Information theoretic properties of flat fading channels with multiple antennas are investigated. Perfect channel knowledge at the receiver is assumed. Expressions for maximum information rates and outage probabilities are derived. The advantages of transmitter channel knowledge are determined and a critical threshold is found beyond which such channel knowledge gains very little. Asymptotic expressions for the error exponent are found. For the case of transmit diversity closed form expressions for the error exponent and cutoff rate are given. The use of orthogonal modulating signals is shown to be asymptotically optimal in terms of information rate.

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In this paper, the distributions of the largest and smallest eigenvalues of complex Wishart matrices and the condition number of complex Gaussian random matrices are derived. These distributions are represented by complex hypergeometric functions of matrix arguments, which can be expressed in terms of complex zonal polynomials. Several results are derived on complex hypergeometric functions and complex zonal polynomials and are used to evaluate these distributions. Finally, applications of these distributions in numerical analysis and statistical hypothesis testing are mentioned.