Self-similarity Characteristics and Finite SNR Diversity-Multiplexing Tradeoff of MIMO Channels: Performance Analysis, Perturbation, and Dynamics

The diversity and multiplexing tradeoff (DMT) of multiple-input-multiple-output (MIMO) systems was recognized as a fundamental limit for evaluating the simultaneously achievable performance of link reliability and transmission rates in MIMO wireless communications. The first research on DMT studied by Zheng and Tse was limited to infinite signal-to-noise ratio (SNR) situations to quantify the DMT. Later, research was also conducted in finite SNR situations; however, this research had significant problems with coarse approximation. In this dissertation, we propose more accurate approximations of the finite-SNR DMT and the outage probability for Rayleigh fading MIMO channels to solve these problems. The proposed formulas provide more general solutions that are applicable not only to uncorrelated and semi-correlated channels but also to fully correlated and fully coupled channels, which have not been considered in the literature. An accurate SNR offset quantity is also derived, which provides a compensated link for transformation of finite-SNR DMT to actual outage probability. Additionally, as small size wireless devices become the trend in wireless communications, more antennas are placed within such a more compact space that the effects of mutual coupling and spatial correlation of multiple antennas significantly increase. Motivated by this trend, the impact of these two effects on the finite-SNR DMT and the outage probability is analyzed. The spatial correlation effect is found to be destructive to the finite-SNR DMT and the outage performance while the mutual coupling effect is in favor of the finite-SNR DMT and the outage performance if the antenna spacing of multiple antennas is adequately specified. The second part focuses on the analysis of dynamic DMT. Because of the large-scale fading effect and the path loss effect in particular, the SNR or the power received by a receiver may be dependent of its positions; the finite-SNR DMT is affected by positions of the receiver. The impact of position estimation errors of the receiver on the finite-SNR DMT of the MIMO system is investigated in this dissertation. Analytic formulas of the biased Cramer-Rao bound and the lower bound for the mean-square error of the perturbed finite-SNR DMT are proposed to better quantify the best possible case of perturbations for the finite-SNR DMT, where the position estimation error is induced by a biased position estimator. Additionally, the dynamic behavior of DMT due to the mobility of the receiver was not investigated previously. Acknowledging this cavity in research, another objective of this dissertation is to better understand the dynamics of finite-SNR DMT in MIMO systems. Assuming that the receiver possesses mobility in the MIMO system, a theoretical framework is proposed to analyze dynamics of the finite-SNR DMT. A mathematical object called the finite-SNR DMT manifold is proposed to offer a generalization and geometrizes the original notion of DMT. The proposed DMT manifold makes it easier to analyze the dynamics of the finite-SNR DMT such as velocity, geodesics, and geodesic curvature (acceleration) of the DMT. The analyses of dynamic DMT are further extended to the case that the receiver follows a specific human mobility pattern called Levy walks. Dynamics of DMT based on the receiver''s diffusion over Levy walks are analyzed. We observe that large-scale (long-time) asymptotic dynamics behaviors of DMT eventually tend to approach a stable state in terms of zero geodesic curvature (zero acceleration on the DMT manifold) even in different diffusive mobility scales for the receiver. Our proposed formulas, the theoretical framework, and analyses for the finite-SNR DMT can offer leverage for designs of future MIMO applications such as rate-adaptive systems and adaptive space-time codes achieving finite-SNR DMT. Considering massive MIMO systems, we propose preliminary concepts of antenna banks and an antenna banking mechanism for the massive MIMO base station to dynamically utilize the resource of a large number of antennas from the DMT point of view and to possibly reduce the decoding complexity at the receiver. In the proposed antenna banking mechanism, mobile receivers can command the massive MIMO base station to provide an additional and adaptive number of transmitter antennas dynamically serving with faster data transmission while their desired outage probability of data rates still can be guaranteed. Furthermore, the noncoherent mode of transmission for massive MIMO systems is also possible to reduce the decoding complexity at the receiver. We investigate the impact of angular parameters, given an uniform circular array (UCA), on the maximum achievable rate of noncoherent MIMO systems. Self-similarity characteristics induced by the angular parameters of the UCA are observed to exist in the maximum achievable rate of noncoherent MIMO systems, which is identified for potential applications in noncoherent massive MIMO systems.