Equalization through large-deviation bounds

Channel equalization methods are used to mitigate the effects of inter-symbol interference (ISI). Traditional methods, maximize the signal to noise ratio (SNR), as a means to convert an ISI channel into a memoryless AWGN channel. Nevertheless, SNR maximization is not reflective of the error probability and lead typically to suboptimal solutions. Our viewpoint is to directly characterize the overall probability of symbol error by means of a Chernoff type bound for a given channel/receiver combination. The main idea behind our technique is to exploit the randomness of transmitted symbols to average out ISI rather than invert the channel dynamics. The problem reduces to choosing a receiver that minimizes the exponent in the Chernoff bound. This problem is shown to reduce to a mixed convex optimization problem. We comment on how the solution methodology can have implications for a fundamental understanding of the tradeoff between channel uncertainty and bit error probability, a situation commonly encountered in wireless communications.