The phase only beamforming synthesis via an accelerated coordinate descent method

Phase-only array transmit beamforming without iterative/numerical optimization methods

“…Besides the goodness of the proposed solutions in terms of optimality, reducing the computational requirements represents another critical aspect related to the design of beamforming methods. This fact is corroborated by the effort of the scientific community aimed at devising fast iterative/ numerical beamforming algorithms (Farina, 1992;Kautz, 1999;Sun and Li, 2003;Demir and Tuncer, 2014;Webster et al, 2015;Tranter et al, 2016;Alhujaili et al, 2019;Liu et al, 2020;Pallotta et al, 2021;Zhang et al, 2021;Angeletti et al, 2022;Cong et al, 2022).…”

“…Most of phase-only (or constant modulus) beamforming techniques are grounded on iterative/numerical optimization procedures. In fact, the constant modulus constraint makes the problem nonconvex and NP-hard (Cong et al, 2022). To solve it, some solutions are obtained through a semidefinite relaxation of the constraint to transform the optimization problem into a convex problem that can be solved by means of well-known numerical tools [ (Gershman et al, 2010;Tranter et al, 2016;Tranter et al, 2017;Rixon Fuchs et al, 2022), and references therein].…”