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

Closed form expressions for the bit error rate (BER) for a multiple input multiple output (MIMO) relay system employing maximum likelihood (ML) based decode and forward (DF) cooperative diversity are obtained. The DF operation at the relay involves maximal ratio combining (MRC) on the source-relay link and space-time coding (STC) on the relay-destination link. Exact expressions of the BER are obtained for the case of a single relay supporting two antennas. For a system employing a large number of relays, each having two antennas, approximate expressions for the BER are obtained using the piecewise linear (PL) approximation for the ML detector. This is done by finding the statistics of conditionally Gaussian random variables, that appear in the decision variable. The validity of the analytical expressions is then verified through simulations. Through numerical results obtained from the BER expressions for large number of relays, it is then shown that the loss in diversity order due to DF can be compensated by using multiple antennas at the relay.