Quadratic forms of complex Gaussian matrices and performance analysis of multiple antenna systems

Multiple-input-multiple-output (MIMO) systems employ multiple antennas at both transmitter and receiver and have been widely accepted as a major breakthrough for high-data-rate wireless communications.; We present in this dissertation a novel analysis of the channel capacity and of optimum diversity combining performance of MIMO systems with finite numbers of antennas. The results in this dissertation can be classified in two categories. Firstly, we consider the channel capacity or the mutual information rate of MIMO channels. When the channel state information is known at the receiver but not at the transmitter, we derive the exact moment generating function (MGF) and moments of the mutual information (MI) with equal power transmission of multiple independent complex Gaussian codes for (i) independent but non-identically distributed (non-iid) Rician, iid Rician, and iid Rayleigh noise-limited MIMO channels, (ii) semi-correlated (either transmit or receive antennas are correlated) noise-limited MIMO channels with an arbitrary covariance matrix, (iii) MIMO Rayleigh channels in the presence of multiple colored Rayleigh interferers and noise, and (iv) MIMO Rician channels in the presence of white Rayleigh interferers. We then use the Gaussian approximation observed by Smith and Shafi and Wang and Giannakis to obtain an accurate approximation to the distribution function of the MI in the above cases. When the transmit antennas are correlated and the covariance matrix is known at the transmitter, we show that finding statistics of the MI with optimum power loading and finding the channel capacity are mathematically equivalent to the corresponding problems in the noise limited MIMO semi-correlated channels without feedback studied in case (ii). For the MIMO interference channel, we show that multiple colored Rayleigh interferers can be modeled as a single additive interferer and as such a simplified interference channel model is obtained. Secondly, we study the performance of optimum MIMO diversity combining (or beamforming) for (i) MIMO maximal-ratio-combining (MRC) over non-iid Rician fading, iid Rician fading, and semi-correlated Rayleigh fading channels, (ii) MIMO optimum combining over Rayleigh fading channels in the presence of multiple colored Rayleigh interferers and noise, and (iii) MIMO optimum combining over Rician fading channels in the presence of multiple white Rayleigh interferers. The results in this category are given in terms of the outage probability of the output signal-to-noise ratio (SNR) for MIMO MRC or the output signal-to-interference-plus-noise ratio (SINK) for MIMO optimum combining. These results also give the exact outage probability of the MI when beamforming transmission of complex Gaussian scalar codes is employed. Based on these results, the effects of the system/channel parameters on the capacity and performance are studied both analytically and numerically.