Abstract

A novel method that allows the evaluation of the performance of an optically preamplified direct-detection baseband orthogonal frequency division multiplexing (OFDM) system with arbitrary optical and electrical filtering at the optical receiver is proposed. The method is based on the moment generating function of the symbol detected in each OFDM subcarrier after equalization and relies on the assumption that the noise samples at the fast Fourier transform (FFT) block input at the receiver side are practically uncorrelated. It is shown that, for typical filter bandwidths used in direct-detection optical OFDM systems (similar to or exceeding the OFDM signal bandwidth), the proposed method provides reasonably accurate estimates of the bit error probability for different electrical and optical filter types with various bandwidths, and for different numbers of OFDM subcarriers. For filter bandwidths smaller than the OFDM signal bandwidth, the proposed method becomes inaccurate due to the high correlation between the noise samples at the FFT block input.

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References

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  1. W. Shieh and I. Djordjevic, Orthogonal Frequency Division Multiplexing for Optical Communications. Academic Press, San Diego, 2010, ch. 1, 2, and 7.
  2. E. Vanin, “Performance evaluation of intensity modulated optical OFDM systems with digital baseband distortion,” Opt. Express, vol. 19, no. 5, pp. 4280–4293, Feb.2011.
    [CrossRef] [PubMed]
  3. W. Peng, K. Feng, A. Willner, and S. Chi, “Estimation of the bit error rate for direct-detected OFDM signals with optically preamplified receivers,” J. Lightwave Technol., vol. 27, no. 10, pp. 1340–1346, May2009.
    [CrossRef]
  4. T. Alves and A. Cartaxo, “Semi-analytical approach for performance evaluation of direct-detection OFDM optical communication systems,” Opt. Express, vol. 17, no. 21, pp. 18714–18729, Oct.2009.
    [CrossRef] [PubMed]
  5. T. Alves and A. Cartaxo, “Analysis of methods of performance evaluation of direct-detection orthogonal frequency division multiplexing communication systems,” Fiber Integr. Opt., vol. 29, no. 3, pp. 170–186, May2010.
    [CrossRef]
  6. E. Forestieri, “Evaluating the error probability in lightwave systems with chromatic dispersion, arbitrary pulse shape and pre- and postdetection filtering,” J. Lightwave Technol., vol. 18, no. 11, pp. 1493–1503, Nov.2000.
    [CrossRef]
  7. E. Forestieri and M. Secondini, “On the error probability evaluation in lightwave systems with optical amplification,” J. Lightwave Technol., vol. 27, no. 6, pp. 706–717, Mar.2009.
    [CrossRef]
  8. A. Lowery, “Amplified-spontaneous noise limit of optical OFDM lightwave systems,” Opt. Express, vol. 16, no. 2, pp. 860–865, Jan.2008.
    [CrossRef] [PubMed]
  9. W. Shieh, H. Bao, and Y. Tang, “Coherent optical OFDM: theory and design,” Opt. Express, vol. 16, no. 2, pp. 842–859, Jan.2008.
  10. C. Helstrom, “Approximate evaluation of detection probabilities in radar and optical communications,” IEEE Trans. Aerosp. Electron. Syst., vol. AES-14, no. 4, pp. 630–640, July1978.
    [CrossRef]
  11. S. Haykin and M. Moher, Communication Systems, 5th ed.John Wiley & Sons, Asia, 2009, ch. 5.
  12. M. Nölle, M. Seimetz, and E. Patzak, “System performance of high-order optical DPSK and star QAM modulation for direct detection analyzed by semi-analytical BER estimation,” J. Lightwave Technol., vol. 27, no. 19, pp. 4319–4329, Oct.2009.
    [CrossRef]
  13. W. Peng, B. Zhang, K. Feng, X. Wu, A. Willner, and S. Chi, “Spectrally efficient direct-detected OFDM transmission incorporating a tunable frequency gap and an iterative detection techniques,” J. Lightwave Technol., vol. 27, no. 24, pp. 5723–5735, Dec.2009.
    [CrossRef]
  14. T. Alves and A. Cartaxo, “Performance degradation due to OFDM-UWB radio signal transmission along dispersive single-mode fiber,” IEEE Photon. Technol. Lett., vol. 21, no. 3, pp. 158–160, Feb.2009.
    [CrossRef]
  15. J. Leibrich, A. Ali, H. Paul, W. Rosenkranz, and K. Kammeyer, “Impact of modulator bias on the OSNR requirement of direct-detection optical OFDM,” IEEE Photon. Technol. Lett., vol. 21, no. 15, pp. 1033–1035, Aug.2009.
    [CrossRef]
  16. D. Qian, J. Yu, J. Hu, L. Zong, L. Xu, and T. Wang, “10 Gbit/s WDM-SSB-OFDM transmission over 1000 km SSMF using conventional DFB lasers and direct-detection,” Electron. Lett., vol. 44, no. 3, pp. 233–235, Jan.2008.
    [CrossRef]
  17. W. Peng, X. Wu, V. Arbab, K. Feng, B. Shamee, L. Christen, J. Yang, A. Willner, and S. Chi, “Theoretical and experimental investigations of direct-detected RF-tone-assisted optical OFDM systems,” J. Lightwave Technol., vol. 27, no. 10, pp. 1332–1339, May2009.
    [CrossRef]
  18. D. Hewitt, “Orthogonal frequency division multiplexing using baseband optical single sideband for simpler adaptive dispersion compensation,” in Optical Fiber Communication Conf. and the Nat. Fiber Optic Engineers Conf., 2007, OME-7.

2011 (1)

2010 (1)

T. Alves and A. Cartaxo, “Analysis of methods of performance evaluation of direct-detection orthogonal frequency division multiplexing communication systems,” Fiber Integr. Opt., vol. 29, no. 3, pp. 170–186, May2010.
[CrossRef]

2009 (8)

T. Alves and A. Cartaxo, “Performance degradation due to OFDM-UWB radio signal transmission along dispersive single-mode fiber,” IEEE Photon. Technol. Lett., vol. 21, no. 3, pp. 158–160, Feb.2009.
[CrossRef]

J. Leibrich, A. Ali, H. Paul, W. Rosenkranz, and K. Kammeyer, “Impact of modulator bias on the OSNR requirement of direct-detection optical OFDM,” IEEE Photon. Technol. Lett., vol. 21, no. 15, pp. 1033–1035, Aug.2009.
[CrossRef]

E. Forestieri and M. Secondini, “On the error probability evaluation in lightwave systems with optical amplification,” J. Lightwave Technol., vol. 27, no. 6, pp. 706–717, Mar.2009.
[CrossRef]

W. Peng, X. Wu, V. Arbab, K. Feng, B. Shamee, L. Christen, J. Yang, A. Willner, and S. Chi, “Theoretical and experimental investigations of direct-detected RF-tone-assisted optical OFDM systems,” J. Lightwave Technol., vol. 27, no. 10, pp. 1332–1339, May2009.
[CrossRef]

W. Peng, K. Feng, A. Willner, and S. Chi, “Estimation of the bit error rate for direct-detected OFDM signals with optically preamplified receivers,” J. Lightwave Technol., vol. 27, no. 10, pp. 1340–1346, May2009.
[CrossRef]

T. Alves and A. Cartaxo, “Semi-analytical approach for performance evaluation of direct-detection OFDM optical communication systems,” Opt. Express, vol. 17, no. 21, pp. 18714–18729, Oct.2009.
[CrossRef] [PubMed]

M. Nölle, M. Seimetz, and E. Patzak, “System performance of high-order optical DPSK and star QAM modulation for direct detection analyzed by semi-analytical BER estimation,” J. Lightwave Technol., vol. 27, no. 19, pp. 4319–4329, Oct.2009.
[CrossRef]

W. Peng, B. Zhang, K. Feng, X. Wu, A. Willner, and S. Chi, “Spectrally efficient direct-detected OFDM transmission incorporating a tunable frequency gap and an iterative detection techniques,” J. Lightwave Technol., vol. 27, no. 24, pp. 5723–5735, Dec.2009.
[CrossRef]

2008 (3)

D. Qian, J. Yu, J. Hu, L. Zong, L. Xu, and T. Wang, “10 Gbit/s WDM-SSB-OFDM transmission over 1000 km SSMF using conventional DFB lasers and direct-detection,” Electron. Lett., vol. 44, no. 3, pp. 233–235, Jan.2008.
[CrossRef]

W. Shieh, H. Bao, and Y. Tang, “Coherent optical OFDM: theory and design,” Opt. Express, vol. 16, no. 2, pp. 842–859, Jan.2008.

A. Lowery, “Amplified-spontaneous noise limit of optical OFDM lightwave systems,” Opt. Express, vol. 16, no. 2, pp. 860–865, Jan.2008.
[CrossRef] [PubMed]

2000 (1)

1978 (1)

C. Helstrom, “Approximate evaluation of detection probabilities in radar and optical communications,” IEEE Trans. Aerosp. Electron. Syst., vol. AES-14, no. 4, pp. 630–640, July1978.
[CrossRef]

Ali, A.

J. Leibrich, A. Ali, H. Paul, W. Rosenkranz, and K. Kammeyer, “Impact of modulator bias on the OSNR requirement of direct-detection optical OFDM,” IEEE Photon. Technol. Lett., vol. 21, no. 15, pp. 1033–1035, Aug.2009.
[CrossRef]

Alves, T.

T. Alves and A. Cartaxo, “Analysis of methods of performance evaluation of direct-detection orthogonal frequency division multiplexing communication systems,” Fiber Integr. Opt., vol. 29, no. 3, pp. 170–186, May2010.
[CrossRef]

T. Alves and A. Cartaxo, “Performance degradation due to OFDM-UWB radio signal transmission along dispersive single-mode fiber,” IEEE Photon. Technol. Lett., vol. 21, no. 3, pp. 158–160, Feb.2009.
[CrossRef]

T. Alves and A. Cartaxo, “Semi-analytical approach for performance evaluation of direct-detection OFDM optical communication systems,” Opt. Express, vol. 17, no. 21, pp. 18714–18729, Oct.2009.
[CrossRef] [PubMed]

Arbab, V.

Bao, H.

W. Shieh, H. Bao, and Y. Tang, “Coherent optical OFDM: theory and design,” Opt. Express, vol. 16, no. 2, pp. 842–859, Jan.2008.

Cartaxo, A.

T. Alves and A. Cartaxo, “Analysis of methods of performance evaluation of direct-detection orthogonal frequency division multiplexing communication systems,” Fiber Integr. Opt., vol. 29, no. 3, pp. 170–186, May2010.
[CrossRef]

T. Alves and A. Cartaxo, “Performance degradation due to OFDM-UWB radio signal transmission along dispersive single-mode fiber,” IEEE Photon. Technol. Lett., vol. 21, no. 3, pp. 158–160, Feb.2009.
[CrossRef]

T. Alves and A. Cartaxo, “Semi-analytical approach for performance evaluation of direct-detection OFDM optical communication systems,” Opt. Express, vol. 17, no. 21, pp. 18714–18729, Oct.2009.
[CrossRef] [PubMed]

Chi, S.

Christen, L.

Djordjevic, I.

W. Shieh and I. Djordjevic, Orthogonal Frequency Division Multiplexing for Optical Communications. Academic Press, San Diego, 2010, ch. 1, 2, and 7.

Feng, K.

Forestieri, E.

Haykin, S.

S. Haykin and M. Moher, Communication Systems, 5th ed.John Wiley & Sons, Asia, 2009, ch. 5.

Helstrom, C.

C. Helstrom, “Approximate evaluation of detection probabilities in radar and optical communications,” IEEE Trans. Aerosp. Electron. Syst., vol. AES-14, no. 4, pp. 630–640, July1978.
[CrossRef]

Hewitt, D.

D. Hewitt, “Orthogonal frequency division multiplexing using baseband optical single sideband for simpler adaptive dispersion compensation,” in Optical Fiber Communication Conf. and the Nat. Fiber Optic Engineers Conf., 2007, OME-7.

Hu, J.

D. Qian, J. Yu, J. Hu, L. Zong, L. Xu, and T. Wang, “10 Gbit/s WDM-SSB-OFDM transmission over 1000 km SSMF using conventional DFB lasers and direct-detection,” Electron. Lett., vol. 44, no. 3, pp. 233–235, Jan.2008.
[CrossRef]

Kammeyer, K.

J. Leibrich, A. Ali, H. Paul, W. Rosenkranz, and K. Kammeyer, “Impact of modulator bias on the OSNR requirement of direct-detection optical OFDM,” IEEE Photon. Technol. Lett., vol. 21, no. 15, pp. 1033–1035, Aug.2009.
[CrossRef]

Leibrich, J.

J. Leibrich, A. Ali, H. Paul, W. Rosenkranz, and K. Kammeyer, “Impact of modulator bias on the OSNR requirement of direct-detection optical OFDM,” IEEE Photon. Technol. Lett., vol. 21, no. 15, pp. 1033–1035, Aug.2009.
[CrossRef]

Lowery, A.

Moher, M.

S. Haykin and M. Moher, Communication Systems, 5th ed.John Wiley & Sons, Asia, 2009, ch. 5.

Nölle, M.

Patzak, E.

Paul, H.

J. Leibrich, A. Ali, H. Paul, W. Rosenkranz, and K. Kammeyer, “Impact of modulator bias on the OSNR requirement of direct-detection optical OFDM,” IEEE Photon. Technol. Lett., vol. 21, no. 15, pp. 1033–1035, Aug.2009.
[CrossRef]

Peng, W.

Qian, D.

D. Qian, J. Yu, J. Hu, L. Zong, L. Xu, and T. Wang, “10 Gbit/s WDM-SSB-OFDM transmission over 1000 km SSMF using conventional DFB lasers and direct-detection,” Electron. Lett., vol. 44, no. 3, pp. 233–235, Jan.2008.
[CrossRef]

Rosenkranz, W.

J. Leibrich, A. Ali, H. Paul, W. Rosenkranz, and K. Kammeyer, “Impact of modulator bias on the OSNR requirement of direct-detection optical OFDM,” IEEE Photon. Technol. Lett., vol. 21, no. 15, pp. 1033–1035, Aug.2009.
[CrossRef]

Secondini, M.

Seimetz, M.

Shamee, B.

Shieh, W.

W. Shieh, H. Bao, and Y. Tang, “Coherent optical OFDM: theory and design,” Opt. Express, vol. 16, no. 2, pp. 842–859, Jan.2008.

W. Shieh and I. Djordjevic, Orthogonal Frequency Division Multiplexing for Optical Communications. Academic Press, San Diego, 2010, ch. 1, 2, and 7.

Tang, Y.

W. Shieh, H. Bao, and Y. Tang, “Coherent optical OFDM: theory and design,” Opt. Express, vol. 16, no. 2, pp. 842–859, Jan.2008.

Vanin, E.

Wang, T.

D. Qian, J. Yu, J. Hu, L. Zong, L. Xu, and T. Wang, “10 Gbit/s WDM-SSB-OFDM transmission over 1000 km SSMF using conventional DFB lasers and direct-detection,” Electron. Lett., vol. 44, no. 3, pp. 233–235, Jan.2008.
[CrossRef]

Willner, A.

Wu, X.

Xu, L.

D. Qian, J. Yu, J. Hu, L. Zong, L. Xu, and T. Wang, “10 Gbit/s WDM-SSB-OFDM transmission over 1000 km SSMF using conventional DFB lasers and direct-detection,” Electron. Lett., vol. 44, no. 3, pp. 233–235, Jan.2008.
[CrossRef]

Yang, J.

Yu, J.

D. Qian, J. Yu, J. Hu, L. Zong, L. Xu, and T. Wang, “10 Gbit/s WDM-SSB-OFDM transmission over 1000 km SSMF using conventional DFB lasers and direct-detection,” Electron. Lett., vol. 44, no. 3, pp. 233–235, Jan.2008.
[CrossRef]

Zhang, B.

Zong, L.

D. Qian, J. Yu, J. Hu, L. Zong, L. Xu, and T. Wang, “10 Gbit/s WDM-SSB-OFDM transmission over 1000 km SSMF using conventional DFB lasers and direct-detection,” Electron. Lett., vol. 44, no. 3, pp. 233–235, Jan.2008.
[CrossRef]

Electron. Lett. (1)

D. Qian, J. Yu, J. Hu, L. Zong, L. Xu, and T. Wang, “10 Gbit/s WDM-SSB-OFDM transmission over 1000 km SSMF using conventional DFB lasers and direct-detection,” Electron. Lett., vol. 44, no. 3, pp. 233–235, Jan.2008.
[CrossRef]

Fiber Integr. Opt. (1)

T. Alves and A. Cartaxo, “Analysis of methods of performance evaluation of direct-detection orthogonal frequency division multiplexing communication systems,” Fiber Integr. Opt., vol. 29, no. 3, pp. 170–186, May2010.
[CrossRef]

IEEE Photon. Technol. Lett. (2)

T. Alves and A. Cartaxo, “Performance degradation due to OFDM-UWB radio signal transmission along dispersive single-mode fiber,” IEEE Photon. Technol. Lett., vol. 21, no. 3, pp. 158–160, Feb.2009.
[CrossRef]

J. Leibrich, A. Ali, H. Paul, W. Rosenkranz, and K. Kammeyer, “Impact of modulator bias on the OSNR requirement of direct-detection optical OFDM,” IEEE Photon. Technol. Lett., vol. 21, no. 15, pp. 1033–1035, Aug.2009.
[CrossRef]

IEEE Trans. Aerosp. Electron. Syst. (1)

C. Helstrom, “Approximate evaluation of detection probabilities in radar and optical communications,” IEEE Trans. Aerosp. Electron. Syst., vol. AES-14, no. 4, pp. 630–640, July1978.
[CrossRef]

J. Lightwave Technol. (6)

Opt. Express (4)

Other (3)

W. Shieh and I. Djordjevic, Orthogonal Frequency Division Multiplexing for Optical Communications. Academic Press, San Diego, 2010, ch. 1, 2, and 7.

S. Haykin and M. Moher, Communication Systems, 5th ed.John Wiley & Sons, Asia, 2009, ch. 5.

D. Hewitt, “Orthogonal frequency division multiplexing using baseband optical single sideband for simpler adaptive dispersion compensation,” in Optical Fiber Communication Conf. and the Nat. Fiber Optic Engineers Conf., 2007, OME-7.

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Figures (9)

Fig. 1
Fig. 1

Block diagram of the optical receiver followed by the baseband OFDM electrical receiver.

Fig. 2
Fig. 2

(Color online) Correlation coefficient as a function of the −3 dB bandwidth of the electrical filter normalized to the OFDM signal bandwidth for different electrical filters.

Fig. 3
Fig. 3

(Color online) Bit error probability as a function of the −3 dB bandwidth (normalized to the OFDM signal bandwidth) of the 6th order Butterworth electrical filter and different numbers of OFDM subcarriers: N=32,N=64 and N=128. Marks: Monte Carlo simulation; lines: bit error probability obtained through the MGF.

Fig. 4
Fig. 4

(Color online) Bit error probability as a function of the −3 dB bandwidth (normalized to the OFDM signal bandwidth) of the 4th order Butterworth electrical filter and different numbers of OFDM subcarriers: N=32,N=64 and N=128. Marks: Monte Carlo simulation; lines: bit error probability obtained through the MGF.

Fig. 5
Fig. 5

(Color online) Bit error probability as a function of the −3 dB bandwidth (normalized to the OFDM signal bandwidth) of the 5th order Bessel electrical filter and different numbers of OFDM subcarriers: N=32,N=64 and N=128. Marks: Monte Carlo simulation; lines: bit error probability obtained through the MGF.

Fig. 6
Fig. 6

(Color online) Bit error probability as a function of the −3 dB bandwidth of the electrical filter (normalized to the OFDM signal bandwidth) for different μ. A 6th order Butterworth electrical filter, η=2 and N=32 subcarriers are considered. Marks: Monte Carlo simulation; lines: bit error probability obtained through the MGF.

Fig. 7
Fig. 7

(Color online) Bit error probability as a function of the −3 dB bandwidth of the electrical filter (normalized to the OFDM signal bandwidth) for different η. A 6th order Butterworth electrical filter, μ=2 and N=32 subcarriers are considered. Marks: Monte Carlo simulation; lines: bit error probability obtained through the MGF.

Fig. 8
Fig. 8

(Color online) Bit error probability as a function of the OFDM subcarrier index for the −3 dB bandwidths of the electrical filter (normalized to the OFDM signal bandwidth) 0.6, 1 and 2. A 6th order Butterworth electrical filter, μ=2, η=1 and N=128 subcarriers are considered. Marks: Monte Carlo simulation; lines: bit error probability obtained through the MGF.

Fig. 9
Fig. 9

(Color online) Bit error probability as a function of the −3 dB bandwidth (normalized to the OFDM signal bandwidth) of the optical filter, for Gaussian and 2nd order Super-Gaussian optical filters, and for N=32 and N=128. An electrical 5th order Bessel filter with −3 dB bandwidth of 1.5 times the OFDM signal bandwidth, μ=2 and η=1 are considered. Marks: Monte Carlo simulation; lines: bit error probability obtained through the MGF.

Equations (17)

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

Y(n)=k=1Nid(tk)ej2π(k1)(n1)N,with n=1,,N.
Xn=YnHeqn,
idtk=l=LLm=LLxlxm*HolTwHRlmTwHo*mTwej2πlmtk/Tw+l=LLm=MMxlnm*HolTwHRlTwmToHo*mToej2πltk/Tw+l=LLm=MMxl*nmHo*lTwHR*lTwmToHomToej2πltk/Tw+l=MMm=MMnlnm*HolToHRlmToHo*mTo
To=μ1Bn,o/2+1Bn,e,
idtk=i=12M+1λizi+bi,kλi2bi,k2λi+dk,
ψidtks=expdksi=12M+111λiSeq/TospexpSeq/Tobi,k2s21λiSeq/Tos,
Yn=k=1Nak,nidtk+jbk,nidtk,
ak,n=cos2πk1n1N,
bk,n=sin2πk1n1N.
Xn=k=1NAk,nidtk+jBk,nidtk,
Ak,n=ak,nReHeqnbk,nImHeqn,
Bk,n=bk,nReHeqn+ak,nImHeqn.
ψReXns=k=1NψidtkAk,ns=k=1NexpdkAk,nsi=12M+111λiSeq/ToAk,nspexpSeq/Tobi,k2Ak,n2s21λiSeq/ToAk,ns,
ψImXns=k=1NψidtkBk,ns=k=1NexpdkBk,nsi=12M+111λiSeq/ToBk,nspexpSeq/Tobi,k2Bk,n2s21λiSeq/ToBk,ns.
BEPn=1211SEPRen1SEPImn.
ρ=EWZEWEZσWσZ,
EWZ1NsamN1i=1Nsamk=1N1Wk,iZk,i.