We present a method to compute, quickly and efficiently, the mutual information achieved by an IID (independent identically distributed) complex Gaussian signal on a block Rayleigh-faded channel without side information at the receiver. The method accommodates both scalar and MIMO (multiple-input multiple-output) settings. Operationally, this mutual information represents the highest spectral efficiency that can be attained using Gaussiancodebooks. Examples are provided that illustrate the loss in spectral efficiency caused by fast fading and how that loss is amplified when multiple transmit antennas are used. 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.

Lozano's work is supported by the Spanish Ministry of Scienceand Innovation (Refs. TEC2009-13000 and CONSOLIDER-INGENIOCSD2008-00010 ”COMONSENS”) and by AGAUR (Catalan Agency forAdministration of University and Research Grants).