Abstract

The interplay between the stochastic intensity fluctuation of Raman pump laser and cross-phase modulation (XPM) effect in transmission optical fiber leads to additional phase noise, namely, relative phase noise (RPN) of signal in multi-level modulated coherent optical communication system. Both theoretical analysis and quantitative simulation have been performed to investigate the characteristics and impact of RPN. Being low-pass in nature, RPN is different from XPM induced phase noise in PSK/OOK hybrid system, and has not been considered yet. The noise power of RPN can accumulate incoherently along transmission links. With a proper signal model, we study the impact of RPN to the coherent optical communication system through Monte Carlo simulation. RPN will cause more cycle slips in Viterbi-and-Viterbi (V-V) phase estimation (PE), and the quantitative analysis of cycle slip probability is carried out. When using sliding window V-V without any optimization, the Q factor penalty of RPN on DQPSK signal can be as large as around 5 dB in strong RPN condition. However, it can be reduced by over 3 dB when using an optimal block size or optimal averaging weights.

© 2014 Optical Society of America

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References

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2013 (1)

2009 (4)

2006 (2)

2001 (1)

Chen, J.

Cheng, J.

Fludger, C. R. S.

Fu, S.

Goldfarb, G.

Handerek, V.

Hoshida, T.

Kam, P. Y.

Katoh, K.

Kikuchi, K.

Li, G.

Liu, D.

Ly-Gagnon, D.-S.

Mears, R. J.

Oda, S.

Rasmussen, J. C.

Shum, P. P.

Tang, M.

Tao, Z.

Taylor, M. G.

Tsukamoto, S.

Yan, W.

Yu, C.

Zhang, S.

Adv. Opt. Photonics (1)

G. Li, “Recent advances in coherent optical communication,” Adv. Opt. Photonics 1(2), 279–307 (2009).
[Crossref]

J. Lightwave Technol. (3)

Opt. Express (3)

Opt. Lett. (1)

Other (4)

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2000).

L. Li, Z. Tao, S. Oda, T. Tanimura, M. Yuki, T. Hoshida, and J. C. Rasmussen, “Adaptive optimization for digital carrier phase estimation in optical coherent receivers,” in Digest IEEE/LEOS Summer Topical Meetings, Acapulco, Mexico, Jul. 2008, pp. 121–122, paper TuC3.3.

L. Li, Z. Tao, L. Liu, W. Yan, S. Oda, T. Hoshida, and J. C. Rasmussen, “XPM tolerant adaptive carrier phase recovery for coherent receiver based on phase noise statistics monitoring,” in Proc. European Conference on Optical Communications (2009), paper P3.16.

T. Tanimura, S. Oda, M. Yuki, H. Zhang, L. Li, Z. Tao, H. Nakashima, T. Hoshida, K. Nakamura, and J. C. Rasmussen, “Non-linearity tolerance of direct detection and coherent receivers for 43 Gb/s RZ-DQPSK signals with co-propagating 11.1 Gb/s NRZ signals over NZ-DSF,” in Tech. Digest of the Conference on Optical Fiber Communication (2008), paper OTuM4.
[Crossref]

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Figures (9)

Fig. 1
Fig. 1

RPN transfer function for both co-pumping and counter-pumping configuration.

Fig. 2
Fig. 2

Phase samples of (a) laser phase noise of beat linewidth of 300 kHz. (b) XPM induced phase noise in PSK/OOK hybrid system. (c) co-pumping RPN. (d) counter-pumping RPN.

Fig. 3
Fig. 3

Cycle slip probability for QPSK signal versus variance of RPN.

Fig. 4
Fig. 4

Variances of RPN versus pump RIN.

Fig. 5
Fig. 5

Signal constellation (a) back-to-back (b) with RPN, pump RIN is −105 dB/Hz.

Fig. 6
Fig. 6

Optimal block size versus Raman pump RIN.

Fig. 7
Fig. 7

Optimal averaging weights.

Fig. 8
Fig. 8

Signal constellation using (a) optimal block size (b) optimal weights.

Fig. 9
Fig. 9

Q factor performance versus pump RIN.

Tables (1)

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Table 1 Simulation Parameters

Equations (17)

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± A p ± z + α p 2 A p ± =i γ p | A p ± | 2 A p ± .
A s z d A s T + α s 2 A s =i γ s (2 f R )| A p ± | 2 A s + g s 2 | A p ± | 2 A s .
RP N s (f)= δ θ 2 θ 2 .
θ co = γ s (2 f R ) P p0 1 e α p z α p .
θ counter = γ s (2 f R ) P p0 e α p L e α p z 1 α p .
RP N s (f) co =RI N p (f) M 2 (z)+ N 2 (z) [ α p 2 + (2πfd) 2 ] 2 α p 2 ( 1 e α p z ) 2 .
RP N s (f) counter =RI N p (f) M 2 (z)+ N 2 (z) [ α p 2 + (2πfd) 2 ] 2 α p 2 ( e α p z 1 ) 2 .
M(z)= e α p z [ α p sin(2πfdz)+2πfdcos(2πfdz) ]2πfd.
N(z)= e α p z [ 2πfdsin(2πfdz) α p cos(2πfdz) ]+ α p .
M (z)= e α p z [ α p sin(2πfdz)+2πfdcos(2πfdz) ]2πfd.
N (z)= e α p z [ 2πfdsin(2πfdz)+ α p cos(2πfdz) ] α p .
σ RPN 2 = θ RPN 2 (t) = ν 1 ν 2 RP N s (f)· θ 2 df .
r k = E s,k exp[ j( θ d,k + θ LW,k + θ ¯ RPN + θ RPN,k ) ]+ n k .
c y c l e s l i p p r o b a b i l i t y = A exp ( B σ R P N 2 ) .
( h( L ) h( L+1 ) h( L ) )= ( R ( 0 ) R ( 1 ) R ( 2L ) R ( 1 ) R ( 0 ) R ( 2L1 ) R ( 2L ) R ( 2L1 ) R ( 0 ) ) 1 ×( R( L ) R( L1 ) R( L ) ).
R( m )=exp{ 16 σ RPN 2 [ ρ( m )1 ] }.
R ( m )=exp{ 16 σ RPN 2 [ ρ( m )1 ] }+16 σ n 2 δ( m ).

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