On the outage capacity distribution of correlated keyhole MIMO channels

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 a 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 number of Tx (Rx) antennas is large, the correlated keyhole channel tends asymptotically to the Rayleigh diversity channel with a single Tx (Rx) and multiple Rx (Tx) antennas. The outage capacity at low outage probabilities and the diversity order of the keyhole channel is upper-bounded by that of the equivalent Rayleigh diversity channel. The asymptotic outage capacity distribution, when the numbers of Tx and Rx antennas are both large, 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. Using the single-parameter exponential correlation matrices, we show that the outage capacity at low outage probabilities decreases with correlation