Closed-Form solution for energy efficiency maximization in uplink IRS-assisted multi-user NOMA network

El-Hadi Meftah, Slimane Benmahmoud

Abstract


Given the growing concerns about energy consumption and its negative impact on the ecosystem, energy efficiency (EE) has become one of the most important key performance indicators in current and future wireless communication tech nologies. In this paper, we address the EE maximization problem in an uplink intelligent reflective surface (IRS)-assisted multi-user non-orthogonal multiple access (NOMA) network. This problem is formulated as a trade-off between the spectral efficiency (SE) and total power consumption, and it appears to be non convex. To avoid the complexity associated with the traditional iteration-based Dinkelbach method, we opt for an alternative closed-form solution for the users’ transmit power based on partial derivative analysis and Lambert function. Simulation results with a realistic power consumption models confirm the accuracy of our theoretical findings.

Keywords


Energy efficiency (EE), intelligent reflecting surface (IRS), non-orthogonal multiple access (NOMA), power consumption, spectral efficiency (SE)

References


Ericsson, “Mobility report,” Nov. 2024. [Online]. Available: https://www.ericsson.com/en/reports-and-papers/mobility-report/reports/november-2024

J. Bieser, R. Hintemann, S. Beucker, S. Schramm, L. Hilty, et al., and M. Kühn, “Klimaschutz durch digitale Technologien? Chancen und Risiken,” Berlin, Tech. Rep., 2020.

J. C. Bieser, R. Hintemann, L. M. Hilty, and S. Beucker, “A review of assessments of the greenhouse gas footprint and abatement potential of information and communication technology,” *Environmental Impact Assessment Review*, vol. 99, p. 107033, 2023.

C. Huang, A. Zappone, G. C. Alexandropoulos, M. Debbah, and C. Yuen, “Reconfigurable intelligent surfaces for energy efficiency in wireless communication,” *IEEE Transactions on Wireless Communications*, vol. 18, no. 8, pp. 4157–4170, 2019.

E. Björnson, Ö. Özdogan, and E. G. Larsson, “Intelligent reflecting surface versus decode-and-forward: How large surfaces are needed to beat relaying?” *IEEE Wireless Communications Letters*, vol. 9, no. 2, pp. 244–248, 2020.

J. He, Y. Mao, Y. Zhou, T. Wang, and Y. Shi, “Reconfigurable intelligent surfaces empowered green wireless networks with user admission control,” *IEEE Transactions on Communications*, vol. 71, no. 7, pp. 4062–4078, 2023.

F. Fang, H. Zhang, J. Cheng, S. Roy, and V. C. M. Leung, “Joint user scheduling and power allocation optimization for energy-efficient NOMA systems with imperfect CSI,” *IEEE Journal on Selected Areas in Communications*, vol. 35, no. 12, pp. 2874–2885, 2017.

Y. Zhang, H.-M. Wang, T.-X. Zheng, and Q. Yang, “Energy-efficient transmission design in nonorthogonal multiple access,” *IEEE Transactions on Vehicular Technology*, vol. 66, no. 3, pp. 2852–2857, 2017.

H. Zhang, F. Fang, J. Cheng, K. Long, W. Wang, and V. C. M. Leung, “Energy-efficient resource allocation in NOMA heterogeneous networks,” *IEEE Wireless Communications*, vol. 25, no. 2, pp. 48–53, 2018.

S. M. R. Islam, N. Avazov, O. A. Dobre, and K.-s. Kwak, “Power-domain non-orthogonal multiple access (NOMA) in 5G systems: Potentials and challenges,” *IEEE Communications Surveys & Tutorials*, vol. 19, no. 2, pp. 721–742, 2017.

Z. Ding, R. Schober, and H. V. Poor, “Unveiling the importance of SIC in NOMA systems—part 1: State of the art and recent findings,” *IEEE Communications Letters*, vol. 24, no. 11, pp. 2373–2377, 2020.

A. S. d. Sena, D. Carrillo, F. Fang, P. H. J. Nardelli, D. B. d. Costa, U. S. Dias, Z. Ding, C. B. Papadias, and W. Saad, “What role do intelligent reflecting surfaces play in multi-antenna non-orthogonal multiple access?” *IEEE Wireless Communications*, vol. 27, no. 5, pp. 24–31, 2020.

W. Ni, X. Liu, Y. Liu, H. Tian, and Y. Chen, “Resource allocation for multi-cell IRS-aided NOMA networks,” *IEEE Transactions on Wireless Communications*, vol. 20, no. 7, pp. 4253–4268, 2021.

X. Yue and Y. Liu, “Performance analysis of intelligent reflecting surface assisted NOMA networks,” *IEEE Transactions on Wireless Communications*, vol. 21, no. 4, pp. 2623–2636, 2022.

Z. Ding and H. Vincent Poor, “A simple design of IRS-NOMA transmission,” *IEEE Communications Letters*, vol. 24, no. 5, pp. 1119–1123, 2020.

H. Wang, C. Liu, Z. Shi, Y. Fu, and R. Song, “On power minimization for IRS-aided downlink NOMA systems,” *IEEE Wireless Communications Letters*, vol. 9, no. 11, pp. 1808–1811, 2020.

F. Fang, Y. Xu, Q.-V. Pham, and Z. Ding, “Energy-efficient design of IRS-NOMA networks,” *IEEE Transactions on Vehicular Technology*, vol. 69, no. 11, pp. 14088–14092, 2020.

J. Wang and J. Li, “Energy efficiency maximization for irs-assisted noma networks,” Physical Communication, vol. 52, p. 101647, 2022.

K. H. Altuwairgi, A. M. T. Khel, and K. A. Hamdi, “On the performance of IRS-assisted multi-user THz-NOMA under beam misalignment,” IEEE Transactions on Vehicular Technology, vol. 73, no. 12, pp. 19140–19155, 2024.

C. Zhang, M. Cui, and G. Zhang, “Throughput optimization for IRS-assisted multi-user NOMA URLLC systems,” Wireless Networks, vol. 29, no. 6, pp. 2505–2517, April 2023.256.

G. Li, M. Zeng, D. Mishra, L. Hao, Z. Ma, and O. A. Dobre, “Energy-efficient design for IRS-empowered uplink MIMO-NOMA systems,” IEEE Transactions on Vehicular Technology, vol. 71, no. 9, pp. 9490-9500, 2022.

M. Zeng, E. Bedeer, O. A. Dobre, P. Fortier, Q.-V. Pham, and W. Hao, “Energy-efficient resource allocation for IRS-assisted multi-antenna uplink systems,” IEEE Wireless Communications Letters, vol. 10,no. 6, pp. 1261–1265, 2021.

X. Yu, G. Wang, X. Huang, K. Wang, W. Xu, and Y. Rui, “Energy efficient resource allocation for uplink RIS-aided millimeter-wave networks with NOMA,” IEEE Transactions on Mobile Computing, vol. 23, no. 1, pp. 423–436, 2024.

T. Qiao, Y. Cao, J. Tang, N. Deng, N. Zhao, and Y. Li, “Energy efficiency maximization for active IRS

assisted uplink NOMA systems,” IEEE Wireless Communications Letters, vol. 13, no. 6, pp. 1561–1565, 2024.

Z. Xu, J. Liu, J. Zou, and Z. Wen, “Energy-efficient design for IRS-assisted NOMA-based mobile edge computing,” IEEE Communications Letters, vol. 26, no. 7, pp. 1618–1622, 2022.

H. Wang, C. Liu, Z. Shi, Y. Fu, and R. Song, “Power minimization for uplink RIS-assisted CoMP-NOMA networks with GSIC,” IEEE Transactions on Communications, vol. 70, no. 7, pp. 4559–4573, 2022.

W. Dinkelbach, “On nonlinear fractional programming,” Management Science, vol. 13, no. 7, pp. 492

, 1967.

Z. Yang, M. Chen, W. Saad, W. Xu, M. Shikh-Bahaei, H. V. Poor, and S. Cui, “Energy-efficient wireless communications with distributed reconfigurable intelligent surfaces,” IEEE Transactions on Wireless

Communications, vol. 21, no. 1, pp. 665–679, 2022.

A. Hoorfar and M. Hassani, “Inequalities on the lambert function and hyperpower function,” JIPAM. Journal of Inequalities in Pure Applied Mathematics, vol. 9, no. 2, pp. 5–9, 2008.

E. U. T. R. Access, “Further advancements for E-UTRA physical layer aspects,” 3GPP Technical Specif ication TR, vol. 36, p. V2, 2010.

B. Zheng and R. Zhang, “Intelligent reflecting surface-enhanced OFDM: Channel estimation and reflection optimization,” IEEE Wireless Communications Letters, vol. 9, no. 4, pp. 518–522, 2020.

C. You, B. Zheng, and R. Zhang, “Channel estimation and passive beamforming for intelligent reflecting surface: Discrete phase shift and progressive refinement,” IEEE Journal on Selected Areas in Communi

cations, vol. 38, no. 11, pp. 2604–2620, 2020.

Z.-Q. He and X. Yuan, “Cascaded channel estimation for large intelligent metasurface assisted massive MIMO,” IEEE Wireless Communications Letters, vol. 9, no. 2, pp. 210–214, 2020.

M. Zeng, X. Li, G. Li, W. Hao, and O. A. Dobre, “Sum rate maximization for IRS-assisted uplink NOMA,” IEEE Communications Letters, vol. 25, no. 1, pp. 234–238, 2021.

Z. Wei, L. Yang, D. W. K. Ng, J. Yuan, and L. Hanzo, “On the performance gain of NOMA over OMA in uplink communication systems,” IEEE Transactions on Communications, vol. 68, no. 1, pp. 536–568, 2020.

M. Vaezi, R. Schober, Z. Ding, and H. V. Poor, “Non-orthogonal multiple access: Common myths and critical questions,” IEEE Wireless Communications, vol. 26, no. 5, pp. 174–180, 2019.

M. Naeem, K. Illanko, A. Karmokar, A. Anpalagan, and M. Jaseemuddin, “Optimal power allocation for green cognitive radio: fractional programming approach,” IET Communications, vol. 7, no. 12, pp. 1279–1286, 2013



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