{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:27:25Z","timestamp":1760232445889,"version":"build-2065373602"},"reference-count":22,"publisher":"MDPI AG","issue":"22","license":[{"start":{"date-parts":[[2022,11,9]],"date-time":"2022-11-09T00:00:00Z","timestamp":1667952000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Shaanxi Provincial Key R&amp;D Plan","award":["2020SF-166"],"award-info":[{"award-number":["2020SF-166"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The topic of joint angle and frequency estimation (JAFE) has aroused extensive interests in the past decades. Current estimation algorithms mainly rely on the Nyquist sampling criterion. In order not to cause ambiguity for parameter estimation, the space\u2013time intervals must be smaller than given thresholds, which results in complicated hardware costs and a huge computational burden. This paper aims to reduce the complexity for JAFE, and a novel sparsity-aware framework is proposed. Unlike the current uniform sampling architectures, the incoming narrow-band singles are sampled by a series of space\u2013time coprime samplers. An improved rotational invariance estimator is introduced, which offers closed-form solutions for both angle and frequency estimation. The mathematical treatments indicate that our methodology is inherent in larger spatial\/temporal aperture than the uniform sampling architectures; hence, it provides more accurate JAFE compared to alternative approaches relying on uniform sampling. Additionally, it attains nearly the same complexity as the current rotational invariance approach. Numerical results agree with the theoretical advantages of our methodology.<\/jats:p>","DOI":"10.3390\/s22228633","type":"journal-article","created":{"date-parts":[[2022,11,10]],"date-time":"2022-11-10T02:11:15Z","timestamp":1668046275000},"page":"8633","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Novel Sparse Framework for Angle and Frequency Estimation"],"prefix":"10.3390","volume":"22","author":[{"given":"Guilian","family":"Zhao","sequence":"first","affiliation":[{"name":"School of Electronic and Information, Yangtze University, Jingzhou 434023, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dongmei","family":"Huang","sequence":"additional","affiliation":[{"name":"Department of Training Management, Naval Command College, Nanjing 210016, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Changxin","family":"Cai","sequence":"additional","affiliation":[{"name":"School of Electronic and Information, Yangtze University, Jingzhou 434023, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peng","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Electronic and Information, Yangtze University, Jingzhou 434023, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Bongseok, K., Sangdong, K., and Jonghun, L. (2018). A novel DFT-based DOA estimation by a virtual array extension using simple multiplications for FMCW radar. Sensors, 18.","DOI":"10.3390\/s18051560"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Lee, S., and Kim, S.C. (2019). Logarithmic-domain array interpolation for improved direction of arrival estimation in automotive radars. Sensors, 19.","DOI":"10.3390\/s19102410"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Hsu, K.C., and Kiang, J.F. (2019). Joint estimation of DOA and frequency of multiple sources with orthogonal coprime arrays. Sensors, 19.","DOI":"10.3390\/s19020335"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"791","DOI":"10.1109\/TCOMM.2015.2394393","article-title":"Minimum power multicast beamforming with superposition coding for multiresolution broadcast and application to NOMA systems","volume":"63","author":"Choi","year":"2015","journal-title":"IEEE Trans. Commun."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Chataut, R., and Akl, R. (2020). Massive MIMO systems for 5G and beyond networks-overview, recent trends, challenges, and future research direction. Sensors, 20.","DOI":"10.3390\/s20102753"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"9055","DOI":"10.3390\/s120709055","article-title":"Game theory for wireless sensor networks: A survey direction","volume":"12","author":"Shi","year":"2012","journal-title":"Sensors"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Ruan, N., Wang, H., Wen, F., and Shi, J. (2022). DOA estimation in B5G\/6G: Trends and challenges. Sensors, 22.","DOI":"10.3390\/s22145125"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"3333","DOI":"10.1109\/TWC.2021.3120926","article-title":"Deep learning-aided off-grid channel estimation for millimeter wave cellular systems","volume":"21","author":"Wan","year":"2022","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Wang, X. (2010). Joint angle and frequency estimation using multiple-delay output based on ESPRIT. EURASIP J. Adv. Signal Process.","DOI":"10.1155\/2010\/358659"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1007\/s11277-008-9652-5","article-title":"Angle-frequency estimation using trilinear decomposition of the oversampled output","volume":"51","author":"Zhang","year":"2009","journal-title":"Wirel. Pers. Commun."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"660","DOI":"10.1109\/LCOMM.2019.2896593","article-title":"A novel unitary PARAFAC algorithm for joint DOA and frequency estimation","volume":"23","author":"Xu","year":"2019","journal-title":"IEEE Commun. Lett."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"4133","DOI":"10.1109\/TSP.2018.2847645","article-title":"DOA estimation using compressed sparse array","volume":"66","author":"Guo","year":"2018","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Wen, F., Gui, G., Gacanin, H., and Sari, H. (IEEE Trans. Wirel. Commun., 2022). Compressive sampling framework for 2D-DOA and polarization estimation in mmWave polarized massive MIMO systems, IEEE Trans. Wirel. Commun., to appear.","DOI":"10.1109\/TWC.2022.3215965"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"4167","DOI":"10.1109\/TSP.2010.2049264","article-title":"Nested arrays: A novel approach to array processing with enhanced degrees of freedom","volume":"58","author":"Pal","year":"2010","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1377","DOI":"10.1109\/TSP.2015.2393838","article-title":"Generalized coprime array configurations for direction-of-arrival estimation","volume":"63","author":"Qin","year":"2015","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Wen, F., Shi, J., He, J., and Truong, T.K. (IEEE Trans. Aerosp. Electron. Syst., 2022). 2D-DOD and 2D-DOA estimation using sparse L-shaped EMVS-MIMO radar, IEEE Trans. Aerosp. Electron. Syst., to appear.","DOI":"10.1109\/TAES.2022.3208858"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"108260","DOI":"10.1016\/j.sigpro.2021.108260","article-title":"Joint spectrum sensing and DOA estimation with sub-Nyquist sampling","volume":"189","author":"Zhang","year":"2021","journal-title":"Signal Process."},{"key":"ref_18","first-page":"1","article-title":"Joint spectrum, carrier, and DOA estimation with Beamforming MWC sampling system","volume":"71","author":"Jiang","year":"2022","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1750136","DOI":"10.1142\/S0218126617501365","article-title":"Joint DOA and frequency estimation for linear array with compressed sensing PARAFAC framework","volume":"26","author":"Li","year":"2017","journal-title":"J. Circuits Syst. Comput."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1373","DOI":"10.1049\/iet-rsn.2016.0511","article-title":"Joint angle-frequency estimation with spatio-temporal nested sampling","volume":"11","author":"He","year":"2017","journal-title":"IET Radar Sonar Navig."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Shi, J., Wen, F., Liu, Y., Liu, Z., and Hu, P. (2022). Enhanced and generalized coprime array for direction of arrival estimation. IEEE Trans. Aerosp. Electron. Syst., 1\u201312.","DOI":"10.1109\/TAES.2022.3200929"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"637","DOI":"10.1109\/TAC.2020.2987307","article-title":"The vulnerability of cyber-physical system under stealthy attacks","volume":"66","author":"Sui","year":"2021","journal-title":"IEEE Trans. Autom. Control"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/22\/8633\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:13:03Z","timestamp":1760145183000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/22\/8633"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,11,9]]},"references-count":22,"journal-issue":{"issue":"22","published-online":{"date-parts":[[2022,11]]}},"alternative-id":["s22228633"],"URL":"https:\/\/doi.org\/10.3390\/s22228633","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2022,11,9]]}}}