Correlated Keyhole MIMO Channels: SNR and Outage Capacity Distributions

Keyhole MIMO channels, which were predicted theoretically and also observed experimentally, have recently received significant attention as they may appear in some practically-important propagation scenarios. This paper concentrates on the capacity study of such channels. Closed-form expressions for the instantaneous SNR and outage capacity distributions of a spatially correlated keyhole MIMO channel are given. The case of non-singular correlation matrices with distinct eigenvalues is considered in detail. When the numbers of Tx and Rx antennas are both large, the asymptotic outage capacity distribution of the keyhole channel is Gaussian under general conditions on the correlation (the average SNR affects the mean and the correlation affects the variance). The Gaussian approximation is accurate already for a reasonably small number of antennas (2times2). Based on the asymptotic capacity analysis, a full ordering scalar measure of MIMO channel correlation and power imbalance is introduced. Using this measure, we show analytically that the outage capacity at low outage probabilities decreases with correlation