Optimum Sequential Detector Performance on Intersymbol Interference Channels

Tight upper and lower bounds on the average probability of error are obtained for the nonlinear optimum sequential detector with zero "look ahead." A linear upper bound is obtained that is very tight over a wide range of signal-to-noise ratios and a wide range of values of the intersymbol interference. The structure of the linear detector whose performance is given by the linear bound is determined and shown to take the form of a semi-infinite transversal equalizer. The tap values of the equalizer are related to the channel impulse response and the performance of realizable truncated equalizers is obtained in the form of the average probability of error versus equalizer length.