461 according to Mg Vi = ~ BmXi_m. [Eqtl. g]
m=1 Within the feedback path, the codeword generator 460 selects the delayed decision vector 461 based on a delayed decision index 451 that is derived by the delay element 450 from a decision index 449.
The differential vector combiner 420 computes the estimated signal vector 421 according to MB
Di 0 Zi - Vi = Zi - ~ B~, Xi-m, [Equ. 9]
rrr-1 which represents an estimate of a desired signal vector [Equ. 10]
Di ~ Bo Xi, also referred to herein as the equalizer target vector. The desired signal vector in turn is specified by an NxN matrix Bo, which may be chosen to optimize performance. According to one advantageous embodiment of the invention, the matrix Bo is chosen to have triangular structure optionally normalized to have unit elements on the main diagonal.
The estimated signal vector 421 (,Di) of the VDFE according to [Equ. 9] is now compared to the signal dNt+n, q according to [Equ. 3] that is computed by the prior-art device in FIG. 2.
The estimated signal vector 421 (,Di) does not depend on q as it does not use the elements co , q . . . Cn_1, q , q= 0 . . . ~-1, of the possible current codewords.
Therefore, in contrast to FIG.
2, a single vector feedback unit 470 is sufficient for the VDFE. Moreover, the VDFE generally does not and need not suppress ICI, because signal Di approximates the desired signal vector [Equ. 10], whose elements may advantageously comprise ICI components. On the other hand, the prior-art estimate [Equ. 3] attempts to suppress ICI (besides suppressing ISI) by subtracting an ICI estimate hypothesized for each possible current transmitted codeword.
The matrix-valued feedforward and feedback coefficients of the VDFE as well as the matrix Bo may be computed and / or adjusted based on the minimum mean squared error (MMSE), the zero-forcing criterion, or other optimization criteria commonly employed in the art of equalization. The coefficients of the VDFE can be adapted to minimize the MMSE in case of time-varying channel conditions. In a preferred embodiment, the VDFE
coefficients are selected such that, in the absence of previous decision errors, the estimated signal vector 421 is given by Di 0 Bo Xi +Ni, [Equ. 11]
where Xi is the current transmitted codeword and Ni is a noise vector with uncorrelated components. The fast Euclidean distance minimizer 440 is employed to select the decision index 449, with q= q,;_, minimizing the squared Euclidean distance ~~, ~r ~ ~~ Di - Bo ~'~r ~~ ~ _ ~~ D= ~~ 2 - ~ Re~pi, q~ + sq~ [Equ. 12]
T
where are defined the codeword vectors Cq= ~ cal, q, . . . , cl, q, co, q ~ , the correlations P=, ~I ~ ~q Bo Di ~ Equ. 13]
and the energy terms ~~r~ ~~Bocq~~ 2~ [Equ. 14]
which may be precomputed and stored in a look-up table for efficiency. The energy terms aq can be adapted in case of time-varying channel conditions. As the term ~~ Di ~~ 2 does not depend on the codeword index q, it is irrelevant for the minimization of [Equ. 12].
Therefore, one may equivalently minimize the metric Mi, q ~ Eq - 2 Ref p~, ~r [Equ. 15]
as shown in the detailed view of the fast Euclidean distance minimizer 440 in FIG. 4. The correlations according to [Equ. 13] can be implemented by the linear transform unit 430 multiplying the estimated signal vector 421 with matrix Bo, followed by a correlator bank 441 that may be efficiently implemented as an FWT device in case of a GRM block code structure.
Alternatively, the linear transform so may be absorbed in filters 410 and 470.
In the following, the same reference signs or numbers are used to denote the same parts or the like.
- ~ FIG. ~5 shows a schematic block diagram of a reduced-state vector sequence estimator (RS-VSE) device 500, where the set of states corresponds to a set of K most likely previous codewords Xi_1 (k), 0 < k < K. For the exemplary embodiment shown in FIG. 5, K= 4. The RS-VSE device 500 comprises the vector feedforward unit 410, a plurality of state-metric processors 520.0 ... 520.I~-1, each of which is associated with one of the most likely previous codewords Xi_1(k), also referred to as one of previous decided codewords X'z_1(k), and a Viterbi survivor metric selector 550. Each state-metric processor 520.k comprises a fast metric calculator 540.k and the vector feedback unit 470.k for computing the feedback-filtered vector 471.k based on the delayed decision vector 461.k. The state-metric processor 520.k computes the estimated signal vector 421.k under the assumption that the delayed decision vector 461.k is given by codeword X'i_1(k). The fast metric calculator 540.k, also called fast Euclidean metric calculator, corresponds to the fast Euclidean distance minimizer 440, as described with reference to FIG. 4, and is used for computing a set of Q Euclidean metrics and then selecting P smallest metrics Milk, 0) ... M;(k, 3) from this set, where P = 4 for the embodiment in FIG. 5, and P
corresponding decision indices qi(k, 0) ... qi(k, 3). The smallest metrics Milk, 0) ... Mi(k, 3) and the corresponding decision indices qi(k, 0) ... qi(k, 3), which can be regarded as best states, are forwarded to the Viterbi survivor metric selector 550, which selects a new set of most likely codewords through decision indices qi (k), 0 < k < K. In the feedback path within each state-metric processor 520.k are provided delay elements labeled with D, a codeword generator for generating the delayed decision vector 461.k, and the vector feedback unit 470.k that computes the feedback-filtered vector 471.k from the delayed decision vector 461.k.
It will be apparent to those skilled in the art of Viterbi decoding that the RS-VSE device 500 will reduce any error-propagation effects associated with a DFE and achieve an error-rate performance close to that of maximum-likelihood sequence estimation. Moreover, compared to a conventional maximum-likelihood sequence estimator, the RS-VSE device 500 reduces the complexity of calculating the metrics associated with the Q trellis branches emanating from every state by using fast metric calculators 540.0 ... 540.k.
Any disclosed embodiment may be combined with one or several of the other embodiments shown and/or described. This is also possible for one or more features of the embodiments.
The present invention can be embedded in a computer program product, which comprises features enabling the implementation described herein, and which - when loaded in a computer system - is able to carry out the method.
Computer program means or computer program in the present context mean any expression, in any language, code or notation, of a set of instructions intended to cause a system having an information processing capability to perform a particular function either directly or after either or both of the following a) conversion to another language, code or notation; b) reproduction in a different material form.

Claims (12)

1. A vector decision feedback equalizer (VDFE) device (400) for the detection of codewords transmitted over a dispersive channel in systems employing a block code, the device comprising:
a vector feedforward unit (410) in which a received signal vector (401) is processed to a feedforward-filtered vector (411);
a vector feedback unit (470) in which a delayed decision vector (461) is processed to a feedback-filtered vector (471);
a differential vector combiner (420) which receives the feedforward-filtered vector (411) and the feedback-filtered vector (471) and delivers an estimated signal vector (421) representing an estimate of a desired signal vector (Di=B o X t);
a Euclidean distance minimizer unit (440) in which a set of metrics ( M i,q) is calculated corresponding to squared Euclidean distances (.DELTA.2i,q) between the estimated signal vector (421) and a desired differential vector combiner output (B o C q) for each possible codeword (C q) being an element of the block code, and a decision index (449) with a corresponding closest codeword (C ~i) is selected such that the closest codeword (C~~) attains the minimum squared Euclidean distance in the set of metrics (Mi,q); and a codeword generator (460) for selecting the delayed decision vector (461) based on a delayed decision index (451) that is derived from the decision index (449).

2. The device according to claim 1, wherein the desired signal vector (D i =B
o X i) comprises a matrix of filter coefficients (B o) which are derived from a measured impulse response of the dispersive channel.

3. The device according to any preceding claim, wherein the Euclidean distance minimizer unit (440) comprises a linear transform unit (430) in which the estimated signal vector (421) is multiplied with the complex-conjugate transpose of the matrix of filter coefficients (B o) to derive a correlator-bank input vector (431).

4. The device according to claim 3, wherein the correlator-bank input vector (431) corresponds to the output of the differential vector combines (420) and multiplications with the complex-conjugate transpose of the matrix of filter coefficients (B o) are performed by the vector feedforward unit (410) and the vector feedback unit (470).

5. The device according to any of the preceding claims, wherein the Euclidean distance minimizes unit (440) computes the set of metrics (M i,q) by subtracting a multiple of the real part of a correlation term (p i, q ) from a precomputed energy term E q.

6. The device according to claims 3 or 4 and 5, wherein each correlation term (p i, q) is computed by means of a correlator bank (441) that correlates the correlator-bank input vector (431) with each codeword (C q) from the block code.

7. The device according to claim 6, Wherein the correlator bank (441) is implemented as a fast transform unit to perform a Fast Walsh Transform (FWT), which results in a fast implementation of the Euclidean distance minimizes unit (440).

8. The device according to any of the preceding claims, wherein the vector feedforward unit (410) uses fractional tap spacing.

9. The device according to any of the preceding claims, wherein the vector feedforward unit (410), the vector feedback unit (470), and the differential vector combines (420) output decimated versions of the feedforward-filtered vector (411), the feedback-filtered vector (471), and the estimated signal vector (421), respectively, for eliminating a redundancy in codewords.

10. A method for the detection of codewords transmitted over a dispersive channel in systems employing a block code comprising the steps of:
processing in a vector feedforward unit (410) a received signal vector (401) to a feedforward-filtered vector (411);
processing in a vector feedback unit (470) a delayed decision vector (461) to a feedback-filtered vector (471);

deriving with a differential vector combines (420) from the feedforward-filtered vector (411) and the feedback-filtered vector (471) an estimated signal vector (421) representing an estimate of a desired signal vector (D i = B o X i);
calculating with a Euclidean distance minimizes unit (440) a set of metrics (M
i,q) corresponding to squared Euclidean distances (.DELTA.2 t,q) between the estimated signal vector (421) and a desired differential vector combines output (B o C q) for each possible codeword (C q) being an element of the block code, and selecting a decision index (449) with a corresponding closest codeword (C~t) such that the closest codeword (C~t) attains the minimum squared Euclidean distance in the set of metrics (M t,q); and selecting the delayed decision vector (461) based on a delay ed decision index (451) that is derived from the decision index (449).

11. A computer program product stored on a computer usable medium, comprising computer readable program means for causing a computer to perform the method according to claim 10.

12. A reduced-state vector sequence estimator (RS-VSE) device (500) for the detection of codewords transmitted over a dispersive channel in systems employing a block code, the device comprising:
a vector feedforward unit (410) in which a received signal vector (401) is processed to a feedforward-filtered vector (411);
a plurality of state-metric processors (520.0 ... 520.K-1) each of which comprises a Euclidean distance minimizes unit (540.k) according to claims 1 to 9 outputting a set of metrics corresponding to smallest squared Euclidean distances and a vector feedback unit (470.k) for computing a feedback-filtered vector (471.k) based on a delayed decision vector (461.k) that corresponds to a previous decided codeword (~i-1(k)); and a Viterbi survivor metric selector (550) which receives the sets of metrics from the plurality of state-metric processors (520.0 ... 520.K-1) and selects therefrom a final set of smallest metrics.