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 language | English (US) |
---|---|
Pages (from-to) | 972-981 |
Number of pages | 10 |
Journal | SIAM Journal on Matrix Analysis and Applications |
Volume | 29 |
Issue number | 3 |
DOIs | |
State | Published - 2007 |
All Science Journal Classification (ASJC) codes
- Analysis
Keywords
- Biorthogonal polynomials
- Correlated complex random matrices
- Joint singular value distribution