Abstract

There has been recent interest in establishing non-line-of-sight links in the solar-blind ultraviolet region for outdoor optical wireless communications. This paper presents a novel channel model combining both photon propagation and detection statistics. The channel capacity with binary inputs is numerically computed for on–off keying and 4-pulse-position modulation (4-PPM) at different baud rates. To approach the capacity, error control coding is applied and a message passing decoding technique is outlined. Simulation results for a running example through the paper indicate that, at a given power, there is an optimum transmitted baud rate that maximizes the achievable data rate on such links. With the application of proper coding techniques, it is demonstrated that a near fifty-fold increase in rate over previous reported designs for this channel is feasible.

© 2012 OSA

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  28. M. D. A. Mohamed and S. Hranilovic, “Information rates of optical impulse modulation over indoor diffuse wireless channels,” in 24th Biennial Symp. on Communications, Kingston, ON, Canada, June 24–26, 2008, pp. 196–199.
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    [CrossRef]
  30. M. Eroz, F.-W. Sun, and L.-N. Lee, “DVB-S2 low density parity check codes with near Shannon limit performance,” Int. J. Satellite Commun. Netw., vol. 22, pp. 269–279, 2004.
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    [CrossRef]

2011 (3)

M. A. Elshimy and S. Hranilovic, “Non-line-of-sight single-scatter propagation model for non-coplanar geometries,” J. Opt. Soc. Am. A., vol. 28, no. 3, pp. 420–428, Mar.2011.
[CrossRef]

R. J. Drost, T. J. Moore, and B. M. Sadler, “UV communications channel modeling incorporating multiple scattering interactions,” J. Opt. Soc. Am. A., vol. 28, no. 4, pp. 686–695, Apr.2011.
[CrossRef]

M. A. Elshimy and S. Hranilovic, “Impact of finite receiver-aperture size in a non-line-of-sight single-scatter propagation model,” J. Opt. Soc. Am. A., vol. 28, no. 12, pp. 2568–2576, Dec.2011.
[CrossRef]

2010 (5)

2009 (2)

2008 (2)

Z. Xu and B. M. Sadler, “Ultraviolet communications: Potential and state-of-the-art,” IEEE Commun. Mag., vol. 46, no. 5, pp. 67–73, May2008.

G. Chen, F. Abou-Galala, Z. Xu, and B. M. Sadler, “Experimental evaluation of LED-based solar blind NLOS communication links,” Opt. Express, vol. 16, no. 19, pp. 15059–15068, Sept.2008.
[CrossRef] [PubMed]

2007 (1)

2006 (2)

G. A. Shaw, A. M. Siegel, and J. Model, “Extending the range and performance of non-line-of-sight ultraviolet communication links,” Proc. SPIE, vol. 6231, 62310C, 2006.

D. M. Arnold, H.-A. Loeliger, P. O. Vontobel, A. Kavcic, and W. Zeng, “Simulation-based computation of information rates for channels with memory,” IEEE Trans. Inf. Theory, vol. 52, no. 8, pp. 3498–3508, Aug.2006.
[CrossRef]

2004 (2)

M. Eroz, F.-W. Sun, and L.-N. Lee, “DVB-S2 low density parity check codes with near Shannon limit performance,” Int. J. Satellite Commun. Netw., vol. 22, pp. 269–279, 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, vol. 5611, pp. 244–254, 2004.
[CrossRef]

2003 (1)

G. A. Shaw, A. M. Siegel, and M. L. Nischan, “Demonstration system and applications for compact wireless ultraviolet communications,” Proc. SPIE, vol. 5071, pp. 241–252, 2003.
[CrossRef]

2001 (1)

F. Kschischang, B. Frey, and H.-A. Loeliger, “Factor graphs and the sum–product algorithm,” IEEE Trans. Inf. Theory, vol. 47, no. 2, pp. 498–519, Feb.2001.
[CrossRef]

2000 (1)

G. A. Shaw, M. Nischan, M. Iyengar, S. Kaushik, and M. K. Griffin, “NLOS UV communication for distributed sensor systems,” Proc. SPIE, vol. 4126, pp. 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. Am. A., vol. 8, no. 12, pp. 1964–1972, Dec.1991.
[CrossRef]

1988 (1)

P. H. Algoet and T. M. Cover, “A sandwich proof of the Shannon-McMillan-Breiman theorem,” Ann. Probab., vol. 16, no. 2, pp. 899–909, 1988.
[CrossRef]

1974 (1)

L. R. Bahl, J. Cocke, F. Jelinek, and J. Raviv, “Optimal decoding of linear codes for minimizing symbol error rate,” IEEE Trans. Inf. Theory, vol. 20, pp. 284–287, Mar.1974.
[CrossRef]

Abou-Galala, F.

Algoet, P. H.

P. H. Algoet and T. M. Cover, “A sandwich proof of the Shannon-McMillan-Breiman theorem,” Ann. Probab., vol. 16, no. 2, pp. 899–909, 1988.
[CrossRef]

Arnold, D. M.

D. M. Arnold, H.-A. Loeliger, P. O. Vontobel, A. Kavcic, and W. Zeng, “Simulation-based computation of information rates for channels with memory,” IEEE Trans. Inf. Theory, vol. 52, no. 8, pp. 3498–3508, Aug.2006.
[CrossRef]

D. M. Arnold and H.-A. Loeliger, “On the information rate of binary-input channels with memory,” in IEEE Int. Conf. Commun., Helsinki, Finland, June 11–14, 2001, vol. 9, pp. 2692–2695.

Bahl, L. R.

L. R. Bahl, J. Cocke, F. Jelinek, and J. Raviv, “Optimal decoding of linear codes for minimizing symbol error rate,” IEEE Trans. Inf. Theory, vol. 20, pp. 284–287, Mar.1974.
[CrossRef]

Barry, J. R.

J. R. Barry, “Sequence detection and equalization for pulse-position modulation,” in IEEE Int. Conf. Commun., New Orleans, LA, May 1994, vol. 3, pp. 1561–1565.

Brandt-Pearce, M.

M. Noshad and M. Brandt-Pearce, “NLOS UV communication systems using spectral amplitude coding,” in 2011 IEEE GLOBECOM Workshops, Dec. 5–9, 2011, pp. 843–848.

Chang, S.

H. Yin, S. Chang, H. Jia, J. Yang, and J. Yang, “Non-line-of-sight multiscatter propagation model,” J. Opt. Soc. Am. A., vol. 26, no. 11, pp. 2466–2469, Nov.2009.
[CrossRef]

Chen, G.

Cocke, J.

L. R. Bahl, J. Cocke, F. Jelinek, and J. Raviv, “Optimal decoding of linear codes for minimizing symbol error rate,” IEEE Trans. Inf. Theory, vol. 20, pp. 284–287, Mar.1974.
[CrossRef]

Cover, T. M.

P. H. Algoet and T. M. Cover, “A sandwich proof of the Shannon-McMillan-Breiman theorem,” Ann. Probab., vol. 16, no. 2, pp. 899–909, 1988.
[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., vol. 2010, pp. 1–12, June2010.
[CrossRef]

Drost, R. J.

R. J. Drost, T. J. Moore, and B. M. Sadler, “UV communications channel modeling incorporating multiple scattering interactions,” J. Opt. Soc. Am. A., vol. 28, no. 4, pp. 686–695, Apr.2011.
[CrossRef]

Elshimy, M. A.

M. A. Elshimy and S. Hranilovic, “Non-line-of-sight single-scatter propagation model for non-coplanar geometries,” J. Opt. Soc. Am. A., vol. 28, no. 3, pp. 420–428, Mar.2011.
[CrossRef]

M. A. Elshimy and S. Hranilovic, “Impact of finite receiver-aperture size in a non-line-of-sight single-scatter propagation model,” J. Opt. Soc. Am. A., vol. 28, no. 12, pp. 2568–2576, Dec.2011.
[CrossRef]

Eroz, M.

M. Eroz, F.-W. Sun, and L.-N. Lee, “DVB-S2 low density parity check codes with near Shannon limit performance,” Int. J. Satellite Commun. Netw., vol. 22, pp. 269–279, 2004.
[CrossRef]

Frey, B.

F. Kschischang, B. Frey, and H.-A. Loeliger, “Factor graphs and the sum–product algorithm,” IEEE Trans. Inf. Theory, vol. 47, no. 2, pp. 498–519, Feb.2001.
[CrossRef]

Goodman, J. W.

J. W. Goodman, Statistical Optics. John Wiley and Sons, Inc., 1985.

Griffin, M. K.

G. A. Shaw, M. Nischan, M. Iyengar, S. Kaushik, and M. K. Griffin, “NLOS UV communication for distributed sensor systems,” Proc. SPIE, vol. 4126, pp. 83–96, 2000.
[CrossRef]

He, Q.

Q. He, Z. Xu, and B. M. Sadler, “Performance of short-range non-line-of-sight LED-based ultraviolet communication receivers,” Opt. Express, vol. 18, no. 12, pp. 12226–12238, May2010.
[CrossRef] [PubMed]

L. Wang, Q. He, Z. Xu, and B. M. Sadler, “Performance of non-line-of-sight ultraviolet communication receiver in ISI channel,” Proc. SPIE, vol. 7814, 781409, Aug.2010.

Hranilovic, S.

M. A. Elshimy and S. Hranilovic, “Impact of finite receiver-aperture size in a non-line-of-sight single-scatter propagation model,” J. Opt. Soc. Am. A., vol. 28, no. 12, pp. 2568–2576, Dec.2011.
[CrossRef]

M. A. Elshimy and S. Hranilovic, “Non-line-of-sight single-scatter propagation model for non-coplanar geometries,” J. Opt. Soc. Am. A., vol. 28, no. 3, pp. 420–428, Mar.2011.
[CrossRef]

M. D. A. Mohamed and S. Hranilovic, “Information rates of optical impulse modulation over indoor diffuse wireless channels,” in 24th Biennial Symp. on Communications, Kingston, ON, Canada, June 24–26, 2008, pp. 196–199.

Huffman, R. E.

R. E. Huffman, Atmospheric Ultraviolet Remote Sensing. Academic Press, 1992.

Iyengar, M.

G. A. Shaw, M. Nischan, M. Iyengar, S. Kaushik, and M. K. Griffin, “NLOS UV communication for distributed sensor systems,” Proc. SPIE, vol. 4126, pp. 83–96, 2000.
[CrossRef]

Jelinek, F.

L. R. Bahl, J. Cocke, F. Jelinek, and J. Raviv, “Optimal decoding of linear codes for minimizing symbol error rate,” IEEE Trans. Inf. Theory, vol. 20, pp. 284–287, Mar.1974.
[CrossRef]

Jia, H.

H. Yin, S. Chang, H. Jia, J. Yang, and J. Yang, “Non-line-of-sight multiscatter propagation model,” J. Opt. Soc. Am. A., vol. 26, no. 11, pp. 2466–2469, Nov.2009.
[CrossRef]

Kaushik, S.

G. A. Shaw, M. Nischan, M. Iyengar, S. Kaushik, and M. K. Griffin, “NLOS UV communication for distributed sensor systems,” Proc. SPIE, vol. 4126, pp. 83–96, 2000.
[CrossRef]

Kavcic, A.

D. M. Arnold, H.-A. Loeliger, P. O. Vontobel, A. Kavcic, and W. Zeng, “Simulation-based computation of information rates for channels with memory,” IEEE Trans. Inf. Theory, vol. 52, no. 8, pp. 3498–3508, Aug.2006.
[CrossRef]

Kedar, D.

Kschischang, F.

F. Kschischang, B. Frey, and H.-A. Loeliger, “Factor graphs and the sum–product algorithm,” IEEE Trans. Inf. Theory, vol. 47, no. 2, pp. 498–519, Feb.2001.
[CrossRef]

Lee, L.-N.

M. Eroz, F.-W. Sun, and L.-N. Lee, “DVB-S2 low density parity check codes with near Shannon limit performance,” Int. J. Satellite Commun. Netw., vol. 22, pp. 269–279, 2004.
[CrossRef]

Li, Y.

L. Wang, Y. Li, Z. Xu, and B. M. Sadler, “Wireless ultraviolet network models and performance in noncoplanar geometry,” in IEEE Globecom 2010 Workshop on Optical Wireless Communications (OWC 2010), Miami, FL, Dec. 6–10, 2010, pp. 1037–1041.

Loeliger, H.-A.

D. M. Arnold, H.-A. Loeliger, P. O. Vontobel, A. Kavcic, and W. Zeng, “Simulation-based computation of information rates for channels with memory,” IEEE Trans. Inf. Theory, vol. 52, no. 8, pp. 3498–3508, Aug.2006.
[CrossRef]

F. Kschischang, B. Frey, and H.-A. Loeliger, “Factor graphs and the sum–product algorithm,” IEEE Trans. Inf. Theory, vol. 47, no. 2, pp. 498–519, Feb.2001.
[CrossRef]

D. M. Arnold and H.-A. Loeliger, “On the information rate of binary-input channels with memory,” in IEEE Int. Conf. Commun., Helsinki, Finland, June 11–14, 2001, vol. 9, pp. 2692–2695.

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. A., vol. 8, no. 12, pp. 1964–1972, Dec.1991.
[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, vol. 5611, pp. 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, vol. 6231, 62310C, 2006.

Mohamed, M. D. A.

M. D. A. Mohamed and S. Hranilovic, “Information rates of optical impulse modulation over indoor diffuse wireless channels,” in 24th Biennial Symp. on Communications, Kingston, ON, Canada, June 24–26, 2008, pp. 196–199.

Moore, T. J.

R. J. Drost, T. J. Moore, and B. M. Sadler, “UV communications channel modeling incorporating multiple scattering interactions,” J. Opt. Soc. Am. A., vol. 28, no. 4, pp. 686–695, Apr.2011.
[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, vol. 5611, pp. 244–254, 2004.
[CrossRef]

Nischan, M.

G. A. Shaw, M. Nischan, M. Iyengar, S. Kaushik, and M. K. Griffin, “NLOS UV communication for distributed sensor systems,” Proc. SPIE, vol. 4126, pp. 83–96, 2000.
[CrossRef]

Nischan, M. L.

G. A. Shaw, A. M. Siegel, and M. L. Nischan, “Demonstration system and applications for compact wireless ultraviolet communications,” Proc. SPIE, vol. 5071, pp. 241–252, 2003.
[CrossRef]

Noshad, M.

M. Noshad and M. Brandt-Pearce, “NLOS UV communication systems using spectral amplitude coding,” in 2011 IEEE GLOBECOM Workshops, Dec. 5–9, 2011, pp. 843–848.

Pfister, J. D.

J. D. Pfister, J. B. Soriaga, and P. H. Siegel, “On the achievable information rates of finite state ISI channels,” in IEEE Global Telecommunications Conf., San Antonio, TX, 2001, vol. 5, pp. 2992–2996.

Raviv, J.

L. R. Bahl, J. Cocke, F. Jelinek, and J. Raviv, “Optimal decoding of linear codes for minimizing symbol error rate,” IEEE Trans. Inf. Theory, vol. 20, pp. 284–287, Mar.1974.
[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, vol. 5611, pp. 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. A., vol. 8, no. 12, pp. 1964–1972, Dec.1991.
[CrossRef]

Sadler, B. M.

R. J. Drost, T. J. Moore, and B. M. Sadler, “UV communications channel modeling incorporating multiple scattering interactions,” J. Opt. Soc. Am. A., vol. 28, no. 4, pp. 686–695, Apr.2011.
[CrossRef]

L. Wang, Z. Xu, and B. M. Sadler, “Non-line-of-sight ultraviolet link loss in noncoplanar geometry,” Opt. Lett., vol. 35, no. 8, pp. 1263–1265, Apr.2010.
[CrossRef] [PubMed]

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., vol. 2010, pp. 1–12, June2010.
[CrossRef]

L. Wang, Q. He, Z. Xu, and B. M. Sadler, “Performance of non-line-of-sight ultraviolet communication receiver in ISI channel,” Proc. SPIE, vol. 7814, 781409, Aug.2010.

G. Chen, Z. Xu, and B. M. Sadler, “Experimental demonstration of ultraviolet pulse broadening in short-range non-line-of-sight communication channels,” Opt. Express, vol. 18, no. 10, pp. 10500–10509, May2010.
[CrossRef] [PubMed]

Q. He, Z. Xu, and B. M. Sadler, “Performance of short-range non-line-of-sight LED-based ultraviolet communication receivers,” Opt. Express, vol. 18, no. 12, pp. 12226–12238, May2010.
[CrossRef] [PubMed]

G. Chen, F. Abou-Galala, H. D. Z. Xu, and B. M. Sadler, “Path loss modeling and performance trade-off study for short-range non-line-of-sight ultraviolet communications,” Opt. Express, vol. 17, no. 5, pp. 3929–3940, Feb.2009.
[CrossRef] [PubMed]

G. Chen, F. Abou-Galala, Z. Xu, and B. M. Sadler, “Experimental evaluation of LED-based solar blind NLOS communication links,” Opt. Express, vol. 16, no. 19, pp. 15059–15068, Sept.2008.
[CrossRef] [PubMed]

Z. Xu and B. M. Sadler, “Ultraviolet communications: Potential and state-of-the-art,” IEEE Commun. Mag., vol. 46, no. 5, pp. 67–73, May2008.

L. Wang, Y. Li, Z. Xu, and B. M. Sadler, “Wireless ultraviolet network models and performance in noncoplanar geometry,” in IEEE Globecom 2010 Workshop on Optical Wireless Communications (OWC 2010), Miami, FL, Dec. 6–10, 2010, pp. 1037–1041.

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. A., vol. 8, no. 12, pp. 1964–1972, Dec.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, vol. 6231, 62310C, 2006.

G. A. Shaw, A. M. Siegel, and M. L. Nischan, “Demonstration system and applications for compact wireless ultraviolet communications,” Proc. SPIE, vol. 5071, pp. 241–252, 2003.
[CrossRef]

G. A. Shaw, M. Nischan, M. Iyengar, S. Kaushik, and M. K. Griffin, “NLOS UV communication for distributed sensor systems,” Proc. SPIE, vol. 4126, pp. 83–96, 2000.
[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, vol. 6231, 62310C, 2006.

G. A. Shaw, A. M. Siegel, and M. L. Nischan, “Demonstration system and applications for compact wireless ultraviolet communications,” Proc. SPIE, vol. 5071, pp. 241–252, 2003.
[CrossRef]

Siegel, P. H.

J. D. Pfister, J. B. Soriaga, and P. H. Siegel, “On the achievable information rates of finite state ISI channels,” in IEEE Global Telecommunications Conf., San Antonio, TX, 2001, vol. 5, pp. 2992–2996.

Soriaga, J. B.

J. D. Pfister, J. B. Soriaga, and P. H. Siegel, “On the achievable information rates of finite state ISI channels,” in IEEE Global Telecommunications Conf., San Antonio, TX, 2001, vol. 5, pp. 2992–2996.

Sun, F.-W.

M. Eroz, F.-W. Sun, and L.-N. Lee, “DVB-S2 low density parity check codes with near Shannon limit performance,” Int. J. Satellite Commun. Netw., vol. 22, pp. 269–279, 2004.
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D. M. Arnold, H.-A. Loeliger, P. O. Vontobel, A. Kavcic, and W. Zeng, “Simulation-based computation of information rates for channels with memory,” IEEE Trans. Inf. Theory, vol. 52, no. 8, pp. 3498–3508, Aug.2006.
[CrossRef]

Wang, L.

L. Wang, Q. He, Z. Xu, and B. M. Sadler, “Performance of non-line-of-sight ultraviolet communication receiver in ISI channel,” Proc. SPIE, vol. 7814, 781409, Aug.2010.

L. Wang, Z. Xu, and B. M. Sadler, “Non-line-of-sight ultraviolet link loss in noncoplanar geometry,” Opt. Lett., vol. 35, no. 8, pp. 1263–1265, Apr.2010.
[CrossRef] [PubMed]

L. Wang, Y. Li, Z. Xu, and B. M. Sadler, “Wireless ultraviolet network models and performance in noncoplanar geometry,” in IEEE Globecom 2010 Workshop on Optical Wireless Communications (OWC 2010), Miami, FL, Dec. 6–10, 2010, pp. 1037–1041.

Xu, H. D. Z.

Xu, Z.

Q. He, Z. Xu, and B. M. Sadler, “Performance of short-range non-line-of-sight LED-based ultraviolet communication receivers,” Opt. Express, vol. 18, no. 12, pp. 12226–12238, May2010.
[CrossRef] [PubMed]

L. Wang, Q. He, Z. Xu, and B. M. Sadler, “Performance of non-line-of-sight ultraviolet communication receiver in ISI channel,” Proc. SPIE, vol. 7814, 781409, Aug.2010.

G. Chen, Z. Xu, and B. M. Sadler, “Experimental demonstration of ultraviolet pulse broadening in short-range non-line-of-sight communication channels,” Opt. Express, vol. 18, no. 10, pp. 10500–10509, May2010.
[CrossRef] [PubMed]

L. Wang, Z. Xu, and B. M. Sadler, “Non-line-of-sight ultraviolet link loss in noncoplanar geometry,” Opt. Lett., vol. 35, no. 8, pp. 1263–1265, Apr.2010.
[CrossRef] [PubMed]

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., vol. 2010, pp. 1–12, June2010.
[CrossRef]

Z. Xu and B. M. Sadler, “Ultraviolet communications: Potential and state-of-the-art,” IEEE Commun. Mag., vol. 46, no. 5, pp. 67–73, May2008.

G. Chen, F. Abou-Galala, Z. Xu, and B. M. Sadler, “Experimental evaluation of LED-based solar blind NLOS communication links,” Opt. Express, vol. 16, no. 19, pp. 15059–15068, Sept.2008.
[CrossRef] [PubMed]

L. Wang, Y. Li, Z. Xu, and B. M. Sadler, “Wireless ultraviolet network models and performance in noncoplanar geometry,” in IEEE Globecom 2010 Workshop on Optical Wireless Communications (OWC 2010), Miami, FL, Dec. 6–10, 2010, pp. 1037–1041.

Yang, J.

H. Yin, S. Chang, H. Jia, J. Yang, and J. Yang, “Non-line-of-sight multiscatter propagation model,” J. Opt. Soc. Am. A., vol. 26, no. 11, pp. 2466–2469, Nov.2009.
[CrossRef]

H. Yin, S. Chang, H. Jia, J. Yang, and J. Yang, “Non-line-of-sight multiscatter propagation model,” J. Opt. Soc. Am. A., vol. 26, no. 11, pp. 2466–2469, Nov.2009.
[CrossRef]

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H. Yin, S. Chang, H. Jia, J. Yang, and J. Yang, “Non-line-of-sight multiscatter propagation model,” J. Opt. Soc. Am. A., vol. 26, no. 11, pp. 2466–2469, Nov.2009.
[CrossRef]

Zeng, W.

D. M. Arnold, H.-A. Loeliger, P. O. Vontobel, A. Kavcic, and W. Zeng, “Simulation-based computation of information rates for channels with memory,” IEEE Trans. Inf. Theory, vol. 52, no. 8, pp. 3498–3508, Aug.2006.
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Appl. Opt. (1)

EURASIP J. Wireless Commun. Netw. (1)

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., vol. 2010, pp. 1–12, June2010.
[CrossRef]

IEEE Commun. Mag. (1)

Z. Xu and B. M. Sadler, “Ultraviolet communications: Potential and state-of-the-art,” IEEE Commun. Mag., vol. 46, no. 5, pp. 67–73, May2008.

IEEE Trans. Inf. Theory (3)

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D. M. Arnold, H.-A. Loeliger, P. O. Vontobel, A. Kavcic, and W. Zeng, “Simulation-based computation of information rates for channels with memory,” IEEE Trans. Inf. Theory, vol. 52, no. 8, pp. 3498–3508, Aug.2006.
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F. Kschischang, B. Frey, and H.-A. Loeliger, “Factor graphs and the sum–product algorithm,” IEEE Trans. Inf. Theory, vol. 47, no. 2, pp. 498–519, Feb.2001.
[CrossRef]

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M. Eroz, F.-W. Sun, and L.-N. Lee, “DVB-S2 low density parity check codes with near Shannon limit performance,” Int. J. Satellite Commun. Netw., vol. 22, pp. 269–279, 2004.
[CrossRef]

J. Opt. Soc. Am. A. (5)

M. A. Elshimy and S. Hranilovic, “Impact of finite receiver-aperture size in a non-line-of-sight single-scatter propagation model,” J. Opt. Soc. Am. A., vol. 28, no. 12, pp. 2568–2576, Dec.2011.
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M. A. Elshimy and S. Hranilovic, “Non-line-of-sight single-scatter propagation model for non-coplanar geometries,” J. Opt. Soc. Am. A., vol. 28, no. 3, pp. 420–428, Mar.2011.
[CrossRef]

H. Yin, S. Chang, H. Jia, J. Yang, and J. Yang, “Non-line-of-sight multiscatter propagation model,” J. Opt. Soc. Am. A., vol. 26, no. 11, pp. 2466–2469, Nov.2009.
[CrossRef]

R. J. Drost, T. J. Moore, and B. M. Sadler, “UV communications channel modeling incorporating multiple scattering interactions,” J. Opt. Soc. Am. A., vol. 28, no. 4, pp. 686–695, Apr.2011.
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Proc. SPIE (5)

G. A. Shaw, A. M. Siegel, and M. L. Nischan, “Demonstration system and applications for compact wireless ultraviolet communications,” Proc. SPIE, vol. 5071, pp. 241–252, 2003.
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Figures (9)

Fig. 1
Fig. 1

(Color online) Schematic drawing showing the NLOS UV link.

Fig. 2
Fig. 2

(Color online) The temporal response h ( t ) at r = 100  m, β T = β R = 90 ° , θ T = θ R = 45 ° and a = 0 . 8  cm.

Fig. 3
Fig. 3

Block diagram of a discrete-time NLOS UV ISI channel model.

Fig. 4
Fig. 4

Factor graph representation of the ISI vector channel model.

Fig. 5
Fig. 5

(Color online) Channel capacity for a uniform input message in bits per channel use versus the transmitted baud rate in Hz for OOK and 4-PPM. The average transmitted power P a v = 100  mW. The discrete points indicate the performance of the coding systems in Subsection V.B at BER = 1 0 5 .

Fig. 6
Fig. 6

(Color online) Channel capacity for a uniform input message in kilobits per second versus the transmitted baud rate in Hz for OOK and 4-PPM. The average transmitted power P a v = 100  mW. The discrete points indicate the performance of the coding systems in Subsection V.B at BER = 1 0 5 .

Fig. 7
Fig. 7

Block diagram of an NLOS UV communication system with an LDPC code and an iterative decoding algorithm.

Fig. 8
Fig. 8

(Color online) Performance of LDPC codes versus the transmitted baud rate for OOK ( N = 64,800 bits, P a v = 100  mW). The performance of uncoded transmission with hard decisions on a BCJR demodulator output is indicated by the dashed line and the code rates are denoted by the labels given in Table II.

Fig. 9
Fig. 9

(Color online) Performance of LDPC codes versus the transmitted baud rate for 4-PPM ( N = 64,800 bits, P a v = 100  mW). The performance of uncoded transmission with hard decisions on a BCJR demodulator output is indicated by the dashed line and the code rates are denoted by the labels given in Table II.

Tables (2)

Tables Icon

Table I Discrete-Time ISI Channel q for Different Baud Rates R B d

Tables Icon

Table II R B d [kHz] at BER = 1 0 5 for the LDPC Codes in Figs. 8 and 9

Equations (36)

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k s P ( cos Θ s ) cos ζ A r 4 π Ω T r T 2 r R 2 exp [ k e ( r T + r R ) ] δ V ,
h ( t ) = H o h o ( t ) ,
h ( t ) = c k s A r exp ( k e c t ) 2 π Ω T r 2 η 1 ( t ) η 2 ( t ) ϕ 1 ( t , η ) ϕ 2 ( t , η ) P ( cos Θ s ) cos ζ ( c t r ) 2 η 2 d ϕ d η ,
H o = t min t max h ( t ) d t ,
P L = 10 log 10 ( H 0 ) = 107 . 9 dB .
D = [ ( t t ̄ ) 2 h ( t ) d t h ( t ) d t ] 1 / 2 = 1 . 125 µ s ,
c ( t ) = p ( t ) * h o ( t ) .
q m = H o t min + m T t min + ( m + 1 ) T c ( t ) d t .
Bin ( z m ; x 0 , q m ) = ( x 0 z m ) q m z m ( 1 q m ) x 0 z m ,
Pos ( z m ; x 0 q m ) = ( x 0 q m ) z m z m ! exp ( x 0 q m ) ,
u i = x i q 0 + m = 1 M x i m q m ,
w i = η ( v i + N b g ) + N dark .
p ( y | x ) = p ( y | u ) = i = 1 I p ( y i | u , y 1 , , y i 1 ) = i = 1 n p ( y i | u i ) .
p ( y i | u i ) = v i p ( y i , v i | u i ) = v i p ( v i | u i ) p ( y i | v i ) = v i Pos ( v i ; u i ) Pos ( y i ; w i ) .
u k = x k Q 0 + f = 1 F x k f Q f ,
Q 0 ( i , j ) = { q j i , i j , 0 , i > j ,
Q F ( i , j ) = { q F L + j i i j , 0 , i < j ,
Q f ( i , j ) = q f L + j i , ( i , j )     &     f { 0 , F } .
I ( X ; Y ) = lim K 1 L K I ( x K ; y K ) , = lim K 1 L K [ H ( y K ) H ( y K | x K ) ] , = 1 L [ H ( Y ) H ( Y | X ) ] ,
1 K log [ p ( y K ) ] H ( Y ) ,
1 K log [ p ( y K | x K ) ] H ( Y | X ) .
p ( y K ) = s α K ( s ) .
N a v = P a v L T λ h P c ,
L ( c k l l + d ) = log p ( c k l l + d = 0 | y K ) p ( c k l l + d = 1 | y K )
L ( c k l l + d ) = log m M d ( 0 ) p ( m k = m | y K ) m M d ( 1 ) p ( m k = m | y K ) ,
L ( c k l l + d ) = log m M d ( 0 ) p ( m k = m , y K ) m M d ( 1 ) p ( m k = m , y K ) .
p ( m k = m , y K ) = s p ( s k = s , m k = m , y K ) = ( s , s ) S ( m ) p ( s k = s , s k + 1 = s , y K ) ,
p ( s k = s , s k + 1 = s , y K ) = p ( s k = s , y 1 k 1 ) p ( s k + 1 = s , y k | s k = s ) p ( y k + 1 K | s k + 1 = s ) ,
p ( s k = s , s k + 1 = s , y 1 K ) = α k 1 ( s ) γ k ( s , s ) β k ( s ) ,
γ k ( s , s ) = p ( s k + 1 = s , y k | s k = s ) = p k ( s | s ) p ( y k | s , s ) ,
α k ( s ) = p ( s k + 1 = s , y 1 k ) = s α k 1 ( s ) γ k ( s , s )
β k 1 ( s ) = p ( y k K | s k = s ) = s γ k ( s , s ) β k ( s ) .
α k ( s ) = A k m α k 1 ( s ) γ k ( s , s ) ,
β k 1 ( s ) = B k 1 s γ k ( s , s ) β k ( s ) ,
α k ( s ) = α k ( s ) A 1 A 2 A k
β k 1 ( s ) = β k 1 ( s ) B k 1 B k B K 1 .