Open AccessArray pattern synthesis using semidefinite programming and a bisection method
Author(s) -
Lee JongHo,
Choi Jeongsik,
Lee WoongHee,
Song Jiho
Publication year - 2019
Publication title -
etri journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.295
H-Index - 46
eISSN - 2233-7326
pISSN - 1225-6463
DOI - 10.4218/etrij.2018-0455
Subject(s) - semidefinite programming , bisection method , mathematical optimization , semidefinite embedding , rank (graph theory) , relaxation (psychology) , mathematics , constraint (computer aided design) , algorithm , computer science , quadratically constrained quadratic program , quadratic programming , combinatorics , geometry , psychology , social psychology
In this paper, we propose an array pattern synthesis scheme using semidefinite programming (SDP) under array excitation power constraints. When an array pattern synthesis problem is formulated as an SDP problem, it is known that an additional rank‐one constraint is generated inevitably and relaxed via semidefinite relaxation. If the solution to the relaxed SDP problem is not of rank one, then conventional SDP‐based array pattern synthesis approaches fail to obtain optimal solutions because the additional rank‐one constraint is not handled appropriately. To overcome this drawback, we adopted a bisection technique combined with a penalty function method. Numerical applications are presented to demonstrate the validity of the proposed scheme.