Optimum Receiver for a Realistic Transmit-Receive Diversity System

We consider a transmit-receive diversity system in correlated Rayleigh fading in which the receiver estimates the channel through pilot symbols, and feeds this information back to the transmitter through a feedback path. The imperfect channel state information is used by the transmitter to obtain the transmit weight vector for data transmission. The optimum receiver in the maximum likelihood sense obtained from the conditional distribution of the received signal vector, conditioned on the imperfect channel estimate and the transmit weight vector, is derived for the system. For the case of M-ary phase-shift keying, an analytical expression for the conditional symbol error probability (SEP), conditioned on the channel estimate and the transmit weight vector, is obtained. The transmit weight vector is chosen to minimize this conditional SEP. Numerical results are presented to compare the performance of our receiver with that of a conventional receiver.