Asymptotic Average Mutual Information Over Finite Input Mixture Gamma Distributed Channels

TL;DR

This paper develops a unified framework to analyze the asymptotic average mutual information of mixture gamma distributed fading channels with finite inputs at high SNR, revealing convergence behavior and optimal power allocation strategies.

Contribution

It introduces a novel analytical approach for AMI in mixture gamma channels and derives asymptotic convergence and power allocation policies for finite input signals.

Findings

AMI converges to a constant at high SNR

Rate of convergence depends on coding gain and diversity order

Optimal power allocation favors sub-channels with lower coding gain or diversity

Abstract

This letter establishes a unified analytical framework to study the asymptotic average mutual information (AMI) of mixture gamma (MG) distributed fading channels driven by finite input signals in the high signal-to-noise ratio (SNR) regime. It is found that the AMI converges to some constant as the average SNR increases and its rate of convergence (ROC) is determined by the coding gain and diversity order. Moreover, the derived results are used to investigate the asymptotic optimal power allocation policy of a bank of parallel fading channels having finite inputs. It is suggested that in the high SNR region, the sub-channel with a lower coding gain or diversity order should be allocated with more power. Finally, numerical results are provided to collaborate the theoretical analyses.