# A Systematic Approach to Deriving the Covariance Matrix of Correlated Nakagami-m Fading Channels

Jia Chin Lin, H. Vincent Poor

Research output: Contribution to journalArticlepeer-review

## Abstract

The covariance matrix plays an important role in second-order statistics, enabling numerous signal processing techniques. By exploiting the multivariate moment-generating function (MGF), this paper analytically derives an exact, closed-form joint probability density function (JPDF) of the envelopes of two correlated Nakagami-m channels and their phase difference when m\geq 1.0$. By exploiting a common-variance approximation, an approximate, closed-form JPDF is derived for .5\leq m< 1.0$ because of the in-phase/quadrature-phase (I/Q) imbalance property of Hoyt fading channels. According to the derived JPDFs, the covariance matrix can be calculated in a form consisting of only one definite integral. Simulations are conducted to confirm the analytical results in terms of the covariance matrix and the PDF of the phase difference.

Original language English (US) 8922729 1612-1625 14 IEEE Transactions on Vehicular Technology 69 2 https://doi.org/10.1109/TVT.2019.2957449 Published - Feb 2020

## All Science Journal Classification (ASJC) codes

• Automotive Engineering
• Aerospace Engineering
• Electrical and Electronic Engineering
• Applied Mathematics

## Keywords

• Covariance matrix
• MGF