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

  • Author / Creator
    Khabbazibasmenj, Arash
  • 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.

  • Subjects / Keywords
  • Graduation date
    2013-11
  • Type of Item
    Thesis
  • Degree
    Doctor of Philosophy
  • DOI
    https://doi.org/10.7939/R3804XW4M
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
  • Language
    English
  • Institution
    University of Alberta
  • Degree level
    Doctoral
  • Department
    • Department of Electrical and Computer Engineering
  • Specialization
    • Communications
  • Supervisor / co-supervisor and their department(s)
    • Sergiy A. Vorobyov
  • Examining committee members and their departments
    • Jiang, Hai ( Electrical and Computer Engineering)
    • Davidson, Tim ( Electrical and Computer Engineering)
    • Jing, Yindi ( Electrical and Computer Engineering)
    • Nikolaidis, Ioanis (Computing Science)