## Abstract

This paper studies the effects of the obstacle on non-line-of-sight ultraviolet communication links using multiple-scatter model based on a Monte Carlo method. On the condition that transmitter beam and receiver FOV just pass the top of the obstacle, and ranges is fixed, the received energy density is at its maximum. The path loss increases when the transmitter or the receiver is much near to the obstacle, because the nearby common scattering volumes decrease intensively. The optimal received range decreases with the increasing of the distance between transmitter and obstacle. The predictions are validated with experimental measurements. This work can be used for the guidance of UV system design and network technology to apply in complex surroundings, such as mountain, buildings, etc.

© 2011 OSA

## 1. Introduction

Strong atmospheric scattering of ultraviolet (UV) radiation provides unique opportunities for establishing non-line-of-sight (NLOS) communication links, relaxing stringent pointing, acquisition and tracking requirements. Other than traditional free-space optical communication, here line of sight between the transmitter and receiver is not required for communication because the signals are transferred through scattering in atmosphere.

Unique properties described above make UV communication a candidate for military applications and civil applications in some particular situations [1, 2], where obstacles, such as mountains and buildings, often exist. UV radiation can round over the obstacle by scattering caused by molecules and aerosols in the atmosphere for establishing a communications link. Consequently, it is important to study the effects of obstacles on UV communication links. However, the effects of obstacles on UV communication, for example, the received energy density, the best elevation angles of transmitter and receiver, are not well studied. An analytical intensity impulse response model was developed to describe the temporal characteristics of single-scatter radiation by Reilly and Warde [3]. The single-scatter theory was further extended to examine angular spectra and path losses [4], and a close approximation provides an analytically tractable model [5]. An analytical model of NLOS single-scatter propagation is presented and has no integral form [6]. Wang and Xu et al. applied trigonometry to develop an analytical path loss model in noncoplanar geometry based on single-scatter propagation theory [7]. Experimental results were used to develop an empirical path loss model [8], and this led to an improved path loss prediction when compared with the single-scatter theory. A stochastic NLOS UV communication channel model is developed using Monte Carlo simulation method based on photon tracing, which incorporates multiple scattering [9]. The developed models were employed to study the characteristics of NLOS UV scattering channels for a variety of conditions, such as atmospheric conditions, source wavelength, transmitter and receiver optical pointing geometries, and range, etc. All of these studies don’t involve the effects of the obstacle on ultraviolet communication links.

In this paper, we present the simulated study of the effects of obstacles on the UV communication using multiple-scatter model based on Monte Carlo [10], and the validity of this model is validated by the outdoor experiment. The conclusions of the studies are used to UV system design and network technology in the condition of obstacles, such as mountain, buildings, etc.

The paper is organized as follows. In Section 2, we introduce the UV communication links with obstacles. In Section 3, detailed numerical results of the system simulation are given. In Section 4, experimental results, tested with obstacles, are given. Finally, we draw our conclusions in Section 5.

## 2. The UV communication link with the obstacle

For NLOS UV communication, scattering serves as the vehicle for information exchange between the transmitter (T) and the receiver (R). The scattered light that reaches the receiver depends on atmospheric conditions, and the link geometry.

Consider typical communication geometry with obstacle, as shown in Fig. 1
. Denote the T beam full-width divergence by *θ _{T}*, the receiver full field-of-view (FOV) angle by

*θ*, the T elevation angle by

_{R}*β*, the R elevation angle by

_{T}*β*, the obstacle’s (O) height and width by

_{R}*h*and

*w,*respectively. The T and the O baseline separation by

*r*the R and the O by

_{T},*r*. The T and the R baseline separation by

_{R}*r*(

*r*=

*r*+

_{T}*r*).

_{R}## 3. Simulation results and discussion

We studied the effects of the obstacle with multiple-scatter propagation model. The NLOS multiple-scatter propagation model is calculated based on Monte Carlo method, each scattering process is set as an event of probability. The propagation model is 2D model. In the simulation procedure, the obstacle’s height and width are taken into account, but the thickness is supposed to be infinitely large. We presented the detailed NLOS multiple-scatter propagation model in [10]. In this method, when the photon hits the obstacle or ground, the photon is absorbed. Simulation parameters are shown in Table 1 .

In Table 1, the wavelength of the UV source is denoted by *λ,* which is 254nm in the solar-blind UV spectrum region. *V _{b}* is meteorologic visibility. The scattering coefficient (

*k*) and the absorption coefficient (

_{s}*k*) represent scattering and absorption by air molecules and aerosol particles at

_{a}*λ*. The g-factor (

*g*) is the asymmetry parameter. $g={\displaystyle {\int}_{4\pi}\text{P(}\mathrm{cos}{\beta}_{s}\text{)}}\xb7\mathrm{cos}{\beta}_{s}d\Omega $. $P(\mathrm{cos}{\beta}_{s})$ is the scattering phase function, which describes the angular distribution of the scattered light.

*β*is the scattering angle between the forward direction of incident waves and the observation direction. For a particle that scatters light isotropically,

_{s}*g*vanishes. If the particle scatters more light toward the forward direction,g is positive; g is negative if the scattering is directed more toward the back direction. The atmospheric coefficients are obtained from LOWTRAN7 in the local atmospheric visibility and altitude conditions (Changsha city, Hunan province, China).

*N*is the photon number carried out in Monte Carlo procedure.

_{P}#### 3.1 Energy density for different β_{R} and β_{T}

Based on Monte Carlo method, the energy density at different T and R elevation angles was shown in Fig. 2
, 3
for *r _{T}* and

*r*fixed to 45m and 75m, respectively. The obstacle’s height is 80m. The width is zero. Other parameters are the same as those in Table 1.

_{R}In Fig. 2, 3, to see how elevation angles explicitly impacts received energy density, we fixed the R elevation angle at 40°, 50°, 61.9°, 70°, 80°, 90°, and fixed the T elevation angle at 40°, 50°, 60°, 75.6°, 80°, respectively. We applied a polynomial curve-fitting technique to find that the energy density can reach maximum with T and R elevation angle to be 75.6° and 61.9°.

We analyzed the above fitting conclusion using geometric optics. Denote *∠ATO* and *∠BRO* to be angles between obstacle and the T, the R, respectively (see Fig. 1). When *β _{T} -θ_{T}/2* =

*∠ATO*, the transmitter beam just passes the top of obstacle, this

*β*is called transmitter-obstacle-critical elevation angle (denoted by

_{T}*β*). When

_{TOC}*β*=

_{R}-θ_{R}/2*∠BRO*, the receiver FOV just passes the top of obstacle, then this

*β*is called receiver-obstacle-critical elevation angle (

_{R}*β*). On the basis of geometric parameter of communications link, we can calculate

_{ROC}*∠ATO*= 60.6°, and

*∠BRO*= 46.9°, then

*β*=

_{TOC}*∠ATO*+

*θ*75.6°,

_{T}/2 =*β*=

_{ROC}*∠BRO*+

*θ*61.9°, which agree with above simulated conclusion.

_{R}/2 =We drew a conclusion from above data that for *r _{T}* and

*r*fixed, the geometric condition of maximal energy density is that transmitter and receiver elevation angles are

_{R}*β*and

_{TOC}*β*, respectively.

_{ROC}We analyzed the full-width half-maximum (FWHM) of the peak in Fig. 2,3 at different transmitter beam divergence (*θ _{T}*) and receiver FOV angle (

*θ*). The transmitter beam divergence and the receiver FOV angle were varied from 4° to 90° isochronously. The other simulation parameters are the same as those in Table 1. We simulated the FWHM on the condition that one of the two elevation angles is various, the other is fixed. The simulated result based on Monte Carlo method was illustrated in Fig. 4 . We made a conclusion that the larger the transmitter beam divergence and the receiver FOV angle are, the wider the FWHM of the peak is. For designing real-world links, increasing

_{R}*θ*and

_{T}*θ*is useful to reduce the degree of sensitivity of T and R elevation angles to the obstacle.

_{R}#### 3.2 Energy density for different r_{T} and r_{R}

The height of obstacle is fixed to 80m. The transmitter and receiver elevation angles are adjusted to *β _{TOC}* and

*β*with the change of

_{ROC}*r*and

_{T}*r*.

_{R}*Other parameters are the same as those in Table 1. Figure 5 presents the energy density at different distances*

_{.}*r*and

_{T}*r*.

_{R}*The results of the numerical model (multiple-scatter model based on Monte Carlo method) and the analytic model (single-scatter model) [11,12] are compared. The shapes of these plots simulated by two models agree with each other. The value of the numerical model is bigger than that of the analytic model because the analytic model neglects multiple scattering.*

_{.}From Fig. 5, the energy density first increases, and then drops with *r _{R.}* increasing from 1 to 1000m for fixed

*r*for each curve. There exists an optimal received range (denote by

_{T}*r*), where the energy density is maximum for each

_{OR}*r*. The optimal received range decreases with

_{T}*r*increasing. In Fig. 5, the optimal received range decreases from 80m to 30m as

_{T}*r*increases from 1m to 50m.

_{T}The above conclusion can be analyzed using single-scatter model (see Eq. (1)) [11,12].

*Ω* is the solid angle of the transmitter, *A _{r}*

**i**s the active detection area.

*r*

_{1}and

*r*

_{2}the distances of the differential volume

*δV*to the T and the R, respectively. ζ is the angle between the receiver axis and a vector from the receiver to the differential volume. In our assumption of link, cosζ≈1. The scattering phase function ($P(\mathrm{cos}{\beta}_{s})$) describes the angular distribution of the scattered light, where

*β*is the scattering angle between the forward direction of incident waves and the observation direction. The phase function is modeled as a weighted sum of the Rayleigh (molecular) and Mie (aerosol) scattering phase functions based on the corresponding scattering coefficients [13]. The Rayleigh and Mie scattering phase functions follow a generalized Rayleigh model [14] and a generalized Henyey–Greenstein function [13], respectively.

_{s}Figure 6
shows the scattering phase function with the scattering angle varying from 0~180°. In Fig. 6, γ, *g*, and *f* are model parameters [13,14]. The scattering energy decreases about 2 orders of magnitude with the scattering angle increasing from 0° to 90°. However, from 90° to 180°, the scattering energy varies gently.

The total received energy is obtained by the integral to the common volume from Eq. (1). In the communication link with obstacle (its height is 80m), when *r _{T}* and

*r*are less than 80m, the scattering angle is larger than 90°. Therefore, from Fig. 6, the scattering phase function affected slightly on the received energy. So, from Eq. (1), the received energy density is mainly dependent on

_{R.}*r*

_{1},

*r*

_{2}, and the common scattering volume

*V. r*

_{1},

*r*

_{2}are the distances of the differential volume

*δV*to the T and the R. The shorter

*r*

_{1},

*r*

_{2}and the bigger the common scattering volume, the more the received energy. This means that the bigger the nearby common scattering volume, the more the received energy.

Based on the above conclusion, if *r _{T}* is fixed to 20m, we can increase

*r*(from 1m to 50m) causing the nearby common scattering volume to increase, then the energy density increases (Fig. 5). However, the overlong

_{R.}*r*, which is farther than the optimal received range, causes

_{R}*r*

_{1}and

*r*

_{2}to be very far, then the energy density decreases.

#### 3.3 Energy density for T divergence and R FOV

Figure 7
shows the energy density at different T divergence and R FOV from 1° to 90°. The height of obstacle is 80m. *r _{T}* and

*r*are fixed to 45m and 75m, respectively. The transmitter and the receiver elevation angles are adjusted to

_{R}*β*and

_{TOC}*β*with the change of T divergence and R FOV. Other parameters in Monte Carlo code are the same as those in Table 1.

_{ROC}Note that the energy density is very sensitive to T divergence and R FOV angles when they are small. We observe that the smaller the divergence, the bigger the energy density. A wider R FOV yield more received energy as the R is able to collect more scattered photons. These conclusions are similar to results without the obstacle reported in [15]. Although energy density may be increased by increasing R FOV, there is also generally a loss of bandwidth [15,16].

#### 3.4 Energy density characteristics for different height of obstacle

Figure 8
shows the effects of the height. *r _{T}* and

*r*were fixed to 150m. (

_{R}*β*) was fixed to (60°, 60°). Other parameters are the same as those in Table 1.

_{T}, β_{R}When the height of obstacle is less than 150m, T beam and R FOV are not obstructed. The curves are plane which means the received energy density is not influenced by the obstacle. The results between Monte Carlo model (multiply scatter) and the analytic model (single scatter) are compared. The single-scatter energy accounts for a major proportion of 77.5%, thus the single-scatter model is also appropriate for analyzing the effect of obstacle on the UV communication. When the height is higher than 150m, but less than 559.8m, T beam and R FOV are partially obstructed. The energy density drops rapidly as the height increases. When the height is higher than 559.8m, T beam and R FOV are obstructed completely. The energy density goes near to zero.

Based on the above predicted results, in the UV communication system with the elevation angles *β _{T}* and

*β*fixed for short range, as long as T beam and R FOV are not obstructed, the obstacle doesn’t affect the UV communication.

_{R}In order to show the effect of the height further, we consider more configurations. The height of obstacle varied from 0.1m to 200m, and *r _{R}* changed from 1m to 1000m with

*r*fixed to 45m. The elevation angles

_{T}*β*and

_{T}*β*are adjusted to

_{R}*β*and

_{TOC}*β*with the change of

_{ROC}*r*and

_{R}*h*. Other parameters in Monte Carlo code are the same as those in Table 1.

From Fig. 9
, the energy density is very sensitive to the height of the obstacle. In particular, when the receiver is close to the obstacle. The energy density decreases about 4 orders of magnitude with the height changing from 0.1m to 200m when *r _{R}* is 10m.

## 4. Experiment results

#### 4.1 Ultraviolet characteristic testbed and experiment condition

We have built an outdoor testbed of UV channel to verify simulated results, as pictured in Fig. 10 . The key components include UV source, parabola reflective mirror, high sensitive PMT detector, interference-typed filter and the lock-in amplifier.

In our testbed, low pressure mercury lamp was used. The electric power is 10W and its electro-photo efficiency is about 10% (254nm). The shape of the lamp is circular of which the diameter is 7.5cm. The lamp was built in parabola reflective mirror to increase utilization ratio of UV light and to control beam full-width divergence. The source modulation was controlled by driving voltage, which produced 2.4kHz sine-wave amplitude modulation.

At the receiver, we employed an interference-typed filter combined with a PMT for photon detection. The filter was placed in front of the sensing window of a Hamamatsu PMT module R7154 (side window). The filter has a full-width half-maximum bandwidth of 10 nm with peak transmission of 10% at 254 nm. The PMT has a rectangle sensing window with 0.8 × 2.4cm, resulting in an active detection area of 1.92 cm^{2}. The detector’s effective FOV was estimated to be about 52°. The weak 2.4kHz periodic signal can be detected with the lock-in amplifier.

Parameters of obstacle are as follows: *h* = 78m, *w* = 32m.

Experiment parameters are shown in Table 2 .

#### 4.2 Experiment results

The path loss was calculated as the ratio between the transmitted photons radiated from the UV source and the signal photons incident on the receiver. Denote the path loss by *PL*. *PL* = 10log(*P _{T}*/

*P*) . The power of the UV source (

_{R}*P*) was calculated based on the measured source radiated power, and received power (

_{T}*P*) was calculated from the signals of PMT, which include filter transmission efficiency (

_{R}*η*) and the PMT detection quantum efficiency (

_{f}*η*). Path loss measurements were obtained for different

_{r}*β*,

_{T}*β*geometries and separation distances.

_{R}The path loss for different *β _{T}* was plot in Fig. 11
. The distances

*r*and

_{T}*r*are 46m and 106m, respectively. In order to better demonstrate how path loss changes with T elevation angle for a fixed R elevation angle, the same data are plot in Fig. 12 . From the measured data, we made the results that the critical elevation angles (

_{R}*β*,

_{TOC}*β*) = (80°,63°), which well agrees with the conclusion of Section 3.1 where we can calculate (

_{ROC}*β*,

_{TOC}*β*) = (78.9°,66.9°) in accordance with geometric parameters of the obstacle and UV outdoor testbed. We compare experimentally measured path loss with that obtained by Monte Carlo method. These results indicate that our Monte Carlo method can provide a good prediction for experimental NLOS UV link performance, even with some mismatch in atmospheric model parameters.

_{ROC}To see how *r _{R}* explicitly impacts received energy, we fixed

*r*at 20m, 100m, respectively. The elevation angles

_{T}*β*and

_{T}*β*are adjusted to

_{R}*β*and

_{TOC}*β*with the change of

_{ROC}*r*and

_{R}*r*. The path loss from outdoor measurement and the simulation are plotted in Fig. 13 . Measured and predicted results show good agreement. When

_{T}*r*is 100m, 20m, respectively, the optimal received range (

_{T}*r*) is 50m, 90m. The nearer the transmitter from the obstacle, the farther the optimal received range.

_{OR}## 5. Conclusions and future work

Using multiple-scatter model based on Monte Carlo, we studied the effects of the obstacle on the received energy for NLOS UV communication channels. Different geometrical parameters were studied, including the height of obstacle, T and R elevation angles, T beam angle, R FOV, and baseline distance. We found that the obstacle intensively restricts the T and R elevation angles. When the T and R elevation angles are equal to obstacle-critical elevation angles(*β _{TOC}*,

*β*), at which the T beam and R FOV just pass the top of obstacle, the received energy is maximum. If the T beam or R FOV is obstructed by the obstacle, the received energy drops rapidly. The closer the transmitter is to the obstacle, the further the received optimal position is from the obstacle. And the measured results of outdoor experiment verified the validity of the simulating results. These findings are valuable for communication system design and application in complex surroundings, such as mountain and buildings, etc. Our future studies will focus on UV communication networks, including interference, throughput, connectivity, etc.

_{ROC}## Acknowledgments

The authors would like to thank Jianfeng Luo and Xiaoyong Zhang for their invaluable help with writing technique. This work was supported in part by the National Natural Science Foundation of China (61007047 and 60607013).

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