紫外线通信的简化模型

A simplified NLOS UV communication model

Ying Ding*, Shoufeng Tong

Institute of Space Photo-electronic Technology Changchun University of Science and Technology

Changchun, China

e-mail: [email protected]

Abstract —Ultraviolet (UV) is a promising enabling technology for signal covering a large area. Receivers with broad acceptance non-line-of-sight (NLOS) optical wireless communication. The angles detect the flux from the scattering volume and UV signal transmission undergoes rich scattering and strong demodulate the message. Atmospheric attenuation significantly absorption by atmospheric particulates. This paper briefly reduces the solar background flux at wavelengths less than introduces the characteristic of UV atmospheric transmission 280nm, which prevents third-party detection and interception at

and the propagation model based on prolate spheroidal ranges beyond a few kilometers.

coordinate system. According to two different kinds of UV communication model, this paper presents simplified computing methods of Non-Line of Sight single scattering channel model; The simulation results show that the simplified models not only achieve accelerated ratio of 105, but also assure the simulation accuracy; Base on this model, it is easy to simulate and analysis the energy loss with different transmitting distance and variety weather conditions, which provides a theoretical basis for fast energy analyzing of UV communication system.

Keywords-ultraviolet communication; non-line-of-sight; ccattering model

I. I NTRODUCTION

Figure 1. diagram of a NLOS UV communication system

Since the use of wireless communications has become critical nowadays, the available RF spectrum has become limited. With the rapid advances in UV devices, unique interaction mechanism between UV radiation and atmosphere constituents, and emerging application needs, UV technology is becoming a tremendous alternative to wireless communications, which can alleviate the spectrum constraint and make a potential alternative to future communication demands. Nowadays UV technology has been used commercially for indoor air purification, germicidal sterilization, monitoring air molecules and particles, and ground sensing networks. NLOS UV communication modulates light in the solar-blind spectral region, so it is an important military application when radio, wire, or fiber communication links are unavailable, unreliable or untrustworthy. At these wavelengths in the atmosphere, ozone is a strong absorber, resulting in propagation extinction lengths of a kilometer or less.

UV communication is NLOS communication mode based on atmospheric scattering, illustrated in Figure 1[1], which shows two sensing nodes separated by tens to hundreds of meters on the ground. Each node is equipped with a UV transceiver. Both the UV transmitter and receiver are zenith-pointed with a wide field of view (FOV), and thus share a high-degree of beam overlap at short ranges. The transmitter modulates light and directs a broad beam angle upwards, and isotropic scattering from air molecules provides a diffuse return

II. C HARACTERISTIC OF UV ATMOSPHERIC TRANSMISSION

The unique properties of the solar blind region are a result of strong interactions in the upper and lower atmospheres. In the upper atmosphere, the ozone layer (nominally 20km altitude) strongly absorbs solar radiation producing. In the lower atmosphere, it appears zero background conditions; molecules and aerosols present in the medium (communication channel) strongly scatter and absorb radiation. Scattered radiation provides a basis for NLOS communication.

The transmission properties of the UV spectrum in background level from 250 to 300 nm are characterized by molecular absorption (primarily O3) and scattering (both by molecules and aerosols) [3]. The ability of molecules and aerosols to absorb and scatter radiation is given by the absorption coefficient k a , scattering coefficients k s and extinction coefficients k e , and k e = ka + ks (in units of km-1). A. Atmospheric absorption

The absorption of UV radiation by molecules and aerosols reduce the potential signal, which is available for communication transmitting. Figure 2a displays plots of the combined aerosol and molecular coefficients of absorption, scattering and extinction across the UV spectrum obtained

from the MODTRAN-4 radiative transfer code [4]. It can be seen that the absorption coefficient is a strong function of wavelength, values of k a range from 1.15 km-1 at 250 nm to 0.03 km-1 at 300 nm, and the scattering coefficient displays little variation, values of k s range from 0.57 km-1 at 250 nm to 0.38 km-1 at 300 nm.

B. Atmospheric scattering

The scattering of the UV radiation provides the primary mechanism for redirecting the upwardly transmitted signal back towards the receiver. The amount of signal redirected towards the receiver is predominantly a function of the scattering properties of molecules and aerosols in the boundary layer. The amount of signal that is redirected back towards the surface is a function not only of the scattering coefficient, but also the angular dispersion properties of the. Because the size of molecules and aerosols are different, the scattering properties are quite different. Molecules are much smaller than UV wavelengths, so it belongs to Rayleigh scatterers. The phase function, used to describe the angular distribution of scattered energy is well known for Rayleigh scattering. Aerosols are larger than the UV wavelength, so Mie scatterers are considered. The phase function varies with size, wavelength and index of refraction of the particle. In Figure 2b, plots of the normalized phase functions for both molecular and aerosol scattering are shown. The x-axis is the scattering angle from 0o to 180o , the minimum is scattering in the forward direction and the maximum is direct backscatter. The y-axis is plotted in logarithmic units to emphasize the large changes in the aerosol phase function from a peak in the forward direction to a minimum beyond 90o . Plots of the aerosol phase function are shown for three wavelengths using rural aerosol model characteristics. There’s small differences can be observed between the three curves. In contrast, the molecular phase function varies slightly, and has the minimum value of 0.75 at 90o

and the maximum of 1.5.

(b) the normalized phase functions for both molecular and aerosol scattering Figure 2. Plots of absorb and scatter radiation for molecules and aerosols

If the normalized phase functions are applied to the scattering coefficients, the scattering coefficient can be obtained directly. From most literature findings, values of k e = 1.23 km-1 and k s = 0.025 km-1sr -1 are reasonable choices at the wavelength of 266 nm, and k s is the scattering coefficient at angle of 150o .

III. NLOS PROPAGATION MODEL A NALYSIS For NLOS UV communication, scattering servers as the vehicle for information exchange between a transmitter (T x ) and a receiver (R x ). The typical communication geometry is illustrated in Figure 3 [7]. Define βt andβr as the T x and R x apex angles between each axis and the horizontal axis, θs =βt +βr is the angle between the forward direction of incident waves and the observation direction, and θt and θr as the T x half beam angle and R x FOV. Let V be the T x and R x common volume, r the distance between T x and R x , and r 1 and r 2 the distances of the common volume to the T x and R x , respectively. A. NLOS UV communication model

(a) the combined aerosol and molecular coefficients of absorption, scattering

and extinction

δV

δE r =

E t k s P (μ) A r δV cos(ζ)exp(−k e (r 1+r 2))

(1)

Ωt r 12r 22

where k s is the scattering coefficient, k e is the extinction coefficient, P (μ) is the scattering phase function, and μ=cos(θs ) , A r is the area of the receiving aperture, ζ is the angle between the receiver axis and a vector from the receiver to the common volume, cos(ζ) is the detector aspect angle, and Ωt =4πsin 2(θt ) is the solid angle of the T x radiation cone. The phase function is modeled as a weighted sum of the Rayleigh and Mie scattering phase functions based on the corresponding scattering coefficients.

Figure 4. prolate spheroidal coordinate system

P (μ) =

k k

p Ray (μ) +p Mie (μ) (2) k s k s

Ray s Mie s

So the coordinate transform of each point from XYZ to prolate spheroidal is modeled as:

where k s =k s Ray +k s Mie , k s Ray and k s Mie are the scattering coefficients of Rayleigh and Mie, p Ray (μ) and p Mie (μ) are the phase functions of Rayleigh and Mie, which follow a generalized Rayleigh model and a generalized Henyey-Greenstein function, respectively:

ξ=(r 1+r 2) /r (1≤ξ≤∞) η=(r 1−r 2) /r (−1≤η≤1)

φ=arctan(x , y ) (−π≤φ≤π) (5)

r 1=[x 2+y 2+(z +r /2) 2]1/2r 2=[x 2+y 2+(z −r /2) 2]1/2

where r is the T x and R x baseline separation, and r 1 and r 2 are the distances of the common volume to the T x and R x , respectively, the coordinate of δV can be signed （ξ，η，Φ）, so

In

prolate spheroidal coordinate system, the received single scattering energy at time t can be expressed by

⎧Ray 3[1+3γ+(1−γ) μ2]⎪p (μ) =

16(1+2) ⎪

(3) ⎨22

g 110.5(3μ1) −−⎪p Mie (μ) =+f [23/223/2⎪g g g +−+4(12) (1) ⎩

where γ, g , f are model parameters。

The total energy at the receiver can be found by integrating

δE r over the common volume using a prolate spheroidal coordinate system. So the path loss is modeled as

δV =(r 3/8)(ξ2−η2) δξδηδφ

cos(ζ) =cos(βR )cos(ψ1) +sin(βR )sin(ψ1)cos(φ)

and

δE r =

E t Ωt r 12r 22L == (4)

−+E r k s P (μ) AV cos(ζ)exp(k (r r )) 2r e 1

It depends on the common volume V that in turn depends

on the shape of the intersection, so the approximate of V directly affect the computational complexity of simulation.

2E t k s P (μ)cos(ζ)exp(−k e r ξ)

δξδηδφ (6) 22

Ωt r (ξ−η)

=(r 1+r 2) /c ，and ξ=ct /r ，the radial per

unit δξ=c δt /r ，so the received energy by a detector can

where t

be found after integrating over time by E r =

E t ck s P (μ) A r

Ωt r

B. prolate spheroidal coordinate system

The single scattering model is based on a prolate spheroidal coordinate system, illustrated in Figure 4. Each point in prolate spheroidal space is defined by a radial coordinate ξ, an angular coordinate η, and an azimuthal coordinate Φ

.

∫ξ∫ηξ∫φξη

min

1(

ξmax η2(ξ) φ2(ξ, η)

)

1(

, )

2exp(−k e r ξ)cos(ζ)

d φd ηd ξ (7)

2−2

where t min

IV. S IMPLIFIED MODEL

As shown in Eq.(7), the NLOS single-scattering model based on prolate spheroidal coordinate system is complex, large computing, and the triple integrals could be calculated by accumulate discrete points. So the number of sampling points directly affects the accuracy of the simulation results, but how to dynamically determine the sampling points is more difficult. Zhengyuan Xu et al. simplified the model, which method is suitable for small common volume V . There are two typical communication modes as shown in Figure 5. Case (b) requires minimum transmitter and receiver positioning in a fully NLOS mode, which has small bandwidth. According to different

communication modes, this paper proposed different simplify

methods for NLOS UV communication.

the ⊙O t and ⊙O r tangent, H min =r/2. if H >H min , let the intersection area of ⊙O t and ⊙O r is S , which is bilateral symmetry, and AB is the symmetric axis, define S 1 as the area of the right semi-part, so S =2S 1; and S 1

=S O −S O r AB , q

r AB

where

S O and S O r AB are the area of sector O r AB and q

r AB

（a ）large bandwidth （b ）small bandwidth

Figure 5. typical communication modes

triangle O r AB respectively. Set βt =βr =90° and θt =θr =45°; By

O r A =H , O r C =O r O t /2=r/2, calculation,

θ=arcsin(O r C /O r A ) =arcsin(r /2H ) ,

2S O =(π−2θ) H q AB

r

, , ,

A. Case (a) with large bandwidth

In case (a), the elevation of transmitter and receiver are less than 90°, path loss is minimum, bandwidth is large, but position range is poor, channel capacity is limited. The above derivation shows that the key of path loss computation is the solving of common volume V .

1

S O r AB =1B *OC θ)*r /2)=1r cos(θ) r ) =(2H cos((A H

S =2S 1=(π−2θ) H 2−Hr cos(θ)

As shown in Figure 5a, the overlapped volume is relatively

small, which can be approximated as a truncated cone, and be

of path loss as θ achieved by subtracting the volume of small cone V min from the

large cone V max . The steps of simplify model are as follows: let k r (sin(θ1) +sin(θ2))

2πr 4sin 2(θ1)sin 2(θ2)[1−cos(θt )]exp(e angle ζ=0, distance r 1=r sin(βr ) /sin(θs ) , distance sin(s ) (9)

2. V =(H −H ) S =(H −r /2)[(π−2θ) H −H r cos(θ)]m in 33

Therefore, approximately calculate ζ=0, θ1=βr −1θr , θ2=βt −11=r sin(θ2) /sin(θs ) , θt , θs =θ1+θ2, r

r 2=r sin(θ1) /sin(θs ) , finally we obtain the simple model

r 2=r sin(βt ) /sin(θs ) , the height of cone V max and V min are evaluated approximately by h 1=r 1+r 2θr and h 2=r 1−r 2θr , and the radius are D 1=h 1θt and D 2=h 2θt , respectively.

Then V =V max −V min =Eq.(4) can be simplified as

L ≈

L ≈

k s P (u ) Ar sin 4(s ) V

π(D 12h 1−D 22h 2)

, Therefore

24r sin(βt )sin 2(βr )(1−cos(θt )) exp(

k e r (sin(βt ) +sin(βr ))

sin(s ) (8)

k s P () A r t r sin(s )(3sin(r ) +r sin (t ))

B. Case (b) with small bandwidth

Case (b) is the most popular mode used in UV communication system, its elevation of transmitter and receiver are 90°, position range is large, even full range, doesn’t require APT, unlimited channel capacity, but bandwidth is small.

As shown in Figure 5b, case (b) is more special, the optical axis of transmitter is parallel to the receiver’s, common volume V related to the height H and the overlapped area of the conic section in height H, define the projection of conic section as disk ⊙O t and ⊙O r .

For example, the transmitter beam divergence and the receiver field of view are both 45°, when the height H has different values, the intersection of ⊙O t and ⊙O r are different, as shown in Figure 6. When H is short, the ⊙O t and ⊙O r separate, volume V is zero; the intersection of ⊙O t and ⊙O r increased with the increase of H , and also the V ; Of course, there’s a height H min that identify the intersecting area from nothing to something as a boundary, namely if H >H min and V>0,

Figure 6. the overlapped area of the conic section for Tx’s volume and Rx’s

V. MODELING PERFORMANCE EXPERIMENTS

A. Accuracy verification

In order to verify the feasibility and accuracy of the simplified model, this paper simulated the changes of path loss with the communication distance using the simplified model, signed model A, and original model, signed model B, respectively. The parameters of the experiment I about case(a) used in the model are βt =βr =60°, θt =θr =15°, k a =0.9, k e =1.4, A r =0.03m2; The parameters of the experiment I about case(b) used in the model are βt =βr =90°, θt =θr =45°, k a =0.9, k e =1.4, A r =0.03m2. It can be observed in Figure 7 that: (a) the errors between the result of model A and model B are less than 3db; (b) In case (b), errors is slowly increased with the increase of the communication distance, so scattering communication is mainly used when the communication distance is less than 1km;

(c) the error varying of case (a) is less. As a result, the simplified model not only solve the complex computation and difficult determine of sampling points, but also accurately

reflect the path loss.

VI. C ONCLUSION

According to the different communication modes in the ultraviolet scattering communication system, this paper proposed a simplified model of the Non-Line of Sight single-scattering model, taken several experiments, compared the calculated results and the runtime with the original model, respectively, the simulation results verified the feasibility and the efficiency of this new model, which offers a new method for real-time simulation of the UV scattering communication system.

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（a ）

in case (a)

（b ）in case (b)

Figure 7. comparison of computing accuracy by simplified model and

original model

B. efficiency verification

In the performance analysis of the communication system, usually require statistical multiple sets of data to draw the curve, in order to summarize the trend of the performance, so the computing time of the simulation model directly affects the simulation efficiency. In order to verify the efficiency of the simplified model, according to different communication modes, selected five kinds of typical structure, tested many times, and statistic the average computing time of path loss by simplified model and original model, respectively. The simulation results are listed in Table , it can be observed that the computing time of original model is more than 400ms, large computing, time consuming; and the computing time of simplified model is less than 0.005ms, accelerated 105 times. Therefore, the simplified model, which is proposed in this paper, not only accurately reflected the path loss, but also greatly saved the calculation time.

TABLE I. No.

THE C OMPARISON OF COMPUTING TIME BY TWO MODELS

Original model

(ms)

2 3256.2 3 2043.9 4 1748.4 Simplified model

(ms)

0.004 0.003 0.004 Speedup 814050 681300 437100

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