On the Scaling Behavior of Average Ergodic Capacity of Distributed MIMO Systems

Different from the classical point-to-point multiple-input- multiple-output (MIMO) system, the ergodic capacity of a distributed MIMO system depends on the large-scale fading coefficients between the user and the geographically separated base-station (BS) antennas. Due to the lack of a closed-form expression, how the average ergodic capacity scales with the number of distributed BS antennas remains largely unknown. In this paper, we focus on the scaling behavior of the average ergodic capacity of a downlink single-user MIMO system where the BS antennas are grouped into uniformly distributed clusters in a circular cell. By assuming that the numbers of antennas at the user and each cluster go to infinity with a fixed ratio β, asymptotic lower-bounds of the average ergodic capacity with and without channel state information at the transmitter side (CSIT) are derived as explicit functions of the ratio β and the number of BS antenna clusters L. The analysis reveals that the asymptotic lower-bounds in both cases logarithmically increase with L, but the scaling order depends on the ratio β and the availability of CSIT. Simulation results verify that the average ergodic capacities with and without CSIT have the same scaling orders as their asymptotic lower-bounds.