A Viterbi-type algorithm for the efficient estimation of a convolutionally/trellis coded, or uncoded M-PSK sequence over the Gaussian channel with unknown carrier phase is presented. It performs coherent detection of M-PSK sequences with no explicit recovery of coherent references. The metric computations involve only linear operations. Theoretical and simulated performance results are presented for various carrier phase processes. The algorithm is called the suboptimum ML estimator (SMLE). Its BER in the presence of a time invariant carrier phase is obtained analytically. The simulation results for the BER with time-invariant as well as time-varying carrier phase processes allow a comparison of the performance of the SMLE with other sequence estimation algorithms, and enable the applicability of the SMLE to burst mode TDMA communications to be ascertained.>

The orthogonal signal structure has been shown to be the superposition of an antipodal signal set and an unmodulated (pilot tone) component which can be used for channel measurement. Starting from this point of view, the quadratic receiver for orthogonal signals over the Gaussian channel with unknown phase/fading has been shown to be equivalent to a detector-estimator receiver. The estimator makes an optimum estimate of the unknown complex channel gain based on the channel measurement provided by the unmodulated component of the received signal. This channel estimate then forms a (partially) coherent reference for the detector in detecting the data carried by the antipodal signaling component of the received signal. This paper exploits this detector-estimator structure of the quadratic receiver, and generalizes it to a receiver in which the estimator makes an estimate of the channel gain in each signaling interval based on the totality of signals received over all the signaling intervals or a subset of these intervals. The generalized quadratic receiver is just as simple to implement as the conventional quadratic receiver, and theoretical and simulation results show that it can achieve substantial performance gains over the conventional receiver. A theory is presented to show that the generalized quadratic receiver is an implementable approximation to the optimum symbol-by-symbol receiver for uncoded orthogonal signals over the Gaussian channel with unknown phase/fading. The theory shows that the structure provides a unified and systematic approach to the design of coherent symbol-by-symbol receivers, and shows that the conventional carrier-loop-type receivers are ad hoc.>

A simple tight upper bound on the BEP of 2DPSK over the AWGN channel with phase noise in the received signal is obtained. The phase is modeled as a Gaussian random process which is slowly varying compared to the bit rate so that a piecewise-constant approximation can be made. The bound is verified by computer simulations, and it provides good estimates of the error probability. It shows that for high SNR the error probability decreases as the reciprocal of the square-root of the SNR. The results are applicable in particular to heterodyne optical communications.>