Scalar multiple-symbol differential detection of MPSK with diversity reception

M.K. Simon and M.S. Alouini (2001) derived the structure of the optimal N-length differential detector for differentially encoded M-ary phase shift keying (MPSK) signals over a slow fading diversity channel. It was demonstrated that as N increases, the error performance of this differential detector approaches that of maximal-ratio combining (with differential encoding). Unfortunately, efficient implementation of this optimal receiver is not possible, and it exhibits high computational complexity. We show that the complexity can be reduced dramatically, if the receiver first performs coherent combining of the received multi-channel baseband signals, followed by single-channel multiple-symbol differential detection (MSDD). Our main contribution is the introduction of a coherent combiner that is capable of cophasing the multi-channel signals, without violating the fundamental nature of differential detection; i.e., avoiding 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. Due to the dramatic reduction in complexity, we are able to use a very large observation window, N=64, with the CC-MSDD. With this window size, 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.