Abstract

A theoretical model for the stochastic time evolution of the intercore crosstalk (ICXT) in homogeneous weakly-coupled multicore fibers (MCF) with multiple interfering cores is proposed and validated experimentally. The model relies on the introduction of non-stationary time varying random phase shifts at every center point between the phase matching points of the MCF where the difference of the effective refractive indexes of the core of the originating signal and the core suffering from ICXT is zero. Closed form-expressions for the autocovariance of the short-term average ICXT (STAXT) with stationary and non-stationary phase shift models in MCFs with multiple excited cores are derived and validated by comparison with experimental results. These expressions enable estimating the decorrelation time of the STAXT generated by multiple interfering cores from the decorrelation times of the STAXT generated by each pair of cores. The proposed model and the ICXT measurements taken continuously over more than 150 hours show that the decorrelation time of the STAXT generated by multiple interfering cores exceeds the one obtained for the pair of cores with shorter decorrelation time. The proposed model is increasingly important to simulate and design MCF-based systems where the ICXT dynamics must be properly accounted for to develop efficient ICXT-tolerant techniques.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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  22. A. Cartaxo, T. Alves, B. Puttnam, R. Luís, Y. Awaji, and N. Wada, “DD-OFDM multicore fiber systems impaired by intercore crosstalk and laser phase noise,” in Proceedings of International Conference on Transparent Optical Networks (ICTON), paper Tu.D1.1 (2017).
  23. T. Alves and A. Cartaxo, “Characterization of ICXT in DD-OFDM MCF-based systems,” in Proceedings of European Conference on Optical Communications (ECOC), paper P2.SC6.29 (2017).
  24. G. Rademacher, R. Luís, B. Puttnam, Y. Awaji, and N. Wada, “Performance fluctuations in direct detection multi-core fiber transmission systems,” in Proceedings of European Conference on Optical Communications (ECOC), paper P2.SC6.16 (2017).
  25. T. Alves, A. Cartaxo, R. Luís, B. Puttnam, Y. Awaji, and N. Wada, “Adaptive loading with extended memory to relax the impact of the phase noise-impaired ICXT in DD-OFDM MCF-based systems,” in Proceedings of International Conference on Transparent Optical Networks (ICTON), paper Tu.D1.2 (2017).
  26. G. Rademacher, R. Luís, B. Puttnam, Y. Awaji, and N. Wada, “Crosstalk dynamics in multi-core fibers,” Opt. Express 25(10), 12020–12028 (2017).
    [Crossref] [PubMed]
  27. T. Alves, A. Cartaxo, R. Luís, B. Puttnam, Y. Awaji, and N. Wada, “Intercore crosstalk in direct-detection homogeneous multicore fiber systems impaired by laser phase noise,” Opt. Express 25(23), 29417–29431 (2017).
    [Crossref]
  28. P. Winzer, A. Gnauck, A. Konczykowska, F. Jorge, and J. Dupuy, “Penalties from in-band crosstalk for advanced optical modulation formats,” in Proceedings of European Conference on Optical Communications (ECOC), paper Tu.5.B.7 (2011).
  29. T. Alves and A. Cartaxo, “Inter-core crosstalk in homogeneous multi-core fibers: theoretical characterization of stochastic time evolution,” J. Lightw. Technol. 35(21), 4613–4623 (2017).
    [Crossref]
  30. J. Franz and V. Jain, Optical Communications: Components and Systems (Alpha Science International Limited, reprint in 2008).
  31. T. Hayashi, T. Nagashima, O. Shimakawa, T. Sasaki, and E. Sasaoka, “Crosstalk variation of multi-core fibre due to fibre bend,” in Proceedings of European Conference on Optical Communications (ECOC), paper We.8.F.6. (2010).

2017 (7)

B. Puttnam, R. Luís, E. Agrell, G. Rademacher, J. Sakaguchi, W. Klaus, G. Saridis, Y. Awaji, and N. Wada, “High capacity transmission systems using homogeneous multi-core fibers,” J. Lightw. Technol. 35(6), 1157–1167 (2017).
[Crossref]

R. Soeiro, T. Alves, and A. Cartaxo, “Dual polarization discrete changes model of inter-core crosstalk in multi-core fibers,” Photon. Technol. Lett. 29(16), 1395–1398 (2017).
[Crossref]

T. Alves, R. Luís, B. Puttnam, A. Cartaxo, Y. Awaji, and N. Wada, “Performance of adaptive DD-OFDM multicore fiber links and its relation with intercore crosstalk,” Opt. Express 25(13), 16017–16027 (2017).
[Crossref] [PubMed]

W. Klaus, B. Puttnam, R. Luis, J. Sakaguchi, J. Mendinueta, Y. Awaji, and N. Wada, “Advanced space division multiplexing technologies for optical networks,” J. Opt. Commun. Netw. 9(4), C1–C11 (2017).
[Crossref]

G. Rademacher, R. Luís, B. Puttnam, Y. Awaji, and N. Wada, “Crosstalk dynamics in multi-core fibers,” Opt. Express 25(10), 12020–12028 (2017).
[Crossref] [PubMed]

T. Alves, A. Cartaxo, R. Luís, B. Puttnam, Y. Awaji, and N. Wada, “Intercore crosstalk in direct-detection homogeneous multicore fiber systems impaired by laser phase noise,” Opt. Express 25(23), 29417–29431 (2017).
[Crossref]

T. Alves and A. Cartaxo, “Inter-core crosstalk in homogeneous multi-core fibers: theoretical characterization of stochastic time evolution,” J. Lightw. Technol. 35(21), 4613–4623 (2017).
[Crossref]

2016 (4)

A. Cartaxo, R. Luís, B. Puttnam, T. Hayashi, Y. Awaji, and N. Wada, “Dispersion impact on the crosstalk amplitude response of homogeneous multi-core fibers,” Photon. Technol. Lett. 28(17), 1858–1861 (2016).
[Crossref]

R. Luís, B. Puttnam, A. Cartaxo, W. Klaus, J. Mendinueta, Y. Awaji, N. Wada, T. Nakanishi, T. Hayashi, and T. Sasaki, “Time and modulation frequency dependence of crosstalk in homogeneous multi-core fibers,” J. Lightw. Technol. 34(2), 441–447 (2016).
[Crossref]

B. Puttnam, R. Luís, T. Eriksson, W. Klaus, J. Mendinueta, Y. Awaji, and N. Wada, “Impact of intercore crosstalk on the transmission distance of QAM formats in multicore fibers,” Photon. J. 8(2), 0601109 (2016).

J. Galvé, I. Gasulla, S. Sales, and J. Capmany, “Reconfigurable radio access networks using multicore fibers,” J. Quantum Electron. 52(1), 0600507 (2016).
[Crossref]

2015 (2)

Z. Feng, B. Li, M. Tang, L. Gan, R. Wang, R. Lin, Z. Xu, S. Fu, L. Deng, W. Tong, S. Long, L. Zhang, H. Zhou, R. Zhang, S. Liu, and P. Shum, “Multicore-fiber-enabled WSDM optical access network with centralized carrier delivery and RSOA-based adaptive modulation,” Photon. J. 7(4), 7201309 (2015).

A. Macho, M. Morant, and R. Llorente, “Experimental evaluation of nonlinear crosstalk in multi-core fiber,” Opt. Express 32, 18712–18720 (2015).
[Crossref]

2012 (1)

M. Koshiba, K. Saitoh, K. Takenaga, and S. Matsuo, “Analytical expression of average power-coupling coefficients for estimating intercore crosstalk in multicore fibers,” Photon. J. 4(5), 1987–1995 (2012).
[Crossref]

2011 (1)

2010 (1)

Agrell, E.

B. Puttnam, R. Luís, E. Agrell, G. Rademacher, J. Sakaguchi, W. Klaus, G. Saridis, Y. Awaji, and N. Wada, “High capacity transmission systems using homogeneous multi-core fibers,” J. Lightw. Technol. 35(6), 1157–1167 (2017).
[Crossref]

Alves, T.

R. Soeiro, T. Alves, and A. Cartaxo, “Dual polarization discrete changes model of inter-core crosstalk in multi-core fibers,” Photon. Technol. Lett. 29(16), 1395–1398 (2017).
[Crossref]

T. Alves and A. Cartaxo, “Inter-core crosstalk in homogeneous multi-core fibers: theoretical characterization of stochastic time evolution,” J. Lightw. Technol. 35(21), 4613–4623 (2017).
[Crossref]

T. Alves, R. Luís, B. Puttnam, A. Cartaxo, Y. Awaji, and N. Wada, “Performance of adaptive DD-OFDM multicore fiber links and its relation with intercore crosstalk,” Opt. Express 25(13), 16017–16027 (2017).
[Crossref] [PubMed]

T. Alves, A. Cartaxo, R. Luís, B. Puttnam, Y. Awaji, and N. Wada, “Intercore crosstalk in direct-detection homogeneous multicore fiber systems impaired by laser phase noise,” Opt. Express 25(23), 29417–29431 (2017).
[Crossref]

T. Alves and A. Cartaxo, “Characterization of ICXT in DD-OFDM MCF-based systems,” in Proceedings of European Conference on Optical Communications (ECOC), paper P2.SC6.29 (2017).

T. Alves, A. Cartaxo, R. Luís, B. Puttnam, Y. Awaji, and N. Wada, “Adaptive loading with extended memory to relax the impact of the phase noise-impaired ICXT in DD-OFDM MCF-based systems,” in Proceedings of International Conference on Transparent Optical Networks (ICTON), paper Tu.D1.2 (2017).

A. Cartaxo, T. Alves, B. Puttnam, R. Luís, Y. Awaji, and N. Wada, “DD-OFDM multicore fiber systems impaired by intercore crosstalk and laser phase noise,” in Proceedings of International Conference on Transparent Optical Networks (ICTON), paper Tu.D1.1 (2017).

A. Cartaxo and T. Alves, “Discrete changes model of inter-core crosstalk of real homogeneous multi-core fibers,” J. Lightw. Technol. DOI (2017).
[Crossref]

Amma, Y.

Y. Amma, Y. Sasaki, K. Takenaga, S. Matsuo, J. Tu, K. Saitoh, M. Koshiba, T. Morioka, and Y. Miyamoto, “High-density multicore fiber with heterogeneous core arrangement,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2015), paper Th4C.4.

Awaji, Y.

B. Puttnam, R. Luís, E. Agrell, G. Rademacher, J. Sakaguchi, W. Klaus, G. Saridis, Y. Awaji, and N. Wada, “High capacity transmission systems using homogeneous multi-core fibers,” J. Lightw. Technol. 35(6), 1157–1167 (2017).
[Crossref]

T. Alves, A. Cartaxo, R. Luís, B. Puttnam, Y. Awaji, and N. Wada, “Intercore crosstalk in direct-detection homogeneous multicore fiber systems impaired by laser phase noise,” Opt. Express 25(23), 29417–29431 (2017).
[Crossref]

G. Rademacher, R. Luís, B. Puttnam, Y. Awaji, and N. Wada, “Crosstalk dynamics in multi-core fibers,” Opt. Express 25(10), 12020–12028 (2017).
[Crossref] [PubMed]

T. Alves, R. Luís, B. Puttnam, A. Cartaxo, Y. Awaji, and N. Wada, “Performance of adaptive DD-OFDM multicore fiber links and its relation with intercore crosstalk,” Opt. Express 25(13), 16017–16027 (2017).
[Crossref] [PubMed]

W. Klaus, B. Puttnam, R. Luis, J. Sakaguchi, J. Mendinueta, Y. Awaji, and N. Wada, “Advanced space division multiplexing technologies for optical networks,” J. Opt. Commun. Netw. 9(4), C1–C11 (2017).
[Crossref]

A. Cartaxo, R. Luís, B. Puttnam, T. Hayashi, Y. Awaji, and N. Wada, “Dispersion impact on the crosstalk amplitude response of homogeneous multi-core fibers,” Photon. Technol. Lett. 28(17), 1858–1861 (2016).
[Crossref]

B. Puttnam, R. Luís, T. Eriksson, W. Klaus, J. Mendinueta, Y. Awaji, and N. Wada, “Impact of intercore crosstalk on the transmission distance of QAM formats in multicore fibers,” Photon. J. 8(2), 0601109 (2016).

R. Luís, B. Puttnam, A. Cartaxo, W. Klaus, J. Mendinueta, Y. Awaji, N. Wada, T. Nakanishi, T. Hayashi, and T. Sasaki, “Time and modulation frequency dependence of crosstalk in homogeneous multi-core fibers,” J. Lightw. Technol. 34(2), 441–447 (2016).
[Crossref]

G. Rademacher, B. Puttnam, R. Luís, Y. Awaji, and N. Wada, “Time-dependent inter-core crosstalk between multiple cores of a homogeneous multi-core fiber,” in Proceedings of Asia Communications and Photonics Conference (ACPC), paper AF1D.2 (2016).

J. Pedro, R. Luís, B. Puttnam, Y. Awaji, N. Wada, and A. Cartaxo, “Experimental assessment of the time-varying impact of multi-core fiber crosstalk on a SSB-OFDM Signal,” in Proceedings of Photonics in Switching (PS), 166–168 (2015).

G. Rademacher, B. Puttnam, R. Luís, Y. Awaji, and N. Wada, “Time-dependent crosstalk from multiple cores in a homogeneous multi-core fiber,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2016), paper Th1H.3.

T. Alves, A. Cartaxo, R. Luís, B. Puttnam, Y. Awaji, and N. Wada, “Adaptive loading with extended memory to relax the impact of the phase noise-impaired ICXT in DD-OFDM MCF-based systems,” in Proceedings of International Conference on Transparent Optical Networks (ICTON), paper Tu.D1.2 (2017).

A. Cartaxo, T. Alves, B. Puttnam, R. Luís, Y. Awaji, and N. Wada, “DD-OFDM multicore fiber systems impaired by intercore crosstalk and laser phase noise,” in Proceedings of International Conference on Transparent Optical Networks (ICTON), paper Tu.D1.1 (2017).

G. Rademacher, R. Luís, B. Puttnam, Y. Awaji, and N. Wada, “Performance fluctuations in direct detection multi-core fiber transmission systems,” in Proceedings of European Conference on Optical Communications (ECOC), paper P2.SC6.16 (2017).

Butler, D.

D. Butler, M. Li, S. Li, Y. Geng, R. Khrapko, R. Modavis, V. Nazarov, and A. Koklyushkin, “Space division multiplexing in short reach optical interconnects,” J. Lightw. Technol. DOI (2017).
[Crossref]

Capmany, J.

J. Galvé, I. Gasulla, S. Sales, and J. Capmany, “Reconfigurable radio access networks using multicore fibers,” J. Quantum Electron. 52(1), 0600507 (2016).
[Crossref]

Cartaxo, A.

R. Soeiro, T. Alves, and A. Cartaxo, “Dual polarization discrete changes model of inter-core crosstalk in multi-core fibers,” Photon. Technol. Lett. 29(16), 1395–1398 (2017).
[Crossref]

T. Alves and A. Cartaxo, “Inter-core crosstalk in homogeneous multi-core fibers: theoretical characterization of stochastic time evolution,” J. Lightw. Technol. 35(21), 4613–4623 (2017).
[Crossref]

T. Alves, R. Luís, B. Puttnam, A. Cartaxo, Y. Awaji, and N. Wada, “Performance of adaptive DD-OFDM multicore fiber links and its relation with intercore crosstalk,” Opt. Express 25(13), 16017–16027 (2017).
[Crossref] [PubMed]

T. Alves, A. Cartaxo, R. Luís, B. Puttnam, Y. Awaji, and N. Wada, “Intercore crosstalk in direct-detection homogeneous multicore fiber systems impaired by laser phase noise,” Opt. Express 25(23), 29417–29431 (2017).
[Crossref]

R. Luís, B. Puttnam, A. Cartaxo, W. Klaus, J. Mendinueta, Y. Awaji, N. Wada, T. Nakanishi, T. Hayashi, and T. Sasaki, “Time and modulation frequency dependence of crosstalk in homogeneous multi-core fibers,” J. Lightw. Technol. 34(2), 441–447 (2016).
[Crossref]

A. Cartaxo, R. Luís, B. Puttnam, T. Hayashi, Y. Awaji, and N. Wada, “Dispersion impact on the crosstalk amplitude response of homogeneous multi-core fibers,” Photon. Technol. Lett. 28(17), 1858–1861 (2016).
[Crossref]

A. Cartaxo and T. Alves, “Discrete changes model of inter-core crosstalk of real homogeneous multi-core fibers,” J. Lightw. Technol. DOI (2017).
[Crossref]

J. Pedro, R. Luís, B. Puttnam, Y. Awaji, N. Wada, and A. Cartaxo, “Experimental assessment of the time-varying impact of multi-core fiber crosstalk on a SSB-OFDM Signal,” in Proceedings of Photonics in Switching (PS), 166–168 (2015).

A. Cartaxo, T. Alves, B. Puttnam, R. Luís, Y. Awaji, and N. Wada, “DD-OFDM multicore fiber systems impaired by intercore crosstalk and laser phase noise,” in Proceedings of International Conference on Transparent Optical Networks (ICTON), paper Tu.D1.1 (2017).

T. Alves and A. Cartaxo, “Characterization of ICXT in DD-OFDM MCF-based systems,” in Proceedings of European Conference on Optical Communications (ECOC), paper P2.SC6.29 (2017).

T. Alves, A. Cartaxo, R. Luís, B. Puttnam, Y. Awaji, and N. Wada, “Adaptive loading with extended memory to relax the impact of the phase noise-impaired ICXT in DD-OFDM MCF-based systems,” in Proceedings of International Conference on Transparent Optical Networks (ICTON), paper Tu.D1.2 (2017).

Deng, L.

Z. Feng, B. Li, M. Tang, L. Gan, R. Wang, R. Lin, Z. Xu, S. Fu, L. Deng, W. Tong, S. Long, L. Zhang, H. Zhou, R. Zhang, S. Liu, and P. Shum, “Multicore-fiber-enabled WSDM optical access network with centralized carrier delivery and RSOA-based adaptive modulation,” Photon. J. 7(4), 7201309 (2015).

Dupuy, J.

P. Winzer, A. Gnauck, A. Konczykowska, F. Jorge, and J. Dupuy, “Penalties from in-band crosstalk for advanced optical modulation formats,” in Proceedings of European Conference on Optical Communications (ECOC), paper Tu.5.B.7 (2011).

Eriksson, T.

B. Puttnam, R. Luís, T. Eriksson, W. Klaus, J. Mendinueta, Y. Awaji, and N. Wada, “Impact of intercore crosstalk on the transmission distance of QAM formats in multicore fibers,” Photon. J. 8(2), 0601109 (2016).

Feng, Z.

Z. Feng, B. Li, M. Tang, L. Gan, R. Wang, R. Lin, Z. Xu, S. Fu, L. Deng, W. Tong, S. Long, L. Zhang, H. Zhou, R. Zhang, S. Liu, and P. Shum, “Multicore-fiber-enabled WSDM optical access network with centralized carrier delivery and RSOA-based adaptive modulation,” Photon. J. 7(4), 7201309 (2015).

Fini, J.

Franz, J.

J. Franz and V. Jain, Optical Communications: Components and Systems (Alpha Science International Limited, reprint in 2008).

Fu, S.

Z. Feng, B. Li, M. Tang, L. Gan, R. Wang, R. Lin, Z. Xu, S. Fu, L. Deng, W. Tong, S. Long, L. Zhang, H. Zhou, R. Zhang, S. Liu, and P. Shum, “Multicore-fiber-enabled WSDM optical access network with centralized carrier delivery and RSOA-based adaptive modulation,” Photon. J. 7(4), 7201309 (2015).

Galvé, J.

J. Galvé, I. Gasulla, S. Sales, and J. Capmany, “Reconfigurable radio access networks using multicore fibers,” J. Quantum Electron. 52(1), 0600507 (2016).
[Crossref]

Gan, L.

Z. Feng, B. Li, M. Tang, L. Gan, R. Wang, R. Lin, Z. Xu, S. Fu, L. Deng, W. Tong, S. Long, L. Zhang, H. Zhou, R. Zhang, S. Liu, and P. Shum, “Multicore-fiber-enabled WSDM optical access network with centralized carrier delivery and RSOA-based adaptive modulation,” Photon. J. 7(4), 7201309 (2015).

Gasulla, I.

J. Galvé, I. Gasulla, S. Sales, and J. Capmany, “Reconfigurable radio access networks using multicore fibers,” J. Quantum Electron. 52(1), 0600507 (2016).
[Crossref]

Geng, Y.

D. Butler, M. Li, S. Li, Y. Geng, R. Khrapko, R. Modavis, V. Nazarov, and A. Koklyushkin, “Space division multiplexing in short reach optical interconnects,” J. Lightw. Technol. DOI (2017).
[Crossref]

Gnauck, A.

P. Winzer, A. Gnauck, A. Konczykowska, F. Jorge, and J. Dupuy, “Penalties from in-band crosstalk for advanced optical modulation formats,” in Proceedings of European Conference on Optical Communications (ECOC), paper Tu.5.B.7 (2011).

Hayashi, T.

A. Cartaxo, R. Luís, B. Puttnam, T. Hayashi, Y. Awaji, and N. Wada, “Dispersion impact on the crosstalk amplitude response of homogeneous multi-core fibers,” Photon. Technol. Lett. 28(17), 1858–1861 (2016).
[Crossref]

R. Luís, B. Puttnam, A. Cartaxo, W. Klaus, J. Mendinueta, Y. Awaji, N. Wada, T. Nakanishi, T. Hayashi, and T. Sasaki, “Time and modulation frequency dependence of crosstalk in homogeneous multi-core fibers,” J. Lightw. Technol. 34(2), 441–447 (2016).
[Crossref]

T. Hayashi, T. Taru, O. Shimakawa, T. Sasaki, and E. Sasaoka, “Design and fabrication of ultra-low crosstalk and low-loss multi-core fiber,” Opt. Express 19(17), 16576–16592 (2011).
[Crossref] [PubMed]

T. Hayashi, T. Nagashima, O. Shimakawa, T. Sasaki, and E. Sasaoka, “Crosstalk variation of multi-core fibre due to fibre bend,” in Proceedings of European Conference on Optical Communications (ECOC), paper We.8.F.6. (2010).

Igarashi, K.

H. Takahashi, K. Igarashi, and T. Tsuritani, “Long-haul transmission using multicore fibers,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2014), paper Tu2J.2.

Jain, V.

J. Franz and V. Jain, Optical Communications: Components and Systems (Alpha Science International Limited, reprint in 2008).

Jorge, F.

P. Winzer, A. Gnauck, A. Konczykowska, F. Jorge, and J. Dupuy, “Penalties from in-band crosstalk for advanced optical modulation formats,” in Proceedings of European Conference on Optical Communications (ECOC), paper Tu.5.B.7 (2011).

Khrapko, R.

D. Butler, M. Li, S. Li, Y. Geng, R. Khrapko, R. Modavis, V. Nazarov, and A. Koklyushkin, “Space division multiplexing in short reach optical interconnects,” J. Lightw. Technol. DOI (2017).
[Crossref]

Klaus, W.

B. Puttnam, R. Luís, E. Agrell, G. Rademacher, J. Sakaguchi, W. Klaus, G. Saridis, Y. Awaji, and N. Wada, “High capacity transmission systems using homogeneous multi-core fibers,” J. Lightw. Technol. 35(6), 1157–1167 (2017).
[Crossref]

W. Klaus, B. Puttnam, R. Luis, J. Sakaguchi, J. Mendinueta, Y. Awaji, and N. Wada, “Advanced space division multiplexing technologies for optical networks,” J. Opt. Commun. Netw. 9(4), C1–C11 (2017).
[Crossref]

B. Puttnam, R. Luís, T. Eriksson, W. Klaus, J. Mendinueta, Y. Awaji, and N. Wada, “Impact of intercore crosstalk on the transmission distance of QAM formats in multicore fibers,” Photon. J. 8(2), 0601109 (2016).

R. Luís, B. Puttnam, A. Cartaxo, W. Klaus, J. Mendinueta, Y. Awaji, N. Wada, T. Nakanishi, T. Hayashi, and T. Sasaki, “Time and modulation frequency dependence of crosstalk in homogeneous multi-core fibers,” J. Lightw. Technol. 34(2), 441–447 (2016).
[Crossref]

Koklyushkin, A.

D. Butler, M. Li, S. Li, Y. Geng, R. Khrapko, R. Modavis, V. Nazarov, and A. Koklyushkin, “Space division multiplexing in short reach optical interconnects,” J. Lightw. Technol. DOI (2017).
[Crossref]

Konczykowska, A.

P. Winzer, A. Gnauck, A. Konczykowska, F. Jorge, and J. Dupuy, “Penalties from in-band crosstalk for advanced optical modulation formats,” in Proceedings of European Conference on Optical Communications (ECOC), paper Tu.5.B.7 (2011).

Koshiba, M.

M. Koshiba, K. Saitoh, K. Takenaga, and S. Matsuo, “Analytical expression of average power-coupling coefficients for estimating intercore crosstalk in multicore fibers,” Photon. J. 4(5), 1987–1995 (2012).
[Crossref]

Y. Amma, Y. Sasaki, K. Takenaga, S. Matsuo, J. Tu, K. Saitoh, M. Koshiba, T. Morioka, and Y. Miyamoto, “High-density multicore fiber with heterogeneous core arrangement,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2015), paper Th4C.4.

Li, B.

Z. Feng, B. Li, M. Tang, L. Gan, R. Wang, R. Lin, Z. Xu, S. Fu, L. Deng, W. Tong, S. Long, L. Zhang, H. Zhou, R. Zhang, S. Liu, and P. Shum, “Multicore-fiber-enabled WSDM optical access network with centralized carrier delivery and RSOA-based adaptive modulation,” Photon. J. 7(4), 7201309 (2015).

Li, M.

D. Butler, M. Li, S. Li, Y. Geng, R. Khrapko, R. Modavis, V. Nazarov, and A. Koklyushkin, “Space division multiplexing in short reach optical interconnects,” J. Lightw. Technol. DOI (2017).
[Crossref]

Li, S.

D. Butler, M. Li, S. Li, Y. Geng, R. Khrapko, R. Modavis, V. Nazarov, and A. Koklyushkin, “Space division multiplexing in short reach optical interconnects,” J. Lightw. Technol. DOI (2017).
[Crossref]

Lin, R.

Z. Feng, B. Li, M. Tang, L. Gan, R. Wang, R. Lin, Z. Xu, S. Fu, L. Deng, W. Tong, S. Long, L. Zhang, H. Zhou, R. Zhang, S. Liu, and P. Shum, “Multicore-fiber-enabled WSDM optical access network with centralized carrier delivery and RSOA-based adaptive modulation,” Photon. J. 7(4), 7201309 (2015).

Liu, S.

Z. Feng, B. Li, M. Tang, L. Gan, R. Wang, R. Lin, Z. Xu, S. Fu, L. Deng, W. Tong, S. Long, L. Zhang, H. Zhou, R. Zhang, S. Liu, and P. Shum, “Multicore-fiber-enabled WSDM optical access network with centralized carrier delivery and RSOA-based adaptive modulation,” Photon. J. 7(4), 7201309 (2015).

Llorente, R.

A. Macho, M. Morant, and R. Llorente, “Experimental evaluation of nonlinear crosstalk in multi-core fiber,” Opt. Express 32, 18712–18720 (2015).
[Crossref]

Long, S.

Z. Feng, B. Li, M. Tang, L. Gan, R. Wang, R. Lin, Z. Xu, S. Fu, L. Deng, W. Tong, S. Long, L. Zhang, H. Zhou, R. Zhang, S. Liu, and P. Shum, “Multicore-fiber-enabled WSDM optical access network with centralized carrier delivery and RSOA-based adaptive modulation,” Photon. J. 7(4), 7201309 (2015).

Luis, R.

Luís, R.

G. Rademacher, R. Luís, B. Puttnam, Y. Awaji, and N. Wada, “Crosstalk dynamics in multi-core fibers,” Opt. Express 25(10), 12020–12028 (2017).
[Crossref] [PubMed]

T. Alves, A. Cartaxo, R. Luís, B. Puttnam, Y. Awaji, and N. Wada, “Intercore crosstalk in direct-detection homogeneous multicore fiber systems impaired by laser phase noise,” Opt. Express 25(23), 29417–29431 (2017).
[Crossref]

T. Alves, R. Luís, B. Puttnam, A. Cartaxo, Y. Awaji, and N. Wada, “Performance of adaptive DD-OFDM multicore fiber links and its relation with intercore crosstalk,” Opt. Express 25(13), 16017–16027 (2017).
[Crossref] [PubMed]

B. Puttnam, R. Luís, E. Agrell, G. Rademacher, J. Sakaguchi, W. Klaus, G. Saridis, Y. Awaji, and N. Wada, “High capacity transmission systems using homogeneous multi-core fibers,” J. Lightw. Technol. 35(6), 1157–1167 (2017).
[Crossref]

B. Puttnam, R. Luís, T. Eriksson, W. Klaus, J. Mendinueta, Y. Awaji, and N. Wada, “Impact of intercore crosstalk on the transmission distance of QAM formats in multicore fibers,” Photon. J. 8(2), 0601109 (2016).

A. Cartaxo, R. Luís, B. Puttnam, T. Hayashi, Y. Awaji, and N. Wada, “Dispersion impact on the crosstalk amplitude response of homogeneous multi-core fibers,” Photon. Technol. Lett. 28(17), 1858–1861 (2016).
[Crossref]

R. Luís, B. Puttnam, A. Cartaxo, W. Klaus, J. Mendinueta, Y. Awaji, N. Wada, T. Nakanishi, T. Hayashi, and T. Sasaki, “Time and modulation frequency dependence of crosstalk in homogeneous multi-core fibers,” J. Lightw. Technol. 34(2), 441–447 (2016).
[Crossref]

J. Pedro, R. Luís, B. Puttnam, Y. Awaji, N. Wada, and A. Cartaxo, “Experimental assessment of the time-varying impact of multi-core fiber crosstalk on a SSB-OFDM Signal,” in Proceedings of Photonics in Switching (PS), 166–168 (2015).

G. Rademacher, B. Puttnam, R. Luís, Y. Awaji, and N. Wada, “Time-dependent crosstalk from multiple cores in a homogeneous multi-core fiber,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2016), paper Th1H.3.

A. Cartaxo, T. Alves, B. Puttnam, R. Luís, Y. Awaji, and N. Wada, “DD-OFDM multicore fiber systems impaired by intercore crosstalk and laser phase noise,” in Proceedings of International Conference on Transparent Optical Networks (ICTON), paper Tu.D1.1 (2017).

G. Rademacher, B. Puttnam, R. Luís, Y. Awaji, and N. Wada, “Time-dependent inter-core crosstalk between multiple cores of a homogeneous multi-core fiber,” in Proceedings of Asia Communications and Photonics Conference (ACPC), paper AF1D.2 (2016).

T. Alves, A. Cartaxo, R. Luís, B. Puttnam, Y. Awaji, and N. Wada, “Adaptive loading with extended memory to relax the impact of the phase noise-impaired ICXT in DD-OFDM MCF-based systems,” in Proceedings of International Conference on Transparent Optical Networks (ICTON), paper Tu.D1.2 (2017).

G. Rademacher, R. Luís, B. Puttnam, Y. Awaji, and N. Wada, “Performance fluctuations in direct detection multi-core fiber transmission systems,” in Proceedings of European Conference on Optical Communications (ECOC), paper P2.SC6.16 (2017).

Macho, A.

A. Macho, M. Morant, and R. Llorente, “Experimental evaluation of nonlinear crosstalk in multi-core fiber,” Opt. Express 32, 18712–18720 (2015).
[Crossref]

Matsuo, S.

M. Koshiba, K. Saitoh, K. Takenaga, and S. Matsuo, “Analytical expression of average power-coupling coefficients for estimating intercore crosstalk in multicore fibers,” Photon. J. 4(5), 1987–1995 (2012).
[Crossref]

Y. Amma, Y. Sasaki, K. Takenaga, S. Matsuo, J. Tu, K. Saitoh, M. Koshiba, T. Morioka, and Y. Miyamoto, “High-density multicore fiber with heterogeneous core arrangement,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2015), paper Th4C.4.

Mendinueta, J.

W. Klaus, B. Puttnam, R. Luis, J. Sakaguchi, J. Mendinueta, Y. Awaji, and N. Wada, “Advanced space division multiplexing technologies for optical networks,” J. Opt. Commun. Netw. 9(4), C1–C11 (2017).
[Crossref]

B. Puttnam, R. Luís, T. Eriksson, W. Klaus, J. Mendinueta, Y. Awaji, and N. Wada, “Impact of intercore crosstalk on the transmission distance of QAM formats in multicore fibers,” Photon. J. 8(2), 0601109 (2016).

R. Luís, B. Puttnam, A. Cartaxo, W. Klaus, J. Mendinueta, Y. Awaji, N. Wada, T. Nakanishi, T. Hayashi, and T. Sasaki, “Time and modulation frequency dependence of crosstalk in homogeneous multi-core fibers,” J. Lightw. Technol. 34(2), 441–447 (2016).
[Crossref]

Miyamoto, Y.

Y. Amma, Y. Sasaki, K. Takenaga, S. Matsuo, J. Tu, K. Saitoh, M. Koshiba, T. Morioka, and Y. Miyamoto, “High-density multicore fiber with heterogeneous core arrangement,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2015), paper Th4C.4.

Modavis, R.

D. Butler, M. Li, S. Li, Y. Geng, R. Khrapko, R. Modavis, V. Nazarov, and A. Koklyushkin, “Space division multiplexing in short reach optical interconnects,” J. Lightw. Technol. DOI (2017).
[Crossref]

Morant, M.

A. Macho, M. Morant, and R. Llorente, “Experimental evaluation of nonlinear crosstalk in multi-core fiber,” Opt. Express 32, 18712–18720 (2015).
[Crossref]

Morioka, T.

Y. Amma, Y. Sasaki, K. Takenaga, S. Matsuo, J. Tu, K. Saitoh, M. Koshiba, T. Morioka, and Y. Miyamoto, “High-density multicore fiber with heterogeneous core arrangement,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2015), paper Th4C.4.

Nagashima, T.

T. Nagashima, O. Shimakawa, T. Sasaki, and E. Sasaoka, “Crosstalk variation of multi-core fibre due to fibre bend,” in European Conference on Optical Communications (ECOC), (2010), paper We.8.F.6.

T. Hayashi, T. Nagashima, O. Shimakawa, T. Sasaki, and E. Sasaoka, “Crosstalk variation of multi-core fibre due to fibre bend,” in Proceedings of European Conference on Optical Communications (ECOC), paper We.8.F.6. (2010).

Nakanishi, T.

R. Luís, B. Puttnam, A. Cartaxo, W. Klaus, J. Mendinueta, Y. Awaji, N. Wada, T. Nakanishi, T. Hayashi, and T. Sasaki, “Time and modulation frequency dependence of crosstalk in homogeneous multi-core fibers,” J. Lightw. Technol. 34(2), 441–447 (2016).
[Crossref]

Nazarov, V.

D. Butler, M. Li, S. Li, Y. Geng, R. Khrapko, R. Modavis, V. Nazarov, and A. Koklyushkin, “Space division multiplexing in short reach optical interconnects,” J. Lightw. Technol. DOI (2017).
[Crossref]

Pedro, J.

J. Pedro, R. Luís, B. Puttnam, Y. Awaji, N. Wada, and A. Cartaxo, “Experimental assessment of the time-varying impact of multi-core fiber crosstalk on a SSB-OFDM Signal,” in Proceedings of Photonics in Switching (PS), 166–168 (2015).

Puttnam, B.

B. Puttnam, R. Luís, E. Agrell, G. Rademacher, J. Sakaguchi, W. Klaus, G. Saridis, Y. Awaji, and N. Wada, “High capacity transmission systems using homogeneous multi-core fibers,” J. Lightw. Technol. 35(6), 1157–1167 (2017).
[Crossref]

G. Rademacher, R. Luís, B. Puttnam, Y. Awaji, and N. Wada, “Crosstalk dynamics in multi-core fibers,” Opt. Express 25(10), 12020–12028 (2017).
[Crossref] [PubMed]

W. Klaus, B. Puttnam, R. Luis, J. Sakaguchi, J. Mendinueta, Y. Awaji, and N. Wada, “Advanced space division multiplexing technologies for optical networks,” J. Opt. Commun. Netw. 9(4), C1–C11 (2017).
[Crossref]

T. Alves, R. Luís, B. Puttnam, A. Cartaxo, Y. Awaji, and N. Wada, “Performance of adaptive DD-OFDM multicore fiber links and its relation with intercore crosstalk,” Opt. Express 25(13), 16017–16027 (2017).
[Crossref] [PubMed]

T. Alves, A. Cartaxo, R. Luís, B. Puttnam, Y. Awaji, and N. Wada, “Intercore crosstalk in direct-detection homogeneous multicore fiber systems impaired by laser phase noise,” Opt. Express 25(23), 29417–29431 (2017).
[Crossref]

B. Puttnam, R. Luís, T. Eriksson, W. Klaus, J. Mendinueta, Y. Awaji, and N. Wada, “Impact of intercore crosstalk on the transmission distance of QAM formats in multicore fibers,” Photon. J. 8(2), 0601109 (2016).

R. Luís, B. Puttnam, A. Cartaxo, W. Klaus, J. Mendinueta, Y. Awaji, N. Wada, T. Nakanishi, T. Hayashi, and T. Sasaki, “Time and modulation frequency dependence of crosstalk in homogeneous multi-core fibers,” J. Lightw. Technol. 34(2), 441–447 (2016).
[Crossref]

A. Cartaxo, R. Luís, B. Puttnam, T. Hayashi, Y. Awaji, and N. Wada, “Dispersion impact on the crosstalk amplitude response of homogeneous multi-core fibers,” Photon. Technol. Lett. 28(17), 1858–1861 (2016).
[Crossref]

J. Pedro, R. Luís, B. Puttnam, Y. Awaji, N. Wada, and A. Cartaxo, “Experimental assessment of the time-varying impact of multi-core fiber crosstalk on a SSB-OFDM Signal,” in Proceedings of Photonics in Switching (PS), 166–168 (2015).

A. Cartaxo, T. Alves, B. Puttnam, R. Luís, Y. Awaji, and N. Wada, “DD-OFDM multicore fiber systems impaired by intercore crosstalk and laser phase noise,” in Proceedings of International Conference on Transparent Optical Networks (ICTON), paper Tu.D1.1 (2017).

G. Rademacher, B. Puttnam, R. Luís, Y. Awaji, and N. Wada, “Time-dependent inter-core crosstalk between multiple cores of a homogeneous multi-core fiber,” in Proceedings of Asia Communications and Photonics Conference (ACPC), paper AF1D.2 (2016).

G. Rademacher, B. Puttnam, R. Luís, Y. Awaji, and N. Wada, “Time-dependent crosstalk from multiple cores in a homogeneous multi-core fiber,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2016), paper Th1H.3.

G. Rademacher, R. Luís, B. Puttnam, Y. Awaji, and N. Wada, “Performance fluctuations in direct detection multi-core fiber transmission systems,” in Proceedings of European Conference on Optical Communications (ECOC), paper P2.SC6.16 (2017).

T. Alves, A. Cartaxo, R. Luís, B. Puttnam, Y. Awaji, and N. Wada, “Adaptive loading with extended memory to relax the impact of the phase noise-impaired ICXT in DD-OFDM MCF-based systems,” in Proceedings of International Conference on Transparent Optical Networks (ICTON), paper Tu.D1.2 (2017).

Rademacher, G.

B. Puttnam, R. Luís, E. Agrell, G. Rademacher, J. Sakaguchi, W. Klaus, G. Saridis, Y. Awaji, and N. Wada, “High capacity transmission systems using homogeneous multi-core fibers,” J. Lightw. Technol. 35(6), 1157–1167 (2017).
[Crossref]

G. Rademacher, R. Luís, B. Puttnam, Y. Awaji, and N. Wada, “Crosstalk dynamics in multi-core fibers,” Opt. Express 25(10), 12020–12028 (2017).
[Crossref] [PubMed]

G. Rademacher, R. Luís, B. Puttnam, Y. Awaji, and N. Wada, “Performance fluctuations in direct detection multi-core fiber transmission systems,” in Proceedings of European Conference on Optical Communications (ECOC), paper P2.SC6.16 (2017).

G. Rademacher, B. Puttnam, R. Luís, Y. Awaji, and N. Wada, “Time-dependent crosstalk from multiple cores in a homogeneous multi-core fiber,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2016), paper Th1H.3.

G. Rademacher, B. Puttnam, R. Luís, Y. Awaji, and N. Wada, “Time-dependent inter-core crosstalk between multiple cores of a homogeneous multi-core fiber,” in Proceedings of Asia Communications and Photonics Conference (ACPC), paper AF1D.2 (2016).

Saitoh, K.

M. Koshiba, K. Saitoh, K. Takenaga, and S. Matsuo, “Analytical expression of average power-coupling coefficients for estimating intercore crosstalk in multicore fibers,” Photon. J. 4(5), 1987–1995 (2012).
[Crossref]

Y. Amma, Y. Sasaki, K. Takenaga, S. Matsuo, J. Tu, K. Saitoh, M. Koshiba, T. Morioka, and Y. Miyamoto, “High-density multicore fiber with heterogeneous core arrangement,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2015), paper Th4C.4.

Sakaguchi, J.

B. Puttnam, R. Luís, E. Agrell, G. Rademacher, J. Sakaguchi, W. Klaus, G. Saridis, Y. Awaji, and N. Wada, “High capacity transmission systems using homogeneous multi-core fibers,” J. Lightw. Technol. 35(6), 1157–1167 (2017).
[Crossref]

W. Klaus, B. Puttnam, R. Luis, J. Sakaguchi, J. Mendinueta, Y. Awaji, and N. Wada, “Advanced space division multiplexing technologies for optical networks,” J. Opt. Commun. Netw. 9(4), C1–C11 (2017).
[Crossref]

Sales, S.

J. Galvé, I. Gasulla, S. Sales, and J. Capmany, “Reconfigurable radio access networks using multicore fibers,” J. Quantum Electron. 52(1), 0600507 (2016).
[Crossref]

Saridis, G.

B. Puttnam, R. Luís, E. Agrell, G. Rademacher, J. Sakaguchi, W. Klaus, G. Saridis, Y. Awaji, and N. Wada, “High capacity transmission systems using homogeneous multi-core fibers,” J. Lightw. Technol. 35(6), 1157–1167 (2017).
[Crossref]

Sasaki, T.

R. Luís, B. Puttnam, A. Cartaxo, W. Klaus, J. Mendinueta, Y. Awaji, N. Wada, T. Nakanishi, T. Hayashi, and T. Sasaki, “Time and modulation frequency dependence of crosstalk in homogeneous multi-core fibers,” J. Lightw. Technol. 34(2), 441–447 (2016).
[Crossref]

T. Hayashi, T. Taru, O. Shimakawa, T. Sasaki, and E. Sasaoka, “Design and fabrication of ultra-low crosstalk and low-loss multi-core fiber,” Opt. Express 19(17), 16576–16592 (2011).
[Crossref] [PubMed]

T. Hayashi, T. Nagashima, O. Shimakawa, T. Sasaki, and E. Sasaoka, “Crosstalk variation of multi-core fibre due to fibre bend,” in Proceedings of European Conference on Optical Communications (ECOC), paper We.8.F.6. (2010).

T. Nagashima, O. Shimakawa, T. Sasaki, and E. Sasaoka, “Crosstalk variation of multi-core fibre due to fibre bend,” in European Conference on Optical Communications (ECOC), (2010), paper We.8.F.6.

Sasaki, Y.

Y. Amma, Y. Sasaki, K. Takenaga, S. Matsuo, J. Tu, K. Saitoh, M. Koshiba, T. Morioka, and Y. Miyamoto, “High-density multicore fiber with heterogeneous core arrangement,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2015), paper Th4C.4.

Sasaoka, E.

T. Hayashi, T. Taru, O. Shimakawa, T. Sasaki, and E. Sasaoka, “Design and fabrication of ultra-low crosstalk and low-loss multi-core fiber,” Opt. Express 19(17), 16576–16592 (2011).
[Crossref] [PubMed]

T. Nagashima, O. Shimakawa, T. Sasaki, and E. Sasaoka, “Crosstalk variation of multi-core fibre due to fibre bend,” in European Conference on Optical Communications (ECOC), (2010), paper We.8.F.6.

T. Hayashi, T. Nagashima, O. Shimakawa, T. Sasaki, and E. Sasaoka, “Crosstalk variation of multi-core fibre due to fibre bend,” in Proceedings of European Conference on Optical Communications (ECOC), paper We.8.F.6. (2010).

Shimakawa, O.

T. Hayashi, T. Taru, O. Shimakawa, T. Sasaki, and E. Sasaoka, “Design and fabrication of ultra-low crosstalk and low-loss multi-core fiber,” Opt. Express 19(17), 16576–16592 (2011).
[Crossref] [PubMed]

T. Hayashi, T. Nagashima, O. Shimakawa, T. Sasaki, and E. Sasaoka, “Crosstalk variation of multi-core fibre due to fibre bend,” in Proceedings of European Conference on Optical Communications (ECOC), paper We.8.F.6. (2010).

T. Nagashima, O. Shimakawa, T. Sasaki, and E. Sasaoka, “Crosstalk variation of multi-core fibre due to fibre bend,” in European Conference on Optical Communications (ECOC), (2010), paper We.8.F.6.

Shum, P.

Z. Feng, B. Li, M. Tang, L. Gan, R. Wang, R. Lin, Z. Xu, S. Fu, L. Deng, W. Tong, S. Long, L. Zhang, H. Zhou, R. Zhang, S. Liu, and P. Shum, “Multicore-fiber-enabled WSDM optical access network with centralized carrier delivery and RSOA-based adaptive modulation,” Photon. J. 7(4), 7201309 (2015).

Soeiro, R.

R. Soeiro, T. Alves, and A. Cartaxo, “Dual polarization discrete changes model of inter-core crosstalk in multi-core fibers,” Photon. Technol. Lett. 29(16), 1395–1398 (2017).
[Crossref]

Takahashi, H.

H. Takahashi, K. Igarashi, and T. Tsuritani, “Long-haul transmission using multicore fibers,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2014), paper Tu2J.2.

Takenaga, K.

M. Koshiba, K. Saitoh, K. Takenaga, and S. Matsuo, “Analytical expression of average power-coupling coefficients for estimating intercore crosstalk in multicore fibers,” Photon. J. 4(5), 1987–1995 (2012).
[Crossref]

Y. Amma, Y. Sasaki, K. Takenaga, S. Matsuo, J. Tu, K. Saitoh, M. Koshiba, T. Morioka, and Y. Miyamoto, “High-density multicore fiber with heterogeneous core arrangement,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2015), paper Th4C.4.

Tang, M.

Z. Feng, B. Li, M. Tang, L. Gan, R. Wang, R. Lin, Z. Xu, S. Fu, L. Deng, W. Tong, S. Long, L. Zhang, H. Zhou, R. Zhang, S. Liu, and P. Shum, “Multicore-fiber-enabled WSDM optical access network with centralized carrier delivery and RSOA-based adaptive modulation,” Photon. J. 7(4), 7201309 (2015).

Taru, T.

Taunay, T.

Tong, W.

Z. Feng, B. Li, M. Tang, L. Gan, R. Wang, R. Lin, Z. Xu, S. Fu, L. Deng, W. Tong, S. Long, L. Zhang, H. Zhou, R. Zhang, S. Liu, and P. Shum, “Multicore-fiber-enabled WSDM optical access network with centralized carrier delivery and RSOA-based adaptive modulation,” Photon. J. 7(4), 7201309 (2015).

Tsuritani, T.

H. Takahashi, K. Igarashi, and T. Tsuritani, “Long-haul transmission using multicore fibers,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2014), paper Tu2J.2.

Tu, J.

Y. Amma, Y. Sasaki, K. Takenaga, S. Matsuo, J. Tu, K. Saitoh, M. Koshiba, T. Morioka, and Y. Miyamoto, “High-density multicore fiber with heterogeneous core arrangement,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2015), paper Th4C.4.

Wada, N.

B. Puttnam, R. Luís, E. Agrell, G. Rademacher, J. Sakaguchi, W. Klaus, G. Saridis, Y. Awaji, and N. Wada, “High capacity transmission systems using homogeneous multi-core fibers,” J. Lightw. Technol. 35(6), 1157–1167 (2017).
[Crossref]

W. Klaus, B. Puttnam, R. Luis, J. Sakaguchi, J. Mendinueta, Y. Awaji, and N. Wada, “Advanced space division multiplexing technologies for optical networks,” J. Opt. Commun. Netw. 9(4), C1–C11 (2017).
[Crossref]

T. Alves, R. Luís, B. Puttnam, A. Cartaxo, Y. Awaji, and N. Wada, “Performance of adaptive DD-OFDM multicore fiber links and its relation with intercore crosstalk,” Opt. Express 25(13), 16017–16027 (2017).
[Crossref] [PubMed]

G. Rademacher, R. Luís, B. Puttnam, Y. Awaji, and N. Wada, “Crosstalk dynamics in multi-core fibers,” Opt. Express 25(10), 12020–12028 (2017).
[Crossref] [PubMed]

T. Alves, A. Cartaxo, R. Luís, B. Puttnam, Y. Awaji, and N. Wada, “Intercore crosstalk in direct-detection homogeneous multicore fiber systems impaired by laser phase noise,” Opt. Express 25(23), 29417–29431 (2017).
[Crossref]

B. Puttnam, R. Luís, T. Eriksson, W. Klaus, J. Mendinueta, Y. Awaji, and N. Wada, “Impact of intercore crosstalk on the transmission distance of QAM formats in multicore fibers,” Photon. J. 8(2), 0601109 (2016).

A. Cartaxo, R. Luís, B. Puttnam, T. Hayashi, Y. Awaji, and N. Wada, “Dispersion impact on the crosstalk amplitude response of homogeneous multi-core fibers,” Photon. Technol. Lett. 28(17), 1858–1861 (2016).
[Crossref]

R. Luís, B. Puttnam, A. Cartaxo, W. Klaus, J. Mendinueta, Y. Awaji, N. Wada, T. Nakanishi, T. Hayashi, and T. Sasaki, “Time and modulation frequency dependence of crosstalk in homogeneous multi-core fibers,” J. Lightw. Technol. 34(2), 441–447 (2016).
[Crossref]

G. Rademacher, B. Puttnam, R. Luís, Y. Awaji, and N. Wada, “Time-dependent inter-core crosstalk between multiple cores of a homogeneous multi-core fiber,” in Proceedings of Asia Communications and Photonics Conference (ACPC), paper AF1D.2 (2016).

J. Pedro, R. Luís, B. Puttnam, Y. Awaji, N. Wada, and A. Cartaxo, “Experimental assessment of the time-varying impact of multi-core fiber crosstalk on a SSB-OFDM Signal,” in Proceedings of Photonics in Switching (PS), 166–168 (2015).

G. Rademacher, B. Puttnam, R. Luís, Y. Awaji, and N. Wada, “Time-dependent crosstalk from multiple cores in a homogeneous multi-core fiber,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2016), paper Th1H.3.

T. Alves, A. Cartaxo, R. Luís, B. Puttnam, Y. Awaji, and N. Wada, “Adaptive loading with extended memory to relax the impact of the phase noise-impaired ICXT in DD-OFDM MCF-based systems,” in Proceedings of International Conference on Transparent Optical Networks (ICTON), paper Tu.D1.2 (2017).

A. Cartaxo, T. Alves, B. Puttnam, R. Luís, Y. Awaji, and N. Wada, “DD-OFDM multicore fiber systems impaired by intercore crosstalk and laser phase noise,” in Proceedings of International Conference on Transparent Optical Networks (ICTON), paper Tu.D1.1 (2017).

G. Rademacher, R. Luís, B. Puttnam, Y. Awaji, and N. Wada, “Performance fluctuations in direct detection multi-core fiber transmission systems,” in Proceedings of European Conference on Optical Communications (ECOC), paper P2.SC6.16 (2017).

Wang, R.

Z. Feng, B. Li, M. Tang, L. Gan, R. Wang, R. Lin, Z. Xu, S. Fu, L. Deng, W. Tong, S. Long, L. Zhang, H. Zhou, R. Zhang, S. Liu, and P. Shum, “Multicore-fiber-enabled WSDM optical access network with centralized carrier delivery and RSOA-based adaptive modulation,” Photon. J. 7(4), 7201309 (2015).

Winzer, P.

P. Winzer, A. Gnauck, A. Konczykowska, F. Jorge, and J. Dupuy, “Penalties from in-band crosstalk for advanced optical modulation formats,” in Proceedings of European Conference on Optical Communications (ECOC), paper Tu.5.B.7 (2011).

Xu, Z.

Z. Feng, B. Li, M. Tang, L. Gan, R. Wang, R. Lin, Z. Xu, S. Fu, L. Deng, W. Tong, S. Long, L. Zhang, H. Zhou, R. Zhang, S. Liu, and P. Shum, “Multicore-fiber-enabled WSDM optical access network with centralized carrier delivery and RSOA-based adaptive modulation,” Photon. J. 7(4), 7201309 (2015).

Yan, M.

Zhang, L.

Z. Feng, B. Li, M. Tang, L. Gan, R. Wang, R. Lin, Z. Xu, S. Fu, L. Deng, W. Tong, S. Long, L. Zhang, H. Zhou, R. Zhang, S. Liu, and P. Shum, “Multicore-fiber-enabled WSDM optical access network with centralized carrier delivery and RSOA-based adaptive modulation,” Photon. J. 7(4), 7201309 (2015).

Zhang, R.

Z. Feng, B. Li, M. Tang, L. Gan, R. Wang, R. Lin, Z. Xu, S. Fu, L. Deng, W. Tong, S. Long, L. Zhang, H. Zhou, R. Zhang, S. Liu, and P. Shum, “Multicore-fiber-enabled WSDM optical access network with centralized carrier delivery and RSOA-based adaptive modulation,” Photon. J. 7(4), 7201309 (2015).

Zhou, H.

Z. Feng, B. Li, M. Tang, L. Gan, R. Wang, R. Lin, Z. Xu, S. Fu, L. Deng, W. Tong, S. Long, L. Zhang, H. Zhou, R. Zhang, S. Liu, and P. Shum, “Multicore-fiber-enabled WSDM optical access network with centralized carrier delivery and RSOA-based adaptive modulation,” Photon. J. 7(4), 7201309 (2015).

Zhu, B.

J. Lightw. Technol. (3)

B. Puttnam, R. Luís, E. Agrell, G. Rademacher, J. Sakaguchi, W. Klaus, G. Saridis, Y. Awaji, and N. Wada, “High capacity transmission systems using homogeneous multi-core fibers,” J. Lightw. Technol. 35(6), 1157–1167 (2017).
[Crossref]

R. Luís, B. Puttnam, A. Cartaxo, W. Klaus, J. Mendinueta, Y. Awaji, N. Wada, T. Nakanishi, T. Hayashi, and T. Sasaki, “Time and modulation frequency dependence of crosstalk in homogeneous multi-core fibers,” J. Lightw. Technol. 34(2), 441–447 (2016).
[Crossref]

T. Alves and A. Cartaxo, “Inter-core crosstalk in homogeneous multi-core fibers: theoretical characterization of stochastic time evolution,” J. Lightw. Technol. 35(21), 4613–4623 (2017).
[Crossref]

J. Opt. Commun. Netw. (1)

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J. Galvé, I. Gasulla, S. Sales, and J. Capmany, “Reconfigurable radio access networks using multicore fibers,” J. Quantum Electron. 52(1), 0600507 (2016).
[Crossref]

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M. Koshiba, K. Saitoh, K. Takenaga, and S. Matsuo, “Analytical expression of average power-coupling coefficients for estimating intercore crosstalk in multicore fibers,” Photon. J. 4(5), 1987–1995 (2012).
[Crossref]

Z. Feng, B. Li, M. Tang, L. Gan, R. Wang, R. Lin, Z. Xu, S. Fu, L. Deng, W. Tong, S. Long, L. Zhang, H. Zhou, R. Zhang, S. Liu, and P. Shum, “Multicore-fiber-enabled WSDM optical access network with centralized carrier delivery and RSOA-based adaptive modulation,” Photon. J. 7(4), 7201309 (2015).

B. Puttnam, R. Luís, T. Eriksson, W. Klaus, J. Mendinueta, Y. Awaji, and N. Wada, “Impact of intercore crosstalk on the transmission distance of QAM formats in multicore fibers,” Photon. J. 8(2), 0601109 (2016).

Photon. Technol. Lett. (2)

A. Cartaxo, R. Luís, B. Puttnam, T. Hayashi, Y. Awaji, and N. Wada, “Dispersion impact on the crosstalk amplitude response of homogeneous multi-core fibers,” Photon. Technol. Lett. 28(17), 1858–1861 (2016).
[Crossref]

R. Soeiro, T. Alves, and A. Cartaxo, “Dual polarization discrete changes model of inter-core crosstalk in multi-core fibers,” Photon. Technol. Lett. 29(16), 1395–1398 (2017).
[Crossref]

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T. Nagashima, O. Shimakawa, T. Sasaki, and E. Sasaoka, “Crosstalk variation of multi-core fibre due to fibre bend,” in European Conference on Optical Communications (ECOC), (2010), paper We.8.F.6.

D. Butler, M. Li, S. Li, Y. Geng, R. Khrapko, R. Modavis, V. Nazarov, and A. Koklyushkin, “Space division multiplexing in short reach optical interconnects,” J. Lightw. Technol. DOI (2017).
[Crossref]

Y. Amma, Y. Sasaki, K. Takenaga, S. Matsuo, J. Tu, K. Saitoh, M. Koshiba, T. Morioka, and Y. Miyamoto, “High-density multicore fiber with heterogeneous core arrangement,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2015), paper Th4C.4.

A. Cartaxo and T. Alves, “Discrete changes model of inter-core crosstalk of real homogeneous multi-core fibers,” J. Lightw. Technol. DOI (2017).
[Crossref]

G. Rademacher, B. Puttnam, R. Luís, Y. Awaji, and N. Wada, “Time-dependent inter-core crosstalk between multiple cores of a homogeneous multi-core fiber,” in Proceedings of Asia Communications and Photonics Conference (ACPC), paper AF1D.2 (2016).

G. Rademacher, B. Puttnam, R. Luís, Y. Awaji, and N. Wada, “Time-dependent crosstalk from multiple cores in a homogeneous multi-core fiber,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2016), paper Th1H.3.

J. Pedro, R. Luís, B. Puttnam, Y. Awaji, N. Wada, and A. Cartaxo, “Experimental assessment of the time-varying impact of multi-core fiber crosstalk on a SSB-OFDM Signal,” in Proceedings of Photonics in Switching (PS), 166–168 (2015).

A. Cartaxo, T. Alves, B. Puttnam, R. Luís, Y. Awaji, and N. Wada, “DD-OFDM multicore fiber systems impaired by intercore crosstalk and laser phase noise,” in Proceedings of International Conference on Transparent Optical Networks (ICTON), paper Tu.D1.1 (2017).

T. Alves and A. Cartaxo, “Characterization of ICXT in DD-OFDM MCF-based systems,” in Proceedings of European Conference on Optical Communications (ECOC), paper P2.SC6.29 (2017).

G. Rademacher, R. Luís, B. Puttnam, Y. Awaji, and N. Wada, “Performance fluctuations in direct detection multi-core fiber transmission systems,” in Proceedings of European Conference on Optical Communications (ECOC), paper P2.SC6.16 (2017).

T. Alves, A. Cartaxo, R. Luís, B. Puttnam, Y. Awaji, and N. Wada, “Adaptive loading with extended memory to relax the impact of the phase noise-impaired ICXT in DD-OFDM MCF-based systems,” in Proceedings of International Conference on Transparent Optical Networks (ICTON), paper Tu.D1.2 (2017).

P. Winzer, A. Gnauck, A. Konczykowska, F. Jorge, and J. Dupuy, “Penalties from in-band crosstalk for advanced optical modulation formats,” in Proceedings of European Conference on Optical Communications (ECOC), paper Tu.5.B.7 (2011).

J. Franz and V. Jain, Optical Communications: Components and Systems (Alpha Science International Limited, reprint in 2008).

T. Hayashi, T. Nagashima, O. Shimakawa, T. Sasaki, and E. Sasaoka, “Crosstalk variation of multi-core fibre due to fibre bend,” in Proceedings of European Conference on Optical Communications (ECOC), paper We.8.F.6. (2010).

H. Takahashi, K. Igarashi, and T. Tsuritani, “Long-haul transmission using multicore fibers,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2014), paper Tu2J.2.

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Figures (6)

Fig. 1
Fig. 1 Experimental setup implemented in the lab to measure the STAXT. (i) Profile of the 19-core MCF.
Fig. 2
Fig. 2 (a) Autocorrelation and (b) autocovariance functions of the STAXT of the central core considering the stationary phase shift model. (c) Autocorrelation and (d) autocovariance functions of the STAXT of the central core considering the non-stationary phase shift model. The results are evaluated considering six interfering cores. Case 1: the STAXT decorrelation time of each pair of cores is 5 minutes. Case 2: the STAXT decorrelation time is 2 minutes for pairs (1,2), (1,3) and (1,4), and 5 minutes for pairs (1,5), (1,6) and (1,7).
Fig. 3
Fig. 3 STAXT of the central core measured over 160 hours for different interfering cores.
Fig. 4
Fig. 4 Normalized autocovariance of the STAXT for the pair of cores (a) (1,2) and (b) (1,6).
Fig. 5
Fig. 5 Decorrelation time of the STAXT measured experimentally at the output of the central core as a function of the extension of the measurement time.
Fig. 6
Fig. 6 (a) STAXT, (b) normalized autocovariance and (c) decorrelation time of the STAXT measured experimentally at the output of the central core. All the results are obtained considering six interfering cores.

Tables (4)

Tables Icon

Table 1 Total fan-in+MCF+fan-out loss.

Tables Icon

Table 2 Skew between the pair of cores.

Tables Icon

Table 3 Parameters used to estimate the discrete coupling coefficients. The mean ICXT power measured experimentally is also shown.

Tables Icon

Table 4 Decorrelation time of the STAXT measured experimentally at the output of the central core.

Equations (20)

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E n ( L , t ) = j m = 1 m n N c K ¯ n , m 2 k = 1 N p [ ζ m v 1 , n , m ( k ) ( t ) 1 ζ m v 2 , n , m ( k ) ( t ) ζ m v 3 , n , m ( k ) ( t ) 1 ζ m v 4 , n , m ( k ) ( t ) ] [ F ¯ n , m ( k ) ( 0 , t ξ ¯ n , m ( k ) ) F ¯ n , m ( k ) ( 0 , t ξ ¯ n , m ( k ) ) ]
v i , n , m ( k ) ( t ) = exp [ j ( Φ i , m ( k ) ( t ) + ϕ ¯ n , m ( k ) ) ] , 1 i 4
F ¯ n , m ( k ) ( 0 , t ) = 1 [ E ˜ m ( 0 , ω ) exp ( j η ¯ n , m ( k ) ω 2 ) ]
ϕ ¯ n , m ( k ) = β ¯ n , 0 ( L z m ( k ) ) + β ¯ m , 0 z m ( k ) ξ ¯ n , m ( k ) = β ¯ n , 1 ( L z m ( k ) ) + β ¯ m , 1 z m ( k )
η ¯ n , m ( k ) = 0.5 [ β ¯ n , 2 ( L z m ( k ) ) + β ¯ m , 2 z m ( k ) ]
Φ i , m ( k ) ( t ) = 2 π 0 t μ i , m ( k ) ( τ ) d τ t > 0
R ns , m 1 , m 2 , k 1 , k 2 ( τ ) = E { exp [ ± j ( Φ i , m 1 ( k 1 ) ( t ) Φ i , m 2 ( k 2 ) ( t + τ ) ) ] } = = { exp ( 0.5 K Φ m | τ | ) for m 1 = m 2 and k 1 = k 2 E { exp [ ± j ( Φ i , m 1 ( k 1 ) ( t ) ) ] } E { exp [ j ( Φ i , m 2 ( k 2 ) ( t + τ ) ) ] } = 0 for m 1 m 2 and k 1 k 2
E n , x ( L , t ) = j m = 1 , m n N c p i , m K ¯ n , m 2 k = 1 N p ( ζ m v 1 , n , m ( k ) ( t ) + 1 ζ m v 2 , n , m ( k ) ( t ) )
E n , y ( L , t ) = j m = 1 , m n N c p i , m K ¯ n , m 2 k = 1 N p ( ζ m v 3 , n , m ( k ) ( t ) + 1 ζ m v 4 , n , m ( k ) ( t ) )
STAXT n ( t ) = 1 T t t + T p ( τ ) d τ p ( t )
R STAXT , n ( τ ) = E [ p ( t ) p ( t + τ ) ] = R STAXT , n , x ( τ ) + R STAXT , n , y ( τ ) + R STAXT , n , x y ( τ )
R STAXT , n , x ( τ ) = 1 2 m 1 = 1 , m 1 n N c m 2 = 1 , m 2 n N c m 3 = 1 m 3 n N c m 4 = 1 , m 4 n N c p i , m 1 p i , m 2 p i , m 3 p i , m 4 K ¯ n , m 1 K ¯ n , m 2 * K ¯ n , m 3 K ¯ n , m 4 * × × k 1 = 1 N p k 2 = 1 N p k 3 = 1 N p k 4 = 1 N p exp [ j ( ϕ n , m 1 ( k 1 ) ϕ n , m 2 ( k 2 ) + ϕ n , m 3 ( k 3 ) ϕ n , m 4 ( k 4 ) ) ] × × ζ m 1 ζ m 2 ζ m 3 ζ m 4 { E [ exp { j ( Φ 1 , m 1 ( k 1 ) ( t ) Φ 1 , m 2 ( k 2 ) ( t ) + Φ 1 , m 3 ( k 3 ) ( t + τ ) Φ 1 , m 4 ( k 4 ) ( t + τ ) ) } ] + + E [ exp { j ( Φ 1 , m 1 ( k 1 ) ( t ) Φ 1 , m 2 ( k 2 ) ( t ) + Φ 3 , m 3 ( k 3 ) ( t + τ ) Φ 3 , m 4 ( k 4 ) ( t + τ ) ) } ] }
R STAXT , n , y ( τ ) = 1 2 m 1 = 1 , m 1 n N c m 2 = 1 , m 2 n N c m 3 = 1 m 3 n N c m 4 = 1 , m 4 n N c p i , m 1 p i , m 2 p i , m 3 p i , m 4 K ¯ n , m 1 K ¯ n , m 2 * K ¯ n , m 3 K ¯ n , m 4 * × × k 1 = 1 N p k 2 = 1 N p k 3 = 1 N p k 4 = 1 N p exp [ j ( ϕ n , m 1 ( k 1 ) ϕ n , m 2 ( k 2 ) + ϕ n , m 3 ( k 3 ) ϕ n , m 4 ( k 4 ) ) ] ( 1 ζ m 1 ) ( 1 ζ m 2 ) ( 1 ζ m 3 ) × × ( 1 ζ m 4 ) { E { exp [ j ( Φ 2 , m 1 ( k 1 ) ( t ) Φ 2 , m 2 ( k 2 ) ( t ) + Φ 2 , m 3 ( k 3 ) ( t + τ ) Φ 2 , m 4 ( k 4 ) ( t + τ ) ) ] + + E [ exp { j ( Φ 2 , m 1 ( k 1 ) ( t ) Φ 2 , m 2 ( k 2 ) ( t ) + Φ 4 , m 3 ( k 3 ) ( t + τ ) Φ 4 , m 4 ( k 4 ) ( t + τ ) ) } ] } }
R STAXT , n , x y ( τ ) = 1 2 m 1 = 1 , m 1 n N c m 2 = 1 , m 2 n N c m 3 = 1 m 3 n N c m 4 = 1 , m 4 n N c p i , m 1 p i , m 2 p i , m 3 p i , m 4 K ¯ n , m 1 K ¯ n , m 2 * K ¯ n , m 3 K ¯ n , m 4 * × × k 1 = 1 N p k 2 = 1 N p k 3 = 1 N p k 4 = 1 N p exp [ j ( ϕ n , m 1 ( k 1 ) ϕ n , m 2 ( k 2 ) + ϕ n , m 3 ( k 3 ) ϕ n , m 4 ( k 4 ) ) ] × × { ζ m 1 ( 1 ζ m 2 ) ζ m 3 ( 1 ζ m 4 ) × × E [ exp { j ( Φ 1 , m 1 ( k 1 ) ( t ) Φ 2 , m 2 ( k 2 ) ( t ) + Φ 1 , m 3 ( k 3 ) ( t + τ ) Φ 2 , m 4 ( k 4 ) ( t + τ ) ) } ] + + ( 1 ζ m 1 ) ζ m 2 ( 1 ζ m 3 ) ζ m 4 × × E [ exp { j ( Φ 2 , m 1 ( k 1 ) ( t ) Φ 1 , m 2 ( k 2 ) ( t ) + Φ 2 , m 3 ( k 3 ) ( t + τ ) Φ 1 , m 4 ( k 4 ) ( t + τ ) ) } ] + + ζ m 1 ζ m 2 ( 1 ζ m 3 ) ( 1 ζ m 4 ) × × E [ exp { j ( Φ 1 , m 1 ( k 1 ) ( t ) Φ 1 , m 2 ( k 2 ) ( t ) + Φ 2 , m 3 ( k 3 ) ( t + τ ) Φ 2 , m 4 ( k 4 ) ( t + τ ) ) } ] + + ζ m 1 ζ m 2 ( 1 ζ m 3 ) ( 1 ζ m 4 ) × × E [ exp { j ( Φ 1 , m 1 ( k 1 ) ( t ) Φ 1 , m 2 ( k 2 ) ( t ) + Φ 4 , m 3 ( k 3 ) ( t + τ ) Φ 4 , m 4 ( k 4 ) ( t + τ ) ) } ] + + ζ m 1 ( 1 ζ m 2 ) ( 1 ζ m 3 ) ζ m 4 × × E [ exp { j ( Φ 1 , m 1 ( k 1 ) ( t ) Φ 2 , m 2 ( k 2 ) ( t ) + Φ 2 , m 3 ( k 3 ) ( t + τ ) Φ 1 , m 4 ( k 4 ) ( t + τ ) ) } ] + + ( 1 ζ m 1 ) ζ m 2 ζ m 3 ( 1 ζ m 4 ) × × E [ exp { j ( Φ 2 , m 1 ( k 1 ) ( t ) Φ 1 , m 2 ( k 2 ) ( t ) + Φ 1 , m 3 ( k 3 ) ( t + τ ) Φ 2 , m 4 ( k 4 ) ( t + τ ) ) } ] + + ( 1 ζ m 1 ) ( 1 ζ m 2 ) ζ m 3 ζ m 4 × × E [ exp { j ( Φ 2 , m 1 ( k 1 ) ( t ) Φ 2 , m 2 ( k 2 ) ( t ) + Φ 1 , m 3 ( k 3 ) ( t + τ ) Φ 1 , m 4 ( k 4 ) ( t + τ ) ) } ] + + ( 1 ζ m 1 ) ( 1 ζ m 2 ) ζ m 3 ζ m 4 × × E [ exp { j ( Φ 2 , m 1 ( k 1 ) ( t ) Φ 2 , m 2 ( k 2 ) ( t ) + Φ 3 , m 3 ( k 3 ) ( t + τ ) Φ 3 , m 4 ( k 4 ) ( t + τ ) ) } ] }
R STAXT , n ( τ ) m = 1 , m n N c p i , m 2 | K ¯ n , m | 4 [ N p 2 + N p 2 ( N p 1 ) R m 2 ( τ ) ] + N p 2 m 1 = 1 , m 1 n N c p i , m 1 2 | K ¯ n , m 1 | 2 × + m 2 = 1 , m 2 n , m 2 m 1 N c p i , m 2 | K ¯ n , m 2 | 2 + N p 2 2 m 1 = 1 , m 1 n N c p i , m 1 | K ¯ n , m 1 | 2 R m 1 ( τ ) m 2 = 1 , m 2 n , m 2 m 1 N c p i , m 2 | K ¯ n , m 2 | 2 R m 2 ( τ )
R Φ l ( τ ) = σ Φ l 2 exp ( α l | τ | ) ( cos ( α l τ ) + sin ( α l | τ | ) )
C STAXT , n ( τ ) = R STAXT , n ( τ ) E 2 [ p ( t ) ] N p ( N p 1 ) 2 m = 1 , m n N c p i , m 2 | K ¯ n , m | 4 R m 2 ( τ ) + + N p 2 2 m 1 = 1 , m 1 n N c p i , m 1 | K ¯ n , m 1 | 2 R m 1 ( τ ) m 2 = 1 , m 2 n , m 2 m 1 N c p i , m 2 | K ¯ n , m 2 | 2 R m 2 ( τ )
E 2 [ p ( t ) ] = N p 2 m = 1 , m n N c p i , m 2 | K ¯ n , m | 4 + N p 2 m 1 = 1 , m 1 n N c p i , m 1 | K ¯ n , m 1 | 2 m 2 = 1 , m 2 n , m 2 m 1 N c p i , m 2 | K ¯ n , m 2 | 2
C STAXT , n ( τ ) ( N c 1 ) [ N p 2 N p 2 + ( N c 2 ) N p 2 2 ] p i , m 2 | K ¯ n , m | 4 R m 2 ( τ )
C STAXT , n ( τ ) = N p ( N p 1 ) 2 p i , m 2 | K ¯ n , m | 4 R m 2 ( τ )

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