Quadratic forms in complex Gaussian matrices and performance analysis of MIMO systems with cochannel interference

This paper establishes an analytical framework for the performance analysis of multiple-input/multiple output (MIMO) systems subject to cochannel interference and operating over fading channels. First, we present some new statistical results dealing with the distribution of the largest eigenvalue of certain quadratic forms in complex Gaussian matrices and establish the connection between these results and the performance analysis of MIMO systems subject to cochannel interference. We consider interference limited systems in which the number of cochannel interferers exceeds or is equal to the number of receiving antenna elements. We then derive new "closed-form" expressions of the probability density function of the outage signal-to-interference ratio and the system outage probability for MIMO systems in Rician-Rayleigh (i.e., the desired user is subject to Rician fading while cochannel interferers are subject to Rayleigh fading) and Rayleigh-Rayleigh fading environments. When applicable, these expressions are compared to special cases previously reported in the literature dealing with the performance of single-input/multiple-output (SIMO) systems. As a double check, these analytical results and assumptions are validated by Monte Carlo simulations and as an illustration of the mathematical formalism some numerical examples for particular cases of interests are plotted and discussed. These results show that under the same the scattering and interfering conditions and given a fixed number of total antenna elements and cochannel interferers: 1) SIMO systems will always outperform multiple-input/single-output systems and 2) it is preferable to distribute the number of antenna elements evenly between the transmitter and the receiver for an optimum performance.