Ergodic capacity of doubly selective Rayleigh fading MIMO channels

The ergodic capacity is investigated for doubly selective (frequency selective and time varying) MIMO Rayleigh fading channels. A closed form formula is derived that quantifies the effect of the ISI fading on the ergodic capacity into an ISI degradation factor. It is discovered that, in general frequency selective MIMO channels, the inter-tap correlations of the ISI fading will reduce the ergodic capacity comparing to the frequency flat fading channel. Only in the special case when the ISI fading does not have inter-tap correlations will the ergodic capacity be the same as that of the frequency flat channel. This new formula is mathematically proved and experimentally verified via Monte-Carlo simulations.