A Systems Approach to Channel Equalization

In this paper we present a control theoretic frame-work for channel equalization. Channel equalization methods are used to mitigate the effects of inter-symbol interference (ISI). Traditional methods, maximize the signal to noise ratio (SNR) in an attempt to convert a bandlimited ISI channel into a memoryless AWGN channel, which is then followed by symbol detection. Nevertheless, for the purpose of reliable symbol detection both problems - SNR maximization and AWGN channel conversion - are not reflective of the error probability and lead typically to suboptimal solutions. Our viewpoint in this paper 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 ℓ₁/ℓ _∞ problem whose solution can be completely characterized. 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.