Abstract

Light emitting diode (LED) nonlinearities have a significant impact on the performance of optical wireless (OW) communication systems based on orthogonal frequency division multiplexing (OFDM) modulation. In this paper, different techniques to compensate for the induced nonlinearity distortions are presented and analyzed. First, single-carrier frequency division multiple access (SC-FDMA) is proposed instead of OFDM for OW systems. In SC-FDMA, some of the major OFDM problems such as high peak-to-average power ratio are inherently resolved. It is shown that the performance of OW OFDM systems and their counterpart SC-FDMA systems are traded off for certain input signal powers and modulation orders. Second, OW OFDM systems with hard, soft, and turbo channel coding techniques are considered. It is reported that significant performance gains can be achieved through channel coding. Finally, a novel method to reduce signal clipping distortion through the use of iterative signal clipping (ISC) and multiple transmit LEDs is proposed. The ISC technique is based on iterative clipping of the time domain OFDM signal and transmission from a multiple LED transmitter. Transmit LEDs are synchronized, located close to each other, and placed to emit light in the same direction. Hence, the channel path gains from each LED to the receiver photodiode are similar. The received signals from the different LEDs add coherently at the receiver. Reported results demonstrate that the effect of distortion is eliminated or significantly reduced based on the considered number of transmit LEDs.

© 2012 OSA

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2012 (1)

2011 (2)

H. Elgala, R. Mesleh, and H. Haas, “Indoor optical wireless communication: Potential and state-of-the-art,” IEEE Commun. Mag., vol. 49, no. 9, pp. 56–62, Sept.2011.
[CrossRef]

R. Mesleh, H. Elgala, and H. Haas, “On the performance of different OFDM based optical wireless communication systems,” J. Opt. Commun. Netw., vol. 3, no. 8, pp. 620–628, Aug.2011.
[CrossRef]

2010 (4)

S. Randel, F. Breyer, S. C. J. Lee, and J. W. Walewski, “Advanced modulation schemes for short-range optical communications,” IEEE J. Sel. Top. Quantum Electron., vol. 16, no. 5, pp. 1280–1289, 2010.
[CrossRef]

A. Farid and S. Hranilovic, “Capacity bounds for wireless optical intensity channels with Gaussian noise,” IEEE Trans. Inf. Theory, vol. 56, no. 12, pp. 6066–6077, Dec.2010.
[CrossRef]

H. Elgala, R. Mesleh, and H. Haas, “An LED model for intensity-modulated optical communication systems,” IEEE Photon. Technol. Lett., vol. 22, no. 11, pp. 835–837, June2010.
[CrossRef]

C. Ciochina and H. Sari, “A review of OFDMA and single-carrier FDMA and some recent results,” IEEE Adv. Electron. Telecommun., vol. 1, no. 1, pp. 706–710, Apr.2010.

2009 (6)

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., vol. 21, no. 23, pp. 1749–1751, Dec.2009.
[CrossRef]

S. Wilson and J. Armstrong, “Transmitter and receiver methods for improving asymmetrically-clipped optical OFDM,” IEEE Trans. Wireless Commun., vol. 8, no. 9, pp. 4561–4567, Sept.2009.
[CrossRef]

H. Elgala, R. Mesleh, and H. Haas, “Indoor broadcasting via white LEDs and OFDM,” IEEE Trans. Consum. Electron., vol. 55, no. 3, pp. 1127–1134, Aug.2009.
[CrossRef]

J. Armstrong, “OFDM for optical communications,” J. Lightwave Technol., vol. 27, no. 3, pp. 189–204, Feb.2009.
[CrossRef]

S. U. Hwang, S. Jeon, S. Lee, and J. Seo, “Soft-output ML detector for spatial modulation OFDM systems,” IEICE Electron. Express, vol. 6, no. 19, pp. 1426–1431, Oct.2009.
[CrossRef]

H. Elgala, R. Mesleh, and H. Haas, “Non-linearity effects and predistortion in optical OFDM wireless transmission using LEDs,” Inderscience Int. J. Ultra Wideband Commun. Syst. (IJUWBCS), vol. 1, no. 2, pp. 143–150, 2009.
[CrossRef]

2008 (2)

R. J. Green, H. Joshi, M. D. Higgins, and M. S. Leeson, “Recent developments in indoor optical wireless,” IET Commun., vol. 2, no. 1, pp. 3–10, Jan.2008.
[CrossRef]

W. Kang and S. Hranilovic, “Power reduction techniques for multiple-subcarrier modulated diffuse wireless optical channels,” IEEE Trans. Commun., vol. 56, no. 2, pp. 279–288, Feb.2008.
[CrossRef]

2007 (2)

S. Slimane, “Reducing the peak-to-average power ratio of OFDM signals through precoding,” IEEE Trans. Veh. Technol., vol. 56, no. 2, pp. 686–695, Mar.2007.
[CrossRef]

D. O’Brien, G. Parry, and P. Stavrinou, “Optical hotspots speed up wireless communication,” Nat. Photonics, vol. 1, pp. 245–247, 2007.
[CrossRef]

2006 (1)

J. Armstrong and A. Lowery, “Power efficient optical OFDM,” Electron. Lett., vol. 42, no. 6, pp. 370–372, Mar.2006.
[CrossRef]

2003 (1)

Y. Tanaka, T. Komine, S. Haruyama, and M. Nakagawa, “Indoor visible light data transmission system utilizing white LED lights,” IEICE Trans. Commun., vol. E86-B, no. 8, pp. 2440–2454, Aug.2003.

2002 (3)

D. Falconer, S. Ariyavisitakul, A. Benyamin-Seeyar, and B. Eidson, “Frequency domain equalization for single-carrier broadband wireless systems,” IEEE Commun. Mag., vol. 40, no. 4, pp. 58–66, Apr.2002.
[CrossRef]

N. Benvenuto and S. Tomasin, “On the comparison between OFDM and single carrier modulation with a DFE using a frequency-domain feedforward filter,” IEEE Trans. Commun., vol. 50, no. 6, pp. 947–955, June2002.
[CrossRef]

K. Cho and D. Yoon, “On the general BER expression of one- and two-dimensional amplitude modulations,” IEEE Trans. Commun., vol. 50, no. 7, pp. 1074–1080, July2002.
[CrossRef]

2001 (1)

D. C. O’Brien, S. H. Khoo, W. Zhang, G. E. Faulkner, and D. J. Edwards, “High-speed optical channel measurement system,” Proc. SPIE, vol. 4530, pp. 135–144, 2001.
[CrossRef]

2000 (2)

V. Tarokh and H. Jafarkhani, “On the computation and reduction of the peak-to-average power ratio in multicarrier communications,” IEEE Trans. Commun., vol. 48, no. 1, pp. 37–44, Jan.2000.
[CrossRef]

A. Jayalath and C. Tellambura, “Reducing the peak-to-average power ratio of orthogonal frequency division multiplexing signal through bit or symbol interleaving,” Electron. Lett., vol. 36, no. 13, pp. 1161–1163, June2000.
[CrossRef]

1999 (1)

J. Davis and J. Jedwab, “Peak-to-mean power control in OFDM, Golay complementary sequences, and Reed-Muller codes,” IEEE Trans. Inf. Theory, vol. 45, no. 7, pp. 2397–2417, Nov.1999.
[CrossRef]

1997 (2)

J. M. Kahn and J. R. Barry, “Wireless infrared communications,” Proc. IEEE, vol. 85, no. 2, pp. 265–298, Feb.1997.
[CrossRef]

A. M. Street, P. N. Stavrinou, D. C. O’Brien, and D. J. Edwards, “Indoor optical wireless systems—A review,” Opt. Quantum Electron., vol. 29, no. 3, pp. 349–378, Mar.1997.
[CrossRef]

1993 (1)

J. Barry, J. Kahn, W. Krause, E. Lee, and D. Messerschmitt, “Simulation of multipath impulse response for indoor wireless optical channels,” IEEE J. Sel. Areas Commun., vol. 11, no. 3, pp. 367–379, Apr.1993.
[CrossRef]

1971 (1)

A. Viterbi, “Convolutional codes and their performance in communication systems,” IEEE Trans. Commun., vol. 19, no. 5, pp. 751–772, Oct.1971.
[CrossRef]

Afgani, M.

M. Afgani, H. Haas, H. Elgala, and D. Knipp, “Visible light communication using OFDM,” in Proc. of the 2nd Int. Conf. on Testbeds and Research Infrastructures for the Development of Networks and Communities (TRIDENTCOM), Barcelona, Spain, Mar. 1–3, 2006, pp. 129–134.

Ariyavisitakul, S.

D. Falconer, S. Ariyavisitakul, A. Benyamin-Seeyar, and B. Eidson, “Frequency domain equalization for single-carrier broadband wireless systems,” IEEE Commun. Mag., vol. 40, no. 4, pp. 58–66, Apr.2002.
[CrossRef]

Armstrong, J.

S. Wilson and J. Armstrong, “Transmitter and receiver methods for improving asymmetrically-clipped optical OFDM,” IEEE Trans. Wireless Commun., vol. 8, no. 9, pp. 4561–4567, Sept.2009.
[CrossRef]

J. Armstrong, “OFDM for optical communications,” J. Lightwave Technol., vol. 27, no. 3, pp. 189–204, Feb.2009.
[CrossRef]

J. Armstrong and A. Lowery, “Power efficient optical OFDM,” Electron. Lett., vol. 42, no. 6, pp. 370–372, Mar.2006.
[CrossRef]

Barry, J.

J. Barry, J. Kahn, W. Krause, E. Lee, and D. Messerschmitt, “Simulation of multipath impulse response for indoor wireless optical channels,” IEEE J. Sel. Areas Commun., vol. 11, no. 3, pp. 367–379, Apr.1993.
[CrossRef]

Barry, J. R.

J. M. Kahn and J. R. Barry, “Wireless infrared communications,” Proc. IEEE, vol. 85, no. 2, pp. 265–298, Feb.1997.
[CrossRef]

Benvenuto, N.

N. Benvenuto and S. Tomasin, “On the comparison between OFDM and single carrier modulation with a DFE using a frequency-domain feedforward filter,” IEEE Trans. Commun., vol. 50, no. 6, pp. 947–955, June2002.
[CrossRef]

Benyamin-Seeyar, A.

D. Falconer, S. Ariyavisitakul, A. Benyamin-Seeyar, and B. Eidson, “Frequency domain equalization for single-carrier broadband wireless systems,” IEEE Commun. Mag., vol. 40, no. 4, pp. 58–66, Apr.2002.
[CrossRef]

Bouchet, O.

K.-D. Langer, J. Grubor, O. Bouchet, M. El Tabach, J. Walewski, S. Randel, M. Franke, S. Nerreter, D. O’Brien, G. Faulkner, I. Neokosmidis, G. Ntogari, and M. Wolf, “Optical wireless communications for broadband access in home area networks,” in Proc. of the 10th Anniversary Int. Conf. on Transparent Optical Networks (ICTON), Athens, Greece, June 22–26, 2008, vol. 4, pp. 149–154.

Breyer, F.

S. Randel, F. Breyer, S. C. J. Lee, and J. W. Walewski, “Advanced modulation schemes for short-range optical communications,” IEEE J. Sel. Top. Quantum Electron., vol. 16, no. 5, pp. 1280–1289, 2010.
[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., vol. 21, no. 23, pp. 1749–1751, Dec.2009.
[CrossRef]

Bussgang, J.

J. Bussgang, Cross correlation function of amplitude-distorted Gaussian signals, Research Laboratory for Electronics, Massachusetts Institute of Technology, Cambridge, MA, , Mar.1952.

Cho, K.

K. Cho and D. Yoon, “On the general BER expression of one- and two-dimensional amplitude modulations,” IEEE Trans. Commun., vol. 50, no. 7, pp. 1074–1080, July2002.
[CrossRef]

Ciochina, C.

C. Ciochina and H. Sari, “A review of OFDMA and single-carrier FDMA and some recent results,” IEEE Adv. Electron. Telecommun., vol. 1, no. 1, pp. 706–710, Apr.2010.

Davis, J.

J. Davis and J. Jedwab, “Peak-to-mean power control in OFDM, Golay complementary sequences, and Reed-Muller codes,” IEEE Trans. Inf. Theory, vol. 45, no. 7, pp. 2397–2417, Nov.1999.
[CrossRef]

Dimitrov, S.

S. Dimitrov, S. Sinanovic, and H. Haas, “Signal shaping and modulation for optical wireless communication,” J. Lightwave Technol., vol. 30, no. 9, pp. 1319–1328, May2012.
[CrossRef]

S. Dimitrov and H. Haas, “On the clipping noise in an ACO-OFDM optical wireless communication system,” in Proc. of IEEE Global Communications Conf. (IEEE GLOBECOM), Miami, FL, Dec. 6–10, 2010.

Edwards, D. J.

D. C. O’Brien, S. H. Khoo, W. Zhang, G. E. Faulkner, and D. J. Edwards, “High-speed optical channel measurement system,” Proc. SPIE, vol. 4530, pp. 135–144, 2001.
[CrossRef]

Edwards, D. J.

A. M. Street, P. N. Stavrinou, D. C. O’Brien, and D. J. Edwards, “Indoor optical wireless systems—A review,” Opt. Quantum Electron., vol. 29, no. 3, pp. 349–378, Mar.1997.
[CrossRef]

Eidson, B.

D. Falconer, S. Ariyavisitakul, A. Benyamin-Seeyar, and B. Eidson, “Frequency domain equalization for single-carrier broadband wireless systems,” IEEE Commun. Mag., vol. 40, no. 4, pp. 58–66, Apr.2002.
[CrossRef]

El Tabach, M.

K.-D. Langer, J. Grubor, O. Bouchet, M. El Tabach, J. Walewski, S. Randel, M. Franke, S. Nerreter, D. O’Brien, G. Faulkner, I. Neokosmidis, G. Ntogari, and M. Wolf, “Optical wireless communications for broadband access in home area networks,” in Proc. of the 10th Anniversary Int. Conf. on Transparent Optical Networks (ICTON), Athens, Greece, June 22–26, 2008, vol. 4, pp. 149–154.

Elgala, H.

H. Elgala, R. Mesleh, and H. Haas, “Indoor optical wireless communication: Potential and state-of-the-art,” IEEE Commun. Mag., vol. 49, no. 9, pp. 56–62, Sept.2011.
[CrossRef]

R. Mesleh, H. Elgala, and H. Haas, “On the performance of different OFDM based optical wireless communication systems,” J. Opt. Commun. Netw., vol. 3, no. 8, pp. 620–628, Aug.2011.
[CrossRef]

H. Elgala, R. Mesleh, and H. Haas, “An LED model for intensity-modulated optical communication systems,” IEEE Photon. Technol. Lett., vol. 22, no. 11, pp. 835–837, June2010.
[CrossRef]

H. Elgala, R. Mesleh, and H. Haas, “Indoor broadcasting via white LEDs and OFDM,” IEEE Trans. Consum. Electron., vol. 55, no. 3, pp. 1127–1134, Aug.2009.
[CrossRef]

H. Elgala, R. Mesleh, and H. Haas, “Non-linearity effects and predistortion in optical OFDM wireless transmission using LEDs,” Inderscience Int. J. Ultra Wideband Commun. Syst. (IJUWBCS), vol. 1, no. 2, pp. 143–150, 2009.
[CrossRef]

R. Mesleh, R. Mehmood, H. Elgala, and H. Haas, “An overview of indoor OFDM/DMT optical wireless communication systems,” in 7th Int. Symp. on Communication Systems, Networks and Digital Signal Processing (CSNDSP), Newcastle, UK, July 21–23, 2010, pp. 566–570.

H. Elgala, R. Mesleh, and H. Haas, “Modeling for predistortion of LEDs in optical wireless transmission using OFDM,” in Proc. of the IEEE 10th Int. Conf. on Hybrid Intelligent Systems (HIS), Shenyang Liaoning, China, Aug. 12–14, 2009.

H. Elgala, R. Mesleh, and H. Haas, “A study of LED nonlinearity effects on optical wireless transmission using OFDM,” in Proc. of the 6th IEEE Int. Conf. on Wireless and Optical Communications Networks (WOCN), Cairo, Egypt, Apr. 28–30, 2009.

H. Elgala, R. Mesleh, and H. Haas, “Practical considerations for indoor wireless optical system implementation using OFDM,” in Proc. of the IEEE 10th Int. Conf. on Telecommunications (ConTel), Zagreb, Croatia, June 8–10, 2009.

M. Afgani, H. Haas, H. Elgala, and D. Knipp, “Visible light communication using OFDM,” in Proc. of the 2nd Int. Conf. on Testbeds and Research Infrastructures for the Development of Networks and Communities (TRIDENTCOM), Barcelona, Spain, Mar. 1–3, 2006, pp. 129–134.

H. Elgala, R. Mesleh, H. Haas, and B. Pricope, “OFDM visible light wireless communication based on white LEDs,” in Proc. of the 64th IEEE Vehicular Technology Conf. (VTC), Dublin, Ireland, Apr. 22–25, 2007.

Falconer, D.

D. Falconer, S. Ariyavisitakul, A. Benyamin-Seeyar, and B. Eidson, “Frequency domain equalization for single-carrier broadband wireless systems,” IEEE Commun. Mag., vol. 40, no. 4, pp. 58–66, Apr.2002.
[CrossRef]

Farid, A.

A. Farid and S. Hranilovic, “Capacity bounds for wireless optical intensity channels with Gaussian noise,” IEEE Trans. Inf. Theory, vol. 56, no. 12, pp. 6066–6077, Dec.2010.
[CrossRef]

Faulkner, G.

K.-D. Langer, J. Grubor, O. Bouchet, M. El Tabach, J. Walewski, S. Randel, M. Franke, S. Nerreter, D. O’Brien, G. Faulkner, I. Neokosmidis, G. Ntogari, and M. Wolf, “Optical wireless communications for broadband access in home area networks,” in Proc. of the 10th Anniversary Int. Conf. on Transparent Optical Networks (ICTON), Athens, Greece, June 22–26, 2008, vol. 4, pp. 149–154.

Faulkner, G. E.

D. C. O’Brien, S. H. Khoo, W. Zhang, G. E. Faulkner, and D. J. Edwards, “High-speed optical channel measurement system,” Proc. SPIE, vol. 4530, pp. 135–144, 2001.
[CrossRef]

Franke, M.

K.-D. Langer, J. Grubor, O. Bouchet, M. El Tabach, J. Walewski, S. Randel, M. Franke, S. Nerreter, D. O’Brien, G. Faulkner, I. Neokosmidis, G. Ntogari, and M. Wolf, “Optical wireless communications for broadband access in home area networks,” in Proc. of the 10th Anniversary Int. Conf. on Transparent Optical Networks (ICTON), Athens, Greece, June 22–26, 2008, vol. 4, pp. 149–154.

Green, R. J.

R. J. Green, H. Joshi, M. D. Higgins, and M. S. Leeson, “Recent developments in indoor optical wireless,” IET Commun., vol. 2, no. 1, pp. 3–10, Jan.2008.
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Grubor, J.

K.-D. Langer, J. Grubor, O. Bouchet, M. El Tabach, J. Walewski, S. Randel, M. Franke, S. Nerreter, D. O’Brien, G. Faulkner, I. Neokosmidis, G. Ntogari, and M. Wolf, “Optical wireless communications for broadband access in home area networks,” in Proc. of the 10th Anniversary Int. Conf. on Transparent Optical Networks (ICTON), Athens, Greece, June 22–26, 2008, vol. 4, pp. 149–154.

J. Grubor, S. Randel, K. Langer, and J. Walewski, “Bandwidth efficient indoor optical wireless communications with white light emitting diodes,” in Proc. of the 6th Int. Symp. on Communication Systems, Networks and Digital Signal Processing, Graz, Austria, June 23–25, 2008, vol. 1, pp. 165–169.

Haas, H.

S. Dimitrov, S. Sinanovic, and H. Haas, “Signal shaping and modulation for optical wireless communication,” J. Lightwave Technol., vol. 30, no. 9, pp. 1319–1328, May2012.
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R. Mesleh, H. Elgala, and H. Haas, “On the performance of different OFDM based optical wireless communication systems,” J. Opt. Commun. Netw., vol. 3, no. 8, pp. 620–628, Aug.2011.
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H. Elgala, R. Mesleh, and H. Haas, “Indoor optical wireless communication: Potential and state-of-the-art,” IEEE Commun. Mag., vol. 49, no. 9, pp. 56–62, Sept.2011.
[CrossRef]

H. Elgala, R. Mesleh, and H. Haas, “An LED model for intensity-modulated optical communication systems,” IEEE Photon. Technol. Lett., vol. 22, no. 11, pp. 835–837, June2010.
[CrossRef]

H. Elgala, R. Mesleh, and H. Haas, “Indoor broadcasting via white LEDs and OFDM,” IEEE Trans. Consum. Electron., vol. 55, no. 3, pp. 1127–1134, Aug.2009.
[CrossRef]

H. Elgala, R. Mesleh, and H. Haas, “Non-linearity effects and predistortion in optical OFDM wireless transmission using LEDs,” Inderscience Int. J. Ultra Wideband Commun. Syst. (IJUWBCS), vol. 1, no. 2, pp. 143–150, 2009.
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S. Dimitrov and H. Haas, “On the clipping noise in an ACO-OFDM optical wireless communication system,” in Proc. of IEEE Global Communications Conf. (IEEE GLOBECOM), Miami, FL, Dec. 6–10, 2010.

R. Mesleh, R. Mehmood, H. Elgala, and H. Haas, “An overview of indoor OFDM/DMT optical wireless communication systems,” in 7th Int. Symp. on Communication Systems, Networks and Digital Signal Processing (CSNDSP), Newcastle, UK, July 21–23, 2010, pp. 566–570.

H. Elgala, R. Mesleh, and H. Haas, “Modeling for predistortion of LEDs in optical wireless transmission using OFDM,” in Proc. of the IEEE 10th Int. Conf. on Hybrid Intelligent Systems (HIS), Shenyang Liaoning, China, Aug. 12–14, 2009.

H. Elgala, R. Mesleh, and H. Haas, “A study of LED nonlinearity effects on optical wireless transmission using OFDM,” in Proc. of the 6th IEEE Int. Conf. on Wireless and Optical Communications Networks (WOCN), Cairo, Egypt, Apr. 28–30, 2009.

H. Elgala, R. Mesleh, H. Haas, and B. Pricope, “OFDM visible light wireless communication based on white LEDs,” in Proc. of the 64th IEEE Vehicular Technology Conf. (VTC), Dublin, Ireland, Apr. 22–25, 2007.

M. Afgani, H. Haas, H. Elgala, and D. Knipp, “Visible light communication using OFDM,” in Proc. of the 2nd Int. Conf. on Testbeds and Research Infrastructures for the Development of Networks and Communities (TRIDENTCOM), Barcelona, Spain, Mar. 1–3, 2006, pp. 129–134.

H. Elgala, R. Mesleh, and H. Haas, “Practical considerations for indoor wireless optical system implementation using OFDM,” in Proc. of the IEEE 10th Int. Conf. on Telecommunications (ConTel), Zagreb, Croatia, June 8–10, 2009.

Haruyama, S.

Y. Tanaka, T. Komine, S. Haruyama, and M. Nakagawa, “Indoor visible light data transmission system utilizing white LED lights,” IEICE Trans. Commun., vol. E86-B, no. 8, pp. 2440–2454, Aug.2003.

Y. Tanaka, T. Komine, S. Haruyama, and M. Nakagawa, “Indoor visible communication utilizing plural white LEDs as lighting,” in Proc. of the 12th IEEE Int. Symp. on Personal, Indoor and Mobile Radio Communications, San Diego, CA, Sept. 30–Oct. 3, 2001, vol. 2, pp. 81–85.

Higgins, M. D.

R. J. Green, H. Joshi, M. D. Higgins, and M. S. Leeson, “Recent developments in indoor optical wireless,” IET Commun., vol. 2, no. 1, pp. 3–10, Jan.2008.
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A. Farid and S. Hranilovic, “Capacity bounds for wireless optical intensity channels with Gaussian noise,” IEEE Trans. Inf. Theory, vol. 56, no. 12, pp. 6066–6077, Dec.2010.
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W. Kang and S. Hranilovic, “Power reduction techniques for multiple-subcarrier modulated diffuse wireless optical channels,” IEEE Trans. Commun., vol. 56, no. 2, pp. 279–288, Feb.2008.
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Hwang, S. U.

S. U. Hwang, S. Jeon, S. Lee, and J. Seo, “Soft-output ML detector for spatial modulation OFDM systems,” IEICE Electron. Express, vol. 6, no. 19, pp. 1426–1431, Oct.2009.
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Jafarkhani, H.

V. Tarokh and H. Jafarkhani, “On the computation and reduction of the peak-to-average power ratio in multicarrier communications,” IEEE Trans. Commun., vol. 48, no. 1, pp. 37–44, Jan.2000.
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Jayalath, A.

A. Jayalath and C. Tellambura, “Reducing the peak-to-average power ratio of orthogonal frequency division multiplexing signal through bit or symbol interleaving,” Electron. Lett., vol. 36, no. 13, pp. 1161–1163, June2000.
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J. Davis and J. Jedwab, “Peak-to-mean power control in OFDM, Golay complementary sequences, and Reed-Muller codes,” IEEE Trans. Inf. Theory, vol. 45, no. 7, pp. 2397–2417, Nov.1999.
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Jeon, S.

S. U. Hwang, S. Jeon, S. Lee, and J. Seo, “Soft-output ML detector for spatial modulation OFDM systems,” IEICE Electron. Express, vol. 6, no. 19, pp. 1426–1431, Oct.2009.
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Joshi, H.

R. J. Green, H. Joshi, M. D. Higgins, and M. S. Leeson, “Recent developments in indoor optical wireless,” IET Commun., vol. 2, no. 1, pp. 3–10, Jan.2008.
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Kahn, J.

J. Barry, J. Kahn, W. Krause, E. Lee, and D. Messerschmitt, “Simulation of multipath impulse response for indoor wireless optical channels,” IEEE J. Sel. Areas Commun., vol. 11, no. 3, pp. 367–379, Apr.1993.
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J. M. Kahn and J. R. Barry, “Wireless infrared communications,” Proc. IEEE, vol. 85, no. 2, pp. 265–298, Feb.1997.
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Kang, W.

W. Kang and S. Hranilovic, “Power reduction techniques for multiple-subcarrier modulated diffuse wireless optical channels,” IEEE Trans. Commun., vol. 56, no. 2, pp. 279–288, Feb.2008.
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Khoo, S. H.

D. C. O’Brien, S. H. Khoo, W. Zhang, G. E. Faulkner, and D. J. Edwards, “High-speed optical channel measurement system,” Proc. SPIE, vol. 4530, pp. 135–144, 2001.
[CrossRef]

Knipp, D.

M. Afgani, H. Haas, H. Elgala, and D. Knipp, “Visible light communication using OFDM,” in Proc. of the 2nd Int. Conf. on Testbeds and Research Infrastructures for the Development of Networks and Communities (TRIDENTCOM), Barcelona, Spain, Mar. 1–3, 2006, pp. 129–134.

Komine, T.

Y. Tanaka, T. Komine, S. Haruyama, and M. Nakagawa, “Indoor visible light data transmission system utilizing white LED lights,” IEICE Trans. Commun., vol. E86-B, no. 8, pp. 2440–2454, Aug.2003.

Y. Tanaka, T. Komine, S. Haruyama, and M. Nakagawa, “Indoor visible communication utilizing plural white LEDs as lighting,” in Proc. of the 12th IEEE Int. Symp. on Personal, Indoor and Mobile Radio Communications, San Diego, CA, Sept. 30–Oct. 3, 2001, vol. 2, pp. 81–85.

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., vol. 21, no. 23, pp. 1749–1751, Dec.2009.
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Krause, W.

J. Barry, J. Kahn, W. Krause, E. Lee, and D. Messerschmitt, “Simulation of multipath impulse response for indoor wireless optical channels,” IEEE J. Sel. Areas Commun., vol. 11, no. 3, pp. 367–379, Apr.1993.
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Langer, K.

J. Grubor, S. Randel, K. Langer, and J. Walewski, “Bandwidth efficient indoor optical wireless communications with white light emitting diodes,” in Proc. of the 6th Int. Symp. on Communication Systems, Networks and Digital Signal Processing, Graz, Austria, June 23–25, 2008, vol. 1, pp. 165–169.

Langer, K.-D.

K.-D. Langer, J. Grubor, O. Bouchet, M. El Tabach, J. Walewski, S. Randel, M. Franke, S. Nerreter, D. O’Brien, G. Faulkner, I. Neokosmidis, G. Ntogari, and M. Wolf, “Optical wireless communications for broadband access in home area networks,” in Proc. of the 10th Anniversary Int. Conf. on Transparent Optical Networks (ICTON), Athens, Greece, June 22–26, 2008, vol. 4, pp. 149–154.

Lee, E.

J. Barry, J. Kahn, W. Krause, E. Lee, and D. Messerschmitt, “Simulation of multipath impulse response for indoor wireless optical channels,” IEEE J. Sel. Areas Commun., vol. 11, no. 3, pp. 367–379, Apr.1993.
[CrossRef]

Lee, S.

S. U. Hwang, S. Jeon, S. Lee, and J. Seo, “Soft-output ML detector for spatial modulation OFDM systems,” IEICE Electron. Express, vol. 6, no. 19, pp. 1426–1431, Oct.2009.
[CrossRef]

Lee, S. C. J.

S. Randel, F. Breyer, S. C. J. Lee, and J. W. Walewski, “Advanced modulation schemes for short-range optical communications,” IEEE J. Sel. Top. Quantum Electron., vol. 16, no. 5, pp. 1280–1289, 2010.
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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., vol. 21, no. 23, pp. 1749–1751, Dec.2009.
[CrossRef]

Leeson, M. S.

R. J. Green, H. Joshi, M. D. Higgins, and M. S. Leeson, “Recent developments in indoor optical wireless,” IET Commun., vol. 2, no. 1, pp. 3–10, Jan.2008.
[CrossRef]

Lowery, A.

J. Armstrong and A. Lowery, “Power efficient optical OFDM,” Electron. Lett., vol. 42, no. 6, pp. 370–372, Mar.2006.
[CrossRef]

Mehmood, R.

R. Mesleh, R. Mehmood, H. Elgala, and H. Haas, “An overview of indoor OFDM/DMT optical wireless communication systems,” in 7th Int. Symp. on Communication Systems, Networks and Digital Signal Processing (CSNDSP), Newcastle, UK, July 21–23, 2010, pp. 566–570.

Mesleh, R.

H. Elgala, R. Mesleh, and H. Haas, “Indoor optical wireless communication: Potential and state-of-the-art,” IEEE Commun. Mag., vol. 49, no. 9, pp. 56–62, Sept.2011.
[CrossRef]

R. Mesleh, H. Elgala, and H. Haas, “On the performance of different OFDM based optical wireless communication systems,” J. Opt. Commun. Netw., vol. 3, no. 8, pp. 620–628, Aug.2011.
[CrossRef]

H. Elgala, R. Mesleh, and H. Haas, “An LED model for intensity-modulated optical communication systems,” IEEE Photon. Technol. Lett., vol. 22, no. 11, pp. 835–837, June2010.
[CrossRef]

H. Elgala, R. Mesleh, and H. Haas, “Indoor broadcasting via white LEDs and OFDM,” IEEE Trans. Consum. Electron., vol. 55, no. 3, pp. 1127–1134, Aug.2009.
[CrossRef]

H. Elgala, R. Mesleh, and H. Haas, “Non-linearity effects and predistortion in optical OFDM wireless transmission using LEDs,” Inderscience Int. J. Ultra Wideband Commun. Syst. (IJUWBCS), vol. 1, no. 2, pp. 143–150, 2009.
[CrossRef]

R. Mesleh, R. Mehmood, H. Elgala, and H. Haas, “An overview of indoor OFDM/DMT optical wireless communication systems,” in 7th Int. Symp. on Communication Systems, Networks and Digital Signal Processing (CSNDSP), Newcastle, UK, July 21–23, 2010, pp. 566–570.

R. Mesleh, “OFDM and SCFDE performance comparison for indoor optical wireless communication systems,” in 19th Int. Conf. on Telecommunications (ICT), Jounieh, Lebanon, Apr. 23–25, 2012.

H. Elgala, R. Mesleh, and H. Haas, “A study of LED nonlinearity effects on optical wireless transmission using OFDM,” in Proc. of the 6th IEEE Int. Conf. on Wireless and Optical Communications Networks (WOCN), Cairo, Egypt, Apr. 28–30, 2009.

H. Elgala, R. Mesleh, and H. Haas, “Modeling for predistortion of LEDs in optical wireless transmission using OFDM,” in Proc. of the IEEE 10th Int. Conf. on Hybrid Intelligent Systems (HIS), Shenyang Liaoning, China, Aug. 12–14, 2009.

H. Elgala, R. Mesleh, and H. Haas, “Practical considerations for indoor wireless optical system implementation using OFDM,” in Proc. of the IEEE 10th Int. Conf. on Telecommunications (ConTel), Zagreb, Croatia, June 8–10, 2009.

H. Elgala, R. Mesleh, H. Haas, and B. Pricope, “OFDM visible light wireless communication based on white LEDs,” in Proc. of the 64th IEEE Vehicular Technology Conf. (VTC), Dublin, Ireland, Apr. 22–25, 2007.

Messerschmitt, D.

J. Barry, J. Kahn, W. Krause, E. Lee, and D. Messerschmitt, “Simulation of multipath impulse response for indoor wireless optical channels,” IEEE J. Sel. Areas Commun., vol. 11, no. 3, pp. 367–379, Apr.1993.
[CrossRef]

Nakagawa, M.

Y. Tanaka, T. Komine, S. Haruyama, and M. Nakagawa, “Indoor visible light data transmission system utilizing white LED lights,” IEICE Trans. Commun., vol. E86-B, no. 8, pp. 2440–2454, Aug.2003.

Y. Tanaka, T. Komine, S. Haruyama, and M. Nakagawa, “Indoor visible communication utilizing plural white LEDs as lighting,” in Proc. of the 12th IEEE Int. Symp. on Personal, Indoor and Mobile Radio Communications, San Diego, CA, Sept. 30–Oct. 3, 2001, vol. 2, pp. 81–85.

Neokosmidis, I.

K.-D. Langer, J. Grubor, O. Bouchet, M. El Tabach, J. Walewski, S. Randel, M. Franke, S. Nerreter, D. O’Brien, G. Faulkner, I. Neokosmidis, G. Ntogari, and M. Wolf, “Optical wireless communications for broadband access in home area networks,” in Proc. of the 10th Anniversary Int. Conf. on Transparent Optical Networks (ICTON), Athens, Greece, June 22–26, 2008, vol. 4, pp. 149–154.

Nerreter, S.

K.-D. Langer, J. Grubor, O. Bouchet, M. El Tabach, J. Walewski, S. Randel, M. Franke, S. Nerreter, D. O’Brien, G. Faulkner, I. Neokosmidis, G. Ntogari, and M. Wolf, “Optical wireless communications for broadband access in home area networks,” in Proc. of the 10th Anniversary Int. Conf. on Transparent Optical Networks (ICTON), Athens, Greece, June 22–26, 2008, vol. 4, pp. 149–154.

Ntogari, G.

K.-D. Langer, J. Grubor, O. Bouchet, M. El Tabach, J. Walewski, S. Randel, M. Franke, S. Nerreter, D. O’Brien, G. Faulkner, I. Neokosmidis, G. Ntogari, and M. Wolf, “Optical wireless communications for broadband access in home area networks,” in Proc. of the 10th Anniversary Int. Conf. on Transparent Optical Networks (ICTON), Athens, Greece, June 22–26, 2008, vol. 4, pp. 149–154.

O’Brien, D.

D. O’Brien, G. Parry, and P. Stavrinou, “Optical hotspots speed up wireless communication,” Nat. Photonics, vol. 1, pp. 245–247, 2007.
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K.-D. Langer, J. Grubor, O. Bouchet, M. El Tabach, J. Walewski, S. Randel, M. Franke, S. Nerreter, D. O’Brien, G. Faulkner, I. Neokosmidis, G. Ntogari, and M. Wolf, “Optical wireless communications for broadband access in home area networks,” in Proc. of the 10th Anniversary Int. Conf. on Transparent Optical Networks (ICTON), Athens, Greece, June 22–26, 2008, vol. 4, pp. 149–154.

O’Brien, D. C.

D. C. O’Brien, S. H. Khoo, W. Zhang, G. E. Faulkner, and D. J. Edwards, “High-speed optical channel measurement system,” Proc. SPIE, vol. 4530, pp. 135–144, 2001.
[CrossRef]

A. M. Street, P. N. Stavrinou, D. C. O’Brien, and D. J. Edwards, “Indoor optical wireless systems—A review,” Opt. Quantum Electron., vol. 29, no. 3, pp. 349–378, Mar.1997.
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Parry, G.

D. O’Brien, G. Parry, and P. Stavrinou, “Optical hotspots speed up wireless communication,” Nat. Photonics, vol. 1, pp. 245–247, 2007.
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Pricope, B.

H. Elgala, R. Mesleh, H. Haas, and B. Pricope, “OFDM visible light wireless communication based on white LEDs,” in Proc. of the 64th IEEE Vehicular Technology Conf. (VTC), Dublin, Ireland, Apr. 22–25, 2007.

Randel, S.

S. Randel, F. Breyer, S. C. J. Lee, and J. W. Walewski, “Advanced modulation schemes for short-range optical communications,” IEEE J. Sel. Top. Quantum Electron., vol. 16, no. 5, pp. 1280–1289, 2010.
[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., vol. 21, no. 23, pp. 1749–1751, Dec.2009.
[CrossRef]

K.-D. Langer, J. Grubor, O. Bouchet, M. El Tabach, J. Walewski, S. Randel, M. Franke, S. Nerreter, D. O’Brien, G. Faulkner, I. Neokosmidis, G. Ntogari, and M. Wolf, “Optical wireless communications for broadband access in home area networks,” in Proc. of the 10th Anniversary Int. Conf. on Transparent Optical Networks (ICTON), Athens, Greece, June 22–26, 2008, vol. 4, pp. 149–154.

J. Grubor, S. Randel, K. Langer, and J. Walewski, “Bandwidth efficient indoor optical wireless communications with white light emitting diodes,” in Proc. of the 6th Int. Symp. on Communication Systems, Networks and Digital Signal Processing, Graz, Austria, June 23–25, 2008, vol. 1, pp. 165–169.

Sari, H.

C. Ciochina and H. Sari, “A review of OFDMA and single-carrier FDMA and some recent results,” IEEE Adv. Electron. Telecommun., vol. 1, no. 1, pp. 706–710, Apr.2010.

Seo, J.

S. U. Hwang, S. Jeon, S. Lee, and J. Seo, “Soft-output ML detector for spatial modulation OFDM systems,” IEICE Electron. Express, vol. 6, no. 19, pp. 1426–1431, Oct.2009.
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Sinanovic, S.

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Stavrinou, P.

D. O’Brien, G. Parry, and P. Stavrinou, “Optical hotspots speed up wireless communication,” Nat. Photonics, vol. 1, pp. 245–247, 2007.
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Stavrinou, P. N.

A. M. Street, P. N. Stavrinou, D. C. O’Brien, and D. J. Edwards, “Indoor optical wireless systems—A review,” Opt. Quantum Electron., vol. 29, no. 3, pp. 349–378, Mar.1997.
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Street, A. M.

A. M. Street, P. N. Stavrinou, D. C. O’Brien, and D. J. Edwards, “Indoor optical wireless systems—A review,” Opt. Quantum Electron., vol. 29, no. 3, pp. 349–378, Mar.1997.
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Tanaka, Y.

Y. Tanaka, T. Komine, S. Haruyama, and M. Nakagawa, “Indoor visible light data transmission system utilizing white LED lights,” IEICE Trans. Commun., vol. E86-B, no. 8, pp. 2440–2454, Aug.2003.

Y. Tanaka, T. Komine, S. Haruyama, and M. Nakagawa, “Indoor visible communication utilizing plural white LEDs as lighting,” in Proc. of the 12th IEEE Int. Symp. on Personal, Indoor and Mobile Radio Communications, San Diego, CA, Sept. 30–Oct. 3, 2001, vol. 2, pp. 81–85.

Tarokh, V.

V. Tarokh and H. Jafarkhani, “On the computation and reduction of the peak-to-average power ratio in multicarrier communications,” IEEE Trans. Commun., vol. 48, no. 1, pp. 37–44, Jan.2000.
[CrossRef]

Tellambura, C.

A. Jayalath and C. Tellambura, “Reducing the peak-to-average power ratio of orthogonal frequency division multiplexing signal through bit or symbol interleaving,” Electron. Lett., vol. 36, no. 13, pp. 1161–1163, June2000.
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Tomasin, S.

N. Benvenuto and S. Tomasin, “On the comparison between OFDM and single carrier modulation with a DFE using a frequency-domain feedforward filter,” IEEE Trans. Commun., vol. 50, no. 6, pp. 947–955, June2002.
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Walewski, J.

J. Grubor, S. Randel, K. Langer, and J. Walewski, “Bandwidth efficient indoor optical wireless communications with white light emitting diodes,” in Proc. of the 6th Int. Symp. on Communication Systems, Networks and Digital Signal Processing, Graz, Austria, June 23–25, 2008, vol. 1, pp. 165–169.

K.-D. Langer, J. Grubor, O. Bouchet, M. El Tabach, J. Walewski, S. Randel, M. Franke, S. Nerreter, D. O’Brien, G. Faulkner, I. Neokosmidis, G. Ntogari, and M. Wolf, “Optical wireless communications for broadband access in home area networks,” in Proc. of the 10th Anniversary Int. Conf. on Transparent Optical Networks (ICTON), Athens, Greece, June 22–26, 2008, vol. 4, pp. 149–154.

Walewski, J. W.

S. Randel, F. Breyer, S. C. J. Lee, and J. W. Walewski, “Advanced modulation schemes for short-range optical communications,” IEEE J. Sel. Top. Quantum Electron., vol. 16, no. 5, pp. 1280–1289, 2010.
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S. Wilson and J. Armstrong, “Transmitter and receiver methods for improving asymmetrically-clipped optical OFDM,” IEEE Trans. Wireless Commun., vol. 8, no. 9, pp. 4561–4567, Sept.2009.
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Wolf, M.

K.-D. Langer, J. Grubor, O. Bouchet, M. El Tabach, J. Walewski, S. Randel, M. Franke, S. Nerreter, D. O’Brien, G. Faulkner, I. Neokosmidis, G. Ntogari, and M. Wolf, “Optical wireless communications for broadband access in home area networks,” in Proc. of the 10th Anniversary Int. Conf. on Transparent Optical Networks (ICTON), Athens, Greece, June 22–26, 2008, vol. 4, pp. 149–154.

Yoon, D.

K. Cho and D. Yoon, “On the general BER expression of one- and two-dimensional amplitude modulations,” IEEE Trans. Commun., vol. 50, no. 7, pp. 1074–1080, July2002.
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Zhang, W.

D. C. O’Brien, S. H. Khoo, W. Zhang, G. E. Faulkner, and D. J. Edwards, “High-speed optical channel measurement system,” Proc. SPIE, vol. 4530, pp. 135–144, 2001.
[CrossRef]

Electron. Lett. (2)

J. Armstrong and A. Lowery, “Power efficient optical OFDM,” Electron. Lett., vol. 42, no. 6, pp. 370–372, Mar.2006.
[CrossRef]

A. Jayalath and C. Tellambura, “Reducing the peak-to-average power ratio of orthogonal frequency division multiplexing signal through bit or symbol interleaving,” Electron. Lett., vol. 36, no. 13, pp. 1161–1163, June2000.
[CrossRef]

IEEE Adv. Electron. Telecommun. (1)

C. Ciochina and H. Sari, “A review of OFDMA and single-carrier FDMA and some recent results,” IEEE Adv. Electron. Telecommun., vol. 1, no. 1, pp. 706–710, Apr.2010.

IEEE Commun. Mag. (2)

D. Falconer, S. Ariyavisitakul, A. Benyamin-Seeyar, and B. Eidson, “Frequency domain equalization for single-carrier broadband wireless systems,” IEEE Commun. Mag., vol. 40, no. 4, pp. 58–66, Apr.2002.
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H. Elgala, R. Mesleh, and H. Haas, “Indoor optical wireless communication: Potential and state-of-the-art,” IEEE Commun. Mag., vol. 49, no. 9, pp. 56–62, Sept.2011.
[CrossRef]

IEEE J. Sel. Areas Commun. (1)

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Figures (14)

Fig. 1
Fig. 1

OW SC-FDMA system model.

Fig. 2
Fig. 2

(Color online) CDF plots of PAPR from ACO and SC-FDMA transmitters with N = 2048 and N = 64 subcarriers and 16QAM modulation.

Fig. 3
Fig. 3

Rate 1/2 convolutional encoder and state transition diagram.

Fig. 4
Fig. 4

Iterative signal clipping and multiple LED assignments system model.

Fig. 5
Fig. 5

(Color online) Signal clipping and LED assignments for the DCO system. The OFDM signal has an electrical average power of 20 dBm, and a 256 QAM constellation is considered. The permissible difference between the maximum voltage and the minimum voltage before clipping is 0.5 V. The positive signal is clipped at 0.25 V, and the negative signal is clipped at −0.25 V. The DC value is set in the middle between the turn-on voltage and the maximum permissible voltage.

Fig. 6
Fig. 6

(Color online) Performance comparison between ACO and SC-FDMA.

Fig. 7
Fig. 7

(Color online) Performance comparison between DCO and SC-FDMA.

Fig. 8
Fig. 8

BER performance of a 64QAM ACO system with hard, soft, and turbo channel coding.

Fig. 9
Fig. 9

BER performance of a 16QAM DCO system with hard, soft, and turbo channel coding.

Fig. 10
Fig. 10

(Color online) Monte Carlo simulation and analytical results for an OW DCO system applying ISC with two transmit LEDs and different modulation orders.

Fig. 11
Fig. 11

(Color online) Monte Carlo simulation and analytical results for an OW ACO system applying ISC with two transmit LEDs and different modulation orders.

Fig. 12
Fig. 12

(Color online) Performance comparison of OW DCO systems with n = 1 and n = 4 and 16QAM and 64QAM modulation orders.

Fig. 13
Fig. 13

(Color online) Simulation results for OW ACO-OFDM and ACO SC-FDMA systems applying ISC with two transmit LEDs and 16QAM modulation order.

Fig. 14
Fig. 14

(Color online) Simulation results for OW DCO OFDM and DCO SC-FDMA systems applying ISC with two transmit LEDs and 16QAM modulation order.

Equations (22)

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s ( k ) = [ 0 s ̌ 0 0 s ̌ 1 0 s ̌ N / 4 0 s ̌ N / 4 * 0 s ̌ 1 * 0 s ̌ 0 * ] T
s ( n ) = 1 N k = 0 N 1 ( ( s ( k ) ) cos ( 2 π k N n ) ( s ( k ) ) sin ( 2 π k N n ) ) + j 1 N k = 0 N 1 ( ( s ( k ) ) sin ( 2 π k N n ) + ( s ( k ) ) cos ( 2 π k N n ) ) = 0 , n = 0 , 1 , , N 1 .
y ( t ) = h ( t ) s ( t ) + w ( t ) ,
s ˆ ( n ) = h ( n ) s ( n ) + w ̃ ( n ) ,
s ˆ ( k ) = H ( k ) s ˆ ( n ) + w ˆ ( k ) ,
s ̇ ( k ) = H o ( k ) s ˆ o ( k ) + w ˆ o ( k ) ,
s ˆ o ( k ) = 1 2 [ s ˆ 0 s ˆ 1 s ˆ N / 4 1 s ˆ N / 4 1 * s ˆ N / 4 2 * s ˆ * 0 ] T .
s ̇ ( k ) = 2 ( H o H H o ) 1 H o H s ˆ o ,
s ( n ) = k = 0 N 1 { x k } cos ( 2 π k n N ) + j k = 0 N 1 { x k } sin ( 2 π k n N ) , n = 0 , 1 , , N 1 ,
F s max 2 ( z ) = ( 1 e z N ) N .
PAPR = s max 2 E [ | s ( n ) | 2 ] = s max 2 N .
Prob ( PAPR > c ) = Prob ( s max 2 > c N ) = ( 1 e c ) N .
L ( ) = log P ( = 1 | y ) P ( = 0 | y ) = log x d S 1 ı p ( y | h ) x d S 0 ı p ( y | h ) = log x d S 1 ı exp ( y h x d 2 σ w 2 ) x d S 0 ı exp ( y h x d 2 σ w 2 ) ,
{ s k } k = 0 N 1 = [ 0 { x k } k = 1 N / 2 1 0 { x k * } k = N / 2 1 1 ] .
g ( t ) = h 1 ( t ) y 1 ( t ) + h 2 ( t ) y 2 ( t ) + + h n ( t ) y n ( t ) + w ( t ) ,
H ( t ) = [ 9 . 93 × 1 0 6 8 . 87 × 1 0 7 6 . 98 × 1 0 7 9 . 29 × 1 0 6 8 . 76 × 1 0 7 6 . 93 × 1 0 7 9 . 82 × 1 0 6 9 . 12 × 1 0 7 6 . 94 × 1 0 7 9 . 18 × 1 0 6 9 . 00 × 1 0 7 6 . 89 × 1 0 7 ] ,
g ( t ) = h ( t ) [ y 1 ( t ) + y 2 ( t ) + + y n ( t ) ] + w ( t ) .
p ( S n = z ) = p ( z ) = 1 2 π σ s 2 exp ( z 2 2 σ s 2 ) .
ρ = OFDM signal power Effective noise power = σ s 2 σ w 2 + σ clip 2 ,
σ clip 2 = σ uc 2 + σ lc 2 ,
σ clip 2 n V + ( z n V + ) 2 p ( z ) d z + n V ( z n V ) 2 p ( z ) d z .
BER { M 1 M log 2 M erfc ( 3 ρ 2 ( M 1 ) ) , square M -QAM 1 log 2 ( I × J ) [ I 1 I erfc ( 3 ρ I 2 + J 2 2 ) + J 1 J erfc ( 3 ρ I 2 + J 2 2 ) ] , M = I × J rectangular QAM    ,