Ratio of the Product-of-Two to One Variates: A Framework - Application to κ-μ and η-μ

Carlos R. N. da Silva, Michel Daoud Yacoub

DOI: 10.14209/sbrt.2022.1570824331

Evento: XL Simpósio Brasileiro de Telecomunicações e Processamento de Sinais (SBrT2022)

Keywords: R/LIS massive MIMO D2D V2V

Abstract

The performance analyses of a number of fading scenarios require the knowledge of some of the statistics of the product and the ratio of the involved variates. With the advent of several enabling technologies, e.g., reconfigurable/large intelligent surfaces, massive MIMO, cooperative communications, device-to-device, vehicle-to-vehicle communications, and others, this is even more evident. In this paper, we provide a framework for the derivation of probability density functions and the cumulative distribution functions for the ratio of the product-of-two to one variates. The framework is then used to derive these statistics for all possible combinations of these variates taken from κ-μ and η-μ fading models. The expressions are obtained in terms of a simple-to-compute single-sum infinite series, with convergence attained very rapidly.

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