Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
JOINT SINGULAR VALUE DISTRIBUTION OF TWO CORRELATED RECTANGULAR GAUSSIAN MATRICES AND ITS APPLICATION
 

Summary: JOINT SINGULAR VALUE DISTRIBUTION OF TWO CORRELATED
RECTANGULAR GAUSSIAN MATRICES AND ITS APPLICATION
SHUANGQUAN WANG AND ALI ABDI
Abstract. Let H = (hij) and G = (gij) be two m n, m n, rectangular random matrices,
each with i.i.d complex zero-mean unit-variance Gaussian entries, with correlation between any two
elements given by E[hijgpq] = ipjq such that || < 1, where denotes the complex conjugate
and ij is the Kronecker delta. Assume {sk}m
k=1 and {rl}m
l=1 are unordered singular values of H
and G, respectively, and s and r are randomly selected from {sk}m
k=1 and {rl}m
l=1, respectively. In
this paper, exact analytical closed-form expressions are derived for the joint probability distribution
function (PDF) of {sk}m
k=1 and {rl}m
l=1 using an Itzykson-Zuber-type integral, as well as the joint
marginal PDF of s and r, by a bi-orthogonal polynomial technique. These PDFs are of interest in
multiple-input multiple-output (MIMO) wireless communication channels and systems.
Key words. correlated complex random matrices, joint singular value distribution, bi-orthogonal
polynomials

  

Source: Abdi, Ali - Department of Electrical and Computer Engineering, New Jersey Institute of Technology

 

Collections: Engineering