Stochastic Analysis and Optimization of Heterogeneous Wireless Networks

In order to improve the performance of mobile networks, one widely promoted approach is to install a diverse set of small-cells overlaying the current macrocell network to form a multi-tier heterogeneous wireless network (HWN). In this thesis, I propose new stochastic approaches to evaluate and design HWNs by investigating user load, interference patterns, and user mobility, the results of which provide new analytical insights and design guidelines to improve future HWNs. In the first part of this thesis, I focus on the evaluation of user load through characterizing the joint distribution of users in different cells in an HWN with arbitrary user movement trajectories and dependently distributed user channel holding times. Through developing a new stochastic network analysis framework, I derive a closed-form expression for the joint user distribution, which is only related to the average arrival rate and the average channel holding time of each cell, and hence it is irrelevant to the general user movement patterns and distributions of channel holding times. This property suggests that accurate evaluation of the user distribution and other associated metrics such as the system workload can be achieved with low complexity, without the need to collect a large amount of user location data. The multi-tier architecture of HWNs introduces complicated interference patterns in the system. In the second part of this thesis, I introduce a stochastic analytical framework to compare the performance of open and closed access modes in a two-tier network with macrocells and femtocells, with regard to uplink interference and outage at both the macrocell and femtocell levels. A stochastic geometric approach is employed as the basis for the analysis to characterize the distributions of uplink interference and the outage probabilities. I further derive sufficient conditions for open and closed access modes to outperform each other in terms of the outage probability at either the macrocell or femtocell level. This leads to closed-form expressions to upper and lower bound the difference in the targeted received power between the two access modes. In the third part of this thesis, I study the resource allocation and user association problem in HWNs with random distributed users and BSs for optimizing the average user data rate. Both the user load and interference patterns are considered. I first derive the average user data rate through stochastic geometric analysis. The expression is employed as the objective function of the optimization problem, which is non-convex in nature and cannot be solved with a standard method. Then, I propose an innovative approach, solving the optimization problem optimally for low user density, and asymptotically optimally for high user density. The deployment of small-cell BSs in HWNs leads to a higher user data rate, but it also introduces more handoffs to the users. In the fourth part of this thesis, I present a new stochastic geometric analysis framework on user mobility in HWNs, which captures the spatial randomness and various scales of cell sizes in different tiers. I derive analytical expressions for the rates of all handoff types experienced by an active user with arbitrary movement trajectory. Noting that the data rate of a user also depends on the set of cell tiers that it is willing to use, I also provide guidelines for tier selection under various user velocity, so that an optimal tradeoff between the handoff rate and the data rate can be achieved.Ph.D