This thesis has made outstanding contributions in the research field of resource allocation for wireless networks. In system modelling aspect, we have brought up quite a lot of networking models to fit into different wireless network scenarios. For instance, we advocated two-tiered model for data transmission from wireless sensor nodes to the data center [27]. To study disaster area wireless networks, we put forward a macroscopic mobility model to analyze moving patterns of first responders [28]. In addition, we also proposed a distributed scheme to model the procedure to implement optimization of wireless regional area networks as in Chapter 5. Last but not least, we incorporate interference alignment into modelling of multi-hop wireless
networks to improve the capacity performance [30]. In theoretic aspect, we explore many optimization algorithms to be applied to various resource allocation problems.
We sought heuristic algorithms to approximate the optimal solution which is of very high complexity or non-obtainable. As an example, for nonlinear problems, we can approximate the optimal solution by iteratively doing linear computation [29]. We can also divide the conquer by splitting the task into subtasks and assign them to multiple entities as in Chapter 5. The main contributions of this dissertation can be summarized as follows:
• Chapter 2
— We study an optimization problem to maximize the total number of information packets received at the base station during the network lifetime.
— We demonstrate a solution to obtain the optimal transmit power for a relay node such that it can send the maximum number of packets to the base station during the network lifetime.
— The proposed weighted clustering algorithm is a heuristic approach to move relay nodes to better locations iteratively to better serve edge nodes in terms of received packets. The proposed scheme demonstrates better perfor-mance than other methods.
• Chapter 3
— The key obstacle lies in the nonlinearity of the objective function. We successfully transform the max-min objective to a more solvable linear objec-tive with additional constraints in compromise of optimality. In particular, we propose a heuristic approach to iteratively increase the minimal throughput of all links tightening the constraint that the capacity of each link is larger than a threshold value.
—We prove that when the sum rate of all links are maximized and each link share the same capacity, it is guaranteed that max-min performance is optimized. Then the upper bound of max-min fairness problem can be easily acquired by solving a linear programming problem. The upper bound offers a benchmark to measure the quality of the feasible solution obtained from the heuristic approach.
• Chapter 4
— We propose a novel and practical mobility model for mobile nodes in disaster area. We describe typical movement pattern of first responders in a disaster area. Since the movement pattern for all the first responders is not random within the disaster area as in the Waypoint model[45], and they basically are heading deep into the disaster area from the boundary, we put forward our mobility model for mobile nodes (MNs) by combining these two traits together. The disaster area are divided into many small square regions (we call them squares in this chapter later), each square with a Catastrophic Intensity (CI) to show how severe the disaster is in that area. The larger the CI value is, the more time and first responders are required to relieve that square. At the beginning, first responders are disseminated into several arbitrarily chosen starting squares on the boundary of the disaster area, and then each time after they finish relieving one region, the first responders in that square are divided into 3 groups, entering the 3 adjacent squares based on their CI values. Therefore, we actually observe the mobility pattern of MNs as a square based moving behavior. Then what is the moving pattern for MNs within each square? We model it by using the Waypoint model that gives MNs freedom to displace themselves within the square, which can be justified
by our ignorance of the situation in each square.
— We strive to place minimum number of relay nodes such that each mo-bile nodes can connect to at least one relay node. We formulate the square disk cover problem and propose three algorithms to solve it, including the Two-Vertex Square Covering (TVSC) algorithm, the Circle Covering algorithm and the binary integer programming algorithm. We also investigate carefully into the performance comparison between the TVSC algorithm, the Circle Cover-ing algorithm, and the binary integer programmCover-ing algorithm. As the optimal approach, the BIP algorithm yields the deployment of the least number of RNs, while having the largest computational complexity O(N3); the TVSC algorithm yields the deployment of the second least number of RNs, and con-suming much less computational resources in O(N2) ; the Circle Covering algorithm yields the deployment of the most number of RNs, but consuming the least computation resources only in O(N). In practice, the TVSC algo-rithm and Circle Covering algoalgo-rithm might be more preferable because they require much less computational complexity, but yield only a small number of the RNs deployed more than the BIP algorithm does.
• Chapter 5
— An overlaid CRN is constructed with existing primary network. We model the opportunistic spectrum access for CRN formulate the cross-layer optimization problem under the interference constraint imposed by the existing primary network.
— A distributed greedy algorithm is proposed to approximate the optimal network throughput. Cross-layer optimization for CRN is often implemented in centralized manner to avoid co-channel interference. The distributed
al-gorithm coordinates the channel assignment with local channel usage infor-mation. Thus the computation complexity is greatly reduced. In particular, we compare the distributed algorithm with 4 other algorithms, the optimal algorithm, two-phased algorithm and dynamic interference graph allocation and power-based algorithm. The computation complexity of the distributed algorithm is O(N4) and the optimal algorithm is of O(2N). Simulation re-sults show that the distributed algorithm outperforms 3 other algorithms and perform close to the optimal.
• Chapter 6
— We study the network throughput optimization problem for a multi-hop wireless network by considering interference alignment at physical layer. We first transform the problem of dividing the set of links into multiple maximal concurrent link sets into finding all maximal cliques of a graph.
—Each concurrent link set is further divided into one or several multi-access interference networks, on which interference alignment is implemented to guarantee simultaneous interference-free transmission. The network through-put optimization problem is then formulated as a non-convex nonlinear pro-gramming (NLP) problem, which is NP-hard generally.
— We resort to developing a branch-and-bound framework, which guar-antees an achievable performance bound. We use numerical results to validate the efficacy of the algorithm and to offer insights on the throughput enhance-ment brought by interference alignenhance-ment.