On the Outage Capacity Distribution of Correlated Keyhole MIMO Channels

Keyhole multiple-input-multiple-output (MIMO) channels have recently received significant attention since they can model, to a certain extend, some practically important propagation scenarios and also relay channels in the amplify-and-forward mode. This paper investigates instantaneous signal-to-noise ratio (SNR) and outage capacity distributions of spatially correlated keyhole MIMO channels with perfect channel state information (CSI) at the receive end and with or without CSI at the transmit end. For a small number of antennas, the impact of correlation on the capacity distribution can be characterized by the effective average SNR. This SNR, as well as the outage capacity, decreases with correlation. For a large number of transmit (receive) antennas, the keyhole channel is asymptotically equivalent (in terms of capacity) to the Rayleigh diversity channel with a single transmit (receive) antenna and multiple receive (transmit) antennas. The outage capacity of the keyhole channel is upper-bounded by that of the equivalent Rayleigh diversity channel. When the number of both transmit and receive antennas is large, the outage capacity distribution of the keyhole channel is asymptotically Gaussian. In some cases, the asymptotic Gaussian approximation is accurate already for a reasonably small number of antennas. The perfect transmit CSI is shown to bring a fixed SNR gain. A more general channel model with multiple keyholes is proposed. For a large number of antennas, the capacity of a multikeyhole channel is a normally distributed sum of the capacities of single keyhole channels. The fact that, despite the strong degenerate nature of the keyhole channel, its outage capacity distribution is asymptotically normal indicates that Gaussian distribution has a high degree of universality for the capacity analysis of MIMO channels.