We extend some previous results on adaptive receivers with memory for slow nonselective Rayleigh fading channels to the case of diversity reception. The Bayes receiver in this case is shown to be a generalized maximal ratio combiner. Error probability performance is obtained for antipodal signals such as BPSK. A simple performance upper bound is also derived. Numerical performance results are presented for the particular case of a Markov channel model.

We consider the problem of simultaneous ML estimation of data and carrier phase from a linear suppressed-carrier modulated signal received in the presence of additive white Gaussian noise. The ML detector of the data sequence is derived, and its error probability performance is analyzed. The result shows that the performance loss due to the unknown carrier phase can be reduced by increasing the sequence length. A suboptimum decision-aided subsequence-by-subsequence detector whose complexity does not increase exponentially with sequence length is proposed, and its performance is analyzed.

The problem of ML estimation of the Phase of a general data-modulated carrier is considered. The shortcomings of current iterative approaches to the problem are pointed out, and the correct conceptual approach is proposed. The true ML estimator is then obtained and found to be nonimplementable. However, by specializing to limits of high and low SNR, the general ML estimator is shown to reduce to implementable DA and NDA ML estimators, respectively. The DA receiver's performance in terms of phase tracking and symbol error probability can be analyzed, and even the effects of past decision errors on current system performance can be assessed. For circular signal constellations, the DA receiver has a simple and totally linear structure which is easy to implement. The NDA ML estimator is shown to be equivalent to the common carrier loops. Our emphasis here on explicit computation of the ML phase estimate from the past received signal leads to detection strategies which do not require a carrier loop and a VCO for coherent detection.

We consider the problem of designing an adaptive receiver with anM-bit memory for binary orthogonal signaling over a slowly fading Rayleigh channel. Both the cases of decision-feedback and no decision-feedback are considered. We present a problem formulation by defining the contents of the receiver's memory. The structure of the Bayes receiver that makes optimum use of the memory information is then established. The LRT that defines the receiver is obtained explicitly, and it dictates a detector-estimator receiver structure. The detector can be interpreted as being partially coherent, with coherence being achieved asymptotically in the limit of perfect estimation of the fading process. Simulation results are given to show the improved error rate performance of the adaptive receiver. Our results also indicate that decision-feedback should be employed in a manner dependent on the SNR.