Contents Online

# Communications in Information and Systems

## Volume 3 (2003)

### Number 2

### Complex random matrices and Rayleigh channel capacity

Pages: 119 – 138

DOI: http://dx.doi.org/10.4310/CIS.2003.v3.n2.a3

#### Authors

#### Abstract

The eigenvalue densities of complex central Wishart matrices are investigated with the objective of studying an open problem in channel capacity. These densities are represented by complex hypergeometric functions of matrix arguments, which can be expressed in terms of complex zonal polynomials. The connection between the complex Wishart matrix theory and information theory is given. This facilitates the evaluation of the most important information-theoretic measure, the so-called channel capacity. In particular, the capacity of multiple input, multiple output (MIMO) Rayleigh distributed channels are fully investigated. We consider both correlated and uncorrelated channels and derive the corresponding channel capacity formulas. It is shown how the channel correlation degrades the capacity of the communication system.

#### Keywords

complex random matrix, complex Wishart matrix, complex zonal polynomials, complex hypergeometric functions, Rayleigh distributed MIMO channel, channel capacity

#### 2010 Mathematics Subject Classification

60E05, 62H10, 94A05, 94A15