Abstract

Orthogonal frequency-division multiplexing (OFDM) is a practical technology in visible light communication (VLC) for high-speed transmissions. However, one of its operational limitations is the peak-to-average power ratio (PAPR) of the transmitted signal. In this paper, we analyze the PAPR distributions of four VLC OFDM schemes, namely DC-biased optical OFDM (DCO-OFDM), asymmetrically clipped optical OFDM (ACO-OFDM), pulse amplitude modulated discrete multitone (PAM-DMT), and Flip-OFDM. Both lower and upper clippings are considered. We analytically derive the complementary cumulative distribution functions (CCDFs) of the PAPRs of the clipped VLC OFDM signals, and investigate the impact of lower and upper clippings on PAPR distributions. Our analytical results, as verified by numerical simulations, provide useful insights and guidelines for VLC OFDM system designs.

© 2016 Optical Society of America

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References

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  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]
  2. T. Komine and M. Nakagawa, “Fundamental analysis for visible-light communication system using LED lights,” IEEE Trans. Consumer Electron. 50(1), 100–107 (2004).
    [Crossref]
  3. R. Zhang, J. Wang, Z. Wang, Z. Xu, L. Hanzo, and C. Zhao, “Visible light communications in heterogeneous networks: Paving the way for user-centric design,” IEEE Wireless Commun.,  22(2), 8–16 (2015).
    [Crossref]
  4. Y. Tao, X. Liang, J. Wang, and C. Zhao, “Scheduling for indoor visible light communication based on graph theory,” Optical Express,  23(3), 2737–2752, (2015).
    [Crossref]
  5. L. Chen, J. Wang, J. Zhou, D. W. K. Ng, R. Schober, and C. Zhao, “Distributed user-centric scheduling for visible light communication networks,” Optical Express,  24(14), 15570–15589, (2016).
    [Crossref]
  6. J. Armstrong, “OFDM for optical communications,” IEEE J. Lightw. Technol. 27(3), 189–204 (2009).
    [Crossref]
  7. J. Armstrong and A. Lowery, “Power efficient optical OFDM,” Electron. Lett. 42(6), 370–372 (2006).
    [Crossref]
  8. S. C. J. Lee, S. Randel, F. Breyer, and A. M. J. Koonen, “PAM-DMT for intensity-modulated and direct-detection optical communication systems,” IEEE Photon. Technol. Lett. 21(23), 1749–1751 (2009).
    [Crossref]
  9. N. Fernando, Y. Hong, and E. Viterbo, “Flip-OFDM for unipolar communication systems,” IEEE Trans. Commun. 60(12), 3726–3733 (2012).
    [Crossref]
  10. S. H. Han and J. H. Lee, “An overview of peak-to-average power ratio reduction techniques for multicarrier transmission,” IEEE Wireless Commun. 12(2), 56–65 (2005).
    [Crossref]
  11. H. Ochiai and H. Imai, “On the distribution of the peak-to-average power ratio in OFDM signals,” IEEE Trans. Commun. 49(2), 282–289 (2001).
    [Crossref]
  12. N. Jacklin and Z. Ding, “A linear programming based tone injection algorithm for PAPR reduction of OFDM and linearly precoded systems,” IEEE Trans. Circuits and Syst. I: Reg. Papers 60(7), 1937–1945 (2013).
    [Crossref]
  13. W. O. Popoola, Z. Ghassemlooy, and B. G. Stewart, “Pilot-assisted PAPR reduction technique for optical OFDM communication systems,” IEEE J. Lightw. Technol. 32(7), 1374–1382 (2014).
    [Crossref]
  14. K. Ying, Z. Yu, R. J. Baxley, and G. T. Zhou, “Constrained clipping for PAPR reduction in VLC systems with dimming control,” in Proc. IEEE GlobalSIP (IEEE, 2015), pp. 1327–1331.
  15. C. Ma, H. Zhang, M. Yao, Z. Xu, and K. Cui, “Distributions of PAPR and crest factor of OFDM signals for VLC,” in Proc. IEEE Photonics Society Summer Topical Meeting Series (IEEE, 2012), pp. 119–120.
  16. Z. Yu, R. J. Baxleyt, and G. T. Zhou, “Distributions of upper PAPR and lower PAPR of OFDM signals in visible light communications,” in Proc. IEEE ICASSP (IEEE, 2014), pp. 355–359.
  17. S. Dimitrov, S. Sinanovic, and H. Haas, “Clipping noise in OFDM-based optical wireless communication systems,” IEEE Trans. Commun. 60(4), 1072–1081 (2012).
    [Crossref]
  18. K. Ying, Z. Yu, R. J. Baxley, H. Qian, G.-K. Chang, and G. T. Zhou, “Nonlinear distortion mitigation in visible light communications,” IEEE Wireless Commun.,  22(2), 36–45 (2015).
    [Crossref]
  19. K. Ying, Z. Yu, R. J. Baxley, and G. T. Zhou, “Optimization of signal-to-noise-plus-distortion ratio for dynamic-rangelimited nonlinearities,” Digital Signal Process.,  36, 104–114 (2015).
    [Crossref]
  20. X. Ling, J. Wang, X. Liang, Z. Ding, and C. Zhao, “Offset and power optimization for DCO-OFDM in visible light communication systems,” IEEE Trans. Signal Process.,  64(2), 349–363 (2016).
    [Crossref]
  21. H. Yu, M. Chen, and G. Wei, “Distribution of PAR in DMT systems,” Electron. Lett. 39(10), 799–801 (2003).
    [Crossref]
  22. N. Johnson, S. Kotz, and N. Balakrishnan, Continuous Univariate Distributions (John Wiley, 1994) 2nd ed.

2016 (2)

L. Chen, J. Wang, J. Zhou, D. W. K. Ng, R. Schober, and C. Zhao, “Distributed user-centric scheduling for visible light communication networks,” Optical Express,  24(14), 15570–15589, (2016).
[Crossref]

X. Ling, J. Wang, X. Liang, Z. Ding, and C. Zhao, “Offset and power optimization for DCO-OFDM in visible light communication systems,” IEEE Trans. Signal Process.,  64(2), 349–363 (2016).
[Crossref]

2015 (4)

K. Ying, Z. Yu, R. J. Baxley, H. Qian, G.-K. Chang, and G. T. Zhou, “Nonlinear distortion mitigation in visible light communications,” IEEE Wireless Commun.,  22(2), 36–45 (2015).
[Crossref]

K. Ying, Z. Yu, R. J. Baxley, and G. T. Zhou, “Optimization of signal-to-noise-plus-distortion ratio for dynamic-rangelimited nonlinearities,” Digital Signal Process.,  36, 104–114 (2015).
[Crossref]

R. Zhang, J. Wang, Z. Wang, Z. Xu, L. Hanzo, and C. Zhao, “Visible light communications in heterogeneous networks: Paving the way for user-centric design,” IEEE Wireless Commun.,  22(2), 8–16 (2015).
[Crossref]

Y. Tao, X. Liang, J. Wang, and C. Zhao, “Scheduling for indoor visible light communication based on graph theory,” Optical Express,  23(3), 2737–2752, (2015).
[Crossref]

2014 (1)

W. O. Popoola, Z. Ghassemlooy, and B. G. Stewart, “Pilot-assisted PAPR reduction technique for optical OFDM communication systems,” IEEE J. Lightw. Technol. 32(7), 1374–1382 (2014).
[Crossref]

2013 (1)

N. Jacklin and Z. Ding, “A linear programming based tone injection algorithm for PAPR reduction of OFDM and linearly precoded systems,” IEEE Trans. Circuits and Syst. I: Reg. Papers 60(7), 1937–1945 (2013).
[Crossref]

2012 (2)

S. Dimitrov, S. Sinanovic, and H. Haas, “Clipping noise in OFDM-based optical wireless communication systems,” IEEE Trans. Commun. 60(4), 1072–1081 (2012).
[Crossref]

N. Fernando, Y. Hong, and E. Viterbo, “Flip-OFDM for unipolar communication systems,” IEEE Trans. Commun. 60(12), 3726–3733 (2012).
[Crossref]

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]

2009 (2)

J. Armstrong, “OFDM for optical communications,” IEEE J. Lightw. Technol. 27(3), 189–204 (2009).
[Crossref]

S. C. J. Lee, S. Randel, F. Breyer, and A. M. J. Koonen, “PAM-DMT for intensity-modulated and direct-detection optical communication systems,” IEEE Photon. Technol. Lett. 21(23), 1749–1751 (2009).
[Crossref]

2006 (1)

J. Armstrong and A. Lowery, “Power efficient optical OFDM,” Electron. Lett. 42(6), 370–372 (2006).
[Crossref]

2005 (1)

S. H. Han and J. H. Lee, “An overview of peak-to-average power ratio reduction techniques for multicarrier transmission,” IEEE Wireless Commun. 12(2), 56–65 (2005).
[Crossref]

2004 (1)

T. Komine and M. Nakagawa, “Fundamental analysis for visible-light communication system using LED lights,” IEEE Trans. Consumer Electron. 50(1), 100–107 (2004).
[Crossref]

2003 (1)

H. Yu, M. Chen, and G. Wei, “Distribution of PAR in DMT systems,” Electron. Lett. 39(10), 799–801 (2003).
[Crossref]

2001 (1)

H. Ochiai and H. Imai, “On the distribution of the peak-to-average power ratio in OFDM signals,” IEEE Trans. Commun. 49(2), 282–289 (2001).
[Crossref]

Armstrong, J.

J. Armstrong, “OFDM for optical communications,” IEEE J. Lightw. Technol. 27(3), 189–204 (2009).
[Crossref]

J. Armstrong and A. Lowery, “Power efficient optical OFDM,” Electron. Lett. 42(6), 370–372 (2006).
[Crossref]

Balakrishnan, N.

N. Johnson, S. Kotz, and N. Balakrishnan, Continuous Univariate Distributions (John Wiley, 1994) 2nd ed.

Baxley, R. J.

K. Ying, Z. Yu, R. J. Baxley, H. Qian, G.-K. Chang, and G. T. Zhou, “Nonlinear distortion mitigation in visible light communications,” IEEE Wireless Commun.,  22(2), 36–45 (2015).
[Crossref]

K. Ying, Z. Yu, R. J. Baxley, and G. T. Zhou, “Optimization of signal-to-noise-plus-distortion ratio for dynamic-rangelimited nonlinearities,” Digital Signal Process.,  36, 104–114 (2015).
[Crossref]

K. Ying, Z. Yu, R. J. Baxley, and G. T. Zhou, “Constrained clipping for PAPR reduction in VLC systems with dimming control,” in Proc. IEEE GlobalSIP (IEEE, 2015), pp. 1327–1331.

Baxleyt, R. J.

Z. Yu, R. J. Baxleyt, and G. T. Zhou, “Distributions of upper PAPR and lower PAPR of OFDM signals in visible light communications,” in Proc. IEEE ICASSP (IEEE, 2014), pp. 355–359.

Breyer, F.

S. C. J. Lee, S. Randel, F. Breyer, and A. M. J. Koonen, “PAM-DMT for intensity-modulated and direct-detection optical communication systems,” IEEE Photon. Technol. Lett. 21(23), 1749–1751 (2009).
[Crossref]

Chang, G.-K.

K. Ying, Z. Yu, R. J. Baxley, H. Qian, G.-K. Chang, and G. T. Zhou, “Nonlinear distortion mitigation in visible light communications,” IEEE Wireless Commun.,  22(2), 36–45 (2015).
[Crossref]

Chen, L.

L. Chen, J. Wang, J. Zhou, D. W. K. Ng, R. Schober, and C. Zhao, “Distributed user-centric scheduling for visible light communication networks,” Optical Express,  24(14), 15570–15589, (2016).
[Crossref]

Chen, M.

H. Yu, M. Chen, and G. Wei, “Distribution of PAR in DMT systems,” Electron. Lett. 39(10), 799–801 (2003).
[Crossref]

Cui, K.

C. Ma, H. Zhang, M. Yao, Z. Xu, and K. Cui, “Distributions of PAPR and crest factor of OFDM signals for VLC,” in Proc. IEEE Photonics Society Summer Topical Meeting Series (IEEE, 2012), pp. 119–120.

Dimitrov, S.

S. Dimitrov, S. Sinanovic, and H. Haas, “Clipping noise in OFDM-based optical wireless communication systems,” IEEE Trans. Commun. 60(4), 1072–1081 (2012).
[Crossref]

Ding, Z.

X. Ling, J. Wang, X. Liang, Z. Ding, and C. Zhao, “Offset and power optimization for DCO-OFDM in visible light communication systems,” IEEE Trans. Signal Process.,  64(2), 349–363 (2016).
[Crossref]

N. Jacklin and Z. Ding, “A linear programming based tone injection algorithm for PAPR reduction of OFDM and linearly precoded systems,” IEEE Trans. Circuits and Syst. I: Reg. Papers 60(7), 1937–1945 (2013).
[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]

Fernando, N.

N. Fernando, Y. Hong, and E. Viterbo, “Flip-OFDM for unipolar communication systems,” IEEE Trans. Commun. 60(12), 3726–3733 (2012).
[Crossref]

Ghassemlooy, Z.

W. O. Popoola, Z. Ghassemlooy, and B. G. Stewart, “Pilot-assisted PAPR reduction technique for optical OFDM communication systems,” IEEE J. Lightw. Technol. 32(7), 1374–1382 (2014).
[Crossref]

Haas, H.

S. Dimitrov, S. Sinanovic, and H. Haas, “Clipping noise in OFDM-based optical wireless communication systems,” IEEE Trans. Commun. 60(4), 1072–1081 (2012).
[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]

Han, S. H.

S. H. Han and J. H. Lee, “An overview of peak-to-average power ratio reduction techniques for multicarrier transmission,” IEEE Wireless Commun. 12(2), 56–65 (2005).
[Crossref]

Hanzo, L.

R. Zhang, J. Wang, Z. Wang, Z. Xu, L. Hanzo, and C. Zhao, “Visible light communications in heterogeneous networks: Paving the way for user-centric design,” IEEE Wireless Commun.,  22(2), 8–16 (2015).
[Crossref]

Hong, Y.

N. Fernando, Y. Hong, and E. Viterbo, “Flip-OFDM for unipolar communication systems,” IEEE Trans. Commun. 60(12), 3726–3733 (2012).
[Crossref]

Imai, H.

H. Ochiai and H. Imai, “On the distribution of the peak-to-average power ratio in OFDM signals,” IEEE Trans. Commun. 49(2), 282–289 (2001).
[Crossref]

Jacklin, N.

N. Jacklin and Z. Ding, “A linear programming based tone injection algorithm for PAPR reduction of OFDM and linearly precoded systems,” IEEE Trans. Circuits and Syst. I: Reg. Papers 60(7), 1937–1945 (2013).
[Crossref]

Johnson, N.

N. Johnson, S. Kotz, and N. Balakrishnan, Continuous Univariate Distributions (John Wiley, 1994) 2nd ed.

Komine, T.

T. Komine and M. Nakagawa, “Fundamental analysis for visible-light communication system using LED lights,” IEEE Trans. Consumer Electron. 50(1), 100–107 (2004).
[Crossref]

Koonen, A. M. J.

S. C. J. Lee, S. Randel, F. Breyer, and A. M. J. Koonen, “PAM-DMT for intensity-modulated and direct-detection optical communication systems,” IEEE Photon. Technol. Lett. 21(23), 1749–1751 (2009).
[Crossref]

Kotz, S.

N. Johnson, S. Kotz, and N. Balakrishnan, Continuous Univariate Distributions (John Wiley, 1994) 2nd ed.

Lee, J. H.

S. H. Han and J. H. Lee, “An overview of peak-to-average power ratio reduction techniques for multicarrier transmission,” IEEE Wireless Commun. 12(2), 56–65 (2005).
[Crossref]

Lee, S. C. J.

S. C. J. Lee, S. Randel, F. Breyer, and A. M. J. Koonen, “PAM-DMT for intensity-modulated and direct-detection optical communication systems,” IEEE Photon. Technol. Lett. 21(23), 1749–1751 (2009).
[Crossref]

Liang, X.

X. Ling, J. Wang, X. Liang, Z. Ding, and C. Zhao, “Offset and power optimization for DCO-OFDM in visible light communication systems,” IEEE Trans. Signal Process.,  64(2), 349–363 (2016).
[Crossref]

Y. Tao, X. Liang, J. Wang, and C. Zhao, “Scheduling for indoor visible light communication based on graph theory,” Optical Express,  23(3), 2737–2752, (2015).
[Crossref]

Ling, X.

X. Ling, J. Wang, X. Liang, Z. Ding, and C. Zhao, “Offset and power optimization for DCO-OFDM in visible light communication systems,” IEEE Trans. Signal Process.,  64(2), 349–363 (2016).
[Crossref]

Lowery, A.

J. Armstrong and A. Lowery, “Power efficient optical OFDM,” Electron. Lett. 42(6), 370–372 (2006).
[Crossref]

Ma, C.

C. Ma, H. Zhang, M. Yao, Z. Xu, and K. Cui, “Distributions of PAPR and crest factor of OFDM signals for VLC,” in Proc. IEEE Photonics Society Summer Topical Meeting Series (IEEE, 2012), pp. 119–120.

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]

Nakagawa, M.

T. Komine and M. Nakagawa, “Fundamental analysis for visible-light communication system using LED lights,” IEEE Trans. Consumer Electron. 50(1), 100–107 (2004).
[Crossref]

Ng, D. W. K.

L. Chen, J. Wang, J. Zhou, D. W. K. Ng, R. Schober, and C. Zhao, “Distributed user-centric scheduling for visible light communication networks,” Optical Express,  24(14), 15570–15589, (2016).
[Crossref]

Ochiai, H.

H. Ochiai and H. Imai, “On the distribution of the peak-to-average power ratio in OFDM signals,” IEEE Trans. Commun. 49(2), 282–289 (2001).
[Crossref]

Popoola, W. O.

W. O. Popoola, Z. Ghassemlooy, and B. G. Stewart, “Pilot-assisted PAPR reduction technique for optical OFDM communication systems,” IEEE J. Lightw. Technol. 32(7), 1374–1382 (2014).
[Crossref]

Qian, H.

K. Ying, Z. Yu, R. J. Baxley, H. Qian, G.-K. Chang, and G. T. Zhou, “Nonlinear distortion mitigation in visible light communications,” IEEE Wireless Commun.,  22(2), 36–45 (2015).
[Crossref]

Randel, S.

S. C. J. Lee, S. Randel, F. Breyer, and A. M. J. Koonen, “PAM-DMT for intensity-modulated and direct-detection optical communication systems,” IEEE Photon. Technol. Lett. 21(23), 1749–1751 (2009).
[Crossref]

Schober, R.

L. Chen, J. Wang, J. Zhou, D. W. K. Ng, R. Schober, and C. Zhao, “Distributed user-centric scheduling for visible light communication networks,” Optical Express,  24(14), 15570–15589, (2016).
[Crossref]

Sinanovic, S.

S. Dimitrov, S. Sinanovic, and H. Haas, “Clipping noise in OFDM-based optical wireless communication systems,” IEEE Trans. Commun. 60(4), 1072–1081 (2012).
[Crossref]

Stewart, B. G.

W. O. Popoola, Z. Ghassemlooy, and B. G. Stewart, “Pilot-assisted PAPR reduction technique for optical OFDM communication systems,” IEEE J. Lightw. Technol. 32(7), 1374–1382 (2014).
[Crossref]

Tao, Y.

Y. Tao, X. Liang, J. Wang, and C. Zhao, “Scheduling for indoor visible light communication based on graph theory,” Optical Express,  23(3), 2737–2752, (2015).
[Crossref]

Viterbo, E.

N. Fernando, Y. Hong, and E. Viterbo, “Flip-OFDM for unipolar communication systems,” IEEE Trans. Commun. 60(12), 3726–3733 (2012).
[Crossref]

Wang, J.

L. Chen, J. Wang, J. Zhou, D. W. K. Ng, R. Schober, and C. Zhao, “Distributed user-centric scheduling for visible light communication networks,” Optical Express,  24(14), 15570–15589, (2016).
[Crossref]

X. Ling, J. Wang, X. Liang, Z. Ding, and C. Zhao, “Offset and power optimization for DCO-OFDM in visible light communication systems,” IEEE Trans. Signal Process.,  64(2), 349–363 (2016).
[Crossref]

Y. Tao, X. Liang, J. Wang, and C. Zhao, “Scheduling for indoor visible light communication based on graph theory,” Optical Express,  23(3), 2737–2752, (2015).
[Crossref]

R. Zhang, J. Wang, Z. Wang, Z. Xu, L. Hanzo, and C. Zhao, “Visible light communications in heterogeneous networks: Paving the way for user-centric design,” IEEE Wireless Commun.,  22(2), 8–16 (2015).
[Crossref]

Wang, Z.

R. Zhang, J. Wang, Z. Wang, Z. Xu, L. Hanzo, and C. Zhao, “Visible light communications in heterogeneous networks: Paving the way for user-centric design,” IEEE Wireless Commun.,  22(2), 8–16 (2015).
[Crossref]

Wei, G.

H. Yu, M. Chen, and G. Wei, “Distribution of PAR in DMT systems,” Electron. Lett. 39(10), 799–801 (2003).
[Crossref]

Xu, Z.

R. Zhang, J. Wang, Z. Wang, Z. Xu, L. Hanzo, and C. Zhao, “Visible light communications in heterogeneous networks: Paving the way for user-centric design,” IEEE Wireless Commun.,  22(2), 8–16 (2015).
[Crossref]

C. Ma, H. Zhang, M. Yao, Z. Xu, and K. Cui, “Distributions of PAPR and crest factor of OFDM signals for VLC,” in Proc. IEEE Photonics Society Summer Topical Meeting Series (IEEE, 2012), pp. 119–120.

Yao, M.

C. Ma, H. Zhang, M. Yao, Z. Xu, and K. Cui, “Distributions of PAPR and crest factor of OFDM signals for VLC,” in Proc. IEEE Photonics Society Summer Topical Meeting Series (IEEE, 2012), pp. 119–120.

Ying, K.

K. Ying, Z. Yu, R. J. Baxley, H. Qian, G.-K. Chang, and G. T. Zhou, “Nonlinear distortion mitigation in visible light communications,” IEEE Wireless Commun.,  22(2), 36–45 (2015).
[Crossref]

K. Ying, Z. Yu, R. J. Baxley, and G. T. Zhou, “Optimization of signal-to-noise-plus-distortion ratio for dynamic-rangelimited nonlinearities,” Digital Signal Process.,  36, 104–114 (2015).
[Crossref]

K. Ying, Z. Yu, R. J. Baxley, and G. T. Zhou, “Constrained clipping for PAPR reduction in VLC systems with dimming control,” in Proc. IEEE GlobalSIP (IEEE, 2015), pp. 1327–1331.

Yu, H.

H. Yu, M. Chen, and G. Wei, “Distribution of PAR in DMT systems,” Electron. Lett. 39(10), 799–801 (2003).
[Crossref]

Yu, Z.

K. Ying, Z. Yu, R. J. Baxley, and G. T. Zhou, “Optimization of signal-to-noise-plus-distortion ratio for dynamic-rangelimited nonlinearities,” Digital Signal Process.,  36, 104–114 (2015).
[Crossref]

K. Ying, Z. Yu, R. J. Baxley, H. Qian, G.-K. Chang, and G. T. Zhou, “Nonlinear distortion mitigation in visible light communications,” IEEE Wireless Commun.,  22(2), 36–45 (2015).
[Crossref]

Z. Yu, R. J. Baxleyt, and G. T. Zhou, “Distributions of upper PAPR and lower PAPR of OFDM signals in visible light communications,” in Proc. IEEE ICASSP (IEEE, 2014), pp. 355–359.

K. Ying, Z. Yu, R. J. Baxley, and G. T. Zhou, “Constrained clipping for PAPR reduction in VLC systems with dimming control,” in Proc. IEEE GlobalSIP (IEEE, 2015), pp. 1327–1331.

Zhang, H.

C. Ma, H. Zhang, M. Yao, Z. Xu, and K. Cui, “Distributions of PAPR and crest factor of OFDM signals for VLC,” in Proc. IEEE Photonics Society Summer Topical Meeting Series (IEEE, 2012), pp. 119–120.

Zhang, R.

R. Zhang, J. Wang, Z. Wang, Z. Xu, L. Hanzo, and C. Zhao, “Visible light communications in heterogeneous networks: Paving the way for user-centric design,” IEEE Wireless Commun.,  22(2), 8–16 (2015).
[Crossref]

Zhao, C.

L. Chen, J. Wang, J. Zhou, D. W. K. Ng, R. Schober, and C. Zhao, “Distributed user-centric scheduling for visible light communication networks,” Optical Express,  24(14), 15570–15589, (2016).
[Crossref]

X. Ling, J. Wang, X. Liang, Z. Ding, and C. Zhao, “Offset and power optimization for DCO-OFDM in visible light communication systems,” IEEE Trans. Signal Process.,  64(2), 349–363 (2016).
[Crossref]

Y. Tao, X. Liang, J. Wang, and C. Zhao, “Scheduling for indoor visible light communication based on graph theory,” Optical Express,  23(3), 2737–2752, (2015).
[Crossref]

R. Zhang, J. Wang, Z. Wang, Z. Xu, L. Hanzo, and C. Zhao, “Visible light communications in heterogeneous networks: Paving the way for user-centric design,” IEEE Wireless Commun.,  22(2), 8–16 (2015).
[Crossref]

Zhou, G. T.

K. Ying, Z. Yu, R. J. Baxley, and G. T. Zhou, “Optimization of signal-to-noise-plus-distortion ratio for dynamic-rangelimited nonlinearities,” Digital Signal Process.,  36, 104–114 (2015).
[Crossref]

K. Ying, Z. Yu, R. J. Baxley, H. Qian, G.-K. Chang, and G. T. Zhou, “Nonlinear distortion mitigation in visible light communications,” IEEE Wireless Commun.,  22(2), 36–45 (2015).
[Crossref]

K. Ying, Z. Yu, R. J. Baxley, and G. T. Zhou, “Constrained clipping for PAPR reduction in VLC systems with dimming control,” in Proc. IEEE GlobalSIP (IEEE, 2015), pp. 1327–1331.

Z. Yu, R. J. Baxleyt, and G. T. Zhou, “Distributions of upper PAPR and lower PAPR of OFDM signals in visible light communications,” in Proc. IEEE ICASSP (IEEE, 2014), pp. 355–359.

Zhou, J.

L. Chen, J. Wang, J. Zhou, D. W. K. Ng, R. Schober, and C. Zhao, “Distributed user-centric scheduling for visible light communication networks,” Optical Express,  24(14), 15570–15589, (2016).
[Crossref]

Digital Signal Process. (1)

K. Ying, Z. Yu, R. J. Baxley, and G. T. Zhou, “Optimization of signal-to-noise-plus-distortion ratio for dynamic-rangelimited nonlinearities,” Digital Signal Process.,  36, 104–114 (2015).
[Crossref]

Electron. Lett. (2)

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Figures (10)

Fig. 1
Fig. 1 Transmitter block diagram of the DCO-OFDM VLC System.
Fig. 2
Fig. 2 Transmitter block diagram of the ACO-OFDM VLC System.
Fig. 3
Fig. 3 Transmitter block diagram of the PAM-DMT VLC System.
Fig. 4
Fig. 4 Transmitter block diagram of the Flip-OFDM VLC System.
Fig. 5
Fig. 5 (a) values of c(l, u) and (b) values of θL and θU for different l and u.
Fig. 6
Fig. 6 PAPR CCDFs of the four VLC OFDM schemes with different subcarrier numbers.
Fig. 7
Fig. 7 DCO-OFDM PAPR CCDF versus PAPR with N = 1024.
Fig. 8
Fig. 8 DCO-OFDM PAPR CCDF versus l and u with N = 1024. In (a) u = 5 and in (b) l = −5.
Fig. 9
Fig. 9 ACO-OFDM, PAM-DMT, Flip-OFDM PAPR CCDFs versus PAPR with N = 1024.
Fig. 10
Fig. 10 Comparison of the PAPR CCDFs of the four VLC OFDM schemes.

Equations (50)

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S k = S N k * , k = 1 , , N 2 1
S = [ 0 , S 1 , S 2 , , S N 2 1 , 0 , S N 2 1 * , , S 2 * , S 1 * ] .
s n = 1 N k = 0 N 1 S k e j 2 π k n N = 2 N k = 1 N 2 1 Re { S k e j 2 π k n N }
s clip , n = Clip [ s n ] = { B U , s n B U s n , B L < s n < B U B L , s n B L
S = [ 0 , S 1 , 0 , , S N 2 1 , 0 , S N 2 1 * , , 0 , S 1 * ] .
s n = 1 N k = 0 N 1 S k e j 2 π k n N = 2 N k = 1 N 2 1 Re { S k e j 2 π k n N } = 2 N t = 1 N / 4 Re { S 2 t 1 e j 2 π ( 2 t 1 ) n N } .
s n + N 2 = 2 N t = 1 N / 4 Re { S 2 t 1 e j 2 π ( 2 t 1 ) ( n + N 2 ) N } = s n , n = 0 , , N 2 1 .
s clip , n = Clip [ s n ] = { B U , s n B U s n , 0 < s n < B U 0 , s n 0 .
S = [ 0 , j A 1 , j A 2 , , j A N 2 1 , 0 , j A N 2 1 , , j A 2 , j A 1 ] .
s n = 1 N k = 0 N 1 S k e j 2 π k n N = 1 N k = 1 N 2 1 [ j A k e j 2 π k n N j A k e j 2 π ( N k ) n N ] = 2 N k = 1 N 2 1 A k sin 2 π k n N
s N n = 2 N k = 1 N 2 1 A k sin 2 π k ( N n ) N = s n n = 1 , , N 2 1
s n + = { s n , if s n 0 0 , otherwise and s n = { s n , if s n < 0 0 , otherwise .
s clip , n = Clip [ s ¯ n ] = { B U , s n B U s n , s n < B U
PAPR = max 0 n N 1 | s clip , n | 2 E [ | s clip , n | 2 ]
l = B L σ s and u = B U σ s .
f dco ( w ) = Φ ( l ) δ ( w + B L ) + 1 2 π σ s e w 2 2 σ s 2 [ u ( w + B L ) u ( w B U ) ] + [ 1 Φ ( u ) ] δ ( w B U ) .
f aco ( w ) = 1 2 δ ( w ) + 1 2 π σ s e w 2 2 σ s 2 [ u ( w ) u ( w B U ) ] + [ 1 Φ ( u ) ] δ ( w B U ) .
P dco ele = E [ | s clip , n | 2 ] = E [ s clip , n 2 ] = + w 2 f dco ( w ) d w = σ s 2 c ( l , u )
c ( l , u ) = ( l 2 1 ) Φ ( l ) ( u 2 1 ) Φ ( u ) + u 2 + lg ( l ) u g ( u ) .
P dco opt = E [ s clip , n ] + B L = + w f dco ( w ) d w = σ s [ l Φ ( l ) + g ( l ) g ( u ) + u ( 1 Φ ( u ) ) ] + B L
F dco ( x ) = P ( PAPR > x ) = { 1 [ 2 Φ ( c ( l , u ) x ) 1 ] N , 0 x < θ min 1 [ Φ ( c ( l , u ) x ) ] N , θ min x < θ max 0 , x θ max
θ L = l 2 c ( l , u ) and θ U = u 2 c ( l , u ) .
F sym ( x ) = { 1 , [ 2 Φ ( c ( u , u ) x ) 1 ] N , 0 x < θ 0 , x θ
F unc ( x ) = 1 [ 2 Φ ( x ) 1 ] N , x 0 .
F dco ( x ) { F unc ( x ) , x < θ min or β x < θ max F unc ( x ) , x θ max or θ min x α
F sym ( x ) { F unc ( x ) , 0 x < θ F unc ( x ) , x θ .
F aco ( x ) = P ( PAPR > x ) = { 1 [ 2 Φ ( c ( 0 , u ) x ) 1 ] N 2 , 0 x < θ 0 , U 0 , x θ 0 , U
F pam ( x ) = P ( PAPR > x ) = { 1 [ 2 Φ ( c ( 0 , u ) x 1 ] N 2 1 , 0 x < θ 0 , U 0 , x θ 0 , U
PAPR = max 0 n 2 N 1 | s clip , n | 2 E [ | s clip , n | 2 ]
F flip ( x ) = P ( PAPR > x ) = { 1 [ 2 Φ ( c ( 0 , u ) x 1 ) ] N , 0 x < θ 0 , U 0 , x θ 0 , U
F aco ( x ) F pam ( x ) F flip ( x )
P ( PAPR x ) = P ( max 0 n N 1 | s clip , n | 2 σ s 2 c ( l , u ) x ) = P ( | s clip , n | 2 σ s 2 c ( l , u ) x , n = 0 , , N 1 )
P ( PAPR x ) = [ P ( | s clip , n | 2 σ s 2 c ( l , u ) x ) ] N .
P ( | s clip , n | 2 σ s 2 c ( l , u ) x ) = P ( σ s c ( l , u ) x s clip , n σ s c ( l , u ) x ) = σ s c ( l , u ) x σ s c ( l , u ) x f dco ( w ) d w = 2 Φ ( c ( l , u ) x ) 1 .
P ( | s clip , n | 2 σ s 2 c ( l , u ) x ) = P ( B L s clip , n B U ) = B L B U f dco ( w ) d w = 1 .
P ( | s clip , n | 2 σ s 2 c ( l , u ) x ) = P ( B L s clip , n σ s c ( l , u ) x ) = B L σ s c ( l , u ) x f dco ( w ) d w = Φ ( c ( l , u ) x ) .
P ( | s clip , n | 2 σ s 2 c ( l , u ) x ) = P ( σ s c ( l , u ) x s clip , n B U ) = σ s c ( l , u ) x B U f dco ( w ) d w = Φ ( c ( l , u ) x ) .
P ( PAPR x ) = { [ 2 Φ ( c ( l , u ) x 1 ) ] N , x < θ min [ Φ ( c ( l , u ) x ) ] N , θ min x < θ max 1 , x θ max .
θ L l = 2 l c ( l , u ) l 2 2 l Φ ( l ) c 2 ( l , u ) = 2 l ( c ( l , u ) l 2 Φ ( l ) ) c 2 ( l , u ) = 2 l ψ L ( l , u ) c 2 ( l , u )
ψ L ( l , u ) l = 2 l Φ ( l ) 2 l Φ ( l ) l 2 g ( l ) = l 2 g ( l ) 0 ,
θ U u = 2 u c ( l , u ) u 2 2 u ( 1 Φ ( u ) ) c 2 ( l , u ) = 2 u ( c ( l , u ) u 2 + u 2 Φ ( u ) ) c 2 ( l , u ) = 2 u ψ U ( l , u ) c 2 ( l , u )
ψ U ( l , u ) u = 2 u ( 1 Φ ( u ) ) 2 u + 2 u Φ ( u ) + u 2 g ( u ) = u 2 g ( u ) 0 ,
d θ d u = 2 u c ( u , u ) u 2 4 u ( 1 Φ ( u ) ) c 2 ( u , u ) = 2 u ( 2 Φ ( u ) 2 u g ( u ) 1 ) c 2 ( u , u ) = 2 u ψ ( u ) c 2 ( u , u )
P ( PAPR x ) = P ( max 0 n N 1 | s clip , n | 2 σ s 2 c ( 0 , u ) x ) = P ( s clip , n σ s c ( 0 , u ) x , n = 0 , , N 1 )
P ( PAPR x ) = n = 0 N 2 1 P ( s clip , n σ s c ( 0 , u ) x , s clip , n + N 2 σ s c ( 0 , u ) x ) .
P ( s clip , n σ s c ( 0 , u ) x , s clip , n + N 2 σ s c ( 0 , u ) x ) = P ( s clip , n σ s c ( 0 , u ) x , s clip , n + N 2 σ s c ( 0 , u ) x , s n 0 ) + P ( s clip , n σ s c ( 0 , u ) x , s clip , n + N 2 σ s c ( 0 , u ) x , s n < 0 ) ( a ) = P ( s clip , n σ s c ( 0 , u ) x , s n 0 ) + P ( s clip , n + N 2 σ s c ( 0 , u ) x , s n < 0 ) ( b ) = 2 P ( s clip , n σ s c ( 0 , u ) x , s n 0 )
P ( s clip , n σ s c ( 0 , u ) x , s n 0 ) = P ( 0 s n σ s c ( 0 , u ) x ) = 0 σ s c ( 0 , u ) x 1 2 π σ s e w 2 2 σ s 2 d w = Φ ( c ( 0 , u ) x ) 0.5 .
P ( PAPR x ) = { [ 2 Φ ( c ( 0 , u ) x ) 1 ] N 2 , 0 x < θ 0 , U 1 , x θ 0 , U
P ( PAPR x ) = P ( s clip , n σ s c ( 0 , u ) x , n = 0 , , 2 N 1 ) = n = 0 N 1 P ( s clip , n σ s c ( 0 , u ) x , s clip , n + N σ s c ( 0 , u ) x )
P ( s clip , n σ s c ( 0 , u ) x , s clip , n + N σ s c ( 0 , u ) x ) = P ( s clip , n σ s c ( 0 , u ) x , s clip , n + N σ s c ( 0 , u ) x , s n 0 ) + P ( s clip , n σ s c ( 0 , u ) x , s clip , n + N σ s c ( 0 , u ) x , s n < 0 ) ( a ) = P ( s clip , n σ s c ( 0 , u ) x , s n 0 ) + P ( s clip , n + N σ s c ( 0 , u ) x , s n < 0 ) ( b ) = 2 P ( s clip , n σ s c ( 0 , u ) x , s n 0 )

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