Abstract

Modeling of the complex atmospheric propagation of deep-ultraviolet (UV) radiation is important for applications such as non-line-of-sight (NLOS) UV communications. Building upon prior work in which it was observed that short-range, singly scattered NLOS path loss varies linearly with range, we formalize this relationship, generalizing it to consider any order of scattering and more-general system characteristics. In particular, we derive the approximate relationship PLr2n between path loss PL and range r for nth-order scattered radiation, and investigate the region of validity of this approximation. Insight arising from the analysis can be invaluable in the development and study of UV systems, as demonstrated by numerical results that illustrate implications of the analysis.

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  1. M. Shatalov, J. Zhang, A. S. Chitnis, V. Adivarahan, J. Yang, G. Simin, and M. A. Khan, “Deep ultraviolet light-emitting diodes using quaternary AlInGaN multiple quantum wells,” IEEE J. Sel. Top. Quantum Electron. 8, 302–309 (2002).
    [CrossRef]
  2. V. Adivarahan, W. Fareed, S. Srivastava, T. Katona, M. Gaevski, and A. Khan, “Robust 285  nm deep UV light emitting diodes over metal organic hydride vapor phase epitaxially grown AIN/sapphire templates,” Jpn J. Appl. Phys. 46, L537–L579 (2007).
  3. S.-C. Shen, Y. Zhang, D. Yoo, J.-B. Limb, J.-H. Ryou, P. D. Yoder, and R. D. Dupuis, “Performance of deep ultraviolet GaN avalance photodiodes grown by MOCVD,” IEEE Photon. Technol. Lett. 19, 1744–1746 (2007).
    [CrossRef]
  4. M. S. Shur and R. Gaska, “Deep-ultraviolet light-emitting diodes,” IEEE Trans. Electron Devices 57, 12–25 (2010).
    [CrossRef]
  5. Z. Xu and B. M. Sadler, “Ultraviolet communications: potential and state-of-the-art,” IEEE Commun. Mag. 46(5), 67–73 (2008).
  6. A. M. Siegel, G. A. Shaw, and J. Model, “Short-range communication with ultraviolet LEDs,” Proc. SPIE 5530, 182–193 (2004).
  7. Z. Xu, “Approximate performance analysis of wireless ultraviolet links,” in IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE, 2007), pp. 577–580.
  8. D. M. Reilly, “Temporal characteristics of single-scatter radiation,” J. Opt. Soc. Am. 69, 464–470 (1979).
    [CrossRef]
  9. M. R. Luettgen, J. H. Shapiro, and D. M. Reilly, “Non-line-of-sight single-scatter propagation model,” J. Opt. Soc. Am. A 8, 1964–1972 (1991).
    [CrossRef]
  10. R. J. Drost, T. J. Moore, and B. M. Sadler, “UV communications channel modeling incorporating multiple scattering interactions,” J. Opt. Soc. Am. A 28, 686–695 (2011).
    [CrossRef]
  11. H. Ding, Z. Xu, and B. M. Sadler, “A path loss model for non-line-of-sight ultraviolet multiple scattering channels,” EURASIP J. Wireless Commun. Netw. 2010, 598572 (2010).
    [CrossRef]
  12. G. A. Shaw, A. M. Siegel, and J. Model, “Extending the range and performance of non-line-of-sight ultraviolet communication links,” Proc. SPIE 6231, 93–104 (2006).
  13. G. Chen, Z. Xu, H. Ding, and B. M. Sadler, “Path loss modeling and performance trade-off study for short-range non-line-of-sight ultraviolet communications,” Opt. Express 17, 3929–3940 (2009).
    [CrossRef]
  14. G. A. Shaw, A. M. Siegel, J. Model, and M. Nischan, “Field testing and evaluation of a solar-blind UV communication link for unattended ground sensors,” Proc. SPIE 5417, 250–261 (2004).
  15. R. J. Drost, T. J. Moore, and B. M. Sadler, “Monte-Carlo-based multiple-scattering channel modeling for non-line-of-sight ultraviolet communications,” Proc. SPIE 8038, 803802 (2011).
  16. H. Ding, G. Chen, Z. Xu, and B. M. Sadler, “Characterization and modeling of non-line-of-sight ultraviolet scattering communication channels,” in 2010 7th International Symposium on Communication Systems Networks and Digital Signal Processing (IEEE, 2010), pp. 593–597.
  17. R. M. Gagliardi and S. Karp, Optical Communications, 2nd ed. (Wiley-Interscience, 1995), pp. 181–185.

2011

R. J. Drost, T. J. Moore, and B. M. Sadler, “Monte-Carlo-based multiple-scattering channel modeling for non-line-of-sight ultraviolet communications,” Proc. SPIE 8038, 803802 (2011).

R. J. Drost, T. J. Moore, and B. M. Sadler, “UV communications channel modeling incorporating multiple scattering interactions,” J. Opt. Soc. Am. A 28, 686–695 (2011).
[CrossRef]

2010

H. Ding, Z. Xu, and B. M. Sadler, “A path loss model for non-line-of-sight ultraviolet multiple scattering channels,” EURASIP J. Wireless Commun. Netw. 2010, 598572 (2010).
[CrossRef]

M. S. Shur and R. Gaska, “Deep-ultraviolet light-emitting diodes,” IEEE Trans. Electron Devices 57, 12–25 (2010).
[CrossRef]

2009

2008

Z. Xu and B. M. Sadler, “Ultraviolet communications: potential and state-of-the-art,” IEEE Commun. Mag. 46(5), 67–73 (2008).

2007

V. Adivarahan, W. Fareed, S. Srivastava, T. Katona, M. Gaevski, and A. Khan, “Robust 285  nm deep UV light emitting diodes over metal organic hydride vapor phase epitaxially grown AIN/sapphire templates,” Jpn J. Appl. Phys. 46, L537–L579 (2007).

S.-C. Shen, Y. Zhang, D. Yoo, J.-B. Limb, J.-H. Ryou, P. D. Yoder, and R. D. Dupuis, “Performance of deep ultraviolet GaN avalance photodiodes grown by MOCVD,” IEEE Photon. Technol. Lett. 19, 1744–1746 (2007).
[CrossRef]

2006

G. A. Shaw, A. M. Siegel, and J. Model, “Extending the range and performance of non-line-of-sight ultraviolet communication links,” Proc. SPIE 6231, 93–104 (2006).

2004

G. A. Shaw, A. M. Siegel, J. Model, and M. Nischan, “Field testing and evaluation of a solar-blind UV communication link for unattended ground sensors,” Proc. SPIE 5417, 250–261 (2004).

A. M. Siegel, G. A. Shaw, and J. Model, “Short-range communication with ultraviolet LEDs,” Proc. SPIE 5530, 182–193 (2004).

2002

M. Shatalov, J. Zhang, A. S. Chitnis, V. Adivarahan, J. Yang, G. Simin, and M. A. Khan, “Deep ultraviolet light-emitting diodes using quaternary AlInGaN multiple quantum wells,” IEEE J. Sel. Top. Quantum Electron. 8, 302–309 (2002).
[CrossRef]

1991

1979

Adivarahan, V.

V. Adivarahan, W. Fareed, S. Srivastava, T. Katona, M. Gaevski, and A. Khan, “Robust 285  nm deep UV light emitting diodes over metal organic hydride vapor phase epitaxially grown AIN/sapphire templates,” Jpn J. Appl. Phys. 46, L537–L579 (2007).

M. Shatalov, J. Zhang, A. S. Chitnis, V. Adivarahan, J. Yang, G. Simin, and M. A. Khan, “Deep ultraviolet light-emitting diodes using quaternary AlInGaN multiple quantum wells,” IEEE J. Sel. Top. Quantum Electron. 8, 302–309 (2002).
[CrossRef]

Chen, G.

G. Chen, Z. Xu, H. Ding, and B. M. Sadler, “Path loss modeling and performance trade-off study for short-range non-line-of-sight ultraviolet communications,” Opt. Express 17, 3929–3940 (2009).
[CrossRef]

H. Ding, G. Chen, Z. Xu, and B. M. Sadler, “Characterization and modeling of non-line-of-sight ultraviolet scattering communication channels,” in 2010 7th International Symposium on Communication Systems Networks and Digital Signal Processing (IEEE, 2010), pp. 593–597.

Chitnis, A. S.

M. Shatalov, J. Zhang, A. S. Chitnis, V. Adivarahan, J. Yang, G. Simin, and M. A. Khan, “Deep ultraviolet light-emitting diodes using quaternary AlInGaN multiple quantum wells,” IEEE J. Sel. Top. Quantum Electron. 8, 302–309 (2002).
[CrossRef]

Ding, H.

H. Ding, Z. Xu, and B. M. Sadler, “A path loss model for non-line-of-sight ultraviolet multiple scattering channels,” EURASIP J. Wireless Commun. Netw. 2010, 598572 (2010).
[CrossRef]

G. Chen, Z. Xu, H. Ding, and B. M. Sadler, “Path loss modeling and performance trade-off study for short-range non-line-of-sight ultraviolet communications,” Opt. Express 17, 3929–3940 (2009).
[CrossRef]

H. Ding, G. Chen, Z. Xu, and B. M. Sadler, “Characterization and modeling of non-line-of-sight ultraviolet scattering communication channels,” in 2010 7th International Symposium on Communication Systems Networks and Digital Signal Processing (IEEE, 2010), pp. 593–597.

Drost, R. J.

R. J. Drost, T. J. Moore, and B. M. Sadler, “Monte-Carlo-based multiple-scattering channel modeling for non-line-of-sight ultraviolet communications,” Proc. SPIE 8038, 803802 (2011).

R. J. Drost, T. J. Moore, and B. M. Sadler, “UV communications channel modeling incorporating multiple scattering interactions,” J. Opt. Soc. Am. A 28, 686–695 (2011).
[CrossRef]

Dupuis, R. D.

S.-C. Shen, Y. Zhang, D. Yoo, J.-B. Limb, J.-H. Ryou, P. D. Yoder, and R. D. Dupuis, “Performance of deep ultraviolet GaN avalance photodiodes grown by MOCVD,” IEEE Photon. Technol. Lett. 19, 1744–1746 (2007).
[CrossRef]

Fareed, W.

V. Adivarahan, W. Fareed, S. Srivastava, T. Katona, M. Gaevski, and A. Khan, “Robust 285  nm deep UV light emitting diodes over metal organic hydride vapor phase epitaxially grown AIN/sapphire templates,” Jpn J. Appl. Phys. 46, L537–L579 (2007).

Gaevski, M.

V. Adivarahan, W. Fareed, S. Srivastava, T. Katona, M. Gaevski, and A. Khan, “Robust 285  nm deep UV light emitting diodes over metal organic hydride vapor phase epitaxially grown AIN/sapphire templates,” Jpn J. Appl. Phys. 46, L537–L579 (2007).

Gagliardi, R. M.

R. M. Gagliardi and S. Karp, Optical Communications, 2nd ed. (Wiley-Interscience, 1995), pp. 181–185.

Gaska, R.

M. S. Shur and R. Gaska, “Deep-ultraviolet light-emitting diodes,” IEEE Trans. Electron Devices 57, 12–25 (2010).
[CrossRef]

Karp, S.

R. M. Gagliardi and S. Karp, Optical Communications, 2nd ed. (Wiley-Interscience, 1995), pp. 181–185.

Katona, T.

V. Adivarahan, W. Fareed, S. Srivastava, T. Katona, M. Gaevski, and A. Khan, “Robust 285  nm deep UV light emitting diodes over metal organic hydride vapor phase epitaxially grown AIN/sapphire templates,” Jpn J. Appl. Phys. 46, L537–L579 (2007).

Khan, A.

V. Adivarahan, W. Fareed, S. Srivastava, T. Katona, M. Gaevski, and A. Khan, “Robust 285  nm deep UV light emitting diodes over metal organic hydride vapor phase epitaxially grown AIN/sapphire templates,” Jpn J. Appl. Phys. 46, L537–L579 (2007).

Khan, M. A.

M. Shatalov, J. Zhang, A. S. Chitnis, V. Adivarahan, J. Yang, G. Simin, and M. A. Khan, “Deep ultraviolet light-emitting diodes using quaternary AlInGaN multiple quantum wells,” IEEE J. Sel. Top. Quantum Electron. 8, 302–309 (2002).
[CrossRef]

Limb, J.-B.

S.-C. Shen, Y. Zhang, D. Yoo, J.-B. Limb, J.-H. Ryou, P. D. Yoder, and R. D. Dupuis, “Performance of deep ultraviolet GaN avalance photodiodes grown by MOCVD,” IEEE Photon. Technol. Lett. 19, 1744–1746 (2007).
[CrossRef]

Luettgen, M. R.

Model, J.

G. A. Shaw, A. M. Siegel, and J. Model, “Extending the range and performance of non-line-of-sight ultraviolet communication links,” Proc. SPIE 6231, 93–104 (2006).

A. M. Siegel, G. A. Shaw, and J. Model, “Short-range communication with ultraviolet LEDs,” Proc. SPIE 5530, 182–193 (2004).

G. A. Shaw, A. M. Siegel, J. Model, and M. Nischan, “Field testing and evaluation of a solar-blind UV communication link for unattended ground sensors,” Proc. SPIE 5417, 250–261 (2004).

Moore, T. J.

R. J. Drost, T. J. Moore, and B. M. Sadler, “Monte-Carlo-based multiple-scattering channel modeling for non-line-of-sight ultraviolet communications,” Proc. SPIE 8038, 803802 (2011).

R. J. Drost, T. J. Moore, and B. M. Sadler, “UV communications channel modeling incorporating multiple scattering interactions,” J. Opt. Soc. Am. A 28, 686–695 (2011).
[CrossRef]

Nischan, M.

G. A. Shaw, A. M. Siegel, J. Model, and M. Nischan, “Field testing and evaluation of a solar-blind UV communication link for unattended ground sensors,” Proc. SPIE 5417, 250–261 (2004).

Reilly, D. M.

Ryou, J.-H.

S.-C. Shen, Y. Zhang, D. Yoo, J.-B. Limb, J.-H. Ryou, P. D. Yoder, and R. D. Dupuis, “Performance of deep ultraviolet GaN avalance photodiodes grown by MOCVD,” IEEE Photon. Technol. Lett. 19, 1744–1746 (2007).
[CrossRef]

Sadler, B. M.

R. J. Drost, T. J. Moore, and B. M. Sadler, “Monte-Carlo-based multiple-scattering channel modeling for non-line-of-sight ultraviolet communications,” Proc. SPIE 8038, 803802 (2011).

R. J. Drost, T. J. Moore, and B. M. Sadler, “UV communications channel modeling incorporating multiple scattering interactions,” J. Opt. Soc. Am. A 28, 686–695 (2011).
[CrossRef]

H. Ding, Z. Xu, and B. M. Sadler, “A path loss model for non-line-of-sight ultraviolet multiple scattering channels,” EURASIP J. Wireless Commun. Netw. 2010, 598572 (2010).
[CrossRef]

G. Chen, Z. Xu, H. Ding, and B. M. Sadler, “Path loss modeling and performance trade-off study for short-range non-line-of-sight ultraviolet communications,” Opt. Express 17, 3929–3940 (2009).
[CrossRef]

Z. Xu and B. M. Sadler, “Ultraviolet communications: potential and state-of-the-art,” IEEE Commun. Mag. 46(5), 67–73 (2008).

H. Ding, G. Chen, Z. Xu, and B. M. Sadler, “Characterization and modeling of non-line-of-sight ultraviolet scattering communication channels,” in 2010 7th International Symposium on Communication Systems Networks and Digital Signal Processing (IEEE, 2010), pp. 593–597.

Shapiro, J. H.

Shatalov, M.

M. Shatalov, J. Zhang, A. S. Chitnis, V. Adivarahan, J. Yang, G. Simin, and M. A. Khan, “Deep ultraviolet light-emitting diodes using quaternary AlInGaN multiple quantum wells,” IEEE J. Sel. Top. Quantum Electron. 8, 302–309 (2002).
[CrossRef]

Shaw, G. A.

G. A. Shaw, A. M. Siegel, and J. Model, “Extending the range and performance of non-line-of-sight ultraviolet communication links,” Proc. SPIE 6231, 93–104 (2006).

G. A. Shaw, A. M. Siegel, J. Model, and M. Nischan, “Field testing and evaluation of a solar-blind UV communication link for unattended ground sensors,” Proc. SPIE 5417, 250–261 (2004).

A. M. Siegel, G. A. Shaw, and J. Model, “Short-range communication with ultraviolet LEDs,” Proc. SPIE 5530, 182–193 (2004).

Shen, S.-C.

S.-C. Shen, Y. Zhang, D. Yoo, J.-B. Limb, J.-H. Ryou, P. D. Yoder, and R. D. Dupuis, “Performance of deep ultraviolet GaN avalance photodiodes grown by MOCVD,” IEEE Photon. Technol. Lett. 19, 1744–1746 (2007).
[CrossRef]

Shur, M. S.

M. S. Shur and R. Gaska, “Deep-ultraviolet light-emitting diodes,” IEEE Trans. Electron Devices 57, 12–25 (2010).
[CrossRef]

Siegel, A. M.

G. A. Shaw, A. M. Siegel, and J. Model, “Extending the range and performance of non-line-of-sight ultraviolet communication links,” Proc. SPIE 6231, 93–104 (2006).

G. A. Shaw, A. M. Siegel, J. Model, and M. Nischan, “Field testing and evaluation of a solar-blind UV communication link for unattended ground sensors,” Proc. SPIE 5417, 250–261 (2004).

A. M. Siegel, G. A. Shaw, and J. Model, “Short-range communication with ultraviolet LEDs,” Proc. SPIE 5530, 182–193 (2004).

Simin, G.

M. Shatalov, J. Zhang, A. S. Chitnis, V. Adivarahan, J. Yang, G. Simin, and M. A. Khan, “Deep ultraviolet light-emitting diodes using quaternary AlInGaN multiple quantum wells,” IEEE J. Sel. Top. Quantum Electron. 8, 302–309 (2002).
[CrossRef]

Srivastava, S.

V. Adivarahan, W. Fareed, S. Srivastava, T. Katona, M. Gaevski, and A. Khan, “Robust 285  nm deep UV light emitting diodes over metal organic hydride vapor phase epitaxially grown AIN/sapphire templates,” Jpn J. Appl. Phys. 46, L537–L579 (2007).

Xu, Z.

H. Ding, Z. Xu, and B. M. Sadler, “A path loss model for non-line-of-sight ultraviolet multiple scattering channels,” EURASIP J. Wireless Commun. Netw. 2010, 598572 (2010).
[CrossRef]

G. Chen, Z. Xu, H. Ding, and B. M. Sadler, “Path loss modeling and performance trade-off study for short-range non-line-of-sight ultraviolet communications,” Opt. Express 17, 3929–3940 (2009).
[CrossRef]

Z. Xu and B. M. Sadler, “Ultraviolet communications: potential and state-of-the-art,” IEEE Commun. Mag. 46(5), 67–73 (2008).

Z. Xu, “Approximate performance analysis of wireless ultraviolet links,” in IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE, 2007), pp. 577–580.

H. Ding, G. Chen, Z. Xu, and B. M. Sadler, “Characterization and modeling of non-line-of-sight ultraviolet scattering communication channels,” in 2010 7th International Symposium on Communication Systems Networks and Digital Signal Processing (IEEE, 2010), pp. 593–597.

Yang, J.

M. Shatalov, J. Zhang, A. S. Chitnis, V. Adivarahan, J. Yang, G. Simin, and M. A. Khan, “Deep ultraviolet light-emitting diodes using quaternary AlInGaN multiple quantum wells,” IEEE J. Sel. Top. Quantum Electron. 8, 302–309 (2002).
[CrossRef]

Yoder, P. D.

S.-C. Shen, Y. Zhang, D. Yoo, J.-B. Limb, J.-H. Ryou, P. D. Yoder, and R. D. Dupuis, “Performance of deep ultraviolet GaN avalance photodiodes grown by MOCVD,” IEEE Photon. Technol. Lett. 19, 1744–1746 (2007).
[CrossRef]

Yoo, D.

S.-C. Shen, Y. Zhang, D. Yoo, J.-B. Limb, J.-H. Ryou, P. D. Yoder, and R. D. Dupuis, “Performance of deep ultraviolet GaN avalance photodiodes grown by MOCVD,” IEEE Photon. Technol. Lett. 19, 1744–1746 (2007).
[CrossRef]

Zhang, J.

M. Shatalov, J. Zhang, A. S. Chitnis, V. Adivarahan, J. Yang, G. Simin, and M. A. Khan, “Deep ultraviolet light-emitting diodes using quaternary AlInGaN multiple quantum wells,” IEEE J. Sel. Top. Quantum Electron. 8, 302–309 (2002).
[CrossRef]

Zhang, Y.

S.-C. Shen, Y. Zhang, D. Yoo, J.-B. Limb, J.-H. Ryou, P. D. Yoder, and R. D. Dupuis, “Performance of deep ultraviolet GaN avalance photodiodes grown by MOCVD,” IEEE Photon. Technol. Lett. 19, 1744–1746 (2007).
[CrossRef]

EURASIP J. Wireless Commun. Netw.

H. Ding, Z. Xu, and B. M. Sadler, “A path loss model for non-line-of-sight ultraviolet multiple scattering channels,” EURASIP J. Wireless Commun. Netw. 2010, 598572 (2010).
[CrossRef]

IEEE Commun. Mag.

Z. Xu and B. M. Sadler, “Ultraviolet communications: potential and state-of-the-art,” IEEE Commun. Mag. 46(5), 67–73 (2008).

IEEE J. Sel. Top. Quantum Electron.

M. Shatalov, J. Zhang, A. S. Chitnis, V. Adivarahan, J. Yang, G. Simin, and M. A. Khan, “Deep ultraviolet light-emitting diodes using quaternary AlInGaN multiple quantum wells,” IEEE J. Sel. Top. Quantum Electron. 8, 302–309 (2002).
[CrossRef]

IEEE Photon. Technol. Lett.

S.-C. Shen, Y. Zhang, D. Yoo, J.-B. Limb, J.-H. Ryou, P. D. Yoder, and R. D. Dupuis, “Performance of deep ultraviolet GaN avalance photodiodes grown by MOCVD,” IEEE Photon. Technol. Lett. 19, 1744–1746 (2007).
[CrossRef]

IEEE Trans. Electron Devices

M. S. Shur and R. Gaska, “Deep-ultraviolet light-emitting diodes,” IEEE Trans. Electron Devices 57, 12–25 (2010).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Jpn J. Appl. Phys.

V. Adivarahan, W. Fareed, S. Srivastava, T. Katona, M. Gaevski, and A. Khan, “Robust 285  nm deep UV light emitting diodes over metal organic hydride vapor phase epitaxially grown AIN/sapphire templates,” Jpn J. Appl. Phys. 46, L537–L579 (2007).

Opt. Express

Proc. SPIE

A. M. Siegel, G. A. Shaw, and J. Model, “Short-range communication with ultraviolet LEDs,” Proc. SPIE 5530, 182–193 (2004).

G. A. Shaw, A. M. Siegel, and J. Model, “Extending the range and performance of non-line-of-sight ultraviolet communication links,” Proc. SPIE 6231, 93–104 (2006).

G. A. Shaw, A. M. Siegel, J. Model, and M. Nischan, “Field testing and evaluation of a solar-blind UV communication link for unattended ground sensors,” Proc. SPIE 5417, 250–261 (2004).

R. J. Drost, T. J. Moore, and B. M. Sadler, “Monte-Carlo-based multiple-scattering channel modeling for non-line-of-sight ultraviolet communications,” Proc. SPIE 8038, 803802 (2011).

Other

H. Ding, G. Chen, Z. Xu, and B. M. Sadler, “Characterization and modeling of non-line-of-sight ultraviolet scattering communication channels,” in 2010 7th International Symposium on Communication Systems Networks and Digital Signal Processing (IEEE, 2010), pp. 593–597.

R. M. Gagliardi and S. Karp, Optical Communications, 2nd ed. (Wiley-Interscience, 1995), pp. 181–185.

Z. Xu, “Approximate performance analysis of wireless ultraviolet links,” in IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE, 2007), pp. 577–580.

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Figures (3)

Fig. 1.
Fig. 1.

Illustration of a planar propagation path.

Fig. 2.
Fig. 2.

Path-loss model predictions by scattering order n for three scenarios, with Monte Carlo evaluations depicted by solid lines and short-range approximations depicted by dotted lines.

Fig. 3.
Fig. 3.

Achievable communication rate as a function of range and transmitter elevation angle, where curves with filled-circle markers (“ALL”) consider all received photons and curves with open-circle markers (“NLOS”) consider only scattered photons.

Tables (1)

Tables Icon

Table 1. Parameters of Scenarios Considered in Fig. 2

Equations (20)

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

SRps(αn,ψn)ekernfR(αn+1,ψn+1)sinαndαndψn,
Pn(r)=P[i=0nfi(αi,ψi)ekeri]ksn×fR(αn+1,ψn+1)1rn2AR[i=0n1sinαidridαidψi],
P(r)n=0Pn(r).
PLn(r)=1/Pn(r)
PL(r)=1/P(r).
Pn(r)=P¯[i=0nfi(α¯i,ψ¯i)ekeρr¯i]ksn×fR(α¯n+1,ψ¯n+1)1ρ2r¯n2AR[i=0n1sinα¯iρdr¯idα¯idψ¯i]ρn2P¯[i=0nfi(α¯i,ψ¯i)eker¯i]ksn×fR(α¯n+1,ψ¯n+1)1r¯n2AR[i=0n1sinα¯idr¯idα¯idψ¯i]=ρn2Pn(r¯)=rn2[Pn(r¯)/r¯n2],
ke(ρ1)ř0.
r[0,rmax]|10log10[P^r¯,0(r)]10log10[P0(r)]|ϵ
rmax=ϵke·ln105.
fT(α,ψ)=CTx[1u(αβT/2)]
fR(α,ψ)=CRx[1u(αβR/2)],
řmin=r¯sin(αTβT/2)+sin(αRβR/2)sin(αTβT/2+αRβR/2)
řmax=r¯sin(αT+βT/2)+sin(αR+βR/2)sin(αT+βT/2+αR+βR/2),
ekeřmax(1ρ)P^r¯,1(ρr¯)/P1(ρr¯)ekeřmin(1ρ)
ekeřmin(1ρ)P^r¯,1(ρr¯)/P1(ρr¯)ekeřmax(1ρ)
|10log10[P^r¯,1(r)]10log10[P1(r)]|ϵ.
|10log10[P^r¯,1(r)]10log10[P1(r)]|>ϵ.
ϵkeCmax·ln105rmaxϵkeCmin·ln105.
PLn=10log10Pn(r)dB,
BER=[Fλ1+λn(τ)+1Fλn(τ)]/2,

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