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

Abstract

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.