Abstract

We investigate the application of time and frequency packing techniques, an extension of the classical faster-than-Nyquist signaling, to long-haul optical links. These techniques provide a significant spectral efficiency increase and represent a viable alternative to overcome the theoretical and technological issues related to the use of high-order modulation formats. Adopting these techniques, we successfully demonstrate through simulations the transmission of 1 Tbps over 200 GHz bandwidth in a realistic (nonlinear) long-haul optical link.

© 2011 OSA

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  1. S. Chandrasekhar and X. Liu, “Enabling components for future high-speed coherent communication systems,” in Proc. Optical Fiber Commun. Conf. (OFC’09) (Los Angeles, CA, USA, 2011), Paper OMU5.
  2. G. Colavolpe, T. Foggi, E. Forestieri, and G. Prati, “Robust multilevel coherent optical systems with linear processing at the receiver,” J. Lightwave Technol. 27, 2357–2369 (2009).
    [CrossRef]
  3. J. Zhao and A. Ellis, “Electronic impairment mitigation in optically multiplexed multicarrier systems,” J. Light-wave Technol. 29, 278–290 (2011).
    [CrossRef]
  4. G. Bosco, V. Curri, A. Carena, P. Poggiolini, and F. Forghieri, “On the performance of nyquist-WDM terabit superchannels based on PM-QPSK, PM-8PSK or PM-16QAM subcarriers,” J. Lightwave Technol. 29, 53–61 (2011).
    [CrossRef]
  5. J. E. Mazo, “Faster-than-Nyquist signaling,” Bell System Tech. J. 54, 1450–1462 (1975).
  6. F. Rusek and J. B. Anderson, “The two dimensional Mazo limit,” in Proc. IEEE International Symposium on Information Theory, (Adelaide, Australia, 2005), pp. 970–974.
  7. A. Barbieri, D. Fertonani, and G. Colavolpe,“ Time-frequency packing for linear modulations: spectral efficiency and practical detection schemes,” IEEE Trans. Commun. 57, 2951–2959 (2009).
  8. N. Merhav, G. Kaplan, A. Lapidoth, and S. Shamai, “On information rates for mismatched decoders,” IEEE Trans. Inform. Theory 40, 1953–1967 (1994).
    [CrossRef]
  9. D. M. Arnold, H.-A. Loeliger, P. O. Vontobel, A. Kavčić, and W. Zeng, “Simulation-based computation of information rates for channels with memory,” IEEE Trans. Inform. Theory 52, 3498–3508 (2006).
    [CrossRef]
  10. G. D. Forney, “Maximum-likelihood sequence estimation of digital sequences in the presence of intersymbol interference,” IEEE Trans. Inform. Theory 18, 284–287 (1972).
    [CrossRef]
  11. L. R. Bahl, L. R. Cocke, F. Jelinek, and J. Raviv, “Optimal decoding of linear codes for minimizing symbol error rate,” IEEE Trans. Inform. Theory 20, 284–287 (1974).
    [CrossRef]
  12. G. Colavolpe and A. Barbieri, “On MAP symbol detection for ISI channels using the Ungerboeck observation model,” IEEE Commun. Lett. 9, 720–722 (2005).
    [CrossRef]
  13. G. Ungerboeck, “Adaptive maximum likelihood receiver for carrier-modulated data-transmission systems,” IEEE Trans. Commun. com-22, 624–636 (1974).
    [CrossRef]
  14. F. Rusek and D. Fertonani, “Lower bounds on the information rate of intersymbol interference channels based on the ungerboeck observation model,” in Proc. IEEE International Symposium on Information Theory (2009).
  15. G. Colavolpe, D. Fertonani, and A. Piemontese, “SISO detection over linear channels with linear complexity in the number of interferers,” IEEE J. Sel. Top. Signal Process. (submitted).
  16. A. Barbieri, G. Colavolpe, T. Foggi, E. Forestieri, and G. Prati, “OFDM vs. single-carrier transmission for 100 Gbps optical communication,” J. Lightwave Technol. 28, 2537–2551 (2010).
    [CrossRef]

2011

2010

2009

G. Colavolpe, T. Foggi, E. Forestieri, and G. Prati, “Robust multilevel coherent optical systems with linear processing at the receiver,” J. Lightwave Technol. 27, 2357–2369 (2009).
[CrossRef]

A. Barbieri, D. Fertonani, and G. Colavolpe,“ Time-frequency packing for linear modulations: spectral efficiency and practical detection schemes,” IEEE Trans. Commun. 57, 2951–2959 (2009).

2006

D. M. Arnold, H.-A. Loeliger, P. O. Vontobel, A. Kavčić, and W. Zeng, “Simulation-based computation of information rates for channels with memory,” IEEE Trans. Inform. Theory 52, 3498–3508 (2006).
[CrossRef]

2005

G. Colavolpe and A. Barbieri, “On MAP symbol detection for ISI channels using the Ungerboeck observation model,” IEEE Commun. Lett. 9, 720–722 (2005).
[CrossRef]

1994

N. Merhav, G. Kaplan, A. Lapidoth, and S. Shamai, “On information rates for mismatched decoders,” IEEE Trans. Inform. Theory 40, 1953–1967 (1994).
[CrossRef]

1975

J. E. Mazo, “Faster-than-Nyquist signaling,” Bell System Tech. J. 54, 1450–1462 (1975).

1974

L. R. Bahl, L. R. Cocke, F. Jelinek, and J. Raviv, “Optimal decoding of linear codes for minimizing symbol error rate,” IEEE Trans. Inform. Theory 20, 284–287 (1974).
[CrossRef]

G. Ungerboeck, “Adaptive maximum likelihood receiver for carrier-modulated data-transmission systems,” IEEE Trans. Commun. com-22, 624–636 (1974).
[CrossRef]

1972

G. D. Forney, “Maximum-likelihood sequence estimation of digital sequences in the presence of intersymbol interference,” IEEE Trans. Inform. Theory 18, 284–287 (1972).
[CrossRef]

Anderson, J. B.

F. Rusek and J. B. Anderson, “The two dimensional Mazo limit,” in Proc. IEEE International Symposium on Information Theory, (Adelaide, Australia, 2005), pp. 970–974.

Arnold, D. M.

D. M. Arnold, H.-A. Loeliger, P. O. Vontobel, A. Kavčić, and W. Zeng, “Simulation-based computation of information rates for channels with memory,” IEEE Trans. Inform. Theory 52, 3498–3508 (2006).
[CrossRef]

Bahl, L. R.

L. R. Bahl, L. R. Cocke, F. Jelinek, and J. Raviv, “Optimal decoding of linear codes for minimizing symbol error rate,” IEEE Trans. Inform. Theory 20, 284–287 (1974).
[CrossRef]

Barbieri, A.

A. Barbieri, G. Colavolpe, T. Foggi, E. Forestieri, and G. Prati, “OFDM vs. single-carrier transmission for 100 Gbps optical communication,” J. Lightwave Technol. 28, 2537–2551 (2010).
[CrossRef]

A. Barbieri, D. Fertonani, and G. Colavolpe,“ Time-frequency packing for linear modulations: spectral efficiency and practical detection schemes,” IEEE Trans. Commun. 57, 2951–2959 (2009).

G. Colavolpe and A. Barbieri, “On MAP symbol detection for ISI channels using the Ungerboeck observation model,” IEEE Commun. Lett. 9, 720–722 (2005).
[CrossRef]

Bosco, G.

Carena, A.

Chandrasekhar, S.

S. Chandrasekhar and X. Liu, “Enabling components for future high-speed coherent communication systems,” in Proc. Optical Fiber Commun. Conf. (OFC’09) (Los Angeles, CA, USA, 2011), Paper OMU5.

Cocke, L. R.

L. R. Bahl, L. R. Cocke, F. Jelinek, and J. Raviv, “Optimal decoding of linear codes for minimizing symbol error rate,” IEEE Trans. Inform. Theory 20, 284–287 (1974).
[CrossRef]

Colavolpe, G.

A. Barbieri, G. Colavolpe, T. Foggi, E. Forestieri, and G. Prati, “OFDM vs. single-carrier transmission for 100 Gbps optical communication,” J. Lightwave Technol. 28, 2537–2551 (2010).
[CrossRef]

G. Colavolpe, T. Foggi, E. Forestieri, and G. Prati, “Robust multilevel coherent optical systems with linear processing at the receiver,” J. Lightwave Technol. 27, 2357–2369 (2009).
[CrossRef]

A. Barbieri, D. Fertonani, and G. Colavolpe,“ Time-frequency packing for linear modulations: spectral efficiency and practical detection schemes,” IEEE Trans. Commun. 57, 2951–2959 (2009).

G. Colavolpe and A. Barbieri, “On MAP symbol detection for ISI channels using the Ungerboeck observation model,” IEEE Commun. Lett. 9, 720–722 (2005).
[CrossRef]

G. Colavolpe, D. Fertonani, and A. Piemontese, “SISO detection over linear channels with linear complexity in the number of interferers,” IEEE J. Sel. Top. Signal Process. (submitted).

Curri, V.

Ellis, A.

J. Zhao and A. Ellis, “Electronic impairment mitigation in optically multiplexed multicarrier systems,” J. Light-wave Technol. 29, 278–290 (2011).
[CrossRef]

Fertonani, D.

A. Barbieri, D. Fertonani, and G. Colavolpe,“ Time-frequency packing for linear modulations: spectral efficiency and practical detection schemes,” IEEE Trans. Commun. 57, 2951–2959 (2009).

F. Rusek and D. Fertonani, “Lower bounds on the information rate of intersymbol interference channels based on the ungerboeck observation model,” in Proc. IEEE International Symposium on Information Theory (2009).

G. Colavolpe, D. Fertonani, and A. Piemontese, “SISO detection over linear channels with linear complexity in the number of interferers,” IEEE J. Sel. Top. Signal Process. (submitted).

Foggi, T.

Forestieri, E.

Forghieri, F.

Forney, G. D.

G. D. Forney, “Maximum-likelihood sequence estimation of digital sequences in the presence of intersymbol interference,” IEEE Trans. Inform. Theory 18, 284–287 (1972).
[CrossRef]

Jelinek, F.

L. R. Bahl, L. R. Cocke, F. Jelinek, and J. Raviv, “Optimal decoding of linear codes for minimizing symbol error rate,” IEEE Trans. Inform. Theory 20, 284–287 (1974).
[CrossRef]

Kaplan, G.

N. Merhav, G. Kaplan, A. Lapidoth, and S. Shamai, “On information rates for mismatched decoders,” IEEE Trans. Inform. Theory 40, 1953–1967 (1994).
[CrossRef]

Kavcic, A.

D. M. Arnold, H.-A. Loeliger, P. O. Vontobel, A. Kavčić, and W. Zeng, “Simulation-based computation of information rates for channels with memory,” IEEE Trans. Inform. Theory 52, 3498–3508 (2006).
[CrossRef]

Lapidoth, A.

N. Merhav, G. Kaplan, A. Lapidoth, and S. Shamai, “On information rates for mismatched decoders,” IEEE Trans. Inform. Theory 40, 1953–1967 (1994).
[CrossRef]

Liu, X.

S. Chandrasekhar and X. Liu, “Enabling components for future high-speed coherent communication systems,” in Proc. Optical Fiber Commun. Conf. (OFC’09) (Los Angeles, CA, USA, 2011), Paper OMU5.

Loeliger, H.-A.

D. M. Arnold, H.-A. Loeliger, P. O. Vontobel, A. Kavčić, and W. Zeng, “Simulation-based computation of information rates for channels with memory,” IEEE Trans. Inform. Theory 52, 3498–3508 (2006).
[CrossRef]

Mazo, J. E.

J. E. Mazo, “Faster-than-Nyquist signaling,” Bell System Tech. J. 54, 1450–1462 (1975).

Merhav, N.

N. Merhav, G. Kaplan, A. Lapidoth, and S. Shamai, “On information rates for mismatched decoders,” IEEE Trans. Inform. Theory 40, 1953–1967 (1994).
[CrossRef]

Piemontese, A.

G. Colavolpe, D. Fertonani, and A. Piemontese, “SISO detection over linear channels with linear complexity in the number of interferers,” IEEE J. Sel. Top. Signal Process. (submitted).

Poggiolini, P.

Prati, G.

Raviv, J.

L. R. Bahl, L. R. Cocke, F. Jelinek, and J. Raviv, “Optimal decoding of linear codes for minimizing symbol error rate,” IEEE Trans. Inform. Theory 20, 284–287 (1974).
[CrossRef]

Rusek, F.

F. Rusek and D. Fertonani, “Lower bounds on the information rate of intersymbol interference channels based on the ungerboeck observation model,” in Proc. IEEE International Symposium on Information Theory (2009).

F. Rusek and J. B. Anderson, “The two dimensional Mazo limit,” in Proc. IEEE International Symposium on Information Theory, (Adelaide, Australia, 2005), pp. 970–974.

Shamai, S.

N. Merhav, G. Kaplan, A. Lapidoth, and S. Shamai, “On information rates for mismatched decoders,” IEEE Trans. Inform. Theory 40, 1953–1967 (1994).
[CrossRef]

Ungerboeck, G.

G. Ungerboeck, “Adaptive maximum likelihood receiver for carrier-modulated data-transmission systems,” IEEE Trans. Commun. com-22, 624–636 (1974).
[CrossRef]

Vontobel, P. O.

D. M. Arnold, H.-A. Loeliger, P. O. Vontobel, A. Kavčić, and W. Zeng, “Simulation-based computation of information rates for channels with memory,” IEEE Trans. Inform. Theory 52, 3498–3508 (2006).
[CrossRef]

Zeng, W.

D. M. Arnold, H.-A. Loeliger, P. O. Vontobel, A. Kavčić, and W. Zeng, “Simulation-based computation of information rates for channels with memory,” IEEE Trans. Inform. Theory 52, 3498–3508 (2006).
[CrossRef]

Zhao, J.

J. Zhao and A. Ellis, “Electronic impairment mitigation in optically multiplexed multicarrier systems,” J. Light-wave Technol. 29, 278–290 (2011).
[CrossRef]

Bell System Tech. J.

J. E. Mazo, “Faster-than-Nyquist signaling,” Bell System Tech. J. 54, 1450–1462 (1975).

IEEE Commun. Lett.

G. Colavolpe and A. Barbieri, “On MAP symbol detection for ISI channels using the Ungerboeck observation model,” IEEE Commun. Lett. 9, 720–722 (2005).
[CrossRef]

IEEE J. Sel. Top. Signal Process

G. Colavolpe, D. Fertonani, and A. Piemontese, “SISO detection over linear channels with linear complexity in the number of interferers,” IEEE J. Sel. Top. Signal Process. (submitted).

IEEE Trans. Commun.

G. Ungerboeck, “Adaptive maximum likelihood receiver for carrier-modulated data-transmission systems,” IEEE Trans. Commun. com-22, 624–636 (1974).
[CrossRef]

A. Barbieri, D. Fertonani, and G. Colavolpe,“ Time-frequency packing for linear modulations: spectral efficiency and practical detection schemes,” IEEE Trans. Commun. 57, 2951–2959 (2009).

IEEE Trans. Inform. Theory

N. Merhav, G. Kaplan, A. Lapidoth, and S. Shamai, “On information rates for mismatched decoders,” IEEE Trans. Inform. Theory 40, 1953–1967 (1994).
[CrossRef]

D. M. Arnold, H.-A. Loeliger, P. O. Vontobel, A. Kavčić, and W. Zeng, “Simulation-based computation of information rates for channels with memory,” IEEE Trans. Inform. Theory 52, 3498–3508 (2006).
[CrossRef]

G. D. Forney, “Maximum-likelihood sequence estimation of digital sequences in the presence of intersymbol interference,” IEEE Trans. Inform. Theory 18, 284–287 (1972).
[CrossRef]

L. R. Bahl, L. R. Cocke, F. Jelinek, and J. Raviv, “Optimal decoding of linear codes for minimizing symbol error rate,” IEEE Trans. Inform. Theory 20, 284–287 (1974).
[CrossRef]

J. Light-wave Technol.

J. Zhao and A. Ellis, “Electronic impairment mitigation in optically multiplexed multicarrier systems,” J. Light-wave Technol. 29, 278–290 (2011).
[CrossRef]

J. Lightwave Technol.

Other

S. Chandrasekhar and X. Liu, “Enabling components for future high-speed coherent communication systems,” in Proc. Optical Fiber Commun. Conf. (OFC’09) (Los Angeles, CA, USA, 2011), Paper OMU5.

F. Rusek and D. Fertonani, “Lower bounds on the information rate of intersymbol interference channels based on the ungerboeck observation model,” in Proc. IEEE International Symposium on Information Theory (2009).

F. Rusek and J. B. Anderson, “The two dimensional Mazo limit,” in Proc. IEEE International Symposium on Information Theory, (Adelaide, Australia, 2005), pp. 970–974.

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Figures (6)

Fig. 1
Fig. 1

Achievable spectral efficiency for different modulation formats with orthogonal signaling and a bandwidth equal to the signaling frequency.

Fig. 2
Fig. 2

Achievable spectral efficiency for different modulation formats with a narrow 4th-order Gaussian optical filtering, frequency packing, and symbol-by-symbol detection.

Fig. 3
Fig. 3

Achievable spectral efficiency for different modulation formats with narrow 4th-order Gaussian optical filtering, frequency packing, and trellis processing.

Fig. 4
Fig. 4

Receiver architecture.

Fig. 5
Fig. 5

Results obtained with practical modulation and coding formats.

Fig. 6
Fig. 6

Normalized PSD of the transmitted eigth QPSK 140 Gbps channels, carrying 1 Tbps over a bandwidth of 200 GHz.

Equations (12)

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

r ( t ) = 2 E s n x n , p ( t n T ) e j 2 π F t + w ( t )
2 E s n x n , p ( t n T ) e j 2 π F t
y k , 0 = 2 E s x k , 0 h ( 0 , 0 , k ) + ( n , ) ( 0 , 0 ) x k n , h ( n , , k ) + z k
y k , 0 = 2 E s x k , 0 h ( 0 , 0 , k ) + v k
N I = ( n , ) ( 0 , 0 ) E s | h ( n , , k ) | 2
I ( x k , 0 ; y k , 0 ) = E x k , 0 , y k , 0 { log 2 ( M p Y k , 0 | X k , 0 ( y k , 0 | x k , 0 ) x χ p Y k | χ ( y k , 0 | x ) ) }
η = 1 F T I ( x k , 0 ; y k , 0 ) [ bit s Hz ] .
η M ( E b / N 0 ) = max T , F > 0 η ( T , F , E b / N 0 ) .
E s N 0 = I ( T i , F j , E s N 0 ) E b N 0
y k , 0 = 2 E s 0 n L f n x k n , 0 + v k
N I = n > L E s | f n | 2 + n 0 E s | h ( n , , k ) | 2 .
I ( x ; y ) = lim n + 1 n I ( x n ; y n ) = lim n + 1 n E { log 2 p ( y n | x n ) p ( y n ) } [ bit ch.use ] .

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