Resource-constrained optimization and algorithms in wireless networks

Abstract

In this thesis, we study the resource-constrained optimization and control of large networks. Our developed techniques find applications in the epidemic evolution problem of broadcast networks and the energy-infeasibility tradeoff problemfor total powerminimization in cognitive radio wireless cellular networks. In a wireless broadcast environment, the solution to the epidemic evolution problem controls how individuals are infected by the spread of a computer virus over a mobile network. This can be modeled by a probabilistic dynamical system over a graph. The goal is to control the speed of the epidemic evolution with limited resources. We consider several prevailing epidemic evolution models, and formulate the control of the spreading under a common general framework that requires solving a non-convex problem involving the spectral radius function of a nonnegative matrix. We propose two algorithms to tackle the non-convexity challenge and solve this nonconvex optimization problem. The first one is a suboptimal but fast algorithm using a successive convex relaxation technique based on geometric programming, while the second one provides a global optimal solution using the branch-and-bound algorithm that leverages some key inequalities in nonnegative matrix theory. Numerical experiments show that our algorithms are stable and computationally fast. Next, we study the energy-infeasibility tradeoff problem for total power minimization subject to resource budget and Signal-to-Interference-plus-Noise Ratio (SINR) constraints in cognitive radio wireless networks. As secondary users can transmit simultaneously along with primary users on a shared spectrum, uncontrolled access of secondary users can lead to network infeasibility. To find the largest feasible set of secondary users that can be supported in the system together with primary users, i.e., the system capacity, we model this problem as a vector-cardinality optimization problem. Motivated by the sum-of-infeasibilities heuristic in optimization theory, we propose a joint power control and admission control algorithm to compute the maximum number of secondary users that can be supported. We also study the fundamental tradeoff between the total energy consumption and the system capacity using convex relaxation. Numerical results are presented to show that our algorithms are theoretically sound and practically implementable.

Date of Award	14 Feb 2014
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	Xiaotie DENG (Co-supervisor), Chee Wei TAN (Supervisor) & Jianping WANG (Co-supervisor)