On the Ergodic Capacity of MIMO Triply Selective Rayleigh Fading Channels

The ergodic capacity is investigated for triply selective MIMO Rayleigh fading channels. A mathematical formula is derived for the ergodic capacity in the case when the channel state information is known to the receiver but unknown to the transmitter. A closed-form formula is derived that quantifies the effect of the frequency-selective fading on the ergodic capacity into an intersymbol interference (ISI) degradation factor. Different from the existing conclusion that the frequency-selective fading channel has the same ergodic capacity as the frequency flat fading channel, we show that the discrete-time inter-tap correlated frequency-selective fading channel has smaller ergodic capacity than 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. Theoretical derivation and computer simulation demonstrate that the inter-tap correlations can have more significant impact on the ergodic capacity than the spatial correlations.