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User grouping and power allocation for energy efficiency maximization in mmWave-NOMA heterogeneous networks

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Abstract

This paper investigates the application of non-orthogonal multiple access (NOMA) and millimeter-wave (mmWave) transmission in the fifth-generation (5G) of heterogeneous cellular networks (HetNets). Due to the high penetration loss of mmWave, we propose that a small cell base station (SBS) serves small cell user (SCU) equipment in the mmWave band, and a macrocell base station (MBS) serves macrocell users (MCUs) in the microwave band. Cell association, user grouping, and power allocation are fundamental challenges in NOMA-based transmission. We formulate optimization problems for SCU and MCU to maximize the energy efficiency (EE) subject to the required minimum data rates and maximum transmission powers. User grouping algorithms are introduced to demonstrate the significance of selecting the best users. To allocate transmission powers, we formulate an EE maximization problem that is non-convex and NP-hard. We propose to use the Bat algorithm, which is one of the popular and efficient metaheuristic algorithms in solving non-convex problems. Analytical expressions for cell association and outage probabilities are derived. We present Monte Carlo simulation results to validate the analytical expressions and show that: (1) choosing the best user among far users influences the overall EE of system impressively; (2) the optimum values of transmission powers can be obtained by Bat algorithm; (3) the proposed grouping algorithms with power allocation methods outperform the other scenarios in terms of EE and spectral efficiency (SE).

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References

  1. Vien, Q. T., Le, T. A., Phan, C. V., & Agyeman, M. O. (2017). An energy-efficient NOMA for small cells in heterogeneous CRAN under QoS constraints. In European Wireless 2017; 23th European Wireless Conference (pp. 1–6). VDE.

  2. Zhu, L., Xiao, Z., Xia, X.-G., & Wu, D. O. (2019). Millimeter-wave communications with non-orthogonal multiple access for B5G/6G. IEEE Access, 7, 116123–116132.

    Article  Google Scholar 

  3. Vaezi, M., Ding, Z., & Poor, H. V. (2019). Multiple access techniques for 5G wireless networks and beyond. Springer.

    Book  Google Scholar 

  4. Bai, T., & Heath, R. W. (2014). Coverage and rate analysis for millimeter-wave cellular networks. IEEE Transactions on Wireless Communications, 14(2), 1100–1114.

    Article  Google Scholar 

  5. Rappaport, T. S., et al. (2013). Millimeter wave mobile communications for 5G cellular: It will work! IEEE access, 1, 335–349.

    Article  Google Scholar 

  6. Rappaport, T. S., Gutierrez, F., Ben-Dor, E., Murdock, J. N., Qiao, Y., & Tamir, J. I. (2012). Broadband millimeter-wave propagation measurements and models using adaptive-beam antennas for outdoor urban cellular communications. IEEE transactions on antennas and propagation, 61(4), 1850–1859.

    Article  Google Scholar 

  7. Alkhateeb, A., Mo, J., Gonzalez-Prelcic, N., & Heath, R. W. (2014). MIMO precoding and combining solutions for millimeter-wave systems. IEEE Communications Magazine, 52(12), 122–131.

    Article  Google Scholar 

  8. Lee, G., Sung, Y., & Kountouris, M. (2016). On the performance of random beamforming in sparse millimeter wave channels. IEEE Journal of Selected Topics in Signal Processing, 10(3), 560–575.

    Article  Google Scholar 

  9. Ding, Z., Lei, X., Karagiannidis, G. K., Schober, R., Yuan, J., & Bhargava, V. K. (2017). A survey on non-orthogonal multiple access for 5G networks: Research challenges and future trends. IEEE Journal on Selected Areas in Communications, 35(10), 2181–2195.

    Article  Google Scholar 

  10. Ali, M. S., Tabassum, H., & Hossain, E. (2016). Dynamic user clustering and power allocation for uplink and downlink non-orthogonal multiple access (NOMA) systems. IEEE access, 4, 6325–6343.

    Google Scholar 

  11. Ding, Z., Fan, P., & Poor, H. V. (2017). Random beamforming in millimeter-wave NOMA networks. IEEE access, 5, 7667–7681.

    Article  Google Scholar 

  12. Wang, C. L., Chen, T. Y., Chen, Y. F., & Wu, D. S. (2018). Low-complexity resource allocation for downlink multicarrier NOMA systems. In 2018 IEEE 29th annual international symposium on personal, indoor and mobile radio communications (PIMRC) (pp. 1–6). IEEE.

  13. Baidas, M. W., Bahbahani, Z., & Alsusa, E. (2019). User association and channel assignment in downlink multi-cell NOMA networks: A matching-theoretic approach. EURASIP Journal on Wireless Communications and Networking, 2019(1), 1–21.

    Article  Google Scholar 

  14. Azam, I., Shahab, M. B., & Shin, S. Y. (2019). User pairing and power allocation for capacity maximization in uplink NOMA. In 2019 42nd international conference on telecommunications and signal processing (tsp) (pp. 690–694). IEEE.

  15. Meng, X., Gao, X., & Liu, Y. (2015). A novel hybrid bat algorithm with differential evolution strategy for constrained optimization. International Journal of Hybrid Information Technology, 8(1), 383–396.

    Article  Google Scholar 

  16. Sedaghat M. A. & Müller R. R. (2017) On user pairing in NOMA uplink, arXiv preprint arXiv:1707.01846

  17. Kang, J.-M., & Kim, I.-M. (2018). Optimal user grouping for downlink NOMA. IEEE Wireless Communications Letters, 7(5), 724–727.

    Article  Google Scholar 

  18. Sayed-Ahmed, A., & Elsabrouty, M. (2017). User selection and power allocation for guaranteed SIC detection in downlink beamforming non-orthogonal multiple access. In 2017 Wireless Days (pp. 188–193). IEEE.

  19. Turgut, E., & Gursoy, M. C. (2017). Coverage in heterogeneous downlink millimeter wave cellular networks. IEEE Transactions on Communications, 65(10), 4463–4477.

    Google Scholar 

  20. Su, Z., et al. (2018). User association and wireless backhaul bandwidth allocation for 5G heterogeneous networks in the millimeter-wave band. China Communications, 15(4), 1–13.

    Article  Google Scholar 

  21. Aboagye, S., Ibrahim, A., & Ngatched, T. M. (2019). Frameworks for energy efficiency maximization in hetnets with millimeter wave backhaul links. IEEE Transactions on Green Communications and Networking. https://doi.org/10.1109/TGCN.2019.2949288

    Article  Google Scholar 

  22. Zhang, H., Huang, S., Jiang, C., Long, K., Leung, V. C., & Poor, H. V. (2017). Energy efficient user association and power allocation in millimeter-wave-based ultra dense networks with energy harvesting base stations. IEEE Journal on Selected Areas in Communications, 35(9), 1936–1947.

    Article  Google Scholar 

  23. Aboagye, S., Ibrahim, A., & Ngatched, T. M. (2019). Energy efficient user association, power, and flow control in millimeter wave backhaul heterogeneous networks. IEEE Open Journal of the Communications Society, 1, 41–59.

    Article  Google Scholar 

  24. Gupta, V. K., Singh, S. K., & Kasbekar, G. S. (2021). Stability analysis of simple and online user association policies for millimeter wave networks. IEEE Access, 9, 62405–62429.

    Article  Google Scholar 

  25. Salh, A., Audah, L., Shah, N. S. M., & Hamzah, S. A. (2020). Energy-efficient power allocation with hybrid beamforming for millimetre-wave 5G massive MIMO system. Wireless Personal Communications, 115, 1–17.

    Article  Google Scholar 

  26. Nguyen, H. T., et al. (2020). Joint user association and power allocation for millimeter-wave ultra-dense networks. Mobile Networks and Applications, 25(1), 274–284.

    Article  Google Scholar 

  27. Wang, X., Chen, R., Xu, Y., & Meng, Q. (2019). Low-complexity power allocation in NOMA systems with imperfect SIC for maximizing weighted sum-rate. IEEE Access, 7, 94238–94253.

    Article  Google Scholar 

  28. Liu, Y., Qin, Z., Elkashlan, M., Nallanathan, A., & McCann, J. A. (2017). Non-orthogonal multiple access in large-scale heterogeneous networks. IEEE Journal on Selected Areas in Communications, 35(12), 2667–2680.

    Article  Google Scholar 

  29. Iraqi, Y., & Al-Dweik, A. (2021). Power allocation for reliable SIC detection of rectangular QAM-based NOMA systems. IEEE Transactions on Vehicular Technology, 70(8), 8355–8360.

    Article  Google Scholar 

  30. Assaf, T., Al-Dweik, A., El Moursi, M., & Zeineldin, H. (2019). Exact BER performance analysis for downlink NOMA systems over Nakagami-$ m $ fading channels. IEEE Access, 7, 134539–134555.

    Article  Google Scholar 

  31. Assaf, T., Al-Dweik, A. J., El Moursi, M. S., Zeineldin, H., & Al-Jarrah, M. (2020). Exact bit error-rate analysis of two-user NOMA using QAM with arbitrary modulation orders. IEEE Communications Letters, 24(12), 2705–2709.

    Article  Google Scholar 

  32. Xiao, Z., Zhu, L., Choi, J., Xia, P., & Xia, X.-G. (2018). Joint power allocation and beamforming for non-orthogonal multiple access (NOMA) in 5G millimeter wave communications. IEEE Transactions on Wireless Communications, 17(5), 2961–2974.

    Article  Google Scholar 

  33. Zhu, L., Zhang, J., Xiao, Z., Cao, X., Wu, D. O., & Xia, X.-G. (2018). Joint power control and beamforming for uplink non-orthogonal multiple access in 5G millimeter-wave communications. IEEE Transactions on Wireless Communications, 17(9), 6177–6189.

    Article  Google Scholar 

  34. Almasi, M. A., Vaezi, M., & Mehrpouyan, H. (2019). Impact of beam misalignment on hybrid beamforming NOMA for mmWave communications. IEEE transactions on communications, 67(6), 4505–4518.

    Article  Google Scholar 

  35. Almasi, M. A., Amiri, R., Vaezi, M., & Mehrpouyan, H. (2019). Lens-based millimeter wave reconfigurable antenna NOMA. In 2019 IEEE international conference on communications workshops (ICC Workshops) (pp. 1-5). IEEE.

  36. Cui, J., Liu, Y., Ding, Z., Fan, P., & Nallanathan, A. (2017). Optimal user scheduling and power allocation for millimeter wave NOMA systems. IEEE Transactions on Wireless Communications, 17(3), 1502–1517.

    Article  Google Scholar 

  37. Yu, X., Xu, F., Yu, K., & Dang, X. (2019). Power allocation for energy efficiency optimization in multi-user mmWave-NOMA system with hybrid precoding. IEEE Access, 7, 109083–109093.

    Article  Google Scholar 

  38. Hao, W., Zeng, M., Chu, Z., & Yang, S. (2017). Energy-efficient power allocation in millimeter wave massive MIMO with non-orthogonal multiple access. IEEE Wireless Communications Letters, 6(6), 782–785.

    Article  Google Scholar 

  39. Zeng, M., Hao, W., Dobre, O. A., & Poor, H. V. (2019). Energy-efficient power allocation in uplink mmWave massive MIMO with NOMA. IEEE Transactions on Vehicular Technology, 68(3), 3000–3004.

    Article  Google Scholar 

  40. Adeogun, R. O., & Falowo, O. E. (2017). Performance analysis of two-tier multiantenna 5G heterogeneous wireless networks with dual band transmission. In 2017 24th International Conference on Telecommunications (ICT) (pp. 1–6). IEEE.

  41. Chen, Y., Ai, B., Niu, Y., He, R., Zhong, Z., & Han, Z. (2019). Resource allocation for device-to-device communications in multi-cell multi-band heterogeneous cellular networks. IEEE Transactions on Vehicular Technology, 68(5), 4760–4773.

    Article  Google Scholar 

  42. Elshaer, H., Kulkarni, M. N., Boccardi, F., Andrews, J. G., & Dohler, M. (2016). Downlink and uplink cell association with traditional macrocells and millimeter wave small cells. IEEE Transactions on Wireless Communications, 15(9), 6244–6258.

    Article  Google Scholar 

  43. Niknam, S., Nasir, A. A., Mehrpouyan, H., & Natarajan, B. (2016). A multiband OFDMA heterogeneous network for millimeter wave 5G wireless applications. Ieee Access, 4, 5640–5648.

    Article  Google Scholar 

  44. Cacciapuoti, A. S. (2017). Mobility-aware user association for 5G mmWave networks. IEEE Access, 5, 21497–21507.

    Article  Google Scholar 

  45. Yang, G., Xiao, M., Alam, M., & Huang, Y. (2018). Low-latency heterogeneous networks with millimeter-wave communications. IEEE Communications Magazine, 56(6), 124–129.

    Article  Google Scholar 

  46. Liu, G., Wang, R., Zhang, H., Kang, W., Tsiftsis, T. A., & Leung, V. C. (2018). Super-modular game-based user scheduling and power allocation for energy-efficient NOMA network. IEEE Transactions on Wireless Communications, 17(6), 3877–3888.

    Article  Google Scholar 

  47. Wang, Q., Chen, T., & Liu, H. L. (2017). Resource allocation for D2D underlay communication systems using PSO. In 2017 13th international conference on computational intelligence and security (CIS) (pp. 202–206). IEEE.

  48. Dawoud, A. E., Rosas, A. A., Shokair, M., Elkordy, M., & El Halafawy, S. (2016). PSO-adaptive power allocation for multiuser GFDM-based cognitive radio networks. In 2016 international conference on selected topics in Mobile & Wireless Networking (MoWNeT) (pp. 1–8). IEEE.

  49. Gandomi, A. H., Yang, X.-S., Alavi, A. H., & Talatahari, S. (2013). Bat algorithm for constrained optimization tasks. Neural Computing and Applications, 22(6), 1239–1255.

    Article  Google Scholar 

  50. Latif, A., & Palensky, P. (2014). Economic dispatch using modified bat algorithm. Algorithms, 7(3), 328–338.

    Article  Google Scholar 

  51. Luo, J., Tang, J., So, D. K., Chen, G., Cumanan, K., & Chambers, J. A. (2019). A deep learning-based approach to power minimization in multi-carrier NOMA with SWIPT. IEEE Access, 7, 17450–17460.

    Article  Google Scholar 

  52. Khazali, A., Sobhi-Givi, S., Kalbkhani, H., & Shayesteh, M. G. (2018). Energy-spectral efficient resource allocation and power control in heterogeneous networks with D2D communication. Wireless Networks, 26, 1–15.

    Google Scholar 

  53. Lv, T., Ma, Y., Zeng, J., & Mathiopoulos, P. T. (2018). Millimeter-wave NOMA transmission in cellular M2M communications for Internet of Things. IEEE Internet of Things Journal, 5(3), 1989–2000.

    Article  Google Scholar 

  54. Lee, G., Sung, Y., & Seo, J. (2015). Randomly-directional beamforming in millimeter-wave multiuser MISO downlink. IEEE Transactions on Wireless Communications, 15(2), 1086–1100.

    Article  Google Scholar 

  55. Liu, Y., Ding, Z., Elkashlan, M., & Poor, H. V. (2016). Cooperative non-orthogonal multiple access with simultaneous wireless information and power transfer. IEEE Journal on Selected Areas in Communications, 34(4), 938–953.

    Article  Google Scholar 

  56. Khazali, A., Tarchi, D., Shayesteh, M. G., Kalbkhani, H., & Bozorgchenani, A. (2021). Energy efficient uplink transmission in cooperative mmWave NOMA networks with wireless power transfer. IEEE Transactions on Vehicular Technology. https://doi.org/10.1109/TVT.2021.3124076

    Article  Google Scholar 

  57. Park, J. J., Moon, J. H., Lee, K. Y., & Kim, D. I. (2018). Dual mode SWIPT: Waveform design and transceiver architecture with adaptive mode switching policy. In 2018 IEEE 87th vehicular technology conference (VTC Spring) (pp. 1–5). IEEE.

  58. Sobhi-Givi, S., Shayesteh, M. G., & Kalbkhani, H. (2020). Energy-efficient power allocation and user selection for mmWave-NOMA transmission in M2M communications underlaying cellular heterogeneous networks. IEEE Transactions on Vehicular Technology, 69(9), 9866–9881.

    Article  Google Scholar 

  59. Sobhi-Givi, S., Khazali, A., Kalbkhani, H., Shayesteh, M. G., & Solouk, V. (2017). Resource allocation and power control for underlay device-to-device communication in fractional frequency reuse cellular networks. Telecommunication Systems, 65(4), 677–697.

    Article  Google Scholar 

  60. Premalatha, J., Anitha, U., Manonmani, V., & Ganesan, P. (2015). Survey on energy saving methods for green communication network. Indian Journal of Science and Technology, 8(18), 1–5.

    Google Scholar 

  61. Noor, F., Ibrahim, A., & AlKhattab, M. M. (2020). Performance of parallel distributed bat algorithm using MPI on a PC cluster. Annals of Emerging Technologies in Computing (AETiC), 4(1), 19.

    Article  Google Scholar 

  62. Karakonstantis, I., & Vlachos, A. (2020). Bat algorithm applied to continuous constrained optimization problems. Journal of Information and Optimization Sciences, 42, 1–19.

    Google Scholar 

  63. Yang, X. S. (2010). A new metaheuristic bat-inspired algorithm. In Nature inspired cooperative strategies for optimization (NICSO 2010) (pp. 65-74). Springer.

  64. Divyesh, V., Sahu, C., Kirubakaran, V., Radhakrishnan, T., & Guruprasath, M. (2018). Energy optimization using metaheuristic bat algorithm assisted controller tuning for industrial and residential applications. Transactions of the Institute of Measurement and Control, 40(7), 2310–2321.

    Article  Google Scholar 

  65. Masaracchia, A., Da Costa, D. B., Duong, T. Q., Nguyen, M.-N., & Nguyen, M. T. (2019). A PSO-based approach for user-pairing schemes in NOMA systems: Theory and applications. IEEE Access, 7, 90550–90564.

    Article  Google Scholar 

  66. Garcia, C. E., Camana, M. R., & Koo, I. (2020). Secrecy energy efficiency maximization in an underlying cognitive radio–NOMA system with a cooperative relay and an energy-harvesting user. Applied Sciences, 10(10), 3630.

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, Urmia University, Urmia, Iran

    Azadeh Khazali & Mahrokh G. Shayesteh

  2. Wireless Research Lab, ACRI, Electrical Engineering Department, Sharif University of Technology, Tehran, Iran

    Mahrokh G. Shayesteh

  3. Faculty of Electrical Engineering, Urmia University of Technology, Urmia, Iran

    Hashem Kalbkhani

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  1. Azadeh Khazali
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Khazali, A., Shayesteh, M.G. & Kalbkhani, H. User grouping and power allocation for energy efficiency maximization in mmWave-NOMA heterogeneous networks. Wireless Netw 28, 2403–2420 (2022). https://doi.org/10.1007/s11276-022-02982-2

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