通过凸结构低方根逼近实现恒定振幅的多通道频率估计

IF 1.5 2区数学 Q2 MATHEMATICS, APPLIED

SIAM Journal on Matrix Analysis and Applications Pub Date : 2024-09-03 DOI:10.1137/23m1587737

Xunmeng Wu, Zai Yang, Zongben Xu

{"title":"通过凸结构低方根逼近实现恒定振幅的多通道频率估计","authors":"Xunmeng Wu, Zai Yang, Zongben Xu","doi":"10.1137/23m1587737","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 3, Page 1643-1668, September 2024. <br/> Abstract. We study the problem of estimating the frequencies of several complex sinusoids with constant amplitude (CA) (also called constant modulus) from multichannel signals of their superposition. To exploit the CA property for frequency estimation in the framework of atomic norm minimization (ANM), we introduce multiple positive-semidenite block matrices composed of Hankel and Toeplitz submatrices and formulate the ANM problem as a convex structured low-rank approximation (SLRA) problem. The proposed SLRA is a semidenite programming and has substantial differences from existing such formulations without using the CA property. The proposed approach is termed as SLRA-based ANM for CA frequency estimation (SACA). We provide theoretical guarantees and extensive simulations that validate the advantages of SACA.","PeriodicalId":49538,"journal":{"name":"SIAM Journal on Matrix Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.5000,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Multichannel Frequency Estimation with Constant Amplitude via Convex Structured Low-Rank Approximation\",\"authors\":\"Xunmeng Wu, Zai Yang, Zongben Xu\",\"doi\":\"10.1137/23m1587737\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 3, Page 1643-1668, September 2024. <br/> Abstract. We study the problem of estimating the frequencies of several complex sinusoids with constant amplitude (CA) (also called constant modulus) from multichannel signals of their superposition. To exploit the CA property for frequency estimation in the framework of atomic norm minimization (ANM), we introduce multiple positive-semidenite block matrices composed of Hankel and Toeplitz submatrices and formulate the ANM problem as a convex structured low-rank approximation (SLRA) problem. The proposed SLRA is a semidenite programming and has substantial differences from existing such formulations without using the CA property. The proposed approach is termed as SLRA-based ANM for CA frequency estimation (SACA). We provide theoretical guarantees and extensive simulations that validate the advantages of SACA.\",\"PeriodicalId\":49538,\"journal\":{\"name\":\"SIAM Journal on Matrix Analysis and Applications\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.5000,\"publicationDate\":\"2024-09-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"SIAM Journal on Matrix Analysis and Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1137/23m1587737\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Matrix Analysis and Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/23m1587737","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

SIAM 矩阵分析与应用期刊》，第 45 卷第 3 期，第 1643-1668 页，2024 年 9 月。摘要我们研究了从多通道信号的叠加中估计几个具有恒定振幅（CA）（也称为恒定模量）的复正弦波频率的问题。为了在原子规范最小化（ANM）框架内利用恒定振幅（CA）特性进行频率估计，我们引入了由 Hankel 和 Toeplitz 子矩阵组成的多个正半封闭块矩阵，并将 ANM 问题表述为凸结构低阶近似（SLRA）问题。所提出的 SLRA 是一种半等式编程，与现有的不使用 CA 属性的此类公式有很大不同。所提出的方法被称为基于 SLRA 的 CA 频率估计 ANM（SACA）。我们提供的理论保证和大量仿真验证了 SACA 的优势。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Multichannel Frequency Estimation with Constant Amplitude via Convex Structured Low-Rank Approximation

SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 3, Page 1643-1668, September 2024.
Abstract. We study the problem of estimating the frequencies of several complex sinusoids with constant amplitude (CA) (also called constant modulus) from multichannel signals of their superposition. To exploit the CA property for frequency estimation in the framework of atomic norm minimization (ANM), we introduce multiple positive-semidenite block matrices composed of Hankel and Toeplitz submatrices and formulate the ANM problem as a convex structured low-rank approximation (SLRA) problem. The proposed SLRA is a semidenite programming and has substantial differences from existing such formulations without using the CA property. The proposed approach is termed as SLRA-based ANM for CA frequency estimation (SACA). We provide theoretical guarantees and extensive simulations that validate the advantages of SACA.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

SIAM Journal on Matrix Analysis and Applications 数学-应用数学

CiteScore

2.90

自引率

6.70%

发文量

审稿时长

6-12 weeks

期刊介绍： The SIAM Journal on Matrix Analysis and Applications contains research articles in matrix analysis and its applications and papers of interest to the numerical linear algebra community. Applications include such areas as signal processing, systems and control theory, statistics, Markov chains, and mathematical biology. Also contains papers that are of a theoretical nature but have a possible impact on applications.