Abstract

Non-line-of-sight optical wireless transmission, operated in the unlicensed ultraviolet UV-C band, has been recently suggested as an alternative means of communication. However, due to limited coverage, relayed UV-C networks need to be deployed in order to supply communication services at large distances. In this paper, we consider a serial multi-hop UV-C network where the nodes are distributed at fixed positions on a given service interval. We adopt a suitable path loss model and derive analytical expressions for the node isolation probability assuming on–off keying and pulse position modulation formats. Moreover, we investigate the node density required to achieve connectivity for several geometrical transceiver configurations. The numerical results of this paper are of significant value for telecom researchers working toward a flexible UV-C network deployment in practice.

© 2011 OSA

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References

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  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).
  2. G. A. Shaw, M. L. Nischan, M. A. Iyengar, S. Kaushik, and M. K. Griffin, "NLOS UV communication for distributed sensor systems," Proc. SPIE 4126, 83‒96 (2000).
  3. Z. Xu and B. M. Sadler, "Ultraviolet communications: Potential and state-of-the-art," IEEE Commun. Mag. 46, (5), 67‒73 (2008).
  4. D. Keddar and S. Arnon, "Non-line-of-sight optical wireless sensor network operating in multiscattering channel," Appl. Opt. 45, (33), 8454‒8461 (2006).
    [CrossRef]
  5. M. Uysal, ed., Cooperative Communications for Improved Wireless Network Transmission: Framework for Virtual Antenna Array Applications, Information Science Reference, 2010.
  6. M. Dohler and Y. Li, Cooperative Communications: Hardware, Channel and PHY, Wiley, 2010.
  7. G. K. Karagiannidis, T. A. Tsiftsis, and H. G. Sandalidis, "Outage probability of relayed free space optical communication systems," Electron. Lett. 42, (17), 994‒995 (2006).
    [CrossRef]
  8. Q. He, Z. Xu, and B. M. Sadler, "Non-line-of-sight serial relayed link for optical wireless communications," IEEE Military Communications Conf., 31 Oct.–3 Nov. 2010, San Jose, CA, pp. 1588‒1593.
  9. The International Commission on Non-Ionizing Radiation and Protection (ICNIRP), "Guidelines on limits of exposure to ultraviolet radiation of wavelengths between 180 nm and 400 nm (incoherent optical radiation)," Health Phys. 87, (2), 171‒186 (2004).
    [CrossRef]
  10. C. Bettstetter, "On the minimum node degree and connectivity of a wireless multihop network," Proc. ACM MobiHoc, 9–11 June 2002, Lausanne, Switzerland, pp. 80‒91.
  11. A. Ghasemi and S. Nader-Esfahani, "Exact probability of connectivity in one-dimensional ad hoc wireless networks," IEEE Commun. Lett. 10, (4), 251‒253 (2006).
    [CrossRef]
  12. A. Behnad and S. Nader-Esfahani, "Probability of node to base station connectivity in one-dimensional ad hoc networks," IEEE Commun. Lett. 14, (7), 650‒652 (2010).
    [CrossRef]
  13. M. Desai and D. Manjunath, "On the connectivity in finite ad hoc networks," IEEE Commun. Lett. 6, (10), 437‒439 (2002).
    [CrossRef]
  14. D. Miorandi and E. Altman, "Connectivity in one-dimensional ad hoc networks: A queueing theoretical approach," Wireless Networks 12, (5), 573‒587 (2006).
    [CrossRef]
  15. A. Vavoulas, H. G. Sandalidis, and D. Varoutas, "Connectivity issues for ultraviolet UV-C networks," J. Opt. Commun. Netw. 3, (3), 199‒205 (2011).
    [CrossRef]
  16. C. Bettstetter and C. Hartmann, "Connectivity of wireless multihop networks in a shadow fading environment," Wireless Networks 11, (5), 571‒579 (2005).
    [CrossRef]
  17. D. Stoyan, W. S. Kendall, and J. Mecke, Stochastic Geometry and Its Applications, Wiley, 1996.
  18. M. Haenggi, "On distances in uniformly random networks," IEEE Trans. Inf. Theory 51, (10), 3584‒3586 (2005).
    [CrossRef]
  19. C. Bettstetter, "On the connectivity of wireless multihop networks with homogeneous and inhomogeneous range assignment," Proc. IEEE VTC Fall, Sept. 24–28 2002, Vancouver, BC, Canada, pp. 1706‒1710.
  20. A. S. Zachor, "Aureole radiance field about a source in a scattering absorbing medium," Appl. Opt. 17, (12), 1911‒1922 (1978).
    [CrossRef]
  21. 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]
  22. 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, (5), 3929‒3940 (2009).
    [CrossRef]
  23. M. Luettgen, J. Shapiro, and D. Reilly, "Non-line-of-sight single-scatter propagation model," J. Opt. Soc. Am. 8, (12), 1964‒1972 (1991).
    [CrossRef]
  24. Q. He, B. M. Sadler, and Z. Xu, "Modulation and coding tradeoffs for non-line-of-sight ultraviolet communications," Proc. SPIE 7464, 74640H (2009).
  25. The Wolfram functions site, [Online]. Available: http://functions.wolfram.com

2011

2010

A. Behnad and S. Nader-Esfahani, "Probability of node to base station connectivity in one-dimensional ad hoc networks," IEEE Commun. Lett. 14, (7), 650‒652 (2010).
[CrossRef]

2009

Q. He, B. M. Sadler, and Z. Xu, "Modulation and coding tradeoffs for non-line-of-sight ultraviolet communications," Proc. SPIE 7464, 74640H (2009).

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, (5), 3929‒3940 (2009).
[CrossRef]

2008

2006

G. K. Karagiannidis, T. A. Tsiftsis, and H. G. Sandalidis, "Outage probability of relayed free space optical communication systems," Electron. Lett. 42, (17), 994‒995 (2006).
[CrossRef]

D. Miorandi and E. Altman, "Connectivity in one-dimensional ad hoc networks: A queueing theoretical approach," Wireless Networks 12, (5), 573‒587 (2006).
[CrossRef]

A. Ghasemi and S. Nader-Esfahani, "Exact probability of connectivity in one-dimensional ad hoc wireless networks," IEEE Commun. Lett. 10, (4), 251‒253 (2006).
[CrossRef]

D. Keddar and S. Arnon, "Non-line-of-sight optical wireless sensor network operating in multiscattering channel," Appl. Opt. 45, (33), 8454‒8461 (2006).
[CrossRef]

2005

C. Bettstetter and C. Hartmann, "Connectivity of wireless multihop networks in a shadow fading environment," Wireless Networks 11, (5), 571‒579 (2005).
[CrossRef]

M. Haenggi, "On distances in uniformly random networks," IEEE Trans. Inf. Theory 51, (10), 3584‒3586 (2005).
[CrossRef]

2004

The International Commission on Non-Ionizing Radiation and Protection (ICNIRP), "Guidelines on limits of exposure to ultraviolet radiation of wavelengths between 180 nm and 400 nm (incoherent optical radiation)," Health Phys. 87, (2), 171‒186 (2004).
[CrossRef]

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).

2002

M. Desai and D. Manjunath, "On the connectivity in finite ad hoc networks," IEEE Commun. Lett. 6, (10), 437‒439 (2002).
[CrossRef]

2000

G. A. Shaw, M. L. Nischan, M. A. Iyengar, S. Kaushik, and M. K. Griffin, "NLOS UV communication for distributed sensor systems," Proc. SPIE 4126, 83‒96 (2000).

1991

M. Luettgen, J. Shapiro, and D. Reilly, "Non-line-of-sight single-scatter propagation model," J. Opt. Soc. Am. 8, (12), 1964‒1972 (1991).
[CrossRef]

1978

Altman, E.

D. Miorandi and E. Altman, "Connectivity in one-dimensional ad hoc networks: A queueing theoretical approach," Wireless Networks 12, (5), 573‒587 (2006).
[CrossRef]

Arnon, S.

Behnad, A.

A. Behnad and S. Nader-Esfahani, "Probability of node to base station connectivity in one-dimensional ad hoc networks," IEEE Commun. Lett. 14, (7), 650‒652 (2010).
[CrossRef]

Bettstetter, C.

C. Bettstetter and C. Hartmann, "Connectivity of wireless multihop networks in a shadow fading environment," Wireless Networks 11, (5), 571‒579 (2005).
[CrossRef]

C. Bettstetter, "On the connectivity of wireless multihop networks with homogeneous and inhomogeneous range assignment," Proc. IEEE VTC Fall, Sept. 24–28 2002, Vancouver, BC, Canada, pp. 1706‒1710.

C. Bettstetter, "On the minimum node degree and connectivity of a wireless multihop network," Proc. ACM MobiHoc, 9–11 June 2002, Lausanne, Switzerland, pp. 80‒91.

Chen, G.

Desai, M.

M. Desai and D. Manjunath, "On the connectivity in finite ad hoc networks," IEEE Commun. Lett. 6, (10), 437‒439 (2002).
[CrossRef]

Ding, H.

Dohler, M.

M. Dohler and Y. Li, Cooperative Communications: Hardware, Channel and PHY, Wiley, 2010.

Ghasemi, A.

A. Ghasemi and S. Nader-Esfahani, "Exact probability of connectivity in one-dimensional ad hoc wireless networks," IEEE Commun. Lett. 10, (4), 251‒253 (2006).
[CrossRef]

Griffin, M. K.

G. A. Shaw, M. L. Nischan, M. A. Iyengar, S. Kaushik, and M. K. Griffin, "NLOS UV communication for distributed sensor systems," Proc. SPIE 4126, 83‒96 (2000).

Haenggi, M.

M. Haenggi, "On distances in uniformly random networks," IEEE Trans. Inf. Theory 51, (10), 3584‒3586 (2005).
[CrossRef]

Hartmann, C.

C. Bettstetter and C. Hartmann, "Connectivity of wireless multihop networks in a shadow fading environment," Wireless Networks 11, (5), 571‒579 (2005).
[CrossRef]

He, Q.

Q. He, B. M. Sadler, and Z. Xu, "Modulation and coding tradeoffs for non-line-of-sight ultraviolet communications," Proc. SPIE 7464, 74640H (2009).

Q. He, Z. Xu, and B. M. Sadler, "Non-line-of-sight serial relayed link for optical wireless communications," IEEE Military Communications Conf., 31 Oct.–3 Nov. 2010, San Jose, CA, pp. 1588‒1593.

Iyengar, M. A.

G. A. Shaw, M. L. Nischan, M. A. Iyengar, S. Kaushik, and M. K. Griffin, "NLOS UV communication for distributed sensor systems," Proc. SPIE 4126, 83‒96 (2000).

Karagiannidis, G. K.

G. K. Karagiannidis, T. A. Tsiftsis, and H. G. Sandalidis, "Outage probability of relayed free space optical communication systems," Electron. Lett. 42, (17), 994‒995 (2006).
[CrossRef]

Kaushik, S.

G. A. Shaw, M. L. Nischan, M. A. Iyengar, S. Kaushik, and M. K. Griffin, "NLOS UV communication for distributed sensor systems," Proc. SPIE 4126, 83‒96 (2000).

Keddar, D.

Kendall, W. S.

D. Stoyan, W. S. Kendall, and J. Mecke, Stochastic Geometry and Its Applications, Wiley, 1996.

Li, Y.

M. Dohler and Y. Li, Cooperative Communications: Hardware, Channel and PHY, Wiley, 2010.

Luettgen, M.

M. Luettgen, J. Shapiro, and D. Reilly, "Non-line-of-sight single-scatter propagation model," J. Opt. Soc. Am. 8, (12), 1964‒1972 (1991).
[CrossRef]

Manjunath, D.

M. Desai and D. Manjunath, "On the connectivity in finite ad hoc networks," IEEE Commun. Lett. 6, (10), 437‒439 (2002).
[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).

Mecke, J.

D. Stoyan, W. S. Kendall, and J. Mecke, Stochastic Geometry and Its Applications, Wiley, 1996.

Miorandi, D.

D. Miorandi and E. Altman, "Connectivity in one-dimensional ad hoc networks: A queueing theoretical approach," Wireless Networks 12, (5), 573‒587 (2006).
[CrossRef]

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).

Nader-Esfahani, S.

A. Behnad and S. Nader-Esfahani, "Probability of node to base station connectivity in one-dimensional ad hoc networks," IEEE Commun. Lett. 14, (7), 650‒652 (2010).
[CrossRef]

A. Ghasemi and S. Nader-Esfahani, "Exact probability of connectivity in one-dimensional ad hoc wireless networks," IEEE Commun. Lett. 10, (4), 251‒253 (2006).
[CrossRef]

Nischan, M. L.

G. A. Shaw, M. L. Nischan, M. A. Iyengar, S. Kaushik, and M. K. Griffin, "NLOS UV communication for distributed sensor systems," Proc. SPIE 4126, 83‒96 (2000).

Reilly, D.

M. Luettgen, J. Shapiro, and D. Reilly, "Non-line-of-sight single-scatter propagation model," J. Opt. Soc. Am. 8, (12), 1964‒1972 (1991).
[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).

Sadler, B. M.

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, (5), 3929‒3940 (2009).
[CrossRef]

Q. He, B. M. Sadler, and Z. Xu, "Modulation and coding tradeoffs for non-line-of-sight ultraviolet communications," Proc. SPIE 7464, 74640H (2009).

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]

Z. Xu and B. M. Sadler, "Ultraviolet communications: Potential and state-of-the-art," IEEE Commun. Mag. 46, (5), 67‒73 (2008).

Q. He, Z. Xu, and B. M. Sadler, "Non-line-of-sight serial relayed link for optical wireless communications," IEEE Military Communications Conf., 31 Oct.–3 Nov. 2010, San Jose, CA, pp. 1588‒1593.

Sandalidis, H. G.

A. Vavoulas, H. G. Sandalidis, and D. Varoutas, "Connectivity issues for ultraviolet UV-C networks," J. Opt. Commun. Netw. 3, (3), 199‒205 (2011).
[CrossRef]

G. K. Karagiannidis, T. A. Tsiftsis, and H. G. Sandalidis, "Outage probability of relayed free space optical communication systems," Electron. Lett. 42, (17), 994‒995 (2006).
[CrossRef]

Shapiro, J.

M. Luettgen, J. Shapiro, and D. Reilly, "Non-line-of-sight single-scatter propagation model," J. Opt. Soc. Am. 8, (12), 1964‒1972 (1991).
[CrossRef]

Shaw, G. A.

G. A. Shaw, M. L. Nischan, M. A. Iyengar, S. Kaushik, and M. K. Griffin, "NLOS UV communication for distributed sensor systems," Proc. SPIE 4126, 83‒96 (2000).

Stoyan, D.

D. Stoyan, W. S. Kendall, and J. Mecke, Stochastic Geometry and Its Applications, Wiley, 1996.

Tsiftsis, T. A.

G. K. Karagiannidis, T. A. Tsiftsis, and H. G. Sandalidis, "Outage probability of relayed free space optical communication systems," Electron. Lett. 42, (17), 994‒995 (2006).
[CrossRef]

Varoutas, D.

Vavoulas, A.

Xu, Z.

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, (5), 3929‒3940 (2009).
[CrossRef]

Q. He, B. M. Sadler, and Z. Xu, "Modulation and coding tradeoffs for non-line-of-sight ultraviolet communications," Proc. SPIE 7464, 74640H (2009).

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]

Z. Xu and B. M. Sadler, "Ultraviolet communications: Potential and state-of-the-art," IEEE Commun. Mag. 46, (5), 67‒73 (2008).

Q. He, Z. Xu, and B. M. Sadler, "Non-line-of-sight serial relayed link for optical wireless communications," IEEE Military Communications Conf., 31 Oct.–3 Nov. 2010, San Jose, CA, pp. 1588‒1593.

Zachor, A. S.

Appl. Opt.

Electron. Lett.

G. K. Karagiannidis, T. A. Tsiftsis, and H. G. Sandalidis, "Outage probability of relayed free space optical communication systems," Electron. Lett. 42, (17), 994‒995 (2006).
[CrossRef]

Health Phys.

The International Commission on Non-Ionizing Radiation and Protection (ICNIRP), "Guidelines on limits of exposure to ultraviolet radiation of wavelengths between 180 nm and 400 nm (incoherent optical radiation)," Health Phys. 87, (2), 171‒186 (2004).
[CrossRef]

IEEE Commun. Lett.

A. Ghasemi and S. Nader-Esfahani, "Exact probability of connectivity in one-dimensional ad hoc wireless networks," IEEE Commun. Lett. 10, (4), 251‒253 (2006).
[CrossRef]

A. Behnad and S. Nader-Esfahani, "Probability of node to base station connectivity in one-dimensional ad hoc networks," IEEE Commun. Lett. 14, (7), 650‒652 (2010).
[CrossRef]

M. Desai and D. Manjunath, "On the connectivity in finite ad hoc networks," IEEE Commun. Lett. 6, (10), 437‒439 (2002).
[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 Trans. Inf. Theory

M. Haenggi, "On distances in uniformly random networks," IEEE Trans. Inf. Theory 51, (10), 3584‒3586 (2005).
[CrossRef]

J. Opt. Commun. Netw.

J. Opt. Soc. Am.

M. Luettgen, J. Shapiro, and D. Reilly, "Non-line-of-sight single-scatter propagation model," J. Opt. Soc. Am. 8, (12), 1964‒1972 (1991).
[CrossRef]

Opt. Express

Opt. Lett.

Proc. SPIE

Q. He, B. M. Sadler, and Z. Xu, "Modulation and coding tradeoffs for non-line-of-sight ultraviolet communications," Proc. SPIE 7464, 74640H (2009).

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).

G. A. Shaw, M. L. Nischan, M. A. Iyengar, S. Kaushik, and M. K. Griffin, "NLOS UV communication for distributed sensor systems," Proc. SPIE 4126, 83‒96 (2000).

Wireless Networks

C. Bettstetter and C. Hartmann, "Connectivity of wireless multihop networks in a shadow fading environment," Wireless Networks 11, (5), 571‒579 (2005).
[CrossRef]

D. Miorandi and E. Altman, "Connectivity in one-dimensional ad hoc networks: A queueing theoretical approach," Wireless Networks 12, (5), 573‒587 (2006).
[CrossRef]

Other

Q. He, Z. Xu, and B. M. Sadler, "Non-line-of-sight serial relayed link for optical wireless communications," IEEE Military Communications Conf., 31 Oct.–3 Nov. 2010, San Jose, CA, pp. 1588‒1593.

M. Uysal, ed., Cooperative Communications for Improved Wireless Network Transmission: Framework for Virtual Antenna Array Applications, Information Science Reference, 2010.

M. Dohler and Y. Li, Cooperative Communications: Hardware, Channel and PHY, Wiley, 2010.

D. Stoyan, W. S. Kendall, and J. Mecke, Stochastic Geometry and Its Applications, Wiley, 1996.

C. Bettstetter, "On the connectivity of wireless multihop networks with homogeneous and inhomogeneous range assignment," Proc. IEEE VTC Fall, Sept. 24–28 2002, Vancouver, BC, Canada, pp. 1706‒1710.

C. Bettstetter, "On the minimum node degree and connectivity of a wireless multihop network," Proc. ACM MobiHoc, 9–11 June 2002, Lausanne, Switzerland, pp. 80‒91.

The Wolfram functions site, [Online]. Available: http://functions.wolfram.com

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Figures (7)

Fig. 1
Fig. 1

Serial UV-C multi-hop network geometry.

Fig. 2
Fig. 2

P iso versus (a) node density, ρ, for various values of P e , (b) node density, ρ, for various values of R b , (c) node density, ρ, for various values of P t , and (d) number of nodes, n, for various lengths, , of service interval assuming OOK modulation.

Fig. 3
Fig. 3

P iso versus (a) node density, ρ, for various values of P e , (b) node density, ρ, for various values of R b , (c) node density, ρ, for various values of P t , and (d) number of nodes, n, for various lengths, , of service interval assuming PPM modulation.

Fig. 4
Fig. 4

Required node density, ρ, to achieve P iso 0 versus elevation angles β T and β R assuming P t = 50 mW , R b = 100 kbps , P e = 1 0 3 , θ T = 10 ° , θ R = 10 ° , and OOK modulation.

Fig. 5
Fig. 5

Required node density, ρ, to achieve P iso 0 versus Tx beam divergence angle θ T and Rx FOV θ R assuming P t = 50 mW , R b = 100 kbps , P e = 1 0 3 , β T = 30 ° , β R = 30 ° , and OOK modulation.

Fig. 6
Fig. 6

Required node density, ρ, to achieve P iso 0 versus elevation angles β T and β R assuming P t = 50 mW , R b = 100 kbps , P e = 1 0 3 , θ T = 10 ° , θ R = 10 ° , and PPM modulation.

Fig. 7
Fig. 7

Required node density, ρ, to achieve P iso 0 versus Tx beam divergence angle θ T and Rx FOV θ R assuming P t = 50 mW , R b = 100 kbps , P e = 1 0 3 , β T = 30 ° , β R = 30 ° , and PPM modulation.

Tables (1)

Tables Icon

Table I System Model Parameters ([2,20])