On the similarity between Nakagami-m Fading distribution and the Gaussian ensembles of random matrix theory

TL;DR

This paper explores the unexpected similarity between the Nakagami-m fading distribution in wireless communication and the Gaussian ensembles of random matrix theory, revealing a connection to chaotic systems.

Contribution

It demonstrates that Nakagami-m distribution acts as a bridge linking different Gaussian ensembles, highlighting a novel intersection between wireless fading models and random matrix theory.

Findings

Nakagami-m distribution maps to Gaussian ensembles

Wireless fading exhibits transitions between ensembles

Provides insight into chaotic system behavior

Abstract

We report the similarity between the Nakagami-m fading distribution and the three Gaussian ensembles of random matrix theory. We provide a brief review of random matrix theory and wireless fading. We show that the Nakagami-m distribution serves as mapping between the three ensembles. The statistics of the wireless fading amplitude, as modeled by Nakagami-m distribution, provide a rare example of a classically chaotic system that exhibits a transition between the Gaussian orthogonal, Gaussian unitary, and Gaussian symplectic ensembles of random matrix theory.