journal article·2025-06-13Open access

A Fast Convergence Scheme Using Chebyshev Iteration Based on SOR and Applied to Uplink M-MIMO B5G Systems for Multi-User Detection

Yung-Ping Tu, Guan-Hong Liu

Applied Sciences· Volume 15· Issue 12

Abstract

Massive multiple input–multiple output (M-MIMO) is a promising and pivotal technology in contemporary wireless communication systems that can effectively enhance link reliability and data throughput, especially in uplink scenarios. Even so, the receiving end requires more computational complexity to reconstitute the signal. This problem has emerged in fourth-generation (4G) MIMO system; with the dramatic increase in demand for devices and data in beyond-5G (B5G) systems, this issue will become yet more obvious. To take into account both complexity and signal-revested capability at the receiver, this study uses the matrix iteration method to avoid the staggering amount of operations produced by the inverse matrix. Then, we propose a highly efficient multi-user detector (MUD) named hybrid SOR-based Chebyshev acceleration (CHSOR) for the uplink of M-MIMO orthogonal frequency-division multiplexing (OFDM) and universal filtered multi-carrier (UFMC) waveforms, which can be promoted to B5G developments. The proposed CHSOR scheme includes two stages: the first consists of successive over-relaxation (SOR) and modified successive over-relaxation (MSOR), combining the advantages of low complexity of both and generating a better initial transmission symbol, iteration matrix, and parameters for the next stage; sequentially, the second stage adopts the low-cost iterative Chebyshev acceleration method for performance refinement to obtain a lower bit error rate (BER). Under constrained evaluation settings, Section (Simulation Results and Discussion) presents the results of simulations performed in MATLAB version R2022a. Results show that the proposed detector can achieve a 91.624% improvement in BER performance compared with Chebyshev successive over-relaxation (CSOR). This is very near to the performance of the minimum mean square error (MMSE) detector and is achieved in only a few iterations. In summary, our proposed CHSOR scheme demonstrates fast convergence compared to previous works and as such possesses excellent BER and complexity performance, making it a competitive solution for uplink M-MIMO B5G systems.
Source: crossref · Quality: baseline

Research context

OpenAlex topics: Advanced MIMO Systems Optimization · Wireless Communication Networks Research · Advanced Wireless Communication Technologies

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

Affiliations

Department of Electronic Engineering, National Formosa University, Yunlin 632301, Taiwan

References (60)

Show source-provided references
1. Conceição, F., Gomes, M., Silva, V., Dinis, R., Silva, A., and Castanheira, D. (2020). A survey of candidate waveforms for beyond 5G systems. Electronics, 10.10.3390/electronics10010021 ↗
2. Berceanu, M.G., Florea, C., and Halunga, S. (2020). Performance comparison of massive MIMO system with orthogonal and nonorthogonal multiple access for uplink in 5G systems. Appl. Sci., 10.10.3390/app10207139 ↗
3. Efficient Subcarrier-Level OFDM Backscatter Communications10.1109/TMC.2025.3529265 ↗
4. Saoud, B., and Shayea, I. (2023, January 26–28). Performance evaluation of MIMO-OFDM system in wireless network. Proceedings of the 2023 10th International Conference on Wireless Networks and Mobile Communications (WINCOM), Istanbul, Turkiye.10.1109/WINCOM59760.2023.10322997 ↗
5. Ismael, W.M., Gao, M., Zahary, A., Yemeni, Z., Ibrahim, Y., and Hawban, A. (2021, January 22–24). Edge-based Anomaly Data Detection Approach for Wireless Sensor Network-based Internet of Things. Proceedings of the 2021 International Conference of Technology, Science and Administration (ICTSA), Taiz, Yemen.10.1109/ICTSA52017.2021.9406548 ↗
6. Nozica, D., Blazevic, D., and Keser, T. (2025). Industrial-Grade Edge Computing Device for Smart Furniture Products. Appl. Sci., 15.10.3390/app15084355 ↗
7. Lee, C., and Fumagalli, A. (2019, January 15–18). Internet of things security-multilayered method for end to end data communications over cellular networks. Proceedings of the 2019 IEEE 5th World Forum on Internet of Things (WF-IoT), Limerick, Ireland.10.1109/WF-IoT.2019.8767227 ↗
8. 5G new radio evaluation against IMT-2020 key performance indicators10.1109/ACCESS.2020.3001641 ↗
9. Usman, M.A., Weerasinghe, N.S., Ansari, R., Usman, M.R., and Politis, C. (2022, January 4–8). Investigating Reliability for URLLC in EUHT-5G a new IMT-2020 Candidate Technology. Proceedings of the 2022 IEEE Globecom Workshops (GC Wkshps), Rio de Janeiro, Brazil.10.1109/GCWkshps56602.2022.10008571 ↗
10. Yamada, H., Suganuma, H., and Maehara, F. (2022, January 16–19). System capacity analysis of asynchronous FBMC and OFDM systems in the presence of adjacent channel interference and multipath fading. Proceedings of the 2022 IEEE Radio and Wireless Symposium (RWS), Las Vegas, NV, USA.10.1109/RWS53089.2022.9719951 ↗
11. Massive MIMO for next generation wireless systems10.1109/MCOM.2014.6736761 ↗
12. Earle, B., Al-Habashna, A., Wainer, G., Li, X., and Xue, G. (2023, January 23–26). Machine Learning Models for Channel Status Classification in M-Mimo Systems Using Limited CSI Feedback. Proceedings of the 2023 Annual Modeling and Simulation Conference (ANNSIM), Hamilton, ON, Canada.
13. On the limitation of linear MMSE detection10.1109/TIT.2006.880039 ↗
14. Kong, B.Y., and Park, I.C. (2016, January 4–8). Low-complexity symbol detection for massive MIMO uplink based on Jacobi method. Proceedings of the 2016 IEEE 27th Annual International Symposium on Personal, Indoor, and Mobile Radio Communications (PIMRC), Valencia, Spain.10.1109/PIMRC.2016.7794623 ↗
15. Shen, D., Chen, L., Li, Q., Chen, T., and Zhao, F. (2023, January 7–9). A Weighted Gauss-Seidel Iterative Algorithm with Fast Convergence. Proceedings of the 2023 3rd International Symposium on Computer Technology and Information Science (ISCTIS), Chengdu, China.10.1109/ISCTIS58954.2023.10213210 ↗
16. Fang, Y., Chen, L., You, C., Wen, D., and Zhu, P. (2025). Finite-Precision Conjugate Gradient Method for Massive MIMO Detection. arXiv.
17. Gao, X., Dai, L., Hu, Y., Wang, Z., and Wang, Z. (2014, January 8–12). Matrix inversion-less signal detection using SOR method for uplink large-scale MIMO systems. Proceedings of the 2014 IEEE Global Communications Conference, Austin, TX, USA.10.1109/GLOCOM.2014.7037314 ↗
18. Accelerated overrelaxation method10.1090/S0025-5718-1978-0483340-6 ↗
19. Yu, A., Zhang, C., Zhang, S., and You, X. (2016, January 25–28). Efficient SOR-based detection and architecture for large-scale MIMO uplink. Proceedings of the 2016 IEEE Asia Pacific Conference on Circuits and Systems (APCCAS), Jeju, Republic of Korea.10.1109/APCCAS.2016.7803987 ↗
20. Ning, J., Lu, Z., Xie, T., and Quan, J. (2015, January 17–19). Low complexity signal detector based on SSOR method for massive MIMO systems. Proceedings of the 2015 IEEE International Symposium on Broadband Multimedia Systems and Broadcasting, Ghent, Belgium.10.1109/BMSB.2015.7177185 ↗
21. Hu, Y., Wu, J., and Wang, Y. (2019, January 11–13). SAOR-based precoding with enhanced BER performance for massive MIMO systems. Proceedings of the 2019 International Conference on Artificial Intelligence in Information and Communication (ICAIIC), Okinawa, Japan.10.1109/ICAIIC.2019.8668984 ↗
22. Yu, A., Yang, C., Zhang, Z., You, X., and Zhang, C. (2018, January 19–21). Efficient SOR based massive MIMO detection using Chebyshev acceleration. Proceedings of the 2018 IEEE 23rd International Conference on Digital Signal Processing (DSP), Shanghai, China.10.1109/ICDSP.2018.8631635 ↗
23. Tu, Y.P., Chen, C.Y., and Lin, K.H. (2021). An Efficient Two-Stage Receiver Base on AOR Iterative Algorithm and Chebyshev Acceleration for Uplink Multiuser Massive-MIMO OFDM Systems. Electronics, 11.10.3390/electronics11010092 ↗
24. A Low Complexity Iterative SC-FDE Receiver for Massive MIMO Systems10.1109/TVT.2024.3381559 ↗
25. Deep unfolding of Chebyshev accelerated iterative method for massive MIMO detection
26. Fast matrix inversion based on Chebyshev acceleration for linear detection in massive MIMO systems10.1049/ell2.12486 ↗
27. Efficient iterative massive MIMO detection using Chebyshev acceleration10.1016/j.phycom.2022.101651 ↗
28. A new randomized iterative detection algorithm for uplink large-scale MIMO systems10.1109/TCOMM.2023.3267551 ↗
29. Liu, H., Cheng, X., Li, W., Feng, F., Wang, L., Xiao, Y., and Fu, S. (2024). A novel iterative detection method based on a lattice reduction-aided algorithm for MIMO OFDM systems. Sci. Rep., 14.10.1038/s41598-024-52602-6 ↗
30. Hazareena, A., and Mustafa, B.A. (2018, January 29–31). A survey: On the waveforms for 5G. Proceedings of the 2018 Second International Conference on Electronics, Communication and Aerospace Technology (ICECA), Coimbatore, India.10.1109/ICECA.2018.8474641 ↗
31. Lee, J., Lou, H.L., Toumpakaris, D., and Cioffi, J.M. (December, January 29). Effect of carrier frequency offset on OFDM systems for multipath fading channels. Proceedings of the IEEE Global Telecommunications Conference, 2004. GLOBECOM’04, Dallas, TX, USA.
32. Robust fast time-varying multipath fading channel estimation and equalization for MIMO-OFDM systems via a fuzzy method10.1109/TVT.2012.2188549 ↗
33. Waveform contenders for 5G: Description, analysis and comparison10.1016/j.phycom.2017.05.004 ↗
34. Suyama, S., Fukuda, H., Suzuki, H., and Fukawa, K. (2012, January 29–30). 10 Gbps 8× 8 MIMO-OFDM broadband experimental system for 11 GHz band super high bit-rate mobile communications. Proceedings of the OFDM 2012: 17th International OFDM Workshop 2012 (InOWo’12), VDE, Essen, Germany.
35. Moreolo, M.S., Fàbrega, J.M., Nadal, L., and Vílchez, F.J. (2012, January 2–5). Software-defined optical OFDM transmission systems: Enabling elasticity in the data plane. Proceedings of the 2012 14th International Conference on Transparent Optical Networks (ICTON), Coventry, UK.10.1109/ICTON.2012.6254504 ↗
36. Rani, P.N., and Rani, C.S. (2016, January 15–17). UFMC: The 5G modulation technique. Proceedings of the 2016 IEEE international conference on computational intelligence and computing research (ICCIC), Chennai, India.10.1109/ICCIC.2016.7919714 ↗
37. Sidiq, S., Mustafa, F., Sheikh, J.A., and Malik, B.A. (2019, January 16–17). FBMC and UFMC: The modulation techniques for 5G. Proceedings of the 2019 International Conference on Power Electronics, Control and Automation (ICPECA), New Delhi, India.10.1109/ICPECA47973.2019.8975581 ↗
38. Optimization of out-of-band emission using kaiser-bessel filter for UFMC in 5G cellular communications10.23919/JCC.2019.08.002 ↗
39. Tuli, E.A., Kim, D.S., and Lee, J.M. (2021, January 20–22). Performance Enhancement of UFMC Systems using Kaiser Window Filter. Proceedings of the 2021 International Conference on Information and Communication Technology Convergence (ICTC), Jeju Island, Republic of Korea.10.1109/ICTC52510.2021.9620960 ↗
40. Massive MIMO detection techniques: A survey10.1109/COMST.2019.2935810 ↗
41. Cho, Y.S., Kim, J., Yang, W.Y., and Kang, C.G. (2010). MIMO-OFDM Wireless Communications with MATLAB, John Wiley & Sons.10.1002/9780470825631 ↗
42. Massive MIMO array design with high isolation by using decoupling cavity
43. Farzamnia, A., Hlaing, N.W., Haldar, M.K., and Rahebi, J. (2017, January 21–23). Channel estimation for sparse channel OFDM systems using least square and minimum mean square error techniques. Proceedings of the 2017 international conference on engineering and technology (ICET), Antalya, Turkey.10.1109/ICEngTechnol.2017.8308193 ↗
44. Firdaus, M., and Moegiharto, Y. (2022). Performance of OFDM System against Different Cyclic Prefix Lengths on Multipath Fading Channels. arXiv.
45. Manda, R., and Gowri, R. (2019, January 21–22). Filter design for universal filtered multicarrier (UFMC) based systems. Proceedings of the 2019 4th International Conference on Information Systems and Computer Networks (ISCON), Mathura, India.10.1109/ISCON47742.2019.9036268 ↗
46. Wang, X., Wild, T., and Schaich, F. (2015, January 11–14). Filter optimization for carrier-frequency-and timing-offset in universal filtered multi-carrier systems. Proceedings of the 2015 IEEE 81st Vehicular Technology Conference (VTC Spring), Glasgow, UK.10.1109/VTCSpring.2015.7145842 ↗
47. Capacity of correlated MIMO Rayleigh channels10.1109/TWC.2006.1576538 ↗
48. Mishra, V., Tripathi, P.K., Rana, P., and Joshi, H.D. (2013, January 26–28). Performance analysis of comb type pilot aided channel estimation in ofdm with different pilot sequences. Proceedings of the 2013 Tenth International Conference on Wireless and Optical Communications Networks (WOCN), Bhopal, India.10.1109/WOCN.2013.6616197 ↗
49. Chen, W., Qi, L., and Yanjun, F. (2010, January 21–24). An improved least square channel estimation algorithm for underwater acoustic OFDM systems. Proceedings of the 2010 2nd International Conference on Future Computer and Communication, Wuhan, China.10.1109/ICFCC.2010.5497494 ↗
50. Low complexity linear detectors for massive MIMO: A comparative study10.1109/ACCESS.2021.3065923 ↗
51. Convergence properties of the symmetric and unsymmetric successive overrelaxation methods and related methods10.1090/S0025-5718-1970-0281331-4 ↗
52. Young, D.M. (2014). Iterative Solution of Large Linear Systems, Elsevier.
53. Mason, J.C., and Handscomb, D.C. (2002). Chebyshev Polynomials, Chapman and Hall/CRC.10.1201/9781420036114 ↗
54. Successive overrelaxation (SOR) and related methods10.1016/S0377-0427(00)00403-9 ↗
55. Haotian, X., Junqin, W., and Jianhao, S. (August, January 30). Massive MIMO joint precoding algorithm based on SORMI and Chebyshev iteration. Proceedings of the 2021 2nd International Conference on Computer Communication and Network Security (CCNS), Xining, China.10.1109/CCNS53852.2021.00031 ↗
56. Efficient successive over relaxation detectors for massive MIMO10.1109/TCSI.2020.2966318 ↗
57. Study and Comparative Analysis of OFDM and UFMC Modulation Schemes
58. Ravindran, R., and Viswakumar, A. (2019, January 6–8). Performance evaluation of 5G waveforms: UFMC and FBMC-OQAM with Cyclic Prefix-OFDM System. Proceedings of the 2019 9th International Conference on Advances in Computing and Communication (ICACC), Kochi, India.10.1109/ICACC48162.2019.8986195 ↗
59. Tu, Y.P., Jian, P.S., and Huang, Y.F. (2023). Novel Hybrid SOR-and AOR-Based Multi-User Detection for Uplink M-MIMO B5G Systems. Electronics, 13.10.3390/electronics13010187 ↗
60. Cox, D.A. (2021). Stickelberger and the eigenvalue theorem. Commutative Algebra: Expository Papers Dedicated to David Eisenbud on the Occasion of his 75th Birthday, Springer.10.1007/978-3-030-89694-2_8 ↗