A Fast Eigen Solution for Homogeneous Quadratic Minimization with at most Three Constraints

TL;DR

This paper introduces a fast eigenvalue-based method for solving homogeneous quadratic minimization problems with up to three constraints, offering a computationally efficient alternative to semi-definite relaxation in signal processing applications.

Contribution

The paper presents a novel eigenvalue technique for HQCQP with up to three constraints, significantly reducing computational complexity compared to existing SDR methods.

Findings

The eigen approach converges to SDR solutions in simulations.

The method reduces computational complexity.

Effective in MIMO relay signal processing.

Abstract

We propose an eigenvalue based technique to solve the Homogeneous Quadratic Constrained Quadratic Programming problem (HQCQP) with at most 3 constraints which arise in many signal processing problems. Semi-Definite Relaxation (SDR) is the only known approach and is computationally intensive. We study the performance of the proposed fast eigen approach through simulations in the context of MIMO relays and show that the solution converges to the solution obtained using the SDR approach with significant reduction in complexity.