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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 12 — Jun. 7, 2010
  • pp: 12226–12238
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Performance of short-range non-line-of-sight LED-based ultraviolet communication receivers

Qunfeng He, Zhengyuan Xu, and Brian M. Sadler  »View Author Affiliations


Optics Express, Vol. 18, Issue 12, pp. 12226-12238 (2010)
http://dx.doi.org/10.1364/OE.18.012226


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Abstract

Utilizing an empirical path loss model proposed in the first paper of a two-part series, the bit error rate performance of short-range non-line-of-sight ultraviolet communication receivers is analyzed. Typical photodetector models and modulation formats are considered. Our results provide semi-analytical prediction of the achievable communication performance as a function of system and channel parameters, and serve as a basis for system design.

© 2010 OSA

1. Introduction

Ultraviolet (UV) technology is a candidate for wireless optical communications (WOC) due to the unique features of non-line-of-sight (NLOS) connectivity and range-dependent attenuation. Aided by recent device technologies in deep UV light emitting diodes [1

1. M. Shatalov, J. Zhang, A. S. Chitnis, V. Adivarahan, J. Yang, G. Simin, and M. A. Kahn, “Deep ultraviolet light-emitting diodes using quaternary AlInGaN multiple quantum wells,” IEEE J. Sel. Top. Quantum Electron. 8(2), 302–309 (2002). [CrossRef]

,2

2. V. Adivarahan, Q. Fareed, S. Srivastava, T. Katona, M. Gaevski, and A. Khan, “Robust 285 nm deep UV light emitting diodes over metal organic hydride vapor phase epitaxially grown AlN/sapphire templates,” Jpn. J. Appl. Phys. 46(23), L537– L539 (2007). [CrossRef]

] and avalanche photodiodes (APDs) [3

3. W. S. Ross and R. S. Kennedy, “An investigation of atmospheric optically scattered non-line-of-sight communication links,” Army Research Office Project Report, Research Triangle Park, NC, January 1980.

,4

4. M. Shatalov, J. Zhang, A. S. Chitnis, V. Adivarahan, J. Yang, G. Simin, and M. A. Kahn, “Deep ultraviolet light-emitting diodes using quaternary AlInGaN multiple quantum wells,” IEEE J. Sel. Top. Quantum Electron. 8(2), 302–309 (2002). [CrossRef]

], short range NLOS UV communications has significant potential [5

5. Z. Xu and B. M. Sadler, “Ultraviolet communications: potential and state-of-the-art,” IEEE Commun. Mag. 46(5), 67–73 (2008). [CrossRef]

].

In this paper, we extend the performance analysis presented in [11

11. 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] [PubMed]

]. Both photomultiplier tube (PMT) and avalanche photodiode (APD) based receiver structures are considered. The device and circuit random characteristics are incorporated along with the channel path loss model from [11

11. 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] [PubMed]

]. To start with, the system architecture and UV NLOS channel path loss model are described in Section 2. With the ideal photon counting receiver, performance results for intensity modulation and direct detection (IM/DD) using OOK and pulse position modulation (PPM) are summarized, and tradeoffs between communication range and data rate are studied to assist the design process, both in Section 3. Following up, we analyze the performance of the practical receivers built upon a PMT or APD to handle weak signal detection. The thermal noise in the electric circuit and the shot noise due to the background radiation add elements to the theoretical analysis. From our analysis, we predict the interactions among different system and geometric parameters in determining the BER performance. Our analytical results and techniques are generally applicable to other WOC systems given a corresponding path loss model.

2. System architecture and NLOS UV channel path loss model

The NLOS UV communication system is depicted in Fig. 1
Fig. 1 Non-line-of-sight UV communications system model.
. The transmitter consists of a modulated UV LED array, with pointing optics. The receiver employs either a PMT or APD aided by a solar-blind optical filter. The post-processing circuit involves integration and detection processing. The NLOS UV channel configuration is uniquely specified by a set of parameters noted in the figure. θ1 and θ2 are the transmitter (Tx) and receiver (Rx) apex angles, and ϕ1 and ϕ2 are the Tx full beam divergence angle and Rx field of view (FOV), respectively. For the purposes of this paper, ϕ1 and ϕ2 are fixed to be 10° and 30°, respectively [11

11. 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] [PubMed]

]. The Tx-Rx baseline separation is r. V is referred to as the optical common volume, and r1 and r2 are the distances of the common volume to the Tx and Rx, respectively.In order to characterize the system performance, we utilize the channel model to predict received optical power, and incorporate stochastic models for the detector and noise sources. We ignore atmospheric turbulence effects, which are generally negligible for ranges on the order of a few hundred meters or less. We model the photodetector output as a Poisson point process with the counting rate λ determined by the instantaneous received optical power such that λS = ηPr/(hν) = ηPt/(Lhν). η, Pr, h, ν, Pt, and L denote the quantum efficiency of the detector including optical filter and photodetector, received power, Planck’s constant, the frequency of the optical field, transmitted power and path loss, respectively. In particular, path loss L can be used to predict the received power given the transmission power.

Experimental results on short-range (up to a few hundred meters) NLOS UV channel path loss for different pointing angles are reported in [12

12. 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]

]. We employ an empirical path loss model given by Eq. (1) [11

11. 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] [PubMed]

]
L=ξrα,
(1)
where path loss exponent α and path loss factor ξ are unknown non-linear functions of the apex angles (cf. Figure 1). These parameters are summarized in Tables 1

Table 1. Path loss factor ξ of the NLOS UV channel model

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and 2

Table 2. Path loss exponent α of the NLOS UV channel model

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below.

The random effects of background radiation, shot noise due to the photon detection process (that differs depending on the type of detector), and thermal noise of the post-processing electric circuit, must all be accounted for in the analysis of system performance. Including both shot noise and thermal noise, the photodetector output statistics are governed by a mixture of a Poisson point process and a Gaussian process. In the following we develop these models and present a unified performance analysis for short range UV-C NLOS communications.

3. Ideal photon counting receiver performance

We first examine the performance of NLOS UV communications within the framework of an ideal Poisson counting receiver that does not require photon multiplication. The integrator output is proportional to the photon count k1 per pulse time out of each modulation symbol period, which also complies with a Poisson distribution with photon arrival rate λ. The probability is given by Eq. (2)
Pk1(j)=λjeλj!,
(2)
where λ = λS + λb when the signal is present and λ = λb when signal is absent, and λb denotes the background radiation photon count rate. Although the ozone layer in the upper atmosphere absorbs most of the radiation in the deep UV, there remains some background radiation, some percentage of which will leak through the optical filter.

r=ηPtξRbhνln(2Pe_OOK)α,   or   rRb1/α=C˜,   where   C˜=ηPtξhνln(2Pe_OOK)α.
(4)

4. Performance of PMT/APD based receivers with thermal noise

The NLOS UV propagation channel incurs severe attenuation. Therefore, it is interesting to investigate a receiver distorted by the random photon amplification process and thermal noise in the post-processing circuit.

4.1 Statistical modeling of the photodetector output

The photomultiplication process is subject to random variation in the output number of secondary photoelectrons k2 in response to the primary photoelectrons k1. The number of secondary photoelectrons is described by the probability mass function in Eq. (6) [13

13. R. M. Gagliardi, and S. Karp, Optical Communications, 2nd ed. (John Wiley & Sons, 1995).

]
Pk2(k2)=k1=0Pk2(k2|k1)Pk1(k1),
(6)
where Pk1(k1) is the primary photoelectron probability described by Eq. (2), and Pk2(k2|k1) is the conditional probability of the secondary photoelectrons given k1. There has been a rich amount of literature since the 1960s on modeling Pk2(k2) for PMT and APD photodetectors. For brevity, we provide only the main results here.

The PMT’s output secondary photoelectrons have the probability Pk2(k2) given by Eq. (7) [13

13. R. M. Gagliardi, and S. Karp, Optical Communications, 2nd ed. (John Wiley & Sons, 1995).

]

Pk2(k2)=Cexp[(k2Aλ)22(ζAλ)2].
(7)

In the equation, C is the normalizing factor, and ζ is the PMT spreading factor that describes the variance of PMT gain A.

For an APD, McIntyre and Conradi have shown that Pk2(k2) follows Eq. (8) [16

16. R. McIntyre, “The distribution of gains in uniformly multiplying avalanche photodiodes: theory,” IEEE Trans. Electron. Dev. 19(6), 703–713 (1972). [CrossRef]

,17

17. J. Conradi, “The distribution of gains in uniformly multiplying avalanche photodiodes: experimental,” IEEE Trans. Electron. Dev. 19(6), 713–718 (1972). [CrossRef]

]
Pk2(k2)=1(2πC12)1/2[11+(k2Aλ)3/2C1C2]exp{(k2Aλ)22C12[1+(k2Aλ)C1C2]},
(8)
where
C1=(Aλ)2F1,         C2=A(λF)1/2/(F1),         F=γA+(21A)(1γ),
and F is the excess noise factor jointly determined by the ionization factor γ and gain A. For PMT and APD cases, F is given by 1 + ζ2 and γA + [2-(1/A)](1-γ), respectively. With the typical values of ζ = 0.1 and γ = 0.028, F takes the values 1.01 and 4.7343 [13

13. R. M. Gagliardi, and S. Karp, Optical Communications, 2nd ed. (John Wiley & Sons, 1995).

] for a PMT and APD (with gain 100), respectively.

Coupled with the output of the photodetector, the number of secondary photoelectrons k2 shifts the pdf of v by changing the mean of n to the form of Eq. (11)
μ=k2e,
(11)
where k2 is a random variable, leading to a random mean. Conditioned on the average count of primary photoelectrons per pulse, denoted as λ, the conditional density of z, pz(z|λ), is the average of the continuous Gaussian distribution over the secondary photoelectron probability given by Eq. (12) [13

13. R. M. Gagliardi, and S. Karp, Optical Communications, 2nd ed. (John Wiley & Sons, 1995).

]
pz(z|λ)=j=0Pk2(j|λ)G(z,je,σn2).
(12)
In the above, G(z,a,b) denotes the pdf of the Gaussian random variable z with mean a and variance b. Pk2(j) is given in Eq. (7) for a PMT, and in Eq. (8) for an APD.

However, note that the application of Eq. (11) to obtain a numerical solution may call for a large quantity of computations in any analysis utilizing the distribution (even with truncating the summation at the higher end). For example, the photoelectron output of a high gain PMT can be on the order of 105~108, such that a probability accumulation will have a corresponding high computational complexity. So, as an alternative, we directly model the random gain effect with the thermal noise, as proposed in [15

15. S. Karp and R. Gagliardi, “The design of a pulse-position modulated optical communication system,” IEEE Trans. Commun. Technol. 17(6), 670–676 (1969). [CrossRef]

].

Consider the realizations of gain {Ai} to be independent and identically distributed (i.i.d.) random variables representing the multiplication gain for each photoelectron. Then z can be written as Eq. (13)
z=v+n=i=1k1Aie+n,
(13)
Approximating the random gain as a Gaussian random variable, z is the summation of k1 Gaussian random variables each with mean Ae and variance (F-1)(Ae)2, plus noise n with zero mean and variance as given in Eq. (10). Conditioned on the primary photon arrival rate which is typically moderate, z is essentially a summation of Gaussian random variables and pz(z|λ) is thus found to follow Eq. (14)
pz(z|λ)=j=0Pk1(j|λ)G(z,jAe,σ2).
(14)
In this equation, Pk1(j) assumes the form of Eq. (2), and σ 2 involves the contributions from thermal noise and the random gain effect of the photodetector, which is

σ2=σpd2+σn2=j(F1)(Ae)2+(2keTo/RL)Tp.

The mean is replaced by its expected value, and the conditional probability is conditioned on the photon arrival instead of the secondary photoelectrons. By substituting the expressions of excess noise factor F for PMT or APD, σ 2 takes the following forms in Eq. (15), respectively

σPMT2=j(ζAe)2+(2keTo/RL)Tp,   σAPD2=j[γA+2(1γ)1γA1](Ae)2+(2keTo/RL)Tp.
(15)

4.2 Receiver performance

For OOK modulation, the receiver adopts threshold-based direct detection, and a general expression of error probability follows Eq. (16)
Pe_OOK=P1zthpz(z|λS+λb)dz+P0zthpz(z|λb)dz.
(16)
where P1 and P0 are probabilities of transmitting information “1” and “0”, respectively. Assume P1 = P0 = 0.5. The optimal detection threshold zth to minimize Pe_OOK can be found by setting the derivative to zero as dPe_OOK/dzth = 0, leading to Eq. (17)
pz(zth|λS+λb)=pz(zth|λb).
(17)
Given the pdf of z in Eq. (14), an equation for the optimal zth will be a mixture of summation and integral. Since a closed form for the optimal zth is not attainable, a numerical solution will be used. Using Eq. (14) for pz(z) and applying the following identity
zthpz(z|λS+λb)dz=1zthpz(z|λS+λb)dz,
the error probability in Eq. (16) can be written in a compact form as Eq. (18)

Pe_OOK=1212j=0[(λS+λb)jj!e(λS+λb)λbjj!eλb]Q(zthjAeσ).
(18)

M-ary pulse position modulation (M-PPM) is widely employed as a pulse-based modulation option, where the receiver is based on the maximum likelihood method by comparing the outputs of different slot positions without a need for the threshold. The probability of correct detection for M-PPM is given by Eq. (19)
PD=pz(z|λS+λb)[zpz(y|λb)dy]M1dz,
(19)
which is the probability that the slot containing the signal arrival has the most significant value exceeding all other slots within each PPM word. This results in the error probability Pe_PPM = 0.5M/(M-1)(1-PD). Combining our results, the correct detection probability can be expressed as Eq. (20) [15

15. S. Karp and R. Gagliardi, “The design of a pulse-position modulated optical communication system,” IEEE Trans. Commun. Technol. 17(6), 670–676 (1969). [CrossRef]

]
PD=12M1j=0(λs+λb)jj!e(λs+λb)G(z,jAe,σ2){1+k=0λbkeλbk!erf(zkAe2σ)}M1dz,
(20)
where erf (x) is the error function defined as
erf(x)=2π0xeu2du.
These analytical results will be evaluated numerically to demonstrate NLOS UV communication receiver performance.

5. Numerical analysis

By varying the pointing angles from small to large, the NLOS UV channel path loss traverses a huge dynamic range of up to 100dB variation. This necessitates a receiver capable of handling the weak optical signal while minimizing the random noise effects. We propose to use PMT/APD in the deep UV range along with a high impedance amplifier, desiring to maintain low noise operation. The NLOS UV channel is primarily path loss limited, although pulse-broadening occurs that induces a channel bandwidth limitation. Here we focus on rates that are sufficiently low to generally avoid the question of bandwidth limits and induced inter-symbol interference (ISI). Also, note that an equalizer can be introduced to improve the bandwidth of a high impedance amplifier [19

19. S. Alexander, Optical Communication Receiver Design (SPIE Optical Engineering Press, 1997.

] even in the absence of channel induced ISI. Our numerical examples use the typical system values listed in Table 3

Table 3. Typical UV communication system parameters

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.

5.1 Rate-range tradeoffs with a photon counting receiver

We begin with an analysis of the rate and range tradeoffs with an ideal photon counting receiver as discussed in Section 3. The path loss is dependent on the geometric setup and baseline range. We adopt three background noise levels considered to be low, medium, and high noise cases, corresponding to 0, 5kHz, 14.5kHz. These levels were selected based on measurements [12

12. 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]

].

5.2 PMT/APD receiver performance with fixed gain

5.3 Improving the performance with detector gain control

Figure 7
Fig. 7 Error probability vs. multiplication gain, Pt = 100mW, PMT (left) and APD (right).
depicts BER against PMT and APD detector gains, at a range of 50 meters. For the PMT, the error probability improves monotonically with increasing gain, but becomes saturated when the gain exceeds about 104. The extent of BER improvement differs with pointing geometry, with the most gain occurring for the smaller pointing angles. For very large gain, the error performance is significantly better at small angles. For the APD, the BER first decreases with increasing gain, but then increases beyond a certain gain point. The variation is more pronounced for smaller pointing angles, and an optimal gain exists in each case. The optimal gain point tends to shift to a larger value as the pointing angles increase. The optimal gain is around 150 for (10°,10°), and approaches 300 for the (40°,40°) pointing case. Overall the PMT shows much better detection performance than the APD. A high gain PMT based receiver is practically feasible for the cases considered. For the APD based receiver, excess noise from random gain fluctuation significantly degrades performance, and an automatic gain control mechanism can be incorporated to adjust the APD bias voltage.

6. Conclusions and future work

Acknowledgements

The authors extend thanks to the anonymous reviewers for their valuable suggestions and comments. This work was supported in part by the United States Army Research Office (USARO) under grants W911NF-09-1-0293 and W911NF-08-1-0163, and the United States Army Research Laboratory (USARL) under the Collaborative Technology Alliance Program, Cooperative Agreement DAAD19-01-2-0011.

References and links

1.

M. Shatalov, J. Zhang, A. S. Chitnis, V. Adivarahan, J. Yang, G. Simin, and M. A. Kahn, “Deep ultraviolet light-emitting diodes using quaternary AlInGaN multiple quantum wells,” IEEE J. Sel. Top. Quantum Electron. 8(2), 302–309 (2002). [CrossRef]

2.

V. Adivarahan, Q. Fareed, S. Srivastava, T. Katona, M. Gaevski, and A. Khan, “Robust 285 nm deep UV light emitting diodes over metal organic hydride vapor phase epitaxially grown AlN/sapphire templates,” Jpn. J. Appl. Phys. 46(23), L537– L539 (2007). [CrossRef]

3.

W. S. Ross and R. S. Kennedy, “An investigation of atmospheric optically scattered non-line-of-sight communication links,” Army Research Office Project Report, Research Triangle Park, NC, January 1980.

4.

M. Shatalov, J. Zhang, A. S. Chitnis, V. Adivarahan, J. Yang, G. Simin, and M. A. Kahn, “Deep ultraviolet light-emitting diodes using quaternary AlInGaN multiple quantum wells,” IEEE J. Sel. Top. Quantum Electron. 8(2), 302–309 (2002). [CrossRef]

5.

Z. Xu and B. M. Sadler, “Ultraviolet communications: potential and state-of-the-art,” IEEE Commun. Mag. 46(5), 67–73 (2008). [CrossRef]

6.

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

8.

Z. Xu, “Approximate performance analysis of wireless ultraviolet links,” in Proceedings of IEEE Intl. Conf. on Acoustics, Speech, and Signal Proc. (IEEE, 2007).

9.

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] [PubMed]

10.

H. Ding, G. Chen, A. Majumdar, B. M. Sadler, and Z. Xu, “Modeling of non-line-of-sight ultraviolet scattering channels for communication,” IEEE J. Sel. Areas Comm. 27(9), 1535–1544 (2009). [CrossRef]

11.

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] [PubMed]

12.

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]

13.

R. M. Gagliardi, and S. Karp, Optical Communications, 2nd ed. (John Wiley & Sons, 1995).

14.

Q. He, B. M. Sadler, and Z. Xu, “On the achievable performance of non-line of sight ultraviolet communications,” Proceedings of OSA Optics & Photonics Congress: Applications of Lasers for Sensing and Free Space Communications (OSA, 2010).

15.

S. Karp and R. Gagliardi, “The design of a pulse-position modulated optical communication system,” IEEE Trans. Commun. Technol. 17(6), 670–676 (1969). [CrossRef]

16.

R. McIntyre, “The distribution of gains in uniformly multiplying avalanche photodiodes: theory,” IEEE Trans. Electron. Dev. 19(6), 703–713 (1972). [CrossRef]

17.

J. Conradi, “The distribution of gains in uniformly multiplying avalanche photodiodes: experimental,” IEEE Trans. Electron. Dev. 19(6), 713–718 (1972). [CrossRef]

18.

K. Kiasaleh, “Performance of APD-based, PPM free-space optical communication systems in atmospheric turbulence,” IEEE Trans. Commun. 53(9), 1455–1461 (2005). [CrossRef]

19.

S. Alexander, Optical Communication Receiver Design (SPIE Optical Engineering Press, 1997.

OCIS Codes
(060.4510) Fiber optics and optical communications : Optical communications
(060.2605) Fiber optics and optical communications : Free-space optical communication

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: December 14, 2009
Revised Manuscript: March 27, 2010
Manuscript Accepted: April 12, 2010
Published: May 25, 2010

Citation
Qunfeng He, Zhengyuan Xu, and Brian M. Sadler, "Performance of short-range non-line-of-sight LED-based ultraviolet communication receivers," Opt. Express 18, 12226-12238 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-12-12226


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References

  1. M. Shatalov, J. Zhang, A. S. Chitnis, V. Adivarahan, J. Yang, G. Simin, and M. A. Kahn, “Deep ultraviolet light-emitting diodes using quaternary AlInGaN multiple quantum wells,” IEEE J. Sel. Top. Quantum Electron. 8(2), 302–309 (2002). [CrossRef]
  2. V. Adivarahan, Q. Fareed, S. Srivastava, T. Katona, M. Gaevski, and A. Khan, “Robust 285 nm deep UV light emitting diodes over metal organic hydride vapor phase epitaxially grown AlN/sapphire templates,” Jpn. J. Appl. Phys. 46(23), L537– L539 (2007). [CrossRef]
  3. W. S. Ross and R. S. Kennedy, “An investigation of atmospheric optically scattered non-line-of-sight communication links,” Army Research Office Project Report, Research Triangle Park, NC, January 1980.
  4. M. Shatalov, J. Zhang, A. S. Chitnis, V. Adivarahan, J. Yang, G. Simin, and M. A. Kahn, “Deep ultraviolet light-emitting diodes using quaternary AlInGaN multiple quantum wells,” IEEE J. Sel. Top. Quantum Electron. 8(2), 302–309 (2002). [CrossRef]
  5. Z. Xu and B. M. Sadler, “Ultraviolet communications: potential and state-of-the-art,” IEEE Commun. Mag. 46(5), 67–73 (2008). [CrossRef]
  6. M. R. Luettgen, J. H. Shapiro, and D. M. Reilly, “Non-line-of-sight single-scatter propagation model,” J. Opt. Soc. Am. A 8(12), 1964–1972 (1991). [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). [CrossRef]
  8. Z. Xu, “Approximate performance analysis of wireless ultraviolet links,” in Proceedings of IEEE Intl. Conf. on Acoustics, Speech, and Signal Proc. (IEEE, 2007).
  9. 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] [PubMed]
  10. H. Ding, G. Chen, A. Majumdar, B. M. Sadler, and Z. Xu, “Modeling of non-line-of-sight ultraviolet scattering channels for communication,” IEEE J. Sel. Areas Comm. 27(9), 1535–1544 (2009). [CrossRef]
  11. 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] [PubMed]
  12. 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]
  13. R. M. Gagliardi and S. Karp, Optical Communications, 2nd ed. (John Wiley & Sons, 1995).
  14. Q. He, B. M. Sadler, and Z. Xu, “On the achievable performance of non-line of sight ultraviolet communications,” Proceedings of OSA Optics & Photonics Congress: Applications of Lasers for Sensing and Free Space Communications (OSA, 2010).
  15. S. Karp and R. Gagliardi, “The design of a pulse-position modulated optical communication system,” IEEE Trans. Commun. Technol. 17(6), 670–676 (1969). [CrossRef]
  16. R. McIntyre, “The distribution of gains in uniformly multiplying avalanche photodiodes: theory,” IEEE Trans. Electron. Dev. 19(6), 703–713 (1972). [CrossRef]
  17. J. Conradi, “The distribution of gains in uniformly multiplying avalanche photodiodes: experimental,” IEEE Trans. Electron. Dev. 19(6), 713–718 (1972). [CrossRef]
  18. K. Kiasaleh, “Performance of APD-based, PPM free-space optical communication systems in atmospheric turbulence,” IEEE Trans. Commun. 53(9), 1455–1461 (2005). [CrossRef]
  19. S. Alexander, Optical Communication Receiver Design (SPIE Optical Engineering Press, 1997.

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