Mutual Information of IID Complex Gaussian Signals on Block Rayleigh-Faded Channels

We present a method to compute, quickly and efficiently, the mutual information achieved by an independent identically distributed (IID) complex Gaussian signal on a block Rayleigh-faded channel without side information at the receiver. The method accommodates both scalar and multiple-input multiple-output (MIMO) settings. Operationally, this mutual information represents the highest spectral efficiency that can be attained using Gaussian codebooks. 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.