Characterization of Mutual Information of Spatially Correlated MIMO Channels with Keyhole

We characterize the statistical properties of the mutual information between the transmitter and the receiver of a multiple-input multiple-output (MIMO) communication system in case of spatially correlated Rayleigh-fading keyhole channels with arbitrarily correlated input signals and potentially colored additive Gaussian noise. The probability density function (pdf) as well as the cumulative distribution function (cdf) of the mutual information are derived in a concise mathematical form and we determine exact analytical closed-form expressions for its mean value as well as the corresponding high SNR asymptotics. Numerical results illustrate the impact of several different parameters on the mutual information statistics and are shown to be in perfect agreement with results obtained from Monte-Carlo simulations, thus verifying the accuracy of our theoretical analysis.