Carrier Frequency Effects on Path Loss

Mathias Riback, Jonas Medbo, Jan-Erik Berg, Fredrik Harrysson and Henrik AsplundEricsson Research, Ericsson AB, Sweden

Email: {mathias.riback, jonas.medbo, jan-erik.berg, fredrik.harrysson, henrik.asplund}@ericsson.com

Abstract- To study the carrier frequency effects on path loss,measurements have been conducted at four discrete frequenciesin the range 460-5100 MHz. The transmitter was placed on theroof of a 36 meters tall building and the receive antennas wereplaced on the roof of a van. Both urban and suburban areas wereincluded in the measurement campaign. The results show thatthere is a frequency dependency, in addition to the well knownfree-space dependency 20 log10(f), in most of the areas includedin the measurements. In non line of sight conditions, the excesspath loss is clearly larger at the higher frequencies than at thelower. A model capturing these effects is presented.

I. INTRODUCTION

2MUGTesttrasmitter Test transmitterSHU# GSM900 GSM1800

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Reliable path loss models are essential when planningmobile communication systems. Several path loss models existthat are valid for the frequency bands used today. Since thesebands are more or less fully utilized, new bands are consideredfor future generation mobile systems. Existing net planningtools and models therefore need to be calibrated for the newfrequency bands. The question is whether the old models canbe used with a simple correction for the free-space frequencydependency 20 log10 (f), or if a more sophisticated model mustbe used in a real scenario.

Several measurements are presented in the literature dealingwith the carrier frequency effects on path loss. The resultsfound in the literature are however not consistent. In [1]path loss measurements were performed at 900 and 1800MHz in different clutter types in Sweden. It was found thatin urban areas the frequency dependency was approximately23 log0 (f). In other clutter types such as suburban andsemi-open the dependency was found to be approximately33log10(f). Path loss measurements in the frequency range450 MHz to 15 GHz for urban areas in Japan are presented in[2]. In this paper it was found that the frequency dependency isapproximately 20 log10 (f), which agrees rather well with theresults for urban areas in [1]. In [3] path loss measurementsat 955 MHz and 1845 MHz were performed in urban areasin Denmark. It was found that the mean difference in pathloss between the two frequencies was approximately lOdBwhich corresponds to a 35log10(f) frequency dependency.This is not consistent with the results from urban areas in[1] and [2]. The same lOdB difference between 900 MHz and1800 MHz was found in suburban areas in [4]. In [5] thepath loss at four frequencies in the range 430-5750 MHz iscompared in an urban environment. It is found that the basictransmission loss slope (e.g. how much the path loss increaseswith distance) increases with frequency. This indicates that afrequency dependency in addition to 20log10(f) exists.

0-7803-9392-9/06/$20.00 (c) 2006 IEEE

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Due to this ambiguity in the literature a measurementcampaign has been conducted measuring the path loss at fourdiscrete frequencies in the range 460-5100 MHz.

II. MEASUREMENTS

The path loss was measured at four discrete frequencies(see table I) almost simultaneously. Four parallel transmitterchains were used to transmit CW (continuous-wave) signals.The output power was approximately +28dBm at the highestfrequency and the power at the other frequencies was set suchthat the received power at 1 meter was approximately the samefor all frequencies. See figure 1 for a schematic overview ofthe transmitter setup. At the receiver four antennas were usedto receive the different CW signals. These signals were thencombined to one signal with wideband combiners and fed toan Agilent E8358A network analyzer via a wideband lownoise amplifier (LNA). The LNA had a frequency range of0.1-6 GHz, 36dB gain and a noise figure of less than 1.3dBover the entire band. The position of the receiver was loggedwith a GPS unit. See figure 2 for a schematic overview of thereceiver setup.The network analyzer used a segmented sweep to measure

the received power at the different frequencies. The sweep

2717

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TABLE ITHE FOUR CARRIER FREQUENCIES USED.

fl M f820 M f1 MHz f547460.025 MHZ | 883.200 MHZ 1858.80 MHZ | 5106.75 MHZ

TABLE IIMEASURED TOTAL ANTENNA GAIN (GCnt = Gt, + Gr,).

Gant (fie) Gant (f2 ) Gant (f3C) Gant (f4 )3.4dBi 3.7dBi 3.8dBi 3.5dBi

consisted of 804 points in total. At each frequency a zero-span sweep (time sweep) of 201 points was performed. Thetotal sweep time was approximately 0.26 seconds and the timebetween two consecutive sweeps, including data storage, wasapproximately 0.4 seconds. The sampling frequency within asweep was approximately 3 kHz and the fast fading couldbe followed as long as the maximum Doppler frequencywas below 1.5 kHz. The time between the last sample of afrequency in one sweep and the first sample of that frequencyin the next sweep was 0.75 0.4 = 0.3 seconds. At a normalmeasurement speed of 15 m/s this corresponds to less than4.5 meters which means that the slow fading can be followedbetween the sweeps. The conclusion is that the fast fadingwas followed within each sweep but not from sweep to sweepwhich however the slow fading was.

A. Antennas and FiltersAt both the transmitter and the receiver and at all fre-

quencies half-wave vertical dipole antennas were used. Theadvantage of using half-wave dipole antennas is that theelevation antenna pattern will have the same shape at allfrequencies. In many other measurement campaigns conductedto investigate the carrier frequency effects on path loss (i.e. [1],[5]) different high gain antennas have been used on differentfrequencies. This results in different elevation antenna patternson different frequencies. In this case a measured path lossdifference in addition to 20log10(f) can be a true path lossdifference but it can as well be a difference in antenna gainat the elevation angle of the incoming rays. The same holdsfor broadband antennas like practical bicones which will havemaximums and minimums in the antenna gain at differentelevation angels for different frequencies. By using separatedipoles this uncertainty is removed. In [2] separate dipoleswere used but they were places close to each other to make thepropagation environment as similar as possible. The problemwith that solution is that two antennas placed close to eachother have a mutual coupling and the antenna patterns areaffected. In our measurements the dipoles were separated atleast 1.5 meters at the receiver and 1 meter at the transmitterto reduce the coupling effects. This makes, however, thepropagation environment less similar but less coupling is toprefer and by collecting a lot of data over large distances theeffects from the difference in propagation environments willaverage out.At the receiver the four dipoles were isolated using filters

before combining the signals. This is to ensure that themeasured received power at one frequency is collected by theantenna intended for this frequency. Without the filters the 450MHz half-wave dipole will, as an example, collect power at

900 MHz since it is a full-wave dipole at that frequency.The transmit antennas were placed 2 meters above the

roof of a 36 meter tall building in Kista, outside Stockholm.They were all mounted on a wooden bar approximately 2meters above the roof. The receive antennas were mountedapproximately 1 meter above the roof of a van and the totalheight above the ground was 2.9 meters.

B. CalibrationThe measurement setup was calibrated by measuring the

received power, Pcal, with the transmit cable ends connecteddirectly to the receive cable ends. The antenna gains were alsocalibrated by measuring the path loss at 1 meter and comparingthese measurement results to the theoretical path loss at 1meter. Both calibration measurements were conducted bothbefore and after the measurement campaign to ensure that itwas no drift in the equipment during the measurements. Theagreement between the two calibration occasions was verygood and mean values from the two calibrations were usedin the analysis. See figure 4 (top) for mean measured pathloss at 1 meter. Measured total antenna gain is presented intable II and should be compared to the theoretical value fortwo dipoles which is 4.3dBi. The measured path loss in dBcan after the calibration be expressed as

Lmeas Pcal -Pmeas + Gant, (1)

where Pmeas is the measured power at the receiver in dBmand Gant is the total antenna gain at the receiver and thetransmitter.

C. Drive routes

The measurement campaign was conducted during daytimein the summer with all trees fully leafed. The transmitterwas placed on the roof of one of the tallest buildings in asmall urban area where most of the buildings are rather tall.The routes covered both the urban area where the transmitterwas placed as well as residential and industrial areas inthe surroundings. During the drives, the area between thetransmitter and the receiver consisted of large open fields,forest areas and residential areas. See figure 3 for maps withall routes marked.

III. DATA PRE-PROCESSING

During the measurements the maximum speed of the re-ceiver was approximately 25 m/s which corresponds to aDoppler frequency of 425 Hz at the highest frequency. Sincethe measurement system was able to handle Doppler fre-quencies up to 1.5 kHz, filtering in the Doppler domain waspossible. In every sweep the maximum Doppler frequency was

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Distance [m] Distance [m]

Fig. 3. Maps of the measurement area with routes marked in black. The base station is marked with a red cross.

Measured Path-Loss at 1 m40 Theoretical Path-Loss at 1im

430 -5

10 *-iFrequency [MHz]

115W

O 135

200 400 600 800 1000 1200 1400 1600Sample number

0 m --O-- ~~~~~~~~~~~~C(f"fc)I -C, ~~~~~~~~~~~~~~C(f,f')

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Fig. 6. CDF of C(fi, fj) for the different frequencies.

Fig. 4. Top: Theoretical and measured path loss at 1 meter. Bottom: Measuredpath loss at 5106 MHz, before and after Doppler filtering.

900

100

120130

0 500 1000 1500 2000 2500 3000 3500 4000 4500Traveled distance [m]

Fig. 5. Example of measured frequency compensated path loss (absolute pathloss at f j and 20 log10 (f) dependency removed at all other frequencies). Top:Before smoothening Bottom: After smoothening.

determined and the useful part of the signal was filtered outresulting in a SNR gain of 5-10dB. See figure 4 (bottom)for an example of SNR gain. Before the carrier frequencyeffects on the path loss were analyzed the received powerwithin each sweep was averaged to remove the fast fading.To better visualize the difference in path loss at the differentfrequencies a running median of length 10 samples wasapplied to the mean values (one mean value per frequency andsweep). See figure 5 for an example of measured 20 log10 (f)-compensated path loss before and after smoothening. At thehighest frequency the received signal power was sometimesclose to or below the noise floor. Samples with low signal tonoise ratio were removed from the analysis.

IV. ANALYSIS

When comparing the path loss on the different frequenciesthe expected free-space difference 20loglo (f) was removedand the difference studied can be expressed as

D (fi, fj) = Lmeas (fi) -Lmeas (fj) + 20 logO(to ) (2)

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TABLE IIIEXAMPLE VALUES OF C(fi, fj).

Clutter type | C(l 2)| (2 3) | C(3 f C)Typical suburban 30 27 22Typical urban 24 16 21

All data 30 23 23

where fi and fj are the two carrier frequencies being com-pared and Lmeas(fi) and Lmpns(fj) are the measured pathloss on these frequencies in dB.The general trend is that an increase in frequency on

average gives an increase in path loss that is larger thanthe free-space frequency dependency 20 log10 (f). Assumethat the measured frequency dependency can be expressedas C(fi, fj) loglo(fj fi). The function C(fi, fj) can then becalculated as

C(ft, fj) = 20 D(fi, fj)log (fj)'

(3)

where D(fi, fj) is the mean value of the difference. Values ofC(fi, fj) are presented in table III for one typical suburbanand one typical urban route. The result when using all availablemeasurement data is also presented. It is seen from these ex-

amples that the frequency dependency is stronger in suburbanareas than in urban areas. This trend is consistent with theresults found in [1]. Note that dependencies even smaller than20 log10 (f) was found in urban areas. Cumulative distributionfunctions (CDFs) of C(fi, fj) from all routes is presented infigure 6.By following how the frequency dependency changes along

the routes it is found that the coherence distance for C(fi, fj)is very short. See figure 7 for plots of C(fi, fj) along one

route. It is therefore very hard to predict the differenceD(fi, fj) in a specific location and to give a physical ex-

planation to the difference. Since the difference in addition to20 log10 (f ) does exist, the propagation must include frequencydependent effects such as diffraction and propagation throughvegetation.

Instead of studying the difference at specific locations thegeneral trends and statistical properties of the difference were

further studied. It was found that the difference in path loss isa function of the excess path loss which is defined as

Lexcess (f ) = Lmeas (f ) -Lf (dmeas, ), (4)

where Lf (dmeas, f) is the theoretical free-space path loss atdistance dmeas (given by the GPS data) and frequency f. Thetheoretical free-space path loss is given by

Lf (d, f) 20 log1o (-) + 20 log1o (d) + 20 log1o (f), (5)

where c is the speed of light, d the distance in meters andf the frequency in Hz. The excess loss used in the analysisis the mean excess path loss at all frequencies, Lexcess. Infigure 8 is D(fi, fj) (with data from all routes) plotted as a

Fig. 7. Example of loglo(f) dependency along one typical urbanroute. The BS is marked by a red cross.

function of Lexcess for the different frequencies. It is seen

that D(fi, fj) increases with increased excess path loss. Astraight line is fitted to the measurement data in the least-squares sense with the restriction that it should pass through(0, 0). This is intuitive since zero excess path loss should givea 20loglo(f) dependency. This means that only the slope ofthe line, K, is fitted to the data.

A. Model

As discussed above the deviation from the 20 log10 (f)dependency is increased with increased excess path loss. Inthis section a model capturing this behavior is presented.The model converts a known path loss at one frequency toan expected path loss at another frequency. Let the knownfrequency be fo and the known path loss at this frequency isthen L(fo). The expected path loss at frequency f can thenbe expressed as

L (f fo, L(fo)) L(fo) + 20 log1 (f)

-K(fo,f)[L(fo)-Lf(fo)], (6)

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1 Vit- -_ rli.ri,tiri- itteci (3aussian ciistroDutionI M Histogram of deviation

0 5 10 15 20Deviation from model [dB]

Fig. 8. Difference in path loss between ff and the other frequencies inaddition to 20loglo(f) as a function of the mean excess path loss at allfrequencies. The red lines are fitted to the data in the LS sense and passes

through (0,0).

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V. SUMMARY AND CONCLUSIONS

The carrier frequency effects on path loss have been studiedand it is found that the path loss on average increases more

TABLE IVMODEL PARAMETERS.

Fig. 10. Histograms of deviation from the model.

than the free space dependency, 20 lglo (f), when the carrierfrequency is increased. This additional loss is quite largewhen going from 450 MHz to 900 MHz which results in a

30loglo(f) dependency on average. When going from 900MHz to 1800 MHz or from 1800 MHz to 5100 MHz theadditional loss is smaller and a 23loglo(0f) dependency isseen on average. In urban areas the deviation seems to besmall over the whole frequency range which is consistentwith [2]. Further analysis shows that the additional loss alsois a function of the excess path loss. A larger excess pathloss results in a larger additional loss. A model capturing thisbehavior is presented. One open issue is whether the modelcan be extrapolated outside the range of the measurements.Additional measurements are needed to answer this question.Since different results were found in urban and suburban areas

the model can be extended to have different parameters fordifferent clutter types. Now the model captures the averageeffects. More measurement data is however needed to be ableto extend the model.

It is established that the propagation depends on the carrierfrequency but it was not possible to identify the mechanisms.This is due to the fact that the difference in path loss betweenthe different frequencies seems to change very fast whichmakes it difficult to associate a difference in path loss witha certain propagation phenomena.

REFERENCES

[1] L. Melin, M. Ronnlund, R. Angbratt, "Radio Wave Propagation - AComparison Between 900 and 1800 MHz", 43rd IEEE VTC Conference,New Jersey, USA, 1993.

[2] Y. Oda, R. Tsuchihashi, K. Tsuenekawa, M. Hata, "Measured PathLoss and Multipath Propagation Characteristics in UHF and MicrowaveFrequency Bands for Urban Mobile Communications", 53rd IEEE VTCConference, 2001.

[3] P.E. Mogensen, P. Eggers, C. Jensen, J.B. Andersen, "Urban Area RadioPropagation Measurements at 955 and 1845 MHz for Small and MicroCells", Global Telecommunications Conference (Globecom), pp 1297-1302, vol. 2, 1991.

[4] B. Lindmark, M. Ahlberg, J. Simons, S. Jonsson, D. Karlsson, C.Beckman "Dual Band Base Station Antenna Systems", Nordic RadioSymposium - Broadband Radio Access, pp 69-74, 1998.

[5] P. Papazian, "Basic Transmission Loss and Delay Spread Measurementsfor Frequencies Between 430 and 5750 MHz", IEEE Transactions on

Antennas and Propagation, vol. 53, no. 2, Feburary 2005.

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20 30 40 50 60460MHzvs. 1858MHz

20 30 40 50 60460MHz vs. 5106MHz

20 30 40 50 60Excess path-loss [dB]

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