A Maximum Likelihood Combining Algorithm for Spatial Multiplexing MIMO Amplify-and-Forward Relaying Systems

Using a spatial multiplexing transmission scheme can improve the data rate in multiple-input-multiple-output (MIMO) relaying systems, while making signal detection more difficult at receivers. Aiming at lowering the computational complexity of the receiver, this paper proposes a maximum likelihood combining (MLC) algorithm for spatial multiplexing MIMO amplify-and-forward (AF) relaying systems in a Rayleigh flat-fading environment, which is implemented before maximum likelihood (ML) detection. The combining signal and equivalent channel are opportunely designed based on the ML rule in the MLC algorithm. We also formulate the diversity gain of the systems that employ the MLC algorithm mathematically, induced by the Chernoff bound of pairwise error probability (PEP). An upper bound on the symbol error probability (SEP) for the MLC algorithm with multiple modulations is also given, based on the derived bound of PEP. Moreover, the complexities of ML receivers adopting the MLC algorithm and the conventional vector combining (VC) algorithm are analyzed. Numerical simulations indicate that systems with the MLC algorithm achieve the same performance while consuming lower computational complexity compared to that with the VC algorithm.