Fast Unit-modulus Least Squares with Applications in Beamforming

Unit-modulus least squares (ULS) problems arise in many applications, including phase-only beamforming, sensor network localization, synchronization, phase retrieval, and radar code design. ULS formulations can always be recast as unit-modulus quadratic programs, to which semidefinite relaxation (SDR) can be applied, and is often the state-of-the-art approach. However, SDR lifts the problem dimens...