Abstract

A low-density parity-check (LDPC) coded orbital angular momentum (OAM)-based uniform circular array (UCA) free space optical (FSO) system exploring linear equalization is investigated with channel estimation over the atmospheric turbulence fading channels. On the basis of the proposed system model, the least square (LS) channel estimator is adopted to obtain the channel state information (CSI) of this OAM-FSO system. Then, the average bit error ratio (ABER) expressions with MP-ary phase shift keying (MPPSK) modulation scheme are derived by ensemble average with the aid of the large number theorem. Besides, LDPC codes are applied in the simulation to improve the ABER performance, and subsequently the probability expressions of the estimated signals with zero forcing (ZF) and minimum mean squared error (MMSE) equalizers for LDPC decoder are achieved, respectively. Results show that the ABER performance of the OAM-FSO system degrades with increasing turbulence strengths. With ZF and MMSE equalization algorithms, the ABER performance is significantly enhanced with an increase in the number of receive antennas for considerable diversity gain. Furthermore, a substantial coding gain can be attained by LDPC codes in this OAM-FSO system, especially under strong turbulence condition. This work will benefit the research and development of OAM-FSO system.

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

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  1. J. Li, M. Zhang, D. Wang, S. Wu, and Y. Zhan, “Joint atmospheric turbulence detection and adaptive demodulation technique using the CNN for the OAM-FSO communication,” Opt. Express 26(8), 10494–10508 (2018).
    [Crossref] [PubMed]
  2. Q. Tian, L. Zhu, Y. Wang, Q. Zhang, B. Liu, and X. Xin, “The propagation properties of a longitudinal orbital angular momentum multiplexing system in atmospheric turbulence,” IEEE Photonics J. 10(1), 1–11 (2018).
    [Crossref]
  3. X. Zhang, Y. He, Y. Cai, M. Su, X. Zhou, Y. Chen, S. Chen, Y. Xiang, L. Chen, C. Su, Y. Li, and D. Fan, “Coherent separation detection for orbital angular momentum multiplexing in free-space optical communications,” IEEE Photonics J. 9(3), 1–11 (2017).
  4. T. Doster and A. T. Watnik, “Machine learning approach to OAM beam demultiplexing via convolutional neural networks,” Appl. Opt. 56(12), 3386–3396 (2017).
    [Crossref] [PubMed]
  5. J. Peng, L. Zhang, K. Zhang, and J. Ma, “Channel capacity of OAM based FSO communication systems with partially coherent Bessel–Gaussian beams in anisotropic turbulence,” Opt. Commun. 418, 32–36 (2018).
    [Crossref]
  6. S. Li, S. Chen, C. Gao, A. E. Willner, and J. Wang, “Atmospheric turbulence compensation in orbital angular momentum communications: Advances and perspectives,” Opt. Commun. 408, 68–81 (2018).
    [Crossref]
  7. X. Hu, Q. Zhao, P. Yu, X. Li, Z. Wang, Y. Li, and L. Gong, “Dynamic shaping of orbital-angular-momentum beams for information encoding,” Opt. Express 26(2), 1796–1808 (2018).
    [Crossref] [PubMed]
  8. L. Li, G. Xie, Y. Ren, N. Ahmed, H. Huang, Z. Zhao, P. Liao, M. P. J. Lavery, Y. Yan, C. Bao, Z. Wang, A. J. Willner, N. Ashrafi, S. Ashrafi, M. Tur, and A. E. Willner, “Orbital-angular-momentum-multiplexed free-space optical communication link using transmitter lenses,” Appl. Opt. 55(8), 2098–2103 (2016).
    [Crossref] [PubMed]
  9. Y. Ren, Z. Wang, P. Liao, L. Li, G. Xie, H. Huang, Z. Zhao, Y. Yan, N. Ahmed, A. Willner, M. P. J. Lavery, N. Ashrafi, S. Ashrafi, R. Bock, M. Tur, I. B. Djordjevic, M. A. Neifeld, and A. E. Willner, “Experimental characterization of a 400 Gbit/s orbital angular momentum multiplexed free-space optical link over 120 m,” Opt. Lett. 41(3), 622–625 (2016).
    [Crossref] [PubMed]
  10. S. Yong, J. Kim, W. Yang, and C. Kang, MIMO-OFDM Wireless Communications with MATLAB (Wiley, 2010).
  11. Z. Zhang, S. Zheng, Y. Chen, X. Jin, H. Chi, and X. Zhang, “The capacity gain of orbital angular momentum based multiple-input-multiple-output system,” Sci. Rep. 6(1), 25418 (2016).
    [Crossref] [PubMed]
  12. A. García-Zambrana, C. Castillo-Vázquez, and B. Castillo-Vázquez, “Outage performance of MIMO FSO links over strong turbulence and misalignment fading channels,” Opt. Express 19(14), 13480–13496 (2011).
    [Crossref] [PubMed]
  13. C. Abou-Rjeily, “On the optimality of the selection transmit diversity for MIMO-FSO links with feedback,” IEEE Commun. Lett. 15(6), 641–643 (2011).
    [Crossref]
  14. M. Qin, L. Chen, and W. Wang, “Generalized selection multiuser scheduling for the MIMO FSO communication system and its performance analysis,” IEEE Photonics J. 8(5), 1–9 (2016).
    [Crossref]
  15. A. Wang, J. Wang, L. Zhu, and J. Liu, “Experimental demonstration of dense fractional orbital angular momentum (OAM) multiplexing with a channel spacing of 0.2 assisted by MIMO equalization,” in Proceedings of Asia Communications and Photonics Conference (OSA 2016), pp. AF1D.1.
    [Crossref]
  16. H. Huang, Y. Cao, G. Xie, Y. Ren, Y. Yan, C. Bao, N. Ahmed, M. A. Neifeld, S. J. Dolinar, and A. E. Willner, “Crosstalk mitigation in a free-space orbital angular momentum multiplexed communication link using 4×4 MIMO equalization,” Opt. Lett. 39(15), 4360–4363 (2014).
    [Crossref] [PubMed]
  17. Z. Xu, “6×6 MIMO equalization assisted fractional orbital angular momentum (OAM) dense mode-division multiplexing (DMDM) for free-space optical communications,” in Proceedings of Asia Communications and Photonics Conference (OSA 2014), pp. AW3F.2.
    [Crossref]
  18. Y. Ren, Z. Wang, G. Xie, L. Li, Y. Cao, C. Liu, P. Liao, Y. Yan, N. Ahmed, Z. Zhao, A. Willner, N. Ashrafi, S. Ashrafi, R. D. Linquist, R. Bock, M. Tur, A. F. Molisch, and A. E. Willner, “Free-space optical communications using orbital-angular-momentum multiplexing combined with MIMO-based spatial multiplexing,” Opt. Lett. 40(18), 4210–4213 (2015).
    [Crossref] [PubMed]
  19. M. Charnotskii, “Turbulence effects on fluctuations of the aperture-averaged orbital angular momentum,” J. Opt. Soc. Am. A 35(5), 702–711 (2018).
    [Crossref] [PubMed]
  20. C. Chen, H. Yang, S. Tong, and Y. Lou, “Changes in orbital-angular-momentum modes of a propagated vortex Gaussian beam through weak-to-strong atmospheric turbulence,” Opt. Express 24(7), 6959–6975 (2016).
    [Crossref] [PubMed]
  21. G. Liang, Y. Wang, Q. Guo, and H. Zhang, “Anisotropic diffraction induced by orbital angular momentum during propagations of optical beams,” Opt. Express 26(7), 8084–8094 (2018).
    [Crossref] [PubMed]
  22. Y. Ren, Z. Wang, G. Xie, L. Li, A. J. Willner, Y. Cao, Z. Zhao, Y. Yan, N. Ashrai, S. Ashrafi, R. Bock, M. Tur, and A. E. Willner, “Demonstration of OAM-based MIMO FSO link using spatial diversity and MIMO equalization for turbulence mitigation,” in Proceedings of Optical Fiber Communication Conference (OSA 2016), pp. Th1H.2.
    [Crossref]
  23. Z. Xu, C. Gui, S. Li, J. Zhou, and J. Wang, “Fractional orbital angular momentum (OAM) free-space optical communications with atmospheric turbulence assisted by MIMO equalization,” in Proceedings of Advanced Photonics for Communications (OSA, 2014), paper JT3A.1.
  24. L. Zou, L. Wang, C. Xing, J. Cui, and S. Zhao, “Turbulence mitigation with MIMO equalization for orbital angular momentum multiplexing communication,” in Proceedings of 8th International Conference on Wireless Communications & Signal Processing (WCSP) (IEEE 2016), paper Th1H.2.
    [Crossref]
  25. Y. Ren, Z. Wang, G. Xie, L. Li, A. J. Willner, Y. Cao, Z. Zhao, Y. Yan, N. Ahmed, N. Ashrafi, S. Ashrafi, R. Bock, M. Tur, and A. E. Willner, “Atmospheric turbulence mitigation in an OAM-based MIMO free-space optical link using spatial diversity combined with MIMO equalization,” Opt. Lett. 41(11), 2406–2409 (2016).
    [Crossref] [PubMed]
  26. Y. Zhang, P. Wang, L. Guo, W. Wang, and H. Tian, “Performance analysis of an OAM multiplexing-based MIMO FSO system over atmospheric turbulence using space-time coding with channel estimation,” Opt. Express 25(17), 19995–20011 (2017).
    [Crossref] [PubMed]
  27. K. A. Opare, Y. Kuang, J. J. Kponyo, K. S. Nwizege, and P. I. Tebe, “The effect of receiver-side circular antenna arrays on bit error probability in a wireless line-of-sight OAM communication system,” in Proceedings of Advanced Computing and Communication Technologies (ACCT) (IEEE, 2015), pp. 614–620.
  28. Y. Yuan, Z. Zhang, C. Ji, and H. Wu, “Capacity analysis of UCA-based OAM multiplexing communication system,” in Proceedings of Wireless Communications and Signal Processing (WCSP) (IEEE, 2015), pp. 1–5.
  29. M. Lin, Y. Gao, P. Liu, and J. Liu, “Theoretical analyses and design of circular array to generate orbital angular momentum,” IEEE Trans. Antenn. Propag. 65(7), 3510–3519 (2017).
    [Crossref]
  30. K. A. Opare and Y. Kuang, “Performance of an ideal wireless orbital angular momentum communication system using multiple-input multiple-output techniques,” in Proceedings of Telecommunications and Multimedia (TEMU) (IEEE, 2014), pp. 144–149.
  31. R. Chen, H. Xu, M. Moretti, and J. Li, “Beam Steering for the Misalignment in UCA-Based OAM Communication Systems,” IEEE Wirel. Commun. Lett. 99, 1–4 (2018).
  32. C. Fan, Principles of Communications (Beijing, 2010).
  33. G. Ungerboeck, “Channel coding with multilevel/phase signals,” IEEE Trans. Inf. Theory 28(1), 55–67 (2003).
    [Crossref]
  34. S. Zhao, L. Wang, L. Zou, L. Gong, W. Cheng, B. Zheng, and H. Chen, “Both channel coding and wavefront correction on the turbulence mitigation of optical communications using orbital angular momentum multiplexing,” Opt. Commun. 376, 92–98 (2016).
    [Crossref]
  35. J. Zhou, Z. Xu, and J. Wang, “Performance evaluation of fractional orbital angular momentum (OAM) based LDPC-coded free-space optical communications with atmospheric turbulence,” in Proceedings of Asia Communications and Photonics Conference (ACPC) (OSA 2014), pp.AF3D.2.
    [Crossref]
  36. Z. Qu and B. Ivan, F. Djordjevic, “Experimental evaluation of LDPC-coded OAM based FSO communication in the presence of atmospheric turbulence,” in Proceedings of International Conference of Telecommunication in Modern Satellite, Cable and Broadcasting Services (TELSIKS) (IEEE 2015), pp.117–122.
  37. Z. Qu and I. B. Djordjevic, “500 Gb/s free-space optical transmission over strong atmospheric turbulence channels,” Opt. Lett. 41(14), 3285–3288 (2016).
    [Crossref] [PubMed]
  38. Z. Qu and I. B. Djordjevic, “Two-stage cross-talk mitigation in an orbital-angular-momentum-based free-space optical communication system,” Opt. Lett. 42(16), 3125–3128 (2017).
    [Crossref] [PubMed]
  39. M. Li, Z. Yu, and M. Cvijetic, “Influence of atmospheric turbulence on OAM-based FSO system with use of realistic link model,” Opt. Commun. 364, 50–54 (2016).
    [Crossref]
  40. J. A. Anguita, M. A. Neifeld, and B. V. Vasic, “Turbulence-induced channel crosstalk in an orbital angular momentum-multiplexed free-space optical link,” Appl. Opt. 47(13), 2414–2429 (2008).
    [Crossref] [PubMed]
  41. S. Fu and C. Gao, “Influences of atmospheric turbulence effects on the orbital angular momentum spectra of vortex beams,” Photon. Res. 4(5), B1–B4 (2016).
    [Crossref]
  42. J. D. Schmidt, Numerical Simulation of Optical Wave Propagation (2010).
  43. S. M. Zhao, J. Leach, L. Y. Gong, J. Ding, and B. Y. Zheng, “Aberration corrections for free-space optical communications in atmosphere turbulence using orbital angular momentum states,” Opt. Express 20(1), 452–461 (2012).
    [Crossref] [PubMed]
  44. P. Wang, L. Zhang, L. Guo, F. Huang, T. Shang, R. Wang, and Y. Yang, “Average BER of subcarrier intensity modulated free space optical systems over the exponentiated Weibull fading channels,” Opt. Express 22(17), 20828–20841 (2014).
    [Crossref] [PubMed]
  45. P. Suthisopapan, K. Kasai, V. Imtawil, and A. Meesomboon, “Approaching capacity of large MIMO systems by non-binary LDPC codes and MMSE detection,” in Proceedings of International Symposium on Information Theory Proceedings (IEEE, 2012), pp. 1712–1716.
    [Crossref]
  46. M. T. Hossain, I. Misra, J. J. Sadique, and S. E. Ullah, “Impact of various signal detection schemes in performance assessment of 5G compatible LDPC encoded GPQSM wireless communication system,” Electr. & Comput. Eng. 1(3), 72–80 (2017).
  47. M. Duan, P. Wang, X. Liu, Y. Li, and W. Chen, and A. L, “ABER performance analysis of LDPC-coded OFDM FSO system under Málaga distribution considering atmospheric attenuation and pointing errors,” Appl. Opt. 57(19), 5505–5513 (2018).

2018 (9)

J. Peng, L. Zhang, K. Zhang, and J. Ma, “Channel capacity of OAM based FSO communication systems with partially coherent Bessel–Gaussian beams in anisotropic turbulence,” Opt. Commun. 418, 32–36 (2018).
[Crossref]

S. Li, S. Chen, C. Gao, A. E. Willner, and J. Wang, “Atmospheric turbulence compensation in orbital angular momentum communications: Advances and perspectives,” Opt. Commun. 408, 68–81 (2018).
[Crossref]

Q. Tian, L. Zhu, Y. Wang, Q. Zhang, B. Liu, and X. Xin, “The propagation properties of a longitudinal orbital angular momentum multiplexing system in atmospheric turbulence,” IEEE Photonics J. 10(1), 1–11 (2018).
[Crossref]

R. Chen, H. Xu, M. Moretti, and J. Li, “Beam Steering for the Misalignment in UCA-Based OAM Communication Systems,” IEEE Wirel. Commun. Lett. 99, 1–4 (2018).

X. Hu, Q. Zhao, P. Yu, X. Li, Z. Wang, Y. Li, and L. Gong, “Dynamic shaping of orbital-angular-momentum beams for information encoding,” Opt. Express 26(2), 1796–1808 (2018).
[Crossref] [PubMed]

G. Liang, Y. Wang, Q. Guo, and H. Zhang, “Anisotropic diffraction induced by orbital angular momentum during propagations of optical beams,” Opt. Express 26(7), 8084–8094 (2018).
[Crossref] [PubMed]

M. Charnotskii, “Turbulence effects on fluctuations of the aperture-averaged orbital angular momentum,” J. Opt. Soc. Am. A 35(5), 702–711 (2018).
[Crossref] [PubMed]

J. Li, M. Zhang, D. Wang, S. Wu, and Y. Zhan, “Joint atmospheric turbulence detection and adaptive demodulation technique using the CNN for the OAM-FSO communication,” Opt. Express 26(8), 10494–10508 (2018).
[Crossref] [PubMed]

M. Duan, P. Wang, X. Liu, Y. Li, and W. Chen, and A. L, “ABER performance analysis of LDPC-coded OFDM FSO system under Málaga distribution considering atmospheric attenuation and pointing errors,” Appl. Opt. 57(19), 5505–5513 (2018).

2017 (6)

T. Doster and A. T. Watnik, “Machine learning approach to OAM beam demultiplexing via convolutional neural networks,” Appl. Opt. 56(12), 3386–3396 (2017).
[Crossref] [PubMed]

Z. Qu and I. B. Djordjevic, “Two-stage cross-talk mitigation in an orbital-angular-momentum-based free-space optical communication system,” Opt. Lett. 42(16), 3125–3128 (2017).
[Crossref] [PubMed]

Y. Zhang, P. Wang, L. Guo, W. Wang, and H. Tian, “Performance analysis of an OAM multiplexing-based MIMO FSO system over atmospheric turbulence using space-time coding with channel estimation,” Opt. Express 25(17), 19995–20011 (2017).
[Crossref] [PubMed]

M. T. Hossain, I. Misra, J. J. Sadique, and S. E. Ullah, “Impact of various signal detection schemes in performance assessment of 5G compatible LDPC encoded GPQSM wireless communication system,” Electr. & Comput. Eng. 1(3), 72–80 (2017).

X. Zhang, Y. He, Y. Cai, M. Su, X. Zhou, Y. Chen, S. Chen, Y. Xiang, L. Chen, C. Su, Y. Li, and D. Fan, “Coherent separation detection for orbital angular momentum multiplexing in free-space optical communications,” IEEE Photonics J. 9(3), 1–11 (2017).

M. Lin, Y. Gao, P. Liu, and J. Liu, “Theoretical analyses and design of circular array to generate orbital angular momentum,” IEEE Trans. Antenn. Propag. 65(7), 3510–3519 (2017).
[Crossref]

2016 (10)

M. Qin, L. Chen, and W. Wang, “Generalized selection multiuser scheduling for the MIMO FSO communication system and its performance analysis,” IEEE Photonics J. 8(5), 1–9 (2016).
[Crossref]

Z. Zhang, S. Zheng, Y. Chen, X. Jin, H. Chi, and X. Zhang, “The capacity gain of orbital angular momentum based multiple-input-multiple-output system,” Sci. Rep. 6(1), 25418 (2016).
[Crossref] [PubMed]

S. Zhao, L. Wang, L. Zou, L. Gong, W. Cheng, B. Zheng, and H. Chen, “Both channel coding and wavefront correction on the turbulence mitigation of optical communications using orbital angular momentum multiplexing,” Opt. Commun. 376, 92–98 (2016).
[Crossref]

M. Li, Z. Yu, and M. Cvijetic, “Influence of atmospheric turbulence on OAM-based FSO system with use of realistic link model,” Opt. Commun. 364, 50–54 (2016).
[Crossref]

Y. Ren, Z. Wang, P. Liao, L. Li, G. Xie, H. Huang, Z. Zhao, Y. Yan, N. Ahmed, A. Willner, M. P. J. Lavery, N. Ashrafi, S. Ashrafi, R. Bock, M. Tur, I. B. Djordjevic, M. A. Neifeld, and A. E. Willner, “Experimental characterization of a 400 Gbit/s orbital angular momentum multiplexed free-space optical link over 120 m,” Opt. Lett. 41(3), 622–625 (2016).
[Crossref] [PubMed]

L. Li, G. Xie, Y. Ren, N. Ahmed, H. Huang, Z. Zhao, P. Liao, M. P. J. Lavery, Y. Yan, C. Bao, Z. Wang, A. J. Willner, N. Ashrafi, S. Ashrafi, M. Tur, and A. E. Willner, “Orbital-angular-momentum-multiplexed free-space optical communication link using transmitter lenses,” Appl. Opt. 55(8), 2098–2103 (2016).
[Crossref] [PubMed]

C. Chen, H. Yang, S. Tong, and Y. Lou, “Changes in orbital-angular-momentum modes of a propagated vortex Gaussian beam through weak-to-strong atmospheric turbulence,” Opt. Express 24(7), 6959–6975 (2016).
[Crossref] [PubMed]

Y. Ren, Z. Wang, G. Xie, L. Li, A. J. Willner, Y. Cao, Z. Zhao, Y. Yan, N. Ahmed, N. Ashrafi, S. Ashrafi, R. Bock, M. Tur, and A. E. Willner, “Atmospheric turbulence mitigation in an OAM-based MIMO free-space optical link using spatial diversity combined with MIMO equalization,” Opt. Lett. 41(11), 2406–2409 (2016).
[Crossref] [PubMed]

Z. Qu and I. B. Djordjevic, “500 Gb/s free-space optical transmission over strong atmospheric turbulence channels,” Opt. Lett. 41(14), 3285–3288 (2016).
[Crossref] [PubMed]

S. Fu and C. Gao, “Influences of atmospheric turbulence effects on the orbital angular momentum spectra of vortex beams,” Photon. Res. 4(5), B1–B4 (2016).
[Crossref]

2015 (1)

2014 (2)

2012 (1)

2011 (2)

2008 (1)

2003 (1)

G. Ungerboeck, “Channel coding with multilevel/phase signals,” IEEE Trans. Inf. Theory 28(1), 55–67 (2003).
[Crossref]

Abou-Rjeily, C.

C. Abou-Rjeily, “On the optimality of the selection transmit diversity for MIMO-FSO links with feedback,” IEEE Commun. Lett. 15(6), 641–643 (2011).
[Crossref]

Ahmed, N.

Y. Ren, Z. Wang, P. Liao, L. Li, G. Xie, H. Huang, Z. Zhao, Y. Yan, N. Ahmed, A. Willner, M. P. J. Lavery, N. Ashrafi, S. Ashrafi, R. Bock, M. Tur, I. B. Djordjevic, M. A. Neifeld, and A. E. Willner, “Experimental characterization of a 400 Gbit/s orbital angular momentum multiplexed free-space optical link over 120 m,” Opt. Lett. 41(3), 622–625 (2016).
[Crossref] [PubMed]

L. Li, G. Xie, Y. Ren, N. Ahmed, H. Huang, Z. Zhao, P. Liao, M. P. J. Lavery, Y. Yan, C. Bao, Z. Wang, A. J. Willner, N. Ashrafi, S. Ashrafi, M. Tur, and A. E. Willner, “Orbital-angular-momentum-multiplexed free-space optical communication link using transmitter lenses,” Appl. Opt. 55(8), 2098–2103 (2016).
[Crossref] [PubMed]

Y. Ren, Z. Wang, G. Xie, L. Li, A. J. Willner, Y. Cao, Z. Zhao, Y. Yan, N. Ahmed, N. Ashrafi, S. Ashrafi, R. Bock, M. Tur, and A. E. Willner, “Atmospheric turbulence mitigation in an OAM-based MIMO free-space optical link using spatial diversity combined with MIMO equalization,” Opt. Lett. 41(11), 2406–2409 (2016).
[Crossref] [PubMed]

Y. Ren, Z. Wang, G. Xie, L. Li, Y. Cao, C. Liu, P. Liao, Y. Yan, N. Ahmed, Z. Zhao, A. Willner, N. Ashrafi, S. Ashrafi, R. D. Linquist, R. Bock, M. Tur, A. F. Molisch, and A. E. Willner, “Free-space optical communications using orbital-angular-momentum multiplexing combined with MIMO-based spatial multiplexing,” Opt. Lett. 40(18), 4210–4213 (2015).
[Crossref] [PubMed]

H. Huang, Y. Cao, G. Xie, Y. Ren, Y. Yan, C. Bao, N. Ahmed, M. A. Neifeld, S. J. Dolinar, and A. E. Willner, “Crosstalk mitigation in a free-space orbital angular momentum multiplexed communication link using 4×4 MIMO equalization,” Opt. Lett. 39(15), 4360–4363 (2014).
[Crossref] [PubMed]

Anguita, J. A.

Ashrafi, N.

Ashrafi, S.

Bao, C.

Bock, R.

Cai, Y.

X. Zhang, Y. He, Y. Cai, M. Su, X. Zhou, Y. Chen, S. Chen, Y. Xiang, L. Chen, C. Su, Y. Li, and D. Fan, “Coherent separation detection for orbital angular momentum multiplexing in free-space optical communications,” IEEE Photonics J. 9(3), 1–11 (2017).

Cao, Y.

Castillo-Vázquez, B.

Castillo-Vázquez, C.

Charnotskii, M.

Chen, C.

Chen, H.

S. Zhao, L. Wang, L. Zou, L. Gong, W. Cheng, B. Zheng, and H. Chen, “Both channel coding and wavefront correction on the turbulence mitigation of optical communications using orbital angular momentum multiplexing,” Opt. Commun. 376, 92–98 (2016).
[Crossref]

Chen, L.

X. Zhang, Y. He, Y. Cai, M. Su, X. Zhou, Y. Chen, S. Chen, Y. Xiang, L. Chen, C. Su, Y. Li, and D. Fan, “Coherent separation detection for orbital angular momentum multiplexing in free-space optical communications,” IEEE Photonics J. 9(3), 1–11 (2017).

M. Qin, L. Chen, and W. Wang, “Generalized selection multiuser scheduling for the MIMO FSO communication system and its performance analysis,” IEEE Photonics J. 8(5), 1–9 (2016).
[Crossref]

Chen, R.

R. Chen, H. Xu, M. Moretti, and J. Li, “Beam Steering for the Misalignment in UCA-Based OAM Communication Systems,” IEEE Wirel. Commun. Lett. 99, 1–4 (2018).

Chen, S.

S. Li, S. Chen, C. Gao, A. E. Willner, and J. Wang, “Atmospheric turbulence compensation in orbital angular momentum communications: Advances and perspectives,” Opt. Commun. 408, 68–81 (2018).
[Crossref]

X. Zhang, Y. He, Y. Cai, M. Su, X. Zhou, Y. Chen, S. Chen, Y. Xiang, L. Chen, C. Su, Y. Li, and D. Fan, “Coherent separation detection for orbital angular momentum multiplexing in free-space optical communications,” IEEE Photonics J. 9(3), 1–11 (2017).

Chen, W.

Chen, Y.

X. Zhang, Y. He, Y. Cai, M. Su, X. Zhou, Y. Chen, S. Chen, Y. Xiang, L. Chen, C. Su, Y. Li, and D. Fan, “Coherent separation detection for orbital angular momentum multiplexing in free-space optical communications,” IEEE Photonics J. 9(3), 1–11 (2017).

Z. Zhang, S. Zheng, Y. Chen, X. Jin, H. Chi, and X. Zhang, “The capacity gain of orbital angular momentum based multiple-input-multiple-output system,” Sci. Rep. 6(1), 25418 (2016).
[Crossref] [PubMed]

Cheng, W.

S. Zhao, L. Wang, L. Zou, L. Gong, W. Cheng, B. Zheng, and H. Chen, “Both channel coding and wavefront correction on the turbulence mitigation of optical communications using orbital angular momentum multiplexing,” Opt. Commun. 376, 92–98 (2016).
[Crossref]

Chi, H.

Z. Zhang, S. Zheng, Y. Chen, X. Jin, H. Chi, and X. Zhang, “The capacity gain of orbital angular momentum based multiple-input-multiple-output system,” Sci. Rep. 6(1), 25418 (2016).
[Crossref] [PubMed]

Cvijetic, M.

M. Li, Z. Yu, and M. Cvijetic, “Influence of atmospheric turbulence on OAM-based FSO system with use of realistic link model,” Opt. Commun. 364, 50–54 (2016).
[Crossref]

Ding, J.

Djordjevic, I. B.

Dolinar, S. J.

Doster, T.

Duan, M.

Fan, D.

X. Zhang, Y. He, Y. Cai, M. Su, X. Zhou, Y. Chen, S. Chen, Y. Xiang, L. Chen, C. Su, Y. Li, and D. Fan, “Coherent separation detection for orbital angular momentum multiplexing in free-space optical communications,” IEEE Photonics J. 9(3), 1–11 (2017).

Fu, S.

Gao, C.

S. Li, S. Chen, C. Gao, A. E. Willner, and J. Wang, “Atmospheric turbulence compensation in orbital angular momentum communications: Advances and perspectives,” Opt. Commun. 408, 68–81 (2018).
[Crossref]

S. Fu and C. Gao, “Influences of atmospheric turbulence effects on the orbital angular momentum spectra of vortex beams,” Photon. Res. 4(5), B1–B4 (2016).
[Crossref]

Gao, Y.

M. Lin, Y. Gao, P. Liu, and J. Liu, “Theoretical analyses and design of circular array to generate orbital angular momentum,” IEEE Trans. Antenn. Propag. 65(7), 3510–3519 (2017).
[Crossref]

García-Zambrana, A.

Gong, L.

X. Hu, Q. Zhao, P. Yu, X. Li, Z. Wang, Y. Li, and L. Gong, “Dynamic shaping of orbital-angular-momentum beams for information encoding,” Opt. Express 26(2), 1796–1808 (2018).
[Crossref] [PubMed]

S. Zhao, L. Wang, L. Zou, L. Gong, W. Cheng, B. Zheng, and H. Chen, “Both channel coding and wavefront correction on the turbulence mitigation of optical communications using orbital angular momentum multiplexing,” Opt. Commun. 376, 92–98 (2016).
[Crossref]

Gong, L. Y.

Guo, L.

Guo, Q.

He, Y.

X. Zhang, Y. He, Y. Cai, M. Su, X. Zhou, Y. Chen, S. Chen, Y. Xiang, L. Chen, C. Su, Y. Li, and D. Fan, “Coherent separation detection for orbital angular momentum multiplexing in free-space optical communications,” IEEE Photonics J. 9(3), 1–11 (2017).

Hossain, M. T.

M. T. Hossain, I. Misra, J. J. Sadique, and S. E. Ullah, “Impact of various signal detection schemes in performance assessment of 5G compatible LDPC encoded GPQSM wireless communication system,” Electr. & Comput. Eng. 1(3), 72–80 (2017).

Hu, X.

Huang, F.

Huang, H.

Imtawil, V.

P. Suthisopapan, K. Kasai, V. Imtawil, and A. Meesomboon, “Approaching capacity of large MIMO systems by non-binary LDPC codes and MMSE detection,” in Proceedings of International Symposium on Information Theory Proceedings (IEEE, 2012), pp. 1712–1716.
[Crossref]

Ji, C.

Y. Yuan, Z. Zhang, C. Ji, and H. Wu, “Capacity analysis of UCA-based OAM multiplexing communication system,” in Proceedings of Wireless Communications and Signal Processing (WCSP) (IEEE, 2015), pp. 1–5.

Jin, X.

Z. Zhang, S. Zheng, Y. Chen, X. Jin, H. Chi, and X. Zhang, “The capacity gain of orbital angular momentum based multiple-input-multiple-output system,” Sci. Rep. 6(1), 25418 (2016).
[Crossref] [PubMed]

Kasai, K.

P. Suthisopapan, K. Kasai, V. Imtawil, and A. Meesomboon, “Approaching capacity of large MIMO systems by non-binary LDPC codes and MMSE detection,” in Proceedings of International Symposium on Information Theory Proceedings (IEEE, 2012), pp. 1712–1716.
[Crossref]

Kponyo, J. J.

K. A. Opare, Y. Kuang, J. J. Kponyo, K. S. Nwizege, and P. I. Tebe, “The effect of receiver-side circular antenna arrays on bit error probability in a wireless line-of-sight OAM communication system,” in Proceedings of Advanced Computing and Communication Technologies (ACCT) (IEEE, 2015), pp. 614–620.

Kuang, Y.

K. A. Opare, Y. Kuang, J. J. Kponyo, K. S. Nwizege, and P. I. Tebe, “The effect of receiver-side circular antenna arrays on bit error probability in a wireless line-of-sight OAM communication system,” in Proceedings of Advanced Computing and Communication Technologies (ACCT) (IEEE, 2015), pp. 614–620.

K. A. Opare and Y. Kuang, “Performance of an ideal wireless orbital angular momentum communication system using multiple-input multiple-output techniques,” in Proceedings of Telecommunications and Multimedia (TEMU) (IEEE, 2014), pp. 144–149.

Lavery, M. P. J.

Leach, J.

Li, J.

R. Chen, H. Xu, M. Moretti, and J. Li, “Beam Steering for the Misalignment in UCA-Based OAM Communication Systems,” IEEE Wirel. Commun. Lett. 99, 1–4 (2018).

J. Li, M. Zhang, D. Wang, S. Wu, and Y. Zhan, “Joint atmospheric turbulence detection and adaptive demodulation technique using the CNN for the OAM-FSO communication,” Opt. Express 26(8), 10494–10508 (2018).
[Crossref] [PubMed]

Li, L.

Li, M.

M. Li, Z. Yu, and M. Cvijetic, “Influence of atmospheric turbulence on OAM-based FSO system with use of realistic link model,” Opt. Commun. 364, 50–54 (2016).
[Crossref]

Li, S.

S. Li, S. Chen, C. Gao, A. E. Willner, and J. Wang, “Atmospheric turbulence compensation in orbital angular momentum communications: Advances and perspectives,” Opt. Commun. 408, 68–81 (2018).
[Crossref]

Li, X.

Li, Y.

Liang, G.

Liao, P.

Lin, M.

M. Lin, Y. Gao, P. Liu, and J. Liu, “Theoretical analyses and design of circular array to generate orbital angular momentum,” IEEE Trans. Antenn. Propag. 65(7), 3510–3519 (2017).
[Crossref]

Linquist, R. D.

Liu, B.

Q. Tian, L. Zhu, Y. Wang, Q. Zhang, B. Liu, and X. Xin, “The propagation properties of a longitudinal orbital angular momentum multiplexing system in atmospheric turbulence,” IEEE Photonics J. 10(1), 1–11 (2018).
[Crossref]

Liu, C.

Liu, J.

M. Lin, Y. Gao, P. Liu, and J. Liu, “Theoretical analyses and design of circular array to generate orbital angular momentum,” IEEE Trans. Antenn. Propag. 65(7), 3510–3519 (2017).
[Crossref]

Liu, P.

M. Lin, Y. Gao, P. Liu, and J. Liu, “Theoretical analyses and design of circular array to generate orbital angular momentum,” IEEE Trans. Antenn. Propag. 65(7), 3510–3519 (2017).
[Crossref]

Liu, X.

Lou, Y.

Ma, J.

J. Peng, L. Zhang, K. Zhang, and J. Ma, “Channel capacity of OAM based FSO communication systems with partially coherent Bessel–Gaussian beams in anisotropic turbulence,” Opt. Commun. 418, 32–36 (2018).
[Crossref]

Meesomboon, A.

P. Suthisopapan, K. Kasai, V. Imtawil, and A. Meesomboon, “Approaching capacity of large MIMO systems by non-binary LDPC codes and MMSE detection,” in Proceedings of International Symposium on Information Theory Proceedings (IEEE, 2012), pp. 1712–1716.
[Crossref]

Misra, I.

M. T. Hossain, I. Misra, J. J. Sadique, and S. E. Ullah, “Impact of various signal detection schemes in performance assessment of 5G compatible LDPC encoded GPQSM wireless communication system,” Electr. & Comput. Eng. 1(3), 72–80 (2017).

Molisch, A. F.

Moretti, M.

R. Chen, H. Xu, M. Moretti, and J. Li, “Beam Steering for the Misalignment in UCA-Based OAM Communication Systems,” IEEE Wirel. Commun. Lett. 99, 1–4 (2018).

Neifeld, M. A.

Nwizege, K. S.

K. A. Opare, Y. Kuang, J. J. Kponyo, K. S. Nwizege, and P. I. Tebe, “The effect of receiver-side circular antenna arrays on bit error probability in a wireless line-of-sight OAM communication system,” in Proceedings of Advanced Computing and Communication Technologies (ACCT) (IEEE, 2015), pp. 614–620.

Opare, K. A.

K. A. Opare, Y. Kuang, J. J. Kponyo, K. S. Nwizege, and P. I. Tebe, “The effect of receiver-side circular antenna arrays on bit error probability in a wireless line-of-sight OAM communication system,” in Proceedings of Advanced Computing and Communication Technologies (ACCT) (IEEE, 2015), pp. 614–620.

K. A. Opare and Y. Kuang, “Performance of an ideal wireless orbital angular momentum communication system using multiple-input multiple-output techniques,” in Proceedings of Telecommunications and Multimedia (TEMU) (IEEE, 2014), pp. 144–149.

Peng, J.

J. Peng, L. Zhang, K. Zhang, and J. Ma, “Channel capacity of OAM based FSO communication systems with partially coherent Bessel–Gaussian beams in anisotropic turbulence,” Opt. Commun. 418, 32–36 (2018).
[Crossref]

Qin, M.

M. Qin, L. Chen, and W. Wang, “Generalized selection multiuser scheduling for the MIMO FSO communication system and its performance analysis,” IEEE Photonics J. 8(5), 1–9 (2016).
[Crossref]

Qu, Z.

Ren, Y.

Y. Ren, Z. Wang, G. Xie, L. Li, A. J. Willner, Y. Cao, Z. Zhao, Y. Yan, N. Ahmed, N. Ashrafi, S. Ashrafi, R. Bock, M. Tur, and A. E. Willner, “Atmospheric turbulence mitigation in an OAM-based MIMO free-space optical link using spatial diversity combined with MIMO equalization,” Opt. Lett. 41(11), 2406–2409 (2016).
[Crossref] [PubMed]

L. Li, G. Xie, Y. Ren, N. Ahmed, H. Huang, Z. Zhao, P. Liao, M. P. J. Lavery, Y. Yan, C. Bao, Z. Wang, A. J. Willner, N. Ashrafi, S. Ashrafi, M. Tur, and A. E. Willner, “Orbital-angular-momentum-multiplexed free-space optical communication link using transmitter lenses,” Appl. Opt. 55(8), 2098–2103 (2016).
[Crossref] [PubMed]

Y. Ren, Z. Wang, P. Liao, L. Li, G. Xie, H. Huang, Z. Zhao, Y. Yan, N. Ahmed, A. Willner, M. P. J. Lavery, N. Ashrafi, S. Ashrafi, R. Bock, M. Tur, I. B. Djordjevic, M. A. Neifeld, and A. E. Willner, “Experimental characterization of a 400 Gbit/s orbital angular momentum multiplexed free-space optical link over 120 m,” Opt. Lett. 41(3), 622–625 (2016).
[Crossref] [PubMed]

Y. Ren, Z. Wang, G. Xie, L. Li, Y. Cao, C. Liu, P. Liao, Y. Yan, N. Ahmed, Z. Zhao, A. Willner, N. Ashrafi, S. Ashrafi, R. D. Linquist, R. Bock, M. Tur, A. F. Molisch, and A. E. Willner, “Free-space optical communications using orbital-angular-momentum multiplexing combined with MIMO-based spatial multiplexing,” Opt. Lett. 40(18), 4210–4213 (2015).
[Crossref] [PubMed]

H. Huang, Y. Cao, G. Xie, Y. Ren, Y. Yan, C. Bao, N. Ahmed, M. A. Neifeld, S. J. Dolinar, and A. E. Willner, “Crosstalk mitigation in a free-space orbital angular momentum multiplexed communication link using 4×4 MIMO equalization,” Opt. Lett. 39(15), 4360–4363 (2014).
[Crossref] [PubMed]

Sadique, J. J.

M. T. Hossain, I. Misra, J. J. Sadique, and S. E. Ullah, “Impact of various signal detection schemes in performance assessment of 5G compatible LDPC encoded GPQSM wireless communication system,” Electr. & Comput. Eng. 1(3), 72–80 (2017).

Schmidt, J. D.

J. D. Schmidt, Numerical Simulation of Optical Wave Propagation (2010).

Shang, T.

Su, C.

X. Zhang, Y. He, Y. Cai, M. Su, X. Zhou, Y. Chen, S. Chen, Y. Xiang, L. Chen, C. Su, Y. Li, and D. Fan, “Coherent separation detection for orbital angular momentum multiplexing in free-space optical communications,” IEEE Photonics J. 9(3), 1–11 (2017).

Su, M.

X. Zhang, Y. He, Y. Cai, M. Su, X. Zhou, Y. Chen, S. Chen, Y. Xiang, L. Chen, C. Su, Y. Li, and D. Fan, “Coherent separation detection for orbital angular momentum multiplexing in free-space optical communications,” IEEE Photonics J. 9(3), 1–11 (2017).

Suthisopapan, P.

P. Suthisopapan, K. Kasai, V. Imtawil, and A. Meesomboon, “Approaching capacity of large MIMO systems by non-binary LDPC codes and MMSE detection,” in Proceedings of International Symposium on Information Theory Proceedings (IEEE, 2012), pp. 1712–1716.
[Crossref]

Tebe, P. I.

K. A. Opare, Y. Kuang, J. J. Kponyo, K. S. Nwizege, and P. I. Tebe, “The effect of receiver-side circular antenna arrays on bit error probability in a wireless line-of-sight OAM communication system,” in Proceedings of Advanced Computing and Communication Technologies (ACCT) (IEEE, 2015), pp. 614–620.

Tian, H.

Tian, Q.

Q. Tian, L. Zhu, Y. Wang, Q. Zhang, B. Liu, and X. Xin, “The propagation properties of a longitudinal orbital angular momentum multiplexing system in atmospheric turbulence,” IEEE Photonics J. 10(1), 1–11 (2018).
[Crossref]

Tong, S.

Tur, M.

Ullah, S. E.

M. T. Hossain, I. Misra, J. J. Sadique, and S. E. Ullah, “Impact of various signal detection schemes in performance assessment of 5G compatible LDPC encoded GPQSM wireless communication system,” Electr. & Comput. Eng. 1(3), 72–80 (2017).

Ungerboeck, G.

G. Ungerboeck, “Channel coding with multilevel/phase signals,” IEEE Trans. Inf. Theory 28(1), 55–67 (2003).
[Crossref]

Vasic, B. V.

Wang, D.

Wang, J.

S. Li, S. Chen, C. Gao, A. E. Willner, and J. Wang, “Atmospheric turbulence compensation in orbital angular momentum communications: Advances and perspectives,” Opt. Commun. 408, 68–81 (2018).
[Crossref]

Wang, L.

S. Zhao, L. Wang, L. Zou, L. Gong, W. Cheng, B. Zheng, and H. Chen, “Both channel coding and wavefront correction on the turbulence mitigation of optical communications using orbital angular momentum multiplexing,” Opt. Commun. 376, 92–98 (2016).
[Crossref]

Wang, P.

Wang, R.

Wang, W.

Y. Zhang, P. Wang, L. Guo, W. Wang, and H. Tian, “Performance analysis of an OAM multiplexing-based MIMO FSO system over atmospheric turbulence using space-time coding with channel estimation,” Opt. Express 25(17), 19995–20011 (2017).
[Crossref] [PubMed]

M. Qin, L. Chen, and W. Wang, “Generalized selection multiuser scheduling for the MIMO FSO communication system and its performance analysis,” IEEE Photonics J. 8(5), 1–9 (2016).
[Crossref]

Wang, Y.

Q. Tian, L. Zhu, Y. Wang, Q. Zhang, B. Liu, and X. Xin, “The propagation properties of a longitudinal orbital angular momentum multiplexing system in atmospheric turbulence,” IEEE Photonics J. 10(1), 1–11 (2018).
[Crossref]

G. Liang, Y. Wang, Q. Guo, and H. Zhang, “Anisotropic diffraction induced by orbital angular momentum during propagations of optical beams,” Opt. Express 26(7), 8084–8094 (2018).
[Crossref] [PubMed]

Wang, Z.

X. Hu, Q. Zhao, P. Yu, X. Li, Z. Wang, Y. Li, and L. Gong, “Dynamic shaping of orbital-angular-momentum beams for information encoding,” Opt. Express 26(2), 1796–1808 (2018).
[Crossref] [PubMed]

Y. Ren, Z. Wang, G. Xie, L. Li, A. J. Willner, Y. Cao, Z. Zhao, Y. Yan, N. Ahmed, N. Ashrafi, S. Ashrafi, R. Bock, M. Tur, and A. E. Willner, “Atmospheric turbulence mitigation in an OAM-based MIMO free-space optical link using spatial diversity combined with MIMO equalization,” Opt. Lett. 41(11), 2406–2409 (2016).
[Crossref] [PubMed]

L. Li, G. Xie, Y. Ren, N. Ahmed, H. Huang, Z. Zhao, P. Liao, M. P. J. Lavery, Y. Yan, C. Bao, Z. Wang, A. J. Willner, N. Ashrafi, S. Ashrafi, M. Tur, and A. E. Willner, “Orbital-angular-momentum-multiplexed free-space optical communication link using transmitter lenses,” Appl. Opt. 55(8), 2098–2103 (2016).
[Crossref] [PubMed]

Y. Ren, Z. Wang, P. Liao, L. Li, G. Xie, H. Huang, Z. Zhao, Y. Yan, N. Ahmed, A. Willner, M. P. J. Lavery, N. Ashrafi, S. Ashrafi, R. Bock, M. Tur, I. B. Djordjevic, M. A. Neifeld, and A. E. Willner, “Experimental characterization of a 400 Gbit/s orbital angular momentum multiplexed free-space optical link over 120 m,” Opt. Lett. 41(3), 622–625 (2016).
[Crossref] [PubMed]

Y. Ren, Z. Wang, G. Xie, L. Li, Y. Cao, C. Liu, P. Liao, Y. Yan, N. Ahmed, Z. Zhao, A. Willner, N. Ashrafi, S. Ashrafi, R. D. Linquist, R. Bock, M. Tur, A. F. Molisch, and A. E. Willner, “Free-space optical communications using orbital-angular-momentum multiplexing combined with MIMO-based spatial multiplexing,” Opt. Lett. 40(18), 4210–4213 (2015).
[Crossref] [PubMed]

Watnik, A. T.

Willner, A.

Willner, A. E.

S. Li, S. Chen, C. Gao, A. E. Willner, and J. Wang, “Atmospheric turbulence compensation in orbital angular momentum communications: Advances and perspectives,” Opt. Commun. 408, 68–81 (2018).
[Crossref]

Y. Ren, Z. Wang, P. Liao, L. Li, G. Xie, H. Huang, Z. Zhao, Y. Yan, N. Ahmed, A. Willner, M. P. J. Lavery, N. Ashrafi, S. Ashrafi, R. Bock, M. Tur, I. B. Djordjevic, M. A. Neifeld, and A. E. Willner, “Experimental characterization of a 400 Gbit/s orbital angular momentum multiplexed free-space optical link over 120 m,” Opt. Lett. 41(3), 622–625 (2016).
[Crossref] [PubMed]

L. Li, G. Xie, Y. Ren, N. Ahmed, H. Huang, Z. Zhao, P. Liao, M. P. J. Lavery, Y. Yan, C. Bao, Z. Wang, A. J. Willner, N. Ashrafi, S. Ashrafi, M. Tur, and A. E. Willner, “Orbital-angular-momentum-multiplexed free-space optical communication link using transmitter lenses,” Appl. Opt. 55(8), 2098–2103 (2016).
[Crossref] [PubMed]

Y. Ren, Z. Wang, G. Xie, L. Li, A. J. Willner, Y. Cao, Z. Zhao, Y. Yan, N. Ahmed, N. Ashrafi, S. Ashrafi, R. Bock, M. Tur, and A. E. Willner, “Atmospheric turbulence mitigation in an OAM-based MIMO free-space optical link using spatial diversity combined with MIMO equalization,” Opt. Lett. 41(11), 2406–2409 (2016).
[Crossref] [PubMed]

Y. Ren, Z. Wang, G. Xie, L. Li, Y. Cao, C. Liu, P. Liao, Y. Yan, N. Ahmed, Z. Zhao, A. Willner, N. Ashrafi, S. Ashrafi, R. D. Linquist, R. Bock, M. Tur, A. F. Molisch, and A. E. Willner, “Free-space optical communications using orbital-angular-momentum multiplexing combined with MIMO-based spatial multiplexing,” Opt. Lett. 40(18), 4210–4213 (2015).
[Crossref] [PubMed]

H. Huang, Y. Cao, G. Xie, Y. Ren, Y. Yan, C. Bao, N. Ahmed, M. A. Neifeld, S. J. Dolinar, and A. E. Willner, “Crosstalk mitigation in a free-space orbital angular momentum multiplexed communication link using 4×4 MIMO equalization,” Opt. Lett. 39(15), 4360–4363 (2014).
[Crossref] [PubMed]

Willner, A. J.

Wu, H.

Y. Yuan, Z. Zhang, C. Ji, and H. Wu, “Capacity analysis of UCA-based OAM multiplexing communication system,” in Proceedings of Wireless Communications and Signal Processing (WCSP) (IEEE, 2015), pp. 1–5.

Wu, S.

Xiang, Y.

X. Zhang, Y. He, Y. Cai, M. Su, X. Zhou, Y. Chen, S. Chen, Y. Xiang, L. Chen, C. Su, Y. Li, and D. Fan, “Coherent separation detection for orbital angular momentum multiplexing in free-space optical communications,” IEEE Photonics J. 9(3), 1–11 (2017).

Xie, G.

L. Li, G. Xie, Y. Ren, N. Ahmed, H. Huang, Z. Zhao, P. Liao, M. P. J. Lavery, Y. Yan, C. Bao, Z. Wang, A. J. Willner, N. Ashrafi, S. Ashrafi, M. Tur, and A. E. Willner, “Orbital-angular-momentum-multiplexed free-space optical communication link using transmitter lenses,” Appl. Opt. 55(8), 2098–2103 (2016).
[Crossref] [PubMed]

Y. Ren, Z. Wang, P. Liao, L. Li, G. Xie, H. Huang, Z. Zhao, Y. Yan, N. Ahmed, A. Willner, M. P. J. Lavery, N. Ashrafi, S. Ashrafi, R. Bock, M. Tur, I. B. Djordjevic, M. A. Neifeld, and A. E. Willner, “Experimental characterization of a 400 Gbit/s orbital angular momentum multiplexed free-space optical link over 120 m,” Opt. Lett. 41(3), 622–625 (2016).
[Crossref] [PubMed]

Y. Ren, Z. Wang, G. Xie, L. Li, A. J. Willner, Y. Cao, Z. Zhao, Y. Yan, N. Ahmed, N. Ashrafi, S. Ashrafi, R. Bock, M. Tur, and A. E. Willner, “Atmospheric turbulence mitigation in an OAM-based MIMO free-space optical link using spatial diversity combined with MIMO equalization,” Opt. Lett. 41(11), 2406–2409 (2016).
[Crossref] [PubMed]

Y. Ren, Z. Wang, G. Xie, L. Li, Y. Cao, C. Liu, P. Liao, Y. Yan, N. Ahmed, Z. Zhao, A. Willner, N. Ashrafi, S. Ashrafi, R. D. Linquist, R. Bock, M. Tur, A. F. Molisch, and A. E. Willner, “Free-space optical communications using orbital-angular-momentum multiplexing combined with MIMO-based spatial multiplexing,” Opt. Lett. 40(18), 4210–4213 (2015).
[Crossref] [PubMed]

H. Huang, Y. Cao, G. Xie, Y. Ren, Y. Yan, C. Bao, N. Ahmed, M. A. Neifeld, S. J. Dolinar, and A. E. Willner, “Crosstalk mitigation in a free-space orbital angular momentum multiplexed communication link using 4×4 MIMO equalization,” Opt. Lett. 39(15), 4360–4363 (2014).
[Crossref] [PubMed]

Xin, X.

Q. Tian, L. Zhu, Y. Wang, Q. Zhang, B. Liu, and X. Xin, “The propagation properties of a longitudinal orbital angular momentum multiplexing system in atmospheric turbulence,” IEEE Photonics J. 10(1), 1–11 (2018).
[Crossref]

Xu, H.

R. Chen, H. Xu, M. Moretti, and J. Li, “Beam Steering for the Misalignment in UCA-Based OAM Communication Systems,” IEEE Wirel. Commun. Lett. 99, 1–4 (2018).

Yan, Y.

Y. Ren, Z. Wang, P. Liao, L. Li, G. Xie, H. Huang, Z. Zhao, Y. Yan, N. Ahmed, A. Willner, M. P. J. Lavery, N. Ashrafi, S. Ashrafi, R. Bock, M. Tur, I. B. Djordjevic, M. A. Neifeld, and A. E. Willner, “Experimental characterization of a 400 Gbit/s orbital angular momentum multiplexed free-space optical link over 120 m,” Opt. Lett. 41(3), 622–625 (2016).
[Crossref] [PubMed]

Y. Ren, Z. Wang, G. Xie, L. Li, A. J. Willner, Y. Cao, Z. Zhao, Y. Yan, N. Ahmed, N. Ashrafi, S. Ashrafi, R. Bock, M. Tur, and A. E. Willner, “Atmospheric turbulence mitigation in an OAM-based MIMO free-space optical link using spatial diversity combined with MIMO equalization,” Opt. Lett. 41(11), 2406–2409 (2016).
[Crossref] [PubMed]

L. Li, G. Xie, Y. Ren, N. Ahmed, H. Huang, Z. Zhao, P. Liao, M. P. J. Lavery, Y. Yan, C. Bao, Z. Wang, A. J. Willner, N. Ashrafi, S. Ashrafi, M. Tur, and A. E. Willner, “Orbital-angular-momentum-multiplexed free-space optical communication link using transmitter lenses,” Appl. Opt. 55(8), 2098–2103 (2016).
[Crossref] [PubMed]

Y. Ren, Z. Wang, G. Xie, L. Li, Y. Cao, C. Liu, P. Liao, Y. Yan, N. Ahmed, Z. Zhao, A. Willner, N. Ashrafi, S. Ashrafi, R. D. Linquist, R. Bock, M. Tur, A. F. Molisch, and A. E. Willner, “Free-space optical communications using orbital-angular-momentum multiplexing combined with MIMO-based spatial multiplexing,” Opt. Lett. 40(18), 4210–4213 (2015).
[Crossref] [PubMed]

H. Huang, Y. Cao, G. Xie, Y. Ren, Y. Yan, C. Bao, N. Ahmed, M. A. Neifeld, S. J. Dolinar, and A. E. Willner, “Crosstalk mitigation in a free-space orbital angular momentum multiplexed communication link using 4×4 MIMO equalization,” Opt. Lett. 39(15), 4360–4363 (2014).
[Crossref] [PubMed]

Yang, H.

Yang, Y.

Yu, P.

Yu, Z.

M. Li, Z. Yu, and M. Cvijetic, “Influence of atmospheric turbulence on OAM-based FSO system with use of realistic link model,” Opt. Commun. 364, 50–54 (2016).
[Crossref]

Yuan, Y.

Y. Yuan, Z. Zhang, C. Ji, and H. Wu, “Capacity analysis of UCA-based OAM multiplexing communication system,” in Proceedings of Wireless Communications and Signal Processing (WCSP) (IEEE, 2015), pp. 1–5.

Zhan, Y.

Zhang, H.

Zhang, K.

J. Peng, L. Zhang, K. Zhang, and J. Ma, “Channel capacity of OAM based FSO communication systems with partially coherent Bessel–Gaussian beams in anisotropic turbulence,” Opt. Commun. 418, 32–36 (2018).
[Crossref]

Zhang, L.

J. Peng, L. Zhang, K. Zhang, and J. Ma, “Channel capacity of OAM based FSO communication systems with partially coherent Bessel–Gaussian beams in anisotropic turbulence,” Opt. Commun. 418, 32–36 (2018).
[Crossref]

P. Wang, L. Zhang, L. Guo, F. Huang, T. Shang, R. Wang, and Y. Yang, “Average BER of subcarrier intensity modulated free space optical systems over the exponentiated Weibull fading channels,” Opt. Express 22(17), 20828–20841 (2014).
[Crossref] [PubMed]

Zhang, M.

Zhang, Q.

Q. Tian, L. Zhu, Y. Wang, Q. Zhang, B. Liu, and X. Xin, “The propagation properties of a longitudinal orbital angular momentum multiplexing system in atmospheric turbulence,” IEEE Photonics J. 10(1), 1–11 (2018).
[Crossref]

Zhang, X.

X. Zhang, Y. He, Y. Cai, M. Su, X. Zhou, Y. Chen, S. Chen, Y. Xiang, L. Chen, C. Su, Y. Li, and D. Fan, “Coherent separation detection for orbital angular momentum multiplexing in free-space optical communications,” IEEE Photonics J. 9(3), 1–11 (2017).

Z. Zhang, S. Zheng, Y. Chen, X. Jin, H. Chi, and X. Zhang, “The capacity gain of orbital angular momentum based multiple-input-multiple-output system,” Sci. Rep. 6(1), 25418 (2016).
[Crossref] [PubMed]

Zhang, Y.

Zhang, Z.

Z. Zhang, S. Zheng, Y. Chen, X. Jin, H. Chi, and X. Zhang, “The capacity gain of orbital angular momentum based multiple-input-multiple-output system,” Sci. Rep. 6(1), 25418 (2016).
[Crossref] [PubMed]

Y. Yuan, Z. Zhang, C. Ji, and H. Wu, “Capacity analysis of UCA-based OAM multiplexing communication system,” in Proceedings of Wireless Communications and Signal Processing (WCSP) (IEEE, 2015), pp. 1–5.

Zhao, Q.

Zhao, S.

S. Zhao, L. Wang, L. Zou, L. Gong, W. Cheng, B. Zheng, and H. Chen, “Both channel coding and wavefront correction on the turbulence mitigation of optical communications using orbital angular momentum multiplexing,” Opt. Commun. 376, 92–98 (2016).
[Crossref]

Zhao, S. M.

Zhao, Z.

Zheng, B.

S. Zhao, L. Wang, L. Zou, L. Gong, W. Cheng, B. Zheng, and H. Chen, “Both channel coding and wavefront correction on the turbulence mitigation of optical communications using orbital angular momentum multiplexing,” Opt. Commun. 376, 92–98 (2016).
[Crossref]

Zheng, B. Y.

Zheng, S.

Z. Zhang, S. Zheng, Y. Chen, X. Jin, H. Chi, and X. Zhang, “The capacity gain of orbital angular momentum based multiple-input-multiple-output system,” Sci. Rep. 6(1), 25418 (2016).
[Crossref] [PubMed]

Zhou, X.

X. Zhang, Y. He, Y. Cai, M. Su, X. Zhou, Y. Chen, S. Chen, Y. Xiang, L. Chen, C. Su, Y. Li, and D. Fan, “Coherent separation detection for orbital angular momentum multiplexing in free-space optical communications,” IEEE Photonics J. 9(3), 1–11 (2017).

Zhu, L.

Q. Tian, L. Zhu, Y. Wang, Q. Zhang, B. Liu, and X. Xin, “The propagation properties of a longitudinal orbital angular momentum multiplexing system in atmospheric turbulence,” IEEE Photonics J. 10(1), 1–11 (2018).
[Crossref]

Zou, L.

S. Zhao, L. Wang, L. Zou, L. Gong, W. Cheng, B. Zheng, and H. Chen, “Both channel coding and wavefront correction on the turbulence mitigation of optical communications using orbital angular momentum multiplexing,” Opt. Commun. 376, 92–98 (2016).
[Crossref]

Appl. Opt. (4)

Electr. & Comput. Eng. (1)

M. T. Hossain, I. Misra, J. J. Sadique, and S. E. Ullah, “Impact of various signal detection schemes in performance assessment of 5G compatible LDPC encoded GPQSM wireless communication system,” Electr. & Comput. Eng. 1(3), 72–80 (2017).

IEEE Commun. Lett. (1)

C. Abou-Rjeily, “On the optimality of the selection transmit diversity for MIMO-FSO links with feedback,” IEEE Commun. Lett. 15(6), 641–643 (2011).
[Crossref]

IEEE Photonics J. (3)

M. Qin, L. Chen, and W. Wang, “Generalized selection multiuser scheduling for the MIMO FSO communication system and its performance analysis,” IEEE Photonics J. 8(5), 1–9 (2016).
[Crossref]

Q. Tian, L. Zhu, Y. Wang, Q. Zhang, B. Liu, and X. Xin, “The propagation properties of a longitudinal orbital angular momentum multiplexing system in atmospheric turbulence,” IEEE Photonics J. 10(1), 1–11 (2018).
[Crossref]

X. Zhang, Y. He, Y. Cai, M. Su, X. Zhou, Y. Chen, S. Chen, Y. Xiang, L. Chen, C. Su, Y. Li, and D. Fan, “Coherent separation detection for orbital angular momentum multiplexing in free-space optical communications,” IEEE Photonics J. 9(3), 1–11 (2017).

IEEE Trans. Antenn. Propag. (1)

M. Lin, Y. Gao, P. Liu, and J. Liu, “Theoretical analyses and design of circular array to generate orbital angular momentum,” IEEE Trans. Antenn. Propag. 65(7), 3510–3519 (2017).
[Crossref]

IEEE Trans. Inf. Theory (1)

G. Ungerboeck, “Channel coding with multilevel/phase signals,” IEEE Trans. Inf. Theory 28(1), 55–67 (2003).
[Crossref]

IEEE Wirel. Commun. Lett. (1)

R. Chen, H. Xu, M. Moretti, and J. Li, “Beam Steering for the Misalignment in UCA-Based OAM Communication Systems,” IEEE Wirel. Commun. Lett. 99, 1–4 (2018).

J. Opt. Soc. Am. A (1)

Opt. Commun. (4)

S. Zhao, L. Wang, L. Zou, L. Gong, W. Cheng, B. Zheng, and H. Chen, “Both channel coding and wavefront correction on the turbulence mitigation of optical communications using orbital angular momentum multiplexing,” Opt. Commun. 376, 92–98 (2016).
[Crossref]

J. Peng, L. Zhang, K. Zhang, and J. Ma, “Channel capacity of OAM based FSO communication systems with partially coherent Bessel–Gaussian beams in anisotropic turbulence,” Opt. Commun. 418, 32–36 (2018).
[Crossref]

S. Li, S. Chen, C. Gao, A. E. Willner, and J. Wang, “Atmospheric turbulence compensation in orbital angular momentum communications: Advances and perspectives,” Opt. Commun. 408, 68–81 (2018).
[Crossref]

M. Li, Z. Yu, and M. Cvijetic, “Influence of atmospheric turbulence on OAM-based FSO system with use of realistic link model,” Opt. Commun. 364, 50–54 (2016).
[Crossref]

Opt. Express (8)

S. M. Zhao, J. Leach, L. Y. Gong, J. Ding, and B. Y. Zheng, “Aberration corrections for free-space optical communications in atmosphere turbulence using orbital angular momentum states,” Opt. Express 20(1), 452–461 (2012).
[Crossref] [PubMed]

P. Wang, L. Zhang, L. Guo, F. Huang, T. Shang, R. Wang, and Y. Yang, “Average BER of subcarrier intensity modulated free space optical systems over the exponentiated Weibull fading channels,” Opt. Express 22(17), 20828–20841 (2014).
[Crossref] [PubMed]

X. Hu, Q. Zhao, P. Yu, X. Li, Z. Wang, Y. Li, and L. Gong, “Dynamic shaping of orbital-angular-momentum beams for information encoding,” Opt. Express 26(2), 1796–1808 (2018).
[Crossref] [PubMed]

J. Li, M. Zhang, D. Wang, S. Wu, and Y. Zhan, “Joint atmospheric turbulence detection and adaptive demodulation technique using the CNN for the OAM-FSO communication,” Opt. Express 26(8), 10494–10508 (2018).
[Crossref] [PubMed]

A. García-Zambrana, C. Castillo-Vázquez, and B. Castillo-Vázquez, “Outage performance of MIMO FSO links over strong turbulence and misalignment fading channels,” Opt. Express 19(14), 13480–13496 (2011).
[Crossref] [PubMed]

C. Chen, H. Yang, S. Tong, and Y. Lou, “Changes in orbital-angular-momentum modes of a propagated vortex Gaussian beam through weak-to-strong atmospheric turbulence,” Opt. Express 24(7), 6959–6975 (2016).
[Crossref] [PubMed]

G. Liang, Y. Wang, Q. Guo, and H. Zhang, “Anisotropic diffraction induced by orbital angular momentum during propagations of optical beams,” Opt. Express 26(7), 8084–8094 (2018).
[Crossref] [PubMed]

Y. Zhang, P. Wang, L. Guo, W. Wang, and H. Tian, “Performance analysis of an OAM multiplexing-based MIMO FSO system over atmospheric turbulence using space-time coding with channel estimation,” Opt. Express 25(17), 19995–20011 (2017).
[Crossref] [PubMed]

Opt. Lett. (6)

Z. Qu and I. B. Djordjevic, “500 Gb/s free-space optical transmission over strong atmospheric turbulence channels,” Opt. Lett. 41(14), 3285–3288 (2016).
[Crossref] [PubMed]

Z. Qu and I. B. Djordjevic, “Two-stage cross-talk mitigation in an orbital-angular-momentum-based free-space optical communication system,” Opt. Lett. 42(16), 3125–3128 (2017).
[Crossref] [PubMed]

Y. Ren, Z. Wang, G. Xie, L. Li, Y. Cao, C. Liu, P. Liao, Y. Yan, N. Ahmed, Z. Zhao, A. Willner, N. Ashrafi, S. Ashrafi, R. D. Linquist, R. Bock, M. Tur, A. F. Molisch, and A. E. Willner, “Free-space optical communications using orbital-angular-momentum multiplexing combined with MIMO-based spatial multiplexing,” Opt. Lett. 40(18), 4210–4213 (2015).
[Crossref] [PubMed]

H. Huang, Y. Cao, G. Xie, Y. Ren, Y. Yan, C. Bao, N. Ahmed, M. A. Neifeld, S. J. Dolinar, and A. E. Willner, “Crosstalk mitigation in a free-space orbital angular momentum multiplexed communication link using 4×4 MIMO equalization,” Opt. Lett. 39(15), 4360–4363 (2014).
[Crossref] [PubMed]

Y. Ren, Z. Wang, P. Liao, L. Li, G. Xie, H. Huang, Z. Zhao, Y. Yan, N. Ahmed, A. Willner, M. P. J. Lavery, N. Ashrafi, S. Ashrafi, R. Bock, M. Tur, I. B. Djordjevic, M. A. Neifeld, and A. E. Willner, “Experimental characterization of a 400 Gbit/s orbital angular momentum multiplexed free-space optical link over 120 m,” Opt. Lett. 41(3), 622–625 (2016).
[Crossref] [PubMed]

Y. Ren, Z. Wang, G. Xie, L. Li, A. J. Willner, Y. Cao, Z. Zhao, Y. Yan, N. Ahmed, N. Ashrafi, S. Ashrafi, R. Bock, M. Tur, and A. E. Willner, “Atmospheric turbulence mitigation in an OAM-based MIMO free-space optical link using spatial diversity combined with MIMO equalization,” Opt. Lett. 41(11), 2406–2409 (2016).
[Crossref] [PubMed]

Photon. Res. (1)

Sci. Rep. (1)

Z. Zhang, S. Zheng, Y. Chen, X. Jin, H. Chi, and X. Zhang, “The capacity gain of orbital angular momentum based multiple-input-multiple-output system,” Sci. Rep. 6(1), 25418 (2016).
[Crossref] [PubMed]

Other (14)

A. Wang, J. Wang, L. Zhu, and J. Liu, “Experimental demonstration of dense fractional orbital angular momentum (OAM) multiplexing with a channel spacing of 0.2 assisted by MIMO equalization,” in Proceedings of Asia Communications and Photonics Conference (OSA 2016), pp. AF1D.1.
[Crossref]

Z. Xu, “6×6 MIMO equalization assisted fractional orbital angular momentum (OAM) dense mode-division multiplexing (DMDM) for free-space optical communications,” in Proceedings of Asia Communications and Photonics Conference (OSA 2014), pp. AW3F.2.
[Crossref]

S. Yong, J. Kim, W. Yang, and C. Kang, MIMO-OFDM Wireless Communications with MATLAB (Wiley, 2010).

C. Fan, Principles of Communications (Beijing, 2010).

J. Zhou, Z. Xu, and J. Wang, “Performance evaluation of fractional orbital angular momentum (OAM) based LDPC-coded free-space optical communications with atmospheric turbulence,” in Proceedings of Asia Communications and Photonics Conference (ACPC) (OSA 2014), pp.AF3D.2.
[Crossref]

Z. Qu and B. Ivan, F. Djordjevic, “Experimental evaluation of LDPC-coded OAM based FSO communication in the presence of atmospheric turbulence,” in Proceedings of International Conference of Telecommunication in Modern Satellite, Cable and Broadcasting Services (TELSIKS) (IEEE 2015), pp.117–122.

K. A. Opare, Y. Kuang, J. J. Kponyo, K. S. Nwizege, and P. I. Tebe, “The effect of receiver-side circular antenna arrays on bit error probability in a wireless line-of-sight OAM communication system,” in Proceedings of Advanced Computing and Communication Technologies (ACCT) (IEEE, 2015), pp. 614–620.

Y. Yuan, Z. Zhang, C. Ji, and H. Wu, “Capacity analysis of UCA-based OAM multiplexing communication system,” in Proceedings of Wireless Communications and Signal Processing (WCSP) (IEEE, 2015), pp. 1–5.

K. A. Opare and Y. Kuang, “Performance of an ideal wireless orbital angular momentum communication system using multiple-input multiple-output techniques,” in Proceedings of Telecommunications and Multimedia (TEMU) (IEEE, 2014), pp. 144–149.

Y. Ren, Z. Wang, G. Xie, L. Li, A. J. Willner, Y. Cao, Z. Zhao, Y. Yan, N. Ashrai, S. Ashrafi, R. Bock, M. Tur, and A. E. Willner, “Demonstration of OAM-based MIMO FSO link using spatial diversity and MIMO equalization for turbulence mitigation,” in Proceedings of Optical Fiber Communication Conference (OSA 2016), pp. Th1H.2.
[Crossref]

Z. Xu, C. Gui, S. Li, J. Zhou, and J. Wang, “Fractional orbital angular momentum (OAM) free-space optical communications with atmospheric turbulence assisted by MIMO equalization,” in Proceedings of Advanced Photonics for Communications (OSA, 2014), paper JT3A.1.

L. Zou, L. Wang, C. Xing, J. Cui, and S. Zhao, “Turbulence mitigation with MIMO equalization for orbital angular momentum multiplexing communication,” in Proceedings of 8th International Conference on Wireless Communications & Signal Processing (WCSP) (IEEE 2016), paper Th1H.2.
[Crossref]

J. D. Schmidt, Numerical Simulation of Optical Wave Propagation (2010).

P. Suthisopapan, K. Kasai, V. Imtawil, and A. Meesomboon, “Approaching capacity of large MIMO systems by non-binary LDPC codes and MMSE detection,” in Proceedings of International Symposium on Information Theory Proceedings (IEEE, 2012), pp. 1712–1716.
[Crossref]

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Figures (6)

Fig. 1
Fig. 1 The proposed LDPC coded OAM-based UCA FSO system with ZF/MMSE equalizer combined with channel estimation
Fig. 2
Fig. 2 (a) ABER performances of OAM-based UCA FSO system with ZF and MMSE equalizers under different atmospheric turbulence strengths. The constellation of the recovered QPSK signals propagated in the proposed system under weak turbulence condition (b) with ZF equalizer, (c) with MMSE equalizer, respectively.
Fig. 3
Fig. 3 ABER performances of OAM-based UCA FSO system with ZF and MMSE equalizers under (a) weak, (b) moderate, and (c) strong turbulence conditions using BPSK, QPSK and 8PSK modulations
Fig. 4
Fig. 4 ABER performances comparison for different receive antenna numbers under weak turbulence considering ZF and MMSE equalizers.
Fig. 5
Fig. 5 ABER performances of uncoded and LDPC coded QPSK OAM-based UCA FSO systems over the atmospheric turbulence with ZF and MMSE equalizers (The straight and dashed lines represent the ABER values of uncoded and LDPC coded FSO system, respectively. The lines in black, red and blue color represent the ABER values of this system under weak, moderate, strong turbulence, respectively. The lines with hollow and solid squares represent the system with ZF and MMSE equalizer, respectively).
Fig. 6
Fig. 6 ABER performances of LDPC coded QPSK OAM-based UCA FSO systems considering ZF and MMSE equalizers with different LDPC code rates under (a) weak, (b) moderate, and (c) strong turbulence conditions, respectively. (The lines in black, blue and red color represent the ABER values with code rates 0.25, 0.5 and 0.75, respectively. The lines with hollow and solid squares represent the FSO system with ZF and MMSE equalizers, respectively)

Equations (32)

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U l ( r,θ,z )= A l ( r,z )exp( ilθ ),
A l ( r,z )= 2p! π( p+| l | )! 1 ω( z ) [ 2 r ω( z ) ] | l | exp[ r 2 ω 2 ( z ) ] L p l [ 2 r 2 ω 2 ( z ) ] ×exp[ ik r 2 z 2( z 2 + z R 2 ) ]exp[ i( 2p+| l |+1 ) tan 1 z z R ] ,
X m ( r,θ,z )= x m (t) U m ( r,θ,z ) = x m (t) A m ( r,z )exp( i l m θ ) .
X Tx (r,θ,t)= m=1 M x m (t) U m (r,θ,z) = m=1 M x m (t) A m ( r,z )exp( i l m θ ) .
Φ n (k)=0.033 C n 2 ( k 2 +1/ L 0 2 ) 11 6 exp( k 2 / k l 2 ),
R n (r,θ,t)= m=1 M x m (t) U m ' (r,θ,z) = m=1 M x m (t) A m ' ( r,z )exp( i l m θ n )exp( ψ(r) ) ,
y n (r,θ,t)= m=1 M x m (t) U m ' (r,θ,z) + w n = m=1 M x m (t) A m ' ( r,z )exp( i l m θ n )exp( ψ(r) ) + w n ,
h n,m = m=1 M A m ' ( r,z )exp( ψ(r) )exp( i l m θ n ) ,
θ n = 2π(n n 0 ) N ,
h n,m = h C n,m h A T n,m ,
h C n,m =exp( i l m θ n ),
h A T n,m = A m ' (r,z) A m (r,z) exp(i l m ( θ ' θ) = A m ' (r,z) A m (r,z) exp( ψ(r) ) .
H C =( exp( i l 1 θ 1 ) exp( i l 2 θ 1 ) exp( i l m θ 1 ) exp( i l 1 θ 2 ) exp( i l 2 θ 2 ) exp( i l m θ 2 ) exp( i l 1 θ n ) exp( i l 2 θ n ) exp( i l m θ n ) ) .
h A T n,m = ( A m ( r,z )exp( i l m θ ) ) 1 ( m=1 M A m ' ( r,z )exp( ψ(r) ) + w n ).
h n,m =exp( i l m θ n ) ( A m ( r,z )exp( i l m θ ) ) 1 ( m=1 M A m ' ( r,z )exp( ψ(r) ) + w n ).
H=( exp( i l 1 θ 1 ) ( A 1 ( r,z )exp( i l 1 θ ) ) 1 ( m=1 M A m ' ( r,z )exp( ψ(r) ) + w 1 ) exp( i l m θ 1 ) ( A m ( r,z )exp( i l m θ ) ) 1 ( m=1 M A m ' ( r,z )exp( ψ(r) ) + w 1 ) exp( i l 1 θ n ) ( A m ( r,z )exp( i l m θ ) ) 1 ( m=1 M A m ' ( r,z )exp( ψ(r) ) + w n ) exp( i l m θ n ) ( A m ( r,z )exp( i l m θ ) ) 1 ( m=1 M A m ' ( r,z )exp( ψ(r) ) + w n ) ).
W ZF = ( H H H) 1 H H
W MMSE = ( H H H+ σ n 2 I) 1 H H .
γ ZF,n =γ [ ( H H H) 1 ] (n,n) 1
γ MMSE,n = γ ( ( H H H+ σ n 2 I) 1 ) (n,n) 1,
P e (γ)= 1 max(lo g 2 M P ,2) erfc( γ sin π M P ),
P e,ZF (γ) = 1 max(lo g 2 M P ,2) erfc( γ [ ( H H H) 1 ] (n,n) 1 sin π M P )
P e,MMSE (γ) = 1 max(lo g 2 M P ,2) erfc( γ ( ( H H H+ σ n 2 I) 1 ) (n,n) 1 sin π M P ) .
x ˜ ZF,m = ( ( H H H) 1 H H ) m y ZF,m = x ZF,m + ( ( H H H) 1 H H ) m w m
x ˜ MMSE,m = ( (H H H + σ n 2 I) 1 H m ) H y MMSE,m = ( (H H H + σ n 2 I) 1 H m ) H (Hx+ w m ),
x ˜ m = μ m x m + z m ,
μ ZF,m = x ZF,m (t)
μ MMSE,m = ( (H H H + σ n 2 I) 1 H m ) H H m .
σ ZF,m 2 = ( ( H H H) 1 H H ) m 2
σ MMSE,m 2 = μ MMSE,m (1 μ MMSE,m ).
P ZF,m ( x ˜ m / x m ) 1 π σ ZF,m 2 exp( | x ˜ m x m | 2 σ ZF,m 2 )
P MMSE,m ( x ˜ m / x m ) 1 π σ MMSE,m 2 exp( | x ˜ m μ MMSE,m x m | 2 σ MMSE,m 2 ).

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