Ergodic capacity of MIMO triply selective Rayleigh fading channels

New results are presented for the ergodic capacity of spatially-correlated, time-varying and frequency-selective (i.e., triply selective) MIMO Rayleigh fading channels. Simplified capacity formulas are also derived for special cases such as SIMO and MISO triply selective fading channels. A closed form formula is proposed that quantifies the effect of the frequency-selective fading on the ergodic capacity into an intersymbol interference (ISI) degradation factor. It is discovered that, in general frequency-selective MIMO channels, the ISI inter-tap correlations reduce the ergodic capacity compared to the frequency flat fading channel. Only in the special case when the fading does not have ISI inter-tap correlations will the ergodic capacity be the same as that of the frequency flat channel. The new capacity results are experimentally verified via Monte-Carlo simulations.