On the Outage Capacity of Correlated Multiple-Path MIMO Channels

The use of multi-antenna arrays in both transmission and reception has been shown to dramatically increase the throughput of wireless communication systems. As a result there has been considerable interest in characterizing the ergodic average of the mutual information for realistic correlated channels. Here, an approach is presented that provides analytic expressions not only for the average, but also the higher cumulant moments of the distribution of the mutual information for zero-mean Gaussian (multiple-input multiple-output) MIMO channels with the most general multipath covariance matrices when the channel is known at the receiver. These channels include multi-tap delay paths, as well as general channels with covariance matrices that cannot be written as a Kronecker product, such as dual-polarized antenna arrays with general correlations at both transmitter and receiver ends. The mathematical methods are formally valid for large antenna numbers, in which limit it is shown that all higher cumulant moments of the distribution, other than the first two scale to zero. Thus, it is confirmed that the distribution of the mutual information tends to a Gaussian, which enables one to calculate the outage capacity. These results are quite accurate even in the case of a few antennas, which makes this approach applicable to realistic situations.