Exact Statistical Characterization of 2x2 Gram Matrices with Arbitrary Variance Profile

Nicolas Auguin, D. Morales-Jimenez, M. R. McKay

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

This paper is concerned with the statistical properties of the Gram matrix W = HH†, where H is a 2 × 2 complex central Gaussian matrix whose elements have arbitrary variances. With such arbitrary variance profile, this random matrix model fundamentally departs from classical Wishart models and presents a significant challenge as the classical analytical toolbox no longer directly applies. We derive new exact expressions for the distribution of W and that of its eigenvalues by means of an explicit parameterization of the group of unitary matrices. Our results yield remarkably simple expressions, which are further leveraged to study the outage data rate of a dual-antenna communication system under different variance profiles.
Original languageEnglish
Pages (from-to)8575-8579
Number of pages5
JournalIEEE Transactions on Vehicular Technology
Volume66
Issue number9
Early online date14 Apr 2017
DOIs
Publication statusPublished - 01 Sep 2017

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