 
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 zeromean unitvariance 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 closedform expressions are derived for the joint probability distribution
function (PDF) of {sk}m
k=1 and {rl}m
l=1 using an ItzyksonZubertype integral, as well as the joint
marginal PDF of s and r, by a biorthogonal polynomial technique. These PDFs are of interest in
multipleinput multipleoutput (MIMO) wireless communication channels and systems.
Key words. correlated complex random matrices, joint singular value distribution, biorthogonal
polynomials
