{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T00:33:15Z","timestamp":1767918795022,"version":"3.49.0"},"reference-count":25,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2020,3,11]],"date-time":"2020-03-11T00:00:00Z","timestamp":1583884800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key R&amp;D Program of China(2017YFE0118900) and the EU H2020 is3DMIMO Project","award":["734798"],"award-info":[{"award-number":["734798"]}]},{"DOI":"10.13039\/100010661","name":"Horizon 2020 Framework Programme","doi-asserted-by":"publisher","award":["734798"],"award-info":[{"award-number":["734798"]}],"id":[{"id":"10.13039\/100010661","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>For multi-user uplink massive multiple input multiple output (MIMO) systems, minimum mean square error (MMSE) criterion-based linear signal detection algorithm achieves nearly optimal performance, on condition that the number of antennas at the base station is asymptotically large. However, it involves prohibitively high complexity in matrix inversion when the number of users is getting large. A low-complexity soft-output signal detection algorithm based on improved Kaczmarz method is proposed in this paper, which circumvents the matrix inversion operation and thus reduces the complexity by an order of magnitude. Meanwhile, an optimal relaxation parameter is introduced to further accelerate the convergence speed of the proposed algorithm and two approximate methods of calculating the log-likelihood ratios (LLRs) for channel decoding are obtained as well. Analysis and simulations verify that the proposed algorithm outperforms various typical low-complexity signal detection algorithms. The proposed algorithm converges rapidly and achieves its performance quite close to that of the MMSE algorithm with only a small number of iterations.<\/jats:p>","DOI":"10.3390\/s20061564","type":"journal-article","created":{"date-parts":[[2020,3,12]],"date-time":"2020-03-12T04:13:57Z","timestamp":1583986437000},"page":"1564","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Low-Complexity Soft-Output Signal Detection Based on Improved Kaczmarz Iteration Algorithm for Uplink Massive MIMO System"],"prefix":"10.3390","volume":"20","author":[{"given":"Hebiao","family":"Wu","sequence":"first","affiliation":[{"name":"Chongqing Key Laboratory of Mobile Communications Technology, School of Communication and Information Engineering (SCIE), Chongqing University of Posts and Telecommunications (CQUPT), Chongqing 400065, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5418-7566","authenticated-orcid":false,"given":"Bin","family":"Shen","sequence":"additional","affiliation":[{"name":"Chongqing Key Laboratory of Mobile Communications Technology, School of Communication and Information Engineering (SCIE), Chongqing University of Posts and Telecommunications (CQUPT), Chongqing 400065, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shufeng","family":"Zhao","sequence":"additional","affiliation":[{"name":"Chongqing Key Laboratory of Mobile Communications Technology, School of Communication and Information Engineering (SCIE), Chongqing University of Posts and Telecommunications (CQUPT), Chongqing 400065, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peng","family":"Gong","sequence":"additional","affiliation":[{"name":"National Key Laboratory of Mechatronical Engineering and Control, School of Mechatronical Engineering, Beijing Institute of Technology (BIT), Beijing 100081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,3,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3590","DOI":"10.1109\/TWC.2010.092810.091092","article-title":"Noncooperative cellular wireless with unlimited numbers of base station antennas","volume":"9","author":"Marzetta","year":"2010","journal-title":"IEEE Trans. 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