On the asymptotic analysis of the high-order statistics of the channel capacity over generalized fading channels

TL;DR

This paper derives simple asymptotic expressions for the higher-order statistics of channel capacity over generalized fading channels, providing insights into diversity gains at extreme SNRs with validated numerical examples.

Contribution

It introduces closed-form asymptotic formulas for higher-order channel capacity statistics, revealing constant gaps and aiding understanding of diversity gains in fading channels.

Findings

Closed-form asymptotic expressions accurately approximate higher-order statistics.

Asymptotic bounds reveal constant gaps at high and low SNRs.

Numerical examples validate the theoretical results.

Abstract

In this article, we provide further asymptotic analysis to the higher-order statistics (HOS) of the channel capacity over generalized fading channels, especially by proposing simple and closed-form expressions each of which can be easily computed as a tight-bound revealing the existence of constant gap between the actual and asymptotic HOS of the channel capacity in the limit of both high- and low-signal to noise ratios (SNRs). As such, we show that these closed-form asymptotic expressions are insightful enough to comprehend the diversity gains. The mathematical formalism we followed in this article is illustrated with some selected numerical examples that validate the correctness of our newly derived asymptotic results.