Capacity of a mobile multiple-antenna wireless link with isotropically random Rician fading

We analyze the capacity of a multiple-antenna wireless link with M antennas at the transmitter and N antennas at the receiver in a Rician fading channel when the channel is unknown at both the transmitter and the receiver. The Rician model is a nonstandard model with a Rayleigh component and an isotropically random rank-one specular component. The Rayleigh and specular components remain constant for T symbol periods, after which they change to completely independent realizations, and so on. To maximize mutual information over the joint density of T (.) M complex transmitted signals it is sufficient to maximize over a joint density of min{T, M} real transmitted signal magnitudes. The capacity-achieving signal matrix is equal to the product of two independent matrices, a T X T isotropically random unitary matrix and a T X M real nonnegative diagonal matrix. If M > T, optimum signaling uses only T out of the M transmit antennas. We derive a novel lower bound on capacity which enables us to compute achievable rate regions for many cases. This lower bound is also valid for the case of purely Rayleigh-fading channels, where it has not been feasible, in general, to compute capacity, or mutual information. Our numerical results also indicate that the Rayleigh model is surprisingly robust: under our Rician model, up to half of the received energy can arrive via the specular component without significant reduction in capacity compared with the purely Rayleigh case.