Abstract

Multiple-input-multiple-output (MIMO) mode-division-multiplexed (MDM) transmission in few-mode fiber (FMF) has been widely investigated to further enhance the capacity of optical systems and networks. In this paper, for the first time, we discuss the impact and mitigation method of random mode crosstalk induced by perturbations in FMF on timing synchronization in MIMO-MDM transmission. We show by simulation that traditional maximum correlation-based synchronization algorithms are vulnerable to random mode crosstalk and consequently cause performance degradation. To solve this problem, a novel synchronization algorithm based on minimum residual inter-block-interference (MRI) criterion is developed for frequency domain equalization (FDE) MDM systems. Theoretical analysis proves that the MRI algorithm can effectively compensate the crosstalk-induced synchronization error. Then Monte Carlo simulations are carried out under different crosstalk conditions. For 100-km 12 × 12 MDM transmission, Q2-factor improvement up to 8.7-dB has been observed and the system outage probability has been substantially reduced from 0.3 to 5e−4. The proposed MRI timing synchronization will be beneficial for the design of practical MIMO-MDM systems.

© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2015 (2)

M. Mlejnek, I. Roudas, J. Downie, N. Kaliteevskiy, and K. Koreshkov, “Coupled-mode theory of multipath interference in quasi-single mode fibers,” Photon. Journal 7(1), 7100116 (2015).

A. Lobato, Y. Chen, Y. Jung, H. Chen, B. Inan, M. Kuschnerov, N. K. Fontaine, R. Ryf, B. Spinnler, and B. Lankl, “12-mode OFDM transmission using reduced-complexity maximum likelihood detection,” Opt. Lett. 40(3), 328–331 (2015).
[PubMed]

2014 (3)

2013 (2)

D. Richardson, J. Fini, and L. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013).

Y. Huang, X. Zhang, and L. Xi, “Modified Synchronization Scheme for Coherent Optical OFDM Systems,” J. Opt. Commun. Netw. 5(6), 584–592 (2013).

2012 (2)

2011 (2)

2010 (1)

L. He, F. Yang, C. Zhang, and Z. Wang, “Synchronization for TDS-OFDM over Multipath Fading Channels,” IEEE Consum. Electr. 56(4), 2141–2147 (2010).

2009 (1)

2007 (1)

F. Mezzadri, “How to Generate Random Matrices from the Classical Compact Groups,” Not. Am. Math. Soc. 54(5), 592–604 (2007).

2002 (1)

D. Lee and K. Cheun, “Coarse symbol synchronization algorithms for OFDM systems in multipath channels,” IEEE Commun. Lett. 6(10), 446–448 (2002).

2000 (1)

B. Yang, K. Letaief, R. Cheng, and Z. Cao, “Timing Recovery for OFDM Transmission,” IEEE J. Sel. Areas Comm. 18(11), 2278–2291 (2000).

Adhikari, S.

Arik, S.

S. Arık, J. Kahn, and K. Ho, “MIMO signal processing for mode-division multiplexing: An overview of channel models and signal processing architectures,” Signal Proc. Mag. 31(2), 25–34 (2014).

Bennett, K.

Bolle, C.

Bolle, C. A.

Burrows, E.

Cao, Z.

B. Yang, K. Letaief, R. Cheng, and Z. Cao, “Timing Recovery for OFDM Transmission,” IEEE J. Sel. Areas Comm. 18(11), 2278–2291 (2000).

Chen, H.

Chen, Y.

Cheng, R.

B. Yang, K. Letaief, R. Cheng, and Z. Cao, “Timing Recovery for OFDM Transmission,” IEEE J. Sel. Areas Comm. 18(11), 2278–2291 (2000).

Cheun, K.

D. Lee and K. Cheun, “Coarse symbol synchronization algorithms for OFDM systems in multipath channels,” IEEE Commun. Lett. 6(10), 446–448 (2002).

Downie, J.

M. Mlejnek, I. Roudas, J. Downie, N. Kaliteevskiy, and K. Koreshkov, “Coupled-mode theory of multipath interference in quasi-single mode fibers,” Photon. Journal 7(1), 7100116 (2015).

Esmaeelpour, M.

Essiambre, R.

Essiambre, R. J.

Faulkner, M.

K. Wang, M. Faulkner, J. Singh, and I. Tolochko, “Timing synchronization for 802.11a WLANs under multipath channels,” in Proceedings of Australasian Telecommunication Networks and Applications Conference (IEEE, 2003), pp. 1–5.

Ferreira, F.

Fini, J.

D. Richardson, J. Fini, and L. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013).

Fontaine, N. K.

Gnauck, A.

Gnauck, A. H.

Hanik, N.

He, L.

L. He, F. Yang, C. Zhang, and Z. Wang, “Synchronization for TDS-OFDM over Multipath Fading Channels,” IEEE Consum. Electr. 56(4), 2141–2147 (2010).

Ho, K.

S. Arık, J. Kahn, and K. Ho, “MIMO signal processing for mode-division multiplexing: An overview of channel models and signal processing architectures,” Signal Proc. Mag. 31(2), 25–34 (2014).

K. Ho and J. Kahn, “Linear propagation effects in mode-division multiplexing systems,” J. Lightwave Technol. 32(4), 614–628 (2014).

K. Ho and J. Kahn, “Frequency Diversity in Mode-Division Multiplexing Systems,” J. Lightwave Technol. 29(24), 3719–3726 (2011).

Hu, J.

Huang, Y.

Inan, B.

Ip, E.

Ishihara, K.

Jansen, S. L.

Jung, Y.

Kahn, J.

K. Ho and J. Kahn, “Linear propagation effects in mode-division multiplexing systems,” J. Lightwave Technol. 32(4), 614–628 (2014).

S. Arık, J. Kahn, and K. Ho, “MIMO signal processing for mode-division multiplexing: An overview of channel models and signal processing architectures,” Signal Proc. Mag. 31(2), 25–34 (2014).

K. Ho and J. Kahn, “Frequency Diversity in Mode-Division Multiplexing Systems,” J. Lightwave Technol. 29(24), 3719–3726 (2011).

Kaliteevskiy, N.

M. Mlejnek, I. Roudas, J. Downie, N. Kaliteevskiy, and K. Koreshkov, “Coupled-mode theory of multipath interference in quasi-single mode fibers,” Photon. Journal 7(1), 7100116 (2015).

Kobayashi, T.

Koreshkov, K.

Korolev, A.

Kudo, R.

Kuschnerov, M.

Lankl, B.

Lee, D.

D. Lee and K. Cheun, “Coarse symbol synchronization algorithms for OFDM systems in multipath channels,” IEEE Commun. Lett. 6(10), 446–448 (2002).

Letaief, K.

B. Yang, K. Letaief, R. Cheng, and Z. Cao, “Timing Recovery for OFDM Transmission,” IEEE J. Sel. Areas Comm. 18(11), 2278–2291 (2000).

Li, M.

Lingle, R.

Lobato, A.

Mateo, E.

McCurdy, A.

Mezzadri, F.

F. Mezzadri, “How to Generate Random Matrices from the Classical Compact Groups,” Not. Am. Math. Soc. 54(5), 592–604 (2007).

Miyamoto, Y.

Mlejnek, M.

M. Mlejnek, I. Roudas, J. Downie, N. Kaliteevskiy, and K. Koreshkov, “Coupled-mode theory of multipath interference in quasi-single mode fibers,” Photon. Journal 7(1), 7100116 (2015).

Mumtaz, S.

Nelson, L.

D. Richardson, J. Fini, and L. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013).

Peckham, D.

Peckham, D. W.

Randel, S.

Richardson, D.

D. Richardson, J. Fini, and L. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013).

Roudas, I.

M. Mlejnek, I. Roudas, J. Downie, N. Kaliteevskiy, and K. Koreshkov, “Coupled-mode theory of multipath interference in quasi-single mode fibers,” Photon. Journal 7(1), 7100116 (2015).

Ryf, R.

Sano, A.

Sierra, A.

Singh, J.

K. Wang, M. Faulkner, J. Singh, and I. Tolochko, “Timing synchronization for 802.11a WLANs under multipath channels,” in Proceedings of Australasian Telecommunication Networks and Applications Conference (IEEE, 2003), pp. 1–5.

Sleiffer, V. A.

Spinnler, B.

Takatori, Y.

Tanaka, A.

Tolochko, I.

K. Wang, M. Faulkner, J. Singh, and I. Tolochko, “Timing synchronization for 802.11a WLANs under multipath channels,” in Proceedings of Australasian Telecommunication Networks and Applications Conference (IEEE, 2003), pp. 1–5.

van den Borne, D.

Wang, D.

D. Wang and J. Zhang, “Timing synchronization for MIMO-OFDM WLAN systems,” in Proceedings of Wireless Communications and Networking Conference (IEEE, 2007), pp. 1177–1182.

Wang, K.

K. Wang, M. Faulkner, J. Singh, and I. Tolochko, “Timing synchronization for 802.11a WLANs under multipath channels,” in Proceedings of Australasian Telecommunication Networks and Applications Conference (IEEE, 2003), pp. 1–5.

Wang, Z.

L. He, F. Yang, C. Zhang, and Z. Wang, “Synchronization for TDS-OFDM over Multipath Fading Channels,” IEEE Consum. Electr. 56(4), 2141–2147 (2010).

Winzer, P.

Winzer, P. J.

Wood, W.

Xi, L.

Yang, B.

B. Yang, K. Letaief, R. Cheng, and Z. Cao, “Timing Recovery for OFDM Transmission,” IEEE J. Sel. Areas Comm. 18(11), 2278–2291 (2000).

Yang, F.

L. He, F. Yang, C. Zhang, and Z. Wang, “Synchronization for TDS-OFDM over Multipath Fading Channels,” IEEE Consum. Electr. 56(4), 2141–2147 (2010).

Yano, Y.

Zhang, C.

L. He, F. Yang, C. Zhang, and Z. Wang, “Synchronization for TDS-OFDM over Multipath Fading Channels,” IEEE Consum. Electr. 56(4), 2141–2147 (2010).

Zhang, J.

D. Wang and J. Zhang, “Timing synchronization for MIMO-OFDM WLAN systems,” in Proceedings of Wireless Communications and Networking Conference (IEEE, 2007), pp. 1177–1182.

Zhang, X.

IEEE Commun. Lett. (1)

D. Lee and K. Cheun, “Coarse symbol synchronization algorithms for OFDM systems in multipath channels,” IEEE Commun. Lett. 6(10), 446–448 (2002).

IEEE Consum. Electr. (1)

L. He, F. Yang, C. Zhang, and Z. Wang, “Synchronization for TDS-OFDM over Multipath Fading Channels,” IEEE Consum. Electr. 56(4), 2141–2147 (2010).

IEEE J. Sel. Areas Comm. (1)

B. Yang, K. Letaief, R. Cheng, and Z. Cao, “Timing Recovery for OFDM Transmission,” IEEE J. Sel. Areas Comm. 18(11), 2278–2291 (2000).

J. Lightwave Technol. (5)

J. Opt. Commun. Netw. (1)

Nat. Photonics (1)

D. Richardson, J. Fini, and L. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013).

Not. Am. Math. Soc. (1)

F. Mezzadri, “How to Generate Random Matrices from the Classical Compact Groups,” Not. Am. Math. Soc. 54(5), 592–604 (2007).

Opt. Express (2)

Opt. Lett. (1)

Photon. Journal (1)

M. Mlejnek, I. Roudas, J. Downie, N. Kaliteevskiy, and K. Koreshkov, “Coupled-mode theory of multipath interference in quasi-single mode fibers,” Photon. Journal 7(1), 7100116 (2015).

Signal Proc. Mag. (1)

S. Arık, J. Kahn, and K. Ho, “MIMO signal processing for mode-division multiplexing: An overview of channel models and signal processing architectures,” Signal Proc. Mag. 31(2), 25–34 (2014).

Other (8)

D. Wang and J. Zhang, “Timing synchronization for MIMO-OFDM WLAN systems,” in Proceedings of Wireless Communications and Networking Conference (IEEE, 2007), pp. 1177–1182.

S. Randel, M. Mestre, R. Ryf, and P. Winzer, “Digital Signal Processing in Spatially Multiplexed Coherent Communications,” in European Conference on Optical Communication (IEEE, 2012), paper Tu.3.C.1.

K. Wang, M. Faulkner, J. Singh, and I. Tolochko, “Timing synchronization for 802.11a WLANs under multipath channels,” in Proceedings of Australasian Telecommunication Networks and Applications Conference (IEEE, 2003), pp. 1–5.

Y. Li, N. Hua, X. Zheng, and G. Li, “CapEx advantages of few-mode fiber networks,” in Optical Fiber Communication Conference (OSA, 2015), paper Th2A.43.

R. Ryf, N. Fontaine, H. Chen, B. Guan, S. Randel, N. Sauer, S. Yoo, A. Koonen, R. Delbue, P. Pupalaikis, A. Sureka, R. Shubochkin, Y. Sun, and R. Lingle, “23 Tbit/s Transmission over 17-km Conventional 50-µm Graded-Index Multimode Fiber,” in Optical Fiber Communication Conference (OSA, 2014), paper Th5B.1.

D. Lee, K. Shibahara, T. Kobayashi, T. Mizuno, H. Takara, A. Sano, H. Kawakami, T. Nakagawa, and Y. Miyamoto, “Adaptive MIMO Equalization for Few-mode Fiber Transmission with Various Differential Mode Delays,” in European Conference on Optical Communication (IEEE, 2015), paper Th.1.6.3.

J. Smith III, Mathematics of the discrete Fourier transform (DFT): with audio applications (W3K Publishing, 2008), Chap. 7.

P. Sillard, “Few-Mode Fibers for Space Division Multiplexing,” in Optical Fiber Communication Conference (OSA, 2016), paper Th1J.1.

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Figures (9)

Fig. 1
Fig. 1 Illustration of the impact of timing synchronization error on CE. (a) CE under ideal timing synchronization. (b) CE when err = 20. (c) CE when err = −20. The length of data block is 256. Modal dispersion lasts 50 samples.
Fig. 2
Fig. 2 Receiver DSP for (a) conventional FDE and (b) MRI-FDE. (c) Principle of MRI timing synchronization. TS: training sequence. CE: channel estimation.
Fig. 3
Fig. 3 Complexity of conventional FDE and FDE with MRI. Markers are for MRI-FDE. Lines are for conventional FDE.
Fig. 4
Fig. 4 Simulation setup of the 240-Gbit/s 12-mode transmission system. PDM: polarization division multiplexing. CRX: coherent receiver.
Fig. 5
Fig. 5 MC timing metric and Q2-factors under different OSNR for three typical conditions of mode crosstalk. (a), (b) and (c) are MC timing metrics. (d), (e) and (f) are the corresponding Q2-factors. The CP length is chosen to be 40.
Fig. 6
Fig. 6 Q2-factor of (a) conventional FDE and (b) MRI-FDE under different conditions of mode crosstalk. The OSNR is 25-dB. The CP length is 40.
Fig. 7
Fig. 7 Probabilistic histogram of Q2-factors for (a) conventional FDE and (b) MRI-FDE. The OSNR is 25-dB. The CP length is 40.
Fig. 8
Fig. 8 Outage possibility under different CP lengths. The OSNR is set to be 25-dB.
Fig. 9
Fig. 9 Outage possibility for different mode numbers and transmission distances. The OSNR is set to be 25-dB.

Equations (12)

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h m n ( l ) = 0 , l [ L , N 1 ] .
y m ( l ) = n = 1 M h m n ( l ) x n ( l ) = n = 1 M k = 0 N 1 h m n ( k ) x n [ ( l k ) mod N ] , l [ 0 , N 1 ] ,
y m ( l e r r ) = n = 1 M k = 0 N-1 h m n ( k ) x n [ ( l e r r k ) mod N ] = n = 1 M k = 0 N-1 h m n [ ( l e r r k ) mod N ] x n ( k ) = n = 1 M k = 0 N-1 h m n { [ ( l e r r ) mod N k ] mod N } x n ( k ) = n = 1 M k = 0 N-1 h ¯ m n ( k ) x n [ ( l k ) mod N ] = n = 1 M h ¯ m n ( l ) x n ( l ) , l [ 0 , N 1 ] ,
h ¯ m n ( l ) = h m n [ ( l e r r ) mod N ] , l [ 0 , N 1 ] .
h ¯ m n ( l ) = { h ¯ m n ( l ) , h ¯ m n ( l + N ) , l [ 0 , N / 2 1 ] l [ N / 2 , 1 ] .
f ( u ) = n = 1 M m = 1 M l = L N 1 | h ¯ m n [ ( l + u ) mod N ] | 2 / n = 1 M m = 1 M l = 0 N 1 | h ¯ m n ( l ) | 2 , u [ S,S ] ,
e r r ¯ ¯ = arg max u [ 1 f ( u ) ] .
R ¯ ¯ 1 ( l ) = R ¯ 1 ( l + e r r ¯ ¯ ) ,
H ¯ ¯ M × M ( k ) = H ¯ M × M ( k ) exp [ j 2 π N k e r r ¯ ¯ ] .
C w/o . MRI = log 2 N + M + T b T c ( log 2 N 2 +M+M 2 ) .
C w . MRI = C w/o . MRI + T b T c ( M 2 log 2 N +2M ) .
ρ ( u ) = k = 1 K s * ( k ) r ( u + k 1 ) k = 1 K | s ( k ) | 2 k = 1 K | r ( u + k 1 ) | 2 ,

Metrics