E.Khan and C.Heneghan

A Closed Form Expression for the Ergodic Capacity of MIMO Systems

Multi-input Multi-output (MIMO) system are today regarded as one of the most promising research areas in wireless communications. This is due to the fact that MIMO channel can offer a significant capacity gain over traditional Single-input single-output (SISO) channel. This paper presents the capacity of an uncorrelated and correlated MIMO channel. The expression for the large system MIMO capacity is calculated in closed form using replica analysis and Grassmann variables. It is assumed that the receiver has perfect knowledge of the channel but no such information is available at the transmitter. It is shown that for large (but finite) number of antennas the capacity scales linearly with the number of antennas. Our expression gives very good approximation of capacity even for 2/3 antenna case. Besides this, using the same analysis we can find the bounds on ergodic capacity when we have noisy channel estimate at the receiver or even when there is co-channel interference (in addition to noise).