{"title":"Phase differences estimation for diagonal ULAs within a fully filled rectangular array based on degenerated spatial ARMA process","authors":"Guijin Yao, Jiye Liu, Hairong Zhang, Yue Li","doi":"10.1016/j.sigpro.2025.109985","DOIUrl":null,"url":null,"abstract":"<div><div>A generalized estimation method of diagonal phase differences of external sources incident upon a fully-filled rectangular array (FFRA) is proposed based on degenerate spatial <em>ARMA</em> process. Various diagonal uniform linear arrays (ULAs) within FFRAs are first classified by function forms of diagonal phase differences, the ULAs sharing the same diagonal phase difference belong to one category. The modified Yule–Walker (MYW) system of linear equations and the root-finding polynomial are first derived for FFRA ULAs. Owing to diagonal interspacings larger than half of carrier wavelength, ambiguity problem of diagonal phase differences has arisen in estimation. Utilizing the explicit linear-combination relationships satisfied by diagonal and axial phase differences, a simple and effective elimination scheme of estimate ambiguity of diagonal phase differences is proposed in which actual intervals of no ambiguity are deduced by making use of the estimates of axial phase differences. With different FFRA diagonal ULAs on <span><math><mrow><mi>X</mi><mo>−</mo><mi>Y</mi></mrow></math></span> sensor plane, it is numerically manifested by Monte-Carlo trials that the proposed method is effective for both independent and coherent sources and the Root mean square errors (RMSEs) are slowly convergent to the corresponding Cramer–Rao bounds (CRBs) after estimate ambiguities are eliminated. The consistency of estimation performance for diagonal ULAs belonging to one category is exhibited by their identical RMSEs. Because of the ability to exploit axial and diagonal ULAs, the proposed estimation method provides the basis of two-dimensional direction of arrival (2-D DoA) estimation with ULA combinations of FFRAs.</div></div>","PeriodicalId":49523,"journal":{"name":"Signal Processing","volume":"234 ","pages":"Article 109985"},"PeriodicalIF":3.4000,"publicationDate":"2025-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Signal Processing","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0165168425000994","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","Score":null,"Total":0}
引用次数: 0
Abstract
A generalized estimation method of diagonal phase differences of external sources incident upon a fully-filled rectangular array (FFRA) is proposed based on degenerate spatial ARMA process. Various diagonal uniform linear arrays (ULAs) within FFRAs are first classified by function forms of diagonal phase differences, the ULAs sharing the same diagonal phase difference belong to one category. The modified Yule–Walker (MYW) system of linear equations and the root-finding polynomial are first derived for FFRA ULAs. Owing to diagonal interspacings larger than half of carrier wavelength, ambiguity problem of diagonal phase differences has arisen in estimation. Utilizing the explicit linear-combination relationships satisfied by diagonal and axial phase differences, a simple and effective elimination scheme of estimate ambiguity of diagonal phase differences is proposed in which actual intervals of no ambiguity are deduced by making use of the estimates of axial phase differences. With different FFRA diagonal ULAs on sensor plane, it is numerically manifested by Monte-Carlo trials that the proposed method is effective for both independent and coherent sources and the Root mean square errors (RMSEs) are slowly convergent to the corresponding Cramer–Rao bounds (CRBs) after estimate ambiguities are eliminated. The consistency of estimation performance for diagonal ULAs belonging to one category is exhibited by their identical RMSEs. Because of the ability to exploit axial and diagonal ULAs, the proposed estimation method provides the basis of two-dimensional direction of arrival (2-D DoA) estimation with ULA combinations of FFRAs.
期刊介绍:
Signal Processing incorporates all aspects of the theory and practice of signal processing. It features original research work, tutorial and review articles, and accounts of practical developments. It is intended for a rapid dissemination of knowledge and experience to engineers and scientists working in the research, development or practical application of signal processing.
Subject areas covered by the journal include: Signal Theory; Stochastic Processes; Detection and Estimation; Spectral Analysis; Filtering; Signal Processing Systems; Software Developments; Image Processing; Pattern Recognition; Optical Signal Processing; Digital Signal Processing; Multi-dimensional Signal Processing; Communication Signal Processing; Biomedical Signal Processing; Geophysical and Astrophysical Signal Processing; Earth Resources Signal Processing; Acoustic and Vibration Signal Processing; Data Processing; Remote Sensing; Signal Processing Technology; Radar Signal Processing; Sonar Signal Processing; Industrial Applications; New Applications.