Suboptimal multiple-symbol differential detection of MPSK with diversity reception

Simon and Alouini (2001) have derived the structure of the optimal N-length differential detector for differentially encoded M-ary phase-shift keying signals, transmitted over a slow fading diversity channel. Even though there is no explicit phase estimation and compensation being performed at the receiver, it was demonstrated that as N increases, the error performance of this multiple-symbol differential detector approaches that of maximal-ratio combining (with differential encoding). Unfortunately, efficient implementation of this optimal receiver is not possible, and it exhibits a computational complexity exponential in N. The computational complexity can be reduced dramatically to N log N if the receiver first performs coherent combining of the received multichannel baseband signals, followed by single-channel multiple-symbol differential detection (MSDD). A coherent combiner is introduced that is capable of cophasing the multichannel signals without violating the fundamental nature of differential detection, i.e. to avoid explicit phase estimation. The proposed suboptimal coherent combining MSDD (CC-MSDD) receiver essentially consists of two differential detectors: one operating across diversity branches, and one operating across time. Owing to the dramatic reduction in complexity, a very large observation window is used with the CC-MSDD. With window size N=64, the asymptotic performance of the CC-MSDD is only 0.5 dB away from maximal-ratio combining with differential encoding. This translates into a 1.5 dB gain in power efficiency over conventional equal gain combining for a second-order diversity system. The authors also investigate suboptimal receivers which perform selection combining, followed by single-channel MSDD. Although these selection combining MSDD receivers provide less than satisfactory performance in stand-alone mode, they are promising candidates for the initial detector in blind, iterative coherent detectors that operate on the principle of decision feedback.