Optimum transmit-receive beamforming with noisy channel estimates for correlated MIMO Rayleigh channels

In this paper, we design jointly optimum transmitter and receiver beamforming structures in correlated MIMO Rayleigh fading channels with noisy channel estimates, and evaluate their performance through a closed-form expression for the probability of error. At the receiver, an estimate of the channel is obtained based on the transmitted pilot symbols. The knowledge of the estimate is then made available to the transmitter through a feedback channel. It is assumed that spatial correlation exists, either at the transmitter or at the receiver. A new exact closed-form expression for the probability of error is derived and the joint effects of diversity order and channel estimation accuracy on system performance are analyzed.