Very tight bounds for the capacity of MIMO correlated Rician fading channels

Abstract

No systematic procedure for tightly bounding the average capacity of MIMO correlated Rician fading channels is available in the literature. The difficulty arises from the complicated non-central Wishart distribution of channel sample matrix, in addition to the involvement of a highly nonlinear log determinant operator in the conditional capacity expression. In this paper, we tackle the problem with arbitrary antenna correlation existing either at the transmitter or at the receiver, but allowing for the numbers of the transmit and receive antennas to be arbitrary. By introducing an exact determinant expansion and by finding the explicit expressions for the expected values of the determinant and log-determinant of the complex non-central Wishart-distributed matrix, we obtain a simple but very tight upper and lower bounds for the average channel capacity. Both bounds are simple, in closed form, easy to be used, and superior in tightness as evidenced by intensive numerical examples.