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.


Electrical and Computer Engineering


National Science Foundation (U.S.)
United States. Office of Naval Research
University of Missouri Research Board

Keywords and Phrases

MIMO Channel; Rayleigh Fading; Ergodic Capacity; Frequency Selective Fading; Triply Selective Fading

Document Type

Article - Journal

Document Version

Final Version

File Type





© 2008 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.

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