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.

MLSE for an unknown channel .I. Optimality considerations

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.

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Nonlinear techniques for the joint estimation of cochannel signals

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.

/pdf/blind-turbo-equalization-in-gaussian-and-impulsive-noise-2bgjd6rp7t.pdf

Blind turbo equalization in Gaussian and impulsive noise

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. >

Bayesian algorithms for blind equalization using parallel adaptive filtering

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. >

Joint demodulation of cochannel signals using MLSE and MAPSD algorithms

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.

Bayesian/decision-feedback algorithm for blind adaptive equalization

Adaptive algorithms with rapid convergence properties for the equalization of time division multiple access (TDMA) mobile radio signals are presented. When the symbol timing is known, these algorithms approximate maximum a posteriori (MAP) sequence estimators that generate reliable estimates of the transmitted signal. For channels with timing jitter (from random Doppler shifts), joint estimation of the channel parameters and the symbol timing using an extended Kalman filter (EKF) algorithm is proposed. Various methods to reduce the computational complexity of the MAP sequence estimator are also described. >

http://ieeexplore.ieee.org/iel2/445/6707/00269178.pdf

K. Giridhar

Papers

Bayesian/decision-feedback algorithm for blind adaptive equalization

Fast dual-mode adaptive algorithms for the equalization and timing recovery of TDMA mobile radio signals