effect of lateral profile on diffraction by natural obstacle

8/8/2019 Effect of Lateral Profile on Diffraction by Natural Obstacle

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Radio Science, olume 17, Number 5, pages1051-1054,September-October 982

Effect of lateral profileon diffractionby natural obstaclesMaura S. Assis

Departamento e Treinamento,EmpresaBrasileirade Telecomunicafdes20.080--Rio de JaneiroRJ, Brazil

(ReceivedAugust27, 1981' revised anuary6, 1982' accepted anuary6, 1982.)

A simpleapproximatemathematicalmodel usingFresnel-Kirchhoff iffraction heory s proposed oinvestigate he frequencydependence f propagationattenuation by natural obstacleswith lateralprofileshavinggeneralshapes.Measurements arried out in several inks in the frequency and from270 to 330 MHz haveshownvariationsof _ 10 dB. Resultsobtained rom this modelagree easonablywith experimental ata. The design eliability of UHF communication ystemss therefore mprovedbyits use.

INTRODUCTIONThis paper deals with the diffraction by naturalobstacleswith lateral profileshaving generalshapes.Daugherty -1969a,b, 1970a] provided the theoreticalbasis for treating irregular profiles (both transverseand on path) as multiple knife-edgediffracting obsta-cles with simple geometrical shapes,whose contri-butions to the received ield may be weighted andcombinedas vector phasers.Bachynski nd Kingsmill[1962] and Bachynski 1963] reported on the experi-mental results of simple transverseprofiles. In thispaper the transversalprofile of a given obstacle sapproximatedby n isolated rectangularknife-edges,each having sufficientlywide, but finite, lateral extent.If the longitudinalcrest adius of each of thesesimpleshapes s small enough, hen the total field may beapproximatedas the vector sum of the phaser fieldsdue to these n isolated knife-edges [Daugherty,1970b; Carlson,1973].The practicalproblem related to this study s theinvestigationof the frequencydependence f propa-gation attenuation with the transversalprofile. Forexample, measurements erformed n several inks inthe frequency band from 270 to 330 MHz have

shown variations of _+10 dB with respect to themedian value. The model described in the next sec-tion enables an estimate of these variations with reas-onably good precision and, consequently, ncreases

Copyright 1982 by the American GeophysicalUnion.Paper number 2S0043.0048-6604/82/0910-004308.00

the design reliability of UHF communication sys-tems.

MATHEMATICAL MODELDiffraction by a knife-edgeof arbitrary transversaprofile can be calculated by the general Fresnel-Kirchhoff theory. The electric field intensity at anobservation point R, generated by a source T, isgiven in the form of a simple surface ntegral in-volving the electric ield intensityat the unobstructedportion of the obstacle plane, and the free-spaceGreen's unction [Born and Wolf, 1970]. Applicationof this theory to the finite isolatedrectangularknife-edge shown in Figure 1, upon introduction of theclassical approximations for the Fresnel region,yields, or the field at R,E(R)/Eo(R= 1 -j e 'm2+u2/2t du (1)

A

where

Eo(R free-spaceield at R;d=di +d2;A = 2 /2 a/R;B = 21/2b/R;R first Fresnelzone radius at apertureplane,equal to(2did2/d)i/;k = 2rr/;t;;t wavelength.

An approximate expression or the field diffractedby an irregular obstaclewith a generalshapecan be1051


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1052 M. S. ASSIS

P(x,z)

.///////////////////////////////x-TRANSVERSAL PLANE

TJ 0

LONGITUDINAL PLANE'

Fig. 1. Single rregularknife-edge bstacle.

obtained rom (1) as follows.The lateral profile of theobstacle is approximately matched by a largenumber of rectanglesdentical o the rectangleshownin Figure 1 (see Figure 2). The horizontal referencelevel was chosenat the point where the line of sightcrosses he transversal plane. The number of rec-

Xn-I-i-l,,-i ////

x x x /t2tl

Xn Xn+ ILine - of -sight

Fig. 2. Rectangular it to lateral profile.

tanglesdependson the profile and the total extensionconsidered (horizontal dimension (Xn+--X) inFigure 2) shouldbe much arger than the largestver-tical dimension maximumheightYi in Figure 2). Ex-pression 1) may now be applied to this geometryasfollows:e -jkdE(R)/Eo(R) - 2

1 j e j'2/2dt e "/2 du (2)Xi , Yi iwhere

Xi = 2/2xi/R Yi= 2/2Yi/REXPERIMENTAL RESULTS

Expression 2) was used n the analysisof the fre-quency dependenceof the propagation attenuationwith the transversalprofile. An application of thisresult to the radio link shown in Figure 3 will bedescribed. n this case the transversal profile wasmatched by 26 rectangles.The minimum horizontaldimension was 50 m, and the total extension con-sidered was 2 km.

An important problem arising at this point is tosuit the knife-edgeresult obtained from (2) to thediffraction by the real convex obstacle.To this aim,the variations with frequencyestimated by (2) werereferred to a straight line defined by linear inter-polation (least squares method); these variationswere then superimposedo the diffraction by the ob-stacle considered uniform with a constant crestradius along the transversaldirectionequal to that inthe longitudinalplane containing he transmitterandreceiver.Figure 4 showsa comparisonof the experi-mental measurements with the theoretical evaluationby the mathematical model discussed above. Asnoted previously, here is good agreementbetweenboth results; the mean error was 1.8 dB with a stan-dard deviation of 2.4 dB.

CONCLUDING REMARKSBesides he importance for link budget calculation,the effect of the transversalprofile is also of interestfor studying he intermodulationnoise.The existenceof two or more components of transmitted signalwith the same order of magnitude may cause nter-channel interference, degrading the system per-


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DIFFRACTION BY NATURAL OBSTACLES

1150

I100

1050

I000

'" 950

; 900

850

800

'750

700

15 I0 5 0 5 I0 15i i I i i t i i ! i i t I I I i i I i i i i i i i i i t i iDISTANCE (Km)

LONGITUDINAL PROFILE

1160

1120

- IO8O IO4O

:z: IOOO960

920

880

Y

LINE-OF-SIGHT/"/ I o

DISTANCE (Kin)TRANSVERSAL PROFILE

Fig. 3. Typical UHF link.


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1054 M. S. ASSIS

150

145

140

Experimental..... Theoretical

.... Smooth diffraction / / \/!" i- I !,',,,1 I_,.__ ...I / ' .__......

.

155270 280 290 $00 $10 $20 $$0

Frequency (MHz)Fig. 4. Effect of lateral profile comparison etween heoreticaland experimental esults.

formance.The simplemathematicalmodel proposedin this paper seems o be useful for estimating helevel of lateral diffraction and, consequently, eems ohelp prevent his kind of problem.Acknowledgment. he author is grateful o C. G. Migliora forvaluablediscussionsnd readingof the manuscript.

REFERENCESBachynski,M.P. (1963), Scale model investigations f electro-magneticwave propagationover natural obstacles, CA Rev.,25(1), 105-144.Bachynski,M.P., and M. G. Kingsmill 1962),Effectof obstacle

profileon knife-edge iffraction, EEE Trans.Antennas ropag.10(2), 201-205.Born, M., and E. Wolf (1970), Principlesof Optics,pp. 382-383,Pergamon,New York.Carlson, A. B. (1973), Shadow-zonediffraction patterns for tri-angular obstacles,EEE Trans. AntennasPropag.,21(1), 121-

124.Dougherty,H. T. (1969a),An expansion f the Helmholtz ntegraland its evaluation,Radio $ci., 4(11), 991-995.Dougherty, H. T. (1969b), Radio wave propagation or irregularboundaries,Radio Sci.,4(11), 997-1004.Dougherty,H. T. (1970a),The applicationof stationaryphase oradio propagation or finite imits of integration,Radio Sci.,5(1),

1-6.Dougherty,H. T. (1970b),Diffraction by irregularapertures, adioSci., 5(1), 55-60.

effect of lateral profile on diffraction by natural obstacle

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