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Generalized Quadratically Constrained Quadratic Programming and its Applications in Array Processing and Cooperative Communications Open Access


Other title
Generalized Quadratically Constrained Quadratic Programming
Cooperative Communications
Array Signal Processing
Type of item
Degree grantor
University of Alberta
Author or creator
Khabbazibasmenj, Arash
Supervisor and department
Sergiy A. Vorobyov
Examining committee member and department
Nikolaidis, Ioanis (Computing Science)
Jiang, Hai ( Electrical and Computer Engineering)
Davidson, Tim ( Electrical and Computer Engineering)
Jing, Yindi ( Electrical and Computer Engineering)
Department of Electrical and Computer Engineering
Date accepted
Graduation date
Doctor of Philosophy
Degree level
In this thesis, we introduce and solve a particular generalization of the quadratically constrained quadratic programming (QCQP) problem which is frequently encountered in the fields of communications and signal processing. Specifically, we consider such generalization of the QCQP problem which can be precisely or approximately recast as the difference-of-convex functions (DC) programming problem. Although the DC programming problem can be solved through the branch-and-bound methods, these methods do not have any worst-case polynomial time complexity guarantees. Therefore, we develop a new approach with worst-case polynomial time complexity that can solve the corresponding DC problem of a generalized QCQP problem. It is analytically guaranteed that the point obtained by this method satisfies the Karsuh-Kuhn-Tucker (KKT) optimality conditions. Furthermore, there is a great evidence of global optimality in polynomial time for the proposed method. In some cases the global optimality is proved analytically as well. In terms of applications, we focus on four different problems from array processing and cooperative communications. These problems boil down to QCQP or its generalization. Specifically, we address the problem of transmit beamspace design for multiple-input multiple-output (MIMO) radar in the application to the direction-of-arrival estimation when certain considerations such as enforcement of the rotational invariance property or energy focusing are taken into account. We also study the robust adaptive beamforming (RAB) problem from a new perspective that allows to develop a new RAB method for the rank-one signal model which uses as little as possible and easy to obtain prior information. We also develop a new general-rank RAB method which outperforms other existing state-of-the-art methods. Finally, we concentrate on the mathematical issues of the relay amplification matrix design problem in a two-way amplify-and-forward (AF) MIMO relaying system when the sum-rate, the max-min rate, and the proportional fairness are used as the design criteria.
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
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