Abstract

In this paper, we propose a novel method to reduce the high peak-to-average power ratio (PAPR) of the optical orthogonal frequency division multiplexing (OFDM) signal. The method is based on the technique of the Hadamard transform combined with a companding transform. We experimentally demonstrate that, in an optical intensity-modulation direct-detection OFDM transmission system, the hybrid method has better performance in reducing the PAPR compared with the case of applying only the Hadamard transform or only a companding transform.

© 2012 OSA

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References

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  1. A. J. Lowery, L. B. Du, and J. Armstrong, “Performance of optical OFDM in ultralong-haul WDM lightwave systems,” J. Lightwave Technol., vol. 25, pp. 131–138, Jan.2007.
    [CrossRef]
  2. W. Shieh, X. Yi, Y. Ma, and Y. Tang, “Theoretical and experimental study on PMD-supported transmission using polarization diversity in coherent optical OFDM systems,” Opt. Express, vol. 15, pp. 9936–9947, July2007.
    [CrossRef] [PubMed]
  3. J. Yu, M. F. Huang, D. Qian, L. Chen, and G.-K. Chang, “Centralized lightwave WDM-PON employing 16-QAM intensity modulated OFDM downstream and OOK modulated upstream signals,” IEEE Photon. Technol. Lett., vol. 20, pp. 1545–1546, Sept.2008.
    [CrossRef]
  4. J. Armstrong, “OFDM for optical communications,” J. Lightwave Technol., vol. 27, pp. 189–204, Feb.2009.
    [CrossRef]
  5. D. Qian, N. Cvijetic, Y. K. Huang, J. Yu, and T. Wang, “100 km long reach upstream 36 Gb/s-OFDMA-PON over a single wavelength with source-free ONUs,” in 35th European Conf. on Optical Communication (ECOC), Vienna, Austria, 20–24 Sept. 2009, 8.5.1.
  6. Y. Gao, J. Yu, J. Xiao, Z. Cao, F. Li, and L. Chen, “Direct-detection optical OFDM transmission system with pre-emphasis technique,” J. Lightwave Technol., vol. 29, pp. 2138–2145, July2011.
    [CrossRef]
  7. H. Takahashi, “Coherent OFDM transmission with high spectral efficiency,” in 35th European Conf. on Optical Communication (ECOC), Vienna, Austria, 20–24 Sept. 2009, 1.3.3.
  8. M. Schuster, S. Randel, C. A. Bunge, S. C. J. Lee, F. Breyer, B. Spinnler, and K. Petermann, “Spectrally efficient compatible single-sideband modulation for OFDM transmission with direct detection,” IEEE Photon. Technol. Lett., vol. 20, pp. 670–672, May2008.
    [CrossRef]
  9. Z. Cao, J. Yu, M. Xia, Q. Tang, Y. Gao, W. Wang, and L. Chen, “Reduction of intersubcarrier interference and frequency-selective fading in OFDM-ROF systems,” J. Lightwave Technol., vol. 28, pp. 2423–2429, Aug.2010.
    [CrossRef]
  10. B. J. C. Schmidt, A. J. Lowery, and J. Armstrong, “Experimental demonstrations of electronic dispersion compensation for long-haul transmission using direct-detection optical OFDM,” J. Lightwave Technol., vol. 26, pp. 196–203, Jan.2008.
    [CrossRef]
  11. B. Goebel, B. Fesl, L. D. Coelho, and N. Hanik, “On the effect of FWM in coherent optical OFDM systems,” in Optical Fiber Communication Conf. and Expo. and the Nat. Fiber Optic Engineers Conf. (OFC/NFOEC), San Diego, CA, USA, 24–28 Feb. 2008, JWA58.
  12. B. S. Krongold and W. Shieh, “Fiber nonlinearity mitigation by PAPR reduction in coherent optical OFDM systems via active constellation extension,” in 34th European Conf. on Optical Communication (ECOC), Brussels, Belgium, 21–25 Sept. 2008, P.4.13.
  13. Ö. Bulakci, M. Schuster, C.-A. Bunge, and B. Spinnler, “Reduced complexity precoding based peak-to-average power ratio reduction applied to optical direct-detection OFDM,” in 34th European Conf. on Optical Communication (ECOC), Brussels, Belgium, 21–25 Sept. 2008, P.4.11.
  14. X. B. Wang, T. T. Tjhung, and C. S. Ng, “Reduction of peak-to-average power ratio of OFDM system using a companding technique,” IEEE Trans. Broadcast., vol. 45, pp. 303–307, Sept.1999.
    [CrossRef]
  15. M. Park, H. Jun, J. Cho, N. Cho, D. Hong, and C. Kang, “PAPR reduction in OFDM transmission using Hadamard transform,” in IEEE Int. Conf. on Communications, Jan. 2000, vol. 1, pp. 430–433.
  16. Z. Wang, S. Zhang, and B. Qiu, “PAPR reduction of OFDM signal by using Hadamard transform in companding techniques,” in 12th IEEE Int. Conf. on Communication Technology (ICCT), Nanjing, China, 11–14 Nov. 2010, pp. 320–323.
  17. T. C. Pratt, N. Jones, L. Srnee, and M. Torrey, “OFDM link performance with companding for PAPR reduction in the presence of nonlinear amplification,” IEEE Trans. Broadcast., vol. 52, pp. 261–267, June2006.
    [CrossRef]

2011 (1)

2010 (1)

2009 (1)

2008 (3)

J. Yu, M. F. Huang, D. Qian, L. Chen, and G.-K. Chang, “Centralized lightwave WDM-PON employing 16-QAM intensity modulated OFDM downstream and OOK modulated upstream signals,” IEEE Photon. Technol. Lett., vol. 20, pp. 1545–1546, Sept.2008.
[CrossRef]

B. J. C. Schmidt, A. J. Lowery, and J. Armstrong, “Experimental demonstrations of electronic dispersion compensation for long-haul transmission using direct-detection optical OFDM,” J. Lightwave Technol., vol. 26, pp. 196–203, Jan.2008.
[CrossRef]

M. Schuster, S. Randel, C. A. Bunge, S. C. J. Lee, F. Breyer, B. Spinnler, and K. Petermann, “Spectrally efficient compatible single-sideband modulation for OFDM transmission with direct detection,” IEEE Photon. Technol. Lett., vol. 20, pp. 670–672, May2008.
[CrossRef]

2007 (2)

2006 (1)

T. C. Pratt, N. Jones, L. Srnee, and M. Torrey, “OFDM link performance with companding for PAPR reduction in the presence of nonlinear amplification,” IEEE Trans. Broadcast., vol. 52, pp. 261–267, June2006.
[CrossRef]

1999 (1)

X. B. Wang, T. T. Tjhung, and C. S. Ng, “Reduction of peak-to-average power ratio of OFDM system using a companding technique,” IEEE Trans. Broadcast., vol. 45, pp. 303–307, Sept.1999.
[CrossRef]

Armstrong, J.

Breyer, F.

M. Schuster, S. Randel, C. A. Bunge, S. C. J. Lee, F. Breyer, B. Spinnler, and K. Petermann, “Spectrally efficient compatible single-sideband modulation for OFDM transmission with direct detection,” IEEE Photon. Technol. Lett., vol. 20, pp. 670–672, May2008.
[CrossRef]

Bulakci, Ö.

Ö. Bulakci, M. Schuster, C.-A. Bunge, and B. Spinnler, “Reduced complexity precoding based peak-to-average power ratio reduction applied to optical direct-detection OFDM,” in 34th European Conf. on Optical Communication (ECOC), Brussels, Belgium, 21–25 Sept. 2008, P.4.11.

Bunge, C. A.

M. Schuster, S. Randel, C. A. Bunge, S. C. J. Lee, F. Breyer, B. Spinnler, and K. Petermann, “Spectrally efficient compatible single-sideband modulation for OFDM transmission with direct detection,” IEEE Photon. Technol. Lett., vol. 20, pp. 670–672, May2008.
[CrossRef]

Bunge, C.-A.

Ö. Bulakci, M. Schuster, C.-A. Bunge, and B. Spinnler, “Reduced complexity precoding based peak-to-average power ratio reduction applied to optical direct-detection OFDM,” in 34th European Conf. on Optical Communication (ECOC), Brussels, Belgium, 21–25 Sept. 2008, P.4.11.

Cao, Z.

Chang, G.-K.

J. Yu, M. F. Huang, D. Qian, L. Chen, and G.-K. Chang, “Centralized lightwave WDM-PON employing 16-QAM intensity modulated OFDM downstream and OOK modulated upstream signals,” IEEE Photon. Technol. Lett., vol. 20, pp. 1545–1546, Sept.2008.
[CrossRef]

Chen, L.

Cho, J.

M. Park, H. Jun, J. Cho, N. Cho, D. Hong, and C. Kang, “PAPR reduction in OFDM transmission using Hadamard transform,” in IEEE Int. Conf. on Communications, Jan. 2000, vol. 1, pp. 430–433.

Cho, N.

M. Park, H. Jun, J. Cho, N. Cho, D. Hong, and C. Kang, “PAPR reduction in OFDM transmission using Hadamard transform,” in IEEE Int. Conf. on Communications, Jan. 2000, vol. 1, pp. 430–433.

Coelho, L. D.

B. Goebel, B. Fesl, L. D. Coelho, and N. Hanik, “On the effect of FWM in coherent optical OFDM systems,” in Optical Fiber Communication Conf. and Expo. and the Nat. Fiber Optic Engineers Conf. (OFC/NFOEC), San Diego, CA, USA, 24–28 Feb. 2008, JWA58.

Cvijetic, N.

D. Qian, N. Cvijetic, Y. K. Huang, J. Yu, and T. Wang, “100 km long reach upstream 36 Gb/s-OFDMA-PON over a single wavelength with source-free ONUs,” in 35th European Conf. on Optical Communication (ECOC), Vienna, Austria, 20–24 Sept. 2009, 8.5.1.

Du, L. B.

Fesl, B.

B. Goebel, B. Fesl, L. D. Coelho, and N. Hanik, “On the effect of FWM in coherent optical OFDM systems,” in Optical Fiber Communication Conf. and Expo. and the Nat. Fiber Optic Engineers Conf. (OFC/NFOEC), San Diego, CA, USA, 24–28 Feb. 2008, JWA58.

Gao, Y.

Goebel, B.

B. Goebel, B. Fesl, L. D. Coelho, and N. Hanik, “On the effect of FWM in coherent optical OFDM systems,” in Optical Fiber Communication Conf. and Expo. and the Nat. Fiber Optic Engineers Conf. (OFC/NFOEC), San Diego, CA, USA, 24–28 Feb. 2008, JWA58.

Hanik, N.

B. Goebel, B. Fesl, L. D. Coelho, and N. Hanik, “On the effect of FWM in coherent optical OFDM systems,” in Optical Fiber Communication Conf. and Expo. and the Nat. Fiber Optic Engineers Conf. (OFC/NFOEC), San Diego, CA, USA, 24–28 Feb. 2008, JWA58.

Hong, D.

M. Park, H. Jun, J. Cho, N. Cho, D. Hong, and C. Kang, “PAPR reduction in OFDM transmission using Hadamard transform,” in IEEE Int. Conf. on Communications, Jan. 2000, vol. 1, pp. 430–433.

Huang, M. F.

J. Yu, M. F. Huang, D. Qian, L. Chen, and G.-K. Chang, “Centralized lightwave WDM-PON employing 16-QAM intensity modulated OFDM downstream and OOK modulated upstream signals,” IEEE Photon. Technol. Lett., vol. 20, pp. 1545–1546, Sept.2008.
[CrossRef]

Huang, Y. K.

D. Qian, N. Cvijetic, Y. K. Huang, J. Yu, and T. Wang, “100 km long reach upstream 36 Gb/s-OFDMA-PON over a single wavelength with source-free ONUs,” in 35th European Conf. on Optical Communication (ECOC), Vienna, Austria, 20–24 Sept. 2009, 8.5.1.

Jones, N.

T. C. Pratt, N. Jones, L. Srnee, and M. Torrey, “OFDM link performance with companding for PAPR reduction in the presence of nonlinear amplification,” IEEE Trans. Broadcast., vol. 52, pp. 261–267, June2006.
[CrossRef]

Jun, H.

M. Park, H. Jun, J. Cho, N. Cho, D. Hong, and C. Kang, “PAPR reduction in OFDM transmission using Hadamard transform,” in IEEE Int. Conf. on Communications, Jan. 2000, vol. 1, pp. 430–433.

Kang, C.

M. Park, H. Jun, J. Cho, N. Cho, D. Hong, and C. Kang, “PAPR reduction in OFDM transmission using Hadamard transform,” in IEEE Int. Conf. on Communications, Jan. 2000, vol. 1, pp. 430–433.

Krongold, B. S.

B. S. Krongold and W. Shieh, “Fiber nonlinearity mitigation by PAPR reduction in coherent optical OFDM systems via active constellation extension,” in 34th European Conf. on Optical Communication (ECOC), Brussels, Belgium, 21–25 Sept. 2008, P.4.13.

Lee, S. C. J.

M. Schuster, S. Randel, C. A. Bunge, S. C. J. Lee, F. Breyer, B. Spinnler, and K. Petermann, “Spectrally efficient compatible single-sideband modulation for OFDM transmission with direct detection,” IEEE Photon. Technol. Lett., vol. 20, pp. 670–672, May2008.
[CrossRef]

Li, F.

Lowery, A. J.

Ma, Y.

Ng, C. S.

X. B. Wang, T. T. Tjhung, and C. S. Ng, “Reduction of peak-to-average power ratio of OFDM system using a companding technique,” IEEE Trans. Broadcast., vol. 45, pp. 303–307, Sept.1999.
[CrossRef]

Park, M.

M. Park, H. Jun, J. Cho, N. Cho, D. Hong, and C. Kang, “PAPR reduction in OFDM transmission using Hadamard transform,” in IEEE Int. Conf. on Communications, Jan. 2000, vol. 1, pp. 430–433.

Petermann, K.

M. Schuster, S. Randel, C. A. Bunge, S. C. J. Lee, F. Breyer, B. Spinnler, and K. Petermann, “Spectrally efficient compatible single-sideband modulation for OFDM transmission with direct detection,” IEEE Photon. Technol. Lett., vol. 20, pp. 670–672, May2008.
[CrossRef]

Pratt, T. C.

T. C. Pratt, N. Jones, L. Srnee, and M. Torrey, “OFDM link performance with companding for PAPR reduction in the presence of nonlinear amplification,” IEEE Trans. Broadcast., vol. 52, pp. 261–267, June2006.
[CrossRef]

Qian, D.

J. Yu, M. F. Huang, D. Qian, L. Chen, and G.-K. Chang, “Centralized lightwave WDM-PON employing 16-QAM intensity modulated OFDM downstream and OOK modulated upstream signals,” IEEE Photon. Technol. Lett., vol. 20, pp. 1545–1546, Sept.2008.
[CrossRef]

D. Qian, N. Cvijetic, Y. K. Huang, J. Yu, and T. Wang, “100 km long reach upstream 36 Gb/s-OFDMA-PON over a single wavelength with source-free ONUs,” in 35th European Conf. on Optical Communication (ECOC), Vienna, Austria, 20–24 Sept. 2009, 8.5.1.

Qiu, B.

Z. Wang, S. Zhang, and B. Qiu, “PAPR reduction of OFDM signal by using Hadamard transform in companding techniques,” in 12th IEEE Int. Conf. on Communication Technology (ICCT), Nanjing, China, 11–14 Nov. 2010, pp. 320–323.

Randel, S.

M. Schuster, S. Randel, C. A. Bunge, S. C. J. Lee, F. Breyer, B. Spinnler, and K. Petermann, “Spectrally efficient compatible single-sideband modulation for OFDM transmission with direct detection,” IEEE Photon. Technol. Lett., vol. 20, pp. 670–672, May2008.
[CrossRef]

Schmidt, B. J. C.

Schuster, M.

M. Schuster, S. Randel, C. A. Bunge, S. C. J. Lee, F. Breyer, B. Spinnler, and K. Petermann, “Spectrally efficient compatible single-sideband modulation for OFDM transmission with direct detection,” IEEE Photon. Technol. Lett., vol. 20, pp. 670–672, May2008.
[CrossRef]

Ö. Bulakci, M. Schuster, C.-A. Bunge, and B. Spinnler, “Reduced complexity precoding based peak-to-average power ratio reduction applied to optical direct-detection OFDM,” in 34th European Conf. on Optical Communication (ECOC), Brussels, Belgium, 21–25 Sept. 2008, P.4.11.

Shieh, W.

W. Shieh, X. Yi, Y. Ma, and Y. Tang, “Theoretical and experimental study on PMD-supported transmission using polarization diversity in coherent optical OFDM systems,” Opt. Express, vol. 15, pp. 9936–9947, July2007.
[CrossRef] [PubMed]

B. S. Krongold and W. Shieh, “Fiber nonlinearity mitigation by PAPR reduction in coherent optical OFDM systems via active constellation extension,” in 34th European Conf. on Optical Communication (ECOC), Brussels, Belgium, 21–25 Sept. 2008, P.4.13.

Spinnler, B.

M. Schuster, S. Randel, C. A. Bunge, S. C. J. Lee, F. Breyer, B. Spinnler, and K. Petermann, “Spectrally efficient compatible single-sideband modulation for OFDM transmission with direct detection,” IEEE Photon. Technol. Lett., vol. 20, pp. 670–672, May2008.
[CrossRef]

Ö. Bulakci, M. Schuster, C.-A. Bunge, and B. Spinnler, “Reduced complexity precoding based peak-to-average power ratio reduction applied to optical direct-detection OFDM,” in 34th European Conf. on Optical Communication (ECOC), Brussels, Belgium, 21–25 Sept. 2008, P.4.11.

Srnee, L.

T. C. Pratt, N. Jones, L. Srnee, and M. Torrey, “OFDM link performance with companding for PAPR reduction in the presence of nonlinear amplification,” IEEE Trans. Broadcast., vol. 52, pp. 261–267, June2006.
[CrossRef]

Takahashi, H.

H. Takahashi, “Coherent OFDM transmission with high spectral efficiency,” in 35th European Conf. on Optical Communication (ECOC), Vienna, Austria, 20–24 Sept. 2009, 1.3.3.

Tang, Q.

Tang, Y.

Tjhung, T. T.

X. B. Wang, T. T. Tjhung, and C. S. Ng, “Reduction of peak-to-average power ratio of OFDM system using a companding technique,” IEEE Trans. Broadcast., vol. 45, pp. 303–307, Sept.1999.
[CrossRef]

Torrey, M.

T. C. Pratt, N. Jones, L. Srnee, and M. Torrey, “OFDM link performance with companding for PAPR reduction in the presence of nonlinear amplification,” IEEE Trans. Broadcast., vol. 52, pp. 261–267, June2006.
[CrossRef]

Wang, T.

D. Qian, N. Cvijetic, Y. K. Huang, J. Yu, and T. Wang, “100 km long reach upstream 36 Gb/s-OFDMA-PON over a single wavelength with source-free ONUs,” in 35th European Conf. on Optical Communication (ECOC), Vienna, Austria, 20–24 Sept. 2009, 8.5.1.

Wang, W.

Wang, X. B.

X. B. Wang, T. T. Tjhung, and C. S. Ng, “Reduction of peak-to-average power ratio of OFDM system using a companding technique,” IEEE Trans. Broadcast., vol. 45, pp. 303–307, Sept.1999.
[CrossRef]

Wang, Z.

Z. Wang, S. Zhang, and B. Qiu, “PAPR reduction of OFDM signal by using Hadamard transform in companding techniques,” in 12th IEEE Int. Conf. on Communication Technology (ICCT), Nanjing, China, 11–14 Nov. 2010, pp. 320–323.

Xia, M.

Xiao, J.

Yi, X.

Yu, J.

Y. Gao, J. Yu, J. Xiao, Z. Cao, F. Li, and L. Chen, “Direct-detection optical OFDM transmission system with pre-emphasis technique,” J. Lightwave Technol., vol. 29, pp. 2138–2145, July2011.
[CrossRef]

Z. Cao, J. Yu, M. Xia, Q. Tang, Y. Gao, W. Wang, and L. Chen, “Reduction of intersubcarrier interference and frequency-selective fading in OFDM-ROF systems,” J. Lightwave Technol., vol. 28, pp. 2423–2429, Aug.2010.
[CrossRef]

J. Yu, M. F. Huang, D. Qian, L. Chen, and G.-K. Chang, “Centralized lightwave WDM-PON employing 16-QAM intensity modulated OFDM downstream and OOK modulated upstream signals,” IEEE Photon. Technol. Lett., vol. 20, pp. 1545–1546, Sept.2008.
[CrossRef]

D. Qian, N. Cvijetic, Y. K. Huang, J. Yu, and T. Wang, “100 km long reach upstream 36 Gb/s-OFDMA-PON over a single wavelength with source-free ONUs,” in 35th European Conf. on Optical Communication (ECOC), Vienna, Austria, 20–24 Sept. 2009, 8.5.1.

Zhang, S.

Z. Wang, S. Zhang, and B. Qiu, “PAPR reduction of OFDM signal by using Hadamard transform in companding techniques,” in 12th IEEE Int. Conf. on Communication Technology (ICCT), Nanjing, China, 11–14 Nov. 2010, pp. 320–323.

IEEE Photon. Technol. Lett. (2)

J. Yu, M. F. Huang, D. Qian, L. Chen, and G.-K. Chang, “Centralized lightwave WDM-PON employing 16-QAM intensity modulated OFDM downstream and OOK modulated upstream signals,” IEEE Photon. Technol. Lett., vol. 20, pp. 1545–1546, Sept.2008.
[CrossRef]

M. Schuster, S. Randel, C. A. Bunge, S. C. J. Lee, F. Breyer, B. Spinnler, and K. Petermann, “Spectrally efficient compatible single-sideband modulation for OFDM transmission with direct detection,” IEEE Photon. Technol. Lett., vol. 20, pp. 670–672, May2008.
[CrossRef]

IEEE Trans. Broadcast. (2)

X. B. Wang, T. T. Tjhung, and C. S. Ng, “Reduction of peak-to-average power ratio of OFDM system using a companding technique,” IEEE Trans. Broadcast., vol. 45, pp. 303–307, Sept.1999.
[CrossRef]

T. C. Pratt, N. Jones, L. Srnee, and M. Torrey, “OFDM link performance with companding for PAPR reduction in the presence of nonlinear amplification,” IEEE Trans. Broadcast., vol. 52, pp. 261–267, June2006.
[CrossRef]

J. Lightwave Technol. (5)

Opt. Express (1)

Other (7)

D. Qian, N. Cvijetic, Y. K. Huang, J. Yu, and T. Wang, “100 km long reach upstream 36 Gb/s-OFDMA-PON over a single wavelength with source-free ONUs,” in 35th European Conf. on Optical Communication (ECOC), Vienna, Austria, 20–24 Sept. 2009, 8.5.1.

B. Goebel, B. Fesl, L. D. Coelho, and N. Hanik, “On the effect of FWM in coherent optical OFDM systems,” in Optical Fiber Communication Conf. and Expo. and the Nat. Fiber Optic Engineers Conf. (OFC/NFOEC), San Diego, CA, USA, 24–28 Feb. 2008, JWA58.

B. S. Krongold and W. Shieh, “Fiber nonlinearity mitigation by PAPR reduction in coherent optical OFDM systems via active constellation extension,” in 34th European Conf. on Optical Communication (ECOC), Brussels, Belgium, 21–25 Sept. 2008, P.4.13.

Ö. Bulakci, M. Schuster, C.-A. Bunge, and B. Spinnler, “Reduced complexity precoding based peak-to-average power ratio reduction applied to optical direct-detection OFDM,” in 34th European Conf. on Optical Communication (ECOC), Brussels, Belgium, 21–25 Sept. 2008, P.4.11.

H. Takahashi, “Coherent OFDM transmission with high spectral efficiency,” in 35th European Conf. on Optical Communication (ECOC), Vienna, Austria, 20–24 Sept. 2009, 1.3.3.

M. Park, H. Jun, J. Cho, N. Cho, D. Hong, and C. Kang, “PAPR reduction in OFDM transmission using Hadamard transform,” in IEEE Int. Conf. on Communications, Jan. 2000, vol. 1, pp. 430–433.

Z. Wang, S. Zhang, and B. Qiu, “PAPR reduction of OFDM signal by using Hadamard transform in companding techniques,” in 12th IEEE Int. Conf. on Communication Technology (ICCT), Nanjing, China, 11–14 Nov. 2010, pp. 320–323.

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Figures (7)

Fig. 1
Fig. 1

(Color online) The principle of an intense-modulation direct-detection (IM-DD) OFDM transmission system based on the technique of the Hadamard transform combined with a companding transform. EDFA: erbium-doped fiber amplifier; OSC: oscilloscope; S/P: parallel-to-serial; P/S: serial-to-parallel; CP: cyclic prefix; DBF: distributed feedback laser; PIN: PIN photodetector.

Fig. 2
Fig. 2

(Color online) CCDF of the conventional OFDM signal, the OFDM signal with the Hadamard transform, the OFDM signal with a companding transform, and the OFDM signal with a hybrid transform.

Fig. 3
Fig. 3

(Color online) The experimental setup for the IM-DD OFDM transmission system with the Hadamard transform combined with a companding transform. PC: polarization controller; ATT: attenuator; PD: photodetector.

Fig. 4
Fig. 4

(Color online) BER curves for different OFDM signals at different launched powers when the received optical power is −24 dBm.

Fig. 5
Fig. 5

(Color online) BER curves for different OFDM signals with μ=2 at the launched power of −2 dBm.

Fig. 6
Fig. 6

(Color online) BER curves for different OFDM signals with μ=2 at the launched power of 3 dBm.

Fig. 7
Fig. 7

(Color online) BER curves for different OFDM signals (μ=2) at the launched power of 8 dBm.

Equations (8)

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

xn=1Nk=0N1Xkej2πnNk,n=0,1,2,3,,N1.
XN=IFFT{xn},n=0,1,2,3,,N1.
HN=[HN/2HN/2HN/2HN/2],
XˆN=IFFT{HNXN}.
PAPR=max|NˆN|2E{|NˆN|2},
P(PAPR>PAPR0)=1(1ePAPR0)N,
XˆN=Asgn(XˆN)ln(1+μ|XˆN/A|)ln(1+μ),
rc(n)=sgn(rc(n))A[exp(|rc(n)|)ln(1+μ)A1]/ln(1+μ).