Centralized and distributed resource allocation with applications to signal processing in communications

Alvarado Ortiz, Alberth

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Description

Title

Centralized and distributed resource allocation with applications to signal processing in communications

Author(s)

Alvarado Ortiz, Alberth

Issue Date

2015-01-21

Director of Research (if dissertation) or Advisor (if thesis)

Pang, Jong-Shi

Doctoral Committee Chair(s)

Nedich, Angelia

Committee Member(s)

• Pang, Jong-Shi
• Sreenivas, Ramavarapu S.
• Scutari, Gesualdo

Department of Study

Industrial&Enterprise Sys Eng

Discipline

Industrial Engineering

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• Distributed optimization
• Resource allocation
• Nash equilibrium
• Game theory
• Difference of convex programming
• Nonconvex and nondifferentiable optimization
• Successive convex approximation
• Multiuser systems
• Dynamic spectrum management
• Cooperative physical layer security
• Cognitive radio

Abstract

Nowadays, wired and wireless networks are used everywhere and everyday. With the increasing popularity of multiuser communication systems, their optimal performance has become a crucial field of study during the last decades. A factor that greatly determines such performance is the optimal allocation of the resources available to the agents in the network. This dissertation provides a set of optimization techniques applicable to rigorously address and deeply analyze multiuser resource allocation problems in different areas, ranging from signal processing, to communications and networking. More specifically, this work focuses on the three main topics that we briefly describe next. First, we study the maximum sum-utility achieved when a noncooperative approach is used to allocate the spectrum in a communication system adopting a dynamic spectrum management framework. In particular, we turn our attention to the case in which the users in the system are endowed with infinite power budgets. This asymptotic analysis, based on the linear complementarity problem theory, leads us characterize the behavior of the system's utility as the power budget is increased toward infinity, and thus draw interesting conclusions on the efficiency of the Nash equilibrium and the Braess-type paradox, among others. Second, we propose a novel class of distributed algorithms for the optimization of nonconvex and nonseparable sum-utility functions subject to convex coupling constraints. Even though, we focus on utility functions of the Difference of Convex (DC) type, further generalizations are possible. Moreover, the obtained iterative schemes are provable convergent to stationary points of such optimization problems. Among the different applications of our Successive Convex Approximationsbased algorithms, we direct our attention to a novel resource allocation problem in the emerging field of physical layer based security, and to the well-known MIMO (Multiple-Input-Multiple-Output) Cognitive Radio sum-rate maximization problem. For the former application, we develop a mathematically rigorous analysis of the nondifferentiable and nonconvex game (of the generalized type) proposed to optimally allocate the network resources in this context; and finally, we apply our algorithms to find relaxed equilibrium points of the mentioned game. For the second application, our theory provides, for the first time, a provable convergent algorithm. The third major topic of this dissertation analyzes a multiuser maximization problem where the utility function has a particular structure, namely, it is the sum of continuous maximum functions, subject to private and coupling constraints. We follow two different approaches in order to design provable convergent algorithms to address this problem. These approaches are based on simpler reformulations of the nondifferentiable and nonconcave optimization problem of interest. A careful analysis relating such problems is also developed. The cited results pave the way to devise (possibly distributed) algorithms for different system designs in the context of physical layer based security, ranging from the secrecy sum-rate maximization to the Max-Min fairness problem. It is important to emphasize that, different from the simple networks models considered in the physical layer security literature, the system designs studied in this dissertation involve networks composed of multiple legitimate users and friendly jammers, and a single eavesdropper, where the main users communicate over multiple (either orthogonal or non-orthogonal) subchannels. Finally, it is worth mentioning that most of the tools and results developed in this work are general enough to encompass applications in many fields different from those described above. This dissertation highlights how the introduction of optimization theory in different signal processing applications has motivated several significant developments in the former field, in particular in the area of multiuser distributed optimization. Future research directions are provided at the end of each chapter.

Graduation Semester

2014-12

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Copyright 2014 Alberth Alvarado Ortiz

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