Ergodic Sum Capacity of Macrodiversity MIMO Systems in Flat Rayleigh Fading

The prospect of base station cooperation leading to joint combining at widely separated antennas has led to increased interest in macrodiversity systems, where both sources and receive antennas are geographically distributed. In this scenario, analytical investigation of channel capacity is extremely challenging for finite-size systems since the channel matrices have a very general form where each path may have a different power. Hence, in this paper, we consider the ergodic sum capacity of a macrodiversity multiple-input multiple-output system with arbitrary numbers of sources and receive antennas operating over Rayleigh fading channels. For this system, we compute the exact ergodic capacity for a system with at most two transmit antennas and a compact approximation for the general system, which is shown to be very accurate over a wide range of cases. Finally, we compare our results with previous asymptotic results and bounds. Results are verified by Monte Carlo simulations and the impact on capacity of various channel power profiles is investigated.