Tree-Search Multiple-Symbol Differential Decoding for Unitary Space-Time Modulation

Differential space-time modulation (DSTM) using unitary-matrix signal constellations is an attractive solution for transmission over multiple-input multiple-output (MIMO) fading channels without requiring channel state information (CSI) at the receiver. To avoid a high error floor for DSTM in relatively fast MIMO fading channels, multiple-symbol differential detection (MSDD) has to be applied at the receiver. MSDD jointly processes blocks of several received matrix-symbols, and power efficiency improves as the blocksize increases. But since the search space of MSDD grows exponentially with the blocksize and also with the number of transmit antennas and the data rate, the complexity of MSDD quickly becomes prohibitive. In this paper, we investigate the application of tree-search algorithms to overcome the complexity limitation of MSDD. We devise a nested MSDD structure consisting of an outer and a number of inner tree-search decoders, which renders MSDD feasible for wide ranges of system parameters. Decoder designs tailored for diagonal and orthogonal DSTM codes are given, and a more power-efficient variant of MSDD, so-called subset MSDD, is proposed. Furthermore, we derive a tight symbol-error rate approximation for MSDD, which lends itself to efficient numerical evaluation. Numerical and simulation results for different DSTM constellations and fading channel scenarios show that the new tree-search MSDD achieves a significantly better performance-complexity tradeoff than benchmark decoders.