Performance Analysis and Simplified Detection for Two-Dimensional Signal Space Diversity with MRC Reception

Signal space diversity (SSD) is a promising technique for obtaining diversity without increases in bandwidth, transmit power or physical hardware at the expense of increased ML detection complexity. Symbol error rate (SER) analysis of a two-dimensional system containing a single transmit antenna and N receive antennas with maximal-ratio combining (MRC) reception is presented here along with a simplified detection scheme for SSD systems. The union bound and the nearest neighbour (NN) approximation are presented in closed form, and a new, simpler SER bound for SSD systems based on the minimum Euclidean distance of a rotated constellation is presented, also in closed form. Performance of the new bound is found to be tight for low signal-to-noise ratios (SNRs), small rotation angles and when the number of receive antennas (N) is large; the new bound is also easily applied to other systems. The simplified detection scheme, while losing diversity and SER performance when N = 1, achieves a 7dB and 4dB performance improvement over non-SSD transmission at SERs of 10⁻³and 10⁻² for 4-QAM and 16-QAM respectively. However, when N ≥ 3, SER performance is close to indistinguishable from that of optimal ML detection while achieving complexity reductions of up to 5.77%, 70.19% and 91.77% for 4-QAM, 16-QAM and 64-QAM respectively.