Channel Variations in MIMO Wireless Communication Systems: Eigen-Structure Perspectives

Many recent research results have concluded that the multiple-input multiple-output (MIMO) wireless communication architecture is a promising approach to achieve high bandwidth efficiencies. MIMO wireless channels can be simply defined as a link for which both the transmitting and receiving ends are equipped with multiple antenna elements. This advanced communication technology has the potential to resolve the bottleneck in traffic capacity for future wireless networks. Applying MIMO techniques to mobile communication systems, the problem of channel fading between the transmitters and receivers, which results in received signal strength fluctuations, is inevitable. The time-varying nature of the mobile channel affects various aspects of receiver design. This thesis provides some analytical methodologies to investigate the variation of MIMO eigenmodes. Although the scope is largely focussed on the temporal variation in this thesis, our results are also extended to frequency variation. Accurate analytical approximations for the level crossing rate (LCR) and average fade duration (AFD) of the MIMO eigenmodes in an independent, identically distributed (i.i.d.) flat-fading channel are derived. Furthermore, since several channel metrics (such as the total power gain, eigenvalue spread, capacity and Demmel condition number) are all related to the eigenmodes, we also derive their LCRs and AFDs using a similar approach. The effectiveness of our method lies in the fact that the eigenvalues and corresponding channel metrics can be well approximated by gamma or Gaussian variables. Our results provide a comprehensive, closed-form analysis for the temporal behavior of MIMO channel metrics that is simple, robust and rapid to compute. An alternative simplified formula for the LCR for MIMO eigenmodes is also presented with applications to different types of autocorrelation functions (ACF). Our analysis has been verified via Monte Carlo computer simulations. The joint probability density function (PDF) for the eigenvalues of a complex Wishart matrix and a perturbed version of it are also derived in this thesis. The latter version can be used to model channel estimation errors and variations over time or frequency. Using this PDF, the probabilities of adaptation error (PAE) due to feedback delay in some adaptive MIMO schemes are evaluated. In particular, finite state Markov chains (FSMC) have been used to model rate-feedback system and dual-mode antenna selection schemes. The PDF is also applied to investigate MIMO systems that merge singular value decomposition (SVD)-based transceiver structure and adaptive modulation. A FSMC is constructed to investigate the modulation state entering rates (MSER), the average stay duration (ASD), and the effects of feedback delay on the accuracy of modulation state selection in mobile radio systems. The system performance of SVD-based transceivers is closely related to the quality of the channel information at both ends of the link. Hence, we examine the effect of feedback time delay, which causes the transmitter to use outdated channel information in time-varying fading channels. In this thesis, we derive an analytical expression for the instantaneous signal to interference plus noise ratio (SINR) of eigenmode transmission with a feedback time delay. Moreover, this expression implies some novel metrics that gauge the system performance sensitivity to time-variations of the steering vectors (eigenvectors of the channel correlation matrix) at the transmitter. Finally, the fluctuation of the channel in the frequency domain is of interest. This is motivated by adaptive orthogonal frequency division multiplexing (OFDM) systems where the signalling parameters per subcarriers are assigned in accordance with some channel quality metrics. A Gaussian distribution has been suggested to approximate the number of subcarriers using certain signalling modes (such as outage/transmission and diversity/multiplexing), as well as the total data rates, per OFDM realization. Additionally, closed-form LCRs for the channel gains (including the individual eigenmode gains) over frequency are also derived for both single-input single-output (SISO) and MIMO-OFDM systems. The corresponding results for the average fade bandwidth (AFB) follow trivially, These results may be useful for system design, for example by calculating the feedback overheads based on subcarrier aggregation