Maximum-likelihood receiver for four-dimensional signaling schemes corrupted by ISI

A maximum-likelihood decision-directed receiver structure is derived for a data transmission system which employs quadrature-quadrature phase shift keying (Q²PSK) as the modulation scheme. The receiver is derived by treating the problem of sequence decision, sample timing, and carrier phase as a composite estimation problem. It is shown that the resulting maximum-likelihood estimates (MLEs) are asymptotically unbiased, and the variances of these estimates are derived. In this receiver, symbol detection is carried out by means of a modified Viterbi algorithm (MVA) while a parallel synchronizer is used for carrier phase and delay recovery. As a measure of performance, an error-event probability bound is derived for the MVA. The effect of intersymbol interference, (ISI) present at the two matched filters´ outputs, on the error bound is analyzed and illustrated. It is shown that the resulting MVA and the parallel estimator are well suited for systolic array implementation