Adaptive channel equalization using approximate Bayesian criterion

The Bayesian solution is known to be optimal for the symbol-by-symbol type of equalizer. However, the computational complexity for the Bayesian equalizer is usually very high. Signal space partitioning technique has been proposed for complexity reduction. It was shown the decision boundary of the equalizer consists of a set of hyperplanes. The disadvantage of the existing approaches is that the number of hyperplane cannot be controlled. Also, to find these hyperplanes, it requires a state searching process which is not efficient for time-varying channels. In this paper, we propose a new algorithm to remedy this problem. We propose an approximate Bayesian criterion such that the number of hyperplanes can be arbitrarily set. As a result, we can trade between performance and computational complexity. In many cases, we can make the performance loss being small while the computational complexity reduction is huge. The resultant equalizer is composed of a set of parallel linear discriminant functions and a maximum operation. An adaptive method using stochastic gradient descent is developed to identify the functions. The proposed algorithm is then inherently applicable to time-varying channels. Also, the computational complexity is low and suitable for real-world implementation.