# Bivariate Rician shadowed fading model

## TL;DR

This paper introduces a bivariate Rician shadowed fading model with Nakagami-m shadowing, providing exact integral and closed-form expressions for key statistical functions, and applies these to analyze wireless communication performance metrics.

## Contribution

It derives new exact and closed-form statistical expressions for the bivariate Rician shadowed fading model, including joint PDF, CDF, MGF, and correlation coefficient formulas.

## Key findings

- Exact integral expressions for joint PDF and CDF.
- Closed-form MGF and power correlation coefficient.
- Application to outage probability, LCR, and AFD analysis.

## Abstract

In this paper we present a bivariate Rician shadowed fading model where the shadowing is assumed to follow a Nakagami-$m$ distribution. We derive exact expressions involving a single integral for both the joint probability density function (PDF) and the joint cumulative distribution function (CDF) and we also derive an exact closed-form expression for the moment generating function (MGF). As a direct consequence we obtain a closed-form expression for the power correlation coefficient between Rician shadowed variables as a function of the correlation coefficient between the underlying variables of the model. Additionally, in the particular case of integer $m$ we show that the PDF can be expressed in closed-form in terms of a sum of m Meijer G-functions of two variables. Results are applied to analyze the outage probability (OT) of a dual-branch selection combiner (SC) in correlated Rician shadowed fading and the evaluation of the level crossing rate (LCR) and average fade duration (AFD) of a sampled Rician shadowed fading envelope.