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

Jia Chin Lin, H. Vincent Poor

Research output: Contribution to journalArticle

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 languageEnglish (US)
Article number8922729
Pages (from-to)1612-1625
Number of pages14
JournalIEEE Transactions on Vehicular Technology
Volume69
Issue number2
DOIs
StatePublished - Feb 2020

All Science Journal Classification (ASJC) codes

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

Keywords

  • Covariance matrix
  • MGF
  • Nakagami-m fading
  • PDF of phase difference
  • spatial correlation

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