## Abstract

Let H = (h_{ij}) and G = (g_{ij}) 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[h_{ij}g _{pg}*] = ρδ_{ip}δ_{jq} such that |ρ| < 1, where * denotes the complex conjugate and δ_{ij} is the Kronecker delta. Assume {S_{k}} _{k=1}^{m} and {r_{l}}_{l=1}^{m} are unordered singular values of H and G, respectively, and s and r are randomly selected from {s_{k})_{k=1}^{m} and {n_{l}} _{l=1}^{m}, respectively. In this paper, exact analytical closed-form expressions are derived for the joint probability distribution function (PDF) of {s_{k}}_{k=1}^{m} and {r _{l}}_{l=1}^{m} 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