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

TL;DR

This paper introduces an efficient method to compute the mutual information for IID complex Gaussian signals over block Rayleigh-faded channels, applicable to both scalar and MIMO systems, highlighting the impact of fading and antenna configurations.

Contribution

It provides a novel, fast computational approach for mutual information in Rayleigh-faded channels without side information, applicable to scalar and MIMO systems, and compares spectral efficiencies under various conditions.

Findings

Fast fading reduces spectral efficiency.

Multiple transmit antennas amplify the loss due to fading.

Spectral efficiency is higher with perfect channel knowledge.

Abstract

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 without side information at the receiver. 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.