Fast Unit-modulus Least Squares with applications in transmit beamforming

John Tranter, Nikolaos Sidiropoulos, Xiao Fu, Ananthram Swami

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations


This paper considers the Unit-modulus Least Squares (ULS) problem, which is commonly seen in signal processing applications, e.g., phase-only beamforming, phase retrieval and radar code design. ULS formulations are easily reformulated as Unit-modulus Quadratic Programs (UQPs), to which Semi-Definite Relaxation (SDR) can be applied, and is often the state-of-the-art approach. SDR has the drawback of squaring the number of variables, which lifts the problem to much higher dimension and renders SDR ill-suited for large-scale ULS/UQP. In this work, we propose first-order algorithms that meet or exceed SDR performance in terms of (approximately) solving ULS problems, and also exhibit much more favorable runtime performance relative to SDR.We specialize to phase-only beamformer design, which entails additional degrees of freedom that we point out and exploit in two custom algorithms that build upon the general first-order algorithm for ULS/UQP. Simulations are used to showcase the effectiveness of the proposed algorithms.

Original languageEnglish (US)
Title of host publication2016 24th European Signal Processing Conference, EUSIPCO 2016
PublisherEuropean Signal Processing Conference, EUSIPCO
Number of pages5
ISBN (Electronic)9780992862657
StatePublished - Nov 28 2016
Event24th European Signal Processing Conference, EUSIPCO 2016 - Budapest, Hungary
Duration: Aug 28 2016Sep 2 2016

Publication series

NameEuropean Signal Processing Conference
ISSN (Print)2219-5491


Other24th European Signal Processing Conference, EUSIPCO 2016


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