{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T15:05:08Z","timestamp":1773414308615,"version":"3.50.1"},"reference-count":22,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2022,7,23]],"date-time":"2022-07-23T00:00:00Z","timestamp":1658534400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>To improve the spectral efficiency of symmetry-based intelligent reconfigurable surface (IRS)-assisted MIMO communication systems, this paper investigates the joint precoding and passive beamforming optimization problem for millimeter-wave point-to-point MIMO systems under both ideal and practical IRS phase shifts. For the ideal IRS phase shifts setup, we derive a simplified approximate spectral efficiency expression based on Jensen\u2019s inequality and propose a minimum mean square error (MMSE)-based algorithm to transform the simplified non-convex problem into a solvable convex function. For the practical IRS phase shifts setup, we propose a multi-start stepwise optimization algorithm to obtain the passive beamforming by stepwise iterative search. Finally, with the above-obtained passive beamforming, the optimal precoding is derived by performing the singular value decomposition (SVD) on the effective channel and water-filling power allocation. The simulation results verify our performance analysis and demonstrate that spectral efficiency can be effectively improved compared to various benchmark schemes.<\/jats:p>","DOI":"10.3390\/sym14081510","type":"journal-article","created":{"date-parts":[[2022,7,25]],"date-time":"2022-07-25T04:52:47Z","timestamp":1658724767000},"page":"1510","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Beamforming Optimization for Intelligent Reflecting Surface-Assisted MIMO Systems"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8281-3125","authenticated-orcid":false,"given":"Wenjuan","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Physics and Electronics, Central South University, Changsha 410083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Honggui","family":"Deng","sequence":"additional","affiliation":[{"name":"School of Physics and Electronics, Central South University, Changsha 410083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Youzhen","family":"Li","sequence":"additional","affiliation":[{"name":"School of Physics and Electronics, Central South University, Changsha 410083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4239-3749","authenticated-orcid":false,"given":"Zaoxing","family":"Zhu","sequence":"additional","affiliation":[{"name":"School of Physics and Electronics, Central South University, Changsha 410083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chengzuo","family":"Peng","sequence":"additional","affiliation":[{"name":"School of Physics and Electronics, Central South University, Changsha 410083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gang","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Physics and Electronics, Central South University, Changsha 410083, China"},{"name":"College of Information Science and Engineering, Changsha Normal University, Changsha 410100, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"17361","DOI":"10.1109\/ACCESS.2018.2819197","article-title":"Energy-Efficient Hybrid Precoding Design for Millimeter-Wave Massive MIMO Systems via Coordinate Update Algorithms","volume":"6","author":"Chen","year":"2018","journal-title":"IEEE Access"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Liu, G., Deng, H., Yang, K., Zhu, Z., Liu, J., and Dong, H. 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