Multiple-symbol differential sphere decoding for unitary space-time modulation

We consider multiple-symbol differential detection (MSDD) for multiple-input multiple-output (MIMO) Rayleigh-fading channels. MSDD, which jointly processes blocks of N received symbols to detect N - 1 data symbols, allows for power-efficient transmission over rapid-fading channels. However, the complexity of the straightforward approach to find the maximum-likelihood (ML) MSDD solution is exponential in N, the number of transmit antennas N_T and the rate R. In this paper, we introduce an MSDD algorithm based on sphere decoding whose average complexity is not exponential in N for interesting ranges of signal-to-noise ratio (SNR) and arbitrary unitary signal constellations. For the interesting special cases of diagonal and orthogonal constellations we achieve a similar complexity reduction in N_T and R. Based on an error-rate analysis for MSDD we also propose a variant of MSDD that considerably improves power efficiency in relatively fast fading at a very moderate increase in complexity.