EXTREME-POINT PURSUIT FOR UNIT-MODULUS OPTIMIZATION

Unit-modulus constrained optimization is frequently encountered in many engineering problems. In our recent study for massive MIMO precoding, we devised a penalty method for unit-modulus optimization. In this paper, we revisit this penalty method in several other unit-modulus applications in signal processing. Moreover, as a new result, we show that the concept of our penalty method can be generalized to handle a much broader class of problems, such as those with semi-orthogonal matrix constraints. The rationale is to relax the constraint set as its convex hull, and at the same time, we add a penalty function to force the solution to be an extreme point?which lies in the original constraint set. We show conditions under which the penalty formulation is equivalent to the original problem. We test the penalty method on classic and one-bit MIMO detection under M-PSK constraints, and on phase retrieval. Simulation results indicate that the penalty method yields competitive performance on the aforementioned applications.