Bayesian algorithms for blind equalization using parallel adaptive filtering

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