## Jianpo Li* and Qiwei Wang*## |

=0.5 | =1 | =100 | |

Improvement of the ergodic sum rate of NOMA compared with that of TDMA (%) | 49.9 | 38.8 | 38.9 |

Improvement of the TDMA FI compared with that of NOMA (%) | 20.1 | 9.6 | 0 |

In order to compare the NOMA and TDMA solutions fairly, Fig. 3 shows the relation between ergodic sum rate and SNR for TDMA and NOMA system at different FI values, where the user number is 5. Fig. 3 shows that as the SINR increases, the system ergodic sum rate of TDMA and NOMA increases. Under the same conditions, the ergodic sum rate of the NOMA system is significantly better than that of TDMA system. When FI=0.6, the system performance is the best, and the ergodic sum rate of the NOMA system is increased by 40.2% compared to the TDMA system.

Fig. 4 shows the relation between ergodic sum rate and FI for TDMA and NOMA system at different user values, where SINR=20dB. The detailed results are shown in Table 2.

Table 2.

k=4 | k=5 | k=6 | |
---|---|---|---|

Improvement of the ergodic sum rate of NOMA compared with that of TDMA (%) | 29.04 | 34.98 | 40.15 |

Fig. 4 and Table 2 show that the ergodic sum rate of TDMA and NOMA decreases as the FI value increases. Under the same conditions, the NOMA system ergodic sum rate is superior to the TDMA system. As shown in Figs. 3 and 4, it can be seen that NOMA provides a significant increase in ergodic sum rate performance over the TDMA scheme at the same required level of fairness.

For the NOMA power allocation part, a power allocation method based on fairness to achieve the maximum ergodic sum rate is proposed. The computational complexity is reduced evidently by penalty function interior point method. It approaches the solution of objective function within the feasible region. This scheme proves the superiority of fair utility function under a single antenna and optimizes the ergodic sum rate under the condition of satisfying fairness among users. This approach achieves user fairness and maximizes ergodic sum rate balance. The numerical results show that compared with the NOMA and TDMA methods using this method, the performance of NOMA is obviously better than that of TDMA. For example, when =0.5, the average ergodic sum rate of NOMA is increased by 49.9% compared with TDMA. When FI=1, the average ergodic sum rate increased by 31% compared with TDMA.

He was born in China in 1980. He received his B.S., M.S., and Ph.D. from the Department of Communication Engineering, Jilin University, China, in 2002, 2005, and 2008, respectively. In 2008, he joined the School of Computer Science, Northeast Electric Power University, where he is currently a professor. His research interests are wireless sensor networks, 5G communication, and intelligent signal processing.

- 1 B. Shi, Y. Wang, W. Li, G. Sun, "Study on communication network effect on system performance of wide area control,"
*Journal of Northeast Electric Power University*, vol. 38, no. 6, pp. 29-34, 2018.custom:[[[-]]] - 2 Z. Ding, Y. Liu, J. Choi, Q. Sun, M. Elkashlan, I. Chih-Lin, H. V. Poor, "Application of non-orthogonal multiple access in LTE and 5G networks,"
*IEEE Communications Magazine*, vol. 55, no. 2, pp. 185-191, 2017.custom:[[[-]]] - 3 P. Xu, Z. Ding, X. Dai, H. V. Poor, "A new evaluation criterion for non-orthogonal multiple access in 5G software defined networks,"
*IEEE Access*, vol. 3, pp. 1633-1639, 2015.custom:[[[-]]] - 4 Q. Bi, L. Liang, S. Yang, P. Chen, "Non-orthogonal multiple access technology for 5G systems,"
*Telecommunications Science*, vol. 31, no. 5, pp. 14-21, 2015.custom:[[[-]]] - 5 Z. Ding, Z. Yang, P. Fan, H. V. Poor, "On the performance of non-orthogonal multiple access in 5G systems with randomly deployed users,"
*IEEE Signal Processing Letters*, vol. 21, no. 12, pp. 1501-1505, 2014.custom:[[[-]]] - 6 L. Zhang, "Application of adaptive anti-intersymbol interference in satellite communication,"
*Journal of Northeast Electric Power University*, vol. 37, no. 3, pp. 103-106, 2017.custom:[[[-]]] - 7 Z. Sun, Y. Li, "Hybrid precoding algorithm based on sum-rate maximization for millimeter wave MIMO system,"
*Journal of Northeast Electric Power University*, vol. 37, no. 6, pp. 100-106, 2017.custom:[[[-]]] - 8 Z. Yang, Z. Ding, P. Fan, G. K. Karagiannidis, "On the performance of non-orthogonal multiple access systems with partial channel information,"
*IEEE Transactions on Communications*, vol. 64, no. 2, pp. 654-667, 2016.custom:[[[-]]] - 9 Y. Liu, Z. Qin, M. Elkashlan, Z. Ding, A. Nallanathan, L. Hanzo, "Non-orthogonal multiple access for 5G and beyond," in
*Proceedings of the IEEE*, 2017;vol. 105, no. 12, pp. 2347-2381. custom:[[[-]]] - 10 S. Timotheou, I. Krikidis, "Fairness for non-orthogonal multiple access in 5G systems,"
*IEEE Signal Processing Letters*, vol. 22, no. 10, pp. 1647-1651, 2015.custom:[[[-]]] - 11 P. Xu, Y. Yuan, Z. Ding, X. Dai, R. Schober, "On the outage performance of non-orthogonal multiple access with 1-bit feedback,"
*IEEE Transactions on Wireless Communications*, vol. 15, no. 10, pp. 6716-6730., 2016.custom:[[[-]]] - 12 S. Shi, L. Yang, H. Zhu, "Outage balancing in downlink nonorthogonal multiple access with statistical channel state information,"
*IEEE Transactions on Wireless Communications*, vol. 15, no. 7, pp. 4718-4731, 2016.custom:[[[-]]] - 13 J. Choi, "Power allocation for max-sum rate and max-min rate proportional fairness in NOMA,"
*IEEE Communications Letters*, vol. 20, no. 10, pp. 2055-2058, 2016.custom:[[[-]]] - 14 Z. F. Fan, C. C. Wen, Z. Q. Wang, X. Y. Wan, "Price-based power allocation with rate proportional fairness constraint in downlink non-orthogonal multiple access systems,"
*IEICE Transactions on Fundamentals of ElectronicsCommunications and Computer Sciences*, vol. 100, no. 11, pp. 2543-2546, 2017.custom:[[[-]]] - 15 S. R. Islam, N. Avazov, O. A. Dobre, 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, 2016.custom:[[[-]]] - 16 Z. Yang, Z. Ding, P. Fan, N. Al-Dhahir, "A general power allocation scheme to guarantee quality of service in downlink and uplink NOMA systems,"
*IEEE Transactions on Wireless Communications*, vol. 15, no. 11, pp. 7244-7257, 2016.custom:[[[-]]] - 17 S. S. Kalamkar, J. P. Jeyaraj, A. Banerjee, K. Rajawat, "Resource allocation and fairness in wireless powered cooperative cognitive radio networks,"
*IEEE Transactions on Communications*, vol. 64, no. 8, pp. 3246-3261, 2016.custom:[[[-]]] - 18 Y. Sun, Y. Guo, S. Li, D. Wu, B. Wang, "Optimal resource allocation for NOMA-TDMA scheme with α-fairness in industrial Internet of Things,"
*Sensors*, vol. 18, no. 5, 2018.doi:[[[10.3390/s18051572]]] - 19 Z. Sun, D. Y ang, "D2D radio resource allocation algorithm based on global fairness,"
*Journal of Northeast Electric Power University*, vol. 39, no. 1, pp. 81-87, 2019.custom:[[[-]]]