Research ArticleElectromagnetic Scattering by MultipleColumns Partially Buried in a Ground Plane

Xin-Cheng Ren Ye Zhao Peng-Ju Yang and Xiao-Min Zhu

School of Physics and Electronic Information Yanan University Yanrsquoan 716000 China

Correspondence should be addressed to Peng-Ju Yang pjyangyeahnet

Received 22 May 2017 Revised 1 October 2017 Accepted 8 October 2017 Published 1 November 2017

Academic Editor Atsushi Mase

Copyright copy 2017 Xin-Cheng Ren et alThis is an open access article distributed under the Creative CommonsAttribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Wideband electromagnetic scattering from multiple objects partially buried beneath rough earth soil surfaces is an importanttopic during recent years due to its extensive applications in several fields such as ground remote sensing ground penetratingradar applications and target identification Due to the advantages of finite-difference time-domain (FDTD)method in calculatingthe wideband electromagnetic scattering from rough surface in the presence of multiple objects the FDTD method underultrawideband (UWB) Gaussian pulse wave incidence is utilized in the present study for analyzing the frequency response ofrough soil surfaces with periodically distributed multiple rectangular cross-section columns buried partially In this paper thedielectric property of the actual land surface is expressed using the four-component model and the actual rough land surface issimulated utilizing Monte Carlo method with exponential correlation function The emphasis of the present study is on analyzingthewideband response signatures of composite backscattering coefficient varyingwith frequency on the basis of extensive numericalsimulations in particular for calculating and discussing in detail the influence of the root-mean-square height and the correlationlength of rough soil surface soil moisture the length and the width of the rectangular cross-section column separation distanceburial depth and tilt angle on the composite backscattering coefficient

1 Introduction

During recent years more and more attentions are paidto the electromagnetic (EM) wave scattering from roughsurface and composite scattering from rough surface withtarget because of their spread application [1ndash5] in envi-ronmental remote sensing target tracking and recognitionradar detection wireless communication and microwaveprobing of composite materials and their surface roughnessIn particular the short pulses and ultrawideband radar arewidely used in target identification and remote sensing [6]Ultrawideband radar needs the wideband RCS of target toachieve long-range detection and tracking stability [7] Themethods of solving scattering problems are plenty such asthe Kirchhoff approximation (KA) [8] small perturbationmethod (SPM) [9] small slope approximation (SSA) [10] theMethod of Moment (MoM) [11] the Finite-Difference Time-Domain (FDTD) [12] and finite element method (FEM)[13] In previous studies the composite scattering from the

rough sea surface and single target under harmonic waveirradiation have been reported and various methods areused in these studies [14ndash20] However the scattering fromrough land surface such as soil surface sand surface andperiodic distributed target under pulse wave irradiation wasconsidered rarely [21 22]

As a numerical method FDTD can calculate the elec-tromagnetic scattering problems under pulse wave and hassuperiority of the time-domain numerical algorithm [23ndash25]In this paper we consider the characteristics of compositewideband electromagnetic scattering from rough soil surfaceand the partially buried periodic distributed rectangularcross-section columns underGaussian pulse wave irradiationusing FDTD and the frequency response curves of backcomposite scattering coefficient are obtained The resultsof numerical calculation have a very great importance forachieving the remote sensing information of the earth underthe complex electromagnetic environment

HindawiInternational Journal of Antennas and PropagationVolume 2017 Article ID 8101509 8 pageshttpsdoiorg10115520178101509

2 International Journal of Antennas and Propagation

d

c

b

a

x

d c

b

f(x)

y

x

a

dd

h

K

Ei

Hi

Figure 1 Geometry of composite scattering from the rough soilsurface and partially buried periodic distributed rectangular cross-section columns

UPM

L

UPM

L

UPML

A B

C D

UPML

Figure 2 FDTD computation in the composite scattering modelfrom the rough surface and partially buried periodic distributedrectangular cross-section columns

2 Composite ScatteringModel and FDTD Method

In the present study the actual rough soil surface 119891(119909) issimulated utilizing Monte Carlo method [26] with 1D expo-nential The scattering geometry in this paper is illustrated inFigure 1

Suppose that the upper of the coordinate axis 119909 ishomogeneous free space and that the lower is isotropichomogeneous soil medium Periodic distributed rectangularcross-section columns are labeled as 119886119887119888119889 which are partiallyburied in soil The separation distance of every two adjacentcolumns is expressed as 119889119889 ℎ is the burial depth and 120593represents tilt angle which is the intersection angle of the sidelength 119886119887 of column and the forward of coordinate axis 119909

As shown in Figure 2 the calculated area of compositescattering model is built by FDTD In the area it is dividedinto scattering field region and total region by setting up adja-cent boundary 119860119861 at the same time setting up extrapolatedboundary119862119863 in the scattering field regionThese two bound-aries are planes and extended to absorption boundary Inorder to absorb incidentwave we set up absorption boundaryconditions which are made of anisotropic medium perfectlymatched layer (PML) of thickness of ten grids outside the

area then selecting Gaussian pulse electromagnetic wave asincident wave and total region from adjacent boundary 119860119861is introduced

The actual rough land surface is modeled as realizationsof a Gaussian random process with exponential correlationfunction by usingMonteCarlomethod [26] and the dielectricconstant of soil using the four-component model establishedby Wang and Schmugge [27] in this work

The power spectral density of exponential correlationrough surface is expressed as [28]

119878 (119896) = 1205752119897120587 (1 + 11989621198972) (1)

where 120575 and 119897 are the root-mean-square and correlationlength of rough soil surface respectively 119896 is spacewave num-ber

The rough soil surface is simulated by Monte Carlomethod and 1D rough surface realization with length 119871 canbe expressed as

119891 (119909119899) = 1119871119895=119873minus1sum119895=0

119865 (119896119895) sdot exp (119894119896119895119909119899) (2)

where 119909119899 = 119899Δ119909 (119899 = 1 119873) and it represents the 119899thdiscrete points of rough surface 119896119895 = 2120587119895119871 is space wavenumber 119865(119896119895) and 119891(119909119899) are Fourierrsquos transformation pairs119865(119896119895) is defined as

119865 (119896119895) = 2120587radic2Δ119870radic119878 (119896119895)

sdot [119873 (0 1) + 119894119873 (0 1)] 119895 = 1 1198732 minus 1119873 (0 1) 119895 = 0 1198732

(3)

where Δ119870 is space wave number difference of wave spectrumsample adjacent spectral domain and 119873(0 1) represents aGaussian random variable that themean is 0 and the varianceis 1 When 119895 gt 1198732 then 119865(119896119895) = 119865(119896119873minus119895)lowast and this ensuresthat the rough surface profile obtained by inverse Fouriertransform is a real number

The dielectric constant of the soil is mainly affected bythe incident frequency 119891 soil moisture119898119881 soil surface tem-perature 119879 soil type and other factors A four-componentmodel is established by Wang and Schmugge assuming thesand content in soil is 119878 clay content in soil is119862 and then thehumidity compression point of soil119882119875 is

119882119875 = 006774 minus 000064119878 + 000478119862 (4)

The critical body humidity of soil is

119898119905 = 049119882119901 + 0165 (5)

Assuming that the rock density of soil is 120588119903 and dry soildensity is 120588119887 then the plot porosity of soil 119901 is

119901 = 1 minus 120588119887120588119903 (6)

International Journal of Antennas and Propagation 3

Under normal circumstances the rock density of soil is 120588119903 =26 gcm3 and 120588119887 is determined by the following formula

120588119887 = 345511987703018 119877 = 251 minus 021119862 + 022119862 (7)

When119898119881 le 119898119905 the effective dielectric constant of the soil is120576 = 119898119881120576119909 + (119901 minus 119898119881) 120576119886 + (1 minus 119901) 120576119903 (8)

where

120576119909 = 120576119894 + (120576119882 minus 120576119894) 120573119898119881119898119905 120573 = minus057119882119875 + 0481

(9)

where 120576119886 = 10 is dielectric constant of air and 120576119894 = 315 minus1198940025 is dielectric constant of ice 120576119882 is dielectric constantof pure water and can be calculated by the Debye equationnamely

120576119882 = 49 + 1205761198820 minus 491 + 1198942120587119891120591119908 (10)

1205761198820 = 88045 minus 04147119879 + 6295 times 10minus41198792 + 1705times 10minus51198793 (11)

2120587120591119908 = 11109 times 10minus10 minus 3824 times 10minus12119879 + 6938times 10minus141198792 minus 5096 times 10minus161198793 (12)

In (11)-(12) 119879 denotes temperature When 119898119881 gt 119898119905 theeffective dielectric constant of the soil is

120576 = 119898119905120576119909 + (119898119881 minus 119898119905) 120576119882 + (119901 minus 119898119881) 120576119886+ (1 minus 119901) 120576119903

120576119909 = 120576119894 + (120576119882 minus 120576119894) 120573(13)

Maxwellrsquos equations are a set of basic equations thatgovern the macroscopic electromagnetic phenomena Fortwo-dimensional electromagnetic scattering problems rect-angular components of the electromagnetic field may beclassified as independent groups namely TM wave and TEwave In TM wave as an example FDTD difference equationhas the following form [29]

119867119899+12119909 (119901 119902 + 12) = 119862119875 (119898)119867119899minus12119909 (119901 119902 + 12)minus 119862119876 (119898) 119864119899119911 (119901 119902 + 1) minus 119864119899119911 (119901 119902)Δ119910

119867119899+12119910 (119901 + 12 119902) = 119862119875 (119898)119867119899minus12119910 (119901 + 12 119902)+ 119862119876 (119898) 119864119899119911 (119901 + 1 119902) minus 119864119899119911 (119901 119902)Δ119909

119864119899+1119911 (119901 119902) = 119862119860 (119898) 119864119899119911 (119901 119902) + 119862119861 (119898)sdot [[119867119899+12119910 (119901 + 12 119902) minus 119867119899+12119910 (119901 minus 12 119902)

Δ119909

minus 119867119899+12119909 (119901 119902 + 12) minus 119867119899+12119909 (119901 119902 minus 12)Δ119910 ]

]

(14)

where 120593 = 40∘ 120590 are discrete grid width along the 120575 =1 cm 119863 = 16 is direction of FDTD computational domainrespectively and the coefficients 119862119860 119862119861 119862119875 and 119862119876 arerespectively

119862119860 (119898) = 120576 (119898) Δ119905 minus 120590 (119898) 2120576 (119898) Δ119905 + 120590 (119898) 2 119862119861 (119898) = 1120576 (119898) Δ119905 + 120590 (119898) 2 119862119875 (119898) = 120583 (119898) Δ119905 minus 120590119898 (119898) 2120583 (119898) Δ119905 + 120590119898 (119898) 2 119862119876 (119898) = 1120583 (119898) Δ119905 + 120590119898 (119898) 2

(15)

where the value of grade 119898 and the left field componentnode labels have the same position In (15) 120590(119898) denotes theelectric conductivity 120576(119898) represents electrical permittivity120583(119898) stands for the magnetic permeability Δ119905 is the timeincrement

FDTD calculation is only in a limited area Thus it isnecessary to set absorbing boundary in truncated bound-ary for open domain electromagnetic scattering problemAnisotropic perfectly matched layer (UPML) absorbingboundary is selected in this work FDTD iteration order ofUPML layers is 119867119909 119867119910 rarr 1198751015840119911 rarr 119875119911 rarr 119864119911 and 119864119911 rarr119861119909 119861119910 rarr 119867119909 119867119910 and the iterative formula of electronicfield 119864119911 of UPML layer of truncated conductive medium isbelow

1198751015840119899+1119911 (119901 119902) = 119862119860 (119898) 1198751015840119899119911 (119901 119902) + 119862119861 (119898)sdot [[119867119899+12119910 (119901 + 12 119902) minus 119867119899+12119910 (119901 minus 12 119902)

Δ119909

4 International Journal of Antennas and Propagation

minus 119867119899+12119909 (119901 119902 + 12) minus 119867119899+12119909 (119901 119902 minus 12)Δ119910 ]

]

119875119899+1119911 (119901 119902) = 1198621 (119898) 119875119899119911 (119901 119902) + 1198622 (119898)sdot [1198751015840119899+1119911 (119901 119902) minus 1198751015840119899119911 (119901 119902)]

119864119899+1119911 (119901 119902) = 1198623 (119898) 119864119899119911 (119901 119902) + 1198624 (119898) sdot [119875119899+1119911 (119901 119902)minus 119875119899119911 (119901 119902)]

(16)

where the coefficients 119862119860(119898) and 119862119861(119898) are the same with(8) and the coefficients1198621(119898)1198622(119898)1198623(119898) and1198624(119898) are

1198621 (119898) = 120581119909 (119898) Δ119905 minus 120590119909 (119898) 21205760120581119909 (119898) Δ119905 + 120590119909 (119898) 21205760 1198622 (119898) = 1Δ119905120581119909 (119898) Δ119905 + 120590119909 (119898) 21205760 1198623 (119898) = 120581119910 (119898) Δ119905 minus 120590119910 (119898) 21205760120581119910 (119898) Δ119905 + 120590119910 (119898) 21205760 1198624 (119898) = 1Δ119905120581119910 (119898) Δ119905 + 120590119910 (119898) 21205760

(17)

where 1205760 is dielectric constant in vacuum and the value of 120590119908and 120581119908 (119908 = 119909 119910) is

120590119908 (119908) = 120590119908max

1003816100381610038161003816119908 minus 11990801003816100381610038161003816119898119889119898 120581119908 (119908) = 1 + (120581119908max minus 1)

1003816100381610038161003816119908 minus 11990801003816100381610038161003816119898119889119898 (18)

where 119889 represents the thickness of the UPML layer and 1199080denotes the interface location that UPML layer is near FDTDarea When 119898 = 4 120590max = (119898 + 1)radic120576119903150120587120575 120581max = 5sim11and the absorption effect is optimal [30]

Near-field scattering data is obtained by the FDTD cal-culation Each time field value on the boundary is recordedand the far-zone scattered field time response is obtainedusing extrapolation methods of transient pulse source exci-tation Then the frequency response of scattering coefficientis obtained through substituting the scattering coefficientformula by the Fourier transform

120590 = 10 lg (NRCS) 119889119861 (19)

Here NRCS represents the Normalization Radar Cross Sec-tion The NRCS is expressed as [24]

NRCS = lim119903rarrinfin

2120587119903119871100381610038161003816100381611986411990410038161003816100381610038162100381610038161003816100381611986411989410038161003816100381610038162 (20)

Here 119903 is distance from observation point to origin 119864119904 iselectric field of scattered wave and 119864119894 is electric field ofincident wave

In this work the Gaussian pulse electromagnetic wave isgiven by [24]

119864119894 (119905) = exp[minus4120587 (119905 minus 1199050)21205912 ] (21)

Here 120591 is constant and decides the pulse width and it is setby 120591 = 2119891 Generally 1199050 = 081205913 Numerical Results

In the following calculations the emphasis is put on the backcomposite scattering coefficient which varies with frequencyIt should be noted that the incident wave is Gaussian pulseelectromagnetic wave of TM polarization the width of grid is119889119909 = 05 cm incident angle is 120579119894 = 30∘ and sampling lengthof rough land surface is 119871 = 1600 cm The final example isan ensemble average over 40 realizations of rough surfacesThe dielectric parameter of soil is calculated using modelsfound by Wang and Schmugge [27] In this part we considerthat type of soil is silty loam Without special explanationin numerical simulations parameters of rectangular cross-section column are given with 119886119887 = 20 cm 119887119888 = 70 cm120593 = 0∘ ℎ = 5 cm and 119889119889 = 50 cm The root-mean-squareof rough surface fluctuation 120575 is 1 cm the correlation lengthof rough surface fluctuation 119897 is 4 cm and soil moisture119898V is02

In order to obtain the characteristics of composite wide-band electromagnetic scattering from the rough soil surfacewith partially buried periodic distributed rectangular cross-section columns the curves of back composite scatteringcoefficient which varies with frequency are studied by numer-ical calculation under different parameters of rough surfaceand column In the following the numerical simulations areperformed on the computer with two 260GHz processors(Intel Xeon E5-2650) 16GB Memory Microsoft Windows7 operation system and the Fortran PowerStation 40 com-piler Under the configuration the computational time andmemory size for one realization are approximately 33min and47MB respectively

Figure 3 depicts the distribution of 120590 with the incidentwave frequency 119891 for 120575 = 1 cm 3 cm and 5 cm respectivelyIt is found that the influence of 120575 on 120590 is obvious With theincrease of 120575 the scattering coefficient 120590 increases except forsome high frequency domain (2215GHz lt 119891 lt 3GHz) Inaddition the position and value for the peaks of 120590 are nearlyunchanged with 120575 On the other hand with the increasingincident wave frequency 119891 the oscillation for the amplitudeof curve becomes small

To examine the scattering coefficient difference betweensingle column case and multiple columns case a comparisonof single column case and multiple columns case is made inFigure 4 In Figure 4 the root-mean-square of rough surfaceis 120575 is 1 cm It can be readily observed that for multiplecolumns case obvious peaks exist which can be attributedto the grating effect due to the scattering from periodicallydistributed rectangular columns

In Figure 5 the dependency of 120590 on 119897 is plotted FromFigure 5 it is found that with the increase of 119897 the scattering

International Journal of Antennas and Propagation 5

= 1 cm = 3 cm = 5 cm

05 10 15 20 2500 30

f (GHz)

minus60

minus45

minus30

minus15

0

15

(d

B)

Figure 3 The influence of 120575 on 120590

Single columnMultiple columns

= 1 cm

minus70

minus60

minus50

minus40

minus30

minus20

minus10

0

10

(d

B)

05 10 15 20 25 3000

f (GHz)

Figure 4A comparison of single column case andmultiple columnscase

coefficient 120590 increases and the position and value for thepeaks of 120590 are nearly unchanged with 119897

The distribution of 120590 with 119891 for different soil moisture119898V with 1205761199031 = 49301 minus 11989404510 (119898V1 = 01 gcm3) 1205761199032 =102802 minus 11989416464 (119898V2 = 02 gcm3) and 1205761199033 = 260279 minus11989452063 (119898V3 = 04 gcm3) is depicted in Figure 6 The soilmoisture represents dielectric parameter of soil It is obviousthat the influence of119898V on 120590 is small and obscure When thefrequency is less than 09GHz (119891 lt 09GHz) all the curvesin Figure 6 are coincident However it can be found that with119898V increases 120590 slightly become greater when the frequency islarger than 09GHz (119891 gt 09GHz)

Figure 7 depicts the distribution of 120590 with 119891 for differentbreadth of column 119886119887 (119886119887 = 20 cm 60 cm 100 cm and160 cm) It is found that the influence of 119886119887 on 120590 is obviousthat is with the increase of 119886119887 the number of rectangularcross-section columns decreases And the oscillation for the

cml = 10

l = 40 cml = 100 cm

minus75

minus60

minus45

minus30

minus15

0

15

(d

B)

05 10 15 20 25 3000

f (GHz)

Figure 5 The influence of 119897 on 120590

minus60

minus45

minus30

minus15

0

15

(dB)

05 10 15 20 25 3000

f (GHz)

m = 01

m = 02

m = 04

Figure 6 The influence of119898V on 120590

amplitude of curve becomes smaller the oscillation for thefrequency of curve becomes greater

Figure 8 depicts the distribution of 120590 with 119891 for differentlength of column 119887119888 (119887119888 = 30 cm 70 cm and 100 cm) It isfound that the influence of 119887119888 on 120590 is complex and obviousthat is at most of the frequency points the larger 119887119888 is thesmaller 120590 is the smaller the peak value of 120590 Moreover as 119891increases the oscillating amplitude of the curve is smaller

Figure 9 depicts the distribution of 120590 with 119891 for differentseparation distance of every two adjacent columns 119889119889 (119889119889 =30 cm 50 cm and 100 cm) It is found that the influence of119889119889 on 120590 is obvious At most of the frequency points withthe increase of 119889119889 the number of rectangular cross-sectioncolumns decreases in the calculated area the oscillatingfrequency of curve is greater and 120590 is larger for the samefrequency point

6 International Journal of Antennas and Propagation

ab = 20 cm ab = 60 cm

ab = 100 cm ab = 160 cm

minus60

minus45

minus30

minus15

0

15

(d

B)

minus60

minus45

minus30

minus15

0

15

(d

B)

05 10 15 20 2500 30

f (GHz)05 10 15 20 2500 30

f (GHz)

minus60

minus45

minus30

minus15

0

15

(d

B)

minus60

minus45

minus30

minus15

0

15

(d

B)

05 10 15 20 2500 30

f (GHz)05 10 15 20 2500 30

f (GHz)

Figure 7 The influence of 119886119887 on 120590

bc = 30 cmbc = 70 cmbc = 100 cm

minus60

minus45

minus30

minus15

0

15

(d

B)

05 10 15 20 2500 30

f (GHz)

Figure 8 The influence of 119887119888 on 120590Figure 10 depicts the distribution of 120590with 119891 for different

burial depth ℎ (ℎ = 5 cm 15 cm and 25 cm) It is obvious

that the influence of ℎ on 120590 is small and obscure Part of thecurves are coincident However it can be found that with theincrease ofℎ120590 becomes greaterwhen frequency is larger than173GHz (119891 gt 173GHz)

Figure 11 shows the relationship of 120590 with 119891 for different120593 (120593 = 10∘ 30∘ and 60∘) when ℎ = 15 cm Obviously theinfluence of 120593 on 120590 is complex When frequency is less than109GHz (119891 lt 109GHz) the bigger 120593 is the smaller 120590 is Iffrequency satisfies the inequality (109GHz lt 119891 lt 25GHz)120590 of 120593 = 30∘ is smaller than others

Hereinbefore the results from Figures 3ndash11 in the caseof TM polarization are obtained by plentiful calculation onthe condition that other parameters are stationary Only onepoint is worth illustrating that is the influence of someparameters on the back composite scattering coefficient isrestricted by other parameters

4 Conclusion

In this paper the problems of composite wideband electro-magnetic scattering from exponential correlation rough soilsurface with partially buried periodic distributed rectangularcross-section columns underGaussian pulse wave irradiation

International Journal of Antennas and Propagation 7

dd = 30 cmdd = 50 cmdd = 100 cm

05 10 15 20 2500 30

f (GHz)

minus60

minus45

minus30

minus15

0

15

(d

B)

Figure 9 The influence of 119889119889 on 120590

ℎ = 5 cmℎ = 15 cmℎ = 25 cm

05 10 15 20 2500 30

f (GHz)

(d

B)

minus60

minus80

minus40

minus20

0

20

Figure 10 The influence of ℎ on 120590are investigated using transient FDTD The influence of theroot-mean-square and the correlation length of rough surfacefluctuation soil moisture the length and the width of therectangular cross-section column separation distance burialdepth and tilt angle on the composite scattering signaturesare discussed in detail The numerical simulations indicatethat the variation of composite scattering coefficient versusfrequency is oscillatory It is also showed that the compositescattering coefficient versus frequency increases with theincrease of root-mean-square of soil surface water ratio ofsoil the target section height and the separation distance oftarget However simulation results indicate that the compos-ite scattering coefficient versus frequency decreases with theincrease of target section width In summary the variationof wideband scattering coefficient is very complicated andis very sensitive to incidence angle of electromagnetic waveHowever the wideband scattering coefficient under Gaussian

= 10∘

= 30∘

= 60∘

05 10 15 20 2500 30

f (GHz)

minus60

minus80

minus40

minus20

0

20

(d

B)

Figure 11 The influence of 120593 on 120590

pulse wave incidence is less sensitive to the correlation lengthof rough soil surface the depth of buried objects and thedielectric constant of target Although the multiple columnspartially buried in a randomly rough surface are a rathersimplified model the present study is potentially valuable formany applications such as ground remote sensing groundpenetrating radar applications undergroundmine detectiontunnel detection and target identification In particular thesimplified model of periodically distributed columns repre-sents many realistic objects such as tree trunks mine propstelegraph poles The future investigation on this topic willinclude electromagnetic scattering from two-dimensionalrough land surface with complex multiple targets

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported in part by the National NaturalScience Foundation of China (Grant no 61379026) in partby the National Science Foundation for Young Scientists ofChina (Grant no 61701428) in part by the foundation of con-struction of high-level university project in Shaanxi Province(Grant no 2015SXTS02) in part by the open foundation ofFudan University Key Laboratory for Information Scienceof Electromagnetic Waves (Grant no EMW201502) in partby the Scientific Research Foundation of Yanan University(Grant nos YDBK2016-17 and YDY2017-06) and in part bythe Natural Science Basic Research Plan in Shaanxi Provinceof China (Grant no 2014JM-6113)

References

[1] M A Nasr I A Eshrah and E A Hashish ldquoElectromagneticscattering from a buried cylinder using a multiple reflection

8 International Journal of Antennas and Propagation

approach TM caserdquo IEEE Transactions on Antennas and Prop-agation vol 62 no 5 pp 2702ndash2707 2014

[2] S Bellez C Bourlier and G Kubicke ldquo3-D scattering froma PEC target buried beneath a dielectric rough surface anefficient PILE-ACA algorithm for solving a hybrid KA-EFIEformulationrdquo Institute of Electrical and Electronics EngineersTransactions on Antennas and Propagation vol 63 no 11 pp5003ndash5014 2015

[3] W Yang and C Qi ldquoA Bi-Iteration Model for ElectromagneticScattering from a 3D Object above a 2D Rough SurfacerdquoElectromagnetics vol 35 no 3 pp 190ndash204 2015

[4] E Rashidi-Ranjbar and M Dehmollaian ldquoTarget Above Ran-dom Rough Surface Scattering Using a Parallelized IPO Accel-erated by MLFMMrdquo IEEE Geoscience and Remote SensingLetters vol 12 no 7 pp 1481ndash1485 2015

[5] R W Xu L X Guo H J He andW Liu ldquoA hybrid FEMMoMtechnique for 3-D electromagnetic scattering from a dielectricobject above a conductive rough surfacerdquo IEEE Geoscience ampRemote Sensing Letters vol 13 pp 314ndash318 2016

[6] X M Zhu X C Ren and L X Guo ldquoStudy on wide-bandscattering from rectangular cross-section above rough landsurface with exponential type distribution using FDTDrdquo ActaPhysica Sinica vol 63 2014

[7] A Chehri P Fortier and P M Tardif ldquoCharacterization ofthe ultra-wideband channel in confined environments withdiffracting rough surfacesrdquoWireless Personal Communicationsvol 62 no 4 pp 859ndash877 2012

[8] M Khemiri and I Sassi ldquoRegions of validity of geometric opticsandKirchhoff approximations for reflection fromGaussian ran-dom rough dielectric surfacesrdquo Waves in random and complexmedia propagation scattering and imaging vol 25 no 4 pp656ndash668 2015

[9] S Afifi R Dusseaux and A Berrouk ldquoElectromagnetic scatter-ing from 3D layered structures with randomly rough interfacesAnalysis with the small perturbation method and the smallslope approximationrdquo IEEE Transactions on Antennas andPropagation vol 62 no 10 pp 5200ndash5208 2014

[10] A Berrouk R Dusseaux and S Affif ldquoElectromagnetic wavescattering from rough layered interfaces Analysis with thesmall perturbationmethod and the small slope approximationrdquoProgress in Electromagnetics Research B no 57 pp 177ndash190 2014

[11] G Apaydin F Hacivelioglu L Sevgi and P Y UfimtsevldquoWedge diffracted waves excited by a line source Method ofMoments (MoM)modeling of fringe wavesrdquo IEEE Transactionson Antennas Propagation vol 62 pp 4368ndash4371 2014

[12] R Xiong B Chen J Han Y Qiu W Yang and Q NingldquoTransient resistance analysis of large grounding systems usingthe FDTD methodrdquo Progress in Electromagnetics Research vol132 pp 159ndash175 2012

[13] O Ozgun andM Kuzuoglu ldquoMonte Carlo-based characteristicbasis finite-element method (MC-CBFEM) for numerical anal-ysis of scattering from objects onabove rough sea surfacesrdquoIEEE Transactions on Geoscience and Remote Sensing vol 50no 3 pp 769ndash783 2012

[14] R Tao Y Li X Bai and A Waheed ldquoFractional weierstrassmodel for rough ocean surface and analytical derivation ofits scattered field in a closed formrdquo IEEE Transactions onGeoscience and Remote Sensing vol 50 no 10 pp 3627ndash36392012

[15] J Li L-X Guo S-R Chai and Y-C Jiao ldquoElectromagneticscattering from a PEC object above a dielectric rough sea

surface by a hybrid POndashPO methodrdquo Waves in Random andComplex Media vol 25 no 1 pp 60ndash74 2015

[16] C G Jia L X Guo and P J Yang ldquoEM scattering from atarget above a 1-D randomly rough sea surface using GPU-based parallel FDTDrdquo IEEE Antennas and Wireless PropagationLetters vol 14 pp 217ndash220 2015

[17] Y Liang L X Guo Z S Wu and Q H Liu ldquoA Study ofComposite Electromagnetic Scattering from an Object Near aRough Sea Surface Using an Efficient Numerical AlgorithmrdquoIEEEAntennas andWireless Propagation Letters vol 15 pp 186ndash190 2016

[18] T Wei X C Ren and L X Guo ldquoStudy on compositeelectromagnetic scattering from the double rectangular cross-section columns above rough sea surface using hybridmethodrdquoActa Physica Sinica vol 64 2015

[19] L-X Guo andR-WXu ldquoAn efficientmultiregion FEM-BIM forcomposite scattering from an arbitrary dielectric target abovedielectric rough sea surfacesrdquo IEEE Transactions on Geoscienceand Remote Sensing vol 53 no 7 pp 3885ndash3896 2015

[20] P-J Yang and L-X Guo ldquoPolarimetric scattering from two-dimensional dielectric rough sea surface with a ship-inducedKelvin wakerdquo International Journal of Antennas and Propaga-tion vol 2016 Article ID 2474708 2016

[21] X C Ren L X Guo and Y C Jiao ldquoInvestigation of elec-tromagnetic scattering interaction between the column withrectangular cross-section and rough land surface covered withsnow using finite difference time domainmethodrdquoActa PhysicaSinica vol 61 article 144101 p 379 2012

[22] R Wang L X Guo and A Q Wang ldquoInvestigation of electro-magnetic scattering interaction between the buried target andthe rough surface in different types of soilrdquo Acta Phys Sin vol59 pp 3179ndash3186 2010

[23] T Meissner and F J Wentz ldquoThe complex dielectric constantof pure and sea water from microwave satellite observationsrdquoIEEE Transactions on Geoscience and Remote Sensing vol 42no 9 pp 1836ndash1849 2004

[24] D Lyzenga ldquoNumerical simulation of synthetic aperture radarimage spectra for ocean wavesrdquo IEEE Transactions on Geo-science and Remote Sensing vol GE-24 no 6 pp 863ndash872 1986

[25] R A Dalrymple and B D Rogers ldquoNumerical modeling ofwaterwaveswith the SPHmethodrdquoCoastal Engineering Journalvol 53 no 2-3 pp 141ndash147 2006

[26] C Br UNingWAlpers andKHasselmann ldquoMonte-carlo sim-ulation studies of the nonlinear imaging of a two dimensionalsurface wave field by a synthetic aperture radarrdquo InternationalJournal of Remote Sensing vol 11 no 10 pp 1695ndash1727 1990

[27] J R Wang and T J Schmugge ldquoAn empirical model for thecomplex dielectric permittivity of soils as a function of watercontentrdquo IEEE Transactions on Geoscience and Remote Sensingvol 18 no 4 pp 288ndash295 1980

[28] L Tsang J A Kong and K H Ding Scattering of Elec-tromagnetic Waves Theories and Applications vol 1 Wiley-Interscience New York NY USA 1 edition 2000

[29] L Sevgi Electromagnetic Modeling and Simulation John Wileyamp Sons Inc Hoboken NJ USA 2014

[30] A Taflove and S C Hagness Computational ElectrodynamicsThe Finite-Difference Time-Domian Method Artech HouseBoston Mass USA 3rd edition 2005

RoboticsJournal of

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Control Scienceand Engineering

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International Journal of

RotatingMachinery

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Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design

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Shock and Vibration

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DistributedSensor Networks

International Journal of

International Journal of Antennas and Propagation 3

Under normal circumstances the rock density of soil is 120588119903 =26 gcm3 and 120588119887 is determined by the following formula

120588119887 = 345511987703018 119877 = 251 minus 021119862 + 022119862 (7)

When119898119881 le 119898119905 the effective dielectric constant of the soil is120576 = 119898119881120576119909 + (119901 minus 119898119881) 120576119886 + (1 minus 119901) 120576119903 (8)

where

120576119909 = 120576119894 + (120576119882 minus 120576119894) 120573119898119881119898119905 120573 = minus057119882119875 + 0481

(9)

where 120576119886 = 10 is dielectric constant of air and 120576119894 = 315 minus1198940025 is dielectric constant of ice 120576119882 is dielectric constantof pure water and can be calculated by the Debye equationnamely

120576119882 = 49 + 1205761198820 minus 491 + 1198942120587119891120591119908 (10)

1205761198820 = 88045 minus 04147119879 + 6295 times 10minus41198792 + 1705times 10minus51198793 (11)

2120587120591119908 = 11109 times 10minus10 minus 3824 times 10minus12119879 + 6938times 10minus141198792 minus 5096 times 10minus161198793 (12)

In (11)-(12) 119879 denotes temperature When 119898119881 gt 119898119905 theeffective dielectric constant of the soil is

120576 = 119898119905120576119909 + (119898119881 minus 119898119905) 120576119882 + (119901 minus 119898119881) 120576119886+ (1 minus 119901) 120576119903

120576119909 = 120576119894 + (120576119882 minus 120576119894) 120573(13)

Maxwellrsquos equations are a set of basic equations thatgovern the macroscopic electromagnetic phenomena Fortwo-dimensional electromagnetic scattering problems rect-angular components of the electromagnetic field may beclassified as independent groups namely TM wave and TEwave In TM wave as an example FDTD difference equationhas the following form [29]

119867119899+12119909 (119901 119902 + 12) = 119862119875 (119898)119867119899minus12119909 (119901 119902 + 12)minus 119862119876 (119898) 119864119899119911 (119901 119902 + 1) minus 119864119899119911 (119901 119902)Δ119910

119867119899+12119910 (119901 + 12 119902) = 119862119875 (119898)119867119899minus12119910 (119901 + 12 119902)+ 119862119876 (119898) 119864119899119911 (119901 + 1 119902) minus 119864119899119911 (119901 119902)Δ119909

119864119899+1119911 (119901 119902) = 119862119860 (119898) 119864119899119911 (119901 119902) + 119862119861 (119898)sdot [[119867119899+12119910 (119901 + 12 119902) minus 119867119899+12119910 (119901 minus 12 119902)

Δ119909

minus 119867119899+12119909 (119901 119902 + 12) minus 119867119899+12119909 (119901 119902 minus 12)Δ119910 ]

]

(14)

where 120593 = 40∘ 120590 are discrete grid width along the 120575 =1 cm 119863 = 16 is direction of FDTD computational domainrespectively and the coefficients 119862119860 119862119861 119862119875 and 119862119876 arerespectively

119862119860 (119898) = 120576 (119898) Δ119905 minus 120590 (119898) 2120576 (119898) Δ119905 + 120590 (119898) 2 119862119861 (119898) = 1120576 (119898) Δ119905 + 120590 (119898) 2 119862119875 (119898) = 120583 (119898) Δ119905 minus 120590119898 (119898) 2120583 (119898) Δ119905 + 120590119898 (119898) 2 119862119876 (119898) = 1120583 (119898) Δ119905 + 120590119898 (119898) 2

(15)

where the value of grade 119898 and the left field componentnode labels have the same position In (15) 120590(119898) denotes theelectric conductivity 120576(119898) represents electrical permittivity120583(119898) stands for the magnetic permeability Δ119905 is the timeincrement

FDTD calculation is only in a limited area Thus it isnecessary to set absorbing boundary in truncated bound-ary for open domain electromagnetic scattering problemAnisotropic perfectly matched layer (UPML) absorbingboundary is selected in this work FDTD iteration order ofUPML layers is 119867119909 119867119910 rarr 1198751015840119911 rarr 119875119911 rarr 119864119911 and 119864119911 rarr119861119909 119861119910 rarr 119867119909 119867119910 and the iterative formula of electronicfield 119864119911 of UPML layer of truncated conductive medium isbelow

1198751015840119899+1119911 (119901 119902) = 119862119860 (119898) 1198751015840119899119911 (119901 119902) + 119862119861 (119898)sdot [[119867119899+12119910 (119901 + 12 119902) minus 119867119899+12119910 (119901 minus 12 119902)

Δ119909

4 International Journal of Antennas and Propagation

minus 119867119899+12119909 (119901 119902 + 12) minus 119867119899+12119909 (119901 119902 minus 12)Δ119910 ]

]

119875119899+1119911 (119901 119902) = 1198621 (119898) 119875119899119911 (119901 119902) + 1198622 (119898)sdot [1198751015840119899+1119911 (119901 119902) minus 1198751015840119899119911 (119901 119902)]

119864119899+1119911 (119901 119902) = 1198623 (119898) 119864119899119911 (119901 119902) + 1198624 (119898) sdot [119875119899+1119911 (119901 119902)minus 119875119899119911 (119901 119902)]

(16)

where the coefficients 119862119860(119898) and 119862119861(119898) are the same with(8) and the coefficients1198621(119898)1198622(119898)1198623(119898) and1198624(119898) are

1198621 (119898) = 120581119909 (119898) Δ119905 minus 120590119909 (119898) 21205760120581119909 (119898) Δ119905 + 120590119909 (119898) 21205760 1198622 (119898) = 1Δ119905120581119909 (119898) Δ119905 + 120590119909 (119898) 21205760 1198623 (119898) = 120581119910 (119898) Δ119905 minus 120590119910 (119898) 21205760120581119910 (119898) Δ119905 + 120590119910 (119898) 21205760 1198624 (119898) = 1Δ119905120581119910 (119898) Δ119905 + 120590119910 (119898) 21205760

(17)

where 1205760 is dielectric constant in vacuum and the value of 120590119908and 120581119908 (119908 = 119909 119910) is

120590119908 (119908) = 120590119908max

1003816100381610038161003816119908 minus 11990801003816100381610038161003816119898119889119898 120581119908 (119908) = 1 + (120581119908max minus 1)

1003816100381610038161003816119908 minus 11990801003816100381610038161003816119898119889119898 (18)

where 119889 represents the thickness of the UPML layer and 1199080denotes the interface location that UPML layer is near FDTDarea When 119898 = 4 120590max = (119898 + 1)radic120576119903150120587120575 120581max = 5sim11and the absorption effect is optimal [30]

Near-field scattering data is obtained by the FDTD cal-culation Each time field value on the boundary is recordedand the far-zone scattered field time response is obtainedusing extrapolation methods of transient pulse source exci-tation Then the frequency response of scattering coefficientis obtained through substituting the scattering coefficientformula by the Fourier transform

120590 = 10 lg (NRCS) 119889119861 (19)

Here NRCS represents the Normalization Radar Cross Sec-tion The NRCS is expressed as [24]

NRCS = lim119903rarrinfin

2120587119903119871100381610038161003816100381611986411990410038161003816100381610038162100381610038161003816100381611986411989410038161003816100381610038162 (20)

Here 119903 is distance from observation point to origin 119864119904 iselectric field of scattered wave and 119864119894 is electric field ofincident wave

In this work the Gaussian pulse electromagnetic wave isgiven by [24]

119864119894 (119905) = exp[minus4120587 (119905 minus 1199050)21205912 ] (21)

Here 120591 is constant and decides the pulse width and it is setby 120591 = 2119891 Generally 1199050 = 081205913 Numerical Results

In the following calculations the emphasis is put on the backcomposite scattering coefficient which varies with frequencyIt should be noted that the incident wave is Gaussian pulseelectromagnetic wave of TM polarization the width of grid is119889119909 = 05 cm incident angle is 120579119894 = 30∘ and sampling lengthof rough land surface is 119871 = 1600 cm The final example isan ensemble average over 40 realizations of rough surfacesThe dielectric parameter of soil is calculated using modelsfound by Wang and Schmugge [27] In this part we considerthat type of soil is silty loam Without special explanationin numerical simulations parameters of rectangular cross-section column are given with 119886119887 = 20 cm 119887119888 = 70 cm120593 = 0∘ ℎ = 5 cm and 119889119889 = 50 cm The root-mean-squareof rough surface fluctuation 120575 is 1 cm the correlation lengthof rough surface fluctuation 119897 is 4 cm and soil moisture119898V is02

In order to obtain the characteristics of composite wide-band electromagnetic scattering from the rough soil surfacewith partially buried periodic distributed rectangular cross-section columns the curves of back composite scatteringcoefficient which varies with frequency are studied by numer-ical calculation under different parameters of rough surfaceand column In the following the numerical simulations areperformed on the computer with two 260GHz processors(Intel Xeon E5-2650) 16GB Memory Microsoft Windows7 operation system and the Fortran PowerStation 40 com-piler Under the configuration the computational time andmemory size for one realization are approximately 33min and47MB respectively

Figure 3 depicts the distribution of 120590 with the incidentwave frequency 119891 for 120575 = 1 cm 3 cm and 5 cm respectivelyIt is found that the influence of 120575 on 120590 is obvious With theincrease of 120575 the scattering coefficient 120590 increases except forsome high frequency domain (2215GHz lt 119891 lt 3GHz) Inaddition the position and value for the peaks of 120590 are nearlyunchanged with 120575 On the other hand with the increasingincident wave frequency 119891 the oscillation for the amplitudeof curve becomes small

To examine the scattering coefficient difference betweensingle column case and multiple columns case a comparisonof single column case and multiple columns case is made inFigure 4 In Figure 4 the root-mean-square of rough surfaceis 120575 is 1 cm It can be readily observed that for multiplecolumns case obvious peaks exist which can be attributedto the grating effect due to the scattering from periodicallydistributed rectangular columns

In Figure 5 the dependency of 120590 on 119897 is plotted FromFigure 5 it is found that with the increase of 119897 the scattering

International Journal of Antennas and Propagation 5

= 1 cm = 3 cm = 5 cm

05 10 15 20 2500 30

f (GHz)

minus60

minus45

minus30

minus15

0

15

(d

B)

Figure 3 The influence of 120575 on 120590

Single columnMultiple columns

= 1 cm

minus70

minus60

minus50

minus40

minus30

minus20

minus10

0

10

(d

B)

05 10 15 20 25 3000

f (GHz)

Figure 4A comparison of single column case andmultiple columnscase

coefficient 120590 increases and the position and value for thepeaks of 120590 are nearly unchanged with 119897

The distribution of 120590 with 119891 for different soil moisture119898V with 1205761199031 = 49301 minus 11989404510 (119898V1 = 01 gcm3) 1205761199032 =102802 minus 11989416464 (119898V2 = 02 gcm3) and 1205761199033 = 260279 minus11989452063 (119898V3 = 04 gcm3) is depicted in Figure 6 The soilmoisture represents dielectric parameter of soil It is obviousthat the influence of119898V on 120590 is small and obscure When thefrequency is less than 09GHz (119891 lt 09GHz) all the curvesin Figure 6 are coincident However it can be found that with119898V increases 120590 slightly become greater when the frequency islarger than 09GHz (119891 gt 09GHz)

Figure 7 depicts the distribution of 120590 with 119891 for differentbreadth of column 119886119887 (119886119887 = 20 cm 60 cm 100 cm and160 cm) It is found that the influence of 119886119887 on 120590 is obviousthat is with the increase of 119886119887 the number of rectangularcross-section columns decreases And the oscillation for the

cml = 10

l = 40 cml = 100 cm

minus75

minus60

minus45

minus30

minus15

0

15

(d

B)

05 10 15 20 25 3000

f (GHz)

Figure 5 The influence of 119897 on 120590

minus60

minus45

minus30

minus15

0

15

(dB)

05 10 15 20 25 3000

f (GHz)

m = 01

m = 02

m = 04

Figure 6 The influence of119898V on 120590

amplitude of curve becomes smaller the oscillation for thefrequency of curve becomes greater

Figure 8 depicts the distribution of 120590 with 119891 for differentlength of column 119887119888 (119887119888 = 30 cm 70 cm and 100 cm) It isfound that the influence of 119887119888 on 120590 is complex and obviousthat is at most of the frequency points the larger 119887119888 is thesmaller 120590 is the smaller the peak value of 120590 Moreover as 119891increases the oscillating amplitude of the curve is smaller

Figure 9 depicts the distribution of 120590 with 119891 for differentseparation distance of every two adjacent columns 119889119889 (119889119889 =30 cm 50 cm and 100 cm) It is found that the influence of119889119889 on 120590 is obvious At most of the frequency points withthe increase of 119889119889 the number of rectangular cross-sectioncolumns decreases in the calculated area the oscillatingfrequency of curve is greater and 120590 is larger for the samefrequency point

6 International Journal of Antennas and Propagation

ab = 20 cm ab = 60 cm

ab = 100 cm ab = 160 cm

minus60

minus45

minus30

minus15

0

15

(d

B)

minus60

minus45

minus30

minus15

0

15

(d

B)

05 10 15 20 2500 30

f (GHz)05 10 15 20 2500 30

f (GHz)

minus60

minus45

minus30

minus15

0

15

(d

B)

minus60

minus45

minus30

minus15

0

15

(d

B)

05 10 15 20 2500 30

f (GHz)05 10 15 20 2500 30

f (GHz)

Figure 7 The influence of 119886119887 on 120590

bc = 30 cmbc = 70 cmbc = 100 cm

minus60

minus45

minus30

minus15

0

15

(d

B)

05 10 15 20 2500 30

f (GHz)

Figure 8 The influence of 119887119888 on 120590Figure 10 depicts the distribution of 120590with 119891 for different

burial depth ℎ (ℎ = 5 cm 15 cm and 25 cm) It is obvious

that the influence of ℎ on 120590 is small and obscure Part of thecurves are coincident However it can be found that with theincrease ofℎ120590 becomes greaterwhen frequency is larger than173GHz (119891 gt 173GHz)

Figure 11 shows the relationship of 120590 with 119891 for different120593 (120593 = 10∘ 30∘ and 60∘) when ℎ = 15 cm Obviously theinfluence of 120593 on 120590 is complex When frequency is less than109GHz (119891 lt 109GHz) the bigger 120593 is the smaller 120590 is Iffrequency satisfies the inequality (109GHz lt 119891 lt 25GHz)120590 of 120593 = 30∘ is smaller than others

Hereinbefore the results from Figures 3ndash11 in the caseof TM polarization are obtained by plentiful calculation onthe condition that other parameters are stationary Only onepoint is worth illustrating that is the influence of someparameters on the back composite scattering coefficient isrestricted by other parameters

4 Conclusion

In this paper the problems of composite wideband electro-magnetic scattering from exponential correlation rough soilsurface with partially buried periodic distributed rectangularcross-section columns underGaussian pulse wave irradiation

International Journal of Antennas and Propagation 7

dd = 30 cmdd = 50 cmdd = 100 cm

05 10 15 20 2500 30

f (GHz)

minus60

minus45

minus30

minus15

0

15

(d

B)

Figure 9 The influence of 119889119889 on 120590

ℎ = 5 cmℎ = 15 cmℎ = 25 cm

05 10 15 20 2500 30

f (GHz)

(d

B)

minus60

minus80

minus40

minus20

0

20

Figure 10 The influence of ℎ on 120590are investigated using transient FDTD The influence of theroot-mean-square and the correlation length of rough surfacefluctuation soil moisture the length and the width of therectangular cross-section column separation distance burialdepth and tilt angle on the composite scattering signaturesare discussed in detail The numerical simulations indicatethat the variation of composite scattering coefficient versusfrequency is oscillatory It is also showed that the compositescattering coefficient versus frequency increases with theincrease of root-mean-square of soil surface water ratio ofsoil the target section height and the separation distance oftarget However simulation results indicate that the compos-ite scattering coefficient versus frequency decreases with theincrease of target section width In summary the variationof wideband scattering coefficient is very complicated andis very sensitive to incidence angle of electromagnetic waveHowever the wideband scattering coefficient under Gaussian

= 10∘

= 30∘

= 60∘

05 10 15 20 2500 30

f (GHz)

minus60

minus80

minus40

minus20

0

20

(d

B)

Figure 11 The influence of 120593 on 120590

pulse wave incidence is less sensitive to the correlation lengthof rough soil surface the depth of buried objects and thedielectric constant of target Although the multiple columnspartially buried in a randomly rough surface are a rathersimplified model the present study is potentially valuable formany applications such as ground remote sensing groundpenetrating radar applications undergroundmine detectiontunnel detection and target identification In particular thesimplified model of periodically distributed columns repre-sents many realistic objects such as tree trunks mine propstelegraph poles The future investigation on this topic willinclude electromagnetic scattering from two-dimensionalrough land surface with complex multiple targets

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported in part by the National NaturalScience Foundation of China (Grant no 61379026) in partby the National Science Foundation for Young Scientists ofChina (Grant no 61701428) in part by the foundation of con-struction of high-level university project in Shaanxi Province(Grant no 2015SXTS02) in part by the open foundation ofFudan University Key Laboratory for Information Scienceof Electromagnetic Waves (Grant no EMW201502) in partby the Scientific Research Foundation of Yanan University(Grant nos YDBK2016-17 and YDY2017-06) and in part bythe Natural Science Basic Research Plan in Shaanxi Provinceof China (Grant no 2014JM-6113)

References

[1] M A Nasr I A Eshrah and E A Hashish ldquoElectromagneticscattering from a buried cylinder using a multiple reflection

8 International Journal of Antennas and Propagation

approach TM caserdquo IEEE Transactions on Antennas and Prop-agation vol 62 no 5 pp 2702ndash2707 2014

[2] S Bellez C Bourlier and G Kubicke ldquo3-D scattering froma PEC target buried beneath a dielectric rough surface anefficient PILE-ACA algorithm for solving a hybrid KA-EFIEformulationrdquo Institute of Electrical and Electronics EngineersTransactions on Antennas and Propagation vol 63 no 11 pp5003ndash5014 2015

[3] W Yang and C Qi ldquoA Bi-Iteration Model for ElectromagneticScattering from a 3D Object above a 2D Rough SurfacerdquoElectromagnetics vol 35 no 3 pp 190ndash204 2015

[4] E Rashidi-Ranjbar and M Dehmollaian ldquoTarget Above Ran-dom Rough Surface Scattering Using a Parallelized IPO Accel-erated by MLFMMrdquo IEEE Geoscience and Remote SensingLetters vol 12 no 7 pp 1481ndash1485 2015

[5] R W Xu L X Guo H J He andW Liu ldquoA hybrid FEMMoMtechnique for 3-D electromagnetic scattering from a dielectricobject above a conductive rough surfacerdquo IEEE Geoscience ampRemote Sensing Letters vol 13 pp 314ndash318 2016

[6] X M Zhu X C Ren and L X Guo ldquoStudy on wide-bandscattering from rectangular cross-section above rough landsurface with exponential type distribution using FDTDrdquo ActaPhysica Sinica vol 63 2014

[7] A Chehri P Fortier and P M Tardif ldquoCharacterization ofthe ultra-wideband channel in confined environments withdiffracting rough surfacesrdquoWireless Personal Communicationsvol 62 no 4 pp 859ndash877 2012

[8] M Khemiri and I Sassi ldquoRegions of validity of geometric opticsandKirchhoff approximations for reflection fromGaussian ran-dom rough dielectric surfacesrdquo Waves in random and complexmedia propagation scattering and imaging vol 25 no 4 pp656ndash668 2015

[9] S Afifi R Dusseaux and A Berrouk ldquoElectromagnetic scatter-ing from 3D layered structures with randomly rough interfacesAnalysis with the small perturbation method and the smallslope approximationrdquo IEEE Transactions on Antennas andPropagation vol 62 no 10 pp 5200ndash5208 2014

[10] A Berrouk R Dusseaux and S Affif ldquoElectromagnetic wavescattering from rough layered interfaces Analysis with thesmall perturbationmethod and the small slope approximationrdquoProgress in Electromagnetics Research B no 57 pp 177ndash190 2014

[11] G Apaydin F Hacivelioglu L Sevgi and P Y UfimtsevldquoWedge diffracted waves excited by a line source Method ofMoments (MoM)modeling of fringe wavesrdquo IEEE Transactionson Antennas Propagation vol 62 pp 4368ndash4371 2014

[12] R Xiong B Chen J Han Y Qiu W Yang and Q NingldquoTransient resistance analysis of large grounding systems usingthe FDTD methodrdquo Progress in Electromagnetics Research vol132 pp 159ndash175 2012

[13] O Ozgun andM Kuzuoglu ldquoMonte Carlo-based characteristicbasis finite-element method (MC-CBFEM) for numerical anal-ysis of scattering from objects onabove rough sea surfacesrdquoIEEE Transactions on Geoscience and Remote Sensing vol 50no 3 pp 769ndash783 2012

[14] R Tao Y Li X Bai and A Waheed ldquoFractional weierstrassmodel for rough ocean surface and analytical derivation ofits scattered field in a closed formrdquo IEEE Transactions onGeoscience and Remote Sensing vol 50 no 10 pp 3627ndash36392012

[15] J Li L-X Guo S-R Chai and Y-C Jiao ldquoElectromagneticscattering from a PEC object above a dielectric rough sea

surface by a hybrid POndashPO methodrdquo Waves in Random andComplex Media vol 25 no 1 pp 60ndash74 2015

[16] C G Jia L X Guo and P J Yang ldquoEM scattering from atarget above a 1-D randomly rough sea surface using GPU-based parallel FDTDrdquo IEEE Antennas and Wireless PropagationLetters vol 14 pp 217ndash220 2015

[17] Y Liang L X Guo Z S Wu and Q H Liu ldquoA Study ofComposite Electromagnetic Scattering from an Object Near aRough Sea Surface Using an Efficient Numerical AlgorithmrdquoIEEEAntennas andWireless Propagation Letters vol 15 pp 186ndash190 2016

[18] T Wei X C Ren and L X Guo ldquoStudy on compositeelectromagnetic scattering from the double rectangular cross-section columns above rough sea surface using hybridmethodrdquoActa Physica Sinica vol 64 2015

[19] L-X Guo andR-WXu ldquoAn efficientmultiregion FEM-BIM forcomposite scattering from an arbitrary dielectric target abovedielectric rough sea surfacesrdquo IEEE Transactions on Geoscienceand Remote Sensing vol 53 no 7 pp 3885ndash3896 2015

[20] P-J Yang and L-X Guo ldquoPolarimetric scattering from two-dimensional dielectric rough sea surface with a ship-inducedKelvin wakerdquo International Journal of Antennas and Propaga-tion vol 2016 Article ID 2474708 2016

[21] X C Ren L X Guo and Y C Jiao ldquoInvestigation of elec-tromagnetic scattering interaction between the column withrectangular cross-section and rough land surface covered withsnow using finite difference time domainmethodrdquoActa PhysicaSinica vol 61 article 144101 p 379 2012

[22] R Wang L X Guo and A Q Wang ldquoInvestigation of electro-magnetic scattering interaction between the buried target andthe rough surface in different types of soilrdquo Acta Phys Sin vol59 pp 3179ndash3186 2010

[23] T Meissner and F J Wentz ldquoThe complex dielectric constantof pure and sea water from microwave satellite observationsrdquoIEEE Transactions on Geoscience and Remote Sensing vol 42no 9 pp 1836ndash1849 2004

[24] D Lyzenga ldquoNumerical simulation of synthetic aperture radarimage spectra for ocean wavesrdquo IEEE Transactions on Geo-science and Remote Sensing vol GE-24 no 6 pp 863ndash872 1986

[25] R A Dalrymple and B D Rogers ldquoNumerical modeling ofwaterwaveswith the SPHmethodrdquoCoastal Engineering Journalvol 53 no 2-3 pp 141ndash147 2006

[26] C Br UNingWAlpers andKHasselmann ldquoMonte-carlo sim-ulation studies of the nonlinear imaging of a two dimensionalsurface wave field by a synthetic aperture radarrdquo InternationalJournal of Remote Sensing vol 11 no 10 pp 1695ndash1727 1990

[27] J R Wang and T J Schmugge ldquoAn empirical model for thecomplex dielectric permittivity of soils as a function of watercontentrdquo IEEE Transactions on Geoscience and Remote Sensingvol 18 no 4 pp 288ndash295 1980

[28] L Tsang J A Kong and K H Ding Scattering of Elec-tromagnetic Waves Theories and Applications vol 1 Wiley-Interscience New York NY USA 1 edition 2000

[29] L Sevgi Electromagnetic Modeling and Simulation John Wileyamp Sons Inc Hoboken NJ USA 2014

[30] A Taflove and S C Hagness Computational ElectrodynamicsThe Finite-Difference Time-Domian Method Artech HouseBoston Mass USA 3rd edition 2005

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

4 International Journal of Antennas and Propagation

minus 119867119899+12119909 (119901 119902 + 12) minus 119867119899+12119909 (119901 119902 minus 12)Δ119910 ]

]

119875119899+1119911 (119901 119902) = 1198621 (119898) 119875119899119911 (119901 119902) + 1198622 (119898)sdot [1198751015840119899+1119911 (119901 119902) minus 1198751015840119899119911 (119901 119902)]

119864119899+1119911 (119901 119902) = 1198623 (119898) 119864119899119911 (119901 119902) + 1198624 (119898) sdot [119875119899+1119911 (119901 119902)minus 119875119899119911 (119901 119902)]

(16)

where the coefficients 119862119860(119898) and 119862119861(119898) are the same with(8) and the coefficients1198621(119898)1198622(119898)1198623(119898) and1198624(119898) are

1198621 (119898) = 120581119909 (119898) Δ119905 minus 120590119909 (119898) 21205760120581119909 (119898) Δ119905 + 120590119909 (119898) 21205760 1198622 (119898) = 1Δ119905120581119909 (119898) Δ119905 + 120590119909 (119898) 21205760 1198623 (119898) = 120581119910 (119898) Δ119905 minus 120590119910 (119898) 21205760120581119910 (119898) Δ119905 + 120590119910 (119898) 21205760 1198624 (119898) = 1Δ119905120581119910 (119898) Δ119905 + 120590119910 (119898) 21205760

(17)

where 1205760 is dielectric constant in vacuum and the value of 120590119908and 120581119908 (119908 = 119909 119910) is

120590119908 (119908) = 120590119908max

1003816100381610038161003816119908 minus 11990801003816100381610038161003816119898119889119898 120581119908 (119908) = 1 + (120581119908max minus 1)

1003816100381610038161003816119908 minus 11990801003816100381610038161003816119898119889119898 (18)

where 119889 represents the thickness of the UPML layer and 1199080denotes the interface location that UPML layer is near FDTDarea When 119898 = 4 120590max = (119898 + 1)radic120576119903150120587120575 120581max = 5sim11and the absorption effect is optimal [30]

Near-field scattering data is obtained by the FDTD cal-culation Each time field value on the boundary is recordedand the far-zone scattered field time response is obtainedusing extrapolation methods of transient pulse source exci-tation Then the frequency response of scattering coefficientis obtained through substituting the scattering coefficientformula by the Fourier transform

120590 = 10 lg (NRCS) 119889119861 (19)

Here NRCS represents the Normalization Radar Cross Sec-tion The NRCS is expressed as [24]

NRCS = lim119903rarrinfin

2120587119903119871100381610038161003816100381611986411990410038161003816100381610038162100381610038161003816100381611986411989410038161003816100381610038162 (20)

Here 119903 is distance from observation point to origin 119864119904 iselectric field of scattered wave and 119864119894 is electric field ofincident wave

In this work the Gaussian pulse electromagnetic wave isgiven by [24]

119864119894 (119905) = exp[minus4120587 (119905 minus 1199050)21205912 ] (21)

Here 120591 is constant and decides the pulse width and it is setby 120591 = 2119891 Generally 1199050 = 081205913 Numerical Results

In the following calculations the emphasis is put on the backcomposite scattering coefficient which varies with frequencyIt should be noted that the incident wave is Gaussian pulseelectromagnetic wave of TM polarization the width of grid is119889119909 = 05 cm incident angle is 120579119894 = 30∘ and sampling lengthof rough land surface is 119871 = 1600 cm The final example isan ensemble average over 40 realizations of rough surfacesThe dielectric parameter of soil is calculated using modelsfound by Wang and Schmugge [27] In this part we considerthat type of soil is silty loam Without special explanationin numerical simulations parameters of rectangular cross-section column are given with 119886119887 = 20 cm 119887119888 = 70 cm120593 = 0∘ ℎ = 5 cm and 119889119889 = 50 cm The root-mean-squareof rough surface fluctuation 120575 is 1 cm the correlation lengthof rough surface fluctuation 119897 is 4 cm and soil moisture119898V is02

In order to obtain the characteristics of composite wide-band electromagnetic scattering from the rough soil surfacewith partially buried periodic distributed rectangular cross-section columns the curves of back composite scatteringcoefficient which varies with frequency are studied by numer-ical calculation under different parameters of rough surfaceand column In the following the numerical simulations areperformed on the computer with two 260GHz processors(Intel Xeon E5-2650) 16GB Memory Microsoft Windows7 operation system and the Fortran PowerStation 40 com-piler Under the configuration the computational time andmemory size for one realization are approximately 33min and47MB respectively

Figure 3 depicts the distribution of 120590 with the incidentwave frequency 119891 for 120575 = 1 cm 3 cm and 5 cm respectivelyIt is found that the influence of 120575 on 120590 is obvious With theincrease of 120575 the scattering coefficient 120590 increases except forsome high frequency domain (2215GHz lt 119891 lt 3GHz) Inaddition the position and value for the peaks of 120590 are nearlyunchanged with 120575 On the other hand with the increasingincident wave frequency 119891 the oscillation for the amplitudeof curve becomes small

To examine the scattering coefficient difference betweensingle column case and multiple columns case a comparisonof single column case and multiple columns case is made inFigure 4 In Figure 4 the root-mean-square of rough surfaceis 120575 is 1 cm It can be readily observed that for multiplecolumns case obvious peaks exist which can be attributedto the grating effect due to the scattering from periodicallydistributed rectangular columns

In Figure 5 the dependency of 120590 on 119897 is plotted FromFigure 5 it is found that with the increase of 119897 the scattering

International Journal of Antennas and Propagation 5

= 1 cm = 3 cm = 5 cm

05 10 15 20 2500 30

f (GHz)

minus60

minus45

minus30

minus15

0

15

(d

B)

Figure 3 The influence of 120575 on 120590

Single columnMultiple columns

= 1 cm

minus70

minus60

minus50

minus40

minus30

minus20

minus10

0

10

(d

B)

05 10 15 20 25 3000

f (GHz)

Figure 4A comparison of single column case andmultiple columnscase

coefficient 120590 increases and the position and value for thepeaks of 120590 are nearly unchanged with 119897

The distribution of 120590 with 119891 for different soil moisture119898V with 1205761199031 = 49301 minus 11989404510 (119898V1 = 01 gcm3) 1205761199032 =102802 minus 11989416464 (119898V2 = 02 gcm3) and 1205761199033 = 260279 minus11989452063 (119898V3 = 04 gcm3) is depicted in Figure 6 The soilmoisture represents dielectric parameter of soil It is obviousthat the influence of119898V on 120590 is small and obscure When thefrequency is less than 09GHz (119891 lt 09GHz) all the curvesin Figure 6 are coincident However it can be found that with119898V increases 120590 slightly become greater when the frequency islarger than 09GHz (119891 gt 09GHz)

Figure 7 depicts the distribution of 120590 with 119891 for differentbreadth of column 119886119887 (119886119887 = 20 cm 60 cm 100 cm and160 cm) It is found that the influence of 119886119887 on 120590 is obviousthat is with the increase of 119886119887 the number of rectangularcross-section columns decreases And the oscillation for the

cml = 10

l = 40 cml = 100 cm

minus75

minus60

minus45

minus30

minus15

0

15

(d

B)

05 10 15 20 25 3000

f (GHz)

Figure 5 The influence of 119897 on 120590

minus60

minus45

minus30

minus15

0

15

(dB)

05 10 15 20 25 3000

f (GHz)

m = 01

m = 02

m = 04

Figure 6 The influence of119898V on 120590

amplitude of curve becomes smaller the oscillation for thefrequency of curve becomes greater

Figure 8 depicts the distribution of 120590 with 119891 for differentlength of column 119887119888 (119887119888 = 30 cm 70 cm and 100 cm) It isfound that the influence of 119887119888 on 120590 is complex and obviousthat is at most of the frequency points the larger 119887119888 is thesmaller 120590 is the smaller the peak value of 120590 Moreover as 119891increases the oscillating amplitude of the curve is smaller

Figure 9 depicts the distribution of 120590 with 119891 for differentseparation distance of every two adjacent columns 119889119889 (119889119889 =30 cm 50 cm and 100 cm) It is found that the influence of119889119889 on 120590 is obvious At most of the frequency points withthe increase of 119889119889 the number of rectangular cross-sectioncolumns decreases in the calculated area the oscillatingfrequency of curve is greater and 120590 is larger for the samefrequency point

6 International Journal of Antennas and Propagation

ab = 20 cm ab = 60 cm

ab = 100 cm ab = 160 cm

minus60

minus45

minus30

minus15

0

15

(d

B)

minus60

minus45

minus30

minus15

0

15

(d

B)

05 10 15 20 2500 30

f (GHz)05 10 15 20 2500 30

f (GHz)

minus60

minus45

minus30

minus15

0

15

(d

B)

minus60

minus45

minus30

minus15

0

15

(d

B)

05 10 15 20 2500 30

f (GHz)05 10 15 20 2500 30

f (GHz)

Figure 7 The influence of 119886119887 on 120590

bc = 30 cmbc = 70 cmbc = 100 cm

minus60

minus45

minus30

minus15

0

15

(d

B)

05 10 15 20 2500 30

f (GHz)

Figure 8 The influence of 119887119888 on 120590Figure 10 depicts the distribution of 120590with 119891 for different

burial depth ℎ (ℎ = 5 cm 15 cm and 25 cm) It is obvious

that the influence of ℎ on 120590 is small and obscure Part of thecurves are coincident However it can be found that with theincrease ofℎ120590 becomes greaterwhen frequency is larger than173GHz (119891 gt 173GHz)

Figure 11 shows the relationship of 120590 with 119891 for different120593 (120593 = 10∘ 30∘ and 60∘) when ℎ = 15 cm Obviously theinfluence of 120593 on 120590 is complex When frequency is less than109GHz (119891 lt 109GHz) the bigger 120593 is the smaller 120590 is Iffrequency satisfies the inequality (109GHz lt 119891 lt 25GHz)120590 of 120593 = 30∘ is smaller than others

Hereinbefore the results from Figures 3ndash11 in the caseof TM polarization are obtained by plentiful calculation onthe condition that other parameters are stationary Only onepoint is worth illustrating that is the influence of someparameters on the back composite scattering coefficient isrestricted by other parameters

4 Conclusion

In this paper the problems of composite wideband electro-magnetic scattering from exponential correlation rough soilsurface with partially buried periodic distributed rectangularcross-section columns underGaussian pulse wave irradiation

International Journal of Antennas and Propagation 7

dd = 30 cmdd = 50 cmdd = 100 cm

05 10 15 20 2500 30

f (GHz)

minus60

minus45

minus30

minus15

0

15

(d

B)

Figure 9 The influence of 119889119889 on 120590

ℎ = 5 cmℎ = 15 cmℎ = 25 cm

05 10 15 20 2500 30

f (GHz)

(d

B)

minus60

minus80

minus40

minus20

0

20

Figure 10 The influence of ℎ on 120590are investigated using transient FDTD The influence of theroot-mean-square and the correlation length of rough surfacefluctuation soil moisture the length and the width of therectangular cross-section column separation distance burialdepth and tilt angle on the composite scattering signaturesare discussed in detail The numerical simulations indicatethat the variation of composite scattering coefficient versusfrequency is oscillatory It is also showed that the compositescattering coefficient versus frequency increases with theincrease of root-mean-square of soil surface water ratio ofsoil the target section height and the separation distance oftarget However simulation results indicate that the compos-ite scattering coefficient versus frequency decreases with theincrease of target section width In summary the variationof wideband scattering coefficient is very complicated andis very sensitive to incidence angle of electromagnetic waveHowever the wideband scattering coefficient under Gaussian

= 10∘

= 30∘

= 60∘

05 10 15 20 2500 30

f (GHz)

minus60

minus80

minus40

minus20

0

20

(d

B)

Figure 11 The influence of 120593 on 120590

pulse wave incidence is less sensitive to the correlation lengthof rough soil surface the depth of buried objects and thedielectric constant of target Although the multiple columnspartially buried in a randomly rough surface are a rathersimplified model the present study is potentially valuable formany applications such as ground remote sensing groundpenetrating radar applications undergroundmine detectiontunnel detection and target identification In particular thesimplified model of periodically distributed columns repre-sents many realistic objects such as tree trunks mine propstelegraph poles The future investigation on this topic willinclude electromagnetic scattering from two-dimensionalrough land surface with complex multiple targets

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported in part by the National NaturalScience Foundation of China (Grant no 61379026) in partby the National Science Foundation for Young Scientists ofChina (Grant no 61701428) in part by the foundation of con-struction of high-level university project in Shaanxi Province(Grant no 2015SXTS02) in part by the open foundation ofFudan University Key Laboratory for Information Scienceof Electromagnetic Waves (Grant no EMW201502) in partby the Scientific Research Foundation of Yanan University(Grant nos YDBK2016-17 and YDY2017-06) and in part bythe Natural Science Basic Research Plan in Shaanxi Provinceof China (Grant no 2014JM-6113)

References

[1] M A Nasr I A Eshrah and E A Hashish ldquoElectromagneticscattering from a buried cylinder using a multiple reflection

8 International Journal of Antennas and Propagation

approach TM caserdquo IEEE Transactions on Antennas and Prop-agation vol 62 no 5 pp 2702ndash2707 2014

[2] S Bellez C Bourlier and G Kubicke ldquo3-D scattering froma PEC target buried beneath a dielectric rough surface anefficient PILE-ACA algorithm for solving a hybrid KA-EFIEformulationrdquo Institute of Electrical and Electronics EngineersTransactions on Antennas and Propagation vol 63 no 11 pp5003ndash5014 2015

[3] W Yang and C Qi ldquoA Bi-Iteration Model for ElectromagneticScattering from a 3D Object above a 2D Rough SurfacerdquoElectromagnetics vol 35 no 3 pp 190ndash204 2015

[4] E Rashidi-Ranjbar and M Dehmollaian ldquoTarget Above Ran-dom Rough Surface Scattering Using a Parallelized IPO Accel-erated by MLFMMrdquo IEEE Geoscience and Remote SensingLetters vol 12 no 7 pp 1481ndash1485 2015

[5] R W Xu L X Guo H J He andW Liu ldquoA hybrid FEMMoMtechnique for 3-D electromagnetic scattering from a dielectricobject above a conductive rough surfacerdquo IEEE Geoscience ampRemote Sensing Letters vol 13 pp 314ndash318 2016

[6] X M Zhu X C Ren and L X Guo ldquoStudy on wide-bandscattering from rectangular cross-section above rough landsurface with exponential type distribution using FDTDrdquo ActaPhysica Sinica vol 63 2014

[7] A Chehri P Fortier and P M Tardif ldquoCharacterization ofthe ultra-wideband channel in confined environments withdiffracting rough surfacesrdquoWireless Personal Communicationsvol 62 no 4 pp 859ndash877 2012

[8] M Khemiri and I Sassi ldquoRegions of validity of geometric opticsandKirchhoff approximations for reflection fromGaussian ran-dom rough dielectric surfacesrdquo Waves in random and complexmedia propagation scattering and imaging vol 25 no 4 pp656ndash668 2015

[9] S Afifi R Dusseaux and A Berrouk ldquoElectromagnetic scatter-ing from 3D layered structures with randomly rough interfacesAnalysis with the small perturbation method and the smallslope approximationrdquo IEEE Transactions on Antennas andPropagation vol 62 no 10 pp 5200ndash5208 2014

[10] A Berrouk R Dusseaux and S Affif ldquoElectromagnetic wavescattering from rough layered interfaces Analysis with thesmall perturbationmethod and the small slope approximationrdquoProgress in Electromagnetics Research B no 57 pp 177ndash190 2014

[11] G Apaydin F Hacivelioglu L Sevgi and P Y UfimtsevldquoWedge diffracted waves excited by a line source Method ofMoments (MoM)modeling of fringe wavesrdquo IEEE Transactionson Antennas Propagation vol 62 pp 4368ndash4371 2014

[12] R Xiong B Chen J Han Y Qiu W Yang and Q NingldquoTransient resistance analysis of large grounding systems usingthe FDTD methodrdquo Progress in Electromagnetics Research vol132 pp 159ndash175 2012

[13] O Ozgun andM Kuzuoglu ldquoMonte Carlo-based characteristicbasis finite-element method (MC-CBFEM) for numerical anal-ysis of scattering from objects onabove rough sea surfacesrdquoIEEE Transactions on Geoscience and Remote Sensing vol 50no 3 pp 769ndash783 2012

[14] R Tao Y Li X Bai and A Waheed ldquoFractional weierstrassmodel for rough ocean surface and analytical derivation ofits scattered field in a closed formrdquo IEEE Transactions onGeoscience and Remote Sensing vol 50 no 10 pp 3627ndash36392012

[15] J Li L-X Guo S-R Chai and Y-C Jiao ldquoElectromagneticscattering from a PEC object above a dielectric rough sea

surface by a hybrid POndashPO methodrdquo Waves in Random andComplex Media vol 25 no 1 pp 60ndash74 2015

[16] C G Jia L X Guo and P J Yang ldquoEM scattering from atarget above a 1-D randomly rough sea surface using GPU-based parallel FDTDrdquo IEEE Antennas and Wireless PropagationLetters vol 14 pp 217ndash220 2015

[17] Y Liang L X Guo Z S Wu and Q H Liu ldquoA Study ofComposite Electromagnetic Scattering from an Object Near aRough Sea Surface Using an Efficient Numerical AlgorithmrdquoIEEEAntennas andWireless Propagation Letters vol 15 pp 186ndash190 2016

[18] T Wei X C Ren and L X Guo ldquoStudy on compositeelectromagnetic scattering from the double rectangular cross-section columns above rough sea surface using hybridmethodrdquoActa Physica Sinica vol 64 2015

[19] L-X Guo andR-WXu ldquoAn efficientmultiregion FEM-BIM forcomposite scattering from an arbitrary dielectric target abovedielectric rough sea surfacesrdquo IEEE Transactions on Geoscienceand Remote Sensing vol 53 no 7 pp 3885ndash3896 2015

[20] P-J Yang and L-X Guo ldquoPolarimetric scattering from two-dimensional dielectric rough sea surface with a ship-inducedKelvin wakerdquo International Journal of Antennas and Propaga-tion vol 2016 Article ID 2474708 2016

[21] X C Ren L X Guo and Y C Jiao ldquoInvestigation of elec-tromagnetic scattering interaction between the column withrectangular cross-section and rough land surface covered withsnow using finite difference time domainmethodrdquoActa PhysicaSinica vol 61 article 144101 p 379 2012

[22] R Wang L X Guo and A Q Wang ldquoInvestigation of electro-magnetic scattering interaction between the buried target andthe rough surface in different types of soilrdquo Acta Phys Sin vol59 pp 3179ndash3186 2010

[23] T Meissner and F J Wentz ldquoThe complex dielectric constantof pure and sea water from microwave satellite observationsrdquoIEEE Transactions on Geoscience and Remote Sensing vol 42no 9 pp 1836ndash1849 2004

[24] D Lyzenga ldquoNumerical simulation of synthetic aperture radarimage spectra for ocean wavesrdquo IEEE Transactions on Geo-science and Remote Sensing vol GE-24 no 6 pp 863ndash872 1986

[25] R A Dalrymple and B D Rogers ldquoNumerical modeling ofwaterwaveswith the SPHmethodrdquoCoastal Engineering Journalvol 53 no 2-3 pp 141ndash147 2006

[26] C Br UNingWAlpers andKHasselmann ldquoMonte-carlo sim-ulation studies of the nonlinear imaging of a two dimensionalsurface wave field by a synthetic aperture radarrdquo InternationalJournal of Remote Sensing vol 11 no 10 pp 1695ndash1727 1990

[27] J R Wang and T J Schmugge ldquoAn empirical model for thecomplex dielectric permittivity of soils as a function of watercontentrdquo IEEE Transactions on Geoscience and Remote Sensingvol 18 no 4 pp 288ndash295 1980

[28] L Tsang J A Kong and K H Ding Scattering of Elec-tromagnetic Waves Theories and Applications vol 1 Wiley-Interscience New York NY USA 1 edition 2000

[29] L Sevgi Electromagnetic Modeling and Simulation John Wileyamp Sons Inc Hoboken NJ USA 2014

[30] A Taflove and S C Hagness Computational ElectrodynamicsThe Finite-Difference Time-Domian Method Artech HouseBoston Mass USA 3rd edition 2005

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of Antennas and Propagation 5

= 1 cm = 3 cm = 5 cm

05 10 15 20 2500 30

f (GHz)

minus60

minus45

minus30

minus15

0

15

(d

B)

Figure 3 The influence of 120575 on 120590

Single columnMultiple columns

= 1 cm

minus70

minus60

minus50

minus40

minus30

minus20

minus10

0

10

(d

B)

05 10 15 20 25 3000

f (GHz)

Figure 4A comparison of single column case andmultiple columnscase

coefficient 120590 increases and the position and value for thepeaks of 120590 are nearly unchanged with 119897

The distribution of 120590 with 119891 for different soil moisture119898V with 1205761199031 = 49301 minus 11989404510 (119898V1 = 01 gcm3) 1205761199032 =102802 minus 11989416464 (119898V2 = 02 gcm3) and 1205761199033 = 260279 minus11989452063 (119898V3 = 04 gcm3) is depicted in Figure 6 The soilmoisture represents dielectric parameter of soil It is obviousthat the influence of119898V on 120590 is small and obscure When thefrequency is less than 09GHz (119891 lt 09GHz) all the curvesin Figure 6 are coincident However it can be found that with119898V increases 120590 slightly become greater when the frequency islarger than 09GHz (119891 gt 09GHz)

Figure 7 depicts the distribution of 120590 with 119891 for differentbreadth of column 119886119887 (119886119887 = 20 cm 60 cm 100 cm and160 cm) It is found that the influence of 119886119887 on 120590 is obviousthat is with the increase of 119886119887 the number of rectangularcross-section columns decreases And the oscillation for the

cml = 10

l = 40 cml = 100 cm

minus75

minus60

minus45

minus30

minus15

0

15

(d

B)

05 10 15 20 25 3000

f (GHz)

Figure 5 The influence of 119897 on 120590

minus60

minus45

minus30

minus15

0

15

(dB)

05 10 15 20 25 3000

f (GHz)

m = 01

m = 02

m = 04

Figure 6 The influence of119898V on 120590

amplitude of curve becomes smaller the oscillation for thefrequency of curve becomes greater

Figure 8 depicts the distribution of 120590 with 119891 for differentlength of column 119887119888 (119887119888 = 30 cm 70 cm and 100 cm) It isfound that the influence of 119887119888 on 120590 is complex and obviousthat is at most of the frequency points the larger 119887119888 is thesmaller 120590 is the smaller the peak value of 120590 Moreover as 119891increases the oscillating amplitude of the curve is smaller

Figure 9 depicts the distribution of 120590 with 119891 for differentseparation distance of every two adjacent columns 119889119889 (119889119889 =30 cm 50 cm and 100 cm) It is found that the influence of119889119889 on 120590 is obvious At most of the frequency points withthe increase of 119889119889 the number of rectangular cross-sectioncolumns decreases in the calculated area the oscillatingfrequency of curve is greater and 120590 is larger for the samefrequency point

6 International Journal of Antennas and Propagation

ab = 20 cm ab = 60 cm

ab = 100 cm ab = 160 cm

minus60

minus45

minus30

minus15

0

15

(d

B)

minus60

minus45

minus30

minus15

0

15

(d

B)

05 10 15 20 2500 30

f (GHz)05 10 15 20 2500 30

f (GHz)

minus60

minus45

minus30

minus15

0

15

(d

B)

minus60

minus45

minus30

minus15

0

15

(d

B)

05 10 15 20 2500 30

f (GHz)05 10 15 20 2500 30

f (GHz)

Figure 7 The influence of 119886119887 on 120590

bc = 30 cmbc = 70 cmbc = 100 cm

minus60

minus45

minus30

minus15

0

15

(d

B)

05 10 15 20 2500 30

f (GHz)

Figure 8 The influence of 119887119888 on 120590Figure 10 depicts the distribution of 120590with 119891 for different

burial depth ℎ (ℎ = 5 cm 15 cm and 25 cm) It is obvious

that the influence of ℎ on 120590 is small and obscure Part of thecurves are coincident However it can be found that with theincrease ofℎ120590 becomes greaterwhen frequency is larger than173GHz (119891 gt 173GHz)

Figure 11 shows the relationship of 120590 with 119891 for different120593 (120593 = 10∘ 30∘ and 60∘) when ℎ = 15 cm Obviously theinfluence of 120593 on 120590 is complex When frequency is less than109GHz (119891 lt 109GHz) the bigger 120593 is the smaller 120590 is Iffrequency satisfies the inequality (109GHz lt 119891 lt 25GHz)120590 of 120593 = 30∘ is smaller than others

Hereinbefore the results from Figures 3ndash11 in the caseof TM polarization are obtained by plentiful calculation onthe condition that other parameters are stationary Only onepoint is worth illustrating that is the influence of someparameters on the back composite scattering coefficient isrestricted by other parameters

4 Conclusion

In this paper the problems of composite wideband electro-magnetic scattering from exponential correlation rough soilsurface with partially buried periodic distributed rectangularcross-section columns underGaussian pulse wave irradiation

International Journal of Antennas and Propagation 7

dd = 30 cmdd = 50 cmdd = 100 cm

05 10 15 20 2500 30

f (GHz)

minus60

minus45

minus30

minus15

0

15

(d

B)

Figure 9 The influence of 119889119889 on 120590

ℎ = 5 cmℎ = 15 cmℎ = 25 cm

05 10 15 20 2500 30

f (GHz)

(d

B)

minus60

minus80

minus40

minus20

0

20

Figure 10 The influence of ℎ on 120590are investigated using transient FDTD The influence of theroot-mean-square and the correlation length of rough surfacefluctuation soil moisture the length and the width of therectangular cross-section column separation distance burialdepth and tilt angle on the composite scattering signaturesare discussed in detail The numerical simulations indicatethat the variation of composite scattering coefficient versusfrequency is oscillatory It is also showed that the compositescattering coefficient versus frequency increases with theincrease of root-mean-square of soil surface water ratio ofsoil the target section height and the separation distance oftarget However simulation results indicate that the compos-ite scattering coefficient versus frequency decreases with theincrease of target section width In summary the variationof wideband scattering coefficient is very complicated andis very sensitive to incidence angle of electromagnetic waveHowever the wideband scattering coefficient under Gaussian

= 10∘

= 30∘

= 60∘

05 10 15 20 2500 30

f (GHz)

minus60

minus80

minus40

minus20

0

20

(d

B)

Figure 11 The influence of 120593 on 120590

pulse wave incidence is less sensitive to the correlation lengthof rough soil surface the depth of buried objects and thedielectric constant of target Although the multiple columnspartially buried in a randomly rough surface are a rathersimplified model the present study is potentially valuable formany applications such as ground remote sensing groundpenetrating radar applications undergroundmine detectiontunnel detection and target identification In particular thesimplified model of periodically distributed columns repre-sents many realistic objects such as tree trunks mine propstelegraph poles The future investigation on this topic willinclude electromagnetic scattering from two-dimensionalrough land surface with complex multiple targets

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported in part by the National NaturalScience Foundation of China (Grant no 61379026) in partby the National Science Foundation for Young Scientists ofChina (Grant no 61701428) in part by the foundation of con-struction of high-level university project in Shaanxi Province(Grant no 2015SXTS02) in part by the open foundation ofFudan University Key Laboratory for Information Scienceof Electromagnetic Waves (Grant no EMW201502) in partby the Scientific Research Foundation of Yanan University(Grant nos YDBK2016-17 and YDY2017-06) and in part bythe Natural Science Basic Research Plan in Shaanxi Provinceof China (Grant no 2014JM-6113)

References

[1] M A Nasr I A Eshrah and E A Hashish ldquoElectromagneticscattering from a buried cylinder using a multiple reflection

8 International Journal of Antennas and Propagation

approach TM caserdquo IEEE Transactions on Antennas and Prop-agation vol 62 no 5 pp 2702ndash2707 2014

[2] S Bellez C Bourlier and G Kubicke ldquo3-D scattering froma PEC target buried beneath a dielectric rough surface anefficient PILE-ACA algorithm for solving a hybrid KA-EFIEformulationrdquo Institute of Electrical and Electronics EngineersTransactions on Antennas and Propagation vol 63 no 11 pp5003ndash5014 2015

[3] W Yang and C Qi ldquoA Bi-Iteration Model for ElectromagneticScattering from a 3D Object above a 2D Rough SurfacerdquoElectromagnetics vol 35 no 3 pp 190ndash204 2015

[4] E Rashidi-Ranjbar and M Dehmollaian ldquoTarget Above Ran-dom Rough Surface Scattering Using a Parallelized IPO Accel-erated by MLFMMrdquo IEEE Geoscience and Remote SensingLetters vol 12 no 7 pp 1481ndash1485 2015

[5] R W Xu L X Guo H J He andW Liu ldquoA hybrid FEMMoMtechnique for 3-D electromagnetic scattering from a dielectricobject above a conductive rough surfacerdquo IEEE Geoscience ampRemote Sensing Letters vol 13 pp 314ndash318 2016

[6] X M Zhu X C Ren and L X Guo ldquoStudy on wide-bandscattering from rectangular cross-section above rough landsurface with exponential type distribution using FDTDrdquo ActaPhysica Sinica vol 63 2014

[7] A Chehri P Fortier and P M Tardif ldquoCharacterization ofthe ultra-wideband channel in confined environments withdiffracting rough surfacesrdquoWireless Personal Communicationsvol 62 no 4 pp 859ndash877 2012

[8] M Khemiri and I Sassi ldquoRegions of validity of geometric opticsandKirchhoff approximations for reflection fromGaussian ran-dom rough dielectric surfacesrdquo Waves in random and complexmedia propagation scattering and imaging vol 25 no 4 pp656ndash668 2015

[9] S Afifi R Dusseaux and A Berrouk ldquoElectromagnetic scatter-ing from 3D layered structures with randomly rough interfacesAnalysis with the small perturbation method and the smallslope approximationrdquo IEEE Transactions on Antennas andPropagation vol 62 no 10 pp 5200ndash5208 2014

[10] A Berrouk R Dusseaux and S Affif ldquoElectromagnetic wavescattering from rough layered interfaces Analysis with thesmall perturbationmethod and the small slope approximationrdquoProgress in Electromagnetics Research B no 57 pp 177ndash190 2014

[11] G Apaydin F Hacivelioglu L Sevgi and P Y UfimtsevldquoWedge diffracted waves excited by a line source Method ofMoments (MoM)modeling of fringe wavesrdquo IEEE Transactionson Antennas Propagation vol 62 pp 4368ndash4371 2014

[12] R Xiong B Chen J Han Y Qiu W Yang and Q NingldquoTransient resistance analysis of large grounding systems usingthe FDTD methodrdquo Progress in Electromagnetics Research vol132 pp 159ndash175 2012

[13] O Ozgun andM Kuzuoglu ldquoMonte Carlo-based characteristicbasis finite-element method (MC-CBFEM) for numerical anal-ysis of scattering from objects onabove rough sea surfacesrdquoIEEE Transactions on Geoscience and Remote Sensing vol 50no 3 pp 769ndash783 2012

[14] R Tao Y Li X Bai and A Waheed ldquoFractional weierstrassmodel for rough ocean surface and analytical derivation ofits scattered field in a closed formrdquo IEEE Transactions onGeoscience and Remote Sensing vol 50 no 10 pp 3627ndash36392012

[15] J Li L-X Guo S-R Chai and Y-C Jiao ldquoElectromagneticscattering from a PEC object above a dielectric rough sea

surface by a hybrid POndashPO methodrdquo Waves in Random andComplex Media vol 25 no 1 pp 60ndash74 2015

[16] C G Jia L X Guo and P J Yang ldquoEM scattering from atarget above a 1-D randomly rough sea surface using GPU-based parallel FDTDrdquo IEEE Antennas and Wireless PropagationLetters vol 14 pp 217ndash220 2015

[17] Y Liang L X Guo Z S Wu and Q H Liu ldquoA Study ofComposite Electromagnetic Scattering from an Object Near aRough Sea Surface Using an Efficient Numerical AlgorithmrdquoIEEEAntennas andWireless Propagation Letters vol 15 pp 186ndash190 2016

[18] T Wei X C Ren and L X Guo ldquoStudy on compositeelectromagnetic scattering from the double rectangular cross-section columns above rough sea surface using hybridmethodrdquoActa Physica Sinica vol 64 2015

[19] L-X Guo andR-WXu ldquoAn efficientmultiregion FEM-BIM forcomposite scattering from an arbitrary dielectric target abovedielectric rough sea surfacesrdquo IEEE Transactions on Geoscienceand Remote Sensing vol 53 no 7 pp 3885ndash3896 2015

[20] P-J Yang and L-X Guo ldquoPolarimetric scattering from two-dimensional dielectric rough sea surface with a ship-inducedKelvin wakerdquo International Journal of Antennas and Propaga-tion vol 2016 Article ID 2474708 2016

[21] X C Ren L X Guo and Y C Jiao ldquoInvestigation of elec-tromagnetic scattering interaction between the column withrectangular cross-section and rough land surface covered withsnow using finite difference time domainmethodrdquoActa PhysicaSinica vol 61 article 144101 p 379 2012

[22] R Wang L X Guo and A Q Wang ldquoInvestigation of electro-magnetic scattering interaction between the buried target andthe rough surface in different types of soilrdquo Acta Phys Sin vol59 pp 3179ndash3186 2010

[23] T Meissner and F J Wentz ldquoThe complex dielectric constantof pure and sea water from microwave satellite observationsrdquoIEEE Transactions on Geoscience and Remote Sensing vol 42no 9 pp 1836ndash1849 2004

[24] D Lyzenga ldquoNumerical simulation of synthetic aperture radarimage spectra for ocean wavesrdquo IEEE Transactions on Geo-science and Remote Sensing vol GE-24 no 6 pp 863ndash872 1986

[25] R A Dalrymple and B D Rogers ldquoNumerical modeling ofwaterwaveswith the SPHmethodrdquoCoastal Engineering Journalvol 53 no 2-3 pp 141ndash147 2006

[26] C Br UNingWAlpers andKHasselmann ldquoMonte-carlo sim-ulation studies of the nonlinear imaging of a two dimensionalsurface wave field by a synthetic aperture radarrdquo InternationalJournal of Remote Sensing vol 11 no 10 pp 1695ndash1727 1990

[27] J R Wang and T J Schmugge ldquoAn empirical model for thecomplex dielectric permittivity of soils as a function of watercontentrdquo IEEE Transactions on Geoscience and Remote Sensingvol 18 no 4 pp 288ndash295 1980

[28] L Tsang J A Kong and K H Ding Scattering of Elec-tromagnetic Waves Theories and Applications vol 1 Wiley-Interscience New York NY USA 1 edition 2000

[29] L Sevgi Electromagnetic Modeling and Simulation John Wileyamp Sons Inc Hoboken NJ USA 2014

[30] A Taflove and S C Hagness Computational ElectrodynamicsThe Finite-Difference Time-Domian Method Artech HouseBoston Mass USA 3rd edition 2005

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

6 International Journal of Antennas and Propagation

ab = 20 cm ab = 60 cm

ab = 100 cm ab = 160 cm

minus60

minus45

minus30

minus15

0

15

(d

B)

minus60

minus45

minus30

minus15

0

15

(d

B)

05 10 15 20 2500 30

f (GHz)05 10 15 20 2500 30

f (GHz)

minus60

minus45

minus30

minus15

0

15

(d

B)

minus60

minus45

minus30

minus15

0

15

(d

B)

05 10 15 20 2500 30

f (GHz)05 10 15 20 2500 30

f (GHz)

Figure 7 The influence of 119886119887 on 120590

bc = 30 cmbc = 70 cmbc = 100 cm

minus60

minus45

minus30

minus15

0

15

(d

B)

05 10 15 20 2500 30

f (GHz)

Figure 8 The influence of 119887119888 on 120590Figure 10 depicts the distribution of 120590with 119891 for different

burial depth ℎ (ℎ = 5 cm 15 cm and 25 cm) It is obvious

that the influence of ℎ on 120590 is small and obscure Part of thecurves are coincident However it can be found that with theincrease ofℎ120590 becomes greaterwhen frequency is larger than173GHz (119891 gt 173GHz)

Figure 11 shows the relationship of 120590 with 119891 for different120593 (120593 = 10∘ 30∘ and 60∘) when ℎ = 15 cm Obviously theinfluence of 120593 on 120590 is complex When frequency is less than109GHz (119891 lt 109GHz) the bigger 120593 is the smaller 120590 is Iffrequency satisfies the inequality (109GHz lt 119891 lt 25GHz)120590 of 120593 = 30∘ is smaller than others

Hereinbefore the results from Figures 3ndash11 in the caseof TM polarization are obtained by plentiful calculation onthe condition that other parameters are stationary Only onepoint is worth illustrating that is the influence of someparameters on the back composite scattering coefficient isrestricted by other parameters

4 Conclusion

In this paper the problems of composite wideband electro-magnetic scattering from exponential correlation rough soilsurface with partially buried periodic distributed rectangularcross-section columns underGaussian pulse wave irradiation

International Journal of Antennas and Propagation 7

dd = 30 cmdd = 50 cmdd = 100 cm

05 10 15 20 2500 30

f (GHz)

minus60

minus45

minus30

minus15

0

15

(d

B)

Figure 9 The influence of 119889119889 on 120590

ℎ = 5 cmℎ = 15 cmℎ = 25 cm

05 10 15 20 2500 30

f (GHz)

(d

B)

minus60

minus80

minus40

minus20

0

20

Figure 10 The influence of ℎ on 120590are investigated using transient FDTD The influence of theroot-mean-square and the correlation length of rough surfacefluctuation soil moisture the length and the width of therectangular cross-section column separation distance burialdepth and tilt angle on the composite scattering signaturesare discussed in detail The numerical simulations indicatethat the variation of composite scattering coefficient versusfrequency is oscillatory It is also showed that the compositescattering coefficient versus frequency increases with theincrease of root-mean-square of soil surface water ratio ofsoil the target section height and the separation distance oftarget However simulation results indicate that the compos-ite scattering coefficient versus frequency decreases with theincrease of target section width In summary the variationof wideband scattering coefficient is very complicated andis very sensitive to incidence angle of electromagnetic waveHowever the wideband scattering coefficient under Gaussian

= 10∘

= 30∘

= 60∘

05 10 15 20 2500 30

f (GHz)

minus60

minus80

minus40

minus20

0

20

(d

B)

Figure 11 The influence of 120593 on 120590

pulse wave incidence is less sensitive to the correlation lengthof rough soil surface the depth of buried objects and thedielectric constant of target Although the multiple columnspartially buried in a randomly rough surface are a rathersimplified model the present study is potentially valuable formany applications such as ground remote sensing groundpenetrating radar applications undergroundmine detectiontunnel detection and target identification In particular thesimplified model of periodically distributed columns repre-sents many realistic objects such as tree trunks mine propstelegraph poles The future investigation on this topic willinclude electromagnetic scattering from two-dimensionalrough land surface with complex multiple targets

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported in part by the National NaturalScience Foundation of China (Grant no 61379026) in partby the National Science Foundation for Young Scientists ofChina (Grant no 61701428) in part by the foundation of con-struction of high-level university project in Shaanxi Province(Grant no 2015SXTS02) in part by the open foundation ofFudan University Key Laboratory for Information Scienceof Electromagnetic Waves (Grant no EMW201502) in partby the Scientific Research Foundation of Yanan University(Grant nos YDBK2016-17 and YDY2017-06) and in part bythe Natural Science Basic Research Plan in Shaanxi Provinceof China (Grant no 2014JM-6113)

References

[1] M A Nasr I A Eshrah and E A Hashish ldquoElectromagneticscattering from a buried cylinder using a multiple reflection

8 International Journal of Antennas and Propagation

approach TM caserdquo IEEE Transactions on Antennas and Prop-agation vol 62 no 5 pp 2702ndash2707 2014

[2] S Bellez C Bourlier and G Kubicke ldquo3-D scattering froma PEC target buried beneath a dielectric rough surface anefficient PILE-ACA algorithm for solving a hybrid KA-EFIEformulationrdquo Institute of Electrical and Electronics EngineersTransactions on Antennas and Propagation vol 63 no 11 pp5003ndash5014 2015

[3] W Yang and C Qi ldquoA Bi-Iteration Model for ElectromagneticScattering from a 3D Object above a 2D Rough SurfacerdquoElectromagnetics vol 35 no 3 pp 190ndash204 2015

[4] E Rashidi-Ranjbar and M Dehmollaian ldquoTarget Above Ran-dom Rough Surface Scattering Using a Parallelized IPO Accel-erated by MLFMMrdquo IEEE Geoscience and Remote SensingLetters vol 12 no 7 pp 1481ndash1485 2015

[5] R W Xu L X Guo H J He andW Liu ldquoA hybrid FEMMoMtechnique for 3-D electromagnetic scattering from a dielectricobject above a conductive rough surfacerdquo IEEE Geoscience ampRemote Sensing Letters vol 13 pp 314ndash318 2016

[6] X M Zhu X C Ren and L X Guo ldquoStudy on wide-bandscattering from rectangular cross-section above rough landsurface with exponential type distribution using FDTDrdquo ActaPhysica Sinica vol 63 2014

[7] A Chehri P Fortier and P M Tardif ldquoCharacterization ofthe ultra-wideband channel in confined environments withdiffracting rough surfacesrdquoWireless Personal Communicationsvol 62 no 4 pp 859ndash877 2012

[8] M Khemiri and I Sassi ldquoRegions of validity of geometric opticsandKirchhoff approximations for reflection fromGaussian ran-dom rough dielectric surfacesrdquo Waves in random and complexmedia propagation scattering and imaging vol 25 no 4 pp656ndash668 2015

[9] S Afifi R Dusseaux and A Berrouk ldquoElectromagnetic scatter-ing from 3D layered structures with randomly rough interfacesAnalysis with the small perturbation method and the smallslope approximationrdquo IEEE Transactions on Antennas andPropagation vol 62 no 10 pp 5200ndash5208 2014

[10] A Berrouk R Dusseaux and S Affif ldquoElectromagnetic wavescattering from rough layered interfaces Analysis with thesmall perturbationmethod and the small slope approximationrdquoProgress in Electromagnetics Research B no 57 pp 177ndash190 2014

[11] G Apaydin F Hacivelioglu L Sevgi and P Y UfimtsevldquoWedge diffracted waves excited by a line source Method ofMoments (MoM)modeling of fringe wavesrdquo IEEE Transactionson Antennas Propagation vol 62 pp 4368ndash4371 2014

[12] R Xiong B Chen J Han Y Qiu W Yang and Q NingldquoTransient resistance analysis of large grounding systems usingthe FDTD methodrdquo Progress in Electromagnetics Research vol132 pp 159ndash175 2012

[13] O Ozgun andM Kuzuoglu ldquoMonte Carlo-based characteristicbasis finite-element method (MC-CBFEM) for numerical anal-ysis of scattering from objects onabove rough sea surfacesrdquoIEEE Transactions on Geoscience and Remote Sensing vol 50no 3 pp 769ndash783 2012

[14] R Tao Y Li X Bai and A Waheed ldquoFractional weierstrassmodel for rough ocean surface and analytical derivation ofits scattered field in a closed formrdquo IEEE Transactions onGeoscience and Remote Sensing vol 50 no 10 pp 3627ndash36392012

[15] J Li L-X Guo S-R Chai and Y-C Jiao ldquoElectromagneticscattering from a PEC object above a dielectric rough sea

surface by a hybrid POndashPO methodrdquo Waves in Random andComplex Media vol 25 no 1 pp 60ndash74 2015

[16] C G Jia L X Guo and P J Yang ldquoEM scattering from atarget above a 1-D randomly rough sea surface using GPU-based parallel FDTDrdquo IEEE Antennas and Wireless PropagationLetters vol 14 pp 217ndash220 2015

[17] Y Liang L X Guo Z S Wu and Q H Liu ldquoA Study ofComposite Electromagnetic Scattering from an Object Near aRough Sea Surface Using an Efficient Numerical AlgorithmrdquoIEEEAntennas andWireless Propagation Letters vol 15 pp 186ndash190 2016

[18] T Wei X C Ren and L X Guo ldquoStudy on compositeelectromagnetic scattering from the double rectangular cross-section columns above rough sea surface using hybridmethodrdquoActa Physica Sinica vol 64 2015

[19] L-X Guo andR-WXu ldquoAn efficientmultiregion FEM-BIM forcomposite scattering from an arbitrary dielectric target abovedielectric rough sea surfacesrdquo IEEE Transactions on Geoscienceand Remote Sensing vol 53 no 7 pp 3885ndash3896 2015

[20] P-J Yang and L-X Guo ldquoPolarimetric scattering from two-dimensional dielectric rough sea surface with a ship-inducedKelvin wakerdquo International Journal of Antennas and Propaga-tion vol 2016 Article ID 2474708 2016

[21] X C Ren L X Guo and Y C Jiao ldquoInvestigation of elec-tromagnetic scattering interaction between the column withrectangular cross-section and rough land surface covered withsnow using finite difference time domainmethodrdquoActa PhysicaSinica vol 61 article 144101 p 379 2012

[22] R Wang L X Guo and A Q Wang ldquoInvestigation of electro-magnetic scattering interaction between the buried target andthe rough surface in different types of soilrdquo Acta Phys Sin vol59 pp 3179ndash3186 2010

[23] T Meissner and F J Wentz ldquoThe complex dielectric constantof pure and sea water from microwave satellite observationsrdquoIEEE Transactions on Geoscience and Remote Sensing vol 42no 9 pp 1836ndash1849 2004

[24] D Lyzenga ldquoNumerical simulation of synthetic aperture radarimage spectra for ocean wavesrdquo IEEE Transactions on Geo-science and Remote Sensing vol GE-24 no 6 pp 863ndash872 1986

[25] R A Dalrymple and B D Rogers ldquoNumerical modeling ofwaterwaveswith the SPHmethodrdquoCoastal Engineering Journalvol 53 no 2-3 pp 141ndash147 2006

[26] C Br UNingWAlpers andKHasselmann ldquoMonte-carlo sim-ulation studies of the nonlinear imaging of a two dimensionalsurface wave field by a synthetic aperture radarrdquo InternationalJournal of Remote Sensing vol 11 no 10 pp 1695ndash1727 1990

[27] J R Wang and T J Schmugge ldquoAn empirical model for thecomplex dielectric permittivity of soils as a function of watercontentrdquo IEEE Transactions on Geoscience and Remote Sensingvol 18 no 4 pp 288ndash295 1980

[28] L Tsang J A Kong and K H Ding Scattering of Elec-tromagnetic Waves Theories and Applications vol 1 Wiley-Interscience New York NY USA 1 edition 2000

[29] L Sevgi Electromagnetic Modeling and Simulation John Wileyamp Sons Inc Hoboken NJ USA 2014

[30] A Taflove and S C Hagness Computational ElectrodynamicsThe Finite-Difference Time-Domian Method Artech HouseBoston Mass USA 3rd edition 2005

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of Antennas and Propagation 7

dd = 30 cmdd = 50 cmdd = 100 cm

05 10 15 20 2500 30

f (GHz)

minus60

minus45

minus30

minus15

0

15

(d

B)

Figure 9 The influence of 119889119889 on 120590

ℎ = 5 cmℎ = 15 cmℎ = 25 cm

05 10 15 20 2500 30

f (GHz)

(d

B)

minus60

minus80

minus40

minus20

0

20

Figure 10 The influence of ℎ on 120590are investigated using transient FDTD The influence of theroot-mean-square and the correlation length of rough surfacefluctuation soil moisture the length and the width of therectangular cross-section column separation distance burialdepth and tilt angle on the composite scattering signaturesare discussed in detail The numerical simulations indicatethat the variation of composite scattering coefficient versusfrequency is oscillatory It is also showed that the compositescattering coefficient versus frequency increases with theincrease of root-mean-square of soil surface water ratio ofsoil the target section height and the separation distance oftarget However simulation results indicate that the compos-ite scattering coefficient versus frequency decreases with theincrease of target section width In summary the variationof wideband scattering coefficient is very complicated andis very sensitive to incidence angle of electromagnetic waveHowever the wideband scattering coefficient under Gaussian

= 10∘

= 30∘

= 60∘

05 10 15 20 2500 30

f (GHz)

minus60

minus80

minus40

minus20

0

20

(d

B)

Figure 11 The influence of 120593 on 120590

pulse wave incidence is less sensitive to the correlation lengthof rough soil surface the depth of buried objects and thedielectric constant of target Although the multiple columnspartially buried in a randomly rough surface are a rathersimplified model the present study is potentially valuable formany applications such as ground remote sensing groundpenetrating radar applications undergroundmine detectiontunnel detection and target identification In particular thesimplified model of periodically distributed columns repre-sents many realistic objects such as tree trunks mine propstelegraph poles The future investigation on this topic willinclude electromagnetic scattering from two-dimensionalrough land surface with complex multiple targets

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported in part by the National NaturalScience Foundation of China (Grant no 61379026) in partby the National Science Foundation for Young Scientists ofChina (Grant no 61701428) in part by the foundation of con-struction of high-level university project in Shaanxi Province(Grant no 2015SXTS02) in part by the open foundation ofFudan University Key Laboratory for Information Scienceof Electromagnetic Waves (Grant no EMW201502) in partby the Scientific Research Foundation of Yanan University(Grant nos YDBK2016-17 and YDY2017-06) and in part bythe Natural Science Basic Research Plan in Shaanxi Provinceof China (Grant no 2014JM-6113)

References

[1] M A Nasr I A Eshrah and E A Hashish ldquoElectromagneticscattering from a buried cylinder using a multiple reflection

8 International Journal of Antennas and Propagation

approach TM caserdquo IEEE Transactions on Antennas and Prop-agation vol 62 no 5 pp 2702ndash2707 2014

[2] S Bellez C Bourlier and G Kubicke ldquo3-D scattering froma PEC target buried beneath a dielectric rough surface anefficient PILE-ACA algorithm for solving a hybrid KA-EFIEformulationrdquo Institute of Electrical and Electronics EngineersTransactions on Antennas and Propagation vol 63 no 11 pp5003ndash5014 2015

[3] W Yang and C Qi ldquoA Bi-Iteration Model for ElectromagneticScattering from a 3D Object above a 2D Rough SurfacerdquoElectromagnetics vol 35 no 3 pp 190ndash204 2015

[4] E Rashidi-Ranjbar and M Dehmollaian ldquoTarget Above Ran-dom Rough Surface Scattering Using a Parallelized IPO Accel-erated by MLFMMrdquo IEEE Geoscience and Remote SensingLetters vol 12 no 7 pp 1481ndash1485 2015

[5] R W Xu L X Guo H J He andW Liu ldquoA hybrid FEMMoMtechnique for 3-D electromagnetic scattering from a dielectricobject above a conductive rough surfacerdquo IEEE Geoscience ampRemote Sensing Letters vol 13 pp 314ndash318 2016

[6] X M Zhu X C Ren and L X Guo ldquoStudy on wide-bandscattering from rectangular cross-section above rough landsurface with exponential type distribution using FDTDrdquo ActaPhysica Sinica vol 63 2014

[7] A Chehri P Fortier and P M Tardif ldquoCharacterization ofthe ultra-wideband channel in confined environments withdiffracting rough surfacesrdquoWireless Personal Communicationsvol 62 no 4 pp 859ndash877 2012

[8] M Khemiri and I Sassi ldquoRegions of validity of geometric opticsandKirchhoff approximations for reflection fromGaussian ran-dom rough dielectric surfacesrdquo Waves in random and complexmedia propagation scattering and imaging vol 25 no 4 pp656ndash668 2015

[9] S Afifi R Dusseaux and A Berrouk ldquoElectromagnetic scatter-ing from 3D layered structures with randomly rough interfacesAnalysis with the small perturbation method and the smallslope approximationrdquo IEEE Transactions on Antennas andPropagation vol 62 no 10 pp 5200ndash5208 2014

[10] A Berrouk R Dusseaux and S Affif ldquoElectromagnetic wavescattering from rough layered interfaces Analysis with thesmall perturbationmethod and the small slope approximationrdquoProgress in Electromagnetics Research B no 57 pp 177ndash190 2014

[11] G Apaydin F Hacivelioglu L Sevgi and P Y UfimtsevldquoWedge diffracted waves excited by a line source Method ofMoments (MoM)modeling of fringe wavesrdquo IEEE Transactionson Antennas Propagation vol 62 pp 4368ndash4371 2014

[12] R Xiong B Chen J Han Y Qiu W Yang and Q NingldquoTransient resistance analysis of large grounding systems usingthe FDTD methodrdquo Progress in Electromagnetics Research vol132 pp 159ndash175 2012

[13] O Ozgun andM Kuzuoglu ldquoMonte Carlo-based characteristicbasis finite-element method (MC-CBFEM) for numerical anal-ysis of scattering from objects onabove rough sea surfacesrdquoIEEE Transactions on Geoscience and Remote Sensing vol 50no 3 pp 769ndash783 2012

[14] R Tao Y Li X Bai and A Waheed ldquoFractional weierstrassmodel for rough ocean surface and analytical derivation ofits scattered field in a closed formrdquo IEEE Transactions onGeoscience and Remote Sensing vol 50 no 10 pp 3627ndash36392012

[15] J Li L-X Guo S-R Chai and Y-C Jiao ldquoElectromagneticscattering from a PEC object above a dielectric rough sea

surface by a hybrid POndashPO methodrdquo Waves in Random andComplex Media vol 25 no 1 pp 60ndash74 2015

[16] C G Jia L X Guo and P J Yang ldquoEM scattering from atarget above a 1-D randomly rough sea surface using GPU-based parallel FDTDrdquo IEEE Antennas and Wireless PropagationLetters vol 14 pp 217ndash220 2015

[17] Y Liang L X Guo Z S Wu and Q H Liu ldquoA Study ofComposite Electromagnetic Scattering from an Object Near aRough Sea Surface Using an Efficient Numerical AlgorithmrdquoIEEEAntennas andWireless Propagation Letters vol 15 pp 186ndash190 2016

[18] T Wei X C Ren and L X Guo ldquoStudy on compositeelectromagnetic scattering from the double rectangular cross-section columns above rough sea surface using hybridmethodrdquoActa Physica Sinica vol 64 2015

[19] L-X Guo andR-WXu ldquoAn efficientmultiregion FEM-BIM forcomposite scattering from an arbitrary dielectric target abovedielectric rough sea surfacesrdquo IEEE Transactions on Geoscienceand Remote Sensing vol 53 no 7 pp 3885ndash3896 2015

[20] P-J Yang and L-X Guo ldquoPolarimetric scattering from two-dimensional dielectric rough sea surface with a ship-inducedKelvin wakerdquo International Journal of Antennas and Propaga-tion vol 2016 Article ID 2474708 2016

[21] X C Ren L X Guo and Y C Jiao ldquoInvestigation of elec-tromagnetic scattering interaction between the column withrectangular cross-section and rough land surface covered withsnow using finite difference time domainmethodrdquoActa PhysicaSinica vol 61 article 144101 p 379 2012

[22] R Wang L X Guo and A Q Wang ldquoInvestigation of electro-magnetic scattering interaction between the buried target andthe rough surface in different types of soilrdquo Acta Phys Sin vol59 pp 3179ndash3186 2010

[23] T Meissner and F J Wentz ldquoThe complex dielectric constantof pure and sea water from microwave satellite observationsrdquoIEEE Transactions on Geoscience and Remote Sensing vol 42no 9 pp 1836ndash1849 2004

[24] D Lyzenga ldquoNumerical simulation of synthetic aperture radarimage spectra for ocean wavesrdquo IEEE Transactions on Geo-science and Remote Sensing vol GE-24 no 6 pp 863ndash872 1986

[25] R A Dalrymple and B D Rogers ldquoNumerical modeling ofwaterwaveswith the SPHmethodrdquoCoastal Engineering Journalvol 53 no 2-3 pp 141ndash147 2006

[26] C Br UNingWAlpers andKHasselmann ldquoMonte-carlo sim-ulation studies of the nonlinear imaging of a two dimensionalsurface wave field by a synthetic aperture radarrdquo InternationalJournal of Remote Sensing vol 11 no 10 pp 1695ndash1727 1990

[27] J R Wang and T J Schmugge ldquoAn empirical model for thecomplex dielectric permittivity of soils as a function of watercontentrdquo IEEE Transactions on Geoscience and Remote Sensingvol 18 no 4 pp 288ndash295 1980

[28] L Tsang J A Kong and K H Ding Scattering of Elec-tromagnetic Waves Theories and Applications vol 1 Wiley-Interscience New York NY USA 1 edition 2000

[29] L Sevgi Electromagnetic Modeling and Simulation John Wileyamp Sons Inc Hoboken NJ USA 2014

[30] A Taflove and S C Hagness Computational ElectrodynamicsThe Finite-Difference Time-Domian Method Artech HouseBoston Mass USA 3rd edition 2005

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

8 International Journal of Antennas and Propagation

approach TM caserdquo IEEE Transactions on Antennas and Prop-agation vol 62 no 5 pp 2702ndash2707 2014

[2] S Bellez C Bourlier and G Kubicke ldquo3-D scattering froma PEC target buried beneath a dielectric rough surface anefficient PILE-ACA algorithm for solving a hybrid KA-EFIEformulationrdquo Institute of Electrical and Electronics EngineersTransactions on Antennas and Propagation vol 63 no 11 pp5003ndash5014 2015

[3] W Yang and C Qi ldquoA Bi-Iteration Model for ElectromagneticScattering from a 3D Object above a 2D Rough SurfacerdquoElectromagnetics vol 35 no 3 pp 190ndash204 2015

[4] E Rashidi-Ranjbar and M Dehmollaian ldquoTarget Above Ran-dom Rough Surface Scattering Using a Parallelized IPO Accel-erated by MLFMMrdquo IEEE Geoscience and Remote SensingLetters vol 12 no 7 pp 1481ndash1485 2015

[5] R W Xu L X Guo H J He andW Liu ldquoA hybrid FEMMoMtechnique for 3-D electromagnetic scattering from a dielectricobject above a conductive rough surfacerdquo IEEE Geoscience ampRemote Sensing Letters vol 13 pp 314ndash318 2016

[6] X M Zhu X C Ren and L X Guo ldquoStudy on wide-bandscattering from rectangular cross-section above rough landsurface with exponential type distribution using FDTDrdquo ActaPhysica Sinica vol 63 2014

[7] A Chehri P Fortier and P M Tardif ldquoCharacterization ofthe ultra-wideband channel in confined environments withdiffracting rough surfacesrdquoWireless Personal Communicationsvol 62 no 4 pp 859ndash877 2012

[8] M Khemiri and I Sassi ldquoRegions of validity of geometric opticsandKirchhoff approximations for reflection fromGaussian ran-dom rough dielectric surfacesrdquo Waves in random and complexmedia propagation scattering and imaging vol 25 no 4 pp656ndash668 2015

[9] S Afifi R Dusseaux and A Berrouk ldquoElectromagnetic scatter-ing from 3D layered structures with randomly rough interfacesAnalysis with the small perturbation method and the smallslope approximationrdquo IEEE Transactions on Antennas andPropagation vol 62 no 10 pp 5200ndash5208 2014

[10] A Berrouk R Dusseaux and S Affif ldquoElectromagnetic wavescattering from rough layered interfaces Analysis with thesmall perturbationmethod and the small slope approximationrdquoProgress in Electromagnetics Research B no 57 pp 177ndash190 2014

[11] G Apaydin F Hacivelioglu L Sevgi and P Y UfimtsevldquoWedge diffracted waves excited by a line source Method ofMoments (MoM)modeling of fringe wavesrdquo IEEE Transactionson Antennas Propagation vol 62 pp 4368ndash4371 2014

[12] R Xiong B Chen J Han Y Qiu W Yang and Q NingldquoTransient resistance analysis of large grounding systems usingthe FDTD methodrdquo Progress in Electromagnetics Research vol132 pp 159ndash175 2012

[13] O Ozgun andM Kuzuoglu ldquoMonte Carlo-based characteristicbasis finite-element method (MC-CBFEM) for numerical anal-ysis of scattering from objects onabove rough sea surfacesrdquoIEEE Transactions on Geoscience and Remote Sensing vol 50no 3 pp 769ndash783 2012

[14] R Tao Y Li X Bai and A Waheed ldquoFractional weierstrassmodel for rough ocean surface and analytical derivation ofits scattered field in a closed formrdquo IEEE Transactions onGeoscience and Remote Sensing vol 50 no 10 pp 3627ndash36392012

[15] J Li L-X Guo S-R Chai and Y-C Jiao ldquoElectromagneticscattering from a PEC object above a dielectric rough sea

surface by a hybrid POndashPO methodrdquo Waves in Random andComplex Media vol 25 no 1 pp 60ndash74 2015

[16] C G Jia L X Guo and P J Yang ldquoEM scattering from atarget above a 1-D randomly rough sea surface using GPU-based parallel FDTDrdquo IEEE Antennas and Wireless PropagationLetters vol 14 pp 217ndash220 2015

[17] Y Liang L X Guo Z S Wu and Q H Liu ldquoA Study ofComposite Electromagnetic Scattering from an Object Near aRough Sea Surface Using an Efficient Numerical AlgorithmrdquoIEEEAntennas andWireless Propagation Letters vol 15 pp 186ndash190 2016

[18] T Wei X C Ren and L X Guo ldquoStudy on compositeelectromagnetic scattering from the double rectangular cross-section columns above rough sea surface using hybridmethodrdquoActa Physica Sinica vol 64 2015

[19] L-X Guo andR-WXu ldquoAn efficientmultiregion FEM-BIM forcomposite scattering from an arbitrary dielectric target abovedielectric rough sea surfacesrdquo IEEE Transactions on Geoscienceand Remote Sensing vol 53 no 7 pp 3885ndash3896 2015

[20] P-J Yang and L-X Guo ldquoPolarimetric scattering from two-dimensional dielectric rough sea surface with a ship-inducedKelvin wakerdquo International Journal of Antennas and Propaga-tion vol 2016 Article ID 2474708 2016

[21] X C Ren L X Guo and Y C Jiao ldquoInvestigation of elec-tromagnetic scattering interaction between the column withrectangular cross-section and rough land surface covered withsnow using finite difference time domainmethodrdquoActa PhysicaSinica vol 61 article 144101 p 379 2012

[22] R Wang L X Guo and A Q Wang ldquoInvestigation of electro-magnetic scattering interaction between the buried target andthe rough surface in different types of soilrdquo Acta Phys Sin vol59 pp 3179ndash3186 2010

[23] T Meissner and F J Wentz ldquoThe complex dielectric constantof pure and sea water from microwave satellite observationsrdquoIEEE Transactions on Geoscience and Remote Sensing vol 42no 9 pp 1836ndash1849 2004

[24] D Lyzenga ldquoNumerical simulation of synthetic aperture radarimage spectra for ocean wavesrdquo IEEE Transactions on Geo-science and Remote Sensing vol GE-24 no 6 pp 863ndash872 1986

[25] R A Dalrymple and B D Rogers ldquoNumerical modeling ofwaterwaveswith the SPHmethodrdquoCoastal Engineering Journalvol 53 no 2-3 pp 141ndash147 2006

[26] C Br UNingWAlpers andKHasselmann ldquoMonte-carlo sim-ulation studies of the nonlinear imaging of a two dimensionalsurface wave field by a synthetic aperture radarrdquo InternationalJournal of Remote Sensing vol 11 no 10 pp 1695ndash1727 1990

[27] J R Wang and T J Schmugge ldquoAn empirical model for thecomplex dielectric permittivity of soils as a function of watercontentrdquo IEEE Transactions on Geoscience and Remote Sensingvol 18 no 4 pp 288ndash295 1980

[28] L Tsang J A Kong and K H Ding Scattering of Elec-tromagnetic Waves Theories and Applications vol 1 Wiley-Interscience New York NY USA 1 edition 2000

[29] L Sevgi Electromagnetic Modeling and Simulation John Wileyamp Sons Inc Hoboken NJ USA 2014

[30] A Taflove and S C Hagness Computational ElectrodynamicsThe Finite-Difference Time-Domian Method Artech HouseBoston Mass USA 3rd edition 2005

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of