Abstract

This paper focuses on the connectivity issues of a non-line-of-sight (NLOS) optical wireless network operating in the ultraviolet UV-C spectral region. NLOS UV-C transmitters have a limited effective coverage and, hence, a dense node distribution is required in order to efficiently cover a large geographical area. Under this assumption, the concept of connectivity is more than important since it provides a strong indication of the network reliability and robustness. In the present study, we consider transmission with on–off keying and pulse position modulation schemes assuming both Gaussian and Poisson noise and adopt an effective experimental path loss model. Then, we evaluate the k-connectivity properties in terms of several network parameters. More precisely, we present and analyze the trade-off between node density and the degree of k-connectivity against other parameters (i.e., transmitted power, supported data rate, and error probability). The derived results are depicted using appropriate figures and tables and constitute the theoretical basis for the design and implementation of a reliable UV-C network 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, A. M. Siegel, and J. Model, "Ultraviolet comm links for distributed sensor systems," IEEE LEOS Newsl. 19(5), 26‒29 (2005).
  3. Z. Xu and B. M. Sadler, "Ultraviolet communications: Potential and state-of-the-art," IEEE Commun. Mag. 46(5), 67‒73 (2008).
  4. G. Chen, F. Abou-Galala, Z. Xu, and B. M. Sadler, "Experimental evaluation of LED-based solar blind NLOS communication links," Opt. Express 16(19), 15059‒15068 (2008).
    [CrossRef]
  5. 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]
  6. D. Keddar, "Multiaccess interference in a non-line-of-sight ultraviolet optical wireless sensor network," Appl. Opt. 46(23), 5895‒5901 (2007).
    [CrossRef]
  7. G. A. Shaw, A. M. Siegel, J. Model, and M. L. Nischan, "Field testing and evaluation of a solar-blind UV communication link for unattended ground sensors," Proc. SPIE 5417, 250‒261 (2004).
  8. G. K. Karagiannidis, D. A. Zogas, N. C. Sagias, T. A. Tsiftsis, and P. T. Mathiopoulos, "Multihop communications with fixed-gain relays over generalized fading channels," Proc. IEEE Globecom, Dec. 2004, Dallas, TX, USA.
  9. G. K. Karagiannidis, T. A. Tsiftsis, and H. G. Sandalidis, "Outage probability of relayed free space optical communication systems," IEE Electron. Lett. 42(17), 994‒995 (2006).
    [CrossRef]
  10. Q. He, Z. Xu, and B. M. Sadler, "Non-line-of-sight serial relayed link for optical wireless communications," IEEE Military Communications Conf., Oct. 31– Nov. 3, 2010, San Jose, CA, USA.
  11. B. Bollobas, Random Graphs, 2nd ed., Cambridge University Press, 2001.
  12. D. Miorandi and E. Altman, "Coverage and connectivity of ad hoc networks in presence of channel randomness," IEEE Proc. of INFOCOM, Vol. 1, Mar. 13–17, 2005, Miami, FL, USA, pp. 491‒502.
  13. L. Zhang, B.-H. Soong, Y. Zhang, M. Ma, and Y. Guan, "An analysis of k-connectivity in shadowing and Nakagami fading wireless multi-hop networks," Proc. IEEE VTC Spring, May 11–14, 2008, Singapore, pp. 395‒399.
  14. C. Bettstetter and C. Hartmann, "Connectivity of wireless multihop networks in a shadow fading environment," Wirel. Netw. 11(5), 571‒579 (2005).
    [CrossRef]
  15. 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.
  16. M. D. Penrose, "On k-connectivity for a geometric random graph," Rand. Struct. Alg. 15(2), 145‒164 (1999).
    [CrossRef]
  17. C. Bettstetter, "On the minimum node degree and connectivity of a wireless multihop network," Proc. ACM MobiHoc, June 9–11, 2002, Lausanne, Switzerland, pp. 80‒91.
  18. 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]
  19. 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]
  20. 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]
  21. Q. He, B. M. Sadler, and Z. Xu, "Modulation and coding tradeoffs for non-line-of-sight ultraviolet communications," Proc. SPIE 7464, 74640H1‒74640H12 (2009).
  22. 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]

2009

Q. He, B. M. Sadler, and Z. Xu, "Modulation and coding tradeoffs for non-line-of-sight ultraviolet communications," Proc. SPIE 7464, 74640H1‒74640H12 (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

2007

2006

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]

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

2005

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

G. A. Shaw, A. M. Siegel, and J. Model, "Ultraviolet comm links for distributed sensor systems," IEEE LEOS Newsl. 19(5), 26‒29 (2005).

2004

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

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]

1999

M. D. Penrose, "On k-connectivity for a geometric random graph," Rand. Struct. Alg. 15(2), 145‒164 (1999).
[CrossRef]

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]

Abou-Galala, F.

Altman, E.

D. Miorandi and E. Altman, "Coverage and connectivity of ad hoc networks in presence of channel randomness," IEEE Proc. of INFOCOM, Vol. 1, Mar. 13–17, 2005, Miami, FL, USA, pp. 491‒502.

Arnon, S.

Bettstetter, C.

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

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

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.

Bollobas, B.

B. Bollobas, Random Graphs, 2nd ed., Cambridge University Press, 2001.

Chen, G.

Ding, H.

Guan, Y.

L. Zhang, B.-H. Soong, Y. Zhang, M. Ma, and Y. Guan, "An analysis of k-connectivity in shadowing and Nakagami fading wireless multi-hop networks," Proc. IEEE VTC Spring, May 11–14, 2008, Singapore, pp. 395‒399.

Hartmann, C.

C. Bettstetter and C. Hartmann, "Connectivity of wireless multihop networks in a shadow fading environment," Wirel. Netw. 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, 74640H1‒74640H12 (2009).

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

Karagiannidis, G. K.

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

G. K. Karagiannidis, D. A. Zogas, N. C. Sagias, T. A. Tsiftsis, and P. T. Mathiopoulos, "Multihop communications with fixed-gain relays over generalized fading channels," Proc. IEEE Globecom, Dec. 2004, Dallas, TX, USA.

Keddar, D.

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]

Ma, M.

L. Zhang, B.-H. Soong, Y. Zhang, M. Ma, and Y. Guan, "An analysis of k-connectivity in shadowing and Nakagami fading wireless multi-hop networks," Proc. IEEE VTC Spring, May 11–14, 2008, Singapore, pp. 395‒399.

Mathiopoulos, P. T.

G. K. Karagiannidis, D. A. Zogas, N. C. Sagias, T. A. Tsiftsis, and P. T. Mathiopoulos, "Multihop communications with fixed-gain relays over generalized fading channels," Proc. IEEE Globecom, Dec. 2004, Dallas, TX, USA.

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).

Miorandi, D.

D. Miorandi and E. Altman, "Coverage and connectivity of ad hoc networks in presence of channel randomness," IEEE Proc. of INFOCOM, Vol. 1, Mar. 13–17, 2005, Miami, FL, USA, pp. 491‒502.

Model, J.

G. A. Shaw, A. M. Siegel, and J. Model, "Ultraviolet comm links for distributed sensor systems," IEEE LEOS Newsl. 19(5), 26‒29 (2005).

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

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).

Nischan, M. L.

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

Penrose, M. D.

M. D. Penrose, "On k-connectivity for a geometric random graph," Rand. Struct. Alg. 15(2), 145‒164 (1999).
[CrossRef]

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.

Q. He, B. M. Sadler, and Z. Xu, "Modulation and coding tradeoffs for non-line-of-sight ultraviolet communications," Proc. SPIE 7464, 74640H1‒74640H12 (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]

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

G. Chen, F. Abou-Galala, Z. Xu, and B. M. Sadler, "Experimental evaluation of LED-based solar blind NLOS communication links," Opt. Express 16(19), 15059‒15068 (2008).
[CrossRef]

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]

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

Sagias, N. C.

G. K. Karagiannidis, D. A. Zogas, N. C. Sagias, T. A. Tsiftsis, and P. T. Mathiopoulos, "Multihop communications with fixed-gain relays over generalized fading channels," Proc. IEEE Globecom, Dec. 2004, Dallas, TX, USA.

Sandalidis, H. G.

G. K. Karagiannidis, T. A. Tsiftsis, and H. G. Sandalidis, "Outage probability of relayed free space optical communication systems," IEE 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, A. M. Siegel, and J. Model, "Ultraviolet comm links for distributed sensor systems," IEEE LEOS Newsl. 19(5), 26‒29 (2005).

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

Siegel, A. M.

G. A. Shaw, A. M. Siegel, and J. Model, "Ultraviolet comm links for distributed sensor systems," IEEE LEOS Newsl. 19(5), 26‒29 (2005).

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

Soong, B.-H.

L. Zhang, B.-H. Soong, Y. Zhang, M. Ma, and Y. Guan, "An analysis of k-connectivity in shadowing and Nakagami fading wireless multi-hop networks," Proc. IEEE VTC Spring, May 11–14, 2008, Singapore, pp. 395‒399.

Tsiftsis, T. A.

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

G. K. Karagiannidis, D. A. Zogas, N. C. Sagias, T. A. Tsiftsis, and P. T. Mathiopoulos, "Multihop communications with fixed-gain relays over generalized fading channels," Proc. IEEE Globecom, Dec. 2004, Dallas, TX, USA.

Xu, Z.

Q. He, B. M. Sadler, and Z. Xu, "Modulation and coding tradeoffs for non-line-of-sight ultraviolet communications," Proc. SPIE 7464, 74640H1‒74640H12 (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]

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

G. Chen, F. Abou-Galala, Z. Xu, and B. M. Sadler, "Experimental evaluation of LED-based solar blind NLOS communication links," Opt. Express 16(19), 15059‒15068 (2008).
[CrossRef]

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]

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

Zhang, L.

L. Zhang, B.-H. Soong, Y. Zhang, M. Ma, and Y. Guan, "An analysis of k-connectivity in shadowing and Nakagami fading wireless multi-hop networks," Proc. IEEE VTC Spring, May 11–14, 2008, Singapore, pp. 395‒399.

Zhang, Y.

L. Zhang, B.-H. Soong, Y. Zhang, M. Ma, and Y. Guan, "An analysis of k-connectivity in shadowing and Nakagami fading wireless multi-hop networks," Proc. IEEE VTC Spring, May 11–14, 2008, Singapore, pp. 395‒399.

Zogas, D. A.

G. K. Karagiannidis, D. A. Zogas, N. C. Sagias, T. A. Tsiftsis, and P. T. Mathiopoulos, "Multihop communications with fixed-gain relays over generalized fading channels," Proc. IEEE Globecom, Dec. 2004, Dallas, TX, USA.

Appl. Opt.

Health Phys.

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]

IEE Electron. Lett.

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

G. A. Shaw, A. M. Siegel, and J. Model, "Ultraviolet comm links for distributed sensor systems," IEEE LEOS Newsl. 19(5), 26‒29 (2005).

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, 74640H1‒74640H12 (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, A. M. Siegel, J. Model, and M. L. Nischan, "Field testing and evaluation of a solar-blind UV communication link for unattended ground sensors," Proc. SPIE 5417, 250‒261 (2004).

Rand. Struct. Alg.

M. D. Penrose, "On k-connectivity for a geometric random graph," Rand. Struct. Alg. 15(2), 145‒164 (1999).
[CrossRef]

Wirel. Netw.

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

Other

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, June 9–11, 2002, Lausanne, Switzerland, pp. 80‒91.

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

B. Bollobas, Random Graphs, 2nd ed., Cambridge University Press, 2001.

D. Miorandi and E. Altman, "Coverage and connectivity of ad hoc networks in presence of channel randomness," IEEE Proc. of INFOCOM, Vol. 1, Mar. 13–17, 2005, Miami, FL, USA, pp. 491‒502.

L. Zhang, B.-H. Soong, Y. Zhang, M. Ma, and Y. Guan, "An analysis of k-connectivity in shadowing and Nakagami fading wireless multi-hop networks," Proc. IEEE VTC Spring, May 11–14, 2008, Singapore, pp. 395‒399.

G. K. Karagiannidis, D. A. Zogas, N. C. Sagias, T. A. Tsiftsis, and P. T. Mathiopoulos, "Multihop communications with fixed-gain relays over generalized fading channels," Proc. IEEE Globecom, Dec. 2004, Dallas, TX, USA.

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Figures (7)

Fig. 1
Fig. 1

UV-C NLOS link geometry.

Fig. 2
Fig. 2

P ( d min > k ) versus ρ for OOK and the Gaussian noise model assuming P t = 50 mW and R b = 10 kbps .

Fig. 3
Fig. 3

P ( d min > k ) versus ρ for OOK and the Poisson noise model assuming P t = 50 mW and R b = 10 kbps .

Fig. 4
Fig. 4

P ( d min > k ) versus ρ for PPM and the Gaussian noise model assuming P t = 50 mW and R b = 10 kbps .

Fig. 5
Fig. 5

P ( d min > k ) versus ρ for PPM and the Poisson noise model assuming P t = 50 mW and R b = 10 kbps .

Fig. 6
Fig. 6

P ( d min > k ) versus transmitted power for R b = 10 kbps and (a) OOK and the Gaussian noise model ( ρ = 5 1 0 2 ), (b) OOK and the Poisson noise model ( ρ = 2 1 0 2 ), (c) PPM and the Gaussian noise model ( ρ = 2 1 0 2 ), and (d) PPM and the Poisson noise model ( ρ = 6 1 0 3 ).

Fig. 7
Fig. 7

P ( d min > k ) versus supported data rate for P e = 1 0 3 and (a) OOK and the Gaussian noise model ( ρ = 5 1 0 2 ), (b) OOK and the Poisson noise model ( ρ = 2 1 0 2 ), (c) PPM and the Gaussian noise model ( ρ = 2 1 0 2 ), and (d) PPM and the Poisson noise model ( ρ = 6 1 0 3 ).

Tables (2)

Tables Icon

Table I System Model Parameters

Tables Icon

Table II Coverage Analysis for the Gaussian Noise Model