MIMO Wireless Networks: Modeling and Optimization

A critical factor affecting the future prospects of wireless networks for wide-scale deployment is network capacity: the end users wish to have their communication experience over wireless networks to be comparable or similar to that for wireline networks. An effective approach to increase network capacity is to increase spectrum efficiency. Such an approach can be achieved by the use of multiple antenna systems (also known as multiple-input multiple-output (MIMO) technology). The benefits of substantial improvements in capacity at no cost of additional spectrum and power have positioned MIMO as one of the breakthrough technologies in modern wireless communications. As expected, research activities on applying MIMO to a variety of wireless networks have soared in recent years.

However, compared with the simple point-to-point MIMO channel, which is relatively well-understood nowadays, network design and performance optimization for MIMO-based wireless networks is considerably more challenging. Many fundamental problems remain unsolved. Due to the complex characteristics of MIMO physical layer technology, it is not only desirable but also necessary to consider models and constraints at multiple layers (e.g., physical, link, and network) jointly. The formulations of these cross-layer problems for MIMO wireless networks, however, are usually mathematically challenging. In this dissertation, we aim to develop some novel algorithmic design and optimization techniques that provide optimal or near-optimal solutions.

Based on network structure, this dissertation is organized into two parts. In the first part, we focus on single-hop MIMO wireless networks, while in the second part, we focus on multi-hop MIMO networks. The main results and contributions of this dissertation are summarized as follows.

Single-hop MIMO Networks. In the first part of this dissertation, we study three different optimization problems for single-hop MIMO networks. The first problem addresses weighted proportional fair (WPF) scheduling associated with MIMO broadcast channels (Chapter 2). For the WPF scheduling problem in MIMO broadcast channels, we develop two algorithms that can efficiently determine the optimal dirty paper encoding order and power allocation to achieve an optimal WPF performance. To our knowledge, our work is the first that provides solutions to the WPF scheduling problem in MIMO broadcast channels.

Our next problem concerns single-hop MIMO ad hoc networks (Chapter 3), which are quite different from the MIMO broadcast channels studied in the previous chapter. Single-hop MIMO ad hoc networks can be simply described as "multiple one-to-one," as compared with MIMO broadcast channels, which are "one-to-many." Performance optimization for such networks is known to be challenging due to the non-convex mathematical structure. Indeed, these networks can be viewed as the general case of interference channels in network information theory context, for which the capacity region remains unknown even under the two-user case. In this chapter, we treat the co-channel interference in the network as noise. We consider the maximum weighted sum rate problem under the single-carrier setting. We propose a global optimization approach that combines branch-and-bound (BB) and the reformulation-linearization technique (RLT). This technique is guaranteed to find a global optimal solution

Multi-hop MIMO Networks. In addition to managing resources such as power and scheduling in single-hop networks, routing and end-to-end session rate control need to be considered in multi-hop MIMO networks. Thus, performance optimization problems in multi-hop MIMO networks are more interesting and yet challenging. In Chapter 4, we first consider the problem of jointly optimizing power and bandwidth allocation at each node and multihop/multipath routing in a multi-hop MIMO network that employs orthogonal channels. We show that this problem has some special structure that admits a decomposition into a set of subproblems in its dual domain. Based on this finding, we propose both centralized and distributed optimization algorithms to solve this problem optimally.

In Chapter 5, we relax the orthogonal channel assumption. More specifically, we exploit the advantage of "dirty paper coding" (DPC) to allow multiple links originated from the same node to share the same channel media simultaneously. However, the formulation of cross-layer optimization problem with DPC has a non-convex structure and an exponentially large search space inherent in enumerating DPC's encoding orders. To address these difficulties, we propose an approach to reformulate and convexify the original problem. Based on the reformulated problem, we design an efficient solution procedure by exploiting decomposable dual structure.

One thing in common in Chapters 4 and 5 is that we adopt the classical matrix-based MIMO channel models at the physical layer. Although this approach has its merit, the complex matrix operations in the classical MIMO models may pose a barrier for researchers in networking research community to gain fundamental understanding on MIMO networks. To bridge this gap between communications and networking communities, in Chapter 6, we propose a simple, accurate, and tractable model to enable the networking community to carry out cross-layer research for multi-hop MIMO networks. At the physical layer, we develop an accurate and simple model for MIMO channel capacity computation that captures the essence of spatial multiplexing and transmit power limit without involving complex matrix operations and the water-filling algorithm. At the link layer, we devise a space-time scheduling scheme called order-based interference cancellation (OBIC) that significantly advances the existing zero-forcing beamforming (ZFBF) to handle interference in a multi-hop network setting. The proposed OBIC scheme employs simple algebraic computation on matrix dimensions to simplify ZFBF in a multi-hop network. Finally, we apply both the new physical and link layer models to study a cross-layer optimization problem for a multi-hop MIMO network.