A Weighted Combining Algorithm for Spatial Multiplexing MIMO DF Relaying Systems

Jointly detecting the signals from the source and relay in a spatial multiplexing (SM) multiple-input multiple-output (MIMO) relaying system improves the transmit reliability significantly. However, the existing joint detection schemes for SM MIMO relaying systems, which achieve full diversity, such as the near maximum likelihood (ML) decoder, suffer from high complexity. In this paper, we propose a weighted combining (WC) algorithm, which is applied before the detector in the SM MIMO decode-and-forward relaying system. The proposed algorithm merges the received signal vectors from the source and relay into a combined signal without expanding their dimension, and formulates an equivalent MIMO channel matrix for the combined signal, resulting in a lower complexity for the subsequent detection. We analyze the performance of the proposed WC algorithm with ML detection in terms of the diversity order and computational complexity. An approximate upper bound on the symbol error probability (SEP) for the proposed algorithm is also derived. Simulation results show that in symmetric networks, the proposed WC algorithm achieves substantially lower complexity, while maintaining an SEP performance similar to that of the benchmark NML decoder. The consistency of the derived upper bound on the SEP is also verified by simulations.