Mutual Information of IID complex Gaussian signals on block Rayleigh-faded channels

In English We present a method to compute, quickly and efficiently, the mutual information achieved by an IID (independent identically distributed) complex Gaussian input
on a block Rayleigh-faded channel. The method accommodates both scalar and MIMO (multiple-input multiple-output) settings.
Operationally, the mutual information thus computed represents the highest spectral efficiency that can be attained using standard Gaussian codebooks.

Examples are provided that
illustrate the loss in spectral efficiency caused by fast fading and how that loss is amplified by the use of multiple transmit antennas.
These examples are further enriched by comparisons with the channel capacity under perfect channel-state information at the receiver, and with the spectral
efficiency attained by pilot-based transmission.