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This paper considers multiple symbol Differential Detection (DD) for both single-antenna and multiple-antenna systems over flat Ricean-fading channels. The authors 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. They also develop a Sphere Decoding Bound Intersection Detector (SD-BID) to optimally solve the MSD problem for DUSTM, which still maintains low complexity.
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