Abstract

A new intersymbol interference (ISI)-free nonlinearity-tolerant frequency domain root M-shaped pulse (RMP) is derived for dispersion unmanaged coherent optical transmission systems. Beginning with the relationship between pulse shaping and intra-channel nonlinearity effects, we derive closed-form expressions for the proposed pulse. Experimental demonstrations reveal that by employing the proposed pulse at a roll-off factor of 1, the maximum transmission reach of a single-channel 56 Gb/s polarization-division-multiplexed quadrature phase-shift keying (PDM-QPSK) system can be extended by 33% and 17%, when compared to systems using a root raised cosine (RRC) pulse and a root optimized pulse (ROP), respectively. For a single-channel 128 Gb/s polarization-division-multiplexed 16-quadrature amplitude modulation (PDM-16QAM) system, the reach can be extended by 44% and 18%, respectively. Reach increases of 30% and 13% are also observed for a dense wavelength-division multiplexing (DWDM) 504 Gb/s PDM-QPSK transmission system. The tolerance to narrow filtering effect for the three pulses is experimentally studied as well.

© 2013 Optical Society of America

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References

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2013 (1)

Y. Gao, J. C. Cartledge, J. D. Downie, J. E. Hurley, D. Pikula, and S. S.-H. Yam, “Nonlinearity compensation of 224 Gb/s dual polarization 16-QAM transmission over 2700 km,” IEEE Photon. Technol. Lett. 25(1), 14–17 (2013).
[Crossref]

2012 (3)

2011 (1)

2010 (4)

2008 (1)

2002 (1)

J. Yang, J.-J. Werner, and G. A. Dumont, “The multimodulus blind equalization and its generalized algorithms,” IEEE J. Sel. Areas Comm. 20(5), 997–1015 (2002).
[Crossref]

1999 (1)

1988 (1)

M. Oerder and H. Meyr, “Digital filter and square timing recovery,” IEEE Trans. Commun. 36(5), 605–612 (1988).
[Crossref]

1980 (1)

D. Godard, “Self-recovering equalization and carrier tracking in two-dimensional data communication systems,” IEEE Trans. Commun. 28(11), 1867–1875 (1980).
[Crossref]

1928 (1)

H. Nyquist, “Certain topics in telegraph transmission theory,” Trans. Am. Inst. Electr. Eng. 47(2), 617–644 (1928).
[Crossref]

Bayvel, P.

Behrens, C.

Borowiec, A.

B. Châtelain, C. Laperle, K. Roberts, M. Chagnon, X. Xu, A. Borowiec, F. Gagnon, and D. V. Plant, “A family of Nyquist pulses for coherent optical communications,” Opt. Express 20(8), 8397–8416 (2012).
[Crossref] [PubMed]

B. Châtelain, C. Laperle, D. Krause, K. Roberts, M. Chagnon, X. Xu, A. Borowiec, F. Gagnon, J. C. Cartledge, and D. V. Plant, “SPM-tolerant pulse shaping for 40- and 100-Gb/s dual-polarization QPSK systems,” IEEE Photon. Technol. Lett. 22, 1641–1643 (2010).

Bosco, G.

Buhl, L. L.

Carena, A.

Cartledge, J. C.

Y. Gao, J. C. Cartledge, J. D. Downie, J. E. Hurley, D. Pikula, and S. S.-H. Yam, “Nonlinearity compensation of 224 Gb/s dual polarization 16-QAM transmission over 2700 km,” IEEE Photon. Technol. Lett. 25(1), 14–17 (2013).
[Crossref]

B. Châtelain, C. Laperle, D. Krause, K. Roberts, M. Chagnon, X. Xu, A. Borowiec, F. Gagnon, J. C. Cartledge, and D. V. Plant, “SPM-tolerant pulse shaping for 40- and 100-Gb/s dual-polarization QPSK systems,” IEEE Photon. Technol. Lett. 22, 1641–1643 (2010).

Chagnon, M.

Châtelain, B.

B. Châtelain, C. Laperle, K. Roberts, M. Chagnon, X. Xu, A. Borowiec, F. Gagnon, and D. V. Plant, “A family of Nyquist pulses for coherent optical communications,” Opt. Express 20(8), 8397–8416 (2012).
[Crossref] [PubMed]

B. Châtelain, C. Laperle, D. Krause, K. Roberts, M. Chagnon, X. Xu, A. Borowiec, F. Gagnon, J. C. Cartledge, and D. V. Plant, “SPM-tolerant pulse shaping for 40- and 100-Gb/s dual-polarization QPSK systems,” IEEE Photon. Technol. Lett. 22, 1641–1643 (2010).

Chen, M.

Curri, V.

Doerr, C. R.

Downie, J. D.

Y. Gao, J. C. Cartledge, J. D. Downie, J. E. Hurley, D. Pikula, and S. S.-H. Yam, “Nonlinearity compensation of 224 Gb/s dual polarization 16-QAM transmission over 2700 km,” IEEE Photon. Technol. Lett. 25(1), 14–17 (2013).
[Crossref]

Du, L. B.

Dumont, G. A.

J. Yang, J.-J. Werner, and G. A. Dumont, “The multimodulus blind equalization and its generalized algorithms,” IEEE J. Sel. Areas Comm. 20(5), 997–1015 (2002).
[Crossref]

El-Sahn, Z. A.

Essiambre, R.

Forghieri, F.

Foschini, G.

Gagnon, F.

B. Châtelain, C. Laperle, K. Roberts, M. Chagnon, X. Xu, A. Borowiec, F. Gagnon, and D. V. Plant, “A family of Nyquist pulses for coherent optical communications,” Opt. Express 20(8), 8397–8416 (2012).
[Crossref] [PubMed]

B. Châtelain, C. Laperle, D. Krause, K. Roberts, M. Chagnon, X. Xu, A. Borowiec, F. Gagnon, J. C. Cartledge, and D. V. Plant, “SPM-tolerant pulse shaping for 40- and 100-Gb/s dual-polarization QPSK systems,” IEEE Photon. Technol. Lett. 22, 1641–1643 (2010).

Gao, Y.

Y. Gao, J. C. Cartledge, J. D. Downie, J. E. Hurley, D. Pikula, and S. S.-H. Yam, “Nonlinearity compensation of 224 Gb/s dual polarization 16-QAM transmission over 2700 km,” IEEE Photon. Technol. Lett. 25(1), 14–17 (2013).
[Crossref]

Gnauck, A. H.

Godard, D.

D. Godard, “Self-recovering equalization and carrier tracking in two-dimensional data communication systems,” IEEE Trans. Commun. 28(11), 1867–1875 (1980).
[Crossref]

Goebel, B.

Hurley, J. E.

Y. Gao, J. C. Cartledge, J. D. Downie, J. E. Hurley, D. Pikula, and S. S.-H. Yam, “Nonlinearity compensation of 224 Gb/s dual polarization 16-QAM transmission over 2700 km,” IEEE Photon. Technol. Lett. 25(1), 14–17 (2013).
[Crossref]

Ip, E.

Kahn, J.

Killey, R. I.

Kramer, G.

Krause, D.

B. Châtelain, C. Laperle, D. Krause, K. Roberts, M. Chagnon, X. Xu, A. Borowiec, F. Gagnon, J. C. Cartledge, and D. V. Plant, “SPM-tolerant pulse shaping for 40- and 100-Gb/s dual-polarization QPSK systems,” IEEE Photon. Technol. Lett. 22, 1641–1643 (2010).

Laperle, C.

B. Châtelain, C. Laperle, K. Roberts, M. Chagnon, X. Xu, A. Borowiec, F. Gagnon, and D. V. Plant, “A family of Nyquist pulses for coherent optical communications,” Opt. Express 20(8), 8397–8416 (2012).
[Crossref] [PubMed]

B. Châtelain, C. Laperle, D. Krause, K. Roberts, M. Chagnon, X. Xu, A. Borowiec, F. Gagnon, J. C. Cartledge, and D. V. Plant, “SPM-tolerant pulse shaping for 40- and 100-Gb/s dual-polarization QPSK systems,” IEEE Photon. Technol. Lett. 22, 1641–1643 (2010).

Lowery, A. J.

Magarini, M.

Makovejs, S.

Mamyshev, P. V.

Mamysheva, N. A.

Meyr, H.

M. Oerder and H. Meyr, “Digital filter and square timing recovery,” IEEE Trans. Commun. 36(5), 605–612 (1988).
[Crossref]

Morsy-Osman, M.

Mousa-Pasandi, M. E.

Nyquist, H.

H. Nyquist, “Certain topics in telegraph transmission theory,” Trans. Am. Inst. Electr. Eng. 47(2), 617–644 (1928).
[Crossref]

Oerder, M.

M. Oerder and H. Meyr, “Digital filter and square timing recovery,” IEEE Trans. Commun. 36(5), 605–612 (1988).
[Crossref]

Pikula, D.

Y. Gao, J. C. Cartledge, J. D. Downie, J. E. Hurley, D. Pikula, and S. S.-H. Yam, “Nonlinearity compensation of 224 Gb/s dual polarization 16-QAM transmission over 2700 km,” IEEE Photon. Technol. Lett. 25(1), 14–17 (2013).
[Crossref]

Plant, D. V.

Poggiolini, P.

Roberts, K.

B. Châtelain, C. Laperle, K. Roberts, M. Chagnon, X. Xu, A. Borowiec, F. Gagnon, and D. V. Plant, “A family of Nyquist pulses for coherent optical communications,” Opt. Express 20(8), 8397–8416 (2012).
[Crossref] [PubMed]

B. Châtelain, C. Laperle, D. Krause, K. Roberts, M. Chagnon, X. Xu, A. Borowiec, F. Gagnon, J. C. Cartledge, and D. V. Plant, “SPM-tolerant pulse shaping for 40- and 100-Gb/s dual-polarization QPSK systems,” IEEE Photon. Technol. Lett. 22, 1641–1643 (2010).

Savory, S. J.

Werner, J.-J.

J. Yang, J.-J. Werner, and G. A. Dumont, “The multimodulus blind equalization and its generalized algorithms,” IEEE J. Sel. Areas Comm. 20(5), 997–1015 (2002).
[Crossref]

Winzer, P.

Winzer, P. J.

Xu, X.

Yam, S. S.-H.

Y. Gao, J. C. Cartledge, J. D. Downie, J. E. Hurley, D. Pikula, and S. S.-H. Yam, “Nonlinearity compensation of 224 Gb/s dual polarization 16-QAM transmission over 2700 km,” IEEE Photon. Technol. Lett. 25(1), 14–17 (2013).
[Crossref]

Yang, J.

J. Yang, J.-J. Werner, and G. A. Dumont, “The multimodulus blind equalization and its generalized algorithms,” IEEE J. Sel. Areas Comm. 20(5), 997–1015 (2002).
[Crossref]

Zhuge, Q.

IEEE J. Sel. Areas Comm. (1)

J. Yang, J.-J. Werner, and G. A. Dumont, “The multimodulus blind equalization and its generalized algorithms,” IEEE J. Sel. Areas Comm. 20(5), 997–1015 (2002).
[Crossref]

IEEE Photon. Technol. Lett. (2)

Y. Gao, J. C. Cartledge, J. D. Downie, J. E. Hurley, D. Pikula, and S. S.-H. Yam, “Nonlinearity compensation of 224 Gb/s dual polarization 16-QAM transmission over 2700 km,” IEEE Photon. Technol. Lett. 25(1), 14–17 (2013).
[Crossref]

B. Châtelain, C. Laperle, D. Krause, K. Roberts, M. Chagnon, X. Xu, A. Borowiec, F. Gagnon, J. C. Cartledge, and D. V. Plant, “SPM-tolerant pulse shaping for 40- and 100-Gb/s dual-polarization QPSK systems,” IEEE Photon. Technol. Lett. 22, 1641–1643 (2010).

IEEE Trans. Commun. (2)

M. Oerder and H. Meyr, “Digital filter and square timing recovery,” IEEE Trans. Commun. 36(5), 605–612 (1988).
[Crossref]

D. Godard, “Self-recovering equalization and carrier tracking in two-dimensional data communication systems,” IEEE Trans. Commun. 28(11), 1867–1875 (1980).
[Crossref]

J. Lightwave Technol. (4)

Opt. Express (4)

Opt. Lett. (1)

Trans. Am. Inst. Electr. Eng. (1)

H. Nyquist, “Certain topics in telegraph transmission theory,” Trans. Am. Inst. Electr. Eng. 47(2), 617–644 (1928).
[Crossref]

Other (9)

X. Xu, B. Châtelain, Q. Zhuge, M. Morsy-Osman, M. Chagnon, M. Qiu, and D. Plant, “Frequency domain M-shaped pulse for SPM nonlinearity mitigation in coherent optical communications,” in Proc. OFC2013, paper JTh2A.38.
[Crossref]

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions: With Formulars, Graphs, and Mathematical Tables (Dover, 1964).

A. V. Oppenheim and R. W. Schafer, Discrete-Time Signal Processing, 3rd ed. (Prentice Hall, 2009).

G. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2006).

S. Makovejs, E. Torrengo, D. Millar, R. Killey, S. Savory, and P. Bayvel, “Comparison of pulse shapes in a 224Gbit/s (28Gbaud) PDM-QAM16 long-haul transmission experiment,” in Proc. OFC2011, paper OMR5.
[Crossref]

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

T. Hoshida, L. Dou, W. Yan, L. Li, Z. Tao, S. Oda, H. Nakashima, C. Ohshima, T. Oyama, and J. Rasmussen, “Advanced and feasible signal processing algorithm for nonlinear mitigation,” in Proc. OFC2013, paper OTh3C.3.
[Crossref]

Y. M. Greshishchev, D. Pollex, S.-C. Wang, M. Besson, P. Flemeke, S. Szilagyi, J. Aguirre, C. Falt, N. Ben-Hamida, R. Gibbins, and P. Schvan, “A 56GS/S 6b DAC in 65nm CMOS with 256×6b memory,” in Proc. ISSCC2011, pp. 194–196.

C. Laperle, “Advances in high-speed ADC, DAC, and DSP for optical transceiversben,” in Proc. OFC2013, paper OTh1F.5.

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Figures (14)

Fig. 1
Fig. 1 The MP’s ideal (a) frequency responses and (b) impulse responses; the RMP’s ideal (c) frequency responses and (d) impulse responses at depth factors βof 1 (red dashed line), 0.5 (black solid line) and 0.25 (blue dotted line) and a roll-off factor of 1.
Fig. 2
Fig. 2 The ideal frequency responses of the RC pulse (black dashed line) and MP (red solid line) at roll-off factors α of (a) 0, (b) 0.5 and (c)1 and the ideal frequency responses of the RRC pulse (black dashed line) and RMP (Red solid line) at roll-off factorsα of (d) 0 (d), (e) 0.5 and (f) 1. (Note: the ideal frequency response of the RC/RRC pulse (black dashed line) is covered by the MP/RMP (red solid line) in Figs. 2(a) and 2(d)).
Fig. 3
Fig. 3 The ideal impulse responses of the RC pulse (black dashed line) and MP (Red solid line) at roll-off factorsα of (a) 0, (b) 0.5 and (c) 1 and the ideal impulse responses of the RRC pulse (black dashed line) and RMP (Red solid line) at roll-off factor α of (d) 0 (d), (e) 0.5 and (f) 1. (Note: the ideal impulse response of the RC/RRC pulse (black dashed line) is covered by the MP/RMP (red solid line) in Figs. 3(a) and 3(d)).
Fig. 4
Fig. 4 The eyediagrams of the MP after matched filtering with a rectangular truncation window of (a) 16, (b) 32 and (c) 64 symbols.
Fig. 5
Fig. 5 The frequency responses of the pulse shaping filters for the RRC pulse, the ROP and the RMP at a roll-off factor of 1 after applying a rectangular window.
Fig. 6
Fig. 6 The power profiles of the RRC pulse, ROP and RMP (a) without CD and (b) with 17000 ps/nm CD.
Fig. 7
Fig. 7 The ratio of σ/T versus the transmission distance in a SSMF for the RRC pulse, ROP and RMP.
Fig. 8
Fig. 8 Schematic of the single-channel experimental setup. (Tx: transmitter; PC: polarization controller; PBS: polarization beam splitter; PBC: polarization beam combiner; ODL: optical delay line; VOA: variable optical attenuator; SW: switch; OSA: optical spectrum analyzer; T-T BPF: tunable bandwidth and tunable central wavelength bandpass filter; LO: local oscillator; Rx: receiver; DSP: digital signal processing; BER: bit error rate.).
Fig. 9
Fig. 9 (a) The back-to-back BER versus the OSNR. (b) The required OSNR versus the launch power for the RMP with β=0.25, 0.5, 0.75, 1 at 4160 km. (c) The required OSNR versus the launch power for the RRC pulse, ROP and RMP with a β=0.5 at 4160 km. (d) The launch power versus the maximum transmission distance for the RRC pulse, ROP and RMP with a β=0.5 for a single-channel 14 Gbaud PDM-QPSK experiment.
Fig. 10
Fig. 10 (a) The back-to-back BER versus the OSNR. (b) The required OSNR versus the launch power for the RMP with β=0.25, 0.5, 0.75, 1 at 1200 km. (c) The required OSNR versus the launch power for the RRC pulse, ROP and RMP with a β=0.75 at 1200 km. (d) The launch power versus the maximum transmission distance for the RRC pulse, ROP and RMP with a β=0.75 for a single-channel 16 Gbaud PDM-16QAM experiment.
Fig. 11
Fig. 11 (a) Schematic of the DWDM PDM-QPSK experimental setup. (CH: channel; DFB: distributed feedback laser; AWG: arrayed waveguide grating; IL: interleaver; ODL: optical delay line.). (b) The spectrum of the 9 channels DWDM signal at OSNR = 29dB, measured from 1% tap out of the signal with an OSA resolution bandwidth of 0.05nm.
Fig. 12
Fig. 12 (a) The back-to-back BER versus the OSNR. (b) The required OSNR versus the launch power for the RMP with β=0.25, 0.5, 0.75, 1 at 4160 km. (c) The required OSNR versus the launch power for the RRC pulse, ROP and RMP with a β=0.5 at 4160 km. (d) The launch power versus the maximum transmission distance for the RRC pulse, ROP and RMP with a β=0.5 for the central channel in the DWDM 14 GBaud PDM-QPSK transmission system.
Fig. 13
Fig. 13 Schematic of the narrow filtering experimental setup.
Fig. 14
Fig. 14 The OSNR penalty versus the filter bandwidth for the RRC pulse, ROP and RMP. The inset figure shows the spectra of the 14 GBaud PDM-QPSK RMP signal with a β=0.5 and the filter with different bandwidths.

Tables (1)

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Table 1 Conclusion of the Experimental Results of the RMP with Respect to the RRC and ROP

Equations (10)

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n= X(f+n/T) =T.
M(f)={   T                                                   | f |< 1α 2T (1β)× T 2 α×(1+β) [ | f | 1α 2T ]+ β×T 1+β    1α 2T | f | 1+α 2T 0                                                      | f |> 1+α 2T .
RM(f)= M(f) ={    T                                                    | f |< 1α 2T (1β)× T 2 α×(1+β) [ | f | 1α 2T ]+ β×T 1+β    1α 2T | f | 1+α 2T 0                                                      | f |> 1+α 2T .
m(t)= (1β) 4α(1+β) { [ (1α)Sinc( 1α 2T t) ] 2 [ (1+α)Sinc( 1+α 2T t) ] 2 } + 1 1+β [ (1+α)Sinc( 1+α T t)+(1α)Sinc( 1α T t) ].
rm(t)=[ p ap/2+b sinc(pt)+n( T an/2+b )sinc(nt)) ] 1 i(4 π t) { e iπct i2πt/a [ erfz( iπ(n+c)t )erfz( iπ(p+c)t ) ]+ e iπct i2πt/a [ erfz( iπ(p+c)t )erfz( iπ(n+c)t ) ] }.
a={ (1β) T 2 α(1+β) α0 0 α=0 .
b={ (αβ+α+β1)T 2α(1+β) α0 T α=0 .
c={ 2b a α0 0 α=0 .
p= 1+α T .
n= 1α T .

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