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 probability density function (PDF), cumulative distribution function (CDF), complementary CDF (C2DF), moment-generating function (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, C2DF 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 maximum a priori (MAP) and maximum likelihood (ML) symbol decisions and thereby obtain closed-form expressions for both bit error rate (BER) of binary modulation schemes and symbol error rate (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.
Highlights
The additive white noise in communication systems [1]–[5, and references therein] is commonly defined as an arbitrarily varying undesired signal that additively corrupts signal transmission over communication channels
As a result of these closed-form expressions, each of which is mathematically tractable and practically understandable, we propose the framework of the laws of McLeish distribution for the first time in the literature
We theoretically justify the existence of McLeish noise distribution in communication systems in case of uncertainty due to that the additive noise distribution has impulsive effects causing the variance of additive noise varies over time
Summary
The additive white noise in communication systems [1]–[5, and references therein] is commonly defined as an arbitrarily varying undesired signal that additively corrupts signal transmission over communication channels. In case of impulsive effects which yields heavy-tailed non-Gaussian noise distribution, there is a demanding need to investigate the statistical laws of the sum of non-Gaussian distributions Due to the purposes mentioned previously, there exists a demand for multivariate CCS / CES non-Gaussian distribution that yields closed-form distribution laws We offer some concluding results in the last section
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