This paper considers multiple symbol differential detection (DD) for both single-antenna and multiple-antenna systems over flat Ricean-fading channels. We derive the optimal multiple symbol detection (MSD) decision rules for both Mary differential phase-shift keying (MDPSK) and differential unitary space-time modulation (DUSTM). The sphere decoder (SD) is adopted to solve the MSD for MDPSK. As well, an improved SD is proposed by using the Schnorr-Euchner strategy. A suboptimal MSD based decision feedback DD algorithm is proposed for the MSD of DUSTM. We also develop a sphere decoding bound intersection detector (SD-BID) to optimally solve the MSD problem for DUSTM, which still maintains low complexity. Simulation results show that our proposed MSD algorithms for both single-antenna and multiple-antenna systems reduce the error floor of conventional DD but with reasonably low computational complexity.udud
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