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2022•arXiv (Cornell University)Open access

A New Expression for the Product of Two $κ-μ$ Shadowed Random Variables and its Application to Wireless Communication

Shashank Shekhar, Sheetal Kalyani

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Abstract

In this work, the product of two independent and non-identically distributed (i.n.i.d) $κ- μ$ shadowed random variables is studied. We derive the series expression for the probability density function (PDF), cumulative distribution function (CDF), and moment generating function (MGF) of the product of two (i.n.i.d) $κ- μ$ shadowed random variables. The derived formulation in this work is quite general as they incorporate most of the typically used fading channels. As an application example, outage probability (OP) has been derived for cascaded wireless systems and relay-assisted communications with a variable gain relay. Extensive Monte-Carlo simulations have also been carried out.

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In this work, the product of two independent and non-identically distributed (i.n.i.d) $κ- μ$ shadowed random variables is studied. We derive the series expression for the probability density function (PDF), cumulative distribution function (CDF), and moment generating function (MGF) of the product of two (i.n.i.d) $κ- μ$ shadowed random variables. The derived formulation in this work is quite general as they incorporate most of the typically used fading channels. As an application example, outage probability (OP) has been derived for cascaded wireless systems and relay-assisted communications with a variable gain relay. Extensive Monte-Carlo simulations have also been carried out.

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Available abstract

In this work, the product of two independent and non-identically distributed (i.n.i.d) $κ- μ$ shadowed random variables is studied. We derive the series expression for the probability density function (PDF), cumulative distribution function (CDF), and moment generating function (MGF) of the product of two (i.n.i.d) $κ- μ$ shadowed random variables. The derived formulation in this work is quite general as they incorporate most of the typically used fading channels. As an application example, outage probability (OP) has been derived for cascaded wireless systems and relay-assisted communications with a variable gain relay. Extensive Monte-Carlo simulations have also been carried out.

Key concepts: Moment-generating function, Random variable, Independent and identically distributed random variables, Cumulative distribution function, Probability density function, Expression (computer science), Relay, Fading

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