Abstract

In order to better evaluate the relationship between reciprocity and time delay of the fiber receiving system in the atmospheric turbulence channel, a time-domain signal generation mathematical model is proposed for the first time. A numerical solution of Johnson SB probability density distribution (PDF) in time-domain is creatively given for evaluating the reciprocity of both communication ends, which relates to the normalized fluctuation variance of the light intensity and the Greenwood frequency. An experiment is then carried out for verifying the time-domain signal generation model and measuring reciprocity. It shows that the excellent fitting accuracy of Johnson SB PDF signal generation model is first experimentally verified. It also indicates that the system reciprocity is improved by 10% after eliminating the system time delay. Meanwhile, the relationship between time delay and reciprocity under different atmospheric environments are analyzed and the relationship between time delay and system reciprocity at different Greenwood frequencies are discussed. This work provides a time parameter reference for the design of adaptive system and free-space optical (FSO) communication system.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Reciprocity-Enhanced Optical Communication Through Atmospheric Turbulence—Part II: Communication Architectures and Performance

Andrew L. Puryear, Jeffrey H. Shapiro, and Ronald R. Parenti
J. Opt. Commun. Netw. 5(8) 888-900 (2013)

Performance Analysis of CDMA-Based Wireless Services Transmission Over a Turbulent RF-on-FSO Channel

Chedlia Ben Naila, Abdelmoula Bekkali, Kazuhiko Wakamori, and Mitsuji Matsumoto
J. Opt. Commun. Netw. 3(5) 475-486 (2011)

Asymptotic error-rate analysis of FSO links using transmit laser selection over gamma-gamma atmospheric turbulence channels with pointing errors

Antonio García-Zambrana, Beatriz Castillo-Vázquez, and Carmen Castillo-Vázquez
Opt. Express 20(3) 2096-2109 (2012)

References

  • View by:
  • |
  • |
  • |

  1. V. P. Lukin and M. I. Charnotskiĭ, “Reciprocity principle and adaptive control of optical radiation parameters,” Sov. J. Quantum Electron. 12, 602–605 (1982).
    [Crossref]
  2. M. A. Vorontsov, G. W. Carhart, M. Cohen, and G. Cauwenberghs, “Adaptive optics based on analog parallel stochastic optimization: analysis and experimental demonstration,” J. Opt. Soc. Am. A 17, 1440–1453 (2000).
    [Crossref]
  3. W.-F. Lin, C.-W. Chow, and C.-H. Yeh, “Using specific and adaptive arrangement of grid-type pilot in channel estimation for white-lightled-based OFDM visible light communication system,” Opt. Commun. 338, 7 – 10 (2015).
    [Crossref]
  4. J. Palastro, J. P. nano, W. Nelson, G. DiComo, M. Helle, A. Johnson, and L. B. Hafizi, “Reciprocity breaking during nonlinear propagation of adapted beams through random media,” Opt. Express 24, 18817–18827 (2016).
    [Crossref] [PubMed]
  5. J. H. Shapiro, “Reciprocity of the turbulent atmosphere,” J. Opt. Soc. Am. 61, 492–495 (1971).
    [Crossref]
  6. J. H. Shapiro and A. L. Puryear, “Reciprocity-enhanced optical communication through atmospheric turbulence- part I: Reciprocity proofs and far-field power transfer optimization,” J. Opt. Commun. Netw. 4, 947–954 (2012).
    [Crossref]
  7. A. L. Puryear, J. H. Shapiro, and R. R. Parenti, “Reciprocity-enhanced optical communication through atmospheric turbulence- part II: Communication architectures and performance,” J. Opt. Commun. Netw. 5, 888–900 (2013).
    [Crossref]
  8. N. Perlot and D. Giggenbach, “Scintillation correlation between forward and return spherical waves,” Appl. Opt. 51, 2888–2893 (2012).
    [Crossref] [PubMed]
  9. J. Minet, M. A. Vorontsov, E. Polnau, and D. Dolfi, “Enhanced correlation of received power-signal fluctuations in bidirectional optical links,” J. Opt. 15, 022401 (2013).
    [Crossref]
  10. J.-M. Conan, C. Robert, N. V édrenne, M.-T. Velluet, P. Wolf, and V. Michau, “Reciprocity principle for the modelling of ground-space adaptive optics assisted optical links: Application to frequency and data transfer,” in Imaging and Applied Optics2016, (2016), p. AOTh1C.4.
    [Crossref]
  11. C. Chen, H. Yang, S. Tong, and Y. Lou, “Mean-square angle-of-arrival difference between two counter-propagating spherical waves in the presence of atmospheric turbulence,” Opt. Express 23, 24657–24668 (2015).
    [Crossref] [PubMed]
  12. C. Chen and H. Yang, “Correlation between light-flux fluctuations of two counter-propagating waves in weak atmospheric turbulence,” Opt. Express 25, 12779–12795 (2017).
    [Crossref] [PubMed]
  13. R. R. Parenti, J. M. Roth, J. H. Shapiro, F. G. Walther, and J. A. Greco, “Experimental observations of channel reciprocity in single-mode free-space optical links,” Opt. Express 20, 21635–21644 (2012).
    [Crossref] [PubMed]
  14. D. Giggenbach, W. Cowley, K. Grant, and N. Perlot, “Experimental verification of the limits of optical channel intensity reciprocity,” Appl. Opt. 51, 3145–3152 (2012).
    [Crossref] [PubMed]
  15. S. Parthasarathy, D. Giggenbach, C. Fuchs, R. Mata-Calvo, R. Barrios, and A. Kirstaedter, “Verification of channel reciprocity in long-range turbulent FSO links,” in Photonic Networks; 19th ITG-Symposium, (2018), pp. 1–6.
  16. H. T. Yura and S. G. Hanson, “Optical beam wave propagation through complex optical systems,” J. Opt. Soc. Am. A 4, 1931–1948 (1987).
    [Crossref]
  17. R. L. Phillips, Laser Beam Propagation through Random Media, 2nd ed. (SPIE Press, 2005).
  18. H.T. Yura and S.G. Hanson, “Digital simulation of an arbitrary stationary stochastic process by spectral representation,” J. Opt. Soc. Am. A 28, 675–685 (2011).
    [Crossref]
  19. C. Chen and H. Yang, “Shared secret key generation from signal fading in a turbulent optical wireless channel using common-transverse-spatial-mode coupling,” Opt. Express 26, 16422–16441 (2018).
    [Crossref] [PubMed]
  20. C. Y. H. Larry, C. Andrews, and L. Ronald Phillips, Laser Beam Scintillation with Applications (SPIE Press, 2001).
  21. A. Neuenkirch and L. Szpruch, “First order strong approximations of scalar SDEs defined in a domain,” Numer. Math. 128, 103–136 (2014).
    [Crossref]
  22. D. Bykhovsky, “Free-space optical channel simulator for weak-turbulence conditions,” Appl. Opt. 54, 9055–9059 (2015).
    [Crossref] [PubMed]
  23. E. P. Peter and E. Kloeden, Numerical Solution of Stochastic Differential Equations (Springer, 1992).
  24. M. A. Kashani, M. Uysal, and M. Kavehrad, “A novel statistical channel model for turbulence-induced fading in free-space optical systems,” J. Lightwave Technol. 33, 2303–2312 (2015).
    [Crossref]
  25. S. Primak, V. Lyandres, and V. Kontorovich, “Markov models of non-Gaussian exponentially correlated processes and their applications,” Phys. Rev. E 63, 061103 (2001).
    [Crossref]
  26. V. L. Serguei Primak and Valeri Kontorovitch, Stochastic methods and their applications to communications: stochastic differential equations approach (Wiley, 2004).
    [Crossref]
  27. D. Fried, “Greenwood frequency measurements,” J. Opt. Soc. Am. 7, 946–947 (1990).
    [Crossref]
  28. T. Morio, T. Hideki, S. Yozo, and T. Yoshihisa, “Frequency characteristics of atmospheric turbulence in space-toground laser links,” Proc. SPIE 7685, 76850G (2010).
    [Crossref]
  29. W. Liu, K. Yao, D. Huang, X. Lin, L. Wang, and Y. Lv, “Performance evaluation of coherent free space optical communications with a double-stage fast-steering-mirror adaptive optics system depending on the Greenwood frequency,” Opt. Express 24, 13288–13302 (2016).
    [Crossref] [PubMed]
  30. B. W. F. Robert and K. Tyson, Field Guide to Adaptive Optics, 2nd ed. (SPIE Press, 2012).
  31. G. A. Tyler, “Bandwidth considerations for tracking through turbulence,” J. Opt. Soc. Am. A 11, 358–367 (1994).
    [Crossref]

2018 (1)

2017 (1)

2016 (2)

2015 (4)

2014 (1)

A. Neuenkirch and L. Szpruch, “First order strong approximations of scalar SDEs defined in a domain,” Numer. Math. 128, 103–136 (2014).
[Crossref]

2013 (2)

J. Minet, M. A. Vorontsov, E. Polnau, and D. Dolfi, “Enhanced correlation of received power-signal fluctuations in bidirectional optical links,” J. Opt. 15, 022401 (2013).
[Crossref]

A. L. Puryear, J. H. Shapiro, and R. R. Parenti, “Reciprocity-enhanced optical communication through atmospheric turbulence- part II: Communication architectures and performance,” J. Opt. Commun. Netw. 5, 888–900 (2013).
[Crossref]

2012 (4)

2011 (1)

2010 (1)

T. Morio, T. Hideki, S. Yozo, and T. Yoshihisa, “Frequency characteristics of atmospheric turbulence in space-toground laser links,” Proc. SPIE 7685, 76850G (2010).
[Crossref]

2001 (1)

S. Primak, V. Lyandres, and V. Kontorovich, “Markov models of non-Gaussian exponentially correlated processes and their applications,” Phys. Rev. E 63, 061103 (2001).
[Crossref]

2000 (1)

1994 (1)

1990 (1)

D. Fried, “Greenwood frequency measurements,” J. Opt. Soc. Am. 7, 946–947 (1990).
[Crossref]

1987 (1)

1982 (1)

V. P. Lukin and M. I. Charnotskiĭ, “Reciprocity principle and adaptive control of optical radiation parameters,” Sov. J. Quantum Electron. 12, 602–605 (1982).
[Crossref]

1971 (1)

Andrews, C.

C. Y. H. Larry, C. Andrews, and L. Ronald Phillips, Laser Beam Scintillation with Applications (SPIE Press, 2001).

Barrios, R.

S. Parthasarathy, D. Giggenbach, C. Fuchs, R. Mata-Calvo, R. Barrios, and A. Kirstaedter, “Verification of channel reciprocity in long-range turbulent FSO links,” in Photonic Networks; 19th ITG-Symposium, (2018), pp. 1–6.

Bykhovsky, D.

Carhart, G. W.

Cauwenberghs, G.

Charnotskii, M. I.

V. P. Lukin and M. I. Charnotskiĭ, “Reciprocity principle and adaptive control of optical radiation parameters,” Sov. J. Quantum Electron. 12, 602–605 (1982).
[Crossref]

Chen, C.

Chow, C.-W.

W.-F. Lin, C.-W. Chow, and C.-H. Yeh, “Using specific and adaptive arrangement of grid-type pilot in channel estimation for white-lightled-based OFDM visible light communication system,” Opt. Commun. 338, 7 – 10 (2015).
[Crossref]

Cohen, M.

Conan, J.-M.

J.-M. Conan, C. Robert, N. V édrenne, M.-T. Velluet, P. Wolf, and V. Michau, “Reciprocity principle for the modelling of ground-space adaptive optics assisted optical links: Application to frequency and data transfer,” in Imaging and Applied Optics2016, (2016), p. AOTh1C.4.
[Crossref]

Cowley, W.

DiComo, G.

Dolfi, D.

J. Minet, M. A. Vorontsov, E. Polnau, and D. Dolfi, “Enhanced correlation of received power-signal fluctuations in bidirectional optical links,” J. Opt. 15, 022401 (2013).
[Crossref]

édrenne, N. V

J.-M. Conan, C. Robert, N. V édrenne, M.-T. Velluet, P. Wolf, and V. Michau, “Reciprocity principle for the modelling of ground-space adaptive optics assisted optical links: Application to frequency and data transfer,” in Imaging and Applied Optics2016, (2016), p. AOTh1C.4.
[Crossref]

Fried, D.

D. Fried, “Greenwood frequency measurements,” J. Opt. Soc. Am. 7, 946–947 (1990).
[Crossref]

Fuchs, C.

S. Parthasarathy, D. Giggenbach, C. Fuchs, R. Mata-Calvo, R. Barrios, and A. Kirstaedter, “Verification of channel reciprocity in long-range turbulent FSO links,” in Photonic Networks; 19th ITG-Symposium, (2018), pp. 1–6.

Giggenbach, D.

Grant, K.

Greco, J. A.

Hafizi, L. B.

Hanson, S. G.

Hanson, S.G.

Helle, M.

Hideki, T.

T. Morio, T. Hideki, S. Yozo, and T. Yoshihisa, “Frequency characteristics of atmospheric turbulence in space-toground laser links,” Proc. SPIE 7685, 76850G (2010).
[Crossref]

Huang, D.

Johnson, A.

Kashani, M. A.

Kavehrad, M.

Kirstaedter, A.

S. Parthasarathy, D. Giggenbach, C. Fuchs, R. Mata-Calvo, R. Barrios, and A. Kirstaedter, “Verification of channel reciprocity in long-range turbulent FSO links,” in Photonic Networks; 19th ITG-Symposium, (2018), pp. 1–6.

Kloeden, E.

E. P. Peter and E. Kloeden, Numerical Solution of Stochastic Differential Equations (Springer, 1992).

Kontorovich, V.

S. Primak, V. Lyandres, and V. Kontorovich, “Markov models of non-Gaussian exponentially correlated processes and their applications,” Phys. Rev. E 63, 061103 (2001).
[Crossref]

Kontorovitch, Valeri

V. L. Serguei Primak and Valeri Kontorovitch, Stochastic methods and their applications to communications: stochastic differential equations approach (Wiley, 2004).
[Crossref]

Larry, C. Y. H.

C. Y. H. Larry, C. Andrews, and L. Ronald Phillips, Laser Beam Scintillation with Applications (SPIE Press, 2001).

Lin, W.-F.

W.-F. Lin, C.-W. Chow, and C.-H. Yeh, “Using specific and adaptive arrangement of grid-type pilot in channel estimation for white-lightled-based OFDM visible light communication system,” Opt. Commun. 338, 7 – 10 (2015).
[Crossref]

Lin, X.

Liu, W.

Lou, Y.

Lukin, V. P.

V. P. Lukin and M. I. Charnotskiĭ, “Reciprocity principle and adaptive control of optical radiation parameters,” Sov. J. Quantum Electron. 12, 602–605 (1982).
[Crossref]

Lv, Y.

Lyandres, V.

S. Primak, V. Lyandres, and V. Kontorovich, “Markov models of non-Gaussian exponentially correlated processes and their applications,” Phys. Rev. E 63, 061103 (2001).
[Crossref]

Mata-Calvo, R.

S. Parthasarathy, D. Giggenbach, C. Fuchs, R. Mata-Calvo, R. Barrios, and A. Kirstaedter, “Verification of channel reciprocity in long-range turbulent FSO links,” in Photonic Networks; 19th ITG-Symposium, (2018), pp. 1–6.

Michau, V.

J.-M. Conan, C. Robert, N. V édrenne, M.-T. Velluet, P. Wolf, and V. Michau, “Reciprocity principle for the modelling of ground-space adaptive optics assisted optical links: Application to frequency and data transfer,” in Imaging and Applied Optics2016, (2016), p. AOTh1C.4.
[Crossref]

Minet, J.

J. Minet, M. A. Vorontsov, E. Polnau, and D. Dolfi, “Enhanced correlation of received power-signal fluctuations in bidirectional optical links,” J. Opt. 15, 022401 (2013).
[Crossref]

Morio, T.

T. Morio, T. Hideki, S. Yozo, and T. Yoshihisa, “Frequency characteristics of atmospheric turbulence in space-toground laser links,” Proc. SPIE 7685, 76850G (2010).
[Crossref]

nano, J. P.

Nelson, W.

Neuenkirch, A.

A. Neuenkirch and L. Szpruch, “First order strong approximations of scalar SDEs defined in a domain,” Numer. Math. 128, 103–136 (2014).
[Crossref]

Palastro, J.

Parenti, R. R.

Parthasarathy, S.

S. Parthasarathy, D. Giggenbach, C. Fuchs, R. Mata-Calvo, R. Barrios, and A. Kirstaedter, “Verification of channel reciprocity in long-range turbulent FSO links,” in Photonic Networks; 19th ITG-Symposium, (2018), pp. 1–6.

Perlot, N.

Peter, E. P.

E. P. Peter and E. Kloeden, Numerical Solution of Stochastic Differential Equations (Springer, 1992).

Phillips, R. L.

R. L. Phillips, Laser Beam Propagation through Random Media, 2nd ed. (SPIE Press, 2005).

Polnau, E.

J. Minet, M. A. Vorontsov, E. Polnau, and D. Dolfi, “Enhanced correlation of received power-signal fluctuations in bidirectional optical links,” J. Opt. 15, 022401 (2013).
[Crossref]

Primak, S.

S. Primak, V. Lyandres, and V. Kontorovich, “Markov models of non-Gaussian exponentially correlated processes and their applications,” Phys. Rev. E 63, 061103 (2001).
[Crossref]

Puryear, A. L.

Robert, B. W. F.

B. W. F. Robert and K. Tyson, Field Guide to Adaptive Optics, 2nd ed. (SPIE Press, 2012).

Robert, C.

J.-M. Conan, C. Robert, N. V édrenne, M.-T. Velluet, P. Wolf, and V. Michau, “Reciprocity principle for the modelling of ground-space adaptive optics assisted optical links: Application to frequency and data transfer,” in Imaging and Applied Optics2016, (2016), p. AOTh1C.4.
[Crossref]

Ronald, L.

C. Y. H. Larry, C. Andrews, and L. Ronald Phillips, Laser Beam Scintillation with Applications (SPIE Press, 2001).

Roth, J. M.

Serguei Primak, V. L.

V. L. Serguei Primak and Valeri Kontorovitch, Stochastic methods and their applications to communications: stochastic differential equations approach (Wiley, 2004).
[Crossref]

Shapiro, J. H.

Szpruch, L.

A. Neuenkirch and L. Szpruch, “First order strong approximations of scalar SDEs defined in a domain,” Numer. Math. 128, 103–136 (2014).
[Crossref]

Tong, S.

Tyler, G. A.

Tyson, K.

B. W. F. Robert and K. Tyson, Field Guide to Adaptive Optics, 2nd ed. (SPIE Press, 2012).

Uysal, M.

Velluet, M.-T.

J.-M. Conan, C. Robert, N. V édrenne, M.-T. Velluet, P. Wolf, and V. Michau, “Reciprocity principle for the modelling of ground-space adaptive optics assisted optical links: Application to frequency and data transfer,” in Imaging and Applied Optics2016, (2016), p. AOTh1C.4.
[Crossref]

Vorontsov, M. A.

J. Minet, M. A. Vorontsov, E. Polnau, and D. Dolfi, “Enhanced correlation of received power-signal fluctuations in bidirectional optical links,” J. Opt. 15, 022401 (2013).
[Crossref]

M. A. Vorontsov, G. W. Carhart, M. Cohen, and G. Cauwenberghs, “Adaptive optics based on analog parallel stochastic optimization: analysis and experimental demonstration,” J. Opt. Soc. Am. A 17, 1440–1453 (2000).
[Crossref]

Walther, F. G.

Wang, L.

Wolf, P.

J.-M. Conan, C. Robert, N. V édrenne, M.-T. Velluet, P. Wolf, and V. Michau, “Reciprocity principle for the modelling of ground-space adaptive optics assisted optical links: Application to frequency and data transfer,” in Imaging and Applied Optics2016, (2016), p. AOTh1C.4.
[Crossref]

Yang, H.

Yao, K.

Yeh, C.-H.

W.-F. Lin, C.-W. Chow, and C.-H. Yeh, “Using specific and adaptive arrangement of grid-type pilot in channel estimation for white-lightled-based OFDM visible light communication system,” Opt. Commun. 338, 7 – 10 (2015).
[Crossref]

Yoshihisa, T.

T. Morio, T. Hideki, S. Yozo, and T. Yoshihisa, “Frequency characteristics of atmospheric turbulence in space-toground laser links,” Proc. SPIE 7685, 76850G (2010).
[Crossref]

Yozo, S.

T. Morio, T. Hideki, S. Yozo, and T. Yoshihisa, “Frequency characteristics of atmospheric turbulence in space-toground laser links,” Proc. SPIE 7685, 76850G (2010).
[Crossref]

Yura, H. T.

Yura, H.T.

Appl. Opt. (3)

J. Lightwave Technol. (1)

J. Opt. (1)

J. Minet, M. A. Vorontsov, E. Polnau, and D. Dolfi, “Enhanced correlation of received power-signal fluctuations in bidirectional optical links,” J. Opt. 15, 022401 (2013).
[Crossref]

J. Opt. Commun. Netw. (2)

J. Opt. Soc. Am. (2)

J. H. Shapiro, “Reciprocity of the turbulent atmosphere,” J. Opt. Soc. Am. 61, 492–495 (1971).
[Crossref]

D. Fried, “Greenwood frequency measurements,” J. Opt. Soc. Am. 7, 946–947 (1990).
[Crossref]

J. Opt. Soc. Am. A (4)

Numer. Math. (1)

A. Neuenkirch and L. Szpruch, “First order strong approximations of scalar SDEs defined in a domain,” Numer. Math. 128, 103–136 (2014).
[Crossref]

Opt. Commun. (1)

W.-F. Lin, C.-W. Chow, and C.-H. Yeh, “Using specific and adaptive arrangement of grid-type pilot in channel estimation for white-lightled-based OFDM visible light communication system,” Opt. Commun. 338, 7 – 10 (2015).
[Crossref]

Opt. Express (6)

Phys. Rev. E (1)

S. Primak, V. Lyandres, and V. Kontorovich, “Markov models of non-Gaussian exponentially correlated processes and their applications,” Phys. Rev. E 63, 061103 (2001).
[Crossref]

Proc. SPIE (1)

T. Morio, T. Hideki, S. Yozo, and T. Yoshihisa, “Frequency characteristics of atmospheric turbulence in space-toground laser links,” Proc. SPIE 7685, 76850G (2010).
[Crossref]

Sov. J. Quantum Electron. (1)

V. P. Lukin and M. I. Charnotskiĭ, “Reciprocity principle and adaptive control of optical radiation parameters,” Sov. J. Quantum Electron. 12, 602–605 (1982).
[Crossref]

Other (7)

J.-M. Conan, C. Robert, N. V édrenne, M.-T. Velluet, P. Wolf, and V. Michau, “Reciprocity principle for the modelling of ground-space adaptive optics assisted optical links: Application to frequency and data transfer,” in Imaging and Applied Optics2016, (2016), p. AOTh1C.4.
[Crossref]

S. Parthasarathy, D. Giggenbach, C. Fuchs, R. Mata-Calvo, R. Barrios, and A. Kirstaedter, “Verification of channel reciprocity in long-range turbulent FSO links,” in Photonic Networks; 19th ITG-Symposium, (2018), pp. 1–6.

C. Y. H. Larry, C. Andrews, and L. Ronald Phillips, Laser Beam Scintillation with Applications (SPIE Press, 2001).

R. L. Phillips, Laser Beam Propagation through Random Media, 2nd ed. (SPIE Press, 2005).

B. W. F. Robert and K. Tyson, Field Guide to Adaptive Optics, 2nd ed. (SPIE Press, 2012).

V. L. Serguei Primak and Valeri Kontorovitch, Stochastic methods and their applications to communications: stochastic differential equations approach (Wiley, 2004).
[Crossref]

E. P. Peter and E. Kloeden, Numerical Solution of Stochastic Differential Equations (Springer, 1992).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1 Schematic of reciprocity for an SMF receiving system. fa and fb are focal length of Alice and Bob; Da and Db are the receiving aperture diameter of the optical antenna of Alice and Bob; two SMF is at focal point of Alice and Bob; Alice is at z = 0, Bobisat z = L.
Fig. 2
Fig. 2 1064 nm laser spectrum. (a) is Alice; (B) is Bob; (c) is a comparison spectrum of Alice and Bob.
Fig. 3
Fig. 3 Reciprocity measurement schematic for an SMF receiving system. Alice and Bob have the same optical structure; detectors, lasers, circulators, single mode fibers and computers are same; atmospheric turbulence channel link is 865 m; server controls two computers synchronously.
Fig. 4
Fig. 4 Measured time-domain signal waveform diagram for reciprocity. (a) is Alice; (b) is Bob; sampling rate is 1000 Hz; there is a time delay between Alice and Bob.
Fig. 5
Fig. 5 Measured CCF η data. Blue triangle represents real measured data (with time delay); purple circle indicates the corrected data (without time delay); black dotted line is mean of real measured data; black solid line denotes mean of corrected data.
Fig. 6
Fig. 6 Measured PDF data of Alice and Bob for an SMF receiving system. C n 2 of (a)-(c) are 9.56×10−15m−2/3, 2.07×10−14m−2/3 and 9.63×10−14m−2/3, respectively; the normalized fluctuation variances σ ζ 2 ¯ are 0.093, 0.2022 and 0.9369; the Greenwood frequencies are 11.3, 21.5 and 42.5; the average wind speeds v is 2.5 m/s, 2.9 m/s, 3.1 m/s; the Johnson SB PDF fitting efficiencies of Alice are 0.9948, 0.9948 and 0.9880; Bob are 0.9947, 0.9949, 0.9930, respectively.
Fig. 7
Fig. 7 Simulated figure by numerical solution. Wherein, the Greenwood frequency fG = 50 Hz; (a)-(c) are time domain signal waveform; (d)-(f) are PDF; (g)-(i) are PSD; the simulation condition of (a), (d) and (g) are δ = 3.0, γ = 4.5, the normalized fluctuation variance σ ζ 2 ¯ is 0.0724, the channel length L = 5000 m, light wavelength λ = 1064 nm, the atmospheric structural constants C n 2 = 6.71 × 10 17 m 2 / 3; (b), (e) and (h) are δ = 2.1, γ = 3.0, σ ζ 2 ¯ = 0.1385, L = 5000 m λ = 1064 nm, C n 2 = 1.26 × 10 15 m 2 / 3; (c), (f) and (i) are δ = 0.8, γ = 2.8, σ ζ 2 ¯ = 1.7186, L = 5000 m λ = 1064 nm, C n 2 = 1.56 × 10 14 m 2 / 3; the fitting efficiencies of (d)-(f) are 0.9987, 0.99515 and 0.9901; the slopes of the fitting curves of (g)-(i) are −2.67, −2.67 and −2.65, respectively.
Fig. 8
Fig. 8 Relationship between CCF and time delay under different atmospheric turbulence conditions. Wherein, Greenwood frequency the fG = 50 Hz.
Fig. 9
Fig. 9 Relationship between atmospheric Greenwood frequency fG and time delay τd on the reciprocity. δ = 0.8, γ = 1.828, the normalized fluctuation variance σ ζ 2 ¯ is 1.718.

Equations (20)

Equations on this page are rendered with MathJax. Learn more.

U b r ( ρ b ; t ) = U a ( ρ a ) H a b ( ρ a , ρ b ; t ) P b ( ρ b ) U m b ( ρ b ) d ρ a d ρ b ,
P b ( ρ b ) = { 1 , 0 < ρ b D b / 2 0 , o t h e r w i s e ,
U m b ( ρ b ) = 2 π W m b λ b f b exp [ ( π W m b ρ b λ b f b ) 2 ] ,
U a r ( ρ a ; t ) = U b ( ρ b ) H b a ( ρ b , ρ a ; t ) P a ( ρ a ) U m a ( ρ b ) d ρ b d ρ a .
U a ( ρ a ) = U b ( ρ b ) , D a = D b , λ a = λ b , W m a = W m b , f a = f b .
H a b ( ρ a , ρ b ; t ) = H b a ( ρ b , ρ a ; t ) .
U a r ( p a ; t ) = U b r ( p b ; t ) .
η = ( [ ζ a r ζ a r 1 ] [ ζ b r ζ b r 1 ] ) 1 ( ζ a r ζ a r 1 ) 2 ( ζ b r ζ b r 1 ) 2 ,
H a b ( ρ a , ρ b ; t ) H b a ( ρ b , ρ a ; t + τ d ) .
p ( ζ ) = δ 2 π 1 ζ ( 1 ζ ) exp { 1 2 [ γ + δ ln ( ζ 1 ζ ) ] 2 } ,
E ( ζ ) = ζ 1 , σ ζ 2 = ζ 2 ζ 1 2 , σ ζ 2 ¯ = ζ 2 ζ 1 ζ 1 2 ,
σ R y t o v 2 = 1.23 C n 2 k 7 / 6 L 11 / 6 ,
σ ζ 2 ¯ = exp [ 0.49 σ R y t o v 2 ( 1 + 1.11 σ R y t o v 12 / 5 ) 7 / 6 + 0.51 σ R y t o v 2 ( 1 + 0.69 σ R y t o v 12 / 5 ) 5 / 6 ] 1 ,
ζ d t = f ( ζ ) + ϒ ( ζ ) Ψ ( t ) .
ϒ ( ζ ) = 2 f G p ( ζ ) 0 ζ ( x ζ 1 ) p ( x ) d x ,
f ( ζ ) = ϒ ( ζ ) 2 d d x ln [ ϒ ( ζ ) p ( ζ ) ] .
f G = 2.31 λ 6 / 5 [ sec θ C h a n n e l C ˜ n 2 ( z ) v ( z ) 5 / 3 d z ] 3 / 5 ,
d ζ = f ( ζ , f G ) Δ t + ϒ ( ζ , f G ) Ψ ( t ) Δ t .
ζ k + 1 = ζ k + f ( ζ k + 1 , f G ) Δ t + ϒ ( ζ k , f G ) Δ t Ψ k + 1 4 ϒ ( ζ k , f G ) ( Ψ k 2 1 ) Δ t .
ζ k + 1 = 4 ϒ ( ζ k , f G ) Δ t Ψ k + [ ϒ ( ζ k , f G ) ( Ψ k 2 1 ) + 4 ζ 1 ] Δ t 4 ( 1 + f G ) .

Metrics