Sample-whitened matched filters

Abstract

A sample-whitened matched filter (SWMF) for a channel with intersymbol interference and additive white Gaussian noise is defined as a linear filter with the properties that its output samples are a sufficient statistic for the MAP estimation of the transmitted sequence and have uncorrelated noise components. These filters are shown to exist for ali realistic channels and the complete set of SWMF's for any channel is determined. It is shown that for nonpathological channels there is a unique SWMF which minimizes the amount of intersymbol interference defined as the discrete-time analog to the rms duration of a continuous-time signal. Finally, the theory is extended to more general modulation systems including pulse position modulation and frequency position modulation.