Abstract

A low-complexity optical phase noise suppression approach based on recursive principal components elimination, R-PCE, is proposed and theoretically derived for CO-OFDM systems. Through frequency domain principal components estimation and elimination, signal distortion caused by optical phase noise is mitigated by R-PCE. Since matrix inversion and domain transformation are completely avoided, compared with the case of the orthogonal basis expansion algorithm (L = 3) that offers a similar laser linewidth tolerance, the computational complexities of multiple principal components estimation are drastically reduced in the R-PCE by factors of about 7 and 5 for q = 3 and 4, respectively. The feasibility of optical phase noise suppression with the R-PCE and its decision-aided version (DA-R-PCE) in the QPSK/16QAM CO-OFDM system are demonstrated by Monte-Carlo simulations, which verify that R-PCE with only a few number of principal components q ( = 3) provides a significantly larger laser linewidth tolerance than conventional algorithms, including the common phase error compensation algorithm and linear interpolation algorithm. Numerical results show that the optimal performance of R-PCE and DA-R-PCE can be achieved with a moderate q, which is beneficial for low-complexity hardware implementation.

© 2015 Optical Society of America

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References

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2015 (1)

2014 (1)

X. Fang, C. Yang, T. Zhang, and F. Zhang, “Orthogonal basis expansion based phase noise suppression for PDM CO-OFDM system,” IEEE Photonics Technol. Lett. 26(4), 376–379 (2014).
[Crossref]

2013 (1)

S. Cao, P. Kam, and C. Yu, “Time-domain blind ICI mitigation for non-constant modulus format in CO-OFDM,” IEEE Photonics Technol. Lett. 25(24), 2490–2493 (2013).
[Crossref]

2012 (3)

2011 (3)

2010 (1)

W. Chung, “A matched filtering approach for phase noise suppression in CO-OFDM systems,” IEEE Photonics Technol. Lett. 22(24), 1802–1804 (2010).
[Crossref]

2008 (3)

2007 (2)

X. Yi, W. Shieh, and Y. Tang, “Phase estimation for coherent optical OFDM,” IEEE Photonics Technol. Lett. 19(12), 919–921 (2007).
[Crossref]

E. Ip and J. Kahn, “Feedforward carrier recovery for coherent optical communications,” J. Lightwave Technol. 25(9), 2675–2692 (2007).
[Crossref]

2004 (1)

S. Wu and Y. Bar-Ness, “OFDM systems in the presence of phase noise: consequences and solutions,” IEEE Trans. Commun. 52(11), 1988–1996 (2004).
[Crossref]

Bar-Ness, Y.

S. Wu and Y. Bar-Ness, “OFDM systems in the presence of phase noise: consequences and solutions,” IEEE Trans. Commun. 52(11), 1988–1996 (2004).
[Crossref]

Buchali, F.

Cao, S.

S. Cao, P. Kam, and C. Yu, “Time-domain blind ICI mitigation for non-constant modulus format in CO-OFDM,” IEEE Photonics Technol. Lett. 25(24), 2490–2493 (2013).
[Crossref]

Chagnon, M.

Chandrasekhar, S.

Chen, X.

Christodoulopoulos, K.

Chung, W.

W. Chung, “A matched filtering approach for phase noise suppression in CO-OFDM systems,” IEEE Photonics Technol. Lett. 22(24), 1802–1804 (2010).
[Crossref]

Cvijetic, N.

Dimarcello, F. V.

El-Sahn, Z. A.

Fang, X.

X. Fang, C. Yang, T. Zhang, and F. Zhang, “Orthogonal basis expansion based phase noise suppression for PDM CO-OFDM system,” IEEE Photonics Technol. Lett. 26(4), 376–379 (2014).
[Crossref]

Fini, J. M.

Fishteyn, M.

He, S.

Ho, K. P.

Y. Tang, K. P. Ho, and W. Shieh, “Coherent optical OFDM transmitter design employing predistortion,” IEEE Photonics Technol. Lett. 20(11), 954–956 (2008).
[Crossref]

Hong, X.

Ip, E.

Kahn, J.

Kam, P.

S. Cao, P. Kam, and C. Yu, “Time-domain blind ICI mitigation for non-constant modulus format in CO-OFDM,” IEEE Photonics Technol. Lett. 25(24), 2490–2493 (2013).
[Crossref]

Kikuchi, K.

Liu, X.

Ma, Y.

Monberg, E. M.

Mousa-Pasandi, M. E.

Osman, M. M.

Pan, Y.

Plant, D. V.

Shieh, W.

X. Yi, W. Shieh, and Y. Ma, “Phase noise effects on high spectral efficiency coherent optical OFDM transmission,” J. Lightwave Technol. 26(10), 1309–1316 (2008).
[Crossref]

Y. Tang, K. P. Ho, and W. Shieh, “Coherent optical OFDM transmitter design employing predistortion,” IEEE Photonics Technol. Lett. 20(11), 954–956 (2008).
[Crossref]

X. Yi, W. Shieh, and Y. Tang, “Phase estimation for coherent optical OFDM,” IEEE Photonics Technol. Lett. 19(12), 919–921 (2007).
[Crossref]

Tang, Y.

Y. Tang, K. P. Ho, and W. Shieh, “Coherent optical OFDM transmitter design employing predistortion,” IEEE Photonics Technol. Lett. 20(11), 954–956 (2008).
[Crossref]

X. Yi, W. Shieh, and Y. Tang, “Phase estimation for coherent optical OFDM,” IEEE Photonics Technol. Lett. 19(12), 919–921 (2007).
[Crossref]

Taunay, T. F.

Tomkos, I.

Varvarigos, E. A.

Wang, Z.

Winzer, P. J.

Wu, S.

S. Wu and Y. Bar-Ness, “OFDM systems in the presence of phase noise: consequences and solutions,” IEEE Trans. Commun. 52(11), 1988–1996 (2004).
[Crossref]

Xu, X.

Yan, M. F.

Yang, C.

X. Fang, C. Yang, T. Zhang, and F. Zhang, “Orthogonal basis expansion based phase noise suppression for PDM CO-OFDM system,” IEEE Photonics Technol. Lett. 26(4), 376–379 (2014).
[Crossref]

C. Yang, F. Yang, and Z. Wang, “Phase noise suppression for coherent optical block transmission systems: a unified framework,” Opt. Express 19(18), 17013–17020 (2011).
[Crossref] [PubMed]

Yang, F.

Yi, X.

X. Yi, W. Shieh, and Y. Ma, “Phase noise effects on high spectral efficiency coherent optical OFDM transmission,” J. Lightwave Technol. 26(10), 1309–1316 (2008).
[Crossref]

X. Yi, W. Shieh, and Y. Tang, “Phase estimation for coherent optical OFDM,” IEEE Photonics Technol. Lett. 19(12), 919–921 (2007).
[Crossref]

Yu, C.

S. Cao, P. Kam, and C. Yu, “Time-domain blind ICI mitigation for non-constant modulus format in CO-OFDM,” IEEE Photonics Technol. Lett. 25(24), 2490–2493 (2013).
[Crossref]

Zhang, F.

X. Fang, C. Yang, T. Zhang, and F. Zhang, “Orthogonal basis expansion based phase noise suppression for PDM CO-OFDM system,” IEEE Photonics Technol. Lett. 26(4), 376–379 (2014).
[Crossref]

Zhang, T.

X. Fang, C. Yang, T. Zhang, and F. Zhang, “Orthogonal basis expansion based phase noise suppression for PDM CO-OFDM system,” IEEE Photonics Technol. Lett. 26(4), 376–379 (2014).
[Crossref]

Zhu, B.

Zhuge, Q.

IEEE Photonics Technol. Lett. (5)

X. Yi, W. Shieh, and Y. Tang, “Phase estimation for coherent optical OFDM,” IEEE Photonics Technol. Lett. 19(12), 919–921 (2007).
[Crossref]

X. Fang, C. Yang, T. Zhang, and F. Zhang, “Orthogonal basis expansion based phase noise suppression for PDM CO-OFDM system,” IEEE Photonics Technol. Lett. 26(4), 376–379 (2014).
[Crossref]

S. Cao, P. Kam, and C. Yu, “Time-domain blind ICI mitigation for non-constant modulus format in CO-OFDM,” IEEE Photonics Technol. Lett. 25(24), 2490–2493 (2013).
[Crossref]

W. Chung, “A matched filtering approach for phase noise suppression in CO-OFDM systems,” IEEE Photonics Technol. Lett. 22(24), 1802–1804 (2010).
[Crossref]

Y. Tang, K. P. Ho, and W. Shieh, “Coherent optical OFDM transmitter design employing predistortion,” IEEE Photonics Technol. Lett. 20(11), 954–956 (2008).
[Crossref]

IEEE Trans. Commun. (1)

S. Wu and Y. Bar-Ness, “OFDM systems in the presence of phase noise: consequences and solutions,” IEEE Trans. Commun. 52(11), 1988–1996 (2004).
[Crossref]

J. Lightwave Technol. (4)

Opt. Express (6)

Other (3)

F. Buchali, X. Xiao, S. Chen, and M. Bernhard, “Towards real-time CO-OFDM transceivers,” in Proc. OFC, paper. OWE1 (2011).
[Crossref]

N. Cvijetic, M. Huang, E. Ip, Y. Shao, Y. Huang, M. Cvijetic, and T. Wang, “Coherent 40Gb/s OFDMA-PON for long-reach (100+ km) high-split ratio (> 1: 64) optical access/metro networks,” in Proc. OFC, paper. OW4B.8 (2012).
[Crossref]

R. Gaudino, V. Curri, G. Bosco, G. Rizzelli, A. Nespola, D. Zeolla, S. Straullu, S. Capriata, and P. Solina, “On the use of DFB lasers for coherent PON,” in Proc. OFC, paper. OTh4G.1 (2011).

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Figures (6)

Fig. 1
Fig. 1 (a) Schematic diagram of the proposed optical phase noise suppression algorithm R-PCE. The red dashed line denotes the decision-aided version of R-PCE. (b) The normalized spectrum |P(k)| of optical phase noise with perfect estimation (black) and the R-PCE algorithm (red, number of principal components q = 5). Only central five components are visible in the R-PCE (q = 5) case as all other components are assumed to be zero values. (c) BER versus OSNR with two different sets of ik (1 ≤ kq = 6) in the 16QAM CO-OFDM system under three different laser linewidths (500 kHz, 1 MHz and 1.5 MHz). Better performance is obtained with set II in which the central frequency components are estimated first.
Fig. 2
Fig. 2 BER versus OSNR for the R-PCE algorithm in the QPSK/16QAM CO-OFDM system under combined laser linewidths of (a) 2 MHz and (b) 500 kHz.
Fig. 3
Fig. 3 (a) Required OSNR at a BER of 3.8 × 10−3 in the back-to-back 16QAM CO-OFDM system with various phase noise suppression algorithms. Unless otherwise marked, all BER results are obtained with ISFA channel estimation (the number of training symbols Nt = 2). (b) The contour plots of the receiver sensitivity at a BER of 3.8 × 10−3 for the R-PCE algorithms with respect to different combined laser linewidths and different numbers of principal components.
Fig. 4
Fig. 4 (a) Mean squared modeling error versus the number of principal components q. (b) Mean squared cascaded estimation error versus the number of principal components q.
Fig. 5
Fig. 5 The contour plots of receiver sensitivity at a BER of 3.8 × 10−3 with respect to different q1 in the PA estimation stage and different q2 in the DA estimation stage of DA-R-PCE under combined laser linewidths of (a) 500 kHz and (b) 2 MHz.
Fig. 6
Fig. 6 BER performance of the 16QAM CO-OFDM system after 320 km SSMF transmission with various phase noise suppression algorithms versus different combined laser linewidths.

Tables (1)

Tables Icon

Table 1 The required number of complex-valued multiplications (RNCM) in different algorithms

Equations (12)

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Y = H ^ 1 H F Φ F H X + W A S E F Φ F H X + W A S E
X F Φ * F H Y + Δ δ
F Φ * F H Y = 1 N [ 1 1 1 1 e j 2 π N e j 2 π ( N 1 ) N 1 e j 2 π ( N 1 ) N e j 2 π ( N 1 ) ( N 1 ) N ] [ e j ϕ ( 0 ) 0 0 0 e j ϕ ( 1 ) 0 0 0 e j ϕ ( N 1 ) ] [ 1 1 1 1 e j 2 π N e j 2 π ( N 1 ) N 1 e j 2 π ( N 1 ) N e j 2 π ( N 1 ) ( N 1 ) N ] [ Y ( 0 ) Y ( 1 ) Y ( N 1 ) ]
P ( k ) = 1 N n = 0 N 1 e j ϕ ( n ) e j 2 π n k N
F Φ * F H Y = 1 N [ Y ( 0 ) Y ( N 1 ) Y ( N 2 ) Y ( 1 ) Y ( 1 ) Y ( 0 ) Y ( N 1 ) Y ( 2 ) Y ( N 1 ) Y ( N 2 ) Y ( N 3 ) Y ( 0 ) ] [ P ( 0 ) P ( 1 ) P ( N 1 ) ]
P q = [ P ( 0 ) P ( L 1 ) P ( N L 2 ) P ( N 1 ) ] , T q = [ Y , Y 1 , , Y L 1 , Y N L 2 , , Y N 2 , Y N 1 ] , where L 2 = q 2 , Y k = 1 N [ Y ( N k ) Y ( N 1 ) Y ( 0 ) Y ( N k 1 ) ]
X T q P q + Δ ζ
X T q 1 P q 1 Y i q P ( i q ) + Δ ζ , where i q = { L 1 , q i s e v e n N- L 2 , q i s odd
P ^ ( i q ) = ( S Y i q ) H S X q ( S Y i q ) H ( S Y i q ) , where X q = X T q 1 P ^ q 1 X q 1 Y i q 1 P ^ ( i q 1 )
P ^ ( 0 ) = ( S Y ) H S X ( S Y ) H ( S Y )
P ^ ( i 1 ) = N exp ( j a n g l e ( P ^ ( 0 ) ) )
X ^ = Θ ( T q P ^ q )

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