Impact of spatial correlation on the performance of orthogonal space-time block codes

We analyze the impact of transmitter and receiver spatial correlation on the performance of a multiple-input multiple-output (MIMO) system which applies an orthogonal space-time block code with no channel state information at the transmitter and perfect channel state information at the receiver. We derive a general formula for the bit error rate of a MIMO system with arbitrary number of transmit and receive antennas as a function of the correlation at the transmitter and the receiver. We prove that the diversity advantage is given by M·N if M is the rank of the transmit correlation matrix and N the rank of the receive correlation matrix, respectively.