Abstract

An analytical model of non-line-of-sight (NLOS) single-scatter propagation is presented that has no integral form and is intended for performance analysis and system design of NLOS UV communication. Based on isotropic scattering and a continuous wave transmitter, the analytical model is verified by the current NLOS single-scatter propagation model, with consistent results. Several rules concerning NLOS UV communication are put forward on the basis of this analytical model, which are shown as follows: on condition that the minimum single-scatter optical depth is less than 0.1, the path loss factor should be 1; to maintain the NLOS UV communication link, the transmitter needs to radiate neither a continuous wave nor a huge pulse but a low-power wave whose duration is approximately the duration of impulse response; the “best” extinction coefficient is approximately the inverse ratio of the efficient single-scatter range; on condition that the radiation intensity of the transmitter is fixed, the half field of views (FOVs) are positive factors, while the elevation angles are negative factors; on condition that the power of the transmitter is fixed, the conclusions mentioned above remain valid with the exception that the half FOV of the transmitter is a negative factor. These rules also apply to anisotropic scattering.

© 2010 Optical Society of America

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References

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  1. D. E. Sunstein, “A scatter communications link at ultraviolet frequencies,” Master’s thesis (MIT, 1968).
  2. D. M. Reilly and C. Warde, “Temporal characteristics of single-scatter radiation,” J. Opt. Soc. Am. A 69, 464–470 (1979).
    [CrossRef]
  3. M. R. Luettgen, J. H. Shapiro, and D. M. Reilly, “Non-line-of-sight single-scatter propagation model,” J. Opt. Soc. Am. 8, 1964–1972 (1991).
    [CrossRef]
  4. Z. Xu, “Approximate performance analysis of wireless ultraviolet links,” in Proceedings of IEEE Conference on Acoustics, Speech, and Signal Processing, Vol. 67 (IEEE Signal Processing Society, 2007).
  5. Z. Xu, H. Ding, and B. M. Sadler, “Analytical performance study of solar blind non-line of sight ultraviolet short-range communication links,” Opt. Lett. 33, 1860–1862 (2008).
    [CrossRef] [PubMed]
  6. H. Yin, S. Chang, and H. Jia, “Non-line-of-sight multiscatter propagation model,” J. Opt. Soc. Am. A 26, 2466–2469 (2009).
    [CrossRef]
  7. H. Ding, G. Chen, A. K. Majumdar, B. M. Sadler, and Z. Xu, “Modeling of non-line-of-sight ultraviolet scattering channels for communication,” IEEE J. Sel. Areas Commun. 27, 1535–1544 (2009).
    [CrossRef]
  8. D. M. Reilly, D. T. Moriarty, and J. A. Maynard, “Unique properties of solar blind ultraviolet communication systems for unattended ground sensor networks,” Proc. SPIE 5611, 244-254 (2004).
    [CrossRef]
  9. G. A. Shaw, A. M. Siegel, and J. Model, “Extending the range and performance of non-line-of-sight ultraviolet communication links,” Proc. SPIE 62310C, 1–12 (2006).
  10. G. Chen, F. Abou-Galala, Z. Xu, and B. M. Sadler, “Experimental evaluation of LED-based solar blind NLOS communication links,” Opt. Express 16, 15059–15068 (2008).
    [CrossRef] [PubMed]
  11. G. Chen, Z. Xu, H. Ding, and B. M. Sadler, “Path loss modeling and performance trade-off study for shortrange non-line-of-sight ultraviolet communications,” Opt. Express 17, 3929–3940 (2009).
    [CrossRef] [PubMed]

2009 (3)

2008 (2)

2007 (1)

Z. Xu, “Approximate performance analysis of wireless ultraviolet links,” in Proceedings of IEEE Conference on Acoustics, Speech, and Signal Processing, Vol. 67 (IEEE Signal Processing Society, 2007).

2006 (1)

G. A. Shaw, A. M. Siegel, and J. Model, “Extending the range and performance of non-line-of-sight ultraviolet communication links,” Proc. SPIE 62310C, 1–12 (2006).

2004 (1)

D. M. Reilly, D. T. Moriarty, and J. A. Maynard, “Unique properties of solar blind ultraviolet communication systems for unattended ground sensor networks,” Proc. SPIE 5611, 244-254 (2004).
[CrossRef]

1991 (1)

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

1979 (1)

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

1968 (1)

D. E. Sunstein, “A scatter communications link at ultraviolet frequencies,” Master’s thesis (MIT, 1968).

Abou-Galala, F.

Chang, S.

Chen, G.

Ding, H.

Jia, H.

Luettgen, M. R.

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

Majumdar, A. K.

H. Ding, G. Chen, A. K. Majumdar, B. M. Sadler, and Z. Xu, “Modeling of non-line-of-sight ultraviolet scattering channels for communication,” IEEE J. Sel. Areas Commun. 27, 1535–1544 (2009).
[CrossRef]

Maynard, J. A.

D. M. Reilly, D. T. Moriarty, and J. A. Maynard, “Unique properties of solar blind ultraviolet communication systems for unattended ground sensor networks,” Proc. SPIE 5611, 244-254 (2004).
[CrossRef]

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 62310C, 1–12 (2006).

Moriarty, D. T.

D. M. Reilly, D. T. Moriarty, and J. A. Maynard, “Unique properties of solar blind ultraviolet communication systems for unattended ground sensor networks,” Proc. SPIE 5611, 244-254 (2004).
[CrossRef]

Reilly, D. M.

D. M. Reilly, D. T. Moriarty, and J. A. Maynard, “Unique properties of solar blind ultraviolet communication systems for unattended ground sensor networks,” Proc. SPIE 5611, 244-254 (2004).
[CrossRef]

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

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

Sadler, B. M.

Shapiro, J. H.

M. R. Luettgen, J. H. Shapiro, and D. M. Reilly, “Non-line-of-sight single-scatter propagation model,” J. Opt. Soc. Am. 8, 1964–1972 (1991).
[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 62310C, 1–12 (2006).

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 62310C, 1–12 (2006).

Sunstein, D. E.

D. E. Sunstein, “A scatter communications link at ultraviolet frequencies,” Master’s thesis (MIT, 1968).

Warde, C.

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

Xu, Z.

Yin, H.

IEEE J. Sel. Areas Commun. (1)

H. Ding, G. Chen, A. K. Majumdar, B. M. Sadler, and Z. Xu, “Modeling of non-line-of-sight ultraviolet scattering channels for communication,” IEEE J. Sel. Areas Commun. 27, 1535–1544 (2009).
[CrossRef]

J. Opt. Soc. Am. (1)

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

J. Opt. Soc. Am. A (2)

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

H. Yin, S. Chang, and H. Jia, “Non-line-of-sight multiscatter propagation model,” J. Opt. Soc. Am. A 26, 2466–2469 (2009).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Proc. SPIE (2)

D. M. Reilly, D. T. Moriarty, and J. A. Maynard, “Unique properties of solar blind ultraviolet communication systems for unattended ground sensor networks,” Proc. SPIE 5611, 244-254 (2004).
[CrossRef]

G. A. Shaw, A. M. Siegel, and J. Model, “Extending the range and performance of non-line-of-sight ultraviolet communication links,” Proc. SPIE 62310C, 1–12 (2006).

Other (2)

D. E. Sunstein, “A scatter communications link at ultraviolet frequencies,” Master’s thesis (MIT, 1968).

Z. Xu, “Approximate performance analysis of wireless ultraviolet links,” in Proceedings of IEEE Conference on Acoustics, Speech, and Signal Processing, Vol. 67 (IEEE Signal Processing Society, 2007).

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Figures (5)

Fig. 1
Fig. 1

Sketch of NLOS single-scatter propagation.

Fig. 2
Fig. 2

Results of two models (closed single-scatter volume with wide FOVs).

Fig. 3
Fig. 3

Results of two models (closed single-scatter volume with narrow FOVs).

Fig. 4
Fig. 4

Results of two models (open single-scatter volume with wide FOVs)

Fig. 5
Fig. 5

Ratios of two models.

Equations (8)

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{ ξ = ( r 1 + r 2 ) r η = ( r 1 r 2 ) r ϕ = arctan ( x , y ) } ,
p ( t ) = { p T 0 t Δ t 0 t < 0 , t > Δ t } ,
E ( ξ ) = c k s 2 π Ω T r 2 t t max t max ( t max Δ t , t min ) p ( t ) η 1 ( ξ ) η 2 ( ξ ) 2 g ( ξ , η ) P ( θ s ) exp ( k e r ξ ) ξ 2 η 2 d t d η = k s 2 π Ω T r ξ ξ max ξ max ( ξ max Δ t c r , ξ min ) p ( ξ r c ) η 1 ( ξ ) η 2 ( ξ ) 2 g ( ξ , η ) P ( θ s ) exp ( k e r ξ ) ξ 2 η 2 d ξ d η ,
{ ξ min = f ( β R θ R , β T θ T ) τ min = k ext r ξ min ξ max = f ( β R + θ R , β T + θ T ) τ max = k ext r ξ max } , ,
f ( β 1 , β 2 ) = { 1 + cos β 1 cos β 2 cos β 1 + cos β 2 + [ ( 1 + cos β 1 cos β 2 cos β 1 + cos β 2 ) 2 1 ] 1 2 0 β 1 + β 2 < 180 ° β 1 + β 2 180 ° } ;
τ min < 0.1.
E = 4 p T k s P ( β T + β R ) exp ( τ eff ) 3 π Ω T r sin ( θ R ) sin ( θ T ) sin ( β T ) sin ( β R ) min [ sin ( β T ) sin ( θ R ) , sin ( β R ) sin ( θ T ) ] ,
E R = 4 ρ T ρ R k s P ( β T + β R ) exp ( τ eff ) 3 π r sin ( θ R ) sin ( θ T ) sin ( β T ) sin ( β R ) min [ sin ( β T ) sin ( θ R ) , sin ( β R ) sin ( θ T ) ] .

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