Abstract

A universal non-line-of-sight (NLOS) ultraviolet single-scatter propagation model in noncoplanar geometry is proposed to generalize an existing restricted analytical model. This generalized model considers that the transmitter and the receiver cone axes lie in the same plane or different planes, where they can be pointed in arbitrary directions. The model is verified by extensive simulations, showing that the proposed model is consistent with the original NLOS single-scatter propagation model and the Monte Carlo model. The path loss performance is further investigated in terms of different noncoplanar geometric settings and path loss dependence is also analyzed for different factors, including scattering volume size, relative position between the scattering volume and the transceiver, and radiation intensity of the transmitter.

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References

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  1. Z. Xu and B. M. Sadler, “Ultraviolet communication: potential and state-of-art,” IEEE Commun. Mag. 46(5), 67–73 (2008).
    [CrossRef]
  2. M. R. Luettgen, J. H. Shapiro, and D. M. Reilly, “Non-line-of-sight single-scatter propagation model,” J. Opt. Soc. A  8(12), 1964–1972 (1991).
    [CrossRef]
  3. D. M. Reilly and C. Warde, “Temporal characteristics of single-scatter radiation,” J. Opt. Soc. A 69(3), 464–470 (1979).
    [CrossRef]
  4. Z. Xu, “Approximate performance analysis of wireless ultraviolet links,” in Proc. IEEE Intl. Conf. on Acoustics, Speech, and Signal Proc. (IEEE, Honolulu, 2007).
  5. Z. Xu, H. Ding, B. M. Sadler, and G. Chen, “Analytical performance study of solar blind non-line-of-sight ultraviolet short-range communication links,” Opt. Lett. 33(16), 1860–1862 (2008).
    [CrossRef] [PubMed]
  6. H. Yin, S. Chang, X. Wang, J. Yang, J. Yang, and J. Tan, “Analytical model of non-line-of-sight single-scatter propagation,” J. Opt. Soc. Am. A 27(7), 1505–1509 (2010).
    [CrossRef] [PubMed]
  7. G. Chen, Z. Xu, H. Ding, and B. Sadler, “Path loss modeling and performance trade-off study for short-range non-line-of-sight ultraviolet communications,” Opt. Express 17(5), 3929–3940 (2009).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  9. L. Wang, Z. Xu, and B. M. Sadler, “An approximate closed-form link loss model for non-line-of-sight ultraviolet communication in noncoplanar geometry,” Opt. Lett. 36(7), 1224–1226 (2011).
    [CrossRef] [PubMed]
  10. G. A. Shaw, M. Nischan, M. Iyengar, and et al.., “NLOS UV Communication for Distributed Sensor Systems,” Proc. SPIE 4126, 83–96 (2000).
    [CrossRef]
  11. G. A. Shaw, A. M. Siegel, J. Model, and et al.., “Field Testing and Evaluation of a Solar-Blind UV Communication Link for Unattended Ground Sensor,” Proc. SPIE 5417, 250–261 (2004).
    [CrossRef]
  12. A. N. Witt, “Multiple scattering in reflection nebulae I: A Monte Carlo approach,” Astrophys. J. Suppl. Ser. 35, 1–6 (1977).
    [CrossRef]
  13. H. Yin, J. Yang, S. Chang, H. Jia, Z. Shao, and J. Yang, “Analysis of several factors influencing range of non-line-of-sight UV transmission,” Proc. SPIE 6783, 67833E, 67833E-6 (2007).
    [CrossRef]
  14. H. Ding, G. Chen, A. K. Majumdar, B. M. Sadler, and Z. Xu, “Non-line-of-sight ultraviolet communication channel characterization: modeling and validation,” Proc. Of SPIE Photonics and Optics – Free Space Laser Communications IX, San Diego, CA, August 2–3, 2009.

2011 (1)

2010 (2)

2009 (1)

2008 (2)

2007 (1)

H. Yin, J. Yang, S. Chang, H. Jia, Z. Shao, and J. Yang, “Analysis of several factors influencing range of non-line-of-sight UV transmission,” Proc. SPIE 6783, 67833E, 67833E-6 (2007).
[CrossRef]

2004 (1)

G. A. Shaw, A. M. Siegel, J. Model, and et al.., “Field Testing and Evaluation of a Solar-Blind UV Communication Link for Unattended Ground Sensor,” Proc. SPIE 5417, 250–261 (2004).
[CrossRef]

2000 (1)

G. A. Shaw, M. Nischan, M. Iyengar, and et al.., “NLOS UV Communication for Distributed Sensor Systems,” Proc. SPIE 4126, 83–96 (2000).
[CrossRef]

1991 (1)

M. R. Luettgen, J. H. Shapiro, and D. M. Reilly, “Non-line-of-sight single-scatter propagation model,” J. Opt. Soc. A  8(12), 1964–1972 (1991).
[CrossRef]

1979 (1)

D. M. Reilly and C. Warde, “Temporal characteristics of single-scatter radiation,” J. Opt. Soc. A 69(3), 464–470 (1979).
[CrossRef]

1977 (1)

A. N. Witt, “Multiple scattering in reflection nebulae I: A Monte Carlo approach,” Astrophys. J. Suppl. Ser. 35, 1–6 (1977).
[CrossRef]

Chang, S.

H. Yin, S. Chang, X. Wang, J. Yang, J. Yang, and J. Tan, “Analytical model of non-line-of-sight single-scatter propagation,” J. Opt. Soc. Am. A 27(7), 1505–1509 (2010).
[CrossRef] [PubMed]

H. Yin, J. Yang, S. Chang, H. Jia, Z. Shao, and J. Yang, “Analysis of several factors influencing range of non-line-of-sight UV transmission,” Proc. SPIE 6783, 67833E, 67833E-6 (2007).
[CrossRef]

Chen, G.

Ding, H.

Iyengar, M.

G. A. Shaw, M. Nischan, M. Iyengar, and et al.., “NLOS UV Communication for Distributed Sensor Systems,” Proc. SPIE 4126, 83–96 (2000).
[CrossRef]

Jia, H.

H. Yin, J. Yang, S. Chang, H. Jia, Z. Shao, and J. Yang, “Analysis of several factors influencing range of non-line-of-sight UV transmission,” Proc. SPIE 6783, 67833E, 67833E-6 (2007).
[CrossRef]

Luettgen, M. R.

M. R. Luettgen, J. H. Shapiro, and D. M. Reilly, “Non-line-of-sight single-scatter propagation model,” J. Opt. Soc. A  8(12), 1964–1972 (1991).
[CrossRef]

Model, J.

G. A. Shaw, A. M. Siegel, J. Model, and et al.., “Field Testing and Evaluation of a Solar-Blind UV Communication Link for Unattended Ground Sensor,” Proc. SPIE 5417, 250–261 (2004).
[CrossRef]

Nischan, M.

G. A. Shaw, M. Nischan, M. Iyengar, and et al.., “NLOS UV Communication for Distributed Sensor Systems,” Proc. SPIE 4126, 83–96 (2000).
[CrossRef]

Reilly, D. M.

M. R. Luettgen, J. H. Shapiro, and D. M. Reilly, “Non-line-of-sight single-scatter propagation model,” J. Opt. Soc. A  8(12), 1964–1972 (1991).
[CrossRef]

D. M. Reilly and C. Warde, “Temporal characteristics of single-scatter radiation,” J. Opt. Soc. A 69(3), 464–470 (1979).
[CrossRef]

Sadler, B.

Sadler, B. M.

Shao, Z.

H. Yin, J. Yang, S. Chang, H. Jia, Z. Shao, and J. Yang, “Analysis of several factors influencing range of non-line-of-sight UV transmission,” Proc. SPIE 6783, 67833E, 67833E-6 (2007).
[CrossRef]

Shapiro, J. H.

M. R. Luettgen, J. H. Shapiro, and D. M. Reilly, “Non-line-of-sight single-scatter propagation model,” J. Opt. Soc. A  8(12), 1964–1972 (1991).
[CrossRef]

Shaw, G. A.

G. A. Shaw, A. M. Siegel, J. Model, and et al.., “Field Testing and Evaluation of a Solar-Blind UV Communication Link for Unattended Ground Sensor,” Proc. SPIE 5417, 250–261 (2004).
[CrossRef]

G. A. Shaw, M. Nischan, M. Iyengar, and et al.., “NLOS UV Communication for Distributed Sensor Systems,” Proc. SPIE 4126, 83–96 (2000).
[CrossRef]

Siegel, A. M.

G. A. Shaw, A. M. Siegel, J. Model, and et al.., “Field Testing and Evaluation of a Solar-Blind UV Communication Link for Unattended Ground Sensor,” Proc. SPIE 5417, 250–261 (2004).
[CrossRef]

Tan, J.

Wang, L.

Wang, X.

Warde, C.

D. M. Reilly and C. Warde, “Temporal characteristics of single-scatter radiation,” J. Opt. Soc. A 69(3), 464–470 (1979).
[CrossRef]

Witt, A. N.

A. N. Witt, “Multiple scattering in reflection nebulae I: A Monte Carlo approach,” Astrophys. J. Suppl. Ser. 35, 1–6 (1977).
[CrossRef]

Xu, Z.

Yang, J.

H. Yin, S. Chang, X. Wang, J. Yang, J. Yang, and J. Tan, “Analytical model of non-line-of-sight single-scatter propagation,” J. Opt. Soc. Am. A 27(7), 1505–1509 (2010).
[CrossRef] [PubMed]

H. Yin, S. Chang, X. Wang, J. Yang, J. Yang, and J. Tan, “Analytical model of non-line-of-sight single-scatter propagation,” J. Opt. Soc. Am. A 27(7), 1505–1509 (2010).
[CrossRef] [PubMed]

H. Yin, J. Yang, S. Chang, H. Jia, Z. Shao, and J. Yang, “Analysis of several factors influencing range of non-line-of-sight UV transmission,” Proc. SPIE 6783, 67833E, 67833E-6 (2007).
[CrossRef]

H. Yin, J. Yang, S. Chang, H. Jia, Z. Shao, and J. Yang, “Analysis of several factors influencing range of non-line-of-sight UV transmission,” Proc. SPIE 6783, 67833E, 67833E-6 (2007).
[CrossRef]

Yin, H.

H. Yin, S. Chang, X. Wang, J. Yang, J. Yang, and J. Tan, “Analytical model of non-line-of-sight single-scatter propagation,” J. Opt. Soc. Am. A 27(7), 1505–1509 (2010).
[CrossRef] [PubMed]

H. Yin, J. Yang, S. Chang, H. Jia, Z. Shao, and J. Yang, “Analysis of several factors influencing range of non-line-of-sight UV transmission,” Proc. SPIE 6783, 67833E, 67833E-6 (2007).
[CrossRef]

Astrophys. J. Suppl. Ser. (1)

A. N. Witt, “Multiple scattering in reflection nebulae I: A Monte Carlo approach,” Astrophys. J. Suppl. Ser. 35, 1–6 (1977).
[CrossRef]

IEEE Commun. Mag. (1)

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

J. Opt. Soc. A (1)

M. R. Luettgen, J. H. Shapiro, and D. M. Reilly, “Non-line-of-sight single-scatter propagation model,” J. Opt. Soc. A  8(12), 1964–1972 (1991).
[CrossRef]

J. Opt. Soc. A (1)

D. M. Reilly and C. Warde, “Temporal characteristics of single-scatter radiation,” J. Opt. Soc. A 69(3), 464–470 (1979).
[CrossRef]

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

Opt. Express (1)

Opt. Lett. (3)

Proc. SPIE (3)

H. Yin, J. Yang, S. Chang, H. Jia, Z. Shao, and J. Yang, “Analysis of several factors influencing range of non-line-of-sight UV transmission,” Proc. SPIE 6783, 67833E, 67833E-6 (2007).
[CrossRef]

G. A. Shaw, M. Nischan, M. Iyengar, and et al.., “NLOS UV Communication for Distributed Sensor Systems,” Proc. SPIE 4126, 83–96 (2000).
[CrossRef]

G. A. Shaw, A. M. Siegel, J. Model, and et al.., “Field Testing and Evaluation of a Solar-Blind UV Communication Link for Unattended Ground Sensor,” Proc. SPIE 5417, 250–261 (2004).
[CrossRef]

Other (2)

Z. Xu, “Approximate performance analysis of wireless ultraviolet links,” in Proc. IEEE Intl. Conf. on Acoustics, Speech, and Signal Proc. (IEEE, Honolulu, 2007).

H. Ding, G. Chen, A. K. Majumdar, B. M. Sadler, and Z. Xu, “Non-line-of-sight ultraviolet communication channel characterization: modeling and validation,” Proc. Of SPIE Photonics and Optics – Free Space Laser Communications IX, San Diego, CA, August 2–3, 2009.

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Figures (7)

Fig. 1
Fig. 1

Single-scatter propagation solid geometry and axis angle sketch.

Fig. 2
Fig. 2

System geometry and ray pointing.

Fig. 3
Fig. 3

Simulation results of the proposed model and the standard model with path loss (per cm2).

Fig. 4
Fig. 4

Simulation results of the proposed model and Monte Carlo model with normalized power.

Fig. 5
Fig. 5

Path loss per cm2 with reference geometry settings.

Fig. 6
Fig. 6

Path loss per cm2 versus some geometry angles.

Fig. 7
Fig. 7

Path loss per cm2 versus range.

Equations (20)

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t T = arctan ( tan θ T / | sin β T | ) , t R = arctan ( tan θ R / | sin β R | ) .
( θ R 0 , θ T 0 , β T 0 ) = ( f 1 ( θ R , β R ) , f 2 ( t T 0 , θ T , β T ) , f 3 ( t T 0 , θ T , β T ) ) ,
δ E 0 = E T k s cos ( ζ ) exp [ k e ( l + L ) ] 4 π ( l L ) 2 Ω T P ( θ S ) δ V .
E 0 = l min l max E T k s cos ( ζ ) exp [ k e ( l + L ) ] 4 π ( l L ) 2 Ω T I P ( θ S ) δ V ,
E 0 = E T k s cos ( θ T ' ) δ φ δ θ 8 π 2 [ 1 cos ( ϕ T / 2 ) ] l min l max I P ( θ S ) cos ( ζ ) L 2 exp [ k e ( l + L ) ] δ l .
cos ζ = l sin θ R 0 sin ( θ T 0 + θ ) + | r l cos ( θ T 0 + θ ) cos ( β 0 + φ ) | cos θ R 0 r 2 + l 2 2 r l cos ( θ T 0 + θ ) cos ( β 0 + φ ) .
E R = E T k s A R θ min θ max cos ( θ T ' ) φ min φ max l min l max I P ( θ S ) cos ( ζ ) L 2 exp [ k e ( l + L ) ] δ l δ φ δ θ 8 π 2 [ 1 cos ( ϕ T / 2 ) ] .
l 2 + L 2 + 2 l L cos θ S = r 2 , ( l l min ) 2 + L 2 + 2 ( l l min ) L cos θ S = r 2 + ( l min ) 2 2 r l min cos ( θ T 0 + θ ) cos ( β T 0 + φ ) .
L = r 2 + l 2 2 r l cos ( θ T 0 + θ ) cos ( β T 0 + φ ) , θ S = arccos [ r cos ( θ T 0 + θ ) cos ( β T 0 + φ ) l r 2 + l 2 2 r l cos ( θ T 0 + θ ) cos ( β T 0 + φ ) ] .
{ t T 0 = t T + ( π / 2 t R ) and M = β T / | β T | , if β R β T > 0 and t R t T t T 0 = π [ t T + ( π / 2 t R ) ] and M = β T / | β T | , if β R β T > 0 and t R < t T Needn't to rotate , so θ R 0 = θ R , θ T 0 = θ T and β T 0 = β T , if β R = 0 or | β R | = π or θ R = π / 2 t T 0 = t R and M = β R / | β R | , if β T = 0 or | β T | = π or θ T = π / 2 t T 0 = t T ( π / 2 t R ) and M = β T / | β T | , if β R β T < 0 ,
θ R 0 = arccos ( cos θ R | cos β R | ) , θ T 0 = arcsin [ sin t T 0 1 cos 2 θ T cos 2 β T ] , { β T 0 = M arctan [ cos ( t T 0 ) 1 / ( cos 2 θ T cos 2 β T ) 1 ] , i f ( 0 | β T | π / 2 ) β T 0 = M { π arctan [ cos ( t T 0 ) 1 / ( cos 2 θ T cos 2 β T ) 1 ] } , i f ( π / 2 < | β T | π ) ,
2 r cos ( ϕ R / 2 ) R A = 2 r sin θ R 0 A A ' + M cos θ R 0 [ ( R A ' ) 2 + r 2 ( T A ' ) 2 ] .
A x 2 + B x + C = 0 ,
A = cos 2 ( ϕ R / 2 ) [ sin θ R 0 sin θ T ' M cos θ R 0 cos θ T ' cos ( β T 0 + φ ) ] 2 , B = 2 r [ cos θ T ' cos ( β T 0 + φ ) ( cos 2 θ R 0 cos 2 ( ϕ R / 2 ) ) M sin θ R 0 cos θ R 0 sin θ T ' ] , C = r 2 [ cos 2 ( ϕ R / 2 ) cos 2 θ R 0 ] .
| β T 0 + φ | A = 0 = arccos ( M ( sin θ R 0 sin θ T ' cos ( ϕ R / 2 ) ) cos θ R 0 cos θ T ' ) ,
| β T 0 + φ | 1 , 2 = arccos ( ± cos 2 θ T ' sin 2 θ R 0 sin 2 ( ϕ R / 2 ) [ cos 2 ( ϕ R / 2 ) cos 2 θ R 0 ] cos 2 θ T ' ) ,
θ T 1 ' = arcsin ( cos 2 ( ϕ R / 2 ) cos 2 θ R 0 / sin θ R 0 ) .
θ T 0 ' = arcsin [ ( cos 2 ( ϕ R / 2 ) cos 2 θ R 0 ) / ( cos ( ϕ R / 2 ) sin θ R 0 ) ]
φ max = φ min = arctan 1 sin 2 θ T 0 sin 2 θ T ' cos 2 ( ϕ T / 2 ) + 2 sin | θ T 0 | sin θ T ' cos ( ϕ T / 2 ) cos ( ϕ T / 2 ) sin | θ T 0 | sin θ T ' .
θ min = max ( ϕ T / 2 , θ T 0 ) , θ max = min ( ϕ T / 2 , π / 2 θ T 0 ) .

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