Generic procedure for tightly bounding the capacity of MIMO correlated Rician fading channels

No systematic procedure for tightly bounding the average capacity of multiple-input-multiple-output (MIMO) correlated Rician fading channels is available in the literature. In addition to the involvement of a highly nonlinear log-determinant operator in the conditional capacity expression, the difficulty arises from the complicated noncentral Wishart distribution of channel sample matrix. 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 an explicit expression for the general moment of the determinant of the channel sample matrix, we obtain a general upper bound for the average channel capacity. To obtain a general lower bound, we construct and prove a multivariate convex function with each of its variables being the log-determinant function of a complex noncentral Wishart-distributed matrix. We further show that the general bounds so obtained can be simplified to explicit expressions for Rician fading channels with arbitrary semicorrelation and a mean matrix of rank one. The new results are simple, easy to be used, and superior in tightness as evidenced by intensive numerical examples.