Channel Capacity Over Generalized Fading Channels: A Novel MGF-Based Approach for Performance Analysis and Design of Wireless Communication Systems

Abstract

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Since the trail-blazing paper of C. Shannon in 1948, channel capacity has been regarded as the fundamental information-theoretic performance measure to predict the maximum information rate of a communication system. However, in contrast with the analysis of other important performance measures of wireless communication systems, a unified and general approach for computing the channel capacity over fading channels has yet to be proposed. Motivated by this consideration, we propose a novel and unified communication-theoretic framework for the analysis of channel capacity over fading channels. It is shown that the framework can handle various fading channel models, communication types, and adaptation transmission policies. In particular, the specific contributions of this paper are as follows: 1) We introduce a transform operator, called the <formula formulatype="inline"><tex Notation="TeX">$E_{i}$</tex> </formula>-transform, which is shown to provide a unified tool to compute the channel capacity with either <emphasis emphasistype="boldital">side information at the receiver or side information at the transmitter and the receiver</emphasis>, directly from the moment-generating function (MGF) or the MGF and the <emphasis emphasistype="boldital">truncated</emphasis> MGF of the Signal-to-Noise-Ratio (SNR) at the receiver, respectively; 2) we show that when either a <emphasis emphasistype="boldital">channel inversion</emphasis> or a <emphasis emphasistype="boldital">truncated channel inversion</emphasis> adaptation policy is considered, the channel capacity can readily be computed from the Mellin or the Hankel transform of the MGF of the received SNR, respectively; 3) a simple yet effective numerical method for the analysis of higher order statistics (HOS) of the channel capacity with <emphasis emphasistype="boldital">side information at the receiver</emphasis> is introduced; and 4) some efficient and ad hoc numerical methods are explicitly introduced to allow the efficient computation of the proposed frameworks. Numerical and simulation results are also shown and compared to substantiate the analytical derivation. </para>