Ergodic Capacity Analysis of Wireless Channels Using Iterated Laplace Transform

In this paper, we establish a unified mathematical approach that connects the ergodic capacity of a wireless channel to the iterated Laplace transform of the channel's statistical characteristics. Particularly, we show that the ergodic capacity of any wireless channel can be interpreted as the iterated Laplace transform of the complementary cumulative distribution function (CCDF) of the effective channel power gain. Building on this intriguing result, we analyze and exemplify the ergodic capacity of a very general class of wireless channels whose CCDF is expressed in terms of a product of a power function and a Fox $H$-function. Interestingly, the ergodic capacity of such a class of wireless channels can be straightforwardly obtained by means of the iterated Laplace transform, thereby circumventing the task of solving intricate integrals that are typically indispensable to quantifying the ergodic capacity. Furthermore, we extend our iterated Laplace transform approach to analyze and exemplify the ergodic capacity in various communication settings, including diversity combining receivers, double fading channels, mobility, and communication in the presence of co-channel interference. Our approach not only simplifies the evaluation of ergodic capacity across these settings but also provides a novel perspective that underscores its merit across a wide range of applications.