Title page for ETD etd-12122007-103152

Type of Document Dissertation
Author Suris, Juan Emilio
Author's Email Address jsuris@vt.edu
URN etd-12122007-103152
Title Cooperative Game Theory and Non-convex Optimization Analysis of Spectrum Sharing
Degree PhD
Department Electrical and Computer Engineering
Advisory Committee
Advisor Name Title
DaSilva, Luiz A. Committee Chair
Gilles, Robert P. Committee Member
MacKenzie, Allen B. Committee Member
Midkiff, Scott F. Committee Member
Reed, Jeffrey Hugh Committee Member
  • Spectrum management
  • Distributed algorithms
  • Power control
  • Cochannel interference
  • Game theory
Date of Defense 2007-11-30
Availability unrestricted
Opportunistic spectrum access has become a high priority research

area in the past few years. The motivation behind this actively

researched area is the fact that the limited spectrum available is

currently being utilized in an inefficient way. The complete

wireless spectrum is assigned and reserved, but not necessarily

being used. At the same time, the demand for innovation in wireless

technology is growing. Since there is no room in the wireless

spectrum to allocate significant frequency bands for future wireless

technologies, the only recourse is to increase utilization of the

spectrum. To achieve this, we must find a way to share the spectrum.

Spectrum sharing techniques will require coordination between all

the layers of the protocol stack. The network and the wireless

medium are inextricably linked and, thus, both must be considered

when optimizing wireless network performance. Unfortunately,

interactions in the wireless medium can lead to non-convex problems

which have been shown to be NP-hard. Techniques must be developed to

tackle the optimization problems that arise from wireless network


In this document we focus on analyzing the spectrum sharing problem

from two perspectives: cooperative game theory and non-convex

optimization. We develop a cooperative game theory model to analyze

a scenario where nodes in a multi-hop wireless network need to agree

on a fair allocation of spectrum. We show that in high interference

environments, the utility space of the game is non-convex, which may

make some optimal allocations unachievable with pure strategies.

However, we show that as the number of channels available increases,

the utility space becomes close to convex and thus optimal

allocations become achievable with pure strategies. We propose the

use of the NBS and show that it achieves a good compromise

between fairness and efficiency, using a small number of channels.

We also propose a distributed algorithm for spectrum sharing and

show that it achieves allocations reasonably close to the NBS.

In our game theory analysis, we studied the possible outcomes of the

spectrum sharing problem and propose the NBS as a desirable

outcome and propose an algorithm to achieve the NBS spectrum

allocation. However, the expression used to compute the NBS is

a non-convex optimization problem. We propose an optimization model

to solve a class of problems that incorporate the non-convex

dynamics of the wireless medium that occur when the objective is a

function of SINR. We present two case studies to show the

application of the model to discrete and continuous optimization

problems. We propose a branch and bound heuristic, based on the

RLT, for approximating the solution of continuous optimization

problems. Finally, we present results for the continuous case study.

We show simulation results for the heuristic compared to a time

constrained mixed integer linear program (MILP) as well as a

nonlinear optimization using random starting points. We show that

for small networks the MILP achieves the optimal in reasonable time

and the heuristic achieves a value close to the optimal. We also

show that for large networks the heuristic outperforms the MILP as

well as the nonlinear search.

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