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

Abstract

The objective of this article is to statistically characterize and describe a more general additive noise distribution, termed as McLeish distribution, whose random nature can model different impulsive noise environments often encountered in practice and provides a robust alternative to Gaussian distribution. Accordingly, we develop circularly and elliptically symmetric multivariate McLeish distribution and introduce additive white McLeish noise (AWMN) channels. In particular, we propose novel analytical and closed-form expressions for the symbol error rate (SER) performance of coherent / non-coherent signaling using various digital modulation techniques over AWMN channels. In that context, we illustrate some novel expressions by some selected numerical examples and verify them by some well chosen computer-based simulations.

Generalized Energy Detection Under Generalized Noise Channels

“…Therefore, combining (B.5) and (B.7), we reach (12). For the alternative case where n ≥ 2 is an even integer, while using the binomial expansion in the left-hand side of (B.6), we arrive at (13) after some straightforward manipulations.…”

“…w ∈ R + and v ∈ R + standing for the noise variance and non-Gaussianity parameter, respectively, with a symmetric and unimodal PDF defined as [12,Eq. (85)]…”

“…However, the bound on the mentioned uncertainty (i.e., ρ) is measurable 2 and thus can be considered as known. To evaluate the worst-case scenario (i.e., the lower bound on P d (•) given a fixed P (τ ) f ), (7) and (12) are directly computed by substituting σ 2 w with ρσ 2 w . Doing so and according to (8), it turns out that λ ⋆ (ρ) ρ p/2 λ ⋆ , reflecting on a corresponding deviation on the decision threshold (thus, on the detector performance) which is proportional to p/2.…”

Moment-based Spectrum Sensing Under Generalized Noise Channels

“…On another front, the McLeish distribution (also known as generalized symmetric Laplace or Bessel function distribution) represents an alternative noise model, appropriate for both Gaussian and non-Gaussian noise channels. It was originated by D. Mcleish in [10] and quite recently it was revisited and thoroughly analyzed in [11], [12]. McLeish distribution resembles the Gaussian distribution; it is unimodal, symmetric, it has all its moments finite, and has tails that are at least as heavy as those of Gaussian distribution.…”

“…McLeish distribution resembles the Gaussian distribution; it is unimodal, symmetric, it has all its moments finite, and has tails that are at least as heavy as those of Gaussian distribution. Moreover, the evolution of its impulsive nature from Gaussian distribution to non-Gaussian distribution is explicitly parameterized in a rigorous way with psychical meaning (please, see the detailed analysis in [11,§IV.B. ]); especially than those of Laplacian, α-stable and generalized Gaussian distributions.…”