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

分集多工權衡被視為是一個基本的物理極限來評量在多輸入輸出無線通訊中同時可被達到的可靠傳輸及傳輸速率效能。由鄭氏與施氏(Zheng and Tse)學者所開啟的分集多工權衡量化研究先河乃是侷限於無限訊雜比之情況。這類研究逐漸被推廣至有限訊雜比之情形；然而，於此情形下此類研究存在粗略近似之嚴重問題。於本論文中，針對瑞利氏(Rayleigh) 衰減通道中有限訊雜比之分集多工權衡及中斷機率兩者，吾人提出更精確的近似公式來解決前人所遭遇之精確量化問題。吾人所提出的理論公式提供了更具一般化的解答，不僅可被應用於獨立通道及半相關通道之中，亦可被應用於全相關通道及全耦合通道之中，尤以後者之應用在文獻中未曾被研究。吾人亦提出一個精確的有限訊雜比補償公式，以作為分集多工權衡及實際中斷機率兩者轉換時之有效補償量。此外，考慮到無線通訊小尺寸元件之趨勢，更多的天線將會被設計在一個更狹小的空間中，這使得多天線之間的互耦合效應及空間相關效應顯著地增加。基於此趨勢發展，本論文針對此二種效應對分集多工權衡及中斷機率之影響做分析。研究結果顯示，針對分集多工權衡及中斷機率，空間相關效應無益於提升效能，但天線間距被適當選取時，互耦合效應則有可能益於效能提升。 本論文第二部分側重在動態分集多工權衡之分析。因大範圍通道衰減效應，尤其是路徑衰減效應之影響，接收端的訊雜比值或接收功率可能受到其所處位置影響；系統之分集多工權衡因而受到接收端之位置影響。本論文針對接收端位置估計誤差對系統分集多工權衡產生的影響進行研究。對於分集多工權衡，吾人提出偏移型克雷曼-勞氏(Cramér-Rao)下界理論公式及均方誤差下界理論公式，兩者用以精確量化分集多工權衡之最佳可能擾動狀況；其中，位置估計誤差乃假設起因於偏移型定位裝置。再者，由接收端移動性引起的分集多工權衡之動態行為研究未曾現於文獻之中。有鑑於此，本論文首度研究分集多工權衡之動力學。當假設接收端具有移動性時，吾人提出一個數學理論框架來分析分集多工權衡之動力學，並提出一個數學概念物件稱為有限訊雜比之分集多工權衡流形，它提供了原先分集多工權衡概念的一般化及幾何化。所提出的流形概念易於分析分集多工權衡動力學之物理量，諸如: 速度、測地線及測地曲率(類加速度) 等。本論文將動態分集多工權衡之分析進一步推廣至當接收端遵循某種人類特定移動情形，此情形稱為列維氏(Lévy) 隨機步行。基於接收端的列維氏型擴散移動，吾人分析相應之分集多工權衡動力學。研究顯示，即使在不同尺度的擴散移動中，在大尺度(長時間) 的分集多工權衡之漸進動力行為最終會趨近於一個具零測地曲率(類零加速) 之穩態。吾人所提出之數學公式、理論框架及分析將可在未來多輸入輸出系統應用設計上提供利基，諸如: 可適性速率系統，以及具最佳分集多工權衡之可適性空時碼設計。 本論文亦考慮到巨量型多輸入輸出系統，吾人提出天線銀行與天線銀行機制之初步概念，從分集多工權衡的角度，基地台允許動態地使用大量天線資源以盡可能地降低接收端之解碼運算複雜度。根據吾人所提出之天線銀行機制，在預設的中斷機率仍能滿足之前提下，移動接收端可要求巨量天線基地台提供額外且動態數量的傳輸天線來服務接收端以達到更快資料傳輸。此外，對於巨量型多輸入輸出系統，非同調傳輸亦可能達到減低接收端解碼複雜度目的。針對非同調傳輸，吾人考慮均勻圓形天線陣列之信號入射角度參數對最大可達傳輸速率的影響進行研究。由角度參數導致的自相似特徵被觀察到存在於非同調傳輸系統的最大可達傳輸速率之中，吾人指出這項發現在巨量型多輸入輸出具有潛在應用之可能性。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