Abstract

We propose a non-orthogonal multiple access (NOMA) scheme combined with orthogonal frequency division multiplexing access (OFDMA) for visible light communications (VLC), which offers a high throughput, flexible bandwidth allocation and a higher system capacity for a larger number of users. Bidirectional NOMA-OFDMA VLC is experimentally demonstrated. The effects of power allocation and channel estimation on the bit error rate performance are investigated. The experiment results indicate that accurate channel estimation can eliminate the inter-user interference more effectively. The optimum power allocation ratios for uplink and downlink are both about 0.25 in the case of two users.

© 2017 Optical Society of America

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References

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  1. Z. Ghassemlooy, W. Popoola, and S. Rajbhandari, Optical Wireless Communications: System and Channel Modelling With MATLAB (Taylor & Francis, 2012).
  2. L. Wu, Z. Zhang, J. Dang, and H. Liu, “Adaptive modulation schemes for visible light communications,” J. Lightwave Technol. 33(1), 117–125 (2015).
    [Crossref]
  3. C.-H. Yeh, H.-Y. Chen, C.-W. Chow, and Y.-L. Liu, “Utilization of multi-band OFDM modulation to increase traffic rate of phosphor-LED wireless VLC,” Opt. Express 23(2), 1133–1138 (2015).
    [Crossref] [PubMed]
  4. B. Lin, X. Tang, Z. Ghassemlooy, X. Fang, C. Lin, Y. Li, and S. Zhang, “Experimental Demonstration of OFDM/OQAM Transmission for Visible Light Communications,” IEEE Photonics J. 8(5), 7906710 (2016).
    [Crossref]
  5. T. Fath and H. Haas, “Performance comparison of MIMO techniques for optical wireless communications in indoor environments,” IEEE Trans. Commun. 61(2), 733–742 (2013).
    [Crossref]
  6. G. Cossu, A. M. Khalid, P. Choudhury, R. Corsini, and E. Ciaramella, “3.4 Gbit/s visible optical wireless transmission based on RGB LED,” Opt. Express 20(26), B501–B506 (2012).
    [Crossref] [PubMed]
  7. H. Elgala, R. Mesleh, and H. Haas, “Indoor optical wireless communication: potential and state-of-the-art,” IEEE Commun. Mag. 49(9), 56–62 (2011).
    [Crossref]
  8. B. Lin, X. Tang, H. Yang, Z. Ghassemlooy, S. Zhang, Y. Li, and C. Lin, “Experimental Demonstration of IFDMA for Uplink Visible Light Communication,” IEEE Photonics Technol. Lett. 28(20), 2218–2220 (2016).
    [Crossref]
  9. 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 (IEEE, 2013), pp. 1–5.
    [Crossref]
  10. Y. Saito, A. Benjebbour, Y. Kishiyama, and T. Nakamura, “System Level Performance Evaluation of Downlink Non-Orthogonal Multiple Access (NOMA),” in Proceedings of IEEE Annual Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC), (IEEE, 2013), pp.611–615.
    [Crossref]
  11. Z. Ding, Z. Yang, P. Fan, and H. Poor, “On the performance of nonorthogonal multiple access in 5G systems with randomly deployed users,” IEEE Signal Process. Lett. 21(12), 1501–1505 (2014).
    [Crossref]
  12. 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]
  13. R. C. Kizilirmak, C. R. Rowell, and M. Uysal, “Non-orthogonal multiple access (NOMA) for indoor visible light communications,” IEEE International Workshop on Optical Wireless Communications, (2015), pp. 98–101.
    [Crossref]
  14. L. Yin, X. Wu, and H. Haas, “On the performance of non-orthogonal multiple access in visible light communication,” IEEE International Symposium on Personal, Indoor, and Mobile Radio Communications, (IEEE, 2015), pp. 1354–1359.
  15. B. Lin, X. Tang, Z. Ghassemlooy, S. Zhang, Y. Li, Y. Wu, and H. Li, “Efficient Frequency Domain Channel Equalization Methods for OFDM Visible Light Communications,” IET Commun. 11(1), 25–29 (2017).
    [Crossref]

2017 (1)

B. Lin, X. Tang, Z. Ghassemlooy, S. Zhang, Y. Li, Y. Wu, and H. Li, “Efficient Frequency Domain Channel Equalization Methods for OFDM Visible Light Communications,” IET Commun. 11(1), 25–29 (2017).
[Crossref]

2016 (3)

B. Lin, X. Tang, Z. Ghassemlooy, X. Fang, C. Lin, Y. Li, and S. Zhang, “Experimental Demonstration of OFDM/OQAM Transmission for Visible Light Communications,” IEEE Photonics J. 8(5), 7906710 (2016).
[Crossref]

B. Lin, X. Tang, H. Yang, Z. Ghassemlooy, S. Zhang, Y. Li, and C. Lin, “Experimental Demonstration of IFDMA for Uplink Visible Light Communication,” IEEE Photonics Technol. Lett. 28(20), 2218–2220 (2016).
[Crossref]

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]

2015 (2)

2014 (1)

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

2013 (1)

T. Fath and H. Haas, “Performance comparison of MIMO techniques for optical wireless communications in indoor environments,” IEEE Trans. Commun. 61(2), 733–742 (2013).
[Crossref]

2012 (1)

2011 (1)

H. Elgala, R. Mesleh, and H. Haas, “Indoor optical wireless communication: potential and state-of-the-art,” IEEE Commun. Mag. 49(9), 56–62 (2011).
[Crossref]

Benjebbour, A.

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 (IEEE, 2013), pp. 1–5.
[Crossref]

Y. Saito, A. Benjebbour, Y. Kishiyama, and T. Nakamura, “System Level Performance Evaluation of Downlink Non-Orthogonal Multiple Access (NOMA),” in Proceedings of IEEE Annual Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC), (IEEE, 2013), pp.611–615.
[Crossref]

Chen, H.-Y.

Choudhury, P.

Chow, C.-W.

Ciaramella, E.

Corsini, R.

Cossu, G.

Dang, J.

Ding, Z.

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

Elgala, H.

H. Elgala, R. Mesleh, and H. Haas, “Indoor optical wireless communication: potential and state-of-the-art,” IEEE Commun. Mag. 49(9), 56–62 (2011).
[Crossref]

Fan, P.

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

Fang, X.

B. Lin, X. Tang, Z. Ghassemlooy, X. Fang, C. Lin, Y. Li, and S. Zhang, “Experimental Demonstration of OFDM/OQAM Transmission for Visible Light Communications,” IEEE Photonics J. 8(5), 7906710 (2016).
[Crossref]

Fath, T.

T. Fath and H. Haas, “Performance comparison of MIMO techniques for optical wireless communications in indoor environments,” IEEE Trans. Commun. 61(2), 733–742 (2013).
[Crossref]

Ghassemlooy, Z.

B. Lin, X. Tang, Z. Ghassemlooy, S. Zhang, Y. Li, Y. Wu, and H. Li, “Efficient Frequency Domain Channel Equalization Methods for OFDM Visible Light Communications,” IET Commun. 11(1), 25–29 (2017).
[Crossref]

B. Lin, X. Tang, H. Yang, Z. Ghassemlooy, S. Zhang, Y. Li, and C. Lin, “Experimental Demonstration of IFDMA for Uplink Visible Light Communication,” IEEE Photonics Technol. Lett. 28(20), 2218–2220 (2016).
[Crossref]

B. Lin, X. Tang, Z. Ghassemlooy, X. Fang, C. Lin, Y. Li, and S. Zhang, “Experimental Demonstration of OFDM/OQAM Transmission for Visible Light Communications,” IEEE Photonics J. 8(5), 7906710 (2016).
[Crossref]

Haas, H.

T. Fath and H. Haas, “Performance comparison of MIMO techniques for optical wireless communications in indoor environments,” IEEE Trans. Commun. 61(2), 733–742 (2013).
[Crossref]

H. Elgala, R. Mesleh, and H. Haas, “Indoor optical wireless communication: potential and state-of-the-art,” IEEE Commun. Mag. 49(9), 56–62 (2011).
[Crossref]

Higuchi, K.

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 (IEEE, 2013), pp. 1–5.
[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]

Khalid, A. M.

Kishiyama, 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 Annual Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC), (IEEE, 2013), pp.611–615.
[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 (IEEE, 2013), pp. 1–5.
[Crossref]

Kizilirmak, R. C.

R. C. Kizilirmak, C. R. Rowell, and M. Uysal, “Non-orthogonal multiple access (NOMA) for indoor visible light communications,” IEEE International Workshop on Optical Wireless Communications, (2015), pp. 98–101.
[Crossref]

Li, A.

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 (IEEE, 2013), pp. 1–5.
[Crossref]

Li, H.

B. Lin, X. Tang, Z. Ghassemlooy, S. Zhang, Y. Li, Y. Wu, and H. Li, “Efficient Frequency Domain Channel Equalization Methods for OFDM Visible Light Communications,” IET Commun. 11(1), 25–29 (2017).
[Crossref]

Li, Y.

B. Lin, X. Tang, Z. Ghassemlooy, S. Zhang, Y. Li, Y. Wu, and H. Li, “Efficient Frequency Domain Channel Equalization Methods for OFDM Visible Light Communications,” IET Commun. 11(1), 25–29 (2017).
[Crossref]

B. Lin, X. Tang, H. Yang, Z. Ghassemlooy, S. Zhang, Y. Li, and C. Lin, “Experimental Demonstration of IFDMA for Uplink Visible Light Communication,” IEEE Photonics Technol. Lett. 28(20), 2218–2220 (2016).
[Crossref]

B. Lin, X. Tang, Z. Ghassemlooy, X. Fang, C. Lin, Y. Li, and S. Zhang, “Experimental Demonstration of OFDM/OQAM Transmission for Visible Light Communications,” IEEE Photonics J. 8(5), 7906710 (2016).
[Crossref]

Lin, B.

B. Lin, X. Tang, Z. Ghassemlooy, S. Zhang, Y. Li, Y. Wu, and H. Li, “Efficient Frequency Domain Channel Equalization Methods for OFDM Visible Light Communications,” IET Commun. 11(1), 25–29 (2017).
[Crossref]

B. Lin, X. Tang, H. Yang, Z. Ghassemlooy, S. Zhang, Y. Li, and C. Lin, “Experimental Demonstration of IFDMA for Uplink Visible Light Communication,” IEEE Photonics Technol. Lett. 28(20), 2218–2220 (2016).
[Crossref]

B. Lin, X. Tang, Z. Ghassemlooy, X. Fang, C. Lin, Y. Li, and S. Zhang, “Experimental Demonstration of OFDM/OQAM Transmission for Visible Light Communications,” IEEE Photonics J. 8(5), 7906710 (2016).
[Crossref]

Lin, C.

B. Lin, X. Tang, Z. Ghassemlooy, X. Fang, C. Lin, Y. Li, and S. Zhang, “Experimental Demonstration of OFDM/OQAM Transmission for Visible Light Communications,” IEEE Photonics J. 8(5), 7906710 (2016).
[Crossref]

B. Lin, X. Tang, H. Yang, Z. Ghassemlooy, S. Zhang, Y. Li, and C. Lin, “Experimental Demonstration of IFDMA for Uplink Visible Light Communication,” IEEE Photonics Technol. Lett. 28(20), 2218–2220 (2016).
[Crossref]

Liu, H.

Liu, Y.-L.

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]

Mesleh, R.

H. Elgala, R. Mesleh, and H. Haas, “Indoor optical wireless communication: potential and state-of-the-art,” IEEE Commun. Mag. 49(9), 56–62 (2011).
[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, A. Benjebbour, Y. Kishiyama, and T. Nakamura, “System Level Performance Evaluation of Downlink Non-Orthogonal Multiple Access (NOMA),” in Proceedings of IEEE Annual Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC), (IEEE, 2013), pp.611–615.
[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 (IEEE, 2013), pp. 1–5.
[Crossref]

Poor, H.

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

Rowell, C. R.

R. C. Kizilirmak, C. R. Rowell, and M. Uysal, “Non-orthogonal multiple access (NOMA) for indoor visible light communications,” IEEE International Workshop on Optical Wireless Communications, (2015), pp. 98–101.
[Crossref]

Saito, 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 (IEEE, 2013), pp. 1–5.
[Crossref]

Y. Saito, A. Benjebbour, Y. Kishiyama, and T. Nakamura, “System Level Performance Evaluation of Downlink Non-Orthogonal Multiple Access (NOMA),” in Proceedings of IEEE Annual Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC), (IEEE, 2013), pp.611–615.
[Crossref]

Tang, X.

B. Lin, X. Tang, Z. Ghassemlooy, S. Zhang, Y. Li, Y. Wu, and H. Li, “Efficient Frequency Domain Channel Equalization Methods for OFDM Visible Light Communications,” IET Commun. 11(1), 25–29 (2017).
[Crossref]

B. Lin, X. Tang, H. Yang, Z. Ghassemlooy, S. Zhang, Y. Li, and C. Lin, “Experimental Demonstration of IFDMA for Uplink Visible Light Communication,” IEEE Photonics Technol. Lett. 28(20), 2218–2220 (2016).
[Crossref]

B. Lin, X. Tang, Z. Ghassemlooy, X. Fang, C. Lin, Y. Li, and S. Zhang, “Experimental Demonstration of OFDM/OQAM Transmission for Visible Light Communications,” IEEE Photonics J. 8(5), 7906710 (2016).
[Crossref]

Uysal, M.

R. C. Kizilirmak, C. R. Rowell, and M. Uysal, “Non-orthogonal multiple access (NOMA) for indoor visible light communications,” IEEE International Workshop on Optical Wireless Communications, (2015), pp. 98–101.
[Crossref]

Wu, L.

Wu, Y.

B. Lin, X. Tang, Z. Ghassemlooy, S. Zhang, Y. Li, Y. Wu, and H. Li, “Efficient Frequency Domain Channel Equalization Methods for OFDM Visible Light Communications,” IET Commun. 11(1), 25–29 (2017).
[Crossref]

Yang, H.

B. Lin, X. Tang, H. Yang, Z. Ghassemlooy, S. Zhang, Y. Li, and C. Lin, “Experimental Demonstration of IFDMA for Uplink Visible Light Communication,” IEEE Photonics Technol. Lett. 28(20), 2218–2220 (2016).
[Crossref]

Yang, Z.

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

Yeh, C.-H.

Zhang, S.

B. Lin, X. Tang, Z. Ghassemlooy, S. Zhang, Y. Li, Y. Wu, and H. Li, “Efficient Frequency Domain Channel Equalization Methods for OFDM Visible Light Communications,” IET Commun. 11(1), 25–29 (2017).
[Crossref]

B. Lin, X. Tang, H. Yang, Z. Ghassemlooy, S. Zhang, Y. Li, and C. Lin, “Experimental Demonstration of IFDMA for Uplink Visible Light Communication,” IEEE Photonics Technol. Lett. 28(20), 2218–2220 (2016).
[Crossref]

B. Lin, X. Tang, Z. Ghassemlooy, X. Fang, C. Lin, Y. Li, and S. Zhang, “Experimental Demonstration of OFDM/OQAM Transmission for Visible Light Communications,” IEEE Photonics J. 8(5), 7906710 (2016).
[Crossref]

Zhang, Z.

IEEE Commun. Mag. (1)

H. Elgala, R. Mesleh, and H. Haas, “Indoor optical wireless communication: potential and state-of-the-art,” IEEE Commun. Mag. 49(9), 56–62 (2011).
[Crossref]

IEEE Photonics J. (1)

B. Lin, X. Tang, Z. Ghassemlooy, X. Fang, C. Lin, Y. Li, and S. Zhang, “Experimental Demonstration of OFDM/OQAM Transmission for Visible Light Communications,” IEEE Photonics J. 8(5), 7906710 (2016).
[Crossref]

IEEE Photonics Technol. Lett. (2)

B. Lin, X. Tang, H. Yang, Z. Ghassemlooy, S. Zhang, Y. Li, and C. Lin, “Experimental Demonstration of IFDMA for Uplink Visible Light Communication,” IEEE Photonics Technol. Lett. 28(20), 2218–2220 (2016).
[Crossref]

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]

IEEE Signal Process. Lett. (1)

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

IEEE Trans. Commun. (1)

T. Fath and H. Haas, “Performance comparison of MIMO techniques for optical wireless communications in indoor environments,” IEEE Trans. Commun. 61(2), 733–742 (2013).
[Crossref]

IET Commun. (1)

B. Lin, X. Tang, Z. Ghassemlooy, S. Zhang, Y. Li, Y. Wu, and H. Li, “Efficient Frequency Domain Channel Equalization Methods for OFDM Visible Light Communications,” IET Commun. 11(1), 25–29 (2017).
[Crossref]

J. Lightwave Technol. (1)

Opt. Express (2)

Other (5)

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 (IEEE, 2013), pp. 1–5.
[Crossref]

Y. Saito, A. Benjebbour, Y. Kishiyama, and T. Nakamura, “System Level Performance Evaluation of Downlink Non-Orthogonal Multiple Access (NOMA),” in Proceedings of IEEE Annual Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC), (IEEE, 2013), pp.611–615.
[Crossref]

Z. Ghassemlooy, W. Popoola, and S. Rajbhandari, Optical Wireless Communications: System and Channel Modelling With MATLAB (Taylor & Francis, 2012).

R. C. Kizilirmak, C. R. Rowell, and M. Uysal, “Non-orthogonal multiple access (NOMA) for indoor visible light communications,” IEEE International Workshop on Optical Wireless Communications, (2015), pp. 98–101.
[Crossref]

L. Yin, X. Wu, and H. Haas, “On the performance of non-orthogonal multiple access in visible light communication,” IEEE International Symposium on Personal, Indoor, and Mobile Radio Communications, (IEEE, 2015), pp. 1354–1359.

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Figures (10)

Fig. 1
Fig. 1 Block diagram of downlink NOMA-OFDMA VLC (DFT: discrete Fourier transform, DAC: digital-to-analog converter, ADC: analog-to-digital converter, DC: direct current, CP: cyclic prefix).
Fig. 2
Fig. 2 Block diagram of uplink NOMA-OFDMA VLC.
Fig. 3
Fig. 3 Power and frequency allocation for NOMA-OFDMA VLC.
Fig. 4
Fig. 4 Experimental setup for downlink NOMA-OFDMA VLC.
Fig. 5
Fig. 5 BER performance for downlink NOMA-OFDMA VLC.
Fig. 6
Fig. 6 BER performance for downlink with LS, ISFA and MMSE methods.
Fig. 7
Fig. 7 Experimental setup for uplink NOMA-OFDMA VLC.
Fig. 8
Fig. 8 Block diagram of the preamble structure.
Fig. 9
Fig. 9 BER performance for uplink VLC based on NOMA-OFDMA.
Fig. 10
Fig. 10 BER performance as a function of distance for uplink VLC based on NOMA-OFDMA.

Tables (1)

Tables Icon

Table 1 System parameters

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

x = i = 1 N p i x i ,
y = h i = 1 N p i x i + w ,
Y = H × i = 1 N p i X i + W ,
Y 1 = X 1 + i = 2 N p i p 1 X i + W H p 1 .
Y 2 = X 2 + i = 3 N p i p 2 X i + W H p 2 .
Y N = X N + W H p N .
y = i = 1 N h i x i + w ,
Y = i = 1 N H i × X i + W ,
Y 1 = X 1 + i = 2 N H i H 1 X i + W H 1 .
Y 2 = X 2 + i = 3 N H i H 2 X i + W H 2 .
Y N = X N + W H N .

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