Bayesian/decision-feedback algorithm for blind adaptive equalization
01 Jun 1992-Optical Engineering (International Society for Optics and Photonics)-Vol. 31, Iss: 6, pp 1211-1223
TL;DR: A new blind equalization algorithm is presented that incorporates a Bayesian channel estimator and a decision-feedback (DF) adaptive filter that is more robust to catastrophic error propagation and only a modest increase in the computational complexity.
Abstract: A new blind equalization algorithm is presented that incorporates a Bayesian channel estimator and a decision-feedback (DF) adaptive filter. The Bayesian algorithm operates as a preprocessor on the received signal to provide an initial estimate of the channel coefficients. It is an approximate maximum a posteriori (MAP) sequence estimator that generates reliable estimates of the transmitted symbols. These decisions are then filtered by an adaptive decision-feedback algorithm to further reduce the intersymbol interference. The new algorithm is more robustto catastrophic error propagation thanthe standard decision-feedback equalizer (DFE), with only a modest increase in the computational complexity.
Citations
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TL;DR: It is shown that a fractionally-spaced whitened matched filter, matched to the known data pulse, provides a set of sufficient statistics when a tapped delay line channel model is assumed, and that the problem is ill-posed when the channel impulse response is generalized to a CT, finite-length model.
Abstract: The problem of performing joint maximum-likelihood (ML) estimation of a digital sequence and unknown dispersive channel impulse response is considered starting from a continuous-time (CT) model. Previous investigations of this problem have not considered the front-end (FE) processing in detail; rather, a discrete-time signal model has been assumed. We show that a fractionally-spaced whitened matched filter, matched to the known data pulse, provides a set of sufficient statistics when a tapped delay line channel model is assumed, and that the problem is ill-posed when the channel impulse response is generalized to a CT, finite-length model. Practical approximations are considered that circumvent this ill-posed condition. Recursive computation of the joint-ML metric is developed. Together, the FE processing and metric recursion provide a receiver structure which may be interpreted as the theoretical foundation for the previously introduced technique of per-survivor processing, and they lead directly to generalizations. Several FE processors representative of those suggested in the literature are developed and related to the practically optimal FE.
115Â citations
TL;DR: Novel joint estimators are proposed that employ a single-input demodulator with oversampling to compensate for timing uncertainties and a (suboptimal) two-stage joint MAP symbol detector (JMAPSD) is introduced that has a lower complexity than the single-stage estimators while accruing only a marginal loss in error-rate performance at high signal-to-interference ratios.
Abstract: Cochannel interference occurs when two or more signals overlap in frequency and are present concurrently. Unlike in spread-spectrum multiple-access systems where the different users necessarily share the same channel, cochannel interference is a severe hindrance to frequency- and time-division multiple-access communications, and is typically minimized by interference rejection/suppression techniques. Rather than using interference suppression, we are interested in the joint estimation of the information-bearing narrow-band cochannel signals. Novel joint estimators are proposed that employ a single-input demodulator with oversampling to compensate for timing uncertainties. Assuming finite impulse-response channel characteristics, maximum likelihood (ML) and maximum a posteriori (MAP) criteria are used to derive cochannel detectors of varying complexities and degrees of performance. In particular, a (suboptimal) two-stage joint MAP symbol detector (JMAPSD) is introduced that has a lower complexity than the single-stage estimators while accruing only a marginal loss in error-rate performance at high signal-to-interference ratios. Assuming only reliable estimates of the primary and secondary signal powers, a blind adaptive JMAPSD algorithm for a priori unknown channels is also derived. The performance of these nonlinear joint estimation algorithms is studied through example computer simulations for two cochannel sources.
113Â citations
Cites methods from "Bayesian/decision-feedback algorith..."
...Complexity reduction techniques, such as the decision-feedback scheme in [29] or metric pruning [22], may be employed by this blind algorithm....
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...In this MAP/decision-feedback (MAP/DF) approach [28], [29], a DF filter of length is cascaded with the MAPSD algorithm to truncate the effective channel memory....
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TL;DR: This work considers the problem of simultaneous parameter estimation and restoration of finite-alphabet symbols that are blurred by an unknown linear intersymbol interference (ISI) channel and contaminated by additive Gaussian or non-Gaussian white noise with unknown parameters.
Abstract: We consider the problem of simultaneous parameter estimation and restoration of finite-alphabet symbols that are blurred by an unknown linear intersymbol interference (ISI) channel and contaminated by additive Gaussian or non-Gaussian white noise with unknown parameters. Non-Gaussian noise is found in many wireless channels due to the impulsive phenomena of radio-frequency interference. Bayesian inference of all unknown quantities is made from the blurred and noisy observations. The Gibbs sampler, a Markov chain Monte Carlo procedure, is employed to calculate the Bayesian estimates. The basic idea is to generate ergodic random samples from the joint posterior distribution of all unknowns and then to average the appropriate samples to obtain the estimates of the unknown quantities. Blind Bayesian equalizers based on the Gibbs sampler are derived for both Gaussian ISI channel and impulsive ISI channel. A salient feature of the proposed blind Bayesian equalizers is that they can incorporate the a priori symbol probabilities, and they produce as output the a posteriori symbol probabilities. (That is, they are "soft-input soft-output" algorithms.) Hence, these methods are well suited for iterative processing in a coded system, which allows the blind Bayesian equalizer to refine its processing based on the information from the decoding stage and vice versa-a receiver structure termed as blind turbo equalizer.
79Â citations
TL;DR: A new blind equalization algorithm based on a suboptimum Bayesian symbol-by-symbol detector is presented and it is shown that the maximum a posteriori (MAP) sequence probabilities can be approximated using the innovations likelihoods generated by a parallel bank of Kalman filters.
Abstract: A new blind equalization algorithm based on a suboptimum Bayesian symbol-by-symbol detector is presented. It is first shown that the maximum a posteriori (MAP) sequence probabilities can be approximated using the innovations likelihoods generated by a parallel bank of Kalman filters. These filters generate a set of channel estimates conditioned on the possible symbol subsequences contributing to the intersymbol interference. The conditional estimates and MAP symbol metrics are then combined using a suboptimum Bayesian formula. Two methods are considered to reduce the computational complexity of the algorithm. First, the technique of reduced-state sequence estimation is adopted to reduce the number of symbol subsequences considered in the channel estimation process and hence the number of parallel filters required. Second, it is shown that the Kalman filters can be replaced by simpler least-mean-square (LMS) adaptive filters. A computational complexity analysis of the LMS Bayesian equalizer demonstrates that its implementation in parallel programmable digital signal processing devices is feasible at 16 kbps. The performance of the resulting algorithms is evaluated through bit-error-rate simulations, which are compared to the performance bounds of the maximum-likelihood sequence estimator. It is shown that the Kalman filter and LMS-based algorithms achieve blind start-up and rapid convergence (typically within 200 iterations) for both BPSK and QPSK modulation formats. >
77Â citations
Cites background or methods from "Bayesian/decision-feedback algorith..."
...with the MAP estimator, and retaining only the N largest metrics p(df>Nblrk) at each iteration [ 12 ]....
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...Finally, it should be mentioned that the number of subsequences that needs to be considered, and hence the computational complexity, can be greatly reduced by incorporating a feedback channel estimator, as described in [ 12 ]....
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27 Apr 1993
TL;DR: In this paper, sequence estimation and symbol detection algorithms for the demodulation of co-channel narrowband signals in additive noise are proposed based on the maximum likelihood (ML) and maximum a posteriori (MAP) criteria for the joint recovery of both cochannel signals.
Abstract: Sequence estimation and symbol detection algorithms for the demodulation of cochannel narrowband signals in additive noise are proposed. These algorithms are based on the maximum likelihood (ML) and maximum a posteriori (MAP) criteria for the joint recovery of both cochannel signals. The error rate performance characteristics of these nonlinear algorithms were investigated through computer simulations. The results are presented. >
49Â citations
References
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IBM1
TL;DR: A coding technique is described which improves error performance of synchronous data links without sacrificing data rate or requiring more bandwidth by channel coding with expanded sets of multilevel/phase signals in a manner which increases free Euclidean distance.
Abstract: A coding technique is described which improves error performance of synchronous data links without sacrificing data rate or requiring more bandwidth. This is achieved by channel coding with expanded sets of multilevel/phase signals in a manner which increases free Euclidean distance. Soft maximum--likelihood (ML) decoding using the Viterbi algorithm is assumed. Following a discussion of channel capacity, simple hand-designed trellis codes are presented for 8 phase-shift keying (PSK) and 16 quadrature amplitude-shift keying (QASK) modulation. These simple codes achieve coding gains in the order of 3-4 dB. It is then shown that the codes can be interpreted as binary convolutional codes with a mapping of coded bits into channel signals, which we call "mapping by set partitioning." Based on a new distance measure between binary code sequences which efficiently lower-bounds the Euclidean distance between the corresponding channel signal sequences, a search procedure for more powerful codes is developed. Codes with coding gains up to 6 dB are obtained for a variety of multilevel/phase modulation schemes. Simulation results are presented and an example of carrier-phase tracking is discussed.
4,091Â citations
TL;DR: In this article, an adaptive digital filtering algorithm that can compensate for both frequency-selective multipath and interference on constant envelope modulated signals is presented, which exploits the fact that multipath reception and various interference sources generate incidental amplitude modulation on the received signal.
Abstract: An adaptive digital filtering algorithm that can compensate for both frequency-selective multipath and interference on constant envelope modulated signals is presented. The method exploits the fact that multipath reception and various interference sources generate incidental amplitude modulation on the received signal. A class of so-called constant modulus performance functions is developed which sense this AM term but are insensitive to the angle modulation. Simple adaptive algorithms for finite-impulse-response (FIR) digital filters are developed which employ a gradient search of the performance function. One of the resulting algorithms is simulated for the example of an FM signal degraded by specular multipath propagation. Substantial improvements in noise power ratio (NPR) are observed (e.g., 25 dB) with moderately rapid convergence time. These results are then extended to include tonal interference on a FM signal and intersymbol interference on a QPSK data signal.
1,339Â citations
NEC1
TL;DR: A self-recovering equalization algorithm, which is employed in multilevel amplitude-modulated data transmission, is presented and the convergence processes of the present self-reaching equalizer are shown by computer simulation.
Abstract: A self-recovering equalization algorithm, which is employed in multilevel amplitude-modulated data transmission, is presented. Such a self-recovering equalizer has been required when time-division multiplexed (TDM) voice or picturephone PCM signals must be transmitted over the existing frequency-division multiplexed (FDM) transmission channel. The present self-recovering equalizer is quite simple, as is a conventional binary equalizer. The convergence processes of the present self-recovering equalizer are shown by computer simulation. Some theoretical considerations on this convergence process are also added.
909Â citations
TL;DR: A simple technique for quadrature partial-response signaling (QPRS) is described that eliminates the quasicatastrophic nature of the ML trellis and shows that a good performance/complexity tradeoff can be obtained.
Abstract: A reduced-state sequence estimator for linear intersymbol interference channels is described. The estimator uses a conventional Viterbi algorithm with decision feedback to search a reduced-state subset trellis that is constructed using set-partitioning principles. The complexity of maximum-likelihood sequence estimation (MLSE) due to the length of the channel memory and the size of the signal set is systematically reduced. An error probability analysis shows that a good performance/complexity tradeoff can be obtained. In particular, the results indicate that the required complexity to achieve the performance of MLSE is independent of the size of the signal set for large enough signal sets. Simulation results are provided for two partial-response systems. A simple technique for quadrature partial-response signaling (QPRS) is described that eliminates the quasicatastrophic nature of the ML trellis. >
780Â citations