Abstract

Orthogonal frequency division multiplexing (OFDM) has recently gained substantial interest in high capacity optical fiber communications. Unlike wireless systems, optical OFDM systems are constrained by the limited resolution of the ultra high-speed digital-to-analog converters (DAC) and analog-to-digital converters (ADC). Additionally, the situation is exacerbated by the large peak-to-average power ratio (PAPR) inherent in OFDM signals. In this paper, we study the effects of clipping and quantization noise on the system performance. We analytically quantify the introduced distortion as a function of bit resolution and clipping ratio, both at the DAC and ADC. With this we provide a back-to-back signal-to-noise ratio analysis to predict the bit error rate of the system, assuming a fixed received optical power and ideal electrical-optical-electrical conversion. Simulation and experimental results are used to confirm the validity of the expressions.

© 2011 OSA

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  1. B. Schmidt, A. Lowery, and J. Armstrong, “Experimental demonstration of electronic dispersion compensation for long-haul transmission using direct-detection optical OFDM,” J. Lightwave Technol. 26, 196–203 (2008).
    [CrossRef]
  2. S. Jansen, I. Morita, T. Schenk, N. Takeda, and H. Tanaka, “Coherent optical 25.8-Gb/s OFDM transmission over 4160-km SSMF,” J. Lightwave Technol. 1, 6–15 (2008).
    [CrossRef]
  3. X. Jin, J. Tang, K. Qiu, and P. Spencer, “Statistical investigation of the transmission performance of adaptively modulated optical OFDM signals in multimode fiber links,” J. Lightwave Technol. 18, 3216–3224 (2008).
    [CrossRef]
  4. J. Armstrong, “OFDM for optical communcations,” J. Lightwave Technol. 27, 189–204 (2009).
    [CrossRef]
  5. Y. Benlachtar, P. Watts, R. Bouziane, P. Milder, D. Rangaraj, A. Cartolano, R. Koutsoyannis, J. Hoe, M. Püschel, M. Glick, and R. Killey, “Generation of optical OFDM signals using 21.4 GS/s real time digital signal processing,” Opt. Express 17, 17658–17668 (2009).
    [CrossRef] [PubMed]
  6. N. Kaneda, Q. Yang, X. Liu, S. Chandrasekhar, W. Shieh, and Y.-K. Chen, “Real-time 2.5 GS/s coherent optical receiver for 53.3-Gb/s sub-banded OFDM,” J. Lightwave Technol. 28, 494–501 (2010).
    [CrossRef]
  7. R. Giddings, E. Hugues-Salas, X. Jin, J. Wei, and J. Tang, “Experimental demonstration of real-time optical OFDM transmission at 7.5 Gb/s over 25-km SSMF using a 1-GHz RSOA,” IEEE Photon. Technol. Lett. 22, 745–747 (2010).
    [CrossRef]
  8. F. Buchali, R. Dischler, A. Klekamp, M. Bernhard, and Y. Ma, “Statistical transmission experiments using a real-time 12.1 Gb/s OFDM transmitter,” in “Optical Fiber Communication Conference and Exposition (OFC),”(San Diego, CA, 2010).
  9. R. Giddings, X. Jin, E. Hugues-Salas, E. Giacoumidis, J. Wei, and J. Tang, “Experimental demonstration of a record high 11.25 Gb/s real-time optical OFDM transceiver supporting 25 km SMF end-to-end transmission in simple IMDD systems,” Opt. Express 18, 5541–5555 (2010).
    [CrossRef] [PubMed]
  10. Y. Benlachtar, P. Watts, R. Bouziane, P. Milder, R. Koutsoyannis, J. Hoe, M. Püschel, M. Glick, and R. Killey, “Real-time digital signal processing for the generation of optical orthogonal frequency-division-multiplexed signals,” IEEE J. Sel. Top. Quantum Electron. 16, 1235–1244 (2010).
    [CrossRef]
  11. B. Inan, O. Karakaya, P. Kainzmaier, S. Adhikari, S. Calabro, V. A. Sleiffer, N. Hanik, and S. L. Jansen, “Realization of a 23.9 Gb/s real time optical-OFDM transmitter with a 1024 point IFFT,” in “Optical Fiber Communication Conference and Exposition (OFC),”(Los Angeles, CA, 2011).
  12. R. Schmogrow, M. Winter, B. Nebendahl, D. Hillerkuss, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “101.5 Gbit/s real-time OFDM transmitter with 16QAM modulated sub-carriers,” in “Optical Fiber Communication Conference and Exposition (OFC),”(Los Angeles, CA, 2011).
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    [CrossRef]
  14. E. Vanin, “Performance evaluation of intensity modulated optical OFDM system with digital baseband distortion,” Opt. Express 19, 4280–4293 (2011).
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  16. Y. Benlachtar, R. Bouziane, R. Killey, C. Berger, P. Milder, R. Koutsoyannis, J. Hoe, M. Püschel, and M. Glick, “Optical OFDM in the data center,” in “Proc. of Intl. Conf. on Transparent Optical Networks,” (Munich, Germany, 2010).
    [CrossRef]
  17. A. Papoulis and S. U. Pillai, Probability, Random Variables and Stochastic Processes (McGraw-Hill, 2002).
  18. For simplicity we neglect the effect of the receive filters and ADC conversion on this noise term.
  19. J. G. Proakis, Digital Communications, 4th ed. (McGraw-Hill, 2001).

2011

2010

R. Giddings, E. Hugues-Salas, X. Jin, J. Wei, and J. Tang, “Experimental demonstration of real-time optical OFDM transmission at 7.5 Gb/s over 25-km SSMF using a 1-GHz RSOA,” IEEE Photon. Technol. Lett. 22, 745–747 (2010).
[CrossRef]

Y. Benlachtar, P. Watts, R. Bouziane, P. Milder, R. Koutsoyannis, J. Hoe, M. Püschel, M. Glick, and R. Killey, “Real-time digital signal processing for the generation of optical orthogonal frequency-division-multiplexed signals,” IEEE J. Sel. Top. Quantum Electron. 16, 1235–1244 (2010).
[CrossRef]

N. Kaneda, Q. Yang, X. Liu, S. Chandrasekhar, W. Shieh, and Y.-K. Chen, “Real-time 2.5 GS/s coherent optical receiver for 53.3-Gb/s sub-banded OFDM,” J. Lightwave Technol. 28, 494–501 (2010).
[CrossRef]

R. Giddings, X. Jin, E. Hugues-Salas, E. Giacoumidis, J. Wei, and J. Tang, “Experimental demonstration of a record high 11.25 Gb/s real-time optical OFDM transceiver supporting 25 km SMF end-to-end transmission in simple IMDD systems,” Opt. Express 18, 5541–5555 (2010).
[CrossRef] [PubMed]

2009

2008

S. Jansen, I. Morita, T. Schenk, N. Takeda, and H. Tanaka, “Coherent optical 25.8-Gb/s OFDM transmission over 4160-km SSMF,” J. Lightwave Technol. 1, 6–15 (2008).
[CrossRef]

X. Jin, J. Tang, K. Qiu, and P. Spencer, “Statistical investigation of the transmission performance of adaptively modulated optical OFDM signals in multimode fiber links,” J. Lightwave Technol. 18, 3216–3224 (2008).
[CrossRef]

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

2006

D. Dardari, “Joint clip and quantization effects characterization in OFDM receivers,” IEEE Trans. Circ. Syst. I 53, 1741–1748 (2006).
[CrossRef]

Adhikari, S.

B. Inan, O. Karakaya, P. Kainzmaier, S. Adhikari, S. Calabro, V. A. Sleiffer, N. Hanik, and S. L. Jansen, “Realization of a 23.9 Gb/s real time optical-OFDM transmitter with a 1024 point IFFT,” in “Optical Fiber Communication Conference and Exposition (OFC),”(Los Angeles, CA, 2011).

Armstrong, J.

Becker, J.

R. Schmogrow, M. Winter, B. Nebendahl, D. Hillerkuss, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “101.5 Gbit/s real-time OFDM transmitter with 16QAM modulated sub-carriers,” in “Optical Fiber Communication Conference and Exposition (OFC),”(Los Angeles, CA, 2011).

Benlachtar, Y.

Y. Benlachtar, P. Watts, R. Bouziane, P. Milder, R. Koutsoyannis, J. Hoe, M. Püschel, M. Glick, and R. Killey, “Real-time digital signal processing for the generation of optical orthogonal frequency-division-multiplexed signals,” IEEE J. Sel. Top. Quantum Electron. 16, 1235–1244 (2010).
[CrossRef]

Y. Benlachtar, P. Watts, R. Bouziane, P. Milder, D. Rangaraj, A. Cartolano, R. Koutsoyannis, J. Hoe, M. Püschel, M. Glick, and R. Killey, “Generation of optical OFDM signals using 21.4 GS/s real time digital signal processing,” Opt. Express 17, 17658–17668 (2009).
[CrossRef] [PubMed]

Y. Benlachtar, R. Bouziane, R. Killey, C. Berger, P. Milder, R. Koutsoyannis, J. Hoe, M. Püschel, and M. Glick, “Optical OFDM in the data center,” in “Proc. of Intl. Conf. on Transparent Optical Networks,” (Munich, Germany, 2010).
[CrossRef]

C. R. Berger, Y. Benlachtar, and R. I. Killey, “Optimum clipping for optical OFDM with limited resolution DAC/ADC,” in “Proc. OSA Advanced Photonics Congress,”(Toronto, CA, 2011).

Berger, C.

Y. Benlachtar, R. Bouziane, R. Killey, C. Berger, P. Milder, R. Koutsoyannis, J. Hoe, M. Püschel, and M. Glick, “Optical OFDM in the data center,” in “Proc. of Intl. Conf. on Transparent Optical Networks,” (Munich, Germany, 2010).
[CrossRef]

Berger, C. R.

C. R. Berger, Y. Benlachtar, and R. I. Killey, “Optimum clipping for optical OFDM with limited resolution DAC/ADC,” in “Proc. OSA Advanced Photonics Congress,”(Toronto, CA, 2011).

Bernhard, M.

F. Buchali, R. Dischler, A. Klekamp, M. Bernhard, and Y. Ma, “Statistical transmission experiments using a real-time 12.1 Gb/s OFDM transmitter,” in “Optical Fiber Communication Conference and Exposition (OFC),”(San Diego, CA, 2010).

Bouziane, R.

Y. Benlachtar, P. Watts, R. Bouziane, P. Milder, R. Koutsoyannis, J. Hoe, M. Püschel, M. Glick, and R. Killey, “Real-time digital signal processing for the generation of optical orthogonal frequency-division-multiplexed signals,” IEEE J. Sel. Top. Quantum Electron. 16, 1235–1244 (2010).
[CrossRef]

Y. Benlachtar, P. Watts, R. Bouziane, P. Milder, D. Rangaraj, A. Cartolano, R. Koutsoyannis, J. Hoe, M. Püschel, M. Glick, and R. Killey, “Generation of optical OFDM signals using 21.4 GS/s real time digital signal processing,” Opt. Express 17, 17658–17668 (2009).
[CrossRef] [PubMed]

Y. Benlachtar, R. Bouziane, R. Killey, C. Berger, P. Milder, R. Koutsoyannis, J. Hoe, M. Püschel, and M. Glick, “Optical OFDM in the data center,” in “Proc. of Intl. Conf. on Transparent Optical Networks,” (Munich, Germany, 2010).
[CrossRef]

Buchali, F.

F. Buchali, R. Dischler, A. Klekamp, M. Bernhard, and Y. Ma, “Statistical transmission experiments using a real-time 12.1 Gb/s OFDM transmitter,” in “Optical Fiber Communication Conference and Exposition (OFC),”(San Diego, CA, 2010).

Calabro, S.

B. Inan, O. Karakaya, P. Kainzmaier, S. Adhikari, S. Calabro, V. A. Sleiffer, N. Hanik, and S. L. Jansen, “Realization of a 23.9 Gb/s real time optical-OFDM transmitter with a 1024 point IFFT,” in “Optical Fiber Communication Conference and Exposition (OFC),”(Los Angeles, CA, 2011).

Cartolano, A.

Chandrasekhar, S.

Chen, Y.-K.

Dardari, D.

D. Dardari, “Joint clip and quantization effects characterization in OFDM receivers,” IEEE Trans. Circ. Syst. I 53, 1741–1748 (2006).
[CrossRef]

Dischler, R.

F. Buchali, R. Dischler, A. Klekamp, M. Bernhard, and Y. Ma, “Statistical transmission experiments using a real-time 12.1 Gb/s OFDM transmitter,” in “Optical Fiber Communication Conference and Exposition (OFC),”(San Diego, CA, 2010).

Dreschmann, M.

R. Schmogrow, M. Winter, B. Nebendahl, D. Hillerkuss, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “101.5 Gbit/s real-time OFDM transmitter with 16QAM modulated sub-carriers,” in “Optical Fiber Communication Conference and Exposition (OFC),”(Los Angeles, CA, 2011).

Freude, W.

R. Schmogrow, M. Winter, B. Nebendahl, D. Hillerkuss, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “101.5 Gbit/s real-time OFDM transmitter with 16QAM modulated sub-carriers,” in “Optical Fiber Communication Conference and Exposition (OFC),”(Los Angeles, CA, 2011).

Giacoumidis, E.

Giddings, R.

R. Giddings, X. Jin, E. Hugues-Salas, E. Giacoumidis, J. Wei, and J. Tang, “Experimental demonstration of a record high 11.25 Gb/s real-time optical OFDM transceiver supporting 25 km SMF end-to-end transmission in simple IMDD systems,” Opt. Express 18, 5541–5555 (2010).
[CrossRef] [PubMed]

R. Giddings, E. Hugues-Salas, X. Jin, J. Wei, and J. Tang, “Experimental demonstration of real-time optical OFDM transmission at 7.5 Gb/s over 25-km SSMF using a 1-GHz RSOA,” IEEE Photon. Technol. Lett. 22, 745–747 (2010).
[CrossRef]

Glick, M.

Y. Benlachtar, P. Watts, R. Bouziane, P. Milder, R. Koutsoyannis, J. Hoe, M. Püschel, M. Glick, and R. Killey, “Real-time digital signal processing for the generation of optical orthogonal frequency-division-multiplexed signals,” IEEE J. Sel. Top. Quantum Electron. 16, 1235–1244 (2010).
[CrossRef]

Y. Benlachtar, P. Watts, R. Bouziane, P. Milder, D. Rangaraj, A. Cartolano, R. Koutsoyannis, J. Hoe, M. Püschel, M. Glick, and R. Killey, “Generation of optical OFDM signals using 21.4 GS/s real time digital signal processing,” Opt. Express 17, 17658–17668 (2009).
[CrossRef] [PubMed]

Y. Benlachtar, R. Bouziane, R. Killey, C. Berger, P. Milder, R. Koutsoyannis, J. Hoe, M. Püschel, and M. Glick, “Optical OFDM in the data center,” in “Proc. of Intl. Conf. on Transparent Optical Networks,” (Munich, Germany, 2010).
[CrossRef]

Hanik, N.

B. Inan, O. Karakaya, P. Kainzmaier, S. Adhikari, S. Calabro, V. A. Sleiffer, N. Hanik, and S. L. Jansen, “Realization of a 23.9 Gb/s real time optical-OFDM transmitter with a 1024 point IFFT,” in “Optical Fiber Communication Conference and Exposition (OFC),”(Los Angeles, CA, 2011).

Hillerkuss, D.

R. Schmogrow, M. Winter, B. Nebendahl, D. Hillerkuss, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “101.5 Gbit/s real-time OFDM transmitter with 16QAM modulated sub-carriers,” in “Optical Fiber Communication Conference and Exposition (OFC),”(Los Angeles, CA, 2011).

Hoe, J.

Y. Benlachtar, P. Watts, R. Bouziane, P. Milder, R. Koutsoyannis, J. Hoe, M. Püschel, M. Glick, and R. Killey, “Real-time digital signal processing for the generation of optical orthogonal frequency-division-multiplexed signals,” IEEE J. Sel. Top. Quantum Electron. 16, 1235–1244 (2010).
[CrossRef]

Y. Benlachtar, P. Watts, R. Bouziane, P. Milder, D. Rangaraj, A. Cartolano, R. Koutsoyannis, J. Hoe, M. Püschel, M. Glick, and R. Killey, “Generation of optical OFDM signals using 21.4 GS/s real time digital signal processing,” Opt. Express 17, 17658–17668 (2009).
[CrossRef] [PubMed]

Y. Benlachtar, R. Bouziane, R. Killey, C. Berger, P. Milder, R. Koutsoyannis, J. Hoe, M. Püschel, and M. Glick, “Optical OFDM in the data center,” in “Proc. of Intl. Conf. on Transparent Optical Networks,” (Munich, Germany, 2010).
[CrossRef]

Huebner, M.

R. Schmogrow, M. Winter, B. Nebendahl, D. Hillerkuss, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “101.5 Gbit/s real-time OFDM transmitter with 16QAM modulated sub-carriers,” in “Optical Fiber Communication Conference and Exposition (OFC),”(Los Angeles, CA, 2011).

Hugues-Salas, E.

R. Giddings, X. Jin, E. Hugues-Salas, E. Giacoumidis, J. Wei, and J. Tang, “Experimental demonstration of a record high 11.25 Gb/s real-time optical OFDM transceiver supporting 25 km SMF end-to-end transmission in simple IMDD systems,” Opt. Express 18, 5541–5555 (2010).
[CrossRef] [PubMed]

R. Giddings, E. Hugues-Salas, X. Jin, J. Wei, and J. Tang, “Experimental demonstration of real-time optical OFDM transmission at 7.5 Gb/s over 25-km SSMF using a 1-GHz RSOA,” IEEE Photon. Technol. Lett. 22, 745–747 (2010).
[CrossRef]

Inan, B.

B. Inan, O. Karakaya, P. Kainzmaier, S. Adhikari, S. Calabro, V. A. Sleiffer, N. Hanik, and S. L. Jansen, “Realization of a 23.9 Gb/s real time optical-OFDM transmitter with a 1024 point IFFT,” in “Optical Fiber Communication Conference and Exposition (OFC),”(Los Angeles, CA, 2011).

Jansen, S.

S. Jansen, I. Morita, T. Schenk, N. Takeda, and H. Tanaka, “Coherent optical 25.8-Gb/s OFDM transmission over 4160-km SSMF,” J. Lightwave Technol. 1, 6–15 (2008).
[CrossRef]

Jansen, S. L.

B. Inan, O. Karakaya, P. Kainzmaier, S. Adhikari, S. Calabro, V. A. Sleiffer, N. Hanik, and S. L. Jansen, “Realization of a 23.9 Gb/s real time optical-OFDM transmitter with a 1024 point IFFT,” in “Optical Fiber Communication Conference and Exposition (OFC),”(Los Angeles, CA, 2011).

Jin, X.

R. Giddings, E. Hugues-Salas, X. Jin, J. Wei, and J. Tang, “Experimental demonstration of real-time optical OFDM transmission at 7.5 Gb/s over 25-km SSMF using a 1-GHz RSOA,” IEEE Photon. Technol. Lett. 22, 745–747 (2010).
[CrossRef]

R. Giddings, X. Jin, E. Hugues-Salas, E. Giacoumidis, J. Wei, and J. Tang, “Experimental demonstration of a record high 11.25 Gb/s real-time optical OFDM transceiver supporting 25 km SMF end-to-end transmission in simple IMDD systems,” Opt. Express 18, 5541–5555 (2010).
[CrossRef] [PubMed]

X. Jin, J. Tang, K. Qiu, and P. Spencer, “Statistical investigation of the transmission performance of adaptively modulated optical OFDM signals in multimode fiber links,” J. Lightwave Technol. 18, 3216–3224 (2008).
[CrossRef]

Kainzmaier, P.

B. Inan, O. Karakaya, P. Kainzmaier, S. Adhikari, S. Calabro, V. A. Sleiffer, N. Hanik, and S. L. Jansen, “Realization of a 23.9 Gb/s real time optical-OFDM transmitter with a 1024 point IFFT,” in “Optical Fiber Communication Conference and Exposition (OFC),”(Los Angeles, CA, 2011).

Kaneda, N.

Karakaya, O.

B. Inan, O. Karakaya, P. Kainzmaier, S. Adhikari, S. Calabro, V. A. Sleiffer, N. Hanik, and S. L. Jansen, “Realization of a 23.9 Gb/s real time optical-OFDM transmitter with a 1024 point IFFT,” in “Optical Fiber Communication Conference and Exposition (OFC),”(Los Angeles, CA, 2011).

Killey, R.

Y. Benlachtar, P. Watts, R. Bouziane, P. Milder, R. Koutsoyannis, J. Hoe, M. Püschel, M. Glick, and R. Killey, “Real-time digital signal processing for the generation of optical orthogonal frequency-division-multiplexed signals,” IEEE J. Sel. Top. Quantum Electron. 16, 1235–1244 (2010).
[CrossRef]

Y. Benlachtar, P. Watts, R. Bouziane, P. Milder, D. Rangaraj, A. Cartolano, R. Koutsoyannis, J. Hoe, M. Püschel, M. Glick, and R. Killey, “Generation of optical OFDM signals using 21.4 GS/s real time digital signal processing,” Opt. Express 17, 17658–17668 (2009).
[CrossRef] [PubMed]

Y. Benlachtar, R. Bouziane, R. Killey, C. Berger, P. Milder, R. Koutsoyannis, J. Hoe, M. Püschel, and M. Glick, “Optical OFDM in the data center,” in “Proc. of Intl. Conf. on Transparent Optical Networks,” (Munich, Germany, 2010).
[CrossRef]

Killey, R. I.

C. R. Berger, Y. Benlachtar, and R. I. Killey, “Optimum clipping for optical OFDM with limited resolution DAC/ADC,” in “Proc. OSA Advanced Photonics Congress,”(Toronto, CA, 2011).

Klekamp, A.

F. Buchali, R. Dischler, A. Klekamp, M. Bernhard, and Y. Ma, “Statistical transmission experiments using a real-time 12.1 Gb/s OFDM transmitter,” in “Optical Fiber Communication Conference and Exposition (OFC),”(San Diego, CA, 2010).

Koos, C.

R. Schmogrow, M. Winter, B. Nebendahl, D. Hillerkuss, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “101.5 Gbit/s real-time OFDM transmitter with 16QAM modulated sub-carriers,” in “Optical Fiber Communication Conference and Exposition (OFC),”(Los Angeles, CA, 2011).

Koutsoyannis, R.

Y. Benlachtar, P. Watts, R. Bouziane, P. Milder, R. Koutsoyannis, J. Hoe, M. Püschel, M. Glick, and R. Killey, “Real-time digital signal processing for the generation of optical orthogonal frequency-division-multiplexed signals,” IEEE J. Sel. Top. Quantum Electron. 16, 1235–1244 (2010).
[CrossRef]

Y. Benlachtar, P. Watts, R. Bouziane, P. Milder, D. Rangaraj, A. Cartolano, R. Koutsoyannis, J. Hoe, M. Püschel, M. Glick, and R. Killey, “Generation of optical OFDM signals using 21.4 GS/s real time digital signal processing,” Opt. Express 17, 17658–17668 (2009).
[CrossRef] [PubMed]

Y. Benlachtar, R. Bouziane, R. Killey, C. Berger, P. Milder, R. Koutsoyannis, J. Hoe, M. Püschel, and M. Glick, “Optical OFDM in the data center,” in “Proc. of Intl. Conf. on Transparent Optical Networks,” (Munich, Germany, 2010).
[CrossRef]

Leuthold, J.

R. Schmogrow, M. Winter, B. Nebendahl, D. Hillerkuss, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “101.5 Gbit/s real-time OFDM transmitter with 16QAM modulated sub-carriers,” in “Optical Fiber Communication Conference and Exposition (OFC),”(Los Angeles, CA, 2011).

Liu, X.

Lowery, A.

Ma, Y.

F. Buchali, R. Dischler, A. Klekamp, M. Bernhard, and Y. Ma, “Statistical transmission experiments using a real-time 12.1 Gb/s OFDM transmitter,” in “Optical Fiber Communication Conference and Exposition (OFC),”(San Diego, CA, 2010).

Meyer, J.

R. Schmogrow, M. Winter, B. Nebendahl, D. Hillerkuss, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “101.5 Gbit/s real-time OFDM transmitter with 16QAM modulated sub-carriers,” in “Optical Fiber Communication Conference and Exposition (OFC),”(Los Angeles, CA, 2011).

Milder, P.

Y. Benlachtar, P. Watts, R. Bouziane, P. Milder, R. Koutsoyannis, J. Hoe, M. Püschel, M. Glick, and R. Killey, “Real-time digital signal processing for the generation of optical orthogonal frequency-division-multiplexed signals,” IEEE J. Sel. Top. Quantum Electron. 16, 1235–1244 (2010).
[CrossRef]

Y. Benlachtar, P. Watts, R. Bouziane, P. Milder, D. Rangaraj, A. Cartolano, R. Koutsoyannis, J. Hoe, M. Püschel, M. Glick, and R. Killey, “Generation of optical OFDM signals using 21.4 GS/s real time digital signal processing,” Opt. Express 17, 17658–17668 (2009).
[CrossRef] [PubMed]

Y. Benlachtar, R. Bouziane, R. Killey, C. Berger, P. Milder, R. Koutsoyannis, J. Hoe, M. Püschel, and M. Glick, “Optical OFDM in the data center,” in “Proc. of Intl. Conf. on Transparent Optical Networks,” (Munich, Germany, 2010).
[CrossRef]

Morita, I.

S. Jansen, I. Morita, T. Schenk, N. Takeda, and H. Tanaka, “Coherent optical 25.8-Gb/s OFDM transmission over 4160-km SSMF,” J. Lightwave Technol. 1, 6–15 (2008).
[CrossRef]

Nebendahl, B.

R. Schmogrow, M. Winter, B. Nebendahl, D. Hillerkuss, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “101.5 Gbit/s real-time OFDM transmitter with 16QAM modulated sub-carriers,” in “Optical Fiber Communication Conference and Exposition (OFC),”(Los Angeles, CA, 2011).

Papoulis, A.

A. Papoulis and S. U. Pillai, Probability, Random Variables and Stochastic Processes (McGraw-Hill, 2002).

Pillai, S. U.

A. Papoulis and S. U. Pillai, Probability, Random Variables and Stochastic Processes (McGraw-Hill, 2002).

Proakis, J. G.

J. G. Proakis, Digital Communications, 4th ed. (McGraw-Hill, 2001).

Püschel, M.

Y. Benlachtar, P. Watts, R. Bouziane, P. Milder, R. Koutsoyannis, J. Hoe, M. Püschel, M. Glick, and R. Killey, “Real-time digital signal processing for the generation of optical orthogonal frequency-division-multiplexed signals,” IEEE J. Sel. Top. Quantum Electron. 16, 1235–1244 (2010).
[CrossRef]

Y. Benlachtar, P. Watts, R. Bouziane, P. Milder, D. Rangaraj, A. Cartolano, R. Koutsoyannis, J. Hoe, M. Püschel, M. Glick, and R. Killey, “Generation of optical OFDM signals using 21.4 GS/s real time digital signal processing,” Opt. Express 17, 17658–17668 (2009).
[CrossRef] [PubMed]

Y. Benlachtar, R. Bouziane, R. Killey, C. Berger, P. Milder, R. Koutsoyannis, J. Hoe, M. Püschel, and M. Glick, “Optical OFDM in the data center,” in “Proc. of Intl. Conf. on Transparent Optical Networks,” (Munich, Germany, 2010).
[CrossRef]

Qiu, K.

X. Jin, J. Tang, K. Qiu, and P. Spencer, “Statistical investigation of the transmission performance of adaptively modulated optical OFDM signals in multimode fiber links,” J. Lightwave Technol. 18, 3216–3224 (2008).
[CrossRef]

Rangaraj, D.

Schenk, T.

S. Jansen, I. Morita, T. Schenk, N. Takeda, and H. Tanaka, “Coherent optical 25.8-Gb/s OFDM transmission over 4160-km SSMF,” J. Lightwave Technol. 1, 6–15 (2008).
[CrossRef]

Schmidt, B.

Schmogrow, R.

R. Schmogrow, M. Winter, B. Nebendahl, D. Hillerkuss, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “101.5 Gbit/s real-time OFDM transmitter with 16QAM modulated sub-carriers,” in “Optical Fiber Communication Conference and Exposition (OFC),”(Los Angeles, CA, 2011).

Shieh, W.

Sleiffer, V. A.

B. Inan, O. Karakaya, P. Kainzmaier, S. Adhikari, S. Calabro, V. A. Sleiffer, N. Hanik, and S. L. Jansen, “Realization of a 23.9 Gb/s real time optical-OFDM transmitter with a 1024 point IFFT,” in “Optical Fiber Communication Conference and Exposition (OFC),”(Los Angeles, CA, 2011).

Spencer, P.

X. Jin, J. Tang, K. Qiu, and P. Spencer, “Statistical investigation of the transmission performance of adaptively modulated optical OFDM signals in multimode fiber links,” J. Lightwave Technol. 18, 3216–3224 (2008).
[CrossRef]

Takeda, N.

S. Jansen, I. Morita, T. Schenk, N. Takeda, and H. Tanaka, “Coherent optical 25.8-Gb/s OFDM transmission over 4160-km SSMF,” J. Lightwave Technol. 1, 6–15 (2008).
[CrossRef]

Tanaka, H.

S. Jansen, I. Morita, T. Schenk, N. Takeda, and H. Tanaka, “Coherent optical 25.8-Gb/s OFDM transmission over 4160-km SSMF,” J. Lightwave Technol. 1, 6–15 (2008).
[CrossRef]

Tang, J.

R. Giddings, X. Jin, E. Hugues-Salas, E. Giacoumidis, J. Wei, and J. Tang, “Experimental demonstration of a record high 11.25 Gb/s real-time optical OFDM transceiver supporting 25 km SMF end-to-end transmission in simple IMDD systems,” Opt. Express 18, 5541–5555 (2010).
[CrossRef] [PubMed]

R. Giddings, E. Hugues-Salas, X. Jin, J. Wei, and J. Tang, “Experimental demonstration of real-time optical OFDM transmission at 7.5 Gb/s over 25-km SSMF using a 1-GHz RSOA,” IEEE Photon. Technol. Lett. 22, 745–747 (2010).
[CrossRef]

X. Jin, J. Tang, K. Qiu, and P. Spencer, “Statistical investigation of the transmission performance of adaptively modulated optical OFDM signals in multimode fiber links,” J. Lightwave Technol. 18, 3216–3224 (2008).
[CrossRef]

Vanin, E.

Watts, P.

Y. Benlachtar, P. Watts, R. Bouziane, P. Milder, R. Koutsoyannis, J. Hoe, M. Püschel, M. Glick, and R. Killey, “Real-time digital signal processing for the generation of optical orthogonal frequency-division-multiplexed signals,” IEEE J. Sel. Top. Quantum Electron. 16, 1235–1244 (2010).
[CrossRef]

Y. Benlachtar, P. Watts, R. Bouziane, P. Milder, D. Rangaraj, A. Cartolano, R. Koutsoyannis, J. Hoe, M. Püschel, M. Glick, and R. Killey, “Generation of optical OFDM signals using 21.4 GS/s real time digital signal processing,” Opt. Express 17, 17658–17668 (2009).
[CrossRef] [PubMed]

Wei, J.

R. Giddings, X. Jin, E. Hugues-Salas, E. Giacoumidis, J. Wei, and J. Tang, “Experimental demonstration of a record high 11.25 Gb/s real-time optical OFDM transceiver supporting 25 km SMF end-to-end transmission in simple IMDD systems,” Opt. Express 18, 5541–5555 (2010).
[CrossRef] [PubMed]

R. Giddings, E. Hugues-Salas, X. Jin, J. Wei, and J. Tang, “Experimental demonstration of real-time optical OFDM transmission at 7.5 Gb/s over 25-km SSMF using a 1-GHz RSOA,” IEEE Photon. Technol. Lett. 22, 745–747 (2010).
[CrossRef]

Winter, M.

R. Schmogrow, M. Winter, B. Nebendahl, D. Hillerkuss, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “101.5 Gbit/s real-time OFDM transmitter with 16QAM modulated sub-carriers,” in “Optical Fiber Communication Conference and Exposition (OFC),”(Los Angeles, CA, 2011).

Yang, Q.

IEEE J. Sel. Top. Quantum Electron.

Y. Benlachtar, P. Watts, R. Bouziane, P. Milder, R. Koutsoyannis, J. Hoe, M. Püschel, M. Glick, and R. Killey, “Real-time digital signal processing for the generation of optical orthogonal frequency-division-multiplexed signals,” IEEE J. Sel. Top. Quantum Electron. 16, 1235–1244 (2010).
[CrossRef]

IEEE Photon. Technol. Lett.

R. Giddings, E. Hugues-Salas, X. Jin, J. Wei, and J. Tang, “Experimental demonstration of real-time optical OFDM transmission at 7.5 Gb/s over 25-km SSMF using a 1-GHz RSOA,” IEEE Photon. Technol. Lett. 22, 745–747 (2010).
[CrossRef]

IEEE Trans. Circ. Syst. I

D. Dardari, “Joint clip and quantization effects characterization in OFDM receivers,” IEEE Trans. Circ. Syst. I 53, 1741–1748 (2006).
[CrossRef]

J. Lightwave Technol.

N. Kaneda, Q. Yang, X. Liu, S. Chandrasekhar, W. Shieh, and Y.-K. Chen, “Real-time 2.5 GS/s coherent optical receiver for 53.3-Gb/s sub-banded OFDM,” J. Lightwave Technol. 28, 494–501 (2010).
[CrossRef]

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

S. Jansen, I. Morita, T. Schenk, N. Takeda, and H. Tanaka, “Coherent optical 25.8-Gb/s OFDM transmission over 4160-km SSMF,” J. Lightwave Technol. 1, 6–15 (2008).
[CrossRef]

X. Jin, J. Tang, K. Qiu, and P. Spencer, “Statistical investigation of the transmission performance of adaptively modulated optical OFDM signals in multimode fiber links,” J. Lightwave Technol. 18, 3216–3224 (2008).
[CrossRef]

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

Opt. Express

Other

C. R. Berger, Y. Benlachtar, and R. I. Killey, “Optimum clipping for optical OFDM with limited resolution DAC/ADC,” in “Proc. OSA Advanced Photonics Congress,”(Toronto, CA, 2011).

Y. Benlachtar, R. Bouziane, R. Killey, C. Berger, P. Milder, R. Koutsoyannis, J. Hoe, M. Püschel, and M. Glick, “Optical OFDM in the data center,” in “Proc. of Intl. Conf. on Transparent Optical Networks,” (Munich, Germany, 2010).
[CrossRef]

A. Papoulis and S. U. Pillai, Probability, Random Variables and Stochastic Processes (McGraw-Hill, 2002).

For simplicity we neglect the effect of the receive filters and ADC conversion on this noise term.

J. G. Proakis, Digital Communications, 4th ed. (McGraw-Hill, 2001).

B. Inan, O. Karakaya, P. Kainzmaier, S. Adhikari, S. Calabro, V. A. Sleiffer, N. Hanik, and S. L. Jansen, “Realization of a 23.9 Gb/s real time optical-OFDM transmitter with a 1024 point IFFT,” in “Optical Fiber Communication Conference and Exposition (OFC),”(Los Angeles, CA, 2011).

R. Schmogrow, M. Winter, B. Nebendahl, D. Hillerkuss, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “101.5 Gbit/s real-time OFDM transmitter with 16QAM modulated sub-carriers,” in “Optical Fiber Communication Conference and Exposition (OFC),”(Los Angeles, CA, 2011).

F. Buchali, R. Dischler, A. Klekamp, M. Bernhard, and Y. Ma, “Statistical transmission experiments using a real-time 12.1 Gb/s OFDM transmitter,” in “Optical Fiber Communication Conference and Exposition (OFC),”(San Diego, CA, 2010).

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Figures (10)

Fig. 1
Fig. 1

Mid-rise quantizer using q = log2(M) bits, the quantization step-size is Δ; any value larger than M/2 ·Δ will be clipped.

Fig. 2
Fig. 2

Plot of mean-square error (MSE) vs. clipping ratio based on Eq. (31) for NAEs = 1; clearly for each DAC resolution of q = log2 M bits, there is an optimal tradeoff between quantization and clipping error that minimizes the total MSE.

Fig. 3
Fig. 3

The DAC and ADC are both simulated using a raised-cosine filter, g LPF(τ), with bandwidth B = 21.4 GHz, roll-off 1/8, and impulse response truncated to 40/B = 1.9 ns.

Fig. 4
Fig. 4

Numerical simulation of electrical back-to-back: MSE for varying DAC resolution and ideal ADC (a), and MSE for DAC and ADC of equal resolution (b); DFT size K = 128.

Fig. 5
Fig. 5

Numerical simulation of electrical back-to-back for several combinations of DAC/ADC resolution and modulation scheme; the optimum clipping ratio in the MSE sense also leads mostly to the lowest BER.

Fig. 6
Fig. 6

Experimental setup; the OFDM signal is generated offline and then fed into a waveform generator that drives a Mach-Zehnder modulator (MZM); the optical signal is converted to an electrical signal using a photo-diode and digitized using a sampling scope, after which receiver processing is done offline.

Fig. 7
Fig. 7

Magnitude response G DAC(f) of the digital-to-analog converter (DAC) used in the experimental setup.

Fig. 8
Fig. 8

Comparison of (a) numerical simulation and (b) experimental results for a 3 bit DAC, 8 bit ADC, and optical SNR of 30 dB; the DAC uses a clipping ratio of 4.5 dB, the ADC distortion is negligible; due to direct-detection, subcarriers |m| < 200 experience IMD.

Fig. 9
Fig. 9

Average signal-to-noise ratio (SNR) for a 3 and 6 bit DAC resolution when varying the clipping ratio; the optimum clipping ratio largely agrees with prediction.

Fig. 10
Fig. 10

Bit error rate (BER) when varying the clipping ratio: for 16-QAM with 3 bit DAC resolution (a), and 64-QAM coupled with 6 bit DAC resolution (b).

Equations (43)

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x [ n ] = k S A s [ k ] e j 2 π n k K , n = N CP , , K 1 .
S A { K / 2 , , K / 2 1 } .
x q [ n ] = x [ n ] + v D [ n ] ,
D DAC = E [ | x q [ n ] x [ n ] | 2 ] = E [ | v D [ n ] | 2 ] ,
x q [ n ] = k = K / 2 K / 2 1 s q [ k ] e j 2 π n k K .
s q [ k ] = { s [ k ] + v ˜ D [ k ] k S A , v ˜ D [ k ] k S A ,
v ˜ D [ k ] = 1 K n = 0 K 1 v D [ n ] e j 2 π n k K .
x ( t ) = ( n = N CP K 1 x q [ n ] δ ( t n T s ) ) g DAC ( τ ) = n = N CP K 1 x q [ n ] g DAC ( t n T s ) ,
x ˜ ( t ) = 2 Re { x ( t ) e j 2 π f c t } = cos ( 2 π f c t ) Re { x ( t ) } + sin ( 2 π f c t ) Im { x ( t ) } .
y ˜ ( t ) = x ˜ ( t ) h ( τ ) + v N ( t ) .
y ( t ) = y ˜ ( t ) e j 2 π f c t = [ y ˜ ( t ) cos ( 2 π f c t ) ] j [ y ˜ ( t ) sin ( 2 π f c t ) ] .
y [ n ] = ( y ( t ) g ADC ( τ ) ) | t = n T s , n = N CP , , K 1 .
y q [ n ] = y [ n ] + v A [ n ] .
z [ m ] = 1 K n = 0 K 1 y q [ n ] e j 2 π n m K ,
= H [ m ] ( s [ m ] + v ˜ D [ m ] ) + v ˜ N [ m ] + v ˜ A [ m ] ,
H [ m ] = G DAC ( f m ) H ( f m ) G ADC ( f m ) , f m = f c + m K B ,
SNR [ m ] = | H [ m ] | 2 E [ | s [ m ] | 2 ] | H [ m ] | 2 E [ | v ˜ D [ m ] | 2 ] + E [ | v ˜ A [ m ] | 2 ] + E [ | v ˜ N [ m ] | 2 ] , m S A .
m = K / 2 K / 2 1 E [ | v ˜ D [ m ] | 2 ] = 1 K n = 0 K 1 E [ | v D [ n ] | 2 ] = D DAC ,
E [ v D [ n ] v D * [ n ] ] = δ ( n n ) D DAC .
E [ | v ˜ D [ m ] | 2 ] = 1 K 2 n = 0 K 1 n = 0 K 1 e j 2 π ( n n ) m K E [ v D [ n ] v D * [ n ] ] = 1 K 2 n = 0 K 1 E [ | v D [ n ] | 2 ] = 1 K D DAC .
N 0 = E [ | v N [ m ] | 2 ] = K E [ | v ˜ N [ m ] | 2 ] ,
SNR [ m ] = | H [ m ] | 2 E [ | s [ m ] | 2 ] 1 K ( | H [ m ] | 2 D DAC + D ADC + N 0 ) , m S A .
E [ x [ n ] ] = k S A E [ s [ k ] ] e j 2 π n k K = 0 ,
E [ | x [ n ] | 2 ] = k S A k S A E [ s [ k ] s * [ k ] ] e j 2 π n ( k k ) K , = k S A E [ | s [ k ] | 2 ] = N A E s .
D DAC = 2 ( t t q ) 2 f ( t ) d t = 4 0 M / 2 Δ ( t t q ) 2 f ( t ) d t quantization error + 4 M / 2 Δ ( t t q ) 2 f ( t ) d t , clipping error
0 M / 2 Δ ( t t q ) 2 f ( t ) d t = m = 0 M / 2 1 m Δ ( m + 1 ) Δ ( t 2 m + 1 2 Δ ) 2 f ( t ) d t ,
M / 2 Δ ( t t q ) 2 f ( t ) d t = M / 2 Δ ( t M 1 2 Δ ) 2 f ( t ) d t .
f ( t ) = 1 2 π σ e t 2 2 σ 2 .
a b ( t c ) 2 f ( t ) d t = ( c 2 + σ 2 ) [ Φ ( b σ ) Φ ( a σ ) ] + 2 σ 2 π [ ( c b 2 ) e b 2 2 σ 2 ( c a 2 ) e a 2 2 σ 2 ] ,
Φ ( t ) = 1 2 π t e τ 2 2 d τ .
D DAC ( M , Δ = γ N A E S = N A E s m = 0 M / 2 1 ( [ ( 2 m + 1 ) 2 γ 2 + 2 ] [ Φ ( 2 ( m + 1 ) γ ) Φ ( 2 m γ ) ] + 2 π γ [ m e ( m + 1 ) 2 γ 2 ( m + 1 ) e m 2 γ 2 ] ) + N A E s ( [ M 1 ) 2 γ 2 + 2 ] [ 1 Φ ( M 2 γ ) ] M 2 π γ e M 2 4 γ 2 )
Δ = γ N A E s ,
clipping ratio : = 1 2 max { | x q [ n ] | 2 } E [ | x [ n ] | 2 ] = ( M / 2 Δ ) 2 N A E s = M 2 4 γ 2 ,
S A = { 56 , , 1 } { 1 , , 56 } ,
SNR [ m ] = K / N A D DAC + D ADC + N 0 , m S A ,
BER QPSK = 1 Φ ( SNR )
BER 16 QAM = 1 1 4 [ 3 Φ ( 1 5 SNR ) + 2 Φ ( 3 5 SNR ) Φ ( SNR ) ]
BER 64 QAM = 1 1 12 [ 7 Φ ( 1 21 SNR ) + 6 Φ ( 3 21 SNR ) Φ ( 5 21 SNR ) + Φ ( 9 21 SNR ) Φ ( 13 21 SNR ) ]
R = B | S A | K + N CP log 2 M .
S A = { 456 , , 257 } { 257 , , 456 } .
E [ | s [ m ] | 2 ] = 1 α 1 | G DAC [ m ] | 2 ,
m S A E [ | s [ m ] | 2 ] = 1 α = m S A 1 | G DAC [ m ] | 2 .
SNR [ m ] = K / N A | G DAC [ m ] | 2 ( α / N A ) D DAC + D ADC + N 0 ,

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