{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,19]],"date-time":"2026-03-19T14:28:28Z","timestamp":1773930508886,"version":"3.50.1"},"reference-count":25,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2019,9,2]],"date-time":"2019-09-02T00:00:00Z","timestamp":1567382400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"This work was supported by Universiti Putra Malaysia under the grant NOMA-MIMO: Optimising 5G Wireless Communication Performance Based on Hybrid NOMA with Partial Feedback for Multiuser MIMO","award":["(GP-IPS\/2018\/9663000, Vot No: 9663000)."],"award-info":[{"award-number":["(GP-IPS\/2018\/9663000, Vot No: 9663000)."]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Symmetrical precoding and algorithms play a vital role in the field of wireless communications and cellular networks. This paper proposed a low-complexity hybrid precoding algorithm for mmWave massive multiple-input multiple-output (MIMO) systems. The traditional orthogonal matching pursuit (OMP) has a large complexity, as it requires matrix inversion and known candidate matrices. Therefore, we propose a bird swarm algorithm (BSA) based matrix-inversion bypass (MIB) OMP (BSAMIBOMP) algorithm which has the feature to quickly search the BSA global optimum value. It only directly finds the array response vector multiplied by the residual inner product, so it does not require the candidate\u2019s matrices. Moreover, it deploys the Banachiewicz\u2013Schur generalized inverse of the partitioned matrix to decompose the high-dimensional matrix into low-dimensional in order to avoid the need for a matrix inversion operation. The simulation results show that the proposed algorithm effectively improves the bit error rate (BER), spectral efficiency (SE), complexity, and energy efficiency of the mmWave massive MIMO system as compared with the existing OMP hybrid and SDRAltMin algorithm without any matrix inversion and known candidate matrix information requirement.<\/jats:p>","DOI":"10.3390\/sym11091099","type":"journal-article","created":{"date-parts":[[2019,9,3]],"date-time":"2019-09-03T03:06:14Z","timestamp":1567479974000},"page":"1099","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["An Efficient Precoding Algorithm for mmWave Massive MIMO Systems"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3821-8024","authenticated-orcid":false,"given":"Imran","family":"Khan","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering, University of Engineering &amp; Technology Peshawar, Peshawar 814 KPK, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shagufta","family":"Henna","sequence":"additional","affiliation":[{"name":"Telecommunications Softwares &amp; Systems Group, Waterford Institute of Technology, Waterford X91, Ireland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nasreen","family":"Anjum","sequence":"additional","affiliation":[{"name":"Department of Informatics, King\u2019s College London, London WC2B 4BG, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Aduwati","family":"Sali","sequence":"additional","affiliation":[{"name":"Wireless and Photonics Networks Research Centre of Excellence, Department of Computer and Communication Systems Engineering, Universiti Putra Malaysia, Selangor 43400, Malaysia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8900-0888","authenticated-orcid":false,"given":"Jonathan","family":"Rodrigues","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA 02139, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yousaf","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, University of Engineering &amp; Technology Peshawar, Peshawar 814 KPK, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Muhammad Irfan","family":"Khattak","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, University of Engineering &amp; Technology Peshawar, Peshawar 814 KPK, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Farhan","family":"Altaf","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, University of Engineering &amp; Technology Peshawar, Peshawar 814 KPK, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,9,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1555","DOI":"10.3390\/s16101555","article-title":"Performance Evaluation of Analog Beamforming with Hardware Impairments for mmWave Massive MIMO Communication in an Urban Scenario","volume":"16","author":"Gomez","year":"2016","journal-title":"Sensors"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Khan, I., Alsharif, M.H., Alassafi, M.O., Ashraf, M., Huang, Y., Kim, J., and Kim, J.H. 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