{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,14]],"date-time":"2026-09-14T11:04:06Z","timestamp":1789383846605,"version":"build-2803163510"},"reference-count":30,"publisher":"MDPI AG","issue":"18","license":[{"start":{"date-parts":[[2026,9,13]],"date-time":"2026-09-13T00:00:00Z","timestamp":1789257600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"State Key Laboratory of Environment Characteristics and Effects for Near-space and the CMA Research Centre on Meteorological Observation Engineering Technology"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Multiple-source DOA (Direction of Arrival) estimation is vital for array processing, radar, and integrated sensing and communications, yet classical subspace methods degrade under low signal-to-noise ratios and snapshot-starved conditions due to inaccurate sample covariance matrices. To address this, we propose a Toeplitz-enhanced neural network (TENN-DOA) for DOA estimation, a hybrid physics-informed framework for uniform linear arrays that combines the array signal processing prior with a lightweight learning-based regressor. The front end explicitly enforces the Hermitian\u2013Toeplitz structure and fuses the projected matrix with the sample covariance via an analytically derived optimal shrinkage coefficient, yielding a robust covariance estimate. This enhanced representation is mapped onto an overcomplete angular dictionary, producing a feature sequence structurally coupled with the array manifold. A pooling-free one-dimensional convolutional neural network with decreasing kernel sizes starts with large kernels to capture the broad spectral envelope from grid mismatch, and then regresses to a pseudo spatial spectrum under multi-hot supervision for grid-point estimates. The Monte Carlo simulation results show that under the conditions of low signal-to-noise ratio, limited snapshots and the simulated ideal uniform linear array scenario, TENN-DOA achieves a higher resolution probability and lower root mean square error compared with MUSIC, TLS-ESPRIT and the deep learning-based baseline algorithm DA-MUSIC.<\/jats:p>","DOI":"10.3390\/s26185803","type":"journal-article","created":{"date-parts":[[2026,9,14]],"date-time":"2026-09-14T10:19:41Z","timestamp":1789381181000},"page":"5803","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Toeplitz-Enhanced Array Covariance Processing for DOA Estimation Under Low SNR and Limited Snapshots"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8078-927X","authenticated-orcid":false,"given":"Xin","family":"Jin","sequence":"first","affiliation":[{"name":"National Space Science Center, Chinese Academy of Sciences, Beijing 100190, China"},{"name":"School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"methodology","vocabulary":"credit"},{"role":"software","vocabulary":"credit"},{"role":"validation","vocabulary":"credit"},{"role":"formal-analysis","vocabulary":"credit"},{"role":"investigation","vocabulary":"credit"},{"role":"writing-original-draft","vocabulary":"credit"}]},{"given":"Yanan","family":"Fan","sequence":"additional","affiliation":[{"name":"National Space Science Center, Chinese Academy of Sciences, Beijing 100190, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"validation","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"},{"role":"supervision","vocabulary":"credit"},{"role":"project-administration","vocabulary":"credit"}]},{"given":"Xiujuan","family":"Yao","sequence":"additional","affiliation":[{"name":"National Space Science Center, Chinese Academy of Sciences, Beijing 100190, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"validation","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"}]},{"given":"Xinyu","family":"Li","sequence":"additional","affiliation":[{"name":"National Space Science Center, Chinese Academy of Sciences, Beijing 100190, China"},{"name":"School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"writing-review-editing","vocabulary":"credit"}]},{"given":"Yanan","family":"Meng","sequence":"additional","affiliation":[{"name":"National Space Science Center, Chinese Academy of Sciences, Beijing 100190, China"},{"name":"School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"writing-review-editing","vocabulary":"credit"}]},{"given":"Yi","family":"Yan","sequence":"additional","affiliation":[{"name":"National Space Science Center, Chinese Academy of Sciences, Beijing 100190, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"writing-review-editing","vocabulary":"credit"}]},{"given":"Xiang","family":"Gao","sequence":"additional","affiliation":[{"name":"National Space Science Center, Chinese Academy of Sciences, Beijing 100190, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"writing-review-editing","vocabulary":"credit"}]}],"member":"1968","published-online":{"date-parts":[[2026,9,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1109\/79.526899","article-title":"Two decades of array signal processing research: The parametric approach","volume":"13","author":"Krim","year":"1996","journal-title":"IEEE Signal Process. 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