Augusto Aubry;Prabhu Babu;Antonio De Maio;Massimo Rosamilia
{"title":"应用于雷达问题的托普利兹结构协方差矩阵 MLE 高级方法","authors":"Augusto Aubry;Prabhu Babu;Antonio De Maio;Massimo Rosamilia","doi":"10.1109/TIT.2024.3474977","DOIUrl":null,"url":null,"abstract":"This work considers Maximum Likelihood Estimation (MLE) of a Toeplitz structured covariance matrix. In this regard, an equivalent reformulation of the MLE problem is introduced, and two iterative algorithms are proposed for the optimization of the equivalent statistical learning framework. Both strategies are based on the Majorization Minimization (MM) paradigm and hence enjoy nice properties such as monotonicity and ensured convergence to a stationary point of the equivalent MLE problem. The proposed framework is also extended to deal with MLE of other practically relevant covariance structures, namely, the banded Toeplitz, block Toeplitz, and Toeplitz-block-Toeplitz. Through numerical simulations, it is shown that the new methods provide excellent performance levels in terms of both mean square estimation error (which is very close to the benchmark Cramér-Rao Bound (CRB)) and signal-to-interference-plus-noise ratio, especially in comparison with state-of-the art strategies. Moreover, the estimation task is accomplished with a remarkable reduction in computational complexity compared with a standard approach relying on a Semidefinite Programming (SDP) solver.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 12","pages":"9277-9292"},"PeriodicalIF":2.2000,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10715588","citationCount":"0","resultStr":"{\"title\":\"Advanced Methods for MLE of Toeplitz Structured Covariance Matrices With Applications to Radar Problems\",\"authors\":\"Augusto Aubry;Prabhu Babu;Antonio De Maio;Massimo Rosamilia\",\"doi\":\"10.1109/TIT.2024.3474977\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This work considers Maximum Likelihood Estimation (MLE) of a Toeplitz structured covariance matrix. In this regard, an equivalent reformulation of the MLE problem is introduced, and two iterative algorithms are proposed for the optimization of the equivalent statistical learning framework. Both strategies are based on the Majorization Minimization (MM) paradigm and hence enjoy nice properties such as monotonicity and ensured convergence to a stationary point of the equivalent MLE problem. The proposed framework is also extended to deal with MLE of other practically relevant covariance structures, namely, the banded Toeplitz, block Toeplitz, and Toeplitz-block-Toeplitz. Through numerical simulations, it is shown that the new methods provide excellent performance levels in terms of both mean square estimation error (which is very close to the benchmark Cramér-Rao Bound (CRB)) and signal-to-interference-plus-noise ratio, especially in comparison with state-of-the art strategies. Moreover, the estimation task is accomplished with a remarkable reduction in computational complexity compared with a standard approach relying on a Semidefinite Programming (SDP) solver.\",\"PeriodicalId\":13494,\"journal\":{\"name\":\"IEEE Transactions on Information Theory\",\"volume\":\"70 12\",\"pages\":\"9277-9292\"},\"PeriodicalIF\":2.2000,\"publicationDate\":\"2024-10-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10715588\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"IEEE Transactions on Information Theory\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://ieeexplore.ieee.org/document/10715588/\",\"RegionNum\":3,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"COMPUTER SCIENCE, INFORMATION SYSTEMS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"IEEE Transactions on Information Theory","FirstCategoryId":"94","ListUrlMain":"https://ieeexplore.ieee.org/document/10715588/","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, INFORMATION SYSTEMS","Score":null,"Total":0}
Advanced Methods for MLE of Toeplitz Structured Covariance Matrices With Applications to Radar Problems
This work considers Maximum Likelihood Estimation (MLE) of a Toeplitz structured covariance matrix. In this regard, an equivalent reformulation of the MLE problem is introduced, and two iterative algorithms are proposed for the optimization of the equivalent statistical learning framework. Both strategies are based on the Majorization Minimization (MM) paradigm and hence enjoy nice properties such as monotonicity and ensured convergence to a stationary point of the equivalent MLE problem. The proposed framework is also extended to deal with MLE of other practically relevant covariance structures, namely, the banded Toeplitz, block Toeplitz, and Toeplitz-block-Toeplitz. Through numerical simulations, it is shown that the new methods provide excellent performance levels in terms of both mean square estimation error (which is very close to the benchmark Cramér-Rao Bound (CRB)) and signal-to-interference-plus-noise ratio, especially in comparison with state-of-the art strategies. Moreover, the estimation task is accomplished with a remarkable reduction in computational complexity compared with a standard approach relying on a Semidefinite Programming (SDP) solver.
期刊介绍:
The IEEE Transactions on Information Theory is a journal that publishes theoretical and experimental papers concerned with the transmission, processing, and utilization of information. The boundaries of acceptable subject matter are intentionally not sharply delimited. Rather, it is hoped that as the focus of research activity changes, a flexible policy will permit this Transactions to follow suit. Current appropriate topics are best reflected by recent Tables of Contents; they are summarized in the titles of editorial areas that appear on the inside front cover.