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Backscattering characteristics ofmillimeter wave radar in sand and duststormsQunfeng Donga, Ying-Le Lib, Jiadong Xuc, Hui Zhanga & MingjunWanga

a Department of Physics and Electronic Engineering, XianyangNormal University, Xianyang 712000, Chinab Department of Physics and Electronic Engineering, ShaanxiXueqian Normal University, Xi'an 710100, Chinac School of Electronic & Information, Northwestern PolytechnicalUniversity, Xi'an, Shaanxi 710072, ChinaPublished online: 08 Apr 2014.

To cite this article: Qunfeng Dong, Ying-Le Li, Jiadong Xu, Hui Zhang & Mingjun Wang (2014)Backscattering characteristics of millimeter wave radar in sand and dust storms, Journal ofElectromagnetic Waves and Applications, 28:9, 1075-1084, DOI: 10.1080/09205071.2014.905213

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Backscattering characteristics of millimeter wave radar in sand anddust storms

Qunfeng Donga*, Ying-Le Lib, Jiadong Xuc, Hui Zhanga and Mingjun Wanga

aDepartment of Physics and Electronic Engineering, Xianyang Normal University, Xianyang712000, China; bDepartment of Physics and Electronic Engineering, Shaanxi Xueqian Normal

University, Xi’an 710100, China; cSchool of Electronic & Information, NorthwesternPolytechnical University, Xi’an, Shaanxi 710072, China

(Received 11 December 2013; accepted 12 March 2014)

The backscatter properties of millimeter wave radar in sand and dust storms havebeen addressed. An expression for signal attenuation of millimeter wave radar isderived in terms of visibility and frequency. The results show that the valuescalculated by the proposed model are in good agreement with those obtained byGoldhirsh’s model and Alhaider’s formula. The general formulas of the backscatterpower and equivalent scattering cross-section through sandstorms, suitable for anyparticle size distribution, are developed in terms of radar range, visibility, and waveattenuation. The results of the calculation show that the equivalent scattering cross-section increases with the increase of radar range less than 35 km, whereas the echopower decreases with the increase of radar range. It is confirmed that the equivalentscattering cross-section and echo power decrease rapidly as the radar range increasesfor the lower visibility, and decrease slowly with the increase of radar range for thebigger visibility. It is found that the particle size distribution is one major factorwhich will affect the backscattering properties of millimeter wave radar in sand anddust storms.

Keywords: sand and dust storms; backscattering; attenuation; millimeter

1. Introduction

When microwaves pass through the random medium containing like rain, snow, or sandparticles, the absorption and scattering effect happens which causes loss in signalenergy and additional phase shift.[1,2] The effects of sand and dust particles on micro-wave propagation have received much attention in the literature owing to the impor-tance of Radio Relay, Satellite Communication, and Remote Sensing. The waveattenuation and cross-polarization due to sand and dust storms have been investigatedby a number of investigators.[3–16]

As reported by the review of Bashir and McEwan [17]: In 1941, Ryde and hiscompanions analyzed the effects of a sandstorm on radar albedo and pointed out thatwhen the frequency was not more than 30 GHz, the sandstorm with a low concentrationhad no influence on the radar signal. Based on Rayleigh scattering approximation,Goldhirsh [18,19] investigated the backscatter and clutter properties of the dustymedium at S and L bands, and derived a dust storm model that enables the convenientcalculation of the two-dimensional structure of radar backscatter. The clutter and

*Corresponding author. Email: qunfengdong1028@163.com

© 2014 Taylor & Francis

Journal of Electromagnetic Waves and Applications, 2014Vol. 28, No. 9, 1075–1084, http://dx.doi.org/10.1080/09205071.2014.905213

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backscatter cross-section of dust storms at x-band have been studied by Sharif [20]. Inorder to arrive at upper limits of echo power, they omitted dust attenuation at S, L, Xband, and smaller frequencies. Wenyan [21] researched the backscattering properties ofdust storms to millimeter wave radar under the log-normal size distribution of dust par-ticles. It was found that the backscatter and clutter properties of the dusty medium aredependent on the particle size distribution, frequency, and dust particle concentration.The investigations carried out by researchers have resulted in a variety of particle sizedistributions (uniform, exponential, Rayleigh, and lognormal).[3,14] Moreover, particlesize distributions will also affect the backscatter properties of millimeter wave radarbecause the radar reflectivity factor depends strongly on the particle size distribution.

In this paper, the backscatter and clutter properties of dust storms are investigated atmillimeter band. For millimeter wave radar, the attenuation of sand and dust storms mustbe considered comparing with the studies about S-, L-, and X-bands radar.[18–20] Andthe formula for attenuation of radar signals is derived in terms of visibility andfrequency. The expression of radar reflectivity factor is derived considering the variousparticle size distributions. The general formulas of the backscatter power and equivalentscattering cross-section through sandstorms, suitable for any particle size distribution,are developed in terms of radar range, visibility, attenuation, and the ratio of the sixth tothird moments of the particle size. The effects of particle size distribution, radar range,and visibility on the backscattering properties are presented.

2. Radar received power

The power received at a pulsed radar from distributed targets such as raindrops is simi-lar to that received from dust as suggested by Goldhirsh [18,19]. The power, referencedto the antenna gain measurement point, is given by

Pr ¼ c

1024 � p2 ln 2hPt � s � k2 � G2 � ðDheÞ:�ðDhhÞ � gR2

i� 10�0:2

R R

0ðadþagÞdR (1)

where c is the speed of light, Pt the transmitted power, τ the pulse width, k the wave-length, G the antenna gain, Δθe, Δθh the vertical and horizontal beamwidths (radians),respectively, η the radar reflectivity of dust (scattering cross-section per unit volume)(m−1), R the radar range, and αd, αg attenuation coefficients due to dust particles andgaseous absorption, respectively (dB/km).

2.1. Microwave attenuation in sand/dust storms

When the radar beam is in the dust particles, the exponent part of expression (1) is

10�0:2R R

0addR. The effects of dust storms on wave propagation are estimated generally

by solving the forward scattering amplitude function of a single particle. The solutionmay be carried out using the Rayleigh approximation or exact Mie equations ornumerical methods. The method depends largely on the factor kr (where k is thewavenumber 2p=k and r is the particle radius).[5] Since the size of sand and dustparticle’s is relatively small, i.e. kr � 1, the values at millimeter-wave frequenciessatisfy Rayleigh scattering approximations.[5,21] Base on Rayleigh scattering approxi-mation, the attenuation coefficient due to dust storms may be expressed by theformulation [5]

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ad ¼ 1:029� 106N0

k

� �� G �

Z 1

0PðrÞ � r3dr ½dB=km� (2)

where λ is the wavelength in meters, G ¼ e00=½ðe0 þ 2Þ2 þ e002�, ε′ and ε″ are the realand imaginary part of the complex dielectric constant of the dust particle, i.e.e�m ¼ e0 � je00 and P(r) is the probability density function, N0 is the number of particlesper unit volume (m3) having radii in the region r ! r þ dr.

The “mass loading” is defined as the relative mass of dust per cubic volume of airand is given by

M ¼ q � vr (3)

where ρ is the mass particle density, which is given by ρ = 2.44 × 103 kg/m3,[6] vr isthe total relative volume of all dust particles per cubic meter of air.

The visibility Vb is related to the mass of sand and dust per cubic volume M by theexpression [19]

M ¼ C

V cb

(4)

where C = 2.3 × 10−5, γ = 1.07.The total number of particles per unit volume N0 is expressed in terms of the mass

loading M. The mass loading may alternately be given by

M ¼ 4

3p � q � N0 �

Z 1

0PðrÞr3dr (5)

Substituting (3), (4) into (5), the total number of particles per unit volume N0 canthen be expressed as

N0 ¼ 2:25� 10�9 � 1

V 1:07b

�Z 1

0PðrÞr3dr (6)

Substituting (6) into (2), the attenuation coefficient can then be expressed as

ad ¼ 7:7� 10�3 F

V cb

G ½dB=km� (7)

where F is the frequency (GHz), Vb is the visibility (km). The expression (7) indicatesthe attenuation is related with frequency, visibility, and complex dielectric constant ofthe dust particle.

2.2. Radar reflectivity factor of dust storms

In the expression (2), η is the radar reflectivity of dust. It may be demonstrated that theradar reflectivity (radar cross-section per unit volume) for a distributed target is givenby [18]

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g ¼ p5

k4� jK0j2 � Z ½m�1� (8)

where

jK0j2 ¼ ðe0 � 1Þ þ e002

ðe0 þ 2Þ þ e002(9)

The radar reflectivity factor Z can be expressed as [19,20]

Z ¼Z Dmax

Dmin

NðDÞD6dD ¼ N0 �Z Dmax

Dmin

PðDÞD6dD ½m3� (10)

where N(D)dD is the number of dust particles whose diameters are between D andD+ dD per unit volume. Dmax, Dmin are the maximum and minimum diameters of theparticles, respectively. The expression (10) indicates the radar reflectivity factor dependsonly on the size distribution of sand and dust particle.

Substituted (7) into (10), and the radar reflectivity factor Z is

Z ¼ 2:88 � 10�7

V 1:07b

� I6I3

(11)

where In ¼R10 rnpðrÞdr, n = 1, 2, …

From the formula (11), besides the visibility, the value of I6I3will also affect the radar

reflectivity factor in sandstorms and the reflectivity factor is proportional to I6I3. Now it

is noted that the value of I6I3depends strongly on the probability density function of sand

particle size distribution.Here, we review various distributions of particle size presented in the literature and

give the value of I6I3for each in Table 1.

3. Dust storms echo power and backscattering cross-section of equivalent pointtarget

We have omitted the attenuation factor of atmospheric gas in (1). Substituting (7), (11)into (1), we obtain the resultant backscatter power from dust; namely [18],

Pr ¼ C1 � jK0j2R2V 1:07

b

� I6I3� 10�0:2

R R

0addR (12)

where C1 is the radar constant, C1 ¼ 3:773 � ½Pt � s � k�2 � G2 � ðDheÞ � ðDhhÞ�.

Table 1. The values of I6I3for different distributions.

Distribution Probability density function I6I3

Uniform pðrÞ ¼ 12a

I6I3¼ 32

7 a3

Exponential pðrÞ ¼ 1a e

�ra

I6I3¼ 120a3

Rayleigh pðrÞ ¼ rm2 e

�r2

2m2I6I3¼ 64

p2 a3; a ¼ m

ffiffip2

pLog-normal pðrÞ ¼ 1ffiffiffiffi

2pp

srexp � ðln r�mÞ2

2s2

� �I6I3¼ a3ð1þ d2Þ12; d ¼ r

a ; r ¼ aðexpðs2Þ � 1Þ12

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For a point target the backscatter power in the far field is given by

Pr ¼ Pt � G2 � k2ð4pÞ3R4

r (13)

where σ is the backscatter cross-section. In order to arrive at a measure of the equiva-lent point target cross-section for distributed scatters such as dust, we equate (12) and(13) and obtain

re ¼ C2R2

V 1:07b

� jK0j2 � I6I3 � 10�0:2R R

0addR (14)

where C2 is the constant, C2 ¼ 7:49� 103½s � he � hh � k�4�.According to (12) and (14), the equivalent scattering cross-section and echo power

can be expressed by

PrðdBmÞ ¼ 10 log10 C1 � 20 log10 R� 10:7 log10 Vb þ 10 log10I6I3

� �� 2:0adR (15)

reðdBÞ ¼ 10 log10 C2 þ 20 log10 R� 10:7 log10 Vb þ 10 log10I6I3

� �� 2:0adR (16)

For nominal radar parameters at 35 GHz, the parameters for nominal radar at 35GHz are given by [22]

Pt ¼ 1� 105 W s ¼ 1� 10�7 she ¼ hh ¼ 1� G ¼ 35:6 dB

�(17)

We obtain the value |K0|2 at 35 GHz

jK0j2 ¼ 0:2836 (18)

Substituting the above parameters into (14) and (12), we obtained the equivalentscattering cross-section and echo power

reðdBÞ ¼ 27:6þ 20 log10 R� 10:7 log10 Vb þ 10 log10I6I3

� �� 2:0adR (19)

PrðdBmÞ ¼ 70:7� 20 log10 R� 10:7 log10 Vb þ 10 log10I6I3

� �� 2:0adR (20)

4. Calculations and results

4.1. Attenuation for sand and dust storms

In this section, in order to check the validity of the proposed attenuation model (7),attenuations calculated by (7) are verified by comparing them to those obtained byGoldhirsh’s formula [19], Ahmed et al.’s formula [5], and Alhaider’s formula [16].

Using the expression (7), the parameters are as follows: frequency F = 35 GHz,e�m ¼ 4:0� j1:3.[20] Figure 1 shows the comparison of attenuation values for sand anddust storms at F = 35 GHz. It shows that the wave attenuation decreases with visibility

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and there is an excellent agreement in the attenuation obtained by our proposed formula(7) and Goldhirsh’s formula, and is close agreement with that obtained by Alhaider’sformula. Among the four attenuation models, Ahmed et al.’s model produces a highervalue of wave attenuation. Our formula and Alhaider’s formula have a lower value ofwave attenuation. As the visibility is getting better, the differences among the five mod-els are becoming better smaller.

Figure 2 shows the relation between the attenuation and visibility at F = 14, 24GHz, complex dielectric constant of dust with 5.0% moisture content e�m ¼ 3:9� j0:62and e�m ¼ 3:6� j0:65,[4] respectively. The results show that the attenuation increaseswith the increase of frequency, and the attenuation decreases sharply as the visibility

0.0 0.5 1.0 1.5 2.00.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0.22

0.24

Att

enua

tion

(dB

/km

)

Visibility (km)

Goldhirsh's formula

Alhaider's formula

Ahmed et al's formula

Proposed formula

Figure 1. Comparison of attenuations obtained by Goldhirsh formula, Ahmed et al.’s formula,Alhaider formula, and our proposed formula (7) at 35 GHz.

Att

enua

tion

(dB

/km

)

0.5 1.0 1.5 2.00.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

0.045

0.050

Visibility (km)

F=14GHz

F=24GHz

Figure 2. Attenuation with visibility at different frequency.

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increases. The wave attenuation in sand and dust storms increases as the visibilitydecreases because wave attenuation is directly proportional to the particle number.

4.2. Equivalent point target backscattering cross-section of sand and dust storms

Figure 3 shows the relationship between the equivalent cross and radar range fordifferent distributions. From Figure 3, the equivalent scattering cross-section increaseswith the increase of radar range less than 35 km, and gradually becomes flat; this isdue to the bigger effect of signal attenuation. However, it is seen that the echo powerdecreases as the radar range increases in Figure 4. Among the four different

1 10 100-105

-100

-95

-90

-85

-80

-75

-70

-65

-60

-55

-50

Radar Range (km)

Uniform Exponential Rayleigh Log-normal

e(d

B)

Figure 3. Equivalent cross with radar range for different distribution.

-110

-100

-90

-80

-70

-60

-50

-40

-30

Pr (

dBm

)

Radar Range (km)

Uniform Exponential Rayleigh Log-normal

20 40 60 80 100

Figure 4. Echo power with radar range for different distribution.

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distributions, the exponential distribution affects the radar backscattering characteristicssignificantly with corresponding to the biggest values of equivalent cross and the echopower, the Log-normal distribution results in a bigger value, the uniform distributiongives the lowest.

Using (19) and (20), the equivalent scattering cross-section and echo power werecalculated at different Visibility Vb for the exponential distribution. The parameters arefrequency F = 35 GHz, permittivity of dust e�m ¼ 4:0� j1:3, and visibility Vb = 10, 50,and 100 m. The results are shown in Figures 5 and 6. It is seen that the equivalent scat-tering cross-section and echo power decrease rapidly as the radar range increases for

-350

-300

-250

-200

-150

-100

-50

Radar Range (km)

Vb=10m

Vb=50m

Vb=100m

20 40 60 80 100

e(d

B)

Figure 5. Equivalent cross with different visibility.

20 40 60 80 100-400

-350

-300

-250

-200

-150

-100

-50

0

Radar Range (km)

Vb=10m

Vb=50m

Vb=100m

Pr (

dBm

)

Figure 6. Echo power with different visibility.

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the lower visibility. This is due to the serious signal attenuation for millimeter wavepropagation in sand and dust storms, which greatly influences the detection range ofradar. For the bigger visibility of storms, the equivalent scattering cross section andecho power decrease slowly with the increase of radar range. The results are inagreement with the findings of Wenyan [21].

5. Conclusions

The problem of backscatter properties of millimeter wave radar has been addressed insand and dust storms. Comparing with S-, L-, and X-bands, the effect of wave attenua-tion in sand and dust storms on backscatter properties of millimeter wave radar mustbe considered. An expression for attenuation of radar signals is derived in terms of visi-bility and frequency. The predicted attenuation values from general formulas are com-pared with those obtained by three formulas: Goldhirsh’s formula, Ahmed et al.’sformula, and Alhaider’s formula. The results show that the values calculated by theproposed model are in good agreement with those obtained by Goldhirsh’s model andAlhaider’s formula.

The general formulas of the backscatter power and equivalent scatteringcross-section through sandstorms are developed in terms of radar range, visibility, waveattenuation, and I6

I3. The results of the calculation show that the equivalent scattering

cross-section increases with the increase of radar range less than 35 km, whereas theecho power decreases with the increase of radar range. Among the four different distri-butions, the exponential distribution affects the radar backscattering characteristics sig-nificantly with corresponding to the biggest values of equivalent cross and the echopower, the Log-normal distribution results in a bigger value, the uniform distributiongives the lowest. And the equivalent scattering cross-section and echo power decreaserapidly as the radar range increases for the lower visibility. This is due to the serioussignal attenuation for millimeter wave propagation in sand and dust storms, whichgreatly influences the detection range of radar. For the bigger visibility of storms, theequivalent scattering cross section and echo power decrease slowly with the increase ofradar range. It is apparent that the particle size distribution function and visibility aretwo major factors which will affect the backscattering properties of millimeter waveradar in sand and dust storms.

FundingThis work is supported by the National Natural Science Foundation of China [grant number61102018], [grant number 61271110].

References[1] Fredrick SS, Jothiram V. Propagation delays induced in GPS signals by dry air, water,

vapor, hydrometeors and other particulates. J. Geophys. Res. D. 1999;104:9663–9670.[2] Dong QF, Xu J-D. Effects of charged particle size distribution on microwave propagation in

sandstorms. J. Electromagnet. Wave. Appl. 2012;25:315–325.[3] Chu TS. Effects of sandstorms on microwave propagation. Bell Syst. Tech. J. 1979;58:

549–555.[4] Ansari AJ, Evans BG. Microwave propagation in sand and dust storms. IEE Proc. F.

Commun. Radar Signal Process. 1982;129:315–322.[5] Ahmed AS, Ali AA, Alhaider MA. Airborne dust size analysis for tropospheric propagation of

millimetric waves into dust storms. IEEE Trans. Geosci. Remote Sens. 1987;GE-25:593–599.

Journal of Electromagnetic Waves and Applications 1083

Dow

nloa

ded

by [

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eå U

nive

rsity

Lib

rary

] at

03:

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[6] Ghobrial SI, Sharief SM. Microwave attenuation and cross polarization in dust storms. IEEETrans. Antennas Propag. 1987;35:418–425.

[7] Ghobrial SI. The effect of sand storms on microwave propagation. In Proc. Nat. Telecom-mun. Conf.; 1980; Houston, TX; Vol. 2; p. 43.5.1–43.5.4.

[8] Chen HY, Ku CC. Calculation of wave attenuation in sand and dust storms by the FDTD andturning bands methods at 10–100 GHz. IEEE Trans. Antennas Propag. 2012;60:2951–2960.

[9] Dong XY, Chen HY. Microwave and millimeter-wave attenuation in sand and dust storms.IEEE Antennas Wireless Propag. Lett. 2011;10:469–471.

[10] Srivastava SK, Vishwakarma BR. Cross-polarization and attenuation of microwave/millime-ter wave propagation in storm layer containing sand, silt and clay as dust constituents. IE (I)J.-ET. 2003;84:30–38.

[11] Vishvakarma BR, Rai CS. Limitations of Rayleigh scattering in the prediction of millimeterwave attenuation in sand and dust storms. In: IEEE International Geoscience and RemoteSensing Symposium; 1993; Tokyo.

[12] Dong QF, Li Y-L, Xu J-d, Zhang H, Wang M-j. Effect of sand and dust storms on micro-wave propagation. IEEE Trans. Antennas Propag. 2013;61:910–916.

[13] Ruike Y, Zhensen W, Jinguang Y. The study of MMW and MW attenuation consideringmultiple scattering effect in sand and dust storms at slant paths. Int. J. Infrared Milli. Wave.2003;24:1383–1392.

[14] Ali AA. Effect of particle size distribution on millimeter wave propagation into sandstorms.Int. J. Infrared milli. wave. 1986;7:857–868.

[15] Ahmed AS. Role of particle-size distributions on millimeter-wave propagation in sand/dust-storms. IEE Proc. 1987;134:55–59.

[16] Alhaider MA. Radio wave propagation into sandstorms-system design based on ten-yearsvisibility data in Riyadh, Saudi Arabia. Int. J. Infrared Milli. Wave. 1986;7:1339–1359.

[17] Bashir AO, Mcewan NJ. Microwave propagation in dust storms: a review. IEEE Proc. H.1986;133:241–247.

[18] Goldhirsh J. A parameter review and assessment of attenuation and backscatter propertiesassociated with dust storms over desert regions in the frequency range of 1 to 10 GHz. IEEETrans. Antennas Propag. 1982;30:1121–1127.

[19] Goldhirsh J. Attenuation and backscatter from a derived two-dimensional duststorm model.IEEE Trans. Antennas Propag. 2001;49:1703–1711.

[20] Sharif SM. Clutter and backscatter cross-section of dust storms at X-band. Sudan Eng. Soc.J. 1997;44:58–70.

[21] Yin WY, Jingming X. The study of backscattering properties of dust storm to millimetricwave radar. Chin. J. Radio Sci. 1990;4:53–59.

[22] Zhao ZW, Lin LK, Wu ZW. Radar backscattering characteristics of fog. Chin. J. Radio Sci.2001;16:498–502.

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