{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T10:05:18Z","timestamp":1771668318642,"version":"3.50.1"},"reference-count":49,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2018,5,14]],"date-time":"2018-05-14T00:00:00Z","timestamp":1526256000000},"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":["61601058, 61671366"],"award-info":[{"award-number":["61601058, 61671366"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["310832173701"],"award-info":[{"award-number":["310832173701"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In spatial spectrum estimation, difference co-array can provide extra degrees-of-freedom (DOFs) for promoting parameter identifiability and parameter estimation accuracy. For the sake of acquiring as more DOFs as possible with a given number of physical sensors, we herein design a novel sensor array geometry named cascade array. This structure is generated by systematically connecting a uniform linear array (ULA) and a non-uniform linear array, and can provide more DOFs than some exist array structures but less than the upper-bound indicated by minimum redundant array (MRA). We further apply this cascade array into multiple input multiple output (MIMO) array systems, and propose a novel joint direction of departure (DOD) and direction of arrival (DOA) estimation algorithm, which is based on a reduced-dimensional weighted subspace fitting technique. The algorithm is angle auto-paired and computationally efficient. Theoretical analysis and numerical simulations prove the advantages and effectiveness of the proposed array structure and the related algorithm.<\/jats:p>","DOI":"10.3390\/s18051557","type":"journal-article","created":{"date-parts":[[2018,5,15]],"date-time":"2018-05-15T03:29:34Z","timestamp":1526354974000},"page":"1557","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Degree-of-Freedom Strengthened Cascade Array for DOD-DOA Estimation in MIMO Array Systems"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3905-3973","authenticated-orcid":false,"given":"Bobin","family":"Yao","sequence":"first","affiliation":[{"name":"School of Electronic and Control Engineering, Chang\u2019an University, Xi\u2019an 710064, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhi","family":"Dong","sequence":"additional","affiliation":[{"name":"School of Highway, Chang\u2019an University, Xi\u2019an 710064, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Weile","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wei","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qisheng","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Electronic and Control Engineering, Chang\u2019an University, Xi\u2019an 710064, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,5,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Van Trees, H.L. 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