Joint singular value distribution of two correlated rectangular Gaussian matrices and its application

Document Type

Article

Publication Date

12-1-2007

Abstract

Let H = (hij) and G = (gij) be two m×n, m ≤ n, rectangular random matrices, each with independently and identically distributed complex zero-mean unit-variance Gaussian entries, with correlation between any two elements given by double-struck E sign[hijg pg*] = ρδipδjq such that |ρ| < 1, where * denotes the complex conjugate and δij is the Kronecker delta. Assume {Sk} k=1m and {rl}l=1m are unordered singular values of H and G, respectively, and s and r are randomly selected from {sk)k=1m and {nl} l=1m, respectively. In this paper, exact analytical closed-form expressions are derived for the joint probability distribution function (PDF) of {sk}k=1m and {r l}l=1m using an Itzykson-Zuber-type integral as well as the joint marginal PDF of s and r by a biorthogonal polynomial technique. These PDFs are of interest in multiple-input multiple-output wireless communication channels and systems. © 2007 Society for Industrial and Applied Mathematics.

Identifier

48249132456 (Scopus)

Publication Title

SIAM Journal on Matrix Analysis and Applications

External Full Text Location

https://doi.org/10.1137/060652907

e-ISSN

10957162

ISSN

08954798

First Page

972

Last Page

981

Issue

3

Volume

29

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