Tight lower bounds on the ergodic capacity of Rayleigh fading MIMO channels

We consider Gaussian multiple-input multiple-output (MIMO) fading channels assuming that the channel is unknown at the transmitter and perfectly known at the receiver. Using results from multivariate statistics, we derive a tight closed-form lower-bound for the ergodic capacity of such channels at any signal-to-noise ratio (SNR). Moreover, we provide an accurate closed-form analytical approximation of ergodic capacity in the high SNR regime. Our analysis incorporates the frequency-selective Rayleigh fading case and/or spatial fading correlation, and allows Important Insights Into optimal (ergodic capacity maximizing) MIMO configurations. Finally, we verify our analytical expressions through comparison with numerical results.