Abstract

This paper investigates a downlink power allocation scheme for application of non-orthogonal multiple access (NOMA) in visible light communication (VLC) systems. Aiming to achieve a flexible tradeoff between sum rate and user fairness depending on administrators’ subjective setting and acquire the optimal solution for any setting, we formulate two optimization problems, which are closely aligned with the practical application. Specifically, one is user fairness-guaranteed sum rate maximization, the other is sum rate-guaranteed user fairness maximization. Moreover, through classified discussion around the threshold guaranteeing user fairness or sum rate, we present rigorous mathematical derivation and optimization analysis, and two corresponding algorithms are proposed. Furthermore, through numerical simulation, the superiority of our proposed algorithms over conventional schemes is verified in terms of meeting the practical demand and performance gain in sum rate, user fairness, and coverage probability.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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  1. J. G. Andrews, S. Buzzi, W. Choi, S. V. Hanly, A. Lozano, A. C. K. Soong, and J. C. Zhang, “What will 5G be?” IEEE J. Sel. Areas Commun. 32(6), 1065–1082 (2014).
    [Crossref]
  2. H. Haas, L. Yin, Y. Wang, and C. Chen, “What is LiFi?” IEEE J. Lightw. Technol. 34(6), 1533–1544 (2016).
    [Crossref]
  3. P. H. Pathak, X. Feng, P. Hu, and P. Mohapatra, “Visible light communication, networking, and sensing: A survey, potential and challenges,” IEEE Commun. Surveys Tuts. 17(4), 2047–2077 (2015).
    [Crossref]
  4. Y. Saito, Y. Kishiyama, A. Benjebbour, T. Nakamura, A. Li, and K. Higuchi, “Non-orthogonal multiple access (NOMA) for cellular future radio access,” in Proceedings of IEEE conference on Vehicular Technology Conference (IEEE, 2013), pp. 1–5.
  5. Y. Saito, A. Benjebbour, Y. Kishiyama, and T. Nakamura, “System level performance evaluation of downlink non-orthogonal multiple access (NOMA),” in Proceedings of IEEE conference on PIMRC (IEEE, 2013), pp. 611–615.
  6. Z. Ding, Z. Yang, P. Fan, and H. V. Poor, “On the performance of non-orthogonal multiple access in 5G systems with randomly deployed users,” IEEE Signal Process. Lett. 21(12), 1501–1505 (2014).
    [Crossref]
  7. L. Yin, W. O. Popoola, X. Wu, and H. Haas, “Performance evaluation of non-orthogonal multiple access in visible light communication,” IEEE Trans. Commun. 64(12), 5162–5175 (2016).
    [Crossref]
  8. X. Guan, Q. Yang, Y. Hong, and C. K. Chan, “Non-orthogonal multiple access with phase pre-distortion in visible light communication,” Opt. Express 24(22), 25816–25823 (2016).
    [Crossref]
  9. B. Lin, W. Ye, X. Tang, and Z. Ghassemlooy, “Experimental demonstration of bidirectional NOMA-OFDMA visible light communications,” Opt. Express 25(4), 4348–4355 (2017).
    [Crossref]
  10. J. Shi, J. He, Y. Hong, J. He, and L.-K. Chen, “Performance-enhanced NOMA-VLC using subcarrier pairwise coding,” Opt. Commun. 450, 141–146 (2019).
    [Crossref]
  11. N. Otao, Y. Kishiyama, and K. Higuchi, “Performance of non-orthogonal access with SIC in cellular downlink using proportional fair-based resource allocation,” in Proceedings of IEEE conference on ISWCS (IEEE, 2012), pp. 476–480.
  12. L. Yin, X. Wu, and H. Haas, “On the performance of non-orthogonal multiple access in visible light communication,” in Proceedings of IEEE conference on PIMRC (IEEE, 2015), pp. 1354–1359.
  13. H. Marshoud, V. M. Kapinas, G. K. Karagiannidis, and S. Muhaidat, “Non-orthogonal multiple access for visible light communications,” IEEE Photonics Technol. Lett. 28(1), 51–54 (2016).
    [Crossref]
  14. C. Chen, W.-D. Zhong, H. Yang, and P. Du, “On the Performance of MIMO-NOMA-Based Visible Light Communication Systems,” IEEE Photonics Technol. Lett. 30(4), 307–310 (2018).
    [Crossref]
  15. A. Li, A. Harada, and H. Kayama, “A novel low computational complexity power assignment method for non-orthogonal multiple access systems,” IEICE Trans. Fundam. Electron. Commu. Comput. Sci. E97.A(1), 57–68 (2014).
    [Crossref]
  16. Z. Yang, W. Xu, and Y. Li, “Fair non-orthogonal multiple access for visible light communication downlinks,” IEEE Wireless Commun. Lett. 6(1), 1 (2016).
    [Crossref]
  17. S. Timotheou and I. Krikidis, “Fairness for non-orthogonal multiple access in 5G systems,” IEEE Signal Process. Lett. 22(10), 1647–1651 (2015).
    [Crossref]
  18. X. Zhang, Q. Gao, C. Gong, and Z. Xu, “User grouping and power allocation for NOMA visible light communication multi-cell networks,” IEEE Commun. Lett. 21(4), 777–780 (2017).
    [Crossref]
  19. J. A. Oviedo and H. R. Sadjadpour, “A Fair Power Allocation Approach to NOMA in Multiuser SISO Systems,” IEEE Trans. on Veh. Technol. 66(9), 7974–7985 (2017).
    [Crossref]

2019 (1)

J. Shi, J. He, Y. Hong, J. He, and L.-K. Chen, “Performance-enhanced NOMA-VLC using subcarrier pairwise coding,” Opt. Commun. 450, 141–146 (2019).
[Crossref]

2018 (1)

C. Chen, W.-D. Zhong, H. Yang, and P. Du, “On the Performance of MIMO-NOMA-Based Visible Light Communication Systems,” IEEE Photonics Technol. Lett. 30(4), 307–310 (2018).
[Crossref]

2017 (3)

X. Zhang, Q. Gao, C. Gong, and Z. Xu, “User grouping and power allocation for NOMA visible light communication multi-cell networks,” IEEE Commun. Lett. 21(4), 777–780 (2017).
[Crossref]

J. A. Oviedo and H. R. Sadjadpour, “A Fair Power Allocation Approach to NOMA in Multiuser SISO Systems,” IEEE Trans. on Veh. Technol. 66(9), 7974–7985 (2017).
[Crossref]

B. Lin, W. Ye, X. Tang, and Z. Ghassemlooy, “Experimental demonstration of bidirectional NOMA-OFDMA visible light communications,” Opt. Express 25(4), 4348–4355 (2017).
[Crossref]

2016 (5)

H. Marshoud, V. M. Kapinas, G. K. Karagiannidis, and S. Muhaidat, “Non-orthogonal multiple access for visible light communications,” IEEE Photonics Technol. Lett. 28(1), 51–54 (2016).
[Crossref]

H. Haas, L. Yin, Y. Wang, and C. Chen, “What is LiFi?” IEEE J. Lightw. Technol. 34(6), 1533–1544 (2016).
[Crossref]

L. Yin, W. O. Popoola, X. Wu, and H. Haas, “Performance evaluation of non-orthogonal multiple access in visible light communication,” IEEE Trans. Commun. 64(12), 5162–5175 (2016).
[Crossref]

X. Guan, Q. Yang, Y. Hong, and C. K. Chan, “Non-orthogonal multiple access with phase pre-distortion in visible light communication,” Opt. Express 24(22), 25816–25823 (2016).
[Crossref]

Z. Yang, W. Xu, and Y. Li, “Fair non-orthogonal multiple access for visible light communication downlinks,” IEEE Wireless Commun. Lett. 6(1), 1 (2016).
[Crossref]

2015 (2)

S. Timotheou and I. Krikidis, “Fairness for non-orthogonal multiple access in 5G systems,” IEEE Signal Process. Lett. 22(10), 1647–1651 (2015).
[Crossref]

P. H. Pathak, X. Feng, P. Hu, and P. Mohapatra, “Visible light communication, networking, and sensing: A survey, potential and challenges,” IEEE Commun. Surveys Tuts. 17(4), 2047–2077 (2015).
[Crossref]

2014 (3)

Z. Ding, Z. Yang, P. Fan, and H. V. Poor, “On the performance of non-orthogonal multiple access in 5G systems with randomly deployed users,” IEEE Signal Process. Lett. 21(12), 1501–1505 (2014).
[Crossref]

J. G. Andrews, S. Buzzi, W. Choi, S. V. Hanly, A. Lozano, A. C. K. Soong, and J. C. Zhang, “What will 5G be?” IEEE J. Sel. Areas Commun. 32(6), 1065–1082 (2014).
[Crossref]

A. Li, A. Harada, and H. Kayama, “A novel low computational complexity power assignment method for non-orthogonal multiple access systems,” IEICE Trans. Fundam. Electron. Commu. Comput. Sci. E97.A(1), 57–68 (2014).
[Crossref]

Andrews, J. G.

J. G. Andrews, S. Buzzi, W. Choi, S. V. Hanly, A. Lozano, A. C. K. Soong, and J. C. Zhang, “What will 5G be?” IEEE J. Sel. Areas Commun. 32(6), 1065–1082 (2014).
[Crossref]

Benjebbour, A.

Y. Saito, A. Benjebbour, Y. Kishiyama, and T. Nakamura, “System level performance evaluation of downlink non-orthogonal multiple access (NOMA),” in Proceedings of IEEE conference on PIMRC (IEEE, 2013), pp. 611–615.

Y. Saito, Y. Kishiyama, A. Benjebbour, T. Nakamura, A. Li, and K. Higuchi, “Non-orthogonal multiple access (NOMA) for cellular future radio access,” in Proceedings of IEEE conference on Vehicular Technology Conference (IEEE, 2013), pp. 1–5.

Buzzi, S.

J. G. Andrews, S. Buzzi, W. Choi, S. V. Hanly, A. Lozano, A. C. K. Soong, and J. C. Zhang, “What will 5G be?” IEEE J. Sel. Areas Commun. 32(6), 1065–1082 (2014).
[Crossref]

Chan, C. K.

Chen, C.

C. Chen, W.-D. Zhong, H. Yang, and P. Du, “On the Performance of MIMO-NOMA-Based Visible Light Communication Systems,” IEEE Photonics Technol. Lett. 30(4), 307–310 (2018).
[Crossref]

H. Haas, L. Yin, Y. Wang, and C. Chen, “What is LiFi?” IEEE J. Lightw. Technol. 34(6), 1533–1544 (2016).
[Crossref]

Chen, L.-K.

J. Shi, J. He, Y. Hong, J. He, and L.-K. Chen, “Performance-enhanced NOMA-VLC using subcarrier pairwise coding,” Opt. Commun. 450, 141–146 (2019).
[Crossref]

Choi, W.

J. G. Andrews, S. Buzzi, W. Choi, S. V. Hanly, A. Lozano, A. C. K. Soong, and J. C. Zhang, “What will 5G be?” IEEE J. Sel. Areas Commun. 32(6), 1065–1082 (2014).
[Crossref]

Ding, Z.

Z. Ding, Z. Yang, P. Fan, and H. V. Poor, “On the performance of non-orthogonal multiple access in 5G systems with randomly deployed users,” IEEE Signal Process. Lett. 21(12), 1501–1505 (2014).
[Crossref]

Du, P.

C. Chen, W.-D. Zhong, H. Yang, and P. Du, “On the Performance of MIMO-NOMA-Based Visible Light Communication Systems,” IEEE Photonics Technol. Lett. 30(4), 307–310 (2018).
[Crossref]

Fan, P.

Z. Ding, Z. Yang, P. Fan, and H. V. Poor, “On the performance of non-orthogonal multiple access in 5G systems with randomly deployed users,” IEEE Signal Process. Lett. 21(12), 1501–1505 (2014).
[Crossref]

Feng, X.

P. H. Pathak, X. Feng, P. Hu, and P. Mohapatra, “Visible light communication, networking, and sensing: A survey, potential and challenges,” IEEE Commun. Surveys Tuts. 17(4), 2047–2077 (2015).
[Crossref]

Gao, Q.

X. Zhang, Q. Gao, C. Gong, and Z. Xu, “User grouping and power allocation for NOMA visible light communication multi-cell networks,” IEEE Commun. Lett. 21(4), 777–780 (2017).
[Crossref]

Ghassemlooy, Z.

Gong, C.

X. Zhang, Q. Gao, C. Gong, and Z. Xu, “User grouping and power allocation for NOMA visible light communication multi-cell networks,” IEEE Commun. Lett. 21(4), 777–780 (2017).
[Crossref]

Guan, X.

Haas, H.

L. Yin, W. O. Popoola, X. Wu, and H. Haas, “Performance evaluation of non-orthogonal multiple access in visible light communication,” IEEE Trans. Commun. 64(12), 5162–5175 (2016).
[Crossref]

H. Haas, L. Yin, Y. Wang, and C. Chen, “What is LiFi?” IEEE J. Lightw. Technol. 34(6), 1533–1544 (2016).
[Crossref]

L. Yin, X. Wu, and H. Haas, “On the performance of non-orthogonal multiple access in visible light communication,” in Proceedings of IEEE conference on PIMRC (IEEE, 2015), pp. 1354–1359.

Hanly, S. V.

J. G. Andrews, S. Buzzi, W. Choi, S. V. Hanly, A. Lozano, A. C. K. Soong, and J. C. Zhang, “What will 5G be?” IEEE J. Sel. Areas Commun. 32(6), 1065–1082 (2014).
[Crossref]

Harada, A.

A. Li, A. Harada, and H. Kayama, “A novel low computational complexity power assignment method for non-orthogonal multiple access systems,” IEICE Trans. Fundam. Electron. Commu. Comput. Sci. E97.A(1), 57–68 (2014).
[Crossref]

He, J.

J. Shi, J. He, Y. Hong, J. He, and L.-K. Chen, “Performance-enhanced NOMA-VLC using subcarrier pairwise coding,” Opt. Commun. 450, 141–146 (2019).
[Crossref]

J. Shi, J. He, Y. Hong, J. He, and L.-K. Chen, “Performance-enhanced NOMA-VLC using subcarrier pairwise coding,” Opt. Commun. 450, 141–146 (2019).
[Crossref]

Higuchi, K.

N. Otao, Y. Kishiyama, and K. Higuchi, “Performance of non-orthogonal access with SIC in cellular downlink using proportional fair-based resource allocation,” in Proceedings of IEEE conference on ISWCS (IEEE, 2012), pp. 476–480.

Y. Saito, Y. Kishiyama, A. Benjebbour, T. Nakamura, A. Li, and K. Higuchi, “Non-orthogonal multiple access (NOMA) for cellular future radio access,” in Proceedings of IEEE conference on Vehicular Technology Conference (IEEE, 2013), pp. 1–5.

Hong, Y.

J. Shi, J. He, Y. Hong, J. He, and L.-K. Chen, “Performance-enhanced NOMA-VLC using subcarrier pairwise coding,” Opt. Commun. 450, 141–146 (2019).
[Crossref]

X. Guan, Q. Yang, Y. Hong, and C. K. Chan, “Non-orthogonal multiple access with phase pre-distortion in visible light communication,” Opt. Express 24(22), 25816–25823 (2016).
[Crossref]

Hu, P.

P. H. Pathak, X. Feng, P. Hu, and P. Mohapatra, “Visible light communication, networking, and sensing: A survey, potential and challenges,” IEEE Commun. Surveys Tuts. 17(4), 2047–2077 (2015).
[Crossref]

Kapinas, V. M.

H. Marshoud, V. M. Kapinas, G. K. Karagiannidis, and S. Muhaidat, “Non-orthogonal multiple access for visible light communications,” IEEE Photonics Technol. Lett. 28(1), 51–54 (2016).
[Crossref]

Karagiannidis, G. K.

H. Marshoud, V. M. Kapinas, G. K. Karagiannidis, and S. Muhaidat, “Non-orthogonal multiple access for visible light communications,” IEEE Photonics Technol. Lett. 28(1), 51–54 (2016).
[Crossref]

Kayama, H.

A. Li, A. Harada, and H. Kayama, “A novel low computational complexity power assignment method for non-orthogonal multiple access systems,” IEICE Trans. Fundam. Electron. Commu. Comput. Sci. E97.A(1), 57–68 (2014).
[Crossref]

Kishiyama, Y.

Y. Saito, Y. Kishiyama, A. Benjebbour, T. Nakamura, A. Li, and K. Higuchi, “Non-orthogonal multiple access (NOMA) for cellular future radio access,” in Proceedings of IEEE conference on Vehicular Technology Conference (IEEE, 2013), pp. 1–5.

Y. Saito, A. Benjebbour, Y. Kishiyama, and T. Nakamura, “System level performance evaluation of downlink non-orthogonal multiple access (NOMA),” in Proceedings of IEEE conference on PIMRC (IEEE, 2013), pp. 611–615.

N. Otao, Y. Kishiyama, and K. Higuchi, “Performance of non-orthogonal access with SIC in cellular downlink using proportional fair-based resource allocation,” in Proceedings of IEEE conference on ISWCS (IEEE, 2012), pp. 476–480.

Krikidis, I.

S. Timotheou and I. Krikidis, “Fairness for non-orthogonal multiple access in 5G systems,” IEEE Signal Process. Lett. 22(10), 1647–1651 (2015).
[Crossref]

Li, A.

A. Li, A. Harada, and H. Kayama, “A novel low computational complexity power assignment method for non-orthogonal multiple access systems,” IEICE Trans. Fundam. Electron. Commu. Comput. Sci. E97.A(1), 57–68 (2014).
[Crossref]

Y. Saito, Y. Kishiyama, A. Benjebbour, T. Nakamura, A. Li, and K. Higuchi, “Non-orthogonal multiple access (NOMA) for cellular future radio access,” in Proceedings of IEEE conference on Vehicular Technology Conference (IEEE, 2013), pp. 1–5.

Li, Y.

Z. Yang, W. Xu, and Y. Li, “Fair non-orthogonal multiple access for visible light communication downlinks,” IEEE Wireless Commun. Lett. 6(1), 1 (2016).
[Crossref]

Lin, B.

Lozano, A.

J. G. Andrews, S. Buzzi, W. Choi, S. V. Hanly, A. Lozano, A. C. K. Soong, and J. C. Zhang, “What will 5G be?” IEEE J. Sel. Areas Commun. 32(6), 1065–1082 (2014).
[Crossref]

Marshoud, H.

H. Marshoud, V. M. Kapinas, G. K. Karagiannidis, and S. Muhaidat, “Non-orthogonal multiple access for visible light communications,” IEEE Photonics Technol. Lett. 28(1), 51–54 (2016).
[Crossref]

Mohapatra, P.

P. H. Pathak, X. Feng, P. Hu, and P. Mohapatra, “Visible light communication, networking, and sensing: A survey, potential and challenges,” IEEE Commun. Surveys Tuts. 17(4), 2047–2077 (2015).
[Crossref]

Muhaidat, S.

H. Marshoud, V. M. Kapinas, G. K. Karagiannidis, and S. Muhaidat, “Non-orthogonal multiple access for visible light communications,” IEEE Photonics Technol. Lett. 28(1), 51–54 (2016).
[Crossref]

Nakamura, T.

Y. Saito, Y. Kishiyama, A. Benjebbour, T. Nakamura, A. Li, and K. Higuchi, “Non-orthogonal multiple access (NOMA) for cellular future radio access,” in Proceedings of IEEE conference on Vehicular Technology Conference (IEEE, 2013), pp. 1–5.

Y. Saito, A. Benjebbour, Y. Kishiyama, and T. Nakamura, “System level performance evaluation of downlink non-orthogonal multiple access (NOMA),” in Proceedings of IEEE conference on PIMRC (IEEE, 2013), pp. 611–615.

Otao, N.

N. Otao, Y. Kishiyama, and K. Higuchi, “Performance of non-orthogonal access with SIC in cellular downlink using proportional fair-based resource allocation,” in Proceedings of IEEE conference on ISWCS (IEEE, 2012), pp. 476–480.

Oviedo, J. A.

J. A. Oviedo and H. R. Sadjadpour, “A Fair Power Allocation Approach to NOMA in Multiuser SISO Systems,” IEEE Trans. on Veh. Technol. 66(9), 7974–7985 (2017).
[Crossref]

Pathak, P. H.

P. H. Pathak, X. Feng, P. Hu, and P. Mohapatra, “Visible light communication, networking, and sensing: A survey, potential and challenges,” IEEE Commun. Surveys Tuts. 17(4), 2047–2077 (2015).
[Crossref]

Poor, H. V.

Z. Ding, Z. Yang, P. Fan, and H. V. Poor, “On the performance of non-orthogonal multiple access in 5G systems with randomly deployed users,” IEEE Signal Process. Lett. 21(12), 1501–1505 (2014).
[Crossref]

Popoola, W. O.

L. Yin, W. O. Popoola, X. Wu, and H. Haas, “Performance evaluation of non-orthogonal multiple access in visible light communication,” IEEE Trans. Commun. 64(12), 5162–5175 (2016).
[Crossref]

Sadjadpour, H. R.

J. A. Oviedo and H. R. Sadjadpour, “A Fair Power Allocation Approach to NOMA in Multiuser SISO Systems,” IEEE Trans. on Veh. Technol. 66(9), 7974–7985 (2017).
[Crossref]

Saito, Y.

Y. Saito, A. Benjebbour, Y. Kishiyama, and T. Nakamura, “System level performance evaluation of downlink non-orthogonal multiple access (NOMA),” in Proceedings of IEEE conference on PIMRC (IEEE, 2013), pp. 611–615.

Y. Saito, Y. Kishiyama, A. Benjebbour, T. Nakamura, A. Li, and K. Higuchi, “Non-orthogonal multiple access (NOMA) for cellular future radio access,” in Proceedings of IEEE conference on Vehicular Technology Conference (IEEE, 2013), pp. 1–5.

Shi, J.

J. Shi, J. He, Y. Hong, J. He, and L.-K. Chen, “Performance-enhanced NOMA-VLC using subcarrier pairwise coding,” Opt. Commun. 450, 141–146 (2019).
[Crossref]

Soong, A. C. K.

J. G. Andrews, S. Buzzi, W. Choi, S. V. Hanly, A. Lozano, A. C. K. Soong, and J. C. Zhang, “What will 5G be?” IEEE J. Sel. Areas Commun. 32(6), 1065–1082 (2014).
[Crossref]

Tang, X.

Timotheou, S.

S. Timotheou and I. Krikidis, “Fairness for non-orthogonal multiple access in 5G systems,” IEEE Signal Process. Lett. 22(10), 1647–1651 (2015).
[Crossref]

Wang, Y.

H. Haas, L. Yin, Y. Wang, and C. Chen, “What is LiFi?” IEEE J. Lightw. Technol. 34(6), 1533–1544 (2016).
[Crossref]

Wu, X.

L. Yin, W. O. Popoola, X. Wu, and H. Haas, “Performance evaluation of non-orthogonal multiple access in visible light communication,” IEEE Trans. Commun. 64(12), 5162–5175 (2016).
[Crossref]

L. Yin, X. Wu, and H. Haas, “On the performance of non-orthogonal multiple access in visible light communication,” in Proceedings of IEEE conference on PIMRC (IEEE, 2015), pp. 1354–1359.

Xu, W.

Z. Yang, W. Xu, and Y. Li, “Fair non-orthogonal multiple access for visible light communication downlinks,” IEEE Wireless Commun. Lett. 6(1), 1 (2016).
[Crossref]

Xu, Z.

X. Zhang, Q. Gao, C. Gong, and Z. Xu, “User grouping and power allocation for NOMA visible light communication multi-cell networks,” IEEE Commun. Lett. 21(4), 777–780 (2017).
[Crossref]

Yang, H.

C. Chen, W.-D. Zhong, H. Yang, and P. Du, “On the Performance of MIMO-NOMA-Based Visible Light Communication Systems,” IEEE Photonics Technol. Lett. 30(4), 307–310 (2018).
[Crossref]

Yang, Q.

Yang, Z.

Z. Yang, W. Xu, and Y. Li, “Fair non-orthogonal multiple access for visible light communication downlinks,” IEEE Wireless Commun. Lett. 6(1), 1 (2016).
[Crossref]

Z. Ding, Z. Yang, P. Fan, and H. V. Poor, “On the performance of non-orthogonal multiple access in 5G systems with randomly deployed users,” IEEE Signal Process. Lett. 21(12), 1501–1505 (2014).
[Crossref]

Ye, W.

Yin, L.

H. Haas, L. Yin, Y. Wang, and C. Chen, “What is LiFi?” IEEE J. Lightw. Technol. 34(6), 1533–1544 (2016).
[Crossref]

L. Yin, W. O. Popoola, X. Wu, and H. Haas, “Performance evaluation of non-orthogonal multiple access in visible light communication,” IEEE Trans. Commun. 64(12), 5162–5175 (2016).
[Crossref]

L. Yin, X. Wu, and H. Haas, “On the performance of non-orthogonal multiple access in visible light communication,” in Proceedings of IEEE conference on PIMRC (IEEE, 2015), pp. 1354–1359.

Zhang, J. C.

J. G. Andrews, S. Buzzi, W. Choi, S. V. Hanly, A. Lozano, A. C. K. Soong, and J. C. Zhang, “What will 5G be?” IEEE J. Sel. Areas Commun. 32(6), 1065–1082 (2014).
[Crossref]

Zhang, X.

X. Zhang, Q. Gao, C. Gong, and Z. Xu, “User grouping and power allocation for NOMA visible light communication multi-cell networks,” IEEE Commun. Lett. 21(4), 777–780 (2017).
[Crossref]

Zhong, W.-D.

C. Chen, W.-D. Zhong, H. Yang, and P. Du, “On the Performance of MIMO-NOMA-Based Visible Light Communication Systems,” IEEE Photonics Technol. Lett. 30(4), 307–310 (2018).
[Crossref]

IEEE Commun. Lett. (1)

X. Zhang, Q. Gao, C. Gong, and Z. Xu, “User grouping and power allocation for NOMA visible light communication multi-cell networks,” IEEE Commun. Lett. 21(4), 777–780 (2017).
[Crossref]

IEEE Commun. Surveys Tuts. (1)

P. H. Pathak, X. Feng, P. Hu, and P. Mohapatra, “Visible light communication, networking, and sensing: A survey, potential and challenges,” IEEE Commun. Surveys Tuts. 17(4), 2047–2077 (2015).
[Crossref]

IEEE J. Lightw. Technol. (1)

H. Haas, L. Yin, Y. Wang, and C. Chen, “What is LiFi?” IEEE J. Lightw. Technol. 34(6), 1533–1544 (2016).
[Crossref]

IEEE J. Sel. Areas Commun. (1)

J. G. Andrews, S. Buzzi, W. Choi, S. V. Hanly, A. Lozano, A. C. K. Soong, and J. C. Zhang, “What will 5G be?” IEEE J. Sel. Areas Commun. 32(6), 1065–1082 (2014).
[Crossref]

IEEE Photonics Technol. Lett. (2)

H. Marshoud, V. M. Kapinas, G. K. Karagiannidis, and S. Muhaidat, “Non-orthogonal multiple access for visible light communications,” IEEE Photonics Technol. Lett. 28(1), 51–54 (2016).
[Crossref]

C. Chen, W.-D. Zhong, H. Yang, and P. Du, “On the Performance of MIMO-NOMA-Based Visible Light Communication Systems,” IEEE Photonics Technol. Lett. 30(4), 307–310 (2018).
[Crossref]

IEEE Signal Process. Lett. (2)

S. Timotheou and I. Krikidis, “Fairness for non-orthogonal multiple access in 5G systems,” IEEE Signal Process. Lett. 22(10), 1647–1651 (2015).
[Crossref]

Z. Ding, Z. Yang, P. Fan, and H. V. Poor, “On the performance of non-orthogonal multiple access in 5G systems with randomly deployed users,” IEEE Signal Process. Lett. 21(12), 1501–1505 (2014).
[Crossref]

IEEE Trans. Commun. (1)

L. Yin, W. O. Popoola, X. Wu, and H. Haas, “Performance evaluation of non-orthogonal multiple access in visible light communication,” IEEE Trans. Commun. 64(12), 5162–5175 (2016).
[Crossref]

IEEE Trans. on Veh. Technol. (1)

J. A. Oviedo and H. R. Sadjadpour, “A Fair Power Allocation Approach to NOMA in Multiuser SISO Systems,” IEEE Trans. on Veh. Technol. 66(9), 7974–7985 (2017).
[Crossref]

IEEE Wireless Commun. Lett. (1)

Z. Yang, W. Xu, and Y. Li, “Fair non-orthogonal multiple access for visible light communication downlinks,” IEEE Wireless Commun. Lett. 6(1), 1 (2016).
[Crossref]

IEICE Trans. Fundam. Electron. Commu. Comput. Sci. (1)

A. Li, A. Harada, and H. Kayama, “A novel low computational complexity power assignment method for non-orthogonal multiple access systems,” IEICE Trans. Fundam. Electron. Commu. Comput. Sci. E97.A(1), 57–68 (2014).
[Crossref]

Opt. Commun. (1)

J. Shi, J. He, Y. Hong, J. He, and L.-K. Chen, “Performance-enhanced NOMA-VLC using subcarrier pairwise coding,” Opt. Commun. 450, 141–146 (2019).
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Y. Saito, Y. Kishiyama, A. Benjebbour, T. Nakamura, A. Li, and K. Higuchi, “Non-orthogonal multiple access (NOMA) for cellular future radio access,” in Proceedings of IEEE conference on Vehicular Technology Conference (IEEE, 2013), pp. 1–5.

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Figures (6)

Fig. 1.
Fig. 1. Achievable sum rates under user fairness constraint of no less than that achieved by: (a) FPA; (b) GRPA.
Fig. 2.
Fig. 2. CDFs of sum rates for $M\textrm{ = 3}$ under user fairness constraint of no less than that achieved by: (a) FPA; (b) GRPA.
Fig. 3.
Fig. 3. Achievable user fairness under sum rate constraint of no less than that achieved by: (a) FPA; (b) GRPA.
Fig. 4.
Fig. 4. CDFs of user fairness for $M\textrm{ = 2}$ and $M\textrm{ = 3}$ under sum rate constraint of no less than that achieved by: (a) FPA; (b) GRPA.
Fig. 5.
Fig. 5. Coverage probability vs. target rate of each user for $M\textrm{ = 3}$ under user fairness constraint of no less than that achieved by: (a) FPA; (b) GRPA.
Fig. 6.
Fig. 6. Coverage probability vs. target rate of each user for $M\textrm{ = 3}$ under sum rate constraint of no less than that achieved by: (a) FPA; (b) GRPA.

Equations (24)

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x = 1 i M P i s i + I D C .
y k = h k ( 1 i M P i s i ) + z k ,
R k = { β log 2 [ 1 + ( h k a k ) 2 / ( k + 1 j M ( h k a j ) 2 + 1 / ρ ) ] , k I , β log 2 [ 1 + ρ ( h k a k ) 2 ] , k = M ,
max A R sum , s . t . 1 i M a i 2 = 1 ; ( constraint 1 ) a 1 a M 0 ; ( constraint 2 ) R k R ~ k , k M ; ( constraint 3 ) η C 1 , C 1 is a constant, and C 1 [ 0 , 1 ] . ( constraint 4 )
R 1 / R 2  =  η and a 1 2 + a 2 2 = 1 ,
{ a j 2 = 1 / ( 1 + 1 k M 1 ( 1 i k α i ( i + 1 ) ) ) , j = 1 , a j 2 = 1 i j 1 α i ( i + 1 ) / ( 1 + 1 k M 1 ( 1 i k α i ( i + 1 ) ) ) , j = 2 , M ,
α i ( i + 1 )  is continuous,  α i ( i + 1 ) [ 0 , 1 ] , i I .
a u 2 = a u 2 + ( a w 2 a u 2 ) / 16 , i f u w = 1 ; o r a u 2 + a w 2 / 8 , else if u = 1 and w = M ; o r a u 2 + min ( a w 2 / 8 , ( a u 1 2 a u 2 ) / 8 ) , else if w = M ; o r a u 2 + ( a w 2 a w + 1 2 ) / 8 , else i f u = 1 ; o r a u 2 + min ( a u 1 2 a u 2 , a w 2 a w + 1 2 ) / 8 , else . a w 2 = a u 2 + a w 2 a u 2 .
max A η , s . t . 1 i M a i 2 = 1 ; ( constraint 1 ) a 1 a M 0 ; ( constraint 2 ) R k R ~ k , k M ; ( constraint 3 ) R sum C 2 . ( constraint 5 )
a u 2 = a u 2 + ( a w 2 a u 2 ) / 4 , i f u w = 1 ; o r a u 2 + min ( a u 1 2 a u 2 , a w 2 a w + 1 2 ) , e l s e , a w 2 = a u 2 + a w 2 a u 2 ,
R sum = β [ log 2 ( 1 + h 1 2 a 1 2 / [ h 1 2 ( 2 j M a j 2 ) + 1 / ρ ] ) + + log 2 ( 1 + ρ h M 2 a M 2 ) ] = β log 2 ( [ h 1 2 + 1 / ρ h 1 2 ( 2 j M a j 2 ) + 1 / ρ ] × × ( h M 2 a M 2 + 1 / ρ 1 / ρ ) ) = β log 2 [ ( h 1 2 + 1 / ρ 1 / ρ ) × [ h 2 2 ( 2 j M a j 2 ) + 1 / ρ h 1 2 ( 2 j M a j 2 ) + 1 / ρ ] × × ( h M 2 a M 2 + 1 / ρ h M 1 2 a M 2 + 1 / ρ ) ] = β log 2 [ ( ρ h 1 2 + 1 ) [ h 2 2 h 1 2 + 1 h 2 2 / h 1 2 ρ h 1 2 ( 2 j M a j 2 ) + 1 ] × × ( h M 2 h M 1 2 + 1 h M 2 / h M 1 2 ρ h M 1 2 a M 2 + 1 ) ] .
a 1 2 S I N R 1 [ 1 + 1 / ( ρ h 1 2 ) ] 1  +  S I N R 1 ,
a k 2 S I N R k [ 1 + 1 / ( ρ h k 2 ) j < k a j 2 ] 1  +  S I N R k , k { 2 , , M 1 } .
a k = S I N R k [ 1 + 1 / ( ρ h k 2 ) j < k a j 2 ] 1  +  S I N R k , k { 2 , , M 1 } , a M = 1 1 k M 1 ( a k ) 2 .
σ = min { R ~ 1 , , R ~ M 1 , β log 2 [ 1 + ρ ( h M a M ) 2 ] } max { R ~ 1 , , R ~ M 1 , β log 2 [ 1 + ρ ( h M a M ) 2 ] } .
a M 2 = ( 2 v / β 1 ) / ( ρ h M 2 ) .
a i 2 = ( 2 v / β 1 ) ( i + 1 j M a i 2 + 1 / h i 2 ) / ρ , i I .
f ( v ) = 1 i M a i 2 ( v ) 1 = 0.
{ h 1 2 a 1 2 / ( h 1 2 ( 1 a 1 2 ) + 1 / ρ ) = h 2 2 a 2 2 / ( h 2 2 a 3 2 + 1 / ρ ) = 2 C 1 R / β 1 , ρ ( h 3 a 3 ) 2 = 2 R / β 1.
{ a 3 2 = ( 2 R / β 1 ) / ( ρ h 3 2 ) , a 2 2 = 2 R / β ( 2 C 1 R / β 1 ) / ( ρ h 3 2 ) , a 1 2 = [ h 1 2 ( 2 ( 1 + 2 C 1 ) R / β 2 C 1 R / β 2 ( 1 + C 1 ) R / β + 1 ) + h 3 2 ( 2 C 1 R / β 1 ) ] / ( ρ h 1 2 h 3 2 ) .
2 ( 1 + 2 C 1 ) R / β + 2 C 1 R / β ( h 3 2 / h 1 2 1 ) = h 3 2 / h 1 2 + ρ h 3 2 .
{ h 1 2 a 1 2 / ( h 1 2 ( 1 a 1 2 ) + 1 / ρ ) = 2 C 1 R b e n / β 1 h 2 2 a 2 2 / ( h 2 2 a 3 2 + 1 / ρ ) = ρ ( h 3 a 3 ) 2 = 2 R b e n / β 1 Δ 1 { a 3 2 = ( 2 R b e n / β 1 ) / ( ρ h 3 2 ) a 2 2 = 2 R b e n / β ( 2 R b e n / β 1 ) / ( ρ h 3 2 ) a 1 2 = [ h 1 2 ( 2 ( 2 + C 1 ) R b e n / β 2 C 1 R b e n / β 2 2 R b e n / β + 1 ) + h 3 2 ( 2 C 1 R b e n / β 1 ) ] / ( ρ h 1 2 h 3 2 ) Δ 2 2 ( 2 + C 1 ) R b e n / β + 2 C 1 R b e n / β ( h 3 2 / h 1 2 1 ) = h 3 2 / h 1 2 + ρ h 3 2 ,
2 ( 1 + 2 C 1 ) R / β + 2 C 1 R / β ( h 3 2 / h 1 2 1 ) = 2 ( 2 + C 1 ) R b e n / β + 2 C 1 R b e n / β ( h 3 2 / h 1 2 1 ) .
2 C 1 R / β ( h 3 2 / h 1 2 1 ) > 2 C 1 R b e n / β ( h 3 2 / h 1 2 1 ) Δ 3 2 ( 1 + 2 C 1 ) R / β < 2 ( 2 + C 1 ) R b e n / β Δ 4 ( 1 + 2 C 1 ) R < ( 2 + C 1 ) R b e n ,