Abstract

In order to achieve multi-gigabit transmission (projected for 2020) for the use in interplanetary communications, the usage of large number of time slots in pulse-position modulation (PPM), typically used in deep-space applications, is needed, which imposes stringent requirements on system design and implementation. As an alternative satisfying high-bandwidth demands of future interplanetary communications, while keeping the system cost and power consumption reasonably low, in this paper, we describe the use of orbital angular momentum (OAM) as an additional degree of freedom. The OAM is associated with azimuthal phase of the complex electric field. Because OAM eigenstates are orthogonal the can be used as basis functions for N-dimensional signaling. The OAM modulation and multiplexing can, therefore, be used, in combination with other degrees of freedom, to solve the high-bandwidth requirements of future deep-space and near-Earth optical communications. The main challenge for OAM deep-space communication represents the link between a spacecraft probe and the Earth station because in the presence of atmospheric turbulence the orthogonality between OAM states is no longer preserved. We will show that in combination with LDPC codes, the OAM-based modulation schemes can operate even under strong atmospheric turbulence regime. In addition, the spectral efficiency of proposed scheme is N2/log2 N times better than that of PPM.

© 2011 OSA

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References

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  1. B. Moision and J. Hamkins, “Deep-space optical communications downlink budget: modulation and coding,“ The Interplanetary Network Progress Report 42-154, April-June 2003 (Jet Propulsion Laboratory, Pasadena, California, 15 August 2003), pp. 1-28, http://ipnpr.jpl.nasa.gov/progress_report/42-154/154K.pdf .
  2. B. Moision and J. Hamkins, “Coded modulation for the deep-space optical channel: serially concatenated pulse-position modulation,“ The Interplanetary Network Progress Report 42-161 (Jet Propulsion Laboratory, Pasadena, California, 15 May 2005), pp. 1-25, http://ipnpr.jpl.nasa.gov/progress_report/42-161/161T.pdf .
  3. F. Xu, M.-A. Khalighi, and S. Bourennane, “Coded PPM and multipulse PPM and iterative detection for free-space optical links,” J. Opt. Commun. Netw. 1(5), 404–415 (2009).
    [CrossRef]
  4. S. J. Dolinar, J. Hamkins, B. E. Moision, and V. A. Vilnrotter, “Optical modulation and coding,” in Deep Space Optical Communications, H. Hemmati, ed. (Wile, 2006), pp. 215–299.
  5. H. Hemmati, “Interplanetary laser communications,” Optics & Photonics News 18(11), 22–27 (2007).
    [CrossRef]
  6. L. C. Andrews and R. L. Philips, Laser Beam Propagation through Random Media (SPIE Press, 2005).
  7. I. B. Djordjevic and M. Arabaci, “LDPC-coded orbital angular momentum (OAM) modulation for free-space optical communication,” Opt. Express 18(24), 24722–24728 (2010).
    [CrossRef] [PubMed]
  8. I. B. Djordjevic, “Orbital angular momentum (OAM) based LDPC-coded deep-space optical communication,” Proc. SPIE 7923, 792306, 792306–792308 (2011) (invited paper).
    [CrossRef]
  9. C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett. 94(15), 153901 (2005).
    [CrossRef] [PubMed]
  10. 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]
  11. J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. 92(1), 013601 (2004).
    [CrossRef] [PubMed]
  12. G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas’ko, S. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12(22), 5448–5456 (2004).
    [CrossRef] [PubMed]
  13. M. T. Gruneisen, W. A. Miller, R. C. Dymale, and A. M. Sweiti, “Holographic generation of complex fields with spatial light modulators: application to quantum key distribution,” Appl. Opt. 47(4), A32–A42 (2008).
    [CrossRef] [PubMed]
  14. M. P. C. Fossorier, “Quasi-cyclic low-density parity-check codes from circulant permutation matrices,” IEEE Trans. Inf. Theory 50(8), 1788–1793 (2004).
    [CrossRef]
  15. S. Lin and D. J. Costello, Error Control Coding: Fundamentals and Applications (Prentice Hall, 2004).
  16. I. B. Djordjevic, M. Arabaci, and L. Minkov, “Next generation FEC for high-capacity communication in optical transport networks,” J. Lightwave Technol. 27(16), 3518–3530 (2009).
    [CrossRef]
  17. J. Chen, A. Dholakia, E. Eleftheriou, M. Fossorier, and X.-Y. Hu, “Reduced-complexity decoding of LDPC codes,” IEEE Trans. Commun. 53(8), 1288–1299 (2005).
    [CrossRef]
  18. I. B. Djordjevic and M. Arabaci, “LDPC-coded orbital angular momentum (OAM) modulation for free-space optical communication,” Opt. Express 18(24), 24722–24728 (2010).
    [CrossRef] [PubMed]
  19. J. D. Jackson, Classical Electrodynamics (Wiley, 1975).
  20. I. B. Djordjevic, M. Arabaci, L. Xu, and T. Wang, “Generalized OFDM (GOFDM) for ultra-high-speed optical transmission,” Opt. Express 19(7), 6969–6979 (2011).
    [CrossRef] [PubMed]
  21. H. G. Batshon and I. B. Djordjevic, “Beyond 240 Gb/s per wavelength optical transmission using coded hybrid subcarrier/amplitude/ phase/polarization modulation,” IEEE Photon. Technol. Lett. 22(5), 299–301 (2010).
    [CrossRef]
  22. H. G. Batshon, I. B. Djordjevic, L. Xu, and T. Wang, “Multidimensional LDPC-coded modulation for beyond 400 Gb/s per wavelength transmission,” IEEE Photon. Technol. Lett. 21(16), 1139–1141 (2009).
    [CrossRef]
  23. I. B. Djordjevic and H. G. Batshon, “Generalized hybrid subcarrier/amplitude/phase/polarization LDPC-coded modulation based FSO Networking,” in Proceedings of IEEE 12th International Conference on Transparent Optical Networks (ICTON 2010) (IEEE, 2010), paper Th.B3.4.
  24. W. Shieh and I. B. Djordjevic, OFDM for Optical Communications (Elsevier/Academic Press, 2009).
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    [CrossRef]
  26. A. Goldsmith, Wireless Communications (Cambridge University Press, 2005).
  27. D. Tse and P. Viswanath, Fundamentals of Wireless Communication (Cambridge University Press, 2005).
  28. T. M. Duman and A. Ghrayeb, Coding for MIMO Communication Systems (Wiley, 2007).
  29. I. B. Djordjevic, L. Xu, and T. Wang, “PMD compensation in multilevel coded-modulation schemes with coherent detection using BLAST algorithm and iterative polarization cancellation,” Opt. Express 16(19), 14845–14852 (2008).
    [CrossRef] [PubMed]
  30. J. G. Proakis, Digital Communication (McGraw Hill, 2001).
  31. I. B. Djordjevic and G. T. Djordjevic, “On the communication over strong atmospheric turbulence channels by adaptive modulation and coding,” Opt. Express 17(20), 18250–18262 (2009).
    [CrossRef] [PubMed]
  32. I. B. Djordjevic, “Adaptive modulation and coding for communication over the atmospheric turbulence channels,” in Proceedings of IEEE Photonics Society Summer Topicals (IEEE, 2009), paper TuD3.3.
  33. M. Arabaci, I. B. Djordjevic, R. Saunders, and R. M. Marcoccia, “Polarization-multiplexed rate-adaptive non-binary-quasi-cyclic-LDPC-coded multilevel modulation with coherent detection for optical transport networks,” Opt. Express 18(3), 1820–1832 (2010).
    [CrossRef] [PubMed]

2011

I. B. Djordjevic, “Orbital angular momentum (OAM) based LDPC-coded deep-space optical communication,” Proc. SPIE 7923, 792306, 792306–792308 (2011) (invited paper).
[CrossRef]

I. B. Djordjevic, M. Arabaci, L. Xu, and T. Wang, “Generalized OFDM (GOFDM) for ultra-high-speed optical transmission,” Opt. Express 19(7), 6969–6979 (2011).
[CrossRef] [PubMed]

2010

2009

2008

2007

H. Hemmati, “Interplanetary laser communications,” Optics & Photonics News 18(11), 22–27 (2007).
[CrossRef]

2005

C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett. 94(15), 153901 (2005).
[CrossRef] [PubMed]

J. Chen, A. Dholakia, E. Eleftheriou, M. Fossorier, and X.-Y. Hu, “Reduced-complexity decoding of LDPC codes,” IEEE Trans. Commun. 53(8), 1288–1299 (2005).
[CrossRef]

2004

M. P. C. Fossorier, “Quasi-cyclic low-density parity-check codes from circulant permutation matrices,” IEEE Trans. Inf. Theory 50(8), 1788–1793 (2004).
[CrossRef]

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. 92(1), 013601 (2004).
[CrossRef] [PubMed]

G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas’ko, S. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12(22), 5448–5456 (2004).
[CrossRef] [PubMed]

1998

S. M. Alamouti, “A simple transmit diversity technique for wireless communications,” IEEE J. Sel. Areas Comm. 16(8), 1451–1458 (1998).
[CrossRef]

Alamouti, S. M.

S. M. Alamouti, “A simple transmit diversity technique for wireless communications,” IEEE J. Sel. Areas Comm. 16(8), 1451–1458 (1998).
[CrossRef]

Anguita, J. A.

Arabaci, M.

Barnett, S.

Barnett, S. M.

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. 92(1), 013601 (2004).
[CrossRef] [PubMed]

Batshon, H. G.

H. G. Batshon and I. B. Djordjevic, “Beyond 240 Gb/s per wavelength optical transmission using coded hybrid subcarrier/amplitude/ phase/polarization modulation,” IEEE Photon. Technol. Lett. 22(5), 299–301 (2010).
[CrossRef]

H. G. Batshon, I. B. Djordjevic, L. Xu, and T. Wang, “Multidimensional LDPC-coded modulation for beyond 400 Gb/s per wavelength transmission,” IEEE Photon. Technol. Lett. 21(16), 1139–1141 (2009).
[CrossRef]

Bourennane, S.

Chen, J.

J. Chen, A. Dholakia, E. Eleftheriou, M. Fossorier, and X.-Y. Hu, “Reduced-complexity decoding of LDPC codes,” IEEE Trans. Commun. 53(8), 1288–1299 (2005).
[CrossRef]

Courtial, J.

G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas’ko, S. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12(22), 5448–5456 (2004).
[CrossRef] [PubMed]

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. 92(1), 013601 (2004).
[CrossRef] [PubMed]

Dholakia, A.

J. Chen, A. Dholakia, E. Eleftheriou, M. Fossorier, and X.-Y. Hu, “Reduced-complexity decoding of LDPC codes,” IEEE Trans. Commun. 53(8), 1288–1299 (2005).
[CrossRef]

Djordjevic, G. T.

Djordjevic, I. B.

I. B. Djordjevic, M. Arabaci, L. Xu, and T. Wang, “Generalized OFDM (GOFDM) for ultra-high-speed optical transmission,” Opt. Express 19(7), 6969–6979 (2011).
[CrossRef] [PubMed]

I. B. Djordjevic, “Orbital angular momentum (OAM) based LDPC-coded deep-space optical communication,” Proc. SPIE 7923, 792306, 792306–792308 (2011) (invited paper).
[CrossRef]

I. B. Djordjevic and M. Arabaci, “LDPC-coded orbital angular momentum (OAM) modulation for free-space optical communication,” Opt. Express 18(24), 24722–24728 (2010).
[CrossRef] [PubMed]

H. G. Batshon and I. B. Djordjevic, “Beyond 240 Gb/s per wavelength optical transmission using coded hybrid subcarrier/amplitude/ phase/polarization modulation,” IEEE Photon. Technol. Lett. 22(5), 299–301 (2010).
[CrossRef]

I. B. Djordjevic and M. Arabaci, “LDPC-coded orbital angular momentum (OAM) modulation for free-space optical communication,” Opt. Express 18(24), 24722–24728 (2010).
[CrossRef] [PubMed]

M. Arabaci, I. B. Djordjevic, R. Saunders, and R. M. Marcoccia, “Polarization-multiplexed rate-adaptive non-binary-quasi-cyclic-LDPC-coded multilevel modulation with coherent detection for optical transport networks,” Opt. Express 18(3), 1820–1832 (2010).
[CrossRef] [PubMed]

I. B. Djordjevic and G. T. Djordjevic, “On the communication over strong atmospheric turbulence channels by adaptive modulation and coding,” Opt. Express 17(20), 18250–18262 (2009).
[CrossRef] [PubMed]

H. G. Batshon, I. B. Djordjevic, L. Xu, and T. Wang, “Multidimensional LDPC-coded modulation for beyond 400 Gb/s per wavelength transmission,” IEEE Photon. Technol. Lett. 21(16), 1139–1141 (2009).
[CrossRef]

I. B. Djordjevic, M. Arabaci, and L. Minkov, “Next generation FEC for high-capacity communication in optical transport networks,” J. Lightwave Technol. 27(16), 3518–3530 (2009).
[CrossRef]

I. B. Djordjevic, L. Xu, and T. Wang, “PMD compensation in multilevel coded-modulation schemes with coherent detection using BLAST algorithm and iterative polarization cancellation,” Opt. Express 16(19), 14845–14852 (2008).
[CrossRef] [PubMed]

Dymale, R. C.

Eleftheriou, E.

J. Chen, A. Dholakia, E. Eleftheriou, M. Fossorier, and X.-Y. Hu, “Reduced-complexity decoding of LDPC codes,” IEEE Trans. Commun. 53(8), 1288–1299 (2005).
[CrossRef]

Fossorier, M.

J. Chen, A. Dholakia, E. Eleftheriou, M. Fossorier, and X.-Y. Hu, “Reduced-complexity decoding of LDPC codes,” IEEE Trans. Commun. 53(8), 1288–1299 (2005).
[CrossRef]

Fossorier, M. P. C.

M. P. C. Fossorier, “Quasi-cyclic low-density parity-check codes from circulant permutation matrices,” IEEE Trans. Inf. Theory 50(8), 1788–1793 (2004).
[CrossRef]

Franke-Arnold, S.

G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas’ko, S. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12(22), 5448–5456 (2004).
[CrossRef] [PubMed]

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. 92(1), 013601 (2004).
[CrossRef] [PubMed]

Gibson, G.

Gruneisen, M. T.

Hemmati, H.

H. Hemmati, “Interplanetary laser communications,” Optics & Photonics News 18(11), 22–27 (2007).
[CrossRef]

Hu, X.-Y.

J. Chen, A. Dholakia, E. Eleftheriou, M. Fossorier, and X.-Y. Hu, “Reduced-complexity decoding of LDPC codes,” IEEE Trans. Commun. 53(8), 1288–1299 (2005).
[CrossRef]

Khalighi, M.-A.

Leach, J.

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. 92(1), 013601 (2004).
[CrossRef] [PubMed]

Marcoccia, R. M.

Miller, W. A.

Minkov, L.

Neifeld, M. A.

Padgett, M.

Padgett, M. J.

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. 92(1), 013601 (2004).
[CrossRef] [PubMed]

Pas’ko, V.

Paterson, C.

C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett. 94(15), 153901 (2005).
[CrossRef] [PubMed]

Saunders, R.

Skeldon, K.

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. 92(1), 013601 (2004).
[CrossRef] [PubMed]

Sweiti, A. M.

Vasic, B. V.

Vasnetsov, M.

Wang, T.

Xu, F.

Xu, L.

Appl. Opt.

IEEE J. Sel. Areas Comm.

S. M. Alamouti, “A simple transmit diversity technique for wireless communications,” IEEE J. Sel. Areas Comm. 16(8), 1451–1458 (1998).
[CrossRef]

IEEE Photon. Technol. Lett.

H. G. Batshon and I. B. Djordjevic, “Beyond 240 Gb/s per wavelength optical transmission using coded hybrid subcarrier/amplitude/ phase/polarization modulation,” IEEE Photon. Technol. Lett. 22(5), 299–301 (2010).
[CrossRef]

H. G. Batshon, I. B. Djordjevic, L. Xu, and T. Wang, “Multidimensional LDPC-coded modulation for beyond 400 Gb/s per wavelength transmission,” IEEE Photon. Technol. Lett. 21(16), 1139–1141 (2009).
[CrossRef]

IEEE Trans. Commun.

J. Chen, A. Dholakia, E. Eleftheriou, M. Fossorier, and X.-Y. Hu, “Reduced-complexity decoding of LDPC codes,” IEEE Trans. Commun. 53(8), 1288–1299 (2005).
[CrossRef]

IEEE Trans. Inf. Theory

M. P. C. Fossorier, “Quasi-cyclic low-density parity-check codes from circulant permutation matrices,” IEEE Trans. Inf. Theory 50(8), 1788–1793 (2004).
[CrossRef]

J. Lightwave Technol.

J. Opt. Commun. Netw.

Opt. Express

I. B. Djordjevic and M. Arabaci, “LDPC-coded orbital angular momentum (OAM) modulation for free-space optical communication,” Opt. Express 18(24), 24722–24728 (2010).
[CrossRef] [PubMed]

I. B. Djordjevic and M. Arabaci, “LDPC-coded orbital angular momentum (OAM) modulation for free-space optical communication,” Opt. Express 18(24), 24722–24728 (2010).
[CrossRef] [PubMed]

G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas’ko, S. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12(22), 5448–5456 (2004).
[CrossRef] [PubMed]

I. B. Djordjevic, M. Arabaci, L. Xu, and T. Wang, “Generalized OFDM (GOFDM) for ultra-high-speed optical transmission,” Opt. Express 19(7), 6969–6979 (2011).
[CrossRef] [PubMed]

I. B. Djordjevic, L. Xu, and T. Wang, “PMD compensation in multilevel coded-modulation schemes with coherent detection using BLAST algorithm and iterative polarization cancellation,” Opt. Express 16(19), 14845–14852 (2008).
[CrossRef] [PubMed]

I. B. Djordjevic and G. T. Djordjevic, “On the communication over strong atmospheric turbulence channels by adaptive modulation and coding,” Opt. Express 17(20), 18250–18262 (2009).
[CrossRef] [PubMed]

M. Arabaci, I. B. Djordjevic, R. Saunders, and R. M. Marcoccia, “Polarization-multiplexed rate-adaptive non-binary-quasi-cyclic-LDPC-coded multilevel modulation with coherent detection for optical transport networks,” Opt. Express 18(3), 1820–1832 (2010).
[CrossRef] [PubMed]

Optics & Photonics News

H. Hemmati, “Interplanetary laser communications,” Optics & Photonics News 18(11), 22–27 (2007).
[CrossRef]

Phys. Rev. Lett.

C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett. 94(15), 153901 (2005).
[CrossRef] [PubMed]

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. 92(1), 013601 (2004).
[CrossRef] [PubMed]

Proc. SPIE

I. B. Djordjevic, “Orbital angular momentum (OAM) based LDPC-coded deep-space optical communication,” Proc. SPIE 7923, 792306, 792306–792308 (2011) (invited paper).
[CrossRef]

Other

L. C. Andrews and R. L. Philips, Laser Beam Propagation through Random Media (SPIE Press, 2005).

S. J. Dolinar, J. Hamkins, B. E. Moision, and V. A. Vilnrotter, “Optical modulation and coding,” in Deep Space Optical Communications, H. Hemmati, ed. (Wile, 2006), pp. 215–299.

B. Moision and J. Hamkins, “Deep-space optical communications downlink budget: modulation and coding,“ The Interplanetary Network Progress Report 42-154, April-June 2003 (Jet Propulsion Laboratory, Pasadena, California, 15 August 2003), pp. 1-28, http://ipnpr.jpl.nasa.gov/progress_report/42-154/154K.pdf .

B. Moision and J. Hamkins, “Coded modulation for the deep-space optical channel: serially concatenated pulse-position modulation,“ The Interplanetary Network Progress Report 42-161 (Jet Propulsion Laboratory, Pasadena, California, 15 May 2005), pp. 1-25, http://ipnpr.jpl.nasa.gov/progress_report/42-161/161T.pdf .

J. D. Jackson, Classical Electrodynamics (Wiley, 1975).

S. Lin and D. J. Costello, Error Control Coding: Fundamentals and Applications (Prentice Hall, 2004).

I. B. Djordjevic, “Adaptive modulation and coding for communication over the atmospheric turbulence channels,” in Proceedings of IEEE Photonics Society Summer Topicals (IEEE, 2009), paper TuD3.3.

J. G. Proakis, Digital Communication (McGraw Hill, 2001).

I. B. Djordjevic and H. G. Batshon, “Generalized hybrid subcarrier/amplitude/phase/polarization LDPC-coded modulation based FSO Networking,” in Proceedings of IEEE 12th International Conference on Transparent Optical Networks (ICTON 2010) (IEEE, 2010), paper Th.B3.4.

W. Shieh and I. B. Djordjevic, OFDM for Optical Communications (Elsevier/Academic Press, 2009).

A. Goldsmith, Wireless Communications (Cambridge University Press, 2005).

D. Tse and P. Viswanath, Fundamentals of Wireless Communication (Cambridge University Press, 2005).

T. M. Duman and A. Ghrayeb, Coding for MIMO Communication Systems (Wiley, 2007).

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Figures (7)

Fig. 1
Fig. 1

Multidimensional LDPC-coded OAM modulation scheme: (a) intensity spatial distribution for p = 0, (b) MMF-based mode-multiplexer and N-dimensional transmitter configurations, (c) MMF-based N-dimensional OAM receiver, (d) overall transmitter architecture and (e) overall receiver architecture. MZM: Mach-Zehnder modulator, MMF: multimode fiber, PD: photodetector, APP: a posteriori probability, LLRs: log-likelihood ratios.

Fig. 2
Fig. 2

Coherent detection based OAM modulation: (a) two-dimensional modulator, (b) four-dimensional modulator and (c) coherent receiver architecture (corresponding to one-dimensional modulators).

Fig. 3
Fig. 3

Deep-space optical communication by orthogonal OAM division multiplexing: (a) transmitter and (b) receiver configurations.

Fig. 4
Fig. 4

LDPC(15120,7560)-coded ND-OAM modulation versus PPM.

Fig. 6
Fig. 6

LDPC(15120,7560)-coded ND-OAM modulation in strong turbulence regime (σR = 2).

Fig. 5
Fig. 5

LDPC(15120,7560)-coded ND-OAM modulation in medium turbulence regime (σR = 1).

Fig. 7
Fig. 7

BER performance of LDPC(4320,3242)-coded OAM modulation based FSO systems in weak (σR = 0.3), medium (σR = 1) and strong (σR = 2) turbulence regimes.

Equations (20)

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

L = 1 4 π c V E × A d V + 1 4 π c V k = x , y , z E k ( r × ) A k d V ,
u l , p ( r , ϕ , z ) = 2 p ! π ( p + | l | ) ! 1 w ( z ) [ r 2 w ( z ) ] | l | L p l ( 2 r 2 w 2 ( z ) ) e r 2 w 2 ( z ) e j k r 2 z 2 ( z 2 + z R 2 ) e j ( 2 p + | l | + 1 ) tan 1 z z R e j l ϕ ,
( u m , p , u n , p ) = u m , p * ( r , ϕ , z ) u n , p ( r , ϕ , z ) r d r d ϕ = { | u m , p | 2 r d r d ϕ ,     n = m 0 ,       n m
s i = C N j = 1 N φ i , j Φ j ;     i = 1 , 2 , , M N
S i = [ S i ( L )     S i ( L + 1 ) S i ( 1 )     S i ( 0 )     S i ( 1 )         S i ( L ) ] T
λ ( S i ) = log [ P ( S i | R i ) P ( S 0 | R i ) ] ,
P ( S i | R i ) = P ( R i | S i ) P ( S i ) S P ( R i | S i ) P ( S i ) .
λ ( S i ) = log [ P ( R i | S i ) P ( S i ) P ( R i | S 0 ) P ( S 0 ) ] = log [ P ( R i | S i ) P ( R i | S 0 ) ] + log [ P ( S i ) P ( S 0 ) ] = log [ P ( R i | S i ) P ( R i | S 0 ) ] + λ a ( S i ) ,    
λ a ( S ) = log P ( S 0 ) P ( S i ) = log j = 0 b 1 P ( c j = 0 ) j = 0 b 1 P ( c j ) = j = 0 b 1 log P ( c j = 0 ) P ( c j ) .
log P ( c j = 0 ) P ( c j ) = { 0 ,       c j = 0 L ( c j ) ,     c j = 1 = c j L ( c j ) ,
λ a ( s ) = j = 1 b c j L ( c j ) .
λ a ( s ^ ) = j = 1 b c j L D , e ( c j ) ,
L D , e ( c ^ j ) = L ( c j ( o u t ) ) L ( c j ( i n ) ) .
L ( c ^ j ) = log c : c j = 0 exp [ λ ( S ) ] exp ( c : c k = 0 , k j L a ( c k ) ) c : c j = 1 exp [ λ ( S ) ] exp ( c : c k = 0 , k j L a ( c k ) ) .
y = H x + w ,       H = [ h 11 h 12 ... h 1 , N h 21 h 22 ... h 2 , N , ... ... ... ... h N , 1 h N , 2 ... h N , N ] ,        
y i = j = 1 N h i , j x j + w i ;         i = 1 , 2 , , N
Y = H X + W ,
Y = [ y 1 , y 2 , ... , y N s ] = ( Y i j ) N × N s , X = [ x 1 , x 2 , ... , x N s ] = ( X i j ) N × N s                                                                     W = [ w 1 , w 2 , ... , w N s ] = ( W i j ) N × N s
X ^ = arg min X X N × N s i = 1 N s y i H x i 2 ,
S E , ND - OAM S E , PPM = log 2 2 N / ( 1 / T s ) log 2 M / ( M / T s ) = N log 2 M / M

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