McLeish Distribution: Performance of Digital Communications over Additive White McLeish Noise (AWMN) Channels

TL;DR

This paper introduces the McLeish distribution as a versatile non-Gaussian noise model for digital communication channels, deriving its properties, extensions to complex and multivariate cases, and analyzing system performance over channels with McLeish noise.

Contribution

It proposes the McLeish distribution and its multivariate and complex extensions, deriving their properties and applying them to model impulsive noise in communication systems.

Findings

Derived closed-form PDFs, CDFs, MGFs, and moments for McLeish distributions.

Established McLeish distribution as a valid noise model in communication channels.

Provided analytical BER and SER expressions for systems affected by McLeish noise.

Abstract

The objective of this article is to propose and statistically validate a more general additive non-Gaussian noise distribution, which we term McLeish distribution, whose random nature can model different impulsive noise environments commonly encountered in practice and provides a robust alternative to Gaussian noise distribution. In particular, for the first time in the literature, we establish the laws of McLeish distribution and therefrom derive the laws of the sum of McLeish distributions by obtaining closed-form expressions for their PDF, CDF, complementary CDF (C$^2$DF), MGF and higher-order moments. Further, for certain problems related to the envelope of complex random signals, we extend McLeish distribution to complex McLeish distribution and thereby propose circularly/elliptically symmetric (CS/ES) complex McLeish distributions with closed-form PDF, CDF, MGF and higher-order moments. For generalization of one-dimensional distribution to multi-dimensional distribution, we develop and propose both multivariate McLeish distribution and multivariate complex CS/ES (CCS/CES) McLeish distribution with analytically tractable and closed-form PDF, CDF, C$^2$DF and MGF. In addition to the proposed McLeish distribution framework and for its practical illustration, we theoretically investigate and prove the existence of McLeish distribution as additive noise in communication systems. Accordingly, we introduce additive white McLeish noise (AWMN) channels. For coherent/non-coherent signaling over AWMN channels, we propose novel expressions for MAP and ML symbol decisions and thereby obtain closed-form expressions for both BER of binary modulation schemes and SER of various M-ary modulation schemes. Further, we verify the validity and accuracy of our novel BER/SER expressions with some selected numerical examples and some computer-based simulations.