Abstract

This paper proposes a maximum-ratio combining (MRC) scheme for a WDM signal and phase-conjugate pair (PCP) diversity transmission to cancel nonlinear phase-shift. A transfer function approximation for nonlinear phase-shift cancellation is formulated. It shows, with the help of a numerical calculation, that span-by-span chromatic dispersion compensation is more effective than the lumped equivalent at the receiver. This is confirmed in a 2-core diversity 5 channel WDM transmission experiment over 3-spans of 60km MCF with 25 Gbit/s-QPSK PCP. The peak Q-value was enhanced by 3.6dB through MRC, resulting in superior bitrate-distance product and optical power density limit, compared to twice the single core transmission.

© 2016 Optical Society of America

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References

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  1. A. Sano, T. Kobayashi, S. Yamanaka, A. Matsuura, H. Kawakami, Y. Miyamoto, K. Ishihara, and H. Masuda, “102.3-Tb/s (224x548-Gb/s) C- and extended L-band all-raman transmission over 240 km using PDM −64-QAM single carrier FDM with digital pilot tone,” in Proceedings of OFC/NFOEC 2012, paper PDP5C.3.
  2. D. Qian, M. Huang, Y. Huang, Y. Shao, J. Hu, and T. Wang, 101.7-Tb/s (370x294-Gb/s) PDM-128QAM-OFDM transmission over 3x55-km SSMF using pilot-based phase noise mitigation,” in Proceedings of OFC/NFOEC 2011, paper PDPB5.
  3. D. G. Foursa, H. G. Batshon, H. Zhang, M. Mazurczyk, J.-X. Cai, O. Sinkin, A. Pilipetskii, G. Mohs, and N. S. Bergano, “44.1 Tb/s transmission over 9,100 km using coded modulation based on 16QAM signals at 4.9 Bits/s/Hz spectral efficiency,” in Proceedings of European Conference on Optical Communication(ECOC) 2013, paper PD3.E.1.
    [Crossref]
  4. S. Todoroki, Fiber Fuse (Springer Press, 2014).
  5. T. Morioka, “New generation optical infrastructure technologies: EXAT initiative towards 2020 and beyond,” in Proceedings of OECC 2009, paper FT4.
    [Crossref]
  6. H. Takara, A. Sano, T. Kobayashi, H. Kubota, H. Kawakami, A. Matsuura, Y. Miyamoto, Y. Abe, H. Ono, K. Shikama, Y. Goto, K. Tsujikawa, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Koshiba, and T. Morioka, “1.01-Pb/s (12 SDM/222 WDM/456 Gb/s) crosstalk-managed transmission with 91.4-b/s/Hz aggregate spectral efficiency,” in Proceedings of ECOC 2012, paper Th.3.c.1.
    [Crossref]
  7. B. J. Puttnam, R. S. Luis, W. Klaus, J. Sakaguchi, J.-M. Delgado Mendinueta, Y. Awaji, and N. Wada, Yoshiaki Tamura, Tetsuya Hayashi, Masaaki Hirano, J. Marciante, “2.15 Pb/s transmission using a 22 core homogeneous single-mode multi-core fiber and wideband optical comb,” in Proceedings of ECOC 2015, paper PDP.3.1.
  8. D. Soma, et al., “2.05 Peta-bit/s super-nyquist-WDM SDM transmission using 9.8-km 6-mode 19-core fiber in full C band,” in Proceedings of ECOC 2015, paper PDP.3.2.
    [Crossref]
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    [Crossref]
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    [Crossref]
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  15. T. Iida, A. Mizutori, and M. Koga, “Optical diversity transmission and maximum-ratio combining in multi-core fiber to mitigate fiber non-linear distortion,” in Proceedings of OECC 2012, paper 6B2–5.
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  17. M. Koga, M. Moroi, and H. Takara, “Nonlinear phase-shift cancellation by maximum-ratio combining WDM phase-conjugate diversity lights transmitted through Multi-core Fiber,” in Proceedings of ECOC 2015, paper We.2.6.6.
    [Crossref]
  18. X. Liu, A. R. Chraplyvy, P. J. Winzer, R. W. Tkach, and S. Chandrasekhar, “Phase-conjugated twin waves for communication beyond the Kerr nonlinearity limit,” Nat. Photonics 7(7), 560–568 (2013).
    [Crossref]
  19. H. Lu, Y. Mori, C. Han, and K. Kikuchi, “Novel polarization-diversity scheme based on mutual phase conjugation for fiber-nonlinearity mitigation in ultra-long coherent optical transmission systems” in Proceedings of ECOC 2013, paper We.3.C.3.
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2013 (1)

X. Liu, A. R. Chraplyvy, P. J. Winzer, R. W. Tkach, and S. Chandrasekhar, “Phase-conjugated twin waves for communication beyond the Kerr nonlinearity limit,” Nat. Photonics 7(7), 560–568 (2013).
[Crossref]

2008 (2)

1996 (1)

S. Watanabe and M. Shirasaki, “Exact compensation for both chromatic dispersion and Kerr effect in a transmission fiber using optical phase conjugation,” IEEE J. Lightwave Tech. 14(3), 243–248 (1996).
[Crossref]

Chandrasekhar, S.

X. Liu, A. R. Chraplyvy, P. J. Winzer, R. W. Tkach, and S. Chandrasekhar, “Phase-conjugated twin waves for communication beyond the Kerr nonlinearity limit,” Nat. Photonics 7(7), 560–568 (2013).
[Crossref]

Chen, X.

Chraplyvy, A. R.

X. Liu, A. R. Chraplyvy, P. J. Winzer, R. W. Tkach, and S. Chandrasekhar, “Phase-conjugated twin waves for communication beyond the Kerr nonlinearity limit,” Nat. Photonics 7(7), 560–568 (2013).
[Crossref]

Goldfarb, G.

Kim, I.

Li, G.

Li, X.

Liu, X.

X. Liu, A. R. Chraplyvy, P. J. Winzer, R. W. Tkach, and S. Chandrasekhar, “Phase-conjugated twin waves for communication beyond the Kerr nonlinearity limit,” Nat. Photonics 7(7), 560–568 (2013).
[Crossref]

Mateo, E.

Shirasaki, M.

S. Watanabe and M. Shirasaki, “Exact compensation for both chromatic dispersion and Kerr effect in a transmission fiber using optical phase conjugation,” IEEE J. Lightwave Tech. 14(3), 243–248 (1996).
[Crossref]

Tkach, R. W.

X. Liu, A. R. Chraplyvy, P. J. Winzer, R. W. Tkach, and S. Chandrasekhar, “Phase-conjugated twin waves for communication beyond the Kerr nonlinearity limit,” Nat. Photonics 7(7), 560–568 (2013).
[Crossref]

Watanabe, S.

S. Watanabe and M. Shirasaki, “Exact compensation for both chromatic dispersion and Kerr effect in a transmission fiber using optical phase conjugation,” IEEE J. Lightwave Tech. 14(3), 243–248 (1996).
[Crossref]

Winzer, P. J.

X. Liu, A. R. Chraplyvy, P. J. Winzer, R. W. Tkach, and S. Chandrasekhar, “Phase-conjugated twin waves for communication beyond the Kerr nonlinearity limit,” Nat. Photonics 7(7), 560–568 (2013).
[Crossref]

Yaman, F.

Zhu, L.

IEEE J. Lightwave Tech. (1)

S. Watanabe and M. Shirasaki, “Exact compensation for both chromatic dispersion and Kerr effect in a transmission fiber using optical phase conjugation,” IEEE J. Lightwave Tech. 14(3), 243–248 (1996).
[Crossref]

Nat. Photonics (1)

X. Liu, A. R. Chraplyvy, P. J. Winzer, R. W. Tkach, and S. Chandrasekhar, “Phase-conjugated twin waves for communication beyond the Kerr nonlinearity limit,” Nat. Photonics 7(7), 560–568 (2013).
[Crossref]

Opt. Express (2)

Other (16)

H. Lu, Y. Mori, C. Han, and K. Kikuchi, “Novel polarization-diversity scheme based on mutual phase conjugation for fiber-nonlinearity mitigation in ultra-long coherent optical transmission systems” in Proceedings of ECOC 2013, paper We.3.C.3.

M. Schwartz, W. R. Bennett, and S. Stein, Communication Systems and Techniques (IEEE Press, 1966).

T. Umeki, T. Kazama, H. Ono, Y. Miyamoto, and H. Takenouchi, “Spectrally efficient optical phase conjugation based on complementary spectral inversion for nonlinearity mitigation” in Proceedings of ECOC 2015, paper We.2.6.2.
[Crossref]

D. Ellis, I. D. Phillips, M. Tan, M. F. C. Stephens, M. E. McCarthy, M. A. Z. Al Kahteeb, M. A. Iqbal, A. Perentos, S. Fabbri, V. Gordienko, D. Lavery, G. Liga, and G. Saavedra, M., R. Maher, S. Sygletos, P. Harper, N. J. Doran, P. Bayvel, S. K. Turitsyn “Enhanced superchannel transmission using phase conjugation” in Proceedings of ECOC 2015, paper We.2.6.4.

T. Iida, A. Mizutori, and M. Koga, “Optical diversity transmission and maximum-ratio combining in multi-core fiber to mitigate fiber non-linear distortion,” in Proceedings of OECC 2012, paper 6B2–5.

M. Koga, A. Mizutori, T. Ohata, and H. Takara, “Optical diversity transmission with signal and its phaseconjugate lights through multi-core Fiber” in Proceedings of OFC 2015, paper Th1D.4.

M. Koga, M. Moroi, and H. Takara, “Nonlinear phase-shift cancellation by maximum-ratio combining WDM phase-conjugate diversity lights transmitted through Multi-core Fiber,” in Proceedings of ECOC 2015, paper We.2.6.6.
[Crossref]

A. Sano, T. Kobayashi, S. Yamanaka, A. Matsuura, H. Kawakami, Y. Miyamoto, K. Ishihara, and H. Masuda, “102.3-Tb/s (224x548-Gb/s) C- and extended L-band all-raman transmission over 240 km using PDM −64-QAM single carrier FDM with digital pilot tone,” in Proceedings of OFC/NFOEC 2012, paper PDP5C.3.

D. Qian, M. Huang, Y. Huang, Y. Shao, J. Hu, and T. Wang, 101.7-Tb/s (370x294-Gb/s) PDM-128QAM-OFDM transmission over 3x55-km SSMF using pilot-based phase noise mitigation,” in Proceedings of OFC/NFOEC 2011, paper PDPB5.

D. G. Foursa, H. G. Batshon, H. Zhang, M. Mazurczyk, J.-X. Cai, O. Sinkin, A. Pilipetskii, G. Mohs, and N. S. Bergano, “44.1 Tb/s transmission over 9,100 km using coded modulation based on 16QAM signals at 4.9 Bits/s/Hz spectral efficiency,” in Proceedings of European Conference on Optical Communication(ECOC) 2013, paper PD3.E.1.
[Crossref]

S. Todoroki, Fiber Fuse (Springer Press, 2014).

T. Morioka, “New generation optical infrastructure technologies: EXAT initiative towards 2020 and beyond,” in Proceedings of OECC 2009, paper FT4.
[Crossref]

H. Takara, A. Sano, T. Kobayashi, H. Kubota, H. Kawakami, A. Matsuura, Y. Miyamoto, Y. Abe, H. Ono, K. Shikama, Y. Goto, K. Tsujikawa, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Koshiba, and T. Morioka, “1.01-Pb/s (12 SDM/222 WDM/456 Gb/s) crosstalk-managed transmission with 91.4-b/s/Hz aggregate spectral efficiency,” in Proceedings of ECOC 2012, paper Th.3.c.1.
[Crossref]

B. J. Puttnam, R. S. Luis, W. Klaus, J. Sakaguchi, J.-M. Delgado Mendinueta, Y. Awaji, and N. Wada, Yoshiaki Tamura, Tetsuya Hayashi, Masaaki Hirano, J. Marciante, “2.15 Pb/s transmission using a 22 core homogeneous single-mode multi-core fiber and wideband optical comb,” in Proceedings of ECOC 2015, paper PDP.3.1.

D. Soma, et al., “2.05 Peta-bit/s super-nyquist-WDM SDM transmission using 9.8-km 6-mode 19-core fiber in full C band,” in Proceedings of ECOC 2015, paper PDP.3.2.
[Crossref]

L. Dou, Z. Tao, L. Li, and W. Yan, Takahito Tanimura, Takeshi Hoshida, and Jens C. Rasmussen, “A low complexity pre-distortion method for intra-channel nonlinearity” in Proceedings of OFC 2011, paper OThF5.

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Figures (9)

Fig. 1
Fig. 1 Optical diversity transmission and maximum-ratio combining model; Pin: Fiber input power, Hi L: channel #i linear transfer function, Zi: Fourier transform of white Gaussian noise, Wi: Weighting function.
Fig. 2
Fig. 2 L-span transmission model for transfer function approximation; DCF; Dispersion compensation fiber, Gl : lth repeater amplifier gain..
Fig. 3
Fig. 3 The vector relationships for phase-conjugate signal pair. A(sig)(z,t) and A(conj)(z,t) symbol points for d = π/4 and 3π/4 are plotted for QPSK modulation in (a). Nonlinear phase shift in phase conjugate symbol pair in (b).
Fig. 4
Fig. 4 Simulated constellation maps for phase-conjugate signal pair. Those for chromatic dispersion (CD) values of 6 and 20.5 ps/nm/km are simulated.
Fig. 5
Fig. 5 Combined symbol point, represented in the frequency domain, for phase-conjugate signal pair.
Fig. 6
Fig. 6 Experimental setup for WDM phase-conjugate pair diversity transmission. DCF was removed in case of lumped compensation. EDFA; Erbium-Doped Fiber Amplifier, AWGen; Arbitarary Waveform Generator, OBPF; Optical Band Pass Filter, PC; Polarization controller, LO; Local Oscillator, ADC; Analogue-to-Digital Converter.
Fig. 7
Fig. 7 Q2-value and its gain vs. fiber launched total power Ptotal for span-by-span and lump CD compensation. Ptotal = Pin for single core transmission and Ptotal = 2xPin for diversity.
Fig. 8
Fig. 8 Measured constellation maps for original and its phase conjugate signal pair and their combination. Fiber launched power Ptotal was 7 and 10dBm.
Fig. 9
Fig. 9 Q2-value and its gain vs. fiber launched total power Ptotal for CD = 6 and 20.5 ps/nm/km. Ptotal = Pin for single core transmission and Ptotal = 2xPin for diversity.

Equations (30)

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e i ( 0 , t ) = 2 P i i n A i ( 0 , t ) cos ( ω 0 t ) = ( 1 / 2 ) A i ( 0 , t ) exp ( j ω 0 t ) + c . c .
A i ( 0 , t ) = 1 2 π A i ( Ω ) e j Ω t d Ω
e i ( z , t ) = e j ω 0 t 1 4 π A i ( Ω ) e { ( α / 2 ) + j β ( ω 0 + Ω ) } z e j Ω t d Ω + c . c .
β i ( ω = ω 0 + Ω ) = β i ( ω 0 ) + β i ω | ω 0 Ω + 1 2 2 β i ω 2 | ω 0 Ω 2 +
e i ( z , t ) = ( 1 / 2 ) exp [ j ( ω 0 t β 0 i z ) ] × [ 1 2 π A i ( Ω ) exp { ( α i / 2 ) + j ( Ω t Ω z v g i 1 2 d d ω ( 1 v g i ) Ω 2 z ) } d Ω ] + c . c .
H i L ( Ω ) = exp { j Ω ( 1 / v g + b i Ω ) z }
e i ( z , t ) = exp [ ( α i / 2 ) + j ( ω 0 t β 0 i z ) ] 1 4 π A i ( Ω ) H i L ( Ω ) exp { j ( Ω t ) } d Ω + c . c .
A o u t ( Ω ) = i = 1 M { W i ( Ω ) ( H i L ( Ω ) A i ( Ω ) + Z i ( Ω ) ) } = i = 1 M { W i ( Ω ) H i L ( Ω ) A i ( Ω ) } + i = 1 M { W i ( Ω ) Z i ( Ω ) } = ( W T H ) A + W T Z
P o u t = E [ ( W T H A ) ( W T H A ) * ] = ( W T H ) E [ A A * ] ( W T H ) * = ( W T H ) ( W T H ) * E [ A A * ] = ( W T H ) ( W T H ) * ( P t o t a l / M )
Z t o t a l = E [ ( i = 1 M W i Z i ) ( i = 1 M W i Z i ) * ] = ( W T Z ) ( W T Z ) * = W * W N i = i = 1 M | W i | 2 N i
Γ = P o u t Z t o t a l = ( W T H ) ( W T H ) * ( P t o t a l / M ) W W N i = | i M W i H i | 2 i | W i | 2 N i ( P t o t a l / M )
Γ max = ( P t o t a l / M ) i M | H i | 2 / N i
W i = a H i L * ( Ω ) / N i
e i , k ( 0 , t ) = ( 1 / 2 ) A i , k ( 0 , t ) exp ( j ω k t ) + c . c .
A i , k l { ( l 1 ) z r , t } = 1 2 π G l ( Ω ) A ˜ i , k l 1 ( Ω ) e j Ω t d Ω
A ˜ i , k l ( Ω ) = A ˜ i , k l 1 ( Ω ) H i , k L ( Ω )
A ˜ i , k l ( Ω ) = A ˜ i , k l 1 ( Ω ) H i , k L ( Ω ) exp { j b i , k Ω 2 z r }
e i , k ( l z , t ) = exp [ ( α i / 2 ) z r + j { ω 0 t β 0 i , k ( l z r ) } ] × 1 4 π A ˜ i , k l ( Ω ) H i , k L ( Ω ) e j Ω t d Ω + c . c .
H i , k N L ( Ω ) = exp { j β i , k N L ( Ω ) z r }
β i , k N L ( Ω ) 2 γ i j = 1 , j k J | A i , j ( Ω ) | 2
H i , k ( Ω ) = H i , k L ( Ω ) H i , k N L ( Ω )
H i , k * ( Ω ) = exp { j Ω ( 1 / v g i , k + b i , k Ω ) z r } exp { j β i , k N L ( Ω ) z r }
A i , k ( s i g ) ( z , t ) A i , k ( z , t ) = A ' i , k ( z , t ) exp { j d ( t ) }
A i , k ( c o n j ) ( z , t ) A i , k * ( z , t ) = A i , k ' * ( z , t ) exp { j d ( t ) }
A i , k o u t ( Ω ) = W i , k ( Ω ) H i , k L ( Ω ) { A ˜ i , k ( Ω ) H i , k N L ( Ω ) + ( A ˜ i , k * ( Ω ) H i , k N L ( Ω ) ) * }
A i , k ( s i g ) ( z , t ) = 1 2 π A ˜ i , k ( Ω ) e j Ω t d Ω
A i , k ( c o n j ) ( z , t ) = 1 2 π A ˜ i , k ( Ω ) e j ( Ω t ) d Ω
A ˜ i , k ( Ω ) H i , k N L ( Ω ) + ( A ˜ i , k * ( Ω ) H i , k N L ( Ω ) ) * = 2 A ˜ i , k ( Ω ) cos { β i , k N L ( Ω ) z r }
Q C o m b = W s i g Q s i g + W c o n j Q c o n j
W s i g + W c o n j = 1

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