{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:44:21Z","timestamp":1760237061819,"version":"build-2065373602"},"reference-count":25,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2020,2,21]],"date-time":"2020-02-21T00:00:00Z","timestamp":1582243200000},"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>Fifth-generation (5G) communications system is commercially introduced by several mobile operators where sub-6 GHz bands are the backbone of the 5G networks. A large-scale multiple-input multiple-output (MIMO), or massive MIMO (mMIMO), technology has a major impact to secure high data rate, high spectral efficiency, and quality of service (QoS). It could also have a major role in the beyond-5G systems. A massive number of antennas seek advanced signal processing to detect and equalize the signal. However, optimal detectors, such as the maximum likelihood (ML) and maximum posterior (MAP), are not desirable in implementation due to extremely high complexity. Therefore, sub-optimum solutions have been introduced to obtain and guarantee enough balance between the performance and the computational complexity. In this paper, a robust and joint low complexity detection algorithm is proposed based on the Jacobi (JA) and Gauss\u2013Seidel (GS) methods. In such iterative methods, the performance, complexity, and convergence rate are highly dependent on the initial vector. In this paper, initial solution is proposed by exploiting the benefits of a stair matrix to obtain a fast convergence rate, high performance, and low complexity. Numerical results show that proposed algorithm achieves high accuracy and relieve the computational complexity even when the BS-to-user-antenna ratio (BUAR) is small.<\/jats:p>","DOI":"10.3390\/sym12020306","type":"journal-article","created":{"date-parts":[[2020,2,26]],"date-time":"2020-02-26T04:18:29Z","timestamp":1582690709000},"page":"306","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["A Robust Hybrid Iterative Linear Detector for Massive MIMO Uplink Systems"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6464-1101","authenticated-orcid":false,"given":"Mahmoud A.","family":"Albreem","sequence":"first","affiliation":[{"name":"Department of Electronics and Communications Engineering, A\u2019Sharqiyah University, Ibra 400, Oman"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8579-5444","authenticated-orcid":false,"given":"Mohammed H.","family":"Alsharif","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, College of Electronics and Information Engineering, Sejong University, 209 Neugdong-ro, Gwangjin-gu, Seoul 05006, Korea"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1762-5915","authenticated-orcid":false,"given":"Sunghwan","family":"Kim","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering, University of Ulsan, Ulsan 44610, Korea"}]}],"member":"1968","published-online":{"date-parts":[[2020,2,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Liu, L., Peng, G., Wang, P., Zhou, S., Wei, Q., Yin, S., and Wei, S. (2020). Energy- and Area-Efficient Recursive-Conjugate-Gradient-Based MMSE Detector for Massive MIMO Systems. IEEE Trans. Signal Process.","DOI":"10.1109\/TSP.2020.2964234"},{"key":"ref_2","first-page":"182","article-title":"Jamming Suppression in Massive MIMO Systems","volume":"67","author":"Akhlaghpasand","year":"2020","journal-title":"IEEE Trans. Circuits Syst. II Express Briefs"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"e3254","DOI":"10.1002\/ett.3254","article-title":"How to make key 5G wireless technologies environmental friendly: A review","volume":"29","author":"Alsharif","year":"2018","journal-title":"Trans. Emerg. Telecommun. Technol."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Mohammed, S.L., Alsharif, M.H., Gharghan, S.K., Khan, I., and Albreem, M. (2019). Robust Hybrid Beamforming Scheme for Millimeter-Wave Massive-MIMO 5G Wireless Networks. Symmetry, 11.","DOI":"10.3390\/sym11111424"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1137","DOI":"10.1109\/LWC.2019.2909019","article-title":"A Partial Learning-Based Detection Scheme for Massive MIMO","volume":"8","author":"Jia","year":"2019","journal-title":"IEEE Wirel. Commun. Lett."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"491","DOI":"10.1109\/JSAC.2005.862402","article-title":"Algorithm and implementation of the K-best sphere decoding for MIMO detection","volume":"24","author":"Guo","year":"2006","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"3397","DOI":"10.1109\/TSP.2008.925260","article-title":"Fixed-Complexity Soft MIMO Detection via Partial Marginalization","volume":"56","author":"Larsson","year":"2008","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Chen, Y., Cheng, C., Tsai, T., Sun, W., Ueng, Y., and Yang, C. (2017, January 5\u20138). A 501mW 7.6lGb\/s integrated message-passing detector and decoder for polar-coded massive MIMO systems. Proceedings of the 2017 Symposium on VLSI Circuits, Kyoto, Japan.","DOI":"10.23919\/VLSIC.2017.8008528"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"7260","DOI":"10.1109\/TVT.2019.2924952","article-title":"A Low-Complexity Massive MIMO Detection Based on Approximate Expectation Propagation","volume":"68","author":"Tan","year":"2019","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Jeon, Y., Hong, S., and Lee, N. (2017, January 21\u201325). Blind detection for MIMO systems with low-resolution ADCs using supervised learning. Proceedings of the 2017 IEEE International Conference on Communications (ICC), Paris, France.","DOI":"10.1109\/ICC.2017.7997434"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"607","DOI":"10.1109\/LSP.2019.2902017","article-title":"Symbol Detection of Phase Noise-Impaired Massive MIMO Using Approximate Bayesian Inference","volume":"26","author":"Yang","year":"2019","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1109\/LWC.2015.2504366","article-title":"Low Complexity Iterative MMSE-PIC Detection for Medium-Size Massive MIMO","volume":"5","author":"Fang","year":"2016","journal-title":"IEEE Wirel. Commun. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"916","DOI":"10.1109\/JSTSP.2014.2313021","article-title":"Large-Scale MIMO Detection for 3GPP LTE: Algorithms and FPGA Implementations","volume":"8","author":"Wu","year":"2014","journal-title":"IEEE J. Sel. Top. Signal Process."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1049\/el.2019.2938","article-title":"Efficient initialisation of iterative linear massive MIMO detectors using a stair matrix","volume":"56","author":"Albreem","year":"2020","journal-title":"Electron. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Jiang, F., Li, C., Gong, Z., and Su, R. (2018). Stair Matrix and its Applications to Massive MIMO Uplink Data Detection. IEEE Trans. Commun.","DOI":"10.1109\/TCOMM.2017.2789211"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Albreem, M.A., Alsharif, M.H., and Kim, S. (2020). Impact of Stair and Diagonal Matrices in Iterative Linear Massive MIMO Uplink Detectors for 5G Wireless Networks. Symmetry, 12.","DOI":"10.3390\/sym12010071"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Liu, X., Zhang, Z., Wang, X., Lian, J., and Dai, X. (2019, January 9\u201310). A Low Complexity High Performance Weighted Neumann Series-based Massive MIMO Detection. Proceedings of the 2019 28th Wireless and Optical Communications Conference (WOCC), Beijing, China.","DOI":"10.1109\/WOCC.2019.8770550"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"748","DOI":"10.1109\/LCOMM.2019.2897798","article-title":"A Low Complexity Signal Detection Scheme Based on Improved Newton Iteration for Massive MIMO Systems","volume":"23","author":"Jin","year":"2019","journal-title":"IEEE Commun. Lett."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"6272","DOI":"10.1109\/TVT.2019.2915171","article-title":"On the Low-Complexity, Hardware-Friendly Tridiagonal Matrix Inversion for Correlated Massive MIMO Systems","volume":"68","author":"Zhang","year":"2019","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Ren, W., Zhou, Y., Ji, W., Li, T., Liang, Y., and Li, F. (2019, January 24\u201328). Matrix Approximate Inversion Based Signal Detection in Large-scale 3D-MIMO Systems. Proceedings of the 2019 15th International Wireless Communications Mobile Computing Conference (IWCMC), Tangier, Morocco.","DOI":"10.1109\/IWCMC.2019.8766789"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Albreem, M.A.M., El-Saleh, A.A., and Juntti, M. (2019, January 15\u201318). On Approximate Matrix Inversion Methods for Massive MIMO Detectors. Proceedings of the 2019 IEEE Wireless Communications and Networking Conference (WCNC), Marrakech, Morocco.","DOI":"10.1109\/WCNC.2019.8885673"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Albreem, M.A.M. (2019, January 19\u201321). Approximate Matrix Inversion Methods for Massive MIMO Detectors. Proceedings of the 2019 IEEE 23rd International Symposium on Consumer Technologies (ISCT), Ancona, Italy.","DOI":"10.1109\/ISCE.2019.8901015"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Nhat Cuong, C., Thi Hong, T., and Duc Khai, L. (2019, January 20\u201322). Hardware Implementation of the Efficient SOR-Based Massive MIMO Detection for Uplink. Proceedings of the 2019 IEEE-RIVF International Conference on Computing and Communication Technologies (RIVF), Danang, Vietnam.","DOI":"10.1109\/RIVF.2019.8713667"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Yu, A., Jing, S., Tan, X., Wu, Z., Yan, Z., Zhang, Z., You, X., and Zhang, C. (2020). Efficient Successive Over Relaxation Detectors for Massive MIMO. IEEE Trans. Circuits Syst. I Regul. Pap., 1\u201312.","DOI":"10.1109\/TCSI.2020.2966318"},{"key":"ref_25","unstructured":"Seidel, P., Gregorek, D., Paul, S., and Rust, J. (2019, January 24\u201326). Efficient Initialization of Iterative Linear Massive MIMO Uplink Detectors by Binary Jacobi Synthesis. Proceedings of the WSA 2019; 23rd International ITG Workshop on Smart Antennas, Vienna, Austria."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/2\/306\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T08:59:37Z","timestamp":1760173177000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/2\/306"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,2,21]]},"references-count":25,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2020,2]]}},"alternative-id":["sym12020306"],"URL":"https:\/\/doi.org\/10.3390\/sym12020306","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2020,2,21]]}}}