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

  • Cooperative Communications
  • Array Signal Processing
  • Generalized Quadratically Constrained Quadratic Programming

• Graduation date

  Fall 2013

• 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.