ML frame synchronization for the Gaussian channel with ISI

The problem of locating a periodically inserted frame synchronization pattern in random data for a binary pulse amplitude modulated (PAM) digital communication system over an additive white Gaussian noise (AWGN) channel with intersymbol interference (ISI) is considered. The optimum maximum-likelihood (ML) decision rule for frame synchronization over an AWGN channel with ISI is derived. The performances of an ordinary correlation rule are compared with those of the ML rule. A high SNR (signal-to-noise ratio) approximation to the ML rule, which can be implemented as simply as the correlation rule, is also derived.<
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