Performance Analysis of Maximum Likelihood Detection for Decode and Forward MIMO Relay Channels in Rayleigh Fading

Maximum-likelihood (ML) detectors for single-input-single-output (SISO) relay systems are well known. In this paper, closed form expressions for the bit error rate (BER) for multiple-input-multiple-output (MIMO) relay systems employing ML based decode and forward (DF) cooperative diversity are obtained. The DF operation at the relay intelligently employs the multiple antennas available at the relay for receive diversity on the source-relay link and space-time coding (STC) on the relay-destination link resulting in an extension of the ML detection rule for SISO systems to MIMO systems as well. For the piecewise linear (PL) approximation to the ML detector, exact expressions for the BER are obtained for single-relay systems with both the source and relay supporting multiple antennas. For a multirelay system, each relay having multiple antennas, approximate expressions for the BER are obtained. This is done by finding the statistics of conditionally Gaussian (CG) random variables, that appear in the decision variable. Through numerical results obtained from the BER expressions, it is shown that using multiple antennas at the source as well as the relay leads to significant improvement in BER performance.