Abstract

In this paper, an improved Flip-OFDM scheme is proposed for IM/DD optical systems, where the modulation/demodulation processing takes advantage of the fast Hartley transform (FHT) algorithm. We realize the improved scheme in one symbol period while conventional Flip-OFDM scheme based on fast Fourier transform (FFT) in two consecutive symbol periods. So the complexity of many operations in improved scheme is half of that in conventional scheme, such as CP operation, polarity inversion and symbol delay. Compared to FFT with complex input constellation, the complexity of FHT with real input constellation is halved. The transmission experiment over 50-km SSMF has been realized to verify the feasibility of improved scheme. In conclusion, the improved scheme has the same BER performance with conventional scheme, but great superiority on complexity.

© 2014 Optical Society of America

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References

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  1. J. Armstrong, “OFDM for optical communications,” J. Lightwave Technol. 27, 189–204 (2009).
    [Crossref]
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  3. X. Liu, S. Chandrasekhar, B. Zhu, P. J. Winzer, A. H. Gnauck, and D. W. Peckham, “448-Gb/s reduced-guard-interval CO-OFDM transmission over 2000 km of ultra-large-area fiber and five 80-GHz-grid ROADMs,” J. Lightwave Technol. 29, 483–490 (2011).
    [Crossref]
  4. W. Shieh, H. Bao, and Y. Tang, “Coherent optical OFDM: theory and design,” Opt. Express 16, 841–859 (2008).
    [Crossref] [PubMed]
  5. F. Buchali, R. Dischler, and X. Liu, ”Optical OFDM: A promising high-speed optical transport technology,” Bell Labs Tech. J. 14, 125–146 (2009).
    [Crossref]
  6. D. Qian, N. Cvijetic, J. Hu, and T. Wang, “108 Gb/s OFDMA-PON with polarization multiplexing and direct detection,” J. Lightwave Technol. 28, 484–493 (2010).
    [Crossref]
  7. O. Gonzalez, R. Perez-Jimenez, S. Rodriguez, J. Rabadn, and A. Ayala, “OFDM over indoor wireless optical channel,” in Optoelectronics, IEE Proceedings-(IET, 2005), pp. 199–204.
  8. Y. Benlachtar, R. Bouziane, R. I. Killey, C. R. Berger, P. Milder, R. Koutsoyannis, J. C. Hoe, M. Puschel, and M. Glick, “Optical OFDM for the data center,” in Transparent Optical Networks (ICTON), 2010 12th International Conference on (IEEE, 2010), pp. 1–4.
  9. J. Armstrong and A. J. Lowery, “Power efficient optical OFDM,” Electron. Lett. 42, 370–372 (2006).
    [Crossref]
  10. J. Armstrong and B. Schmidt, “Comparison of asymmetrically clipped optical OFDM and DC-biased optical OFDM in AWGN,” Commun. Lett. 12, 343–345 (2008).
    [Crossref]
  11. S. D. Dissanayake and J. Armstrong, “Comparison of ACO-OFDM, DCO-OFDM and ADO-OFDM in IM/DD systems,” J. Lightwave Technol. 31, 1063–1072 (2013).
    [Crossref]
  12. N. Fernando, Y. Hong, and E. Viterbo, “Flip-OFDM for optical wireless communications,” in Information Theory Workshop (ITW), 2011 IEEE (IEEE, 2011), pp. 5–9.
  13. N. Fernando, Y. Hong, and E. Viterbo, “Flip-OFDM for unipolar communication systems,” Communications, IEEE Transactions on 60, 3726–3733 (2012).
    [Crossref]
  14. P. Saengudomlert, “On the benefits of Pre-Equalization for ACO-OFDM and Flip-OFDM indoor wireless optical transmissions over dispersive channels,” J. Lightwave Technol. 32, 70–80 (2014).
    [Crossref]
  15. M. Svaluto Moreolo, R. Munoz, and G. Junyent, “Novel power efficient optical OFDM based on Hartley transform for intensity-modulated direct-detection systems,” J. Lightwave Technol. 28, 798–805 (2010).
    [Crossref]
  16. M. Svaluto Moreolo, J. M. Fabrega, and G. Junyent, “Characterization of fast and power efficient optical OFDM transmission system based on Hartley transform,” in CLEO: Science and Innovations (Optical Society of America, 2011), p. O2.
  17. M. Svaluto Moreolo, J. M. Fabrega, L. Nadal, and G. Junyent, “FHT-based architectures for multicarrier modulation in direct detection and coherent optical systems,” in Transparent Optical Networks (ICTON), 2011 13th International Conference on (IEEE, 2011), pp. 1–4.
  18. M. Vetterli and H. J. Nussbaumer, “Simple FFT and DCT algorithms with reduced number of operations,” Signal Processing 6, 267–278 (1984).
    [Crossref]
  19. P. Duhamel and M. Vetterli, “Cyclic convolution of real sequences: Hartley versus fourier and new schemes,” in Acoustics, Speech, and Signal Processing, International Conference on ICASSP’86. (IEEE, 1986), pp. 229–232.
  20. P. Duhamel and M. Vetterli, “Improved Fourier and Hartley transform algorithms: Application to cyclic convolution of real data,” Acoustics, Speech and Signal Processing, IEEE Transactions on 35, 818–824 (1987).
    [Crossref]

2014 (1)

2013 (1)

2012 (1)

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

2011 (1)

2010 (2)

2009 (2)

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

F. Buchali, R. Dischler, and X. Liu, ”Optical OFDM: A promising high-speed optical transport technology,” Bell Labs Tech. J. 14, 125–146 (2009).
[Crossref]

2008 (2)

J. Armstrong and B. Schmidt, “Comparison of asymmetrically clipped optical OFDM and DC-biased optical OFDM in AWGN,” Commun. Lett. 12, 343–345 (2008).
[Crossref]

W. Shieh, H. Bao, and Y. Tang, “Coherent optical OFDM: theory and design,” Opt. Express 16, 841–859 (2008).
[Crossref] [PubMed]

2006 (2)

1987 (1)

P. Duhamel and M. Vetterli, “Improved Fourier and Hartley transform algorithms: Application to cyclic convolution of real data,” Acoustics, Speech and Signal Processing, IEEE Transactions on 35, 818–824 (1987).
[Crossref]

1984 (1)

M. Vetterli and H. J. Nussbaumer, “Simple FFT and DCT algorithms with reduced number of operations,” Signal Processing 6, 267–278 (1984).
[Crossref]

Armstrong, J.

S. D. Dissanayake and J. Armstrong, “Comparison of ACO-OFDM, DCO-OFDM and ADO-OFDM in IM/DD systems,” J. Lightwave Technol. 31, 1063–1072 (2013).
[Crossref]

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

J. Armstrong and B. Schmidt, “Comparison of asymmetrically clipped optical OFDM and DC-biased optical OFDM in AWGN,” Commun. Lett. 12, 343–345 (2008).
[Crossref]

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

Ayala, A.

O. Gonzalez, R. Perez-Jimenez, S. Rodriguez, J. Rabadn, and A. Ayala, “OFDM over indoor wireless optical channel,” in Optoelectronics, IEE Proceedings-(IET, 2005), pp. 199–204.

Bao, H.

Benlachtar, Y.

Y. Benlachtar, R. Bouziane, R. I. Killey, C. R. Berger, P. Milder, R. Koutsoyannis, J. C. Hoe, M. Puschel, and M. Glick, “Optical OFDM for the data center,” in Transparent Optical Networks (ICTON), 2010 12th International Conference on (IEEE, 2010), pp. 1–4.

Berger, C. R.

Y. Benlachtar, R. Bouziane, R. I. Killey, C. R. Berger, P. Milder, R. Koutsoyannis, J. C. Hoe, M. Puschel, and M. Glick, “Optical OFDM for the data center,” in Transparent Optical Networks (ICTON), 2010 12th International Conference on (IEEE, 2010), pp. 1–4.

Bouziane, R.

Y. Benlachtar, R. Bouziane, R. I. Killey, C. R. Berger, P. Milder, R. Koutsoyannis, J. C. Hoe, M. Puschel, and M. Glick, “Optical OFDM for the data center,” in Transparent Optical Networks (ICTON), 2010 12th International Conference on (IEEE, 2010), pp. 1–4.

Buchali, F.

F. Buchali, R. Dischler, and X. Liu, ”Optical OFDM: A promising high-speed optical transport technology,” Bell Labs Tech. J. 14, 125–146 (2009).
[Crossref]

Chandrasekhar, S.

Cvijetic, N.

Dischler, R.

F. Buchali, R. Dischler, and X. Liu, ”Optical OFDM: A promising high-speed optical transport technology,” Bell Labs Tech. J. 14, 125–146 (2009).
[Crossref]

Dissanayake, S. D.

Djordjevic, I. B.

Duhamel, P.

P. Duhamel and M. Vetterli, “Improved Fourier and Hartley transform algorithms: Application to cyclic convolution of real data,” Acoustics, Speech and Signal Processing, IEEE Transactions on 35, 818–824 (1987).
[Crossref]

P. Duhamel and M. Vetterli, “Cyclic convolution of real sequences: Hartley versus fourier and new schemes,” in Acoustics, Speech, and Signal Processing, International Conference on ICASSP’86. (IEEE, 1986), pp. 229–232.

Fabrega, J. M.

M. Svaluto Moreolo, J. M. Fabrega, and G. Junyent, “Characterization of fast and power efficient optical OFDM transmission system based on Hartley transform,” in CLEO: Science and Innovations (Optical Society of America, 2011), p. O2.

M. Svaluto Moreolo, J. M. Fabrega, L. Nadal, and G. Junyent, “FHT-based architectures for multicarrier modulation in direct detection and coherent optical systems,” in Transparent Optical Networks (ICTON), 2011 13th International Conference on (IEEE, 2011), pp. 1–4.

Fernando, N.

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

N. Fernando, Y. Hong, and E. Viterbo, “Flip-OFDM for optical wireless communications,” in Information Theory Workshop (ITW), 2011 IEEE (IEEE, 2011), pp. 5–9.

Glick, M.

Y. Benlachtar, R. Bouziane, R. I. Killey, C. R. Berger, P. Milder, R. Koutsoyannis, J. C. Hoe, M. Puschel, and M. Glick, “Optical OFDM for the data center,” in Transparent Optical Networks (ICTON), 2010 12th International Conference on (IEEE, 2010), pp. 1–4.

Gnauck, A. H.

Gonzalez, O.

O. Gonzalez, R. Perez-Jimenez, S. Rodriguez, J. Rabadn, and A. Ayala, “OFDM over indoor wireless optical channel,” in Optoelectronics, IEE Proceedings-(IET, 2005), pp. 199–204.

Hoe, J. C.

Y. Benlachtar, R. Bouziane, R. I. Killey, C. R. Berger, P. Milder, R. Koutsoyannis, J. C. Hoe, M. Puschel, and M. Glick, “Optical OFDM for the data center,” in Transparent Optical Networks (ICTON), 2010 12th International Conference on (IEEE, 2010), pp. 1–4.

Hong, Y.

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

N. Fernando, Y. Hong, and E. Viterbo, “Flip-OFDM for optical wireless communications,” in Information Theory Workshop (ITW), 2011 IEEE (IEEE, 2011), pp. 5–9.

Hu, J.

Junyent, G.

M. Svaluto Moreolo, R. Munoz, and G. Junyent, “Novel power efficient optical OFDM based on Hartley transform for intensity-modulated direct-detection systems,” J. Lightwave Technol. 28, 798–805 (2010).
[Crossref]

M. Svaluto Moreolo, J. M. Fabrega, and G. Junyent, “Characterization of fast and power efficient optical OFDM transmission system based on Hartley transform,” in CLEO: Science and Innovations (Optical Society of America, 2011), p. O2.

M. Svaluto Moreolo, J. M. Fabrega, L. Nadal, and G. Junyent, “FHT-based architectures for multicarrier modulation in direct detection and coherent optical systems,” in Transparent Optical Networks (ICTON), 2011 13th International Conference on (IEEE, 2011), pp. 1–4.

Killey, R. I.

Y. Benlachtar, R. Bouziane, R. I. Killey, C. R. Berger, P. Milder, R. Koutsoyannis, J. C. Hoe, M. Puschel, and M. Glick, “Optical OFDM for the data center,” in Transparent Optical Networks (ICTON), 2010 12th International Conference on (IEEE, 2010), pp. 1–4.

Koutsoyannis, R.

Y. Benlachtar, R. Bouziane, R. I. Killey, C. R. Berger, P. Milder, R. Koutsoyannis, J. C. Hoe, M. Puschel, and M. Glick, “Optical OFDM for the data center,” in Transparent Optical Networks (ICTON), 2010 12th International Conference on (IEEE, 2010), pp. 1–4.

Liu, X.

Lowery, A. J.

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

Milder, P.

Y. Benlachtar, R. Bouziane, R. I. Killey, C. R. Berger, P. Milder, R. Koutsoyannis, J. C. Hoe, M. Puschel, and M. Glick, “Optical OFDM for the data center,” in Transparent Optical Networks (ICTON), 2010 12th International Conference on (IEEE, 2010), pp. 1–4.

Munoz, R.

Nadal, L.

M. Svaluto Moreolo, J. M. Fabrega, L. Nadal, and G. Junyent, “FHT-based architectures for multicarrier modulation in direct detection and coherent optical systems,” in Transparent Optical Networks (ICTON), 2011 13th International Conference on (IEEE, 2011), pp. 1–4.

Nussbaumer, H. J.

M. Vetterli and H. J. Nussbaumer, “Simple FFT and DCT algorithms with reduced number of operations,” Signal Processing 6, 267–278 (1984).
[Crossref]

Peckham, D. W.

Perez-Jimenez, R.

O. Gonzalez, R. Perez-Jimenez, S. Rodriguez, J. Rabadn, and A. Ayala, “OFDM over indoor wireless optical channel,” in Optoelectronics, IEE Proceedings-(IET, 2005), pp. 199–204.

Puschel, M.

Y. Benlachtar, R. Bouziane, R. I. Killey, C. R. Berger, P. Milder, R. Koutsoyannis, J. C. Hoe, M. Puschel, and M. Glick, “Optical OFDM for the data center,” in Transparent Optical Networks (ICTON), 2010 12th International Conference on (IEEE, 2010), pp. 1–4.

Qian, D.

Rabadn, J.

O. Gonzalez, R. Perez-Jimenez, S. Rodriguez, J. Rabadn, and A. Ayala, “OFDM over indoor wireless optical channel,” in Optoelectronics, IEE Proceedings-(IET, 2005), pp. 199–204.

Rodriguez, S.

O. Gonzalez, R. Perez-Jimenez, S. Rodriguez, J. Rabadn, and A. Ayala, “OFDM over indoor wireless optical channel,” in Optoelectronics, IEE Proceedings-(IET, 2005), pp. 199–204.

Saengudomlert, P.

Schmidt, B.

J. Armstrong and B. Schmidt, “Comparison of asymmetrically clipped optical OFDM and DC-biased optical OFDM in AWGN,” Commun. Lett. 12, 343–345 (2008).
[Crossref]

Shieh, W.

Svaluto Moreolo, M.

M. Svaluto Moreolo, R. Munoz, and G. Junyent, “Novel power efficient optical OFDM based on Hartley transform for intensity-modulated direct-detection systems,” J. Lightwave Technol. 28, 798–805 (2010).
[Crossref]

M. Svaluto Moreolo, J. M. Fabrega, L. Nadal, and G. Junyent, “FHT-based architectures for multicarrier modulation in direct detection and coherent optical systems,” in Transparent Optical Networks (ICTON), 2011 13th International Conference on (IEEE, 2011), pp. 1–4.

M. Svaluto Moreolo, J. M. Fabrega, and G. Junyent, “Characterization of fast and power efficient optical OFDM transmission system based on Hartley transform,” in CLEO: Science and Innovations (Optical Society of America, 2011), p. O2.

Tang, Y.

Vasic, B.

Vetterli, M.

P. Duhamel and M. Vetterli, “Improved Fourier and Hartley transform algorithms: Application to cyclic convolution of real data,” Acoustics, Speech and Signal Processing, IEEE Transactions on 35, 818–824 (1987).
[Crossref]

M. Vetterli and H. J. Nussbaumer, “Simple FFT and DCT algorithms with reduced number of operations,” Signal Processing 6, 267–278 (1984).
[Crossref]

P. Duhamel and M. Vetterli, “Cyclic convolution of real sequences: Hartley versus fourier and new schemes,” in Acoustics, Speech, and Signal Processing, International Conference on ICASSP’86. (IEEE, 1986), pp. 229–232.

Viterbo, E.

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

N. Fernando, Y. Hong, and E. Viterbo, “Flip-OFDM for optical wireless communications,” in Information Theory Workshop (ITW), 2011 IEEE (IEEE, 2011), pp. 5–9.

Wang, T.

Winzer, P. J.

Zhu, B.

Acoustics, Speech and Signal Processing, IEEE Transactions on (1)

P. Duhamel and M. Vetterli, “Improved Fourier and Hartley transform algorithms: Application to cyclic convolution of real data,” Acoustics, Speech and Signal Processing, IEEE Transactions on 35, 818–824 (1987).
[Crossref]

Bell Labs Tech. J. (1)

F. Buchali, R. Dischler, and X. Liu, ”Optical OFDM: A promising high-speed optical transport technology,” Bell Labs Tech. J. 14, 125–146 (2009).
[Crossref]

Commun. Lett. (1)

J. Armstrong and B. Schmidt, “Comparison of asymmetrically clipped optical OFDM and DC-biased optical OFDM in AWGN,” Commun. Lett. 12, 343–345 (2008).
[Crossref]

Communications, IEEE Transactions on (1)

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

Electron. Lett. (1)

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

J. Lightwave Technol. (6)

Opt. Express (2)

Signal Processing (1)

M. Vetterli and H. J. Nussbaumer, “Simple FFT and DCT algorithms with reduced number of operations,” Signal Processing 6, 267–278 (1984).
[Crossref]

Other (6)

P. Duhamel and M. Vetterli, “Cyclic convolution of real sequences: Hartley versus fourier and new schemes,” in Acoustics, Speech, and Signal Processing, International Conference on ICASSP’86. (IEEE, 1986), pp. 229–232.

N. Fernando, Y. Hong, and E. Viterbo, “Flip-OFDM for optical wireless communications,” in Information Theory Workshop (ITW), 2011 IEEE (IEEE, 2011), pp. 5–9.

M. Svaluto Moreolo, J. M. Fabrega, and G. Junyent, “Characterization of fast and power efficient optical OFDM transmission system based on Hartley transform,” in CLEO: Science and Innovations (Optical Society of America, 2011), p. O2.

M. Svaluto Moreolo, J. M. Fabrega, L. Nadal, and G. Junyent, “FHT-based architectures for multicarrier modulation in direct detection and coherent optical systems,” in Transparent Optical Networks (ICTON), 2011 13th International Conference on (IEEE, 2011), pp. 1–4.

O. Gonzalez, R. Perez-Jimenez, S. Rodriguez, J. Rabadn, and A. Ayala, “OFDM over indoor wireless optical channel,” in Optoelectronics, IEE Proceedings-(IET, 2005), pp. 199–204.

Y. Benlachtar, R. Bouziane, R. I. Killey, C. R. Berger, P. Milder, R. Koutsoyannis, J. C. Hoe, M. Puschel, and M. Glick, “Optical OFDM for the data center,” in Transparent Optical Networks (ICTON), 2010 12th International Conference on (IEEE, 2010), pp. 1–4.

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Figures (7)

Fig. 1
Fig. 1 Experiment setup for improved FHT-based Flip-OFDM. MZM, Mach-Zehnder modulator; SSMF, standard single-mode fiber; VOA, variable optical attenuator; EDFA, erbium doped fiber amplifier; PD, photodiode.
Fig. 2
Fig. 2 (a) Structure of Flip module; (b) Structure of De-Flip module.
Fig. 3
Fig. 3 (a) Half-wave even symmetrical OFDM symbol based on 64-order FHT; (b) Improved Flip-OFDM symbol based on 64-order FHT.
Fig. 4
Fig. 4 OFDM frame structure used to compare conventional FFT-based Flip-OFDM and improved FHT-based Flip-OFDM. N denotes the FFT and FHT size for each case.
Fig. 5
Fig. 5 Comparison of BER performance between conventional FFT-based Flip-OFDM and improved FHT-based Flip-OFDM in AWGN channel. The size of FHT and FFT is 64.
Fig. 6
Fig. 6 BER versus received power for improved Flip-OFDM systems based on FHT after B2B, 25-km and 50-km SSMF transmission.
Fig. 7
Fig. 7 Comparison of BER performance between conventional FFT-based Flip-OFDM and improved FHT-based Flip-OFDM over 50-km SSMF. The size of FHT and FFT is 64.

Tables (1)

Tables Icon

Table 1 Comparison between the improved FHT-based Flip-OFDM and conventional FFT-based Flip-OFDM. T denotes the sampling period, N denotes the FFT and FHT size

Equations (7)

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

x n = 1 N k = 0 N 1 X k cas ( 2 π k n N ) , n = 0 , 1 , , N 1
X k = 1 N n = 0 N 1 x n cas ( 2 π k n N ) , k = 0 , 1 , , N 1
x n + N / 2 = 1 N k = 0 N / 2 1 X 2 k cas ( 2 π × 2 k ( n + N / 2 ) N ) = 1 N k = 0 N / 2 1 X 2 k cas ( 2 π × 2 k n N + 2 k π ) = x n
y k = x k , k = 0 , 1 , 2 , , N / 2 1
y k = y k + + y k , k = 0 , 1 , 2 , , N / 2 1
y k + = { y k y k > 0 0 otherwise y k = { y k y k < 0 0 otherwise
x ¯ k = { y k + 0 k N / 2 1 y k N / 2 N / 2 k N 1

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