126 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 51, NO. 1, JANUARY 2003

Communications______________________________________________________________________

UHF and L Band Propagation Measurementsto Obtain Log-Normal Shadowing Parameters

for Mobile Satellite Link Design

I. Hakki Cavdar

Abstract—Tree shadowing is significant for mobile satellite radiopropagation investigation and must be known for successful link design.Therefore, there are limited data on the relevant problem. For thispurpose, propagation measurements at L and UHF band were performedin Trabzon, Turkey, in 1993 and 1996, respectively. These experimentswere executed with a transmitter on the top of a high building, andthe receiver system was located in a van outfitted with the antennaon its roof and receiver equipment in its interior. Measurements werecarried out for 14 different tree types, and the results of both bands arepresented in tabular and graphical forms. Experiments were repeatedfor the same trees during the months April to September. The variationsof the tree attenuation were examined during these months with andwithout foliage. Average values of the tree attenuations were found to be8.60 and 11.00 dB for UHF and L band, respectively. The scaling factorbetween L and UHF band attenuations in decibels was determined tobe approximately 1.32. Using these measured parameters, fade depthstatistics were calculated using a lognormal shadowing model. To establishvalidity of obtained results for the design of mobile satellite links, theresults were compared with previous investigations.

Index Terms—Fading, log-normal shadowing, mobile satellite link, prop-agation measurements, tree attenuation, tree shadowing.

I. INTRODUCTION

I IN land mobile satellite communications for both L and UHFbands, and terrestrial mobile communication such as land mobile

radio, cellular mobile radio, and GSM at UHF band, propagationmay take place through groves of trees. The attenuation contributionfor this configuration is due to combined absorption and multiplescattering from the conglomeration of tree canopies and trunks.These multipath effects cause signal fading and can be modeled asthe shadowing propagation based on a lognormal distribution. Inthis system, designers need two parameters to calculate the receivedsignal level: the average attenuation caused by trees and the standarddeviation of the shadowing effect.

To date, important experiments related propagation investigationsfor mobile satellite system design have been pursued at UHF, L, S, andK bands. These experiments can be classified into two groups: singletree measurements and fading statistics measurements. Although manypropagation measurements have been conducted on the fading statisticsin the different regions, only a few systematic single tree measurementshave been conducted. There are limited data on the attenuation due totrees for land mobile system at both L and UHF bands.

The previous works may be summarized for both single tree and thefading statistics measurements as follows. Static measurements of at-tenuation due to trees for land mobile satellite system were performedat UHF and L band by Vogel and Goldhirsh [1], Goldhirsh and Vogel[2], Vogel and Goldhirsh [3], Butterworth [4], [5], Ulabyet al. [6], andCavdaret al. [7]. In these tests, the average attenuation of trees were

Manuscript received June 2, 2000; revised April 20, 2001.The author is with the Department of Electrical and Electronics Engi-

neering, Karadeniz Technical University, Trabzon, 61080 Turkey (e-mail:cavdar@ktu.edu.tr).

Digital Object Identifier 10.1109/TAP.2003.808545

measured and the ratio between L band and UHF dB attenuation wasdetermined. On the other hand, Goldhirsh and Vogel measured fadestatistics for shadowing and multipath from roadside trees at UHF andL bands in 1985, 1986, and 1987 for mobile scenarios [8]. These testswere performed in Central Maryland and involved a helicopter andmobile van as the source and receiving platforms, respectively. Vogeland Goldhirsh performed mobile satellite propagation measurements atL band using MARECS-B2 in Central Maryland in 1987 [9]. The ob-jectives of the MARECS-B2 mobile satellite system test were to estab-lish cumulative fade distributions for the particular satellite geometryfor driving along rural and suburban roads, to validate the consistencyof previous roadside tree measurements which employed a helicopteras the transmitter platform for the same system of roads, to obtain addi-tional set of fade levels at a lower angle hitherto not measured in CentralMaryland, and to combine the satellite acquired data set with their pre-vious helicopter results [8]. Vogel and Hong reported on L band fadestatistics derived from measurements from a beacon located on a strato-spheric balloon [10]. These experiments were performed in the regionfrom New Mexico to Alabama in 1984 and 1986. Butterworth mea-sured fade statistics in suburban and rural areas at approximately 800and 1542 MHz [4], [5] in Ottawa, ON, Canada, using the MARECS-Ageostationary satellite. He obtained the distributions corresponding tosuburban, rural-forested, and rural-farmland data. Vogelet al.also mea-sured cumulative fade distributions at L band in Australia employingthe ETS-V and INMARSAT-Pacific geostationary satellites as trans-mitter platforms in 1988 [11]. Bundrock and Harvey reported on cu-mulative fade distributions obtained on typical double lane roads forboth UHF and L band [12]. Jongejanset al. measured L band fadingstatistics using MARECS-B2 satellite in Europe in 1984 [13]. Cumu-lative distributions for eight roads in central MD at L band at severalelevation angles were obtained from measurements by Goldhirsh andVogel in 1995 [14].

All previous works, such as measurements, studies, and modeling inthis area, were collected and published as a reference book by Gold-hirsh and Vogel [15]. They reviewed and evaluated all these works andpresented very useful suggestions and comments for land mobile satel-lite system designers in this book.

Designers of planned land mobile satellite systems require in-formation regarding signal degradation effects of trees at differentfrequencies and tree types for various geographic locations. An aimof mobile satellite systems is to ensure the possibility of serviceinternationally. It is important to investigate new data belonging toother geographic locations for a true system design and tree atten-uation analysis. For this purpose, tree attenuation measurements atL band were performed in Trabzon, Turkey, in 1993 [7] and repeatedfor the same trees at UHF band in 1996. The measurements werecarried out from the beginning of April to the end of September todescribe the effects of full blossom, with and without leaves andmoisture in the trees at both the UHF and L bands. In May and inJune, trees have full leaves and maximum moisture, in April, theyjust start growing leaves and are less dense and less moist, whereasin September, the leaves are relatively dry and ready to fall off.

Results of these experiments were applied to the developed mobilesatellite propagation model to predict the received signal level for var-ious conditions of shadowing.

II. M ETHOD OFMEASUREMENTS OFTREE ATTENUATION

Measurements were conducted at the Karadeniz Technical Univer-sity campus and in the villages nearby. First, the kinds of tree to be

0018-926X/03$17.00 © 2003 IEEE

IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 51, NO. 1, JANUARY 2003 127

Fig. 1. Experimental hardware at UHF band.

measured was chosen, and then, information regarding their leaf types,sizes, and the periods they have their leaves were determined [16]. Thephysical characteristics of trees suggested that the most suitable periodfor the attenuation measurements was between April and Septemberto be able observe such effects as with and without leaves, blossom,and moisture. The two frequencies 1600 MHz (L band) and 800 MHz(UHF band) were selected because these frequencies belong to thebands suitable for mobile satellite and terrestrial mobile communica-tion systems. The transmitter and receiver used in these experiments forUHF band are described in Fig. 1. Table I is a summary of experimentalaspects for UHF and L bands. Continuous-wave sinusoidal signal gen-erators were used as the transmitter sources with powers of 0.5 and0.25 W at the UHF and L bands, respectively. Dipole antennas withvertical polarizations were used at the transmitter sides for both bands.The L band receiver antenna was a drooping dipole, and the UHF re-ceiver antenna was a quarterwave dipole antenna. The transmitter waslocated on top of a high building, whereas the receiver was in a van.The height of the building chosen as the transmitter platform was de-termined for every experiment to provide an elevation of 30�. Theseplatforms were selected because of the unavailability of a geostationarysatellite carrying L and UHF band beacons. This angle was selected inthe experiments because it is a typical value in the northern parts of theworld for real geostationary mobile satellite applications.

A specific modulation technique was not used for these experimentsbecause the aim of the measurements was to determine the degrada-tions in the received signal level. Constant envelope signals were there-fore transmitted from the sources. This is a suitable choice for FM andthe other constant envelope digital modulation applications. At the re-ceiver side, the received signal entered a low-noise amplifier and passedthrough a low-noise down converter to obtain the baseband signal. Atthe output of the low noise down converter, an envelope detector wasused. The received signal at the output of the envelope detector was thefaded signal that was recorded on tape in analog form. These recordswere applied to an 8-bit analog-to-digital converter, and the digitalforms of the fading signals were obtained. Received signals in digitalform were entered into a PC. Statistical calculations were performedusing a developed software.

TABLE ISUMMARY OF EXPERIMENTAL PARAMETERS

TABLE IISUMMARY OF SINGLE TREE ATTENUATIONS AT BOTH UHF AND L BANDS

In every measurement of single trees, the transmitters were first lo-cated in a position that provided an elevation of 30�. Thereafter, thevan moved along the paths that were shadowed by the trees. At thesetimes, while the van was moving, the received signals were recorded.On the other hand, a reference signal without the tree shadowing wasalso recorded for every measured tree. The measurements for a treedepend on the distance of the transmitter and the receiver and otherphysical conditions. To determine the average attenuation for a tree, theshadowed record of that tree was compared with its reference signal inthe unshadowed position.

The results of L and UHF band tree measurements, average atten-uations (in decibels), average attenuation coefficients (in decibels permeter), and standard deviations (decibels) are given in Table II. The

128 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 51, NO. 1, JANUARY 2003

TABLE IIIFULL FOLIAGE ATTENUATIONS FORDIFFERENTTREESFROM MAY TO

AUGUST AT BOTH BANDS

results of these single tree tests for both L and UHF band can be sum-marized as follows:

1) For the L band, the average tree attenuations varied from 2.75 to20.10 dB, whereas the attenuation coefficient was between 0.70and 2.00 dB/m.

2) At the UHF band, the min and max values of average tree atten-uation were measured to be 2.13 and 16.10 dB, respectively. At-tenuation coefficients varied from 0.50 to 1.50 dB/m at the UHFband.

3) The scaling factors between the L and UHF band attenuationsin decibels were calculated and added to the table for every tree.Scaling factors are between 1.20 and 1.80 with an average of1.32.

4) The overall average tree attenuations were found to be 11.00 and8.60 dB.

5) The overall average standard deviations of the individual stan-dard deviations for different trees were calculated to be 3 dB and2 for L and UHF bands, respectively.

Table III shows full foliage attenuations for different trees at bothbands in May, June, July, and August. Low foliage attenuations aregiven in Table IV at both bands in April and September. Fig. 2 showsthe average tree attenuations and their seasonal effects for both bandsfrom April through September. Clearly, the attenuation is maximum inMay and June due to full blossom and moisture conditions.

III. M OBILE-SATELLITE LINK DESIGN

USING MEASUREDPARAMETERS

A successful model for mobile satellite propagation was developedby Loo [17] and is given by

fv(v) =

p2Kv

sp�

�1

0

1

zexp � (ln(z)�m)2

2s2�K(v2 + z

2) Io(2Kvz)dz

(1)

wherefv(v) is the probability density function of the random variablev, z is a random variable of the lognormal distribution,m ands are

TABLE IVLOW FOLIAGE ATTENUATIONS FORDIFFERENT TREES IN APRIL AND

SEPTEMBER ATBOTH BANDS

Fig. 2. Seasonal variations in the average tree attenuations at both UHF andL bands.

the mean and standard deviation ofln(z), andIo( ) is the zeroth-ordermodified Bessel function.K is reciprocal of the average normalizedmutipath power and is given by

K =1

2�2(2)

where2�2 is the average multipath power. This model assumes thatthe amplitude of the line-of-sight component under foliage attenuation(shadowing) is lognormally distributed and that the received multipathinterference has a Rayleigh distribution. This statistical model can beused to determine the fading statistics on the received signal in a satel-lite mobile link.

System designers would only need the mean value and standarddeviation of the foliage attenuation to predict fading depth. Sincethe complicated integral given by (1) must be evaluated numerically,an algorithm was developed to solve it.

IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 51, NO. 1, JANUARY 2003 129

Fig. 3. Fade distributions calculated using the lognormal model for 100% ofoptical shadowing. A: Butterworth, UHF, mean= 7 dB [5]. B: UHF band,mean= 8.6 dB (this study). C: Ulabyet al., L band, mean= 9.2 dB [6].D: Vogel–Goldhirsh, UHF band, mean= 10.6 dB [1], [2]. E: Cavdaret al.,L band, mean= 11 dB [7]. F: Goldhirsh–Vogel, L band, mean= 11.6 dB [15].

Fade depths (F ) were calculated using the measured parametersgiven in Section II for both bands using the Loo’s model and com-pared with the fade depths the under no shadowing effect case onthe line-of-sight component. Fig. 3 shows the variations on fadingdepth for both bands using the measured parameters. In Fig. 3, theordinate represents the percentage of the distance the fade depth isgreater than the abscissa value. In these calculations, average treeattenuations are 11 and 8.60 dB, and standard deviations are 3 and2 dB for L and UHF bands, respectively. The Rayleigh propagation

parameter�

K is between 10–20 dB; an average value of the�

K

parameter is taken 15 dB. The obtained results of fading depths fromthese measurements are shown in Fig. 3 at both the L and UHF bands.In order to compare the obtained results with previous works, theexisting data in literature are used to predict fading depths. The resultsof previous works on the single tree measurements are summarized asVogel and Goldhirsh and Goldhirsh and Vogel performed single treemeasurements at the UHF band over ten different trees in Virginia andin Central Maryland in 1985 and 1986. The average attenuation was10.6 dB [1], [2]. Butterworth carried out single tree measurementsat the UHF band in Ottawa, ON, Canada, in 1981, and he reportedthat the median attenuation was 7 dB [5]. Ulabyet al. measured theattenuations properties of a canopy at the L band in Michigan in 1990[6]. Their measurements gave rise to an average attenuation of 9.2 dB.Goldhirsh and Vogel conducted the propagation tests for single treesat the L band in Austin, TX, in 1991, and they determined a 11.6–dBaverage attenuation [15]. Unfortunately, the standard deviations werenot reported in the previous works described above. The values ofstandard deviations for previous works in Fig. 3 were taken to be 3 and2 dB at the L and UHF bands, respectively. Therefore, the comparisonswere only done by using the standard deviations measured in thisstudy. Although the standard deviations were not reported by authors,they are expected to be close to the values obtained here. Loo reportedstandard deviations between 0.5 and 3.5 dB for infrequent light andfrequent heavy shadowing, respectively [17]. On the other hand, Bartsand Stutzman solved Loo’s model and developed a mathematicalapproach [18]. The simplified lognormal shadowing model developedby Barts and Stutzman has tree input parameters such asK, meanvalue, and standard deviation of tree attenuation. It is clearly shownusing this model that standard deviation has a small effect on thefading distribution.

Fig. 4. UHF and L bands fade exceeded versus Rayleigh parameterK forfamily of indicated constant percentages.

Fig. 5. Fade distributions for the minimum and maximum attenuation months.

Fading statistics for the shadowing parameters given above were alsocalculated and added in Fig. 3. The calculated results are quite similar toeach other. In Fig. 3, the line-of-sight signal is fully shadowed by trees.Therefore, these results can be used as the worst-case values for fadingdepths on the mobile satellite link design. For example, the worst-casefade values are 21–26 dB at the UHF band and 25.5–28.8 dB at theL band forP = 1%, whereP is the percentage of the distance traveledover which the fade is exceeded.

The variations in�

K parameters do not play an important role in

the fading depth. Fig. 4 shows the effect of variations of�

K in the the

UHF and L bands. While�

K parameter varies from 10 to 20 dB, thefading depths decrease from 30 to 25 dB for the L band and from26 to 20 dB for the UHF band atP = 1%. The lognormal shad-owing parameters,m and� used in Fig. 4 were the same values as inFig. 3. Monthly effects on the fading statistics were carried out at bothbands. In these calculations, the minimum and the maximum attenua-tions for both bands are plotted in Fig. 5. Minimum attenuation occuredin September, whereas the maximum attenuation was observed in May

130 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 51, NO. 1, JANUARY 2003

for both bands. It is clearly shown that seasonal effects cause approxi-mately 6 dB difference for the L band and 7 dB difference for the UHFband in the fading depths forP = 1 and 100% optical obstruction.

IV. CONCLUSION

In this study, the average and the standard deviation for treeattenuations are determined experimentally. These findings are veryimportant in solving the lognormal shadowing model given by (1)for mobile satellite communication links at the UHF and L bands.The measured parameters were applied to the link model, and thefading depths were calculated under various situations. The resultsof this study are as follows: 1) Mean values of tree attenuations are11 and 8.60 dB at the L and UHF bands, respectively. 2) Averagesof the individual standard deviations were 3 dB for the L bandand 2 dB for the UHF band. 3) A scaling factor was found tobe 1.32 between the L and UHF band tree attenuations. 4) Theminimum attenuations occurred in September, whereas the maximumattenuation was observed in May for both bands. 5) The seasonaleffects cause approximately 6–dB difference for the L band and7–dB difference for the UHF band in the fading depths forP = 1

and 100% optical obstruction. 6) Fading depths were determinedto be 27 dB for the L band and 23.5 dB for the UHF band usingLoo’s propagation model with measured parameters forP = 1%.

REFERENCES

[1] W. J. Vogel and J. Goldhirsh, “Tree attenuations at 869 MHz derivedfrom remotely piloted aircraft measurements,”IEEE Trans. AntennasPropagat., vol. AP-34, pp. 1460–1464, Dec. 1986.

[2] J. Goldhirsh and W. J. Vogel, “Roadside tree attenuation measurementsat UHF for land-mobile satellite systems,”IEEE Trans. Antennas Prop-agat., vol. AP-35, pp. 589–596, May 1987.

[3] W. J. Vogel and J. Goldhirsh, “Earth-satellite tree attenuation at 20 GHzfoliage effects,”Electron. Lett., vol. 29, pp. 1640–1641, Sept. 1993.

[4] J. S. Butterworth, “Propagation measurements for land-mobile satelliteservices at 1542 MHz,” Commun. Res. Center, Ottawa, ON, Canada,Tech. Note 723, 1984.

[5] , “Propagation measurements for land-mobile satellite services inthe 800 MHz,” Commun. Res. Center, Ottawa, ON, Canada, Tech. Note724, 1984.

[6] F. T. Ulaby, M. W. Whitt, and M. C. Dobson, “Measuring the propagationproperties of a forest canopy using a polarimetric scatterometer,”IEEETrans. Antennas Propagat., vol. 38, pp. 251–258, Feb. 1990.

[7] I. H. Cavdar, H. Dincer, and K. Erdogdu, “Propagation measurements atL-band for land mobile satellite link design,” inProc. 7th MediterraneanElectrotechn. Conf., Antalya, Turkey, Apr. 1994, pp. 1162–1165.

[8] J. Goldhirsh and W. J. Vogel, “Mobile satellite system fade statistics forshadowing and multipath from roadside trees at UHF and L-band,”IEEETrans. Antennas Propagat., vol. 37, pp. 489–498, Apr. 1989.

[9] W. J. Vogel and J. Goldhirsh, “Mobile satellite system propagation mea-surements at L-band using MARECS-B2,”IEEE Trans. Antennas Prop-agat., vol. 38, pp. 259–264, Feb. 1990.

[10] W. J. Vogel and U. S. Hong, “Measurements and modeling of land mo-bile satellite propagation at UHF and L-band,”IEEE Trans. AntennasPropagat., vol. 36, pp. 707–719, May 1988.

[11] W. J. Vogel, J. Goldhirsh, and Y. Hase, “Land-mobile satellite fademeasurements in Australia,”AIAA J. Spacecraft Rockets, vol. 29, pp.123–128, Jan.-Feb. 1992.

[12] A. Bundrock and R. Harvey, “Propagation measurements for an Aus-tralian land-mobile satellite system,”Austral. Telecommun. Res., vol. 23,no. 1, pp. 19–25, 1989.

[13] A. Jongejans, A. Dissanayake, N. Hart, H. Haugli, C. Loisy, and R.Rogard, “PROSAT-Phase 1 Report,” Eur. Space Agency, Paris, France,ESA-STR 216, 1986.

[14] J. Goldhirsh and W. J. Vogel, “An extended empirical roadside shad-owing model for estimating fade distributions from UHF to K-band formobile satellite communications,”Space Commun., vol. 13, no. 3, pp.225–237, 1995.

[15] , Handbook of Propagation Effects for Vehicular and Personal Mo-bile Satellite Systems – Overview Experimental and Modeling Results,2nd ed. Houston, TX: NASA, 1999.

[16] G. Rabinette,The Design Characteristics of Plant Materials FromStudies, 1st ed. Madison, WI: College Print, 1967.

[17] C. Loo, “A statistical model for a land mobile satellite link,”IEEE Trans.Veh. Technol., vol. VT-34, pp. 122–127, Aug. 1985.

[18] R. M. Barts and W. L. Stutzman, “Modeling and simulation of mo-bile satellite propagation,”IEEE Trans. Antennas Propagat., vol. 40, pp.375–382, Apr. 1991.

Finite Element Analysis of Electromagnetic ScatteringFrom a Cavity

Tri Van and Aihua W. Wood

Abstract—In this paper, a finite element method (FEM) is implementedto compute the radar cross section of a two-dimensional (2-D) cavity em-bedded in an infinite ground plane. The method is based on the variationalformulation which uses the Fourier transform to couple the fields outsidethe cavity and those inside the cavity; hence, the scattering problem can bereduced to a bounded domain. The convergence of the discrete finite ele-ment problem is analyzed. Numerical results are presented and comparedwith those obtained by the standard finite element-Green function methodand by the 2-D integral equation method.

Index Terms—Dirichlet-Neumann map, finite element method, 2-Dcavity.

I. INTRODUCTION

The study of the scattering of electromagnetic plane waves by atwo-dimensional (2-D) cavity-backed aperture in the infinite groundplane has been of great importance in aircraft industries. Accuratecomputational methods in predicting the radar cross section (RCS) ofcavities are very much desired. Integral equation methods have beenwidely used by many authors (see, for example, [1] and referencestherein). However, they have the disadvantage of being difficult toimplement for complex bodies. A hybrid method, known as thefinite element-boundary integral method, is also often applied inscattering problems (see, for example, [2] and references therein).Using the field continuity conditions at the cavity aperture, thishybrid method combines the analytical solution above the groundplane in terms of Hankel functions and the approximate solutioninside the cavity. However, little is known about the well-posednessand convergence of this method. In this paper, a variational approachthat couples the finite-element method (FEM) and Fourier transformsis considered. This approach reduces the computational efforts to abounded domain by introducing a Dirichlet–Neumann map. We alsoanalyze the existence, uniqueness, and convergence properties ofthe finite element-Fourier transform method. Some numerical results

Manuscript received November 30, 1999; revised January 29, 2001. The workof A. W. Wood was supported in part by the Air Force Office of Scientific Re-search under Grant AFOSR-PO-990025. The views expressed in this paper arethose of the authors and do not reflect the official policy or position of the UnitedStates Air Force, Department of Defense, or the U.S. Government.

The authors are with the Air Force Institute of Technology, AFIT/ENC,Wright-Patterson Air Force Base, OH 45433 USA (e-mail: Tri.Van@afit.af.mil;Aihua.Wood@afit.af.mil).

Digital Object Identifier 10.1109/TAP.2003.808517

0018-926X/03$17.00 © 2003 IEEE