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

Shuangquan Wang, Ali Abdi

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)972-981
Number of pages10
JournalSIAM Journal on Matrix Analysis and Applications
Volume29
Issue number3
DOIs
StatePublished - 2007

All Science Journal Classification (ASJC) codes

  • Analysis

Keywords

  • Biorthogonal polynomials
  • Correlated complex random matrices
  • Joint singular value distribution

Fingerprint Dive into the research topics of 'Joint singular value distribution of two correlated rectangular Gaussian matrices and its application'. Together they form a unique fingerprint.

Cite this