The Shannon and Rényi Differential Entropies of the Weighted Sum of Squared Nakagami-m Random Variables

Antônio Alisson Pessoa Guimarães, Charles Casimiro Cavalcante

DOI: 10.14209/sbrt.2021.1570731409

Evento: XXXIX Simpósio Brasileiro de Telecomunicações e Processamento de Sinais (SBrT2021)

Keywords: Shannon differential entropy Rényi differential entropy Nakagami-m random variable

Abstract

This paper investigates the Shannon and Rényi differential entropies over the weighted sum of squared Nakagami-m mutually independent random variables. Based on the probability density function (PDF) of the sum of Gamma variables, we provide, in terms of special functions, simple closed-form expressions for such entropy measures. Here, we also present the numerical results of a particular case involving the weighted sum of two squared Nakagami-m random variables, in order to graphically represent the theoretical analysis. Finally, we hope that this work will be a useful reference in wireless communication systems over Nakagami-m fading channels.

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