Making MLSD-decisions on some individual symbols in a sequence by thresholding the matched filter output

We present a detector that, by thresholding the output of the matched filter, gives MLSD-decisions on binary, antipodally modulated symbols that have been corrupted by intersymbol interference and additive Gaussian noise. The detector is simple in structure, consisting of a whitened matched filter and two variable thresholds for each symbol to be detected. The detector will make decisions on some, but most often not all, of the symbols in a transmitted sequence, and those decisions will be the same decisions as the maximum likelihood sequence detector (MLSD) would have made. The number of symbols that are detected is stochastic, varying from sequence to sequence. The basis of the detector is a bound on a cross-product of the quadratic form in the log-likelihood function for the transmitted sequence