Abstract

A demonstration of ultraviolet-B (UVB) communication link is implemented utilizing quadrature amplitude modulation (QAM) orthogonal frequency-division multiplexing (OFDM). The demonstration is based on a 294-nm UVB-light-emitting-diode (UVB-LED) with a full-width at half-maximum (FWHM) of 9 nm and light output power of 190 μW, at 7 V, with a special silica gel lens on top of it. A −3-dB bandwidth of 29 MHz was measured and a high-speed near-solar-blind communication link with a data rate of 71 Mbit/s was achieved using 8-QAM-OFDM at perfect alignment. 23.6 Mbit/s using 2-QAM-OFDM when the angle subtended by the pointing directions of the UVB-LED and photodetector (PD) is 12 degrees, thus establishing a diffuse-line-of-sight (LOS) link. The measured bit-error rate (BER) of 2.8 × 104 and 2.4 × 104, respectively, are well below the forward error correction (FEC) criterion of 3.8 × 103. The demonstrated high data-rate OFDM-based UVB communication link paves the way for realizing high-speed non-line-of-sight free-space optical communications.

© 2017 Optical Society of America

Full Article  |  PDF Article
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References

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    [Crossref]

2016 (3)

2015 (5)

2014 (1)

L. C. Liao, Z. N. Li, T. Lang, B. M. Sadler, and G. Chen, “Turbulence channel test and analysis for NLOS UV communication,” Proc. SPIE 9224, 92241A (2014).
[Crossref]

2012 (1)

2011 (1)

2010 (1)

2009 (3)

2008 (2)

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] [PubMed]

2007 (1)

T. Feng, F. Xiong, Q. Ye, Z. Q. Pan, Z. R. Dong, and Z. J. Fang, “Non-line-of-sight optical scattering communication based on solar-blind ultraviolet light,” Proc. SPIE 6783, 67833X (2007).
[Crossref]

2006 (4)

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]

1994 (2)

B. Charles, B. Hughes, A. Erickson, J. Wilkins, and E. A. Teppo, “Ultraviolet-laser based communication-system for short-range tactical application,” Proc. SPIE 2115, 79–86 (1994).
[Crossref]

B. Charles, B. Hughes, A. Erickson, J. Wilkins, and E. Teppo, “An ultraviolet laser based communication system for short range tactical applications,” Proc. SPIE 2115, 79–86 (1994).
[Crossref]

1979 (1)

Abou-Galala, F.

Alias, M. S.

C. Shen, T. K. Ng, J. T. Leonard, A. Pourhashemi, H. M. Oubei, M. S. Alias, S. Nakamura, S. P. DenBaars, J. S. Speck, A. Y. Alyamani, M. M. Eldesouki, and B. S. Ooi, “High-Modulation-Efficiency, Integrated Waveguide Modulator-Laser Diode at 448 nm,” ACS Photonics 3(2), 262–268 (2016).
[Crossref]

Alyamani, A. Y.

C. Shen, T. K. Ng, J. T. Leonard, A. Pourhashemi, H. M. Oubei, M. S. Alias, S. Nakamura, S. P. DenBaars, J. S. Speck, A. Y. Alyamani, M. M. Eldesouki, and B. S. Ooi, “High-Modulation-Efficiency, Integrated Waveguide Modulator-Laser Diode at 448 nm,” ACS Photonics 3(2), 262–268 (2016).
[Crossref]

C. Shen, C. Lee, T. K. Ng, S. Nakamura, J. S. Speck, S. P. DenBaars, A. Y. Alyamani, M. M. El-Desouki, and B. S. Ooi, “High-speed 405-nm superluminescent diode (SLD) with 807-MHz modulation bandwidth,” Opt. Express 24(18), 20281–20286 (2016).
[Crossref] [PubMed]

Arnon, S.

Bayse, R.

J. J. Puschell and R. Bayse, “High data rate ultraviolet communication systems for the tactical battlefield,” Proc. of Tactical Communications Conf., 253–267 (1990).
[Crossref]

Cantore, M.

Chang, S.

Charles, B.

B. Charles, B. Hughes, A. Erickson, J. Wilkins, and E. Teppo, “An ultraviolet laser based communication system for short range tactical applications,” Proc. SPIE 2115, 79–86 (1994).
[Crossref]

B. Charles, B. Hughes, A. Erickson, J. Wilkins, and E. A. Teppo, “Ultraviolet-laser based communication-system for short-range tactical application,” Proc. SPIE 2115, 79–86 (1994).
[Crossref]

Chen, G.

R. J. Drost, T. Lang, G. Chen, L. Liao, Z. Li, and B. M. Sadler, “Long-distance non-line-of-sight ultraviolet communication channel analysis: experimentation and modelling,” IET Optoelectron. 9(5), 223–231 (2015).
[Crossref]

L. C. Liao, Z. N. Li, T. Lang, B. M. Sadler, and G. Chen, “Turbulence channel test and analysis for NLOS UV communication,” Proc. SPIE 9224, 92241A (2014).
[Crossref]

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 18(10), 10500–10509 (2010).
[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 16(19), 15059–15068 (2008).
[Crossref] [PubMed]

Chi, Y.-C.

Cong, P.

J. Yan, J. Wang, Y. Zhang, P. Cong, L. Sun, Y. Tian, C. Zhao, and J. Li, “AlGaN-based deep-ultraviolet light-emitting diodes grown on high-quality AlN template using MOVPE,” J. Cryst. Growth 414, 254–257 (2015).
[Crossref]

DenBaars, S. P.

Dong, Z. R.

T. Feng, F. Xiong, Q. Ye, Z. Q. Pan, Z. R. Dong, and Z. J. Fang, “Non-line-of-sight optical scattering communication based on solar-blind ultraviolet light,” Proc. SPIE 6783, 67833X (2007).
[Crossref]

Drost, R. J.

R. J. Drost, T. Lang, G. Chen, L. Liao, Z. Li, and B. M. Sadler, “Long-distance non-line-of-sight ultraviolet communication channel analysis: experimentation and modelling,” IET Optoelectron. 9(5), 223–231 (2015).
[Crossref]

Durand, G.

Eldesouki, M. M.

C. Shen, T. K. Ng, J. T. Leonard, A. Pourhashemi, H. M. Oubei, M. S. Alias, S. Nakamura, S. P. DenBaars, J. S. Speck, A. Y. Alyamani, M. M. Eldesouki, and B. S. Ooi, “High-Modulation-Efficiency, Integrated Waveguide Modulator-Laser Diode at 448 nm,” ACS Photonics 3(2), 262–268 (2016).
[Crossref]

El-Desouki, M. M.

Erickson, A.

B. Charles, B. Hughes, A. Erickson, J. Wilkins, and E. A. Teppo, “Ultraviolet-laser based communication-system for short-range tactical application,” Proc. SPIE 2115, 79–86 (1994).
[Crossref]

B. Charles, B. Hughes, A. Erickson, J. Wilkins, and E. Teppo, “An ultraviolet laser based communication system for short range tactical applications,” Proc. SPIE 2115, 79–86 (1994).
[Crossref]

Fang, Z. J.

T. Feng, F. Xiong, Q. Ye, Z. Q. Pan, Z. R. Dong, and Z. J. Fang, “Non-line-of-sight optical scattering communication based on solar-blind ultraviolet light,” Proc. SPIE 6783, 67833X (2007).
[Crossref]

Farrell, R. M.

Feng, T.

T. Feng, F. Xiong, Q. Ye, Z. Q. Pan, Z. R. Dong, and Z. J. Fang, “Non-line-of-sight optical scattering communication based on solar-blind ultraviolet light,” Proc. SPIE 6783, 67833X (2007).
[Crossref]

Haas, H.

Han, D.

He, J.-H.

Hughes, B.

B. Charles, B. Hughes, A. Erickson, J. Wilkins, and E. A. Teppo, “Ultraviolet-laser based communication-system for short-range tactical application,” Proc. SPIE 2115, 79–86 (1994).
[Crossref]

B. Charles, B. Hughes, A. Erickson, J. Wilkins, and E. Teppo, “An ultraviolet laser based communication system for short range tactical applications,” Proc. SPIE 2115, 79–86 (1994).
[Crossref]

Janjua, B.

Jia, H.

Kedar, D.

Kuo, H.-C.

Lang, T.

R. J. Drost, T. Lang, G. Chen, L. Liao, Z. Li, and B. M. Sadler, “Long-distance non-line-of-sight ultraviolet communication channel analysis: experimentation and modelling,” IET Optoelectron. 9(5), 223–231 (2015).
[Crossref]

L. C. Liao, Z. N. Li, T. Lang, B. M. Sadler, and G. Chen, “Turbulence channel test and analysis for NLOS UV communication,” Proc. SPIE 9224, 92241A (2014).
[Crossref]

Lavigne, C.

Lee, C.

Leonard, J. T.

C. Shen, T. K. Ng, J. T. Leonard, A. Pourhashemi, H. M. Oubei, M. S. Alias, S. Nakamura, S. P. DenBaars, J. S. Speck, A. Y. Alyamani, M. M. Eldesouki, and B. S. Ooi, “High-Modulation-Efficiency, Integrated Waveguide Modulator-Laser Diode at 448 nm,” ACS Photonics 3(2), 262–268 (2016).
[Crossref]

Li, J.

J. Yan, J. Wang, Y. Zhang, P. Cong, L. Sun, Y. Tian, C. Zhao, and J. Li, “AlGaN-based deep-ultraviolet light-emitting diodes grown on high-quality AlN template using MOVPE,” J. Cryst. Growth 414, 254–257 (2015).
[Crossref]

Li, Z.

R. J. Drost, T. Lang, G. Chen, L. Liao, Z. Li, and B. M. Sadler, “Long-distance non-line-of-sight ultraviolet communication channel analysis: experimentation and modelling,” IET Optoelectron. 9(5), 223–231 (2015).
[Crossref]

Li, Z. N.

L. C. Liao, Z. N. Li, T. Lang, B. M. Sadler, and G. Chen, “Turbulence channel test and analysis for NLOS UV communication,” Proc. SPIE 9224, 92241A (2014).
[Crossref]

Liao, L.

R. J. Drost, T. Lang, G. Chen, L. Liao, Z. Li, and B. M. Sadler, “Long-distance non-line-of-sight ultraviolet communication channel analysis: experimentation and modelling,” IET Optoelectron. 9(5), 223–231 (2015).
[Crossref]

Liao, L. C.

L. C. Liao, Z. N. Li, T. Lang, B. M. Sadler, and G. Chen, “Turbulence channel test and analysis for NLOS UV communication,” Proc. SPIE 9224, 92241A (2014).
[Crossref]

Lin, G.-R.

Liu, Y.

Luo, P.

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 6231, 62310C (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).
[Crossref]

Nakamura, S.

Ng, T. K.

Ooi, B. S.

Oubei, H. M.

Pan, Z. Q.

T. Feng, F. Xiong, Q. Ye, Z. Q. Pan, Z. R. Dong, and Z. J. Fang, “Non-line-of-sight optical scattering communication based on solar-blind ultraviolet light,” Proc. SPIE 6783, 67833X (2007).
[Crossref]

Pikasis, E.

Pourhashemi, A.

C. Shen, T. K. Ng, J. T. Leonard, A. Pourhashemi, H. M. Oubei, M. S. Alias, S. Nakamura, S. P. DenBaars, J. S. Speck, A. Y. Alyamani, M. M. Eldesouki, and B. S. Ooi, “High-Modulation-Efficiency, Integrated Waveguide Modulator-Laser Diode at 448 nm,” ACS Photonics 3(2), 262–268 (2016).
[Crossref]

Puschell, J. J.

J. J. Puschell and R. Bayse, “High data rate ultraviolet communication systems for the tactical battlefield,” Proc. of Tactical Communications Conf., 253–267 (1990).
[Crossref]

Raptis, N.

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]

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

Retamal, J. R. D.

Roblin, A.

Sadler, B. M.

R. J. Drost, T. Lang, G. Chen, L. Liao, Z. Li, and B. M. Sadler, “Long-distance non-line-of-sight ultraviolet communication channel analysis: experimentation and modelling,” IET Optoelectron. 9(5), 223–231 (2015).
[Crossref]

L. C. Liao, Z. N. Li, T. Lang, B. M. Sadler, and G. Chen, “Turbulence channel test and analysis for NLOS UV communication,” Proc. SPIE 9224, 92241A (2014).
[Crossref]

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 18(10), 10500–10509 (2010).
[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 16(19), 15059–15068 (2008).
[Crossref] [PubMed]

Z. Xu and B. M. Sadler, “Ultraviolet Communications: Potential and State-Of-The-Art,” IEEE Commun. Mag. 46(5), 67–73 (2008).

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 6231, 62310C (2006).
[Crossref]

Shen, C.

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 6231, 62310C (2006).
[Crossref]

Speck, J. S.

Sun, L.

J. Yan, J. Wang, Y. Zhang, P. Cong, L. Sun, Y. Tian, C. Zhao, and J. Li, “AlGaN-based deep-ultraviolet light-emitting diodes grown on high-quality AlN template using MOVPE,” J. Cryst. Growth 414, 254–257 (2015).
[Crossref]

Syvridis, D.

Teppo, E.

B. Charles, B. Hughes, A. Erickson, J. Wilkins, and E. Teppo, “An ultraviolet laser based communication system for short range tactical applications,” Proc. SPIE 2115, 79–86 (1994).
[Crossref]

Teppo, E. A.

B. Charles, B. Hughes, A. Erickson, J. Wilkins, and E. A. Teppo, “Ultraviolet-laser based communication-system for short-range tactical application,” Proc. SPIE 2115, 79–86 (1994).
[Crossref]

Tian, Y.

J. Yan, J. Wang, Y. Zhang, P. Cong, L. Sun, Y. Tian, C. Zhao, and J. Li, “AlGaN-based deep-ultraviolet light-emitting diodes grown on high-quality AlN template using MOVPE,” J. Cryst. Growth 414, 254–257 (2015).
[Crossref]

Tsai, C.-T.

Tsonev, D.

Videv, S.

Wang, H.-Y.

Wang, J.

J. Yan, J. Wang, Y. Zhang, P. Cong, L. Sun, Y. Tian, C. Zhao, and J. Li, “AlGaN-based deep-ultraviolet light-emitting diodes grown on high-quality AlN template using MOVPE,” J. Cryst. Growth 414, 254–257 (2015).
[Crossref]

Warde, C.

Wilkins, J.

B. Charles, B. Hughes, A. Erickson, J. Wilkins, and E. Teppo, “An ultraviolet laser based communication system for short range tactical applications,” Proc. SPIE 2115, 79–86 (1994).
[Crossref]

B. Charles, B. Hughes, A. Erickson, J. Wilkins, and E. A. Teppo, “Ultraviolet-laser based communication-system for short-range tactical application,” Proc. SPIE 2115, 79–86 (1994).
[Crossref]

Xiong, F.

T. Feng, F. Xiong, Q. Ye, Z. Q. Pan, Z. R. Dong, and Z. J. Fang, “Non-line-of-sight optical scattering communication based on solar-blind ultraviolet light,” Proc. SPIE 6783, 67833X (2007).
[Crossref]

Xu, Z.

Yan, J.

J. Yan, J. Wang, Y. Zhang, P. Cong, L. Sun, Y. Tian, C. Zhao, and J. Li, “AlGaN-based deep-ultraviolet light-emitting diodes grown on high-quality AlN template using MOVPE,” J. Cryst. Growth 414, 254–257 (2015).
[Crossref]

Yang, J.

Ye, Q.

T. Feng, F. Xiong, Q. Ye, Z. Q. Pan, Z. R. Dong, and Z. J. Fang, “Non-line-of-sight optical scattering communication based on solar-blind ultraviolet light,” Proc. SPIE 6783, 67833X (2007).
[Crossref]

Yin, H.

Zhang, H.

Zhang, K.

Zhang, M.

Zhang, Y.

J. Yan, J. Wang, Y. Zhang, P. Cong, L. Sun, Y. Tian, C. Zhao, and J. Li, “AlGaN-based deep-ultraviolet light-emitting diodes grown on high-quality AlN template using MOVPE,” J. Cryst. Growth 414, 254–257 (2015).
[Crossref]

Zhao, C.

J. Yan, J. Wang, Y. Zhang, P. Cong, L. Sun, Y. Tian, C. Zhao, and J. Li, “AlGaN-based deep-ultraviolet light-emitting diodes grown on high-quality AlN template using MOVPE,” J. Cryst. Growth 414, 254–257 (2015).
[Crossref]

ACS Photonics (1)

C. Shen, T. K. Ng, J. T. Leonard, A. Pourhashemi, H. M. Oubei, M. S. Alias, S. Nakamura, S. P. DenBaars, J. S. Speck, A. Y. Alyamani, M. M. Eldesouki, and B. S. Ooi, “High-Modulation-Efficiency, Integrated Waveguide Modulator-Laser Diode at 448 nm,” ACS Photonics 3(2), 262–268 (2016).
[Crossref]

Appl. Opt. (4)

IEEE Commun. Mag. (1)

Z. Xu and B. M. Sadler, “Ultraviolet Communications: Potential and State-Of-The-Art,” IEEE Commun. Mag. 46(5), 67–73 (2008).

IET Optoelectron. (1)

R. J. Drost, T. Lang, G. Chen, L. Liao, Z. Li, and B. M. Sadler, “Long-distance non-line-of-sight ultraviolet communication channel analysis: experimentation and modelling,” IET Optoelectron. 9(5), 223–231 (2015).
[Crossref]

J. Cryst. Growth (1)

J. Yan, J. Wang, Y. Zhang, P. Cong, L. Sun, Y. Tian, C. Zhao, and J. Li, “AlGaN-based deep-ultraviolet light-emitting diodes grown on high-quality AlN template using MOVPE,” J. Cryst. Growth 414, 254–257 (2015).
[Crossref]

J. Opt. Soc. Am. (1)

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

Opt. Eng. (1)

D. Kedar and S. Arnon, “Subsea ultraviolet solar-blind broadband free-space optics communication,” Opt. Eng. 48(4), 046001 (2009).
[Crossref]

Opt. Express (8)

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] [PubMed]

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 18(10), 10500–10509 (2010).
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H. Zhang, H. Yin, H. Jia, J. Yang, and S. Chang, “Study of effects of obstacle on non-line-of-sight ultraviolet communication links,” Opt. Express 19(22), 21216–21226 (2011).
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D. Han, Y. Liu, K. Zhang, P. Luo, and M. Zhang, “Theoretical and experimental research on diversity reception technology in NLOS UV communication system,” Opt. Express 20(14), 15833–15842 (2012).
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D. Tsonev, S. Videv, and H. Haas, “Towards a 100 Gb/s visible light wireless access network,” Opt. Express 23(2), 1627–1637 (2015).
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B. Janjua, H. M. Oubei, J. R. D. Retamal, T. K. Ng, C.-T. Tsai, H.-Y. Wang, Y.-C. Chi, H.-C. Kuo, G.-R. Lin, J.-H. He, and B. S. Ooi, “Going beyond 4 Gbps data rate by employing RGB laser diodes for visible light communication,” Opt. Express 23(14), 18746–18753 (2015).
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C. Lee, C. Shen, H. M. Oubei, M. Cantore, B. Janjua, T. K. Ng, R. M. Farrell, M. M. El-Desouki, J. S. Speck, S. Nakamura, B. S. Ooi, and S. P. DenBaars, “2 Gbit/s data transmission from an unfiltered laser-based phosphor-converted white lighting communication system,” Opt. Express 23(23), 29779–29787 (2015).
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C. Shen, C. Lee, T. K. Ng, S. Nakamura, J. S. Speck, S. P. DenBaars, A. Y. Alyamani, M. M. El-Desouki, and B. S. Ooi, “High-speed 405-nm superluminescent diode (SLD) with 807-MHz modulation bandwidth,” Opt. Express 24(18), 20281–20286 (2016).
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Opt. Lett. (1)

Proc. SPIE (6)

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

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[Crossref]

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[Crossref]

Other (5)

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[Crossref]

M. Geller, et, “Optical Non-Line- of-Sight Covert, Secure High-Data Communication System,” Nava Ocean Systems Center, San Diego, California, U. S. Patent Number 4,493,114, (1985).

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Figures (6)

Fig. 1
Fig. 1

Schematic of the near solar-blind UV communication testbed for the LED based UV communication measurement. The set up consists of an Agilent Technologies 81150A Arbitrary Waveform Generator (AWG), a Tektronix DPO70404C Digital Phosphor Oscilloscope (DPO), a UVB-LED, Thorlabs LA4052-UV plano convex lens, as well as a Thorlabs APD 430A2/M avalanche photodetector.

Fig. 2
Fig. 2

(a) Voltage vs. current and optical power (Pout) vs. current characteristics of the UVB-LED. (b) Photo of the packaged UVB-LED soldered onto a PCB with sub-miniature version A (SMA) connector.

Fig. 3
Fig. 3

(a) Optical spectra of the LED under a bias voltage of 7V. (b) Small signal frequency response of the system. The dashed line indicates the −3dB bandwidth, which is approximately 29 MHz at distance = 0.

Fig. 4
Fig. 4

(a) Captured photo of the experimental set up for the LED based UV communication link. (b) Measured receiving power vs. distance between LED and PD.

Fig. 5
Fig. 5

(a) Received power vs. angle, and (b) data rate and BER vs. angle, between LED and PD.

Fig. 6
Fig. 6

(a)~(f): The corresponding constellation maps for angles of 2, 4, 6, 8, 10, and 12 degrees.

Tables (1)

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Table 1 Comparison of UV Systems Configurations and Performance

Equations (3)

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Ω= A x 2 .
I( x )=  I 0 e αx .
Data Rate=  S × N × log 2 M  L .

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