IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, VOL. 10, 2011 469

Microwave and Millimeter-Wave Attenuationin Sand and Dust Storms

Xiao-Ying Dong, Hsing-Yi Chen, Senior Member, IEEE, and Dong-Hui Guo, Member, IEEE

Abstract—The attenuation and phase delay due to sand and duststorms are obtained by using the effective material property tech-nique and general formulation of the complex propagation factor.The validity of attenuation is verified by Ghobrial et al.’s formula.Attenuations obtained for various frequencies are shown in thisletter. It is found that the attenuation decreases sharply as the vis-ibility increases. It is also proven that the attenuation is negligibleexcept for frequencies above 30 GHz and for very dense storms. Itis found that cross polarization may be serious when a wave propa-gation path over 1 km has visibilities below 10 m, which may causesignal loss in microwave and millimeter-wave links. The effectivematerial property technique and general formulation of the com-plex propagation factor have shown a quick and easy way of calcu-lating the attenuation and phase delay due to sand and dust storms,which otherwise requires complicated and expensive methods ofcalculation and measurement.

Index Terms—Attenuation, complex propagation factor,microwave and millimeter-wave links, sand and dust storms.

I. INTRODUCTION

S AND and dust storms may play an important role inthe Earth’s climate system and communication link

performance. The Earth’s radiation balance, global rain falldistribution, and cloud properties can be changed due to sandand dust storms [1]. Sand and dust storms can also affectmicrowave and millimeter-wave links due to the attenuationand cross polarization produced by storm particles [2]–[11].

The attenuation and cross polarization of wave propagationresult mainly from scattering and absorption by storm parti-cles. Numerous calculations of wave attenuation in sand anddust storms are based on Rayleigh scattering approximation orMie scattering theory [3]–[7], [9]. Attenuation calculated byRayleigh scattering approximation is suitable for particles muchsmaller than a wavelength. The Mie scattering theory is elegantand still famous in today’s research of scattering and absorptionby spherical particles. However, calculations of wave attenua-tion in sand and dust storms by Rayleigh scattering approxi-mation and Mie scattering theory do not include the multiplescattering effect or mutual interaction phenomenon. Sand anddust particles are randomly distributed in the air. Their orien-tation depends on the direction and speed of the wind. Their

Manuscript received March 25, 2011; revised April 18, 2011; accepted May07, 2011. Date of publication May 19, 2011; date of current version May 26,2011.

X.-Y. Dong and D.-H. Guo are with the Department of Electronic Engi-neering, Xiamen University, Xiamen 361005, China.

H. Y. Chen is with the Department of Communications Engineering, YuanZe University, Chung-Li 32003, Taiwan (e-mail: eehychen@saturn.yzu.edu).

Color versions of one or more of the figures in this letter are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/LAWP.2011.2154374

geometries cannot be classified as spheres, ellipsoids, cubes,or otherwise. Their radius distribution may vary from 0.05 to150 m [5], [11], [12]. Particles with radius smaller than 60 mare defined as dust, while particles with radius lager than 60 mare referred as sand [3]. Computations of attenuation of wavepropagation in sand and dust storms need the knowledge of pre-cise particle size, shapes, dielectric constant, number densityfunctions, frequencies, etc. Since a storm is a random discretescattering medium, the multiple scattering effects should be in-cluded in the calculation of wave attenuation. Many studies onsand and dust storms confirm that attenuation for high visibilityand frequencies below 30 GHz is small, but a quantitative com-parison is still lacking. In this letter, the attenuation is obtaineddirectly from the general formulation of wave propagation con-stant based on an equivalent complex permittivity of the stormmedium. The equivalent complex permittivity is a function ofsand and dust composition and visibility. The obtained attenua-tions of sand and dust storms are compared to other theoreticalresults calculated by the scattering theory.

II. COMPLEX PERMITTIVITIES OF SAND AND DUST STORMS

Several investigations on the complex permittivities of sandand dust samples have been reported in the literature [2], [4]–[6],[13]–[15]. The values of complex permittivities may be obtainedby resonant cavity measurement, waveguide measurement, andextrapolation results. The complex permittivities of sand anddust have a variation depending on frequency, temperature, andmoisture content. For dry sand and dust, the complex permit-tivity varies negligibly over 0.3–24 GHz. However, the changeis greater as the moisture content increases [5]. The complexpermittivity is almost unaffected by the chemical and mineralcomposition of sand and dust except where significant amountsof metallic or magnetic mineral are present [16]. Table I summa-rizes the measurement data of complex relative permittivities ofsand and dust at frequencies of 3–100 GHz [5], [17], [18]. Thecomplex permittivity is defined by

(1)

where and are the dielectric constant of air and the angularfrequency, and are the relative dielectric constant and con-ductivity of a lossy medium, and is the complexrelative dielectric constant of the lossy medium, respectively.

The mediums of sand and dust storms are far from solid mate-rial. There is no precise theory existing for calculating the com-plex permittivities of sand and dust storms. Up to now, there isuncertainty about the complex permittivities of sand and dustparticles mixing with air and moisture content. The equivalentcomplex relative permittivities of sand and dust storms can

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470 IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, VOL. 10, 2011

TABLE ICOMPLEX PERMITTIVITIES OF SAND AND DUST IN

THE FREQUENCY RANGE 3–100 GHZ

be obtained by using the effective material property technique[19]

(2)

where and are the relative dielectric constant of air andvolume fraction occupied by sand and dust particles in a unitvolume, and are the real and imaginary parts of , and

is the complex relative permittivity of sand and dust, respec-tively. The volume fraction occupied by sand and dust parti-cles in a storm can be obtained by assuming the mass density of2.44 g/cm for sand and dust [3]

(3)

where is the visibility in kilometers and constant .Finally, the equivalent complex relative permittivities of stormsare a function of visibility.

III. ATTENUATION AND PHASE SHIFT

Assuming that the magnetic loss of a sand and dust stormis negligible, the attenuation and phase shift factors of atransversal electromagnetic wave traveling in the storm can beobtained from the following equation:

(4)

where and are the complex propagation factor and angularfrequency, and are the attenuation and phase shift, and

are the dielectric constant and permeability of air, and isthe complex relative permittivity of a sand and dust storm, re-spectively. The loss tangent of the storm can be expressedby

(5)

where and are the real and imaginary parts of the equiva-lent complex relative permittivity of the sand and dust storm.Then, and can be obtained from (4) and (5) expressed by

Np/m (6)

Fig. 1. Comparison of attenuations obtained by (6) and Ghobrial et al.’s for-mula at 10.5 GHz.

rad/m (7)

where is the wavelength in air. The attenuation can beexpressed in decibels per meter by taking

dB/m (8)

where is the traveling length in meters. The phase delay perunit length of a wave propagating through a sand and dust stormrelative to a wave propagation in air can be obtained from (7)expressed as

degrees/m (9)

IV. CALCULATIONS OF ATTENUATION AND PHASE SHIFT

Based on suspending ellipsoid particles, Ghobrial et al. [3],[11] derived an attenuation formula for microwave propagationin sand and dust storms at 10.5 GHz expressed by

Attenuation (dB/km)

dry dust

dust with 4% H O(10)

where is the wavelength in air (unit in centimeters), is thevisibility in kilometers, and , respectively.

In order to check the validity of attenuation formulated by (6),attenuations calculated by (6) are verified by comparing them tothose obtained by using Ghobrial et al.’s formula expressed by(10). Fig. 1 shows the comparison of attenuation values obtainedby (6) and (10) for dry dust and dust with 4% H O at 10.5 GHz,respectively. The complex relative permittivities of dry dust anddust with 4% H O at 10.5 GHz are adopted to be

and , respectively. From Fig. 1, it canbe seen that there is an excellent agreement in the attenuationobtained by (6) and Ghobrial et al.’s formula.

After checking the validity of (6), (6) is used to investigatethe attenuations at various frequencies. The complex relativepermittivities of sand and dust are adopted from the litera-ture [5], [17], [18] at frequencies of 3–100 GHz. Attenuationsobtained by (6) for various frequencies are shown in Fig. 2.From Fig. 2, it is found that the attenuation decreases sharply

DONG et al.: MICROWAVE AND MILLIMETER-WAVE ATTENUATION IN SAND AND DUST STORMS 471

Fig. 2. Attenuations obtained by (6) at frequencies of 3–100 GHz.

Fig. 3. Results of phase delay obtained by (9) at frequencies of 3–100 GHz.

as the visibility increases. It is also proven that the attenuationis negligible except for frequencies above 30 GHz and verydense storms [3], [4], [6]. The phase delay is also calculated by(9) for various frequencies as shown in Fig. 3. From Fig. 3, itis found that phase delay can be serious when visibilities fallbelow 10 m over 1 km of the wave propagation path. Significantcross polarization can occur due to differential phase delay,which may cause signal loss in microwave and millimeter-wavelinks [3].

V. CONCLUSION

The attenuation and phase delay due to sand and dust stormsare studied by using the effective material property techniqueand the general formulation of complex propagation factor. Thevalidity of attenuation is checked by other simulation methods.The variation of attenuation depends on the complex permit-tivity, frequency, and visibility of sand and dust storms. It isshown that attenuation decreases sharply as the visibility in-creases from 1 m to 1 km. It can be concluded that the at-tenuation caused by sand and dust storms is not serious ex-cept for storms with visibilities less than a few meters. The mi-crowave and millimeter-wave bands are in the very short wave-length range. The shorter the wavelength the more attenuationwill be induced by scattering and absorption due to sand anddust particles in the wave propagation path. The attenuation

caused by sand and dust storms is one of the important prob-lems in microwave and millimeter-wave links for terrestrial andspace communications. Cross polarization may be serious whena wave propagation path over 1 km has visibilities below 10m. Significant cross polarization can occur due to differentialphase delay, which may cause signal loss in microwave and mil-limeter-wave links. In this letter, it is clear that the effective ma-terial property technique and general formulation of complexpropagation factors provide a quick and easy way of calculatingthe attenuation and phase delay due to sand and dust storms,which otherwise requires complicated and expensive methodsof calculation and measurement.

REFERENCES

[1] R. J. Charison, S. E. Schwartz, J. M. Hales, R. D. Cess, J. A. JrCoakley,J. E. Hansen, and D. J. Hofmann, “Climate forcing by anthropogenicaerosols,” Science, vol. 255, no. 5043, pp. 423–430, Jan. 1992.

[2] I. Y. Ahmed, “Microwave propagation through sand and dust storms,”Ph.D. dissertation, Univ. Newcastle Upon Tyne, Newcastle upon Tyne,U.K., 1976.

[3] S. I. Ghobrial and S. M. Sharief, “Microwave attenuation and cross po-larization in dust storms,” IEEE Trans. Antennas Propag., vol. AP-35,no. 4, pp. 418–425, Apr. 1987.

[4] J. Goldhirsh, “A parameter review and assessment of attenuation andbackscatter properties associated with dust storms over desert regionsin frequency range 1 to 10 GHz,” IEEE Trans. Antennas Propag., vol.AP-30, no. 6, pp. 1121–1127, Nov. 1982.

[5] A. J. Ansari and B. G. Evans, “Microwave propagation in sand and duststorms,” Proc. Inst. Elect. Eng. F, vol. 129, pp. 315–322, 1982.

[6] T. S. Chu, “Effect of sandstorms on microwave propagation,” Bell Syst.Tech. J., vol. 58, pp. 549–555, Feb. 1979.

[7] S. A. A. Abdulla, H. M. Al-Rizzo, and M. M. Cyril, “Particles-size dis-tribution of Iraqi sand and dust storms and their influence on microwavecommunication systems,” IEEE Trans. Antennas Propag., vol. 36, no.1, pp. 114–126, Jan. 1988.

[8] S. O. Bashir and N. J. McEwan, “Microwave propagation in duststorms: A review,” Proc. Inst. Elect. Eng. H, vol. 133, no. 3, pp.241–247, Jun. 1986.

[9] A. A. Ali, “Millimeter wave propagation in arid land: The effect of rainand sand storms,” Int. J. Infr. Millim. Waves, vol. 7, no. 4, pp. 583–598,1986.

[10] A. S. Ahmed, A. A. Ali, and M. A. Alhaider, “Airborne wave intodust storms,” IEEE Trans. Geosci. Remote Sens., vol. GE-25, no. 5,pp. 593–595, Sep. 1987.

[11] S. I. Ghobrial and J. A. Jervase, “Microwave propagation in duststorms at 10.5 GHz—A case study in Khartoum, Sudan,” IEICE Trans.Commun., vol. E80-B, no. 11, pp. 1722–1727, Nov. 1997.

[12] A. S. Ahmed, “Role of particle-size distributions on millimeter-wavepropagation in sand/dust storms,” Proc. Inst. Elect. Eng. H, vol. 134,no. 1, pp. 55–59, Feb. 1987.

[13] S. I. Ghobrial, “Effect of hydroscopic water on dielectric constant ofdust at X-band,” Electron. Lett., vol. 16, pp. 393–394, 1980.

[14] A. J. Ansari and B. G. Evans, “Microwave propagation in sand and duststorms,” Proc. Inst. Elect. Eng. F, Commun., Radar Signal Process.,vol. 129, pp. 315–322.

[15] H. M. Al-Rizzo and H. T. Al-Hafid, “Measurement of the complexdielectric constant of sand and dust particles at 11 GHz,” IEEE Trans.Instrum. Meas., vol. 37, no. 1, pp. 110–113, Mar. 1988.

[16] J. Cihlar and F. T. Ulaby, “Dielectric properties of soil as a function ofmoisture content,” University of Kansas Center for Research, NASA,CR-141868, Lawrence, KS, RSL Tech. Rep. 177-47, 1974.

[17] W. Y. Yin and J. M. Xiao, “The effects of sand and dust storms onmicrowave links,” J. China Inst. Commun., vol. 12, no. 5, pp. 91–96,Sept. 1991.

[18] A. R. Von Hippel, Dielectric Materials and Applications. Boston,MA: Artech House, 1995.

[19] S. K. Patil, M. Y. Koledintseva, R. W. Schwartz, and W. Huebner,“Prediction of effective permittivity of diphasic dielectrics using anequivalent capacitance model,” J. Appl. Phys., vol. 104, pp. 074108-1–074108-11, 2008.