{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,14]],"date-time":"2026-03-14T18:59:35Z","timestamp":1773514775612,"version":"3.50.1"},"reference-count":54,"publisher":"MDPI AG","issue":"13","license":[{"start":{"date-parts":[[2021,6,30]],"date-time":"2021-06-30T00:00:00Z","timestamp":1625011200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61772397"],"award-info":[{"award-number":["61772397"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Key R&amp;D Program of China","award":["2016YFE0200400"],"award-info":[{"award-number":["2016YFE0200400"]}]},{"name":"Science and Technology Innovation Team of Shaanxi Province","award":["2019TD-002"],"award-info":[{"award-number":["2019TD-002"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Spatial spectrum estimation, also known as direction of arrival (DOA) detection, is a popular issue in many fields, including remote sensing, radar, communication, sonar, seismic exploration, radio astronomy, and biomedical engineering. MUltiple SIgnal Classification (MUSIC) and Estimation Signal Parameter via Rotational Invariance Technique (ESPRIT), which are well-known for their high-resolution capability for detecting DOA, are two examples of an eigen-subspace algorithm. However, missed detection and estimation accuracy reduction often occur due to the low signal-to-noise ratio (SNR) and snapshot deficiency (small time-domain samples of the observed signal), especially for sources with different SNRs. To avoid the above problems, in this study, we develop a DOA detection approach through signal subspace reconstruction using Quantum-Behaved Particle Swarm Optimization (QPSO). In the developed scheme, according to received data, a noise subspace is established through performing an eigen-decomposition operation on a sampling covariance matrix. Then, a collection of angles randomly selected from the observation space are used to build a potential signal subspace on the basis of the steering matrix of the array. Afterwards, making use of the fact that the signal space is orthogonal to the noise subspace, a cost function, which contains the desired DOA information, is designed. Thus, the problem of capturing the DOA information can be transformed into the optimization of the already constructed cost function. In this respect, the DOA finding of multiple signal sources\u2014that is, the multi-objective optimization problem\u2014can be regarded as a single objective optimization problem, which can effectively reduce the probability of missed detection of the signals. Subsequently, the QPSO is employed to determine an optimal signal subspace by minimizing the orthogonality error so as to obtain the DOA. Ultimately, the performance of DOA detection is improved. An explicit analysis and derivation of the developed scheme are provided. The results of computer simulation show that the proposed scheme has superior estimation performance when detecting signals with very different SNR levels and small snapshots.<\/jats:p>","DOI":"10.3390\/rs13132560","type":"journal-article","created":{"date-parts":[[2021,7,1]],"date-time":"2021-07-01T02:44:39Z","timestamp":1625107479000},"page":"2560","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Signal Subspace Reconstruction for DOA Detection Using Quantum-Behaved Particle Swarm Optimization"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5509-9894","authenticated-orcid":false,"given":"Rui","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Electronic Engineering, Xidian University, Xi\u2019an 710071, China"},{"name":"National Laboratory of Radar Signal Processing, Xidian University, Xi\u2019an 710071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4408-9070","authenticated-orcid":false,"given":"Kaijie","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Electronic Engineering, Xidian University, Xi\u2019an 710071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yinghui","family":"Quan","sequence":"additional","affiliation":[{"name":"School of Electronic Engineering, Xidian University, Xi\u2019an 710071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shengqi","family":"Zhu","sequence":"additional","affiliation":[{"name":"National Laboratory of Radar Signal Processing, Xidian University, Xi\u2019an 710071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mengdao","family":"Xing","sequence":"additional","affiliation":[{"name":"School of Electronic Engineering, Xidian University, Xi\u2019an 710071, China"},{"name":"National Laboratory of Radar Signal Processing, Xidian University, Xi\u2019an 710071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,6,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Xiong, C., Fan, C., and Huang, X. 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