A Novel Approach for Unit-Modulus Least-Squares Optimization Problems

Cristian Rusu, Nuria González-Prelcic

Abstract: We describe a novel constrained least-squares (LS) optimization problem and propose an iterative solution that deals with the constraints of placing variables on the complex unit circle. We reformulate the LS problem with unit magnitude constraints so that we obtain efficient closed-form local updates based on Procrustes orthogonal solutions that monotonically improve the objective function. We show the performance of the proposed algorithm in a synthetic experiment and an application to hybrid precoding/combining in mmWave MIMO communications.