GPS signal fading model for urban centres

R. Klukas, G. Lachapelle, C. Ma and G.-I. Jee

Abstract: The use of GPS receivers in wireless telephones has been proposed as a means ofautomatically identifying the position of wireless 911 callers. GPS simulators are an efficient meansof testing the accuracy of such technology but require a channel model for GPS satellite signals.This paper presents a methodology for measuring and modelling the fading distribution of GPSsatellite signals received in outdoor urban centres. GPS fading data, as collected in the downtownareas of Calgary and Vancouver, Canada, are used to generate fade histograms as a function ofsatellite elevation angle. These histograms are found to be sufficiently similar between the two citiesand, therefore, lead to the conclusion that a generic fade distribution for urban centres isreasonable. Parameters for the Urban Three-state Fade Model are estimated from the empiricalfading data collected in each city. Correlation between the model parameters derived for each city issignificant and also suggests that a generic model may be derived. The parameters from the twocites are averaged to produce a generic Urban Three-state Fade Model, which adequatelyrepresents the fade histograms of each city. These averaged parameters generally agree withparameters derived from data collected in Tokyo, Japan.

1 Introduction

The incorporation of GPS (Global Positioning System)receivers in wireless telephones is being pursued as a meansto automatically locate wireless 911 callers. This is necessaryto meet the mandate of the Federal CommunicationCommission (FCC) regarding enhanced 911 services forwireless subscribers [1]. Depending on the means in whichE-911 is implemented, the position accuracy required by theFCC ranges from 50m to 100m in 67% of all cases. A costefficient and flexible means of testing GPS-enabled wirelesshandsets is to simulate GPS satellite signals as received by awireless handset.As a result, GPS simulators that are able to simulate

received satellite signals for various environments arenecessary. A crucial component of such simulation is amodel that accounts for fading of the satellite signals as theypropagate from satellites to the wireless handset. Fadingmodels for such an outdoor propagation channel have beeninvestigated. Briso and Alonso [2] suggest a modelconsisting of two states, a direct state and a shadowedstate. The direct state is modelled by the combination of alognormal process and a Rayleigh process. The shadowedstate is modelled by a Ricean process. Another model is theUrban Three-state Fade Model (UTSFM) developed byAkturan and Vogel [3] and based on a similar modeldeveloped by Karasawa et al. [4]. Akturan and Vogel [3]and Goldhirsh and Vogel [9] used fisheye lens images takenat various potential handset user locations in urban Tokyo,Japan to predict the parameters in their model. They thencompared the cumulative fade distribution predicted by

their model to the cumulative fade distribution of satellitebeacon measurements made in urban Japan at 1.5GHz.The aim of this paper is to estimate the parameters of

Akturan and Vogel’s [3] UTSFM from C/No measurementsmade outdoors with GPS receivers in urban Calgary andVancouver, Canada. The model parameters between thetwo cities are compared as a function of satellite elevation inorder to determine whether a generalised set of modelparameters may be generated. If so, the UTSFM with theseparameters may be used in GPS simulators to simulate thefading of GPS satellite signals in outdoor urban areas as afunction of satellite elevation.

2 The Urban Three-state Fade Model

Karasawa et al. [4] assume that the satellite to earth-mobilechannel consists of three main states. In the first, the line-of-sight or clear state, the signals received are the line-of-sightsignal and multipath signals. The fading distribution for thisstate is modelled by the Ricean distribution as expressed by

fRiceðvÞ ¼ 2Kv exp� Kðv2 þ 1ÞI0ð2KvÞ ð1Þwhere K is the ratio of the direct power received to that ofmultipath, v is the received voltage relative to the voltage ofthe clear path, and I0 is the modified 0th order Besselfunction with argument v. The second state consists of aline-of-sight arrival and multipath arrivals as well. However,the line-of-sight arrival is assumed to be attenuated (orshadowed), by foliage for example. The fading of theattenuated line-of-sight arrival is assumed to be lognormally distributed and the fading of the multipatharrivals is Rayleigh distributed. Loo [5] developed astatistical model for such a channel and the probabilitydensity function for the received signal amplitude is

fLooðvÞ ¼8:686ffiffiffi2

p

rKvs

Z 1

0

1

v

� exp �ð20logðvÞ � mÞ2

2s2� Kðv2 þ z2Þ

" #

� I0ð2KvzÞexp dz

ð2ÞR. Klukas, G. Lachapelle, C. Ma and G.-I. Jee are with the Department ofGeomatics Engineering, University of Calgary, 2500 University Drive NW,Calgary, Alberta, T2N 1N4, Canada

G.-I. Jee is also the Visiting Professor at, Konkuk University, Seoul, SouthKorea

r IEE, 2003

IEE Proceedings online no. 20030546

doi:10.1049/ip-map:20030546

Paper first received 28th June 2002 and in revised form 3rd March 2003. Onlinepublishing date: 22 July 2003

IEE Proc.-Microw. Antennas Propag., Vol. 150, No. 4, August 2003 245

where s and m are the standard deviation and mean oflog(v) and z is the amplitude of the line-of-sight component.The third state is referred to as the blocked state. In this

state, the line-of-sight path is blocked by some obstructionsuch as a building or mountain. As a result, the receivedsignal consists entirely of multipath arrivals. The fadingdistribution of such a channel is expressed by the Rayleighdistribution which is the special case of the Riceandistribution without a line-of-sight arrival. The Rayleighprobability density function is given by

fRayleighðvÞ ¼ 2Kv expð � Kv2Þ ð3ÞAccording to Karasawa et al. [4], the overall probabilitydensity function of the received signal envelope v is aweighted combination of the Rice, Loo, and Rayleighprobability density functions and may be expressed as

fvðvÞ ¼C � fRiceðvÞ þ S � fLooðvÞþ B � fRayleighðvÞ

ð4Þ

where

C þ S þ B ¼ 1 ð5ÞAkturan and Vogel [3] note that the Rice and Rayleighdistributions in (4) do not account for specular reflectionsnor for building diffracted arrivals. Therefore, they call (4)the rural three-state model. In urban areas, it is likely thatwhen the line-of-sight path is blocked, received power willbe due to specular reflections and diffractions fromnearby buildings. As a result, Akturan and Vogel [3]replaced the Rayleigh distribution for the blocked statewith that of Loo [5]. The resulting overall distribution isthen

fvðv; aÞ ¼CðaÞ � fRiceðvÞ þ SðaÞ � fLoo;ShadowedðvÞþ BðaÞ � fLoo;BlockedðvÞ

ð6Þ

where a is satellite elevation angle. The fading distributionof (6) is called the Urban Three-state Fade Model. Akturanand Vogel [3] demonstrate that the RMS error in themodelled cumulative fade distribution, with respect to thecumulative fade distribution measured in Japan, drops fromapproximately 1.5dB to 0.7dB when the urban model (6) isused in place of the rural model (4). Therefore, in this paper,parameters for the UTSFM are estimated from GPS fadingdata.

3 Methodology

GPS signal fading data was generated by measuringreceived C/No with two GPS receivers – a reference receiverand a rover receiver. Both receivers were 12 channelreceivers operating at L1 (1.57542GHz) and manufacturedby SiRF Technology, Inc. The reference receiver wasSiRF’s standard receiver whereas the rover receiver was anunaided, high sensitivity model developed to operate inchallenging RF environments. The performance of this highsensitivity receiver in urban canyons and indoors wasinvestigated by MacGougan et al. [6]. The two receiversdiffer most significantly in terms of signal integration time.In order to increase sensitivity, the high sensitivity modelnon-coherently integrates over periods of 340 to 800ms.The integration time for the standard model is only 12ms.The two receivers also differ slightly with respect to themanner in which they compute C/No. On a zero-baselinetest (both receivers connected to the same antenna), thedifference in C/No for identical satellites was found to be0.8dB. This value was taken into account when C/No

differences were computed.

The reference receiver antenna was mounted in such away that, to the greatest extent possible, it had a clear viewof the sky. In Vancouver, the reference receiver antenna wasmounted on the roof of a two-story house in a residentialarea approximately 4km from the downtown area ofVancouver. In Calgary, the reference antenna was mountedon the roof of the four-story Engineering building at theUniversity of Calgary which is approximately 3km fromCalgary’s downtown.The rover GPS receiver was installed in an automobile

with the antenna mounted on the roof. The automobilethen circuited a set trajectory in the downtown area. Fig. 1shows the test trajectory in downtown Vancouver as derivedfrom a single-point GPS position solution. During the test,both the reference and rover GPS receivers collected GPSsatellite data at a rate of 1Hz including the received C/No

for each satellite visible. In the Calgary test, approximately2.5 hours of data was collected as the automobile travelledapproximately 40km at speeds of up to 50km/h. InVancouver, approximately 3.5 hours of data was collectedas the automobile travelled 50km at speeds of up to50km/h.

To generate the fading data, the C/No of the referencereceiver was differenced with that of the rover receiver on anepoch-by-epoch and satellite-by-satellite basis. Since thereference receiver antenna had a clear view of each satellite,an assumption was made that the C/No measured by thatreceiver was a function of free space loss and atmosphericabsorption only. It is very possible, however, that somemultipath fading still occurred at the reference receiver. Inany case, any multipath fading at the reference is assumedto be small compared to that at the rover and the differenceinC/No between the two receivers is assumed to be due onlyto fading experienced by the signal received at the roverantenna. It is, of course, possible that the multipathexperienced by signals impinging on the rover antennacaused constructive interference and hence an increase inreceived signal power. In such a case, the result could be ahigher received signal strength at the rover than at thereference.The fade differences were then binned according to

satellite elevation angle. Histograms of the fade differenceswere generated for satellite elevation angles of 151 to 851 inincrements of 101. The parameters of the UTSFM werethen estimated for each satellite elevation bin such that theprobability density function of the model fit the histogramaccording to some criteria.

Fig. 1 Test trajectory in downtown Vancouver

246 IEE Proc.-Microw. Antennas Propag., Vol. 150, No. 4, August 2003

4 Estimation of UTSFM parameters

Assume N data points ðvi; yiÞ, i ¼ 1; 2; . . . ;N from themeasured fade histogram for a particular satellite elevationangle where the value yi is the probability of a fade of valuevi. We then wish to estimate values for the ten parameters ofthe UTSFM such that the model best fits the measured datain some sense. The parameters to be estimated are

b ¼½CðaÞ; SðaÞ; BðaÞ; KC;Rice; KS;Loo;

mS;Loo; sS;Loo; KB;Loo; mB;Loo; sB;Looð7Þ

The model parameters are estimated in such a way as tosatisfy

argminb

XNi¼1

ðyi � fvðb; viÞÞ2 ð8Þ

This is the well-known least squares criterion.The UTSFM is non-linear and estimation of the

parameters is subject to the following constraints.

CðaÞ þ SðaÞ þ BðaÞ ¼ 1 ð9Þ

CðaÞ � 0; SðaÞ � 0; BðaÞ � 0 ð10Þ

KC;Rice40; KS;Loo40; KB;Loo40 ð11Þ

sS;Loo40; sB;Loo40 ð12ÞThe Levenberg–Marquardt (L–M) algorithm [7] is apopular solution for unconstrained, non-linear least squaresproblems and was chosen here. The algorithm can beexpressed as

bkþ1 ¼ bk � ðJðbkÞTJðbkÞ þ mkIÞ�1JðbkÞT rðbkÞ ð13Þwhere bk is the parameter vector, JðbkÞ is the Jacobi matrix,rðbkÞ is the fitting error vector, and mk is the iterationcontrol factor. The L–M algorithm has an elegant schemeto choose mk in order to keep the algorithm from diverging.To apply the L–M algorithm to the present application,

the estimation problem must first be transformed into anunconstrained problem. To accomplish this, the followingparameter transformations were performed such that theoriginal constraints (9) through (12) are automaticallysatisfied.

CðaÞ ¼ cos2ðgÞ ð14Þ

SðaÞ ¼ sin2ðgÞ cos2ðdÞ ð15Þ

BðaÞ ¼ sin2ðgÞ sin2ðdÞ ð16Þ

KC;Rice ¼ k2C;Rice ð17Þ

KS;Loo ¼ k2S;Loo ð18Þ

KB;Loo ¼ k2B;Loo ð19Þ

sS;Loo ¼ �2S;Loo ð20Þ

sB;Loo ¼ �2B;Loo ð21ÞFollowing these transformations, the unconstrained opti-misation problem was constructed and the L–M methodused. MINPACK [8], a public domain optimisation soft-ware package, was used to implement the L–M method.

5 Results

Histograms of the empirical fade data from Calgary andVancouver (as described under Methodology) are shown in

Figs. 2 and 3. Each plot in Figs. 2 and 3 contains thehistogram from the Calgary data and the histogram fromthe Vancouver data for a particular satellite elevation angle.In each histogram there are 101 fade bins and each bin isjust over 1dB wide.There is a striking similarity between the Calgary and

Vancouver histograms. A significant difference between thehistograms of the two cities occurs at an elevation angle of151. In that case, the dominant group of Vancouver fadevalues is centred at 0dB whereas the dominant group in theCalgary histogram is at 35dB to 40dB. This may beattributed to the location of the reference receiver inVancouver. The reference receiver antenna in Vancouverwas located on the roof of a two-story house. It is possiblethat some low elevation satellites were no more visible to thereference antenna than they were to the rover antenna. Thiswould cause a greater number of rover fade values near0dB. The reference antenna in Calgary, however, beinglocated on the roof of a four-story building, had a clearerview of the sky at low elevation angles.For elevation angles from 551 to 851, the Calgary and

Vancouver histograms again largely agree, with theexception of higher probabilities for negative fade valuesin the Vancouver histograms. Consider the histogram ofFig. 3b. Whereas the Calgary histogram smoothly drops tozero probability at approximately �10dB, the Vancouverhistogram exhibits a significant and consistent probabilitylevel for fades as low as �20dB. At that point, thehistogram drops off sharply. The location of the Vancouverreference antenna is again the most likely cause for thisbehaviour. As the satellite elevation angles are high, it is nota matter of signal blockage by surrounding obstacles. It ismore likely that multipath is causing a significant amount ofdestructive interference at the Vancouver reference antennawhich reduces the received SNR relative to that of theVancouver rover antenna.The results of fitting the UTSFM, for satellite elevations

151, 351, 551, and 751, to the Calgary and Vancouverempirical fade data are shown in Figs. 4 and 5 respectively.In each plot, the dashed line corresponds to the UTSFMand the solid line to the empirical fade histogram. As seen inFigs. 4 and 5, the UTSFM has little difficulty modelling theempirical data.The estimated values of the UTSFM clear, shadowed,

and blocked probabilities are given in Table 1. Also shownin Table 1 are the sample correlation coefficients for eachstate probability. These correlation coefficients give anindication of how correlated the state probabilities esti-mated from the Calgary empirical data are to thoseestimated from the Vancouver empirical data. The esti-mated state probabilities are also plotted in Fig. 6.The first observation made from the results of Fig. 6 is

that all three state probabilities for Calgary vary moresmoothly with satellite elevation angle than do those forVancouver. The Vancouver state probabilities tend tooscillate as satellite elevation changes. A possible explana-tion is the homogeneity, or lack thereof, of the buildingtypes in the two cities. The Calgary downtown area has arelatively large number of tall buildings in a small area. As aresult, the height of the buildings or depth of the urbancanyons along much of the test route is similar. Vancouver’sdowntown, however, has more diversity in the height andtypes of buildings. It is possible, therefore, that along thetest route in Vancouver, the probability of a satellite signalbeing received via a clear, shadowed, or blocked state willvary widely as a function of satellite elevation angle. Theresult will be an inconsistent relationship between stateprobability and satellite elevation angle.

IEE Proc.-Microw. Antennas Propag., Vol. 150, No. 4, August 2003 247

Fig. 2 Empirical fade histograms for Calgary and VancouverSatellite elevation angles (a) 151, (b) 251, (c) 351, (d) 451

Fig. 3 Empirical fade histograms for Calgary and VancouverSatellite elevation angles (a) 551, (b) 651, (c) 751, (d) 851

248 IEE Proc.-Microw. Antennas Propag., Vol. 150, No. 4, August 2003

Fig. 4 Empirical and UTSFM fade histograms for CalgarySatellite elevation angles (a) 151, (b) 351, (c) 551, (d) 751

Fig. 5 Empirical and UTSFM fade histograms for VancouverSatellite elevation angles (a) 151, (b) 351, (c) 551, (d) 751

IEE Proc.-Microw. Antennas Propag., Vol. 150, No. 4, August 2003 249

In the case of Fig. 6a, it may be argued that there is noclear trend in the clear state probability for Calgary. Thereappears to be a consistent probability of a satellite signalbeing received via a clear path. This is expected since aswath of clear sky generally exists directly above and alongan urban canyon. On the other hand, one would expect thatas satellite elevation increases, the probability of a signalbeing blocked decreases. This indeed is shown to be the casein Fig. 6c. Given the relatively constant clear stateprobability, it remains for the shadowed state probabilityto increase, as seen in Fig. 6b, in order to make up for thedecrease in the blocked state probability as satelliteelevation angle increases. Although more noisy, theVancouver clear state and shadowed state probabilitiesexhibit the same long-term trends as the correspondingCalgary probabilities. There seems to be no conclusive trendin the Vancouver blocked state probability.Correlation coefficients for the other seven UTSFM

parameters estimated are shown in Table 2. The values inTable 2 indicate a relatively strong correlation between theparameter values estimated from the Calgary data set andthose estimated from the Vancouver data set. This suggeststhat the dependence of the UTSFM parameters on satelliteelevation angle is similar for the Calgary and Vancouverdowntown environments.The results indicate that the empirical fade histograms

measured in Calgary are sufficiently similar to thosemeasured in Vancouver that a generic UTSFM for GPSsignal fading in outdoor, downtown environments ispossible. Towards that end, the UTSFM parametersestimated from the Calgary data were averaged with thoseestimated from the Vancouver data. UTSFM fadehistograms were then generated from this set of average

parameters. The results are plotted in Fig. 7 along with theempirical Calgary and Vancouver histograms.The plots of Fig. 7 indicate that a simple average of the

UTSFM parameters estimated from the Calgary andVancouver data set results in a fade histogram which istypical of both cities. In most cases, the average UTSFMhistogram is a reasonable compromise between theempirical histograms. Only in the case of a 551 satelliteelevation angle (Fig. 7c) does the average UTSFMhistogram not follow one or the other empirical histogramsnor the middle ground between them. In that case, the peakof the average UTSFM histogram lies below that of bothempirical histograms.The averaged UTSFM parameters are compared, in

Table 3, to parameters estimated by Goldhirsh and Vogel[9] for urban Tokyo. The parameters from the Tokyo dataare for a satellite elevation angle of 321, and the averagedparameters presented are for the 351 satellite elevation bin.The blocked state probability for urban Tokyo is verysimilar to that of urban Calgary/Vancouver. However, theshadowed state probability for the Tokyo data is almostzero (0.07) whereas for the Calgary/Vancouver data it issignificant (0.21). This may be due to differences in theenvironment or the manner in which the state probabilitieswere estimated. The probabilities for Tokyo were derivedfrom a photogrammetric technique whereas the probabil-ities for Calgary/Vancouver were estimated from fadingdata.The shadowed and blocked K values for the Calgary/

Vancouver data are much larger than those for the Tokyodata. It was found that the Loo distribution is relativelyinsensitive to the value of K when K is large. As a result, theCalgary/VancouverK values could be made smaller withoutsacrificing the fit of the histograms. Finally, the value ofmS,Loo for the Calgary/Vancouver data is significantlysmaller than that for the Tokyo data. Since a smallermS,Loo indicates less multipath, this may again be due todifferences in the propagation environment.

6 Conclusions

The methodology described herein was able to generateempirical fade histograms for GPS satellite signals receivedoutdoors in urban centres. An important assumption madein the methodology is that free-space loss but no fading isexperienced by the signal impinging on the referencereceiver antenna. Ideally, then, the reference antenna shouldbe located in a multipath free environment with a clear view

Table 1: Clear, shadowed, and blocked state probability values

Satelliteelevation angle

C(a) Clear stateprobability

S(a) Shadowed stateprobability

B(a) Blocked stateprobability

Calgary Vancouver Calgary Vancouver Calgary Vancouver

151 0.15 0.00 0.21 0.40 0.64 0.60

251 0.33 0.42 0.18 0.48 0.49 0.09

351 0.25 0.37 0.17 0.24 0.58 0.39

451 0.22 0.04 0.25 0.61 0.54 0.35

551 0.26 0.62 0.28 0.27 0.46 0.11

651 0.01 0.00 0.63 0.46 0.36 0.54

751 0.18 0.01 0.67 0.85 0.15 0.13

851 0.28 0.60 0.72 0.40 0.00 0.00

Correlationcoefficient

0.73 0.44 0.63

Table 2: Correlation coefficients for UTSFM parameters

Parameter CorrelationCoefficient

KC,Rice 0.97

KS,Loo 0.70

ms,Loo 0.73

sS,Loo 0.44

KB,Loo 0.64

mB,Loo 0.78

sB,Loo 0.88

250 IEE Proc.-Microw. Antennas Propag., Vol. 150, No. 4, August 2003

of the sky in all directions and to the horizon. If thereference antenna is not located in such an environment,there may be a higher probability of negative fade values asseen in the empirical Vancouver histograms.Apart from a few small exceptions, the empirical fade

histograms for Calgary and Vancouver are sufficientlysimilar to allow one to conclude that a generic UTSFM forthe downtown areas of large cities is reasonable. Analysis ofthe correlation coefficients of these parameters indicatesthat the dependence of these parameters on satelliteelevation angle is similar for the Calgary and Vancouverdowntown environments. Although the relationship be-tween the state probabilities and satellite elevation angle wasless consistent in the case of Vancouver than in the case of

Fig. 6 Estimated clear (a), shadowed (b), and blocked state (c)probabilities

Fig. 7 Calgary and Vancouver empirical fade data and averageUTSFMSatellite elevation angles (a) 151, (b) 351, (c) 551, (d) 751

IEE Proc.-Microw. Antennas Propag., Vol. 150, No. 4, August 2003 251

Calgary, in both cases an overall trend is generally apparent.Testing in other cities may help determine whether therelative consistency in the relationship between stateprobability and satellite elevation is a function of buildingtypes and mix.A generic UTSFM was generated by simply averaging

the UTSFM parameters derived from the Calgary andVancouver data sets. The fade histograms obtained fromthis generic UTSFM adequately represent the empiricalfade histograms for both cities. The averaged UTSFMparameters generally agree with those derived frommeasurements made in urban Tokyo. If data is alsocollected in other cities, it may be worthwhile investigatingother means of deriving the parameters of a generic model.This will be especially true if the empirical fade histogramsfor other cities significantly differ from those presented here.In any case, a generic UTSFM model generated by themethods described here should prove useful to manufac-turers of GPS simulators.

7 Acknowledgments

The assistance of Glenn MacGougan and Lie Dong in thecollection and processing of the GPS fading data isgratefully acknowledged.

8 References

1 Federal Communications Commission: ‘Fact Sheet – FCC Wireless911 Requirements’. http://www.fcc.gov/911/enhanced/factsheet_requir-ements_012001.pdf, United States Federal Communications Commis-sion, January 2001

2 Brisco, C., and J.I. Alonso: ‘Statistical and empirical models for LMSCfading based on GPS measurement’, First International Workshop onRadiowave Propagation Modelling for SatCom Services at Ku-Bandand above, October 1998, ESTEC, Noordwijk, The Netherlands,http://www.estec.esa.nl/xewww/cost255/ws/98c08/98c08pgm.html

3 Akturan, R., and Vogel, W.J.: ‘Path diversity for LEO satellite-PCS inthe urban environment’, IEEE Trans. Antennas Propag., 1997, 45, (7),pp. 1107–1116

4 Karasawa, Y., Minamisono, K., and Matsudo, T.: ‘A propagationchannel model for personal mobile-satellite services’. Progress ofElectromagnetic Research Symposium of the European Space Agency(ESA), Noordwijk, The Netherlands, July 1995, pp. 11–15

5 Loo, C.: ‘A statistical model for a land mobile satellite link’, IEEETrans. Vehicular Technol., 1985, 34, (3), pp. 122–127

6 Macgougan, G., Lachapelle, G., Klukas, R., Siu, K., Garin, L.,Shewfelt, J., and Cox, G.: ‘Degraded GPS signal measurements with astand-alone high sensitivity receiver’. Proceedings of Institute ofNavigation’s 2002 National Technical Meeting, San Diego,California, January 2002, pp. 191–204

7 Wertz, J.R.: ‘Spacecraft attitude determination and control’(D. Reidel Publishing Company, Dordrecht, 1978)

8 Cowell, W.: ‘Sources and development of mathematical software’(Prentice-Hall, Inc., Englewood Cliffs, 1984)

9 Goldhirsh, J., and Vogel, W.J.: ‘Handbook of propagation effects forvehicular and personal mobile satellite systems – overview ofexperimental and modeling results’, The John Hopkins University,The University of Texas at Austin, http://www.utexas.edu/research/mopro/index.html, December 1998, pp. 10-5 to 10-11

Table 3: Comparison of UTSFM parameters for urban Tokyo and urban Calgary/Vancouver (satellite elevation angles, a, of321 and 351 respectively)

Fade state and distribution Parameter Urban Tokyoreference [9]

UrbanCalgary/Vancouver

Clear Rice distribution C(a) 0.51 0.31

KC,Rice 7.7dB 13dB

Shadowed Loo distribution S(a) 0.07 0.21

KS,Loo 13dB 50dB

ms,Loo 10dB �8.2dB

sS,Loo 3dB 1.1dB

Blocked Loo distribution B(a) 0.42 0.48

KB,Loo 27dB 47dB

mB,Loo 20dB 11dB

sB,Loo 7.3dB 8.3dB

252 IEE Proc.-Microw. Antennas Propag., Vol. 150, No. 4, August 2003