Multi-user multiple-input multiple-output (MU-MIMO) technology is widely regarded as a key enabler for next-generation wireless communication systems (WCS), since it exploits spatial degrees of freedom to increase system throughput without requiring additional bandwidth. However, realizing these gains in practice depends on effective base station (BS)-to-user association and transmit power allocation policies, and on accurate channel state information (CSI) for interference-suppressing precoding. Because uplink feedback bandwidth is limited, base stations in practical MU-MIMO deployments typically operate with only partial CSI, which weakens interference suppression, lowers the signal-to-interference-plus-noise ratio (SINR), and ultimately reduces both the achievable data rate and the energy efficiency (EE) of the system. At the same time, the growing energy demand of wireless networks makes energy-efficient design, rather than throughput alone, an increasingly urgent objective. Motivated by this gap, this paper investigates the joint optimization of user selection and power allocation for maximizing system EE in MU-MIMO systems operating under limited feedback, subject to constraints on maximum transmit power and quality of service (QoS). The resulting optimization problem is formulated as a mixed-integer nonlinear programming (MINLP) model, which is both non-convex and NP-hard, making it intractable to solve directly. To overcome this difficulty, fractional programming is used to recast the problem into an equivalent subtractive form, after which an iterative algorithm is developed that combines a modified Kuhn-Munkres algorithm for optimal user selection with a Lagrangian dual decomposition technique for optimal power allocation. Extensive simulation results show that the proposed algorithm consistently achieves higher system EE and throughput than existing energy-efficient joint user selection and power allocation (JUSPA) schemes under limited feedback, while converging within a small number of iterations and incurring only modest computational overhead. These findings confirm that explicitly accounting for the impact of limited feedback on SINR, rather than assuming perfect CSI, is essential for realizing energy-efficient resource allocation in practical MU-MIMO networks.
| Published in | International Journal of Wireless Communications and Mobile Computing (Volume 13, Issue 1) |
| DOI | 10.11648/j.wcmc.20261301.12 |
| Page(s) | 23-44 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2026. Published by Science Publishing Group |
Energy Efficiency, User Selection, Power Allocation, Limited Feedback, MU-MIMO
| [1] | Hieu Trong Dao, Sunghwan Kim. Pilot power allocation for maximising the sum rate in massive MIMO systems. IET Communications. 2018, 12(11). pp. 1367--1372. |
| [2] | Su Pan, Yan Yan, Kusi Ankrah Bonsu, Weiwei Zhou. Resource allocation algorithm for MU-MIMO systems with double-objective optimization under the existence of the rank deficient channel matrix. IEEE Access. 2019, 7. pp. 61307--61319. |
| [3] | Xin Liu, Edwin KP Chong, Ness B Shroff. Joint scheduling and power-allocation for interference management in wireless networks. Proceedings IEEE 56th vehicular technology conference. 2002, 3. pp. 1892--1896. |
| [4] | Jaya B Rao, Abraham O Fapojuwo. A survey of energy efficient resource management techniques for multicell cellular networks. IEEE Communications Surveys & Tutorials. 2014, 16(1). pp. 154--180. |
| [5] | Liangrui Tang, Hailin Hu, Yanhua He. Energy efficient joint power control and user association optimization in massive MIMO enabled HetNets. Applied Sciences. 2018, 8(4). pp. 584. |
| [6] | Jilei Yan, Jiandong Li, Linjing Zhao. Joint user scheduling and power allocation with quality of service guarantees in downlink distributed antennas system. IET Communications. 2014, 8(3). pp. 299--307. |
| [7] | Wei Yu, Taesoo Kwon, Changyong Shin. Multicell coordination via joint scheduling, beamforming, and power spectrum adaptation. IEEE Transactions on Wireless Communications. 2013, 12(7). pp. 3300--3313. |
| [8] | Jun Zhu, Robert Schober, Vijay Bhargava. Joint beamforming, resource allocation, and scheduling for multi-cell multi-user MIMO-OFDMA systems. 2012 IEEE Global Communications Conference (GLOBECOM). 2012. pp. 4594--4599. |
| [9] | Trinh Van Chien, Emil Björnson, Erik G Larsson. Joint power allocation and user association optimization for massive MIMO systems. IEEE Transactions on Wireless Communications. 2016, 15(9). pp. 6384--6399. |
| [10] | Mikhail Bakulin, Taoufik Ben Rejeb, Vitaly Kreyndelin, Denis Pankratov, Aleksei Smirnov. Multi-user mimo downlink precoding with dynamic user selection for limited feedback. Sensors. 2025, 25(3). pp. 866. |
| [11] | ZHANG Xinyue, DU Fei, FAN Jingyi, GENG Suiyan, ZHAO Xiongwen. Energy-efficient optimization algorithm for massive MIMO systems with joint antenna selection and user scheduling. CHINESE JOURNAL OF RADIO SCIENCE. 2022, 38(5). pp. 853--860. |
| [12] | Ebenezer Baidoo Bediako, Kusi Ankrah Bonsu, Kwaku Fokuoh Darkwah, John Amoah-Mensah, Joseph Wumboranaan Nanjo, Kwame Oteng Gyasi. Energy-Efficient Power Allocation for Cell-Free Massive MIMO Systems. Applied Mathematics and Statistics. 2026, 3(2). pp. 11. |
| [13] | Kusi Ankrah Bonsu, Su Pan, James Adu Ansere, Weiwei Zhou. Joint user selection and power allocation optimization for energy-efficient MU-MIMO systems with limited feedback. Telecommunication Systems. 2021, 77(3). pp. 479--492. |
| [14] | Hien Quoc Ngo, Le-Nam Tran, Trung Q Duong, Michail Matthaiou, Erik G Larsson. On the total energy efficiency of cell-free massive MIMO. IEEE Transactions on Green Communications and Networking. 2018, 2(1). pp. 25--39. |
| [15] | Long Chen, Zhi Chen, Li Liu, Bin Fu. Successive precoding and user selection in MU-MIMO broadcast channel with limited feedback. 2014 Wireless Telecommunications Symposium. 2014. pp. 1--5. |
| [16] | Jiwook Choi, Namyoon Lee, Song-Nam Hong, Giuseppe Caire. Joint user scheduling, power allocation, and precoding design for massive MIMO systems: A principal component analysis approach. 2018 IEEE International Symposium on Information Theory (ISIT). 2018. pp. 396--400. |
| [17] | Guannan Dong, Haixia Zhang, Shi Jin, Dongfeng Yuan. Energy-efficiency-oriented joint user association and power allocation in distributed massive MIMO systems. IEEE Transactions on Vehicular Technology. 2019, 68(6). pp. 5794--5808. |
| [18] | Yan Lin, Yi Wang, Chunguo Li, Yongming Huang, Luxi Yang. Joint design of user association and power allocation with proportional fairness in massive MIMO HetNets. IEEE Access. 2017, 5. pp. 6560--6569. |
| [19] | Kai Zhu, Li Guo, Kai Niu, Wenjun Xu, Zhiqiang He, Jiaru Lin. Joint uplink user scheduling and power allocation in cognitive MIMO system. IET International Conference on Communication Technology and Application (ICCTA 2011). 2011. pp. 589--593. |
| [20] | Li-Chun Wang, Chu-Jung Yeh. Adaptive joint subchannel and power allocation for multi-user MIMO-OFDM systems. 2008 IEEE 19th International Symposium on Personal, Indoor and Mobile Radio Communications. 2008. pp. 1--5. |
| [21] | Feng Jiang, Jianchi Zhu, Guona Hu, Ying Wang, Guangyi Liu, Ping Zhang. Joint space-frequency-power scheduling algorithm for real time service in cellular MIMO-OFDM system. VTC Spring 2008-IEEE Vehicular Technology Conference. 2008. pp. 2461--2466. citecolor. |
| [22] | Lin Shan, Ryu Miura. Energy-efficient scheduling under hard delay constraints for multi-user MIMO system. 2014 International Symposium on Wireless Personal Multimedia Communications (WPMC). 2014. pp. 696--699. |
| [23] | Li-ping Yao, Quan-sheng Xu, Xi Li, Hong Ji. Joint user pairing and power allocation in uplink virtual MIMO with imperfect CSI. The Journal of China Universities of Posts and Telecommunications. 2013, 20(3). pp. 32--36. |
| [24] | Albrecht J Fehske, Fred Richter, Gerhard P Fettweis. Energy efficiency improvements through micro sites in cellular mobile radio networks. 2009 IEEE Globecom Workshops. 2009. pp. 1--5. |
| [25] | Endre Pap, Mirjana Štrboja. Jensen type inequality for extremal universal integrals. 2012 IEEE 10th Jubilee International Symposium on Intelligent Systems and Informatics. 2012. pp. 525--529. |
| [26] | Elina Nayebi, Alexei Ashikhmin, Thomas L Marzetta, Bhaskar D Rao. Performance of cell-free massive MIMO systems with MMSE and LSFD receivers. 2016 50th Asilomar Conference on Signals, Systems and Computers. 2016. pp. 203--207. |
| [27] | Shen-Yu Peng, Tzu-Chi Huang, Yu-Huei Lee, Chao-Chang Chiu, Ke-Horng Chen, Ying-Hsi Lin, Chao-Cheng Lee, Tsung-Yen Tsai, Chen-Chih Huang, Long-Der Chen, et al. Instruction-cycle-based dynamic voltage scaling power management for low-power digital signal processor with 53% power savings. IEEE Journal of Solid-State Circuits. 2013, 48(11). pp. 2649--2661. |
| [28] | Daquan Feng, Chenzi Jiang, Gubong Lim, Leonard J Cimini, Gang Feng, Geoffrey Ye Li. A survey of energy-efficient wireless communications. IEEE Communications Surveys & Tutorials. 2013, 15(1). pp. 167--178. |
| [29] | Xin-Yuan Zhang, Jun Zhang, Yue-Jiao Gong, Zhi-Hui Zhan, Wei-Neng Chen, Yun Li. Kuhn-Munkres parallel genetic algorithm for the set cover problem and its application to large-scale wireless sensor networks. IEEE Transactions on Evolutionary Computation. 2016, 20(5). pp. 695--710. |
| [30] | John Mattingley, Stephen Boyd. Real-time convex optimization in signal processing. IEEE Signal processing magazine. 2010, 27(3). pp. 50--61. |
| [31] | KA Bonsu, Kwame Osei Boateng, JK Oppong, Koffi A Dotche. Small-scale fading characteristics in cellular networks in ghana. International Journal of Interdisciplinary Telecommunications and Networking (IJITN). 2013, 5(3). pp. 23--33. |
APA Style
Bonsu, K. A., Bediako, E. B., Tengviel, J., Gyasi, K. O., Affum, E. A., et al. (2026). Energy-Efficient Joint User Selection and Power Allocation Optimization for MU-MIMO Systems with Limited Feedback. International Journal of Wireless Communications and Mobile Computing, 13(1), 23-44. https://doi.org/10.11648/j.wcmc.20261301.12
ACS Style
Bonsu, K. A.; Bediako, E. B.; Tengviel, J.; Gyasi, K. O.; Affum, E. A., et al. Energy-Efficient Joint User Selection and Power Allocation Optimization for MU-MIMO Systems with Limited Feedback. Int. J. Wirel. Commun. Mobile Comput. 2026, 13(1), 23-44. doi: 10.11648/j.wcmc.20261301.12
@article{10.11648/j.wcmc.20261301.12,
author = {Kusi Ankrah Bonsu and Ebenezer Baidoo Bediako and John Tengviel and Kwame Oteng Gyasi and Emmanuel Ampoma Affum and Kwasi Adu-Boahene Opare},
title = {Energy-Efficient Joint User Selection and Power Allocation Optimization for MU-MIMO Systems with Limited Feedback},
journal = {International Journal of Wireless Communications and Mobile Computing},
volume = {13},
number = {1},
pages = {23-44},
doi = {10.11648/j.wcmc.20261301.12},
url = {https://doi.org/10.11648/j.wcmc.20261301.12},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.wcmc.20261301.12},
abstract = {Multi-user multiple-input multiple-output (MU-MIMO) technology is widely regarded as a key enabler for next-generation wireless communication systems (WCS), since it exploits spatial degrees of freedom to increase system throughput without requiring additional bandwidth. However, realizing these gains in practice depends on effective base station (BS)-to-user association and transmit power allocation policies, and on accurate channel state information (CSI) for interference-suppressing precoding. Because uplink feedback bandwidth is limited, base stations in practical MU-MIMO deployments typically operate with only partial CSI, which weakens interference suppression, lowers the signal-to-interference-plus-noise ratio (SINR), and ultimately reduces both the achievable data rate and the energy efficiency (EE) of the system. At the same time, the growing energy demand of wireless networks makes energy-efficient design, rather than throughput alone, an increasingly urgent objective. Motivated by this gap, this paper investigates the joint optimization of user selection and power allocation for maximizing system EE in MU-MIMO systems operating under limited feedback, subject to constraints on maximum transmit power and quality of service (QoS). The resulting optimization problem is formulated as a mixed-integer nonlinear programming (MINLP) model, which is both non-convex and NP-hard, making it intractable to solve directly. To overcome this difficulty, fractional programming is used to recast the problem into an equivalent subtractive form, after which an iterative algorithm is developed that combines a modified Kuhn-Munkres algorithm for optimal user selection with a Lagrangian dual decomposition technique for optimal power allocation. Extensive simulation results show that the proposed algorithm consistently achieves higher system EE and throughput than existing energy-efficient joint user selection and power allocation (JUSPA) schemes under limited feedback, while converging within a small number of iterations and incurring only modest computational overhead. These findings confirm that explicitly accounting for the impact of limited feedback on SINR, rather than assuming perfect CSI, is essential for realizing energy-efficient resource allocation in practical MU-MIMO networks.},
year = {2026}
}
TY - JOUR T1 - Energy-Efficient Joint User Selection and Power Allocation Optimization for MU-MIMO Systems with Limited Feedback AU - Kusi Ankrah Bonsu AU - Ebenezer Baidoo Bediako AU - John Tengviel AU - Kwame Oteng Gyasi AU - Emmanuel Ampoma Affum AU - Kwasi Adu-Boahene Opare Y1 - 2026/11/14 PY - 2026 N1 - https://doi.org/10.11648/j.wcmc.20261301.12 DO - 10.11648/j.wcmc.20261301.12 T2 - International Journal of Wireless Communications and Mobile Computing JF - International Journal of Wireless Communications and Mobile Computing JO - International Journal of Wireless Communications and Mobile Computing SP - 23 EP - 44 PB - Science Publishing Group SN - 2330-1015 UR - https://doi.org/10.11648/j.wcmc.20261301.12 AB - Multi-user multiple-input multiple-output (MU-MIMO) technology is widely regarded as a key enabler for next-generation wireless communication systems (WCS), since it exploits spatial degrees of freedom to increase system throughput without requiring additional bandwidth. However, realizing these gains in practice depends on effective base station (BS)-to-user association and transmit power allocation policies, and on accurate channel state information (CSI) for interference-suppressing precoding. Because uplink feedback bandwidth is limited, base stations in practical MU-MIMO deployments typically operate with only partial CSI, which weakens interference suppression, lowers the signal-to-interference-plus-noise ratio (SINR), and ultimately reduces both the achievable data rate and the energy efficiency (EE) of the system. At the same time, the growing energy demand of wireless networks makes energy-efficient design, rather than throughput alone, an increasingly urgent objective. Motivated by this gap, this paper investigates the joint optimization of user selection and power allocation for maximizing system EE in MU-MIMO systems operating under limited feedback, subject to constraints on maximum transmit power and quality of service (QoS). The resulting optimization problem is formulated as a mixed-integer nonlinear programming (MINLP) model, which is both non-convex and NP-hard, making it intractable to solve directly. To overcome this difficulty, fractional programming is used to recast the problem into an equivalent subtractive form, after which an iterative algorithm is developed that combines a modified Kuhn-Munkres algorithm for optimal user selection with a Lagrangian dual decomposition technique for optimal power allocation. Extensive simulation results show that the proposed algorithm consistently achieves higher system EE and throughput than existing energy-efficient joint user selection and power allocation (JUSPA) schemes under limited feedback, while converging within a small number of iterations and incurring only modest computational overhead. These findings confirm that explicitly accounting for the impact of limited feedback on SINR, rather than assuming perfect CSI, is essential for realizing energy-efficient resource allocation in practical MU-MIMO networks. VL - 13 IS - 1 ER -