Modeling Received Signal Strength Measurementsfor Cellular Network Based Positioning

Jukka Talvitie, Elena Simona Lohan, Member, IEEEDepartment of Electronics and Communications Engineering

Tampere University of TechnologyTampere, Finland

jukka.talvitie@tut.fi, elena-simona.lohan@tut.fi

Abstract—This paper introduces a novel approach to modelReceived Signal Strength (RSS) measurements in cellularnetworks for user positioning needs. The RSS measurements aresimulated by constructing a synthetic statistical cellular network,based on empirical data collected from a real life network. Thesestatistics include conventional path loss model parameters,shadowing phenomenon including spatial correlation, andprobabilities describing how many cell identities are measured ata time. The performance of user terminal positioning in thesynthetic model is compared with real life measurement scenarioby using a fingerprinting based K-nearest neighbor algorithm. Itis shown that the obtained position error distributions match wellwith each other. The main advantage of the introduced networkdesign is the possibility to study the performance of variousposition algorithms without requiring extensive measurementcampaigns. In particular the model is useful in dimensioningdifferent radio environment scenarios and support inpreplanning of measurement campaigns. In addition, repeatingthe modeling process with different random values, it is possibleto study uncommon occurrences in the system which would bedifficult to reveal with limited real life measurement sets.

Keywords-component; cellular network; positioning; receivedsignal strength; radio environment modeling

I. INTRODUCTION

Although the availability and performance of GlobalNavigation Satellite System (GNSS) based positioning serviceshas been continuously improved, interest in cellular networkbased positioning has not diminished. Many applicationsassociated to safety, emergency services, gaming and othercommercial services can be operated using cellular basedpositioning [1][2]. In addition, security services, (e.g. inmonitoring stolen property) and invoicing applications, such astraffic tariff collection, are possible use cases for cellular basedpositioning. Moreover, as indicated in [3], a single positiontechnology is unable to meet all the requirements set by theindustry, for which reason continuing research over variety ofpositioning technologies is necessary.

One of the greatest advantages of cellular based positioningagainst the GNSS is reduced energy consumption. Particularlywith Received Signal Strength (RSS) based methods,positioning can be performed by using the RSS values in thenetwork basic measurement set. Conventionally, there are twoseparate stages in the RSS based positioning: the learning stageand the positioning stage. In the learning stage data is collectedfrom the target area and stored into form of fingerprints

including the location and measured RSS values from each cellidentity (cell ID). Here, with the cell ID we refer to BaseStation (BS) or BS sector that has a unique identity code andRSS value observable from the measurement set. In thepositioning stage, the user terminal position is estimated byexploiting the pre-collected learning data and available RSSmeasurements. Due to high dynamic radio environment, RSSbased methods are applicable mainly in dense urban andsuburban cellular networks.

There are numerous different RSS based positioningalgorithms for cellular networks available in the literature, e.g.[4][5], and most of them are validated with real lifemeasurement campaigns. This is because it is extremelychallenging to simulate realistic RSS measurements in cellularnetworks due to high dynamics in radio network planning andsome obscure network configuration algorithms affecting themeasured RSS values. For example, from the positioning pointof view, it is critical to be able to model the number ofmonitored cell IDs at each measurement location, which is oneof the most essential contributions in this paper.

We propose a synthetic statistical model to create learningstage data (fingerprints) and positioning stage data (userterminal measurements) in cellular networks for userpositioning purposes. The introduced modeling approach isbased on real-life measurements taken from a cellular networkin suburban scenario. Methods of discovering the requiredstatistical parameters from the real life measurements aredescribed thoroughly, which enables the employment of themodel with also other measurement sets. Furthermore, many ofthe used statistical parameters are well known from theliterature (e.g. shadowing standard deviation), for which reasonit is also possible to create different scenarios based onmeasurement results given in the literature.

Section II introduces the exploited network measurementset and defines the modeled radio environment parameters andtheir estimation procedures. Then, based on the achieved radioenvironment statistics, the synthetic network model isconstructed in Section III. Finally, the model is simulated andcompared with real life measurements in Section IV andconclusions are drawn in Section V.

II. RADIO ENVIRONMENT MODELING

A. Real life measurement setThe modeling and results are based on real life

measurements taken in Hervanta suburb, Tampere, Finland,

978-1-4799-0486-0/13/$31.00 ©2013 IEEE

from 3G Universal Mobile Telecommunications System(UMTS) network. The measured data set consists offingerprints which include the fingerprint location (based onGlobal Positioning System (GPS)) and the heard cell IDs andtheir RSS values, based on Received Signal Code Power(RSCP) indicator.

To reduce the size of the required learning data base,fingerprints are compiled into form of rectangular grid usinggrid interval of g=50m. In case that multiple measurementsfrom the same cell ID are heard within a single grid point, themean of the heard RSS values is stored.

B. Modeling RSS ValuesFor simplicity, the modeled radio environment is

considered only in 2D. This is because in typical cellularnetworks, vertical distances are relatively small compared tohorizontal distances, and because no information regarding thenetwork structure (e.g. antenna heights or antenna downtilting)is available. Assuming a traditional single slope path lossmodel [6], the RSS value (in dB) at distance d can be written as

10 log( )P A n d W

where A indicates the RSS value at 1m distance, n is thepathloss exponent, and 2~ (0, )WW N is zero mean Gaussianrandom variable presenting shadowing (or slow fading) withstandard deviation W . Shadowing is induced by obstaclessuch as buildings and hills in the radio path. However, usuallya BS comprises a number of individual sectors, each includingits own directional antenna and cell ID. As a result, theobserved RSS value becomes dependent on measurementcoordinates, not the distance. Now, assuming the BS position atcoordinates (xBS,yBS), the RSS value at (x,y) is given as

1

2 2

( , ) ( ) 10 log( ) ( , ), where

tan , and

( ) ( ) .

BS

BS

BS BS

P x y A n d W x y

y yx x

d x x y y

Here ( )A is the RSS value at 1m distance pointing at thedirection angle . Notice that in stationary network theshadowing variable W(x,y) is considered to be fixed at eachcoordinate (x,y).

Because shadowing is caused by stationary obstacles in theradio path, the impact of the obstacle is affecting similarly innearby coordinates. This distance dependent correlation can bemodeled by an environment specific autocorrelation function[7]. The shape the function depends on the radio environment,and based on the Gudmudnson model, it can be written as [8]

/( ) decord DR d e

where d is the difference of distance and decorD is de-correlation distance which depends on the radio environment.

C. Estimation of Radio Environment ParametersAssuming the simple pathloss model given in (1), pathloss

parameters A and n can be straightforwardly estimated withlinear regression. Here, for simplicity, it is assumed that A isnot dependent on the direction, but the direction dependency isadded only in the BS modeling stage. Although this may seemas rough approximation, majority of the measured RSS valuesare found either in close proximity of the BS or inside thesector. This is because of the drastic drop of RSS levelsoutside the sector, which reduces the probability of havingsuch measurements as shown in Sections III and Section IV

Before it is possible to estimate the path loss parameters,the position of BSs has to be determined to attain d. Here, forsimplicity, the BS position (xBS,yBS) is estimated by taking theaverage of coordinates of Nhigh highest observed RSS values:

1 1

0 0

1 1 andhigh highN N

BS i BS ii ihigh high

x x y yN N

where xi and yi are the coordinates of Nhigh highest RSS valuesof the BS in fingerprint data base with i=0…Nhigh -1. Here it isworth of noticing that it is not essential to estimate the real lifeBS position, but to achieve a good fit for the estimated pathloss models. Moreover, considering real life BS positionswould require 3D modeling with information concerningantenna heights, vertical antenna patterns, and antennadowntilting. Otherwise it would be difficult to reach a good fitwith the distance based path loss model.

Considering a single BS with Nmeas observed RSS valuesand exploiting the path loss model given in (1), themeasurement model can be described as

0 0

1 1

10 0

10 1

ˆ1 10log ( )with ,

ˆ1 10log ( )

meas meas

meas

N N

N

P WA

Hn

P W

dH

d

where Pi, Wi, and di are the RSS value, shadowing value, andthe estimated distance (based on (xBS,yBS)) for the ith

measurement. Now, the least squares estimate for A and n isstraightforwardly given as

01

1

ˆ( ) .

ˆmeas

T T

N

PA H H Hn P

The maximum likelihood (ML) fitted Gaussian distributionparameters for the A and n including all detected cell IDs inthe measurement set are shown in Table I. Notice that thesevalues depend on radio environment, and they are applicable

TABLE I. ESTIMATED RADIO ENVIRONMENT PARAMETER STATISTICS

Parameter mean Standarddeviation Truncation

A [dBm] 10.6 38 [-50, 50]n 3.9 1.5 [2, 6]

W [dBm] 0.0 8.7 [- ]

decorD [m] 124 m 76 m [0, ]

only in the considered scenario and in similar radioenvironments. In addition, the truncation limits shown in thetable are used in the simulations in Section IV to maintainphysical sensibility of the parameters. The correlation betweenA and n is found to be as high as ˆ ˆ,

0.982A n

. Withouttaking this correlation into account in creating synthetic BSmodels in Section III, it is likely to have unrealistic RSSmeasurements in the models.

With the estimated path loss parameters A and n it is nowpossible to study the shadowing statistics. Using (1) theshadowing components can be estimated as

ˆˆˆ ˆ10 log( ).i i iW P A n d

In addition to this, we are interested in the spatial correlation,which is mandatory to study in 2D. Because of this, we haveto consider the coordinate based model W(x,y) given in (2).However, to achieve this, learning data with P(x,y) defined inall (x,y) coordinates would be required. For this reason theRSS values at the missing coordinates are approximated usinglinear interpolation. Then, using the interpolated RSS values,denoted as Pint(x,y), the shadowing values for each (x,y) can becalculated as

ˆˆˆ ˆ( , ) ( , ) 10 log( )intW x y P x y A n d

and the desired autocorrelation function for ˆ ( , )W x y as

( , ) ( , ) ( , )x y x yx y

R W x y W x y

Due to symmetry between x and y, ( , )x yR is close to

circular form (only depending on distance 2 2x y ) and the

de-correlation distance decorD is estimated by taking the meanover x and y components. The ML fitted Gaussian distributionparameters for estimated ˆ

iW and decorD are found in Table I.

III. NETWORK MODELING

A. Base Station Sector ModelingWe consider a 3-sectored BS as a fundamental building

block of the modeled cellular network. For this purpose anantenna with approximately 120 degree beam width is requiredto cover all directions. For the antenna pattern model we use areal life antenna element from Vecima Networks (RWB-80014/120) [9].

First, using the desired radio environment parameters, theaverage RSS values around the BS is created using (2) withoutyet considering the shadowing term W(x,y). Here, the antennapattern effect is included in ( )A by adding the antennaspecified horizontal loss in the used value of A. Notice thatmodeling of A assumes 0dB antenna loss in sector direction.

The diversity and randomness of the radio environment ismodeled with the shadowing parameter W(x,y). As indicated inSection II, W(x,y) is Gaussian distributed and has decorDdependent autocorrelation function given in (3). Consequently,to create W(x,y), we generate independent Gaussian distributedvalues 2( , ) ~ (0, )WW x y N , where W is the desiredshadowing standard deviation. Then, to include the preferredcorrelation into the samples, the result is filtered with

/ 2 2( , )= with ,decord Dx y x yR e d

which is a 2D extension of (3), and whose energy is normalizedto one. Here, the square root is needed, since theautocorrelation function describes second order statistics.

As an example, the process of modeling RSS values aroundone BS sector is illustrated in Fig. 1. In addition, aninterpolated RSS map of a real life BS sector with similarpathloss environment statistics is also given.

B. Network Topology DesignThe baseline for the coverage design of the network is

based on conventional hexagonal layout shown in Fig. 2. Byfixing the employment area size, the cell edge distance (seeFig. 2) defines the density of the network. It is widely knownthat the positioning accuracy is greatly dependent on the cellcoverage size. This is why cellular based positioning methodsare more accurate in dense urban areas compared to rural areas.

In practice, cellular network topology is not homogenous,but the BS density varies along with the local communicationsneeds. For example, public places like market squares andshopping malls are often carried out with denser networkplanning compared to common residential areas. These type oflocal variations are modeled by adding random fluctuation tohexagonal grid based BS positions (xBS,hex, yBS,hex) as

, ,, ,BS BS hex x BS BS hex yx x w y y w

where 2~ (0, )i BSposw N . Similarly, it is possible to createvariations also to sector directions, but it is not considered here.

Although the physical BS position is the same for allsectors, due to antenna height, antenna downtilting, and verticalantenna pattern properties, the highest measured RSS for eachsector on the ground level is further away from the physicallocation. Without taking this issue into account, the maximumRSS values of the sectors would be located in the samecoordinate. To overcome this issue, we create virtual BSpositions for each sector (i.e. cell ID) by shifting the originalBS position into the direction of the sector as follows:

,cos( ), sin( )BS BS sec BS BS hex secx x w y y w

Figure 2. Hexagonal cellular network topology

Figure 1. Illustration of BS sector modeling process (values in dB): average RSS value map without shadowing (upper left), randomly created correlatedshadowing samples (upper right), complete RSS value map with shadowing (lower left), and real life RSS measurement from a single BS with same radioenvironment parameters and BS position (lower right)

-500 -400 -300 -200 -100 0 100 200-300

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where secw is taken from a truncated Gaussian distribution as2~ (0, ), with 0sec sec secw N w . These virtual BS positions are

then used in the network model for each cell ID.By using the above described methods a network is created

with the a set of BS sectors including simulated RSS values ateach point of the map. However, in practice learning datacannot be collected in all locations due to building plan of thearea. Moreover, most of the measurements are forced to betaken from streets and walkways. In the model this isconsidered by utilizing a mesh-like street plan and maintainonly every Nstr

th grid point in x and y directions (i.e. a grid pointis maintained IF mod(x, Nstr·g)=0 OR mod(y, Nstr·g)=0, where gis the grid interval).

C. Defining the Number of Heard Base StationsAlthough in the simulation model it is possible to define the

RSS for each cell ID at each coordinate, in real-life only smallpart of the RSS values are measured at a time. The number ofmonitored cell IDs is dependent on obscure networkfunctionalities that are not expected to be known beforehand.However, the number of monitored cell IDs has significanteffect on the positioning performance, and therefore, it has tobe taken into account in the simulation environment.

In the ideal case, the network should always listen to the

cell ID with the highest measured RSS value. However,because for needs of certain network functionalities, such ashandovers, typically more than one cell IDs are monitored at atime. To simplify the design, it is assumed that the measuredRSS values in the terminal are always the highest availableones. Thus, it is required to model only the number of heardcell IDs and then pick up Nhear measurements with highest RSSvalues. Moreover, the modeling should be different for thelearning stage and the positioning stage. In the learning stageusually several measurements are collected within one gridpoint, which increases the probability of hearing more cell IDsthan by only taking a single measurement as done in thepositioning stage.

We start the modeling of Nhear by analyzing real lifelearning data. First, the data is organized based on the numberof stored cell IDs per fingerprint. From here we define theoverall probabilities for observing Nhear cell IDs, denoted as

hearN . In addition, we study the RSS distributions for each Nhear

value and calculate corresponding ML fitted Gaussiandistribution parameters

hearN andhearN . The corresponding

processing is performed also for the positioning stage data,where terminal measurements are used instead of fingerprints.The ML fitted Gaussian distributions of observed RSS valuesfor each Nhear, weighted with

hearN are shown in Fig. 3 for thepositioning stage data. It can be clearly seen that the larger arethe RSS values in the measurement set, the less cell IDs areusually measured at a time and vice versa. This supports theintuition of monitoring more cell IDs in cases where no highquality connection is available (e.g. to be better prepared forhandovers). All distribution statistics regarding the fittedGaussians are given in Table II.

The fundamental thinking behind the modeling is torandomly pick up Nhear highest RSS measurements from the

TABLE II. DISTRIBUTION STATISTICS FOR MODELING THE NUMBER OF MONITORED CELL IDS

Nhear 1 2 3 4 5 6 7 8 9 10Learning

stage0.13 0.26 0.23 0.18 0.11 0.07 0.014 0.004 0.001 0.001

μ [dB] -66 -75 -78 -83 -87 -88 -89 -91 -95 -88 [dB] 14 15 13 13 11 11 10 8 5 4

Positioningstage

0.25 0.33 0.18 0.12 0.09 0.028 0.002 - - - [dB] -54 -63 -70 -74 -78 -84 -83 - - -

μ [dB] 7 11 11 12 9 8 11 - - -

Figure 3. Distribution of RSS values for different Nhear cases

-110 -100 -90 -80 -70 -60 -50 -40 -300

0.002

0.004

0.006

0.008

0.01

0.012

0.014

RSS [dB]

prob

abilit

yde

nsity

1 heard2 heard3 heard4 heard5 heard6 heard7 heard

synthetic measurement model at each coordinate (x,y) based onthe distributions and probabilities shown in Table II. First, wedefine the set of RSS values (one RSS from each cell ID) ateach coordinate (x,y) as 0 1 1, ,...,

BSP NP P P , where Pi aresorted in descending order, and NBS is the number of modeledBS sectors. Now, the problem is to define how many RSSvalues are preserved in the set. Based on likelihood principle,the average log-likelihood of observing Nhear cell identities canbe formulated as

0 1 1

21

220

( , ,..., | , , )

1 log exp22

hear hear hear hear

hearhearhear

hearhear

N N N N

NN iN

ihear NN

L P P P

P

N

wherehearN ,

hearN , andhearN are the weight, mean, and

standard deviation for the Gaussian distribution of observingNhear RSS values described in Table. II. The likelihood iscalculated for all distributions, which means Nhear,max=10 for thelearning data and Nhear,max=7 for the positioning data. Now, bynormalizing the sum of Nhear,max likelihoods to one, we haveapproximate mass density probability function p(Nhear) forobserving Nhear cell IDs given a measurement set P as

,max

0 1 1

0 1 11

( , ,..., | , , )( )

( , ,..., | , , )

hear hear hear hear

hear

N N N Nhear N

k k k kk

L P P Pp N

L P P P

By using p(Nhear), we are able to generate a stochastic Nhearvalue for each fingerprint and user measurement.

IV. SIMULATION MODEL

To validate the proposed synthetic network model, wecompare the positioning performance of a synthetic model withthe performance using real life measurements. As thepositioning algorithm we choose the simple K-nearestneighbors method [10], since it is widely recognized in thecontext of cellular based positioning. In order to maintain thefocus on the RSS measurement modeling, studies consideringother positioning methods are considered out of the scope ofthis paper. Here, the Euclidian distance between the heardmeasurement set P and each fingerprint is calculated as

12

,0

( )measN

m m i ii

D P P

where Pm,i is the RSS value of ith cell ID in mth fingerprint. Incase that the observed cell ID is not heard in the fingerprint, itis neglected in the calculation. Then, the position estimate isgiven as the mean of Knearest fingerprint locations with smallestEuclidian distances as

1

0

1ˆ ˆ( , ) ( , )nearestK

k kknearest

x y x yK

where k includes the fingerprint indices with the smallestEuclidian distances. For simplicity, we consider static userposition estimates, meaning that the estimates are not filteredor processed in any way. This is actually necessary, sincecurrently we have not considered any time correlation for thestochastic Nhear value, although it is present in real life scenario.

The synthetic network topology is created by using themethods described in Section III. The deployment area size isset to be 2km x 2km, similar to the real life data set. The celledge distance is adjusted to 200 m to achieve comparable BSdensity with the real life data. Both the deviation of thetopology based BS position BSpos and the deviation of virtualBS position sec is determined as 100m.

To model the building plan of the area, we use Nstr=3 whichresults in a block size of 150m (with the used grid interval of50 m). This is approximately the average block size in thestudied area including streets and walkways.

The shape of the synthetic user test track is inherited fromthe real life user measurement track, which includes 3413measurements taken at approximately on 1s intervals. The trueuser position is based on GPS measurements, which offerssatisfactory position reference compared to the studied cellularpositioning accuracy. The length of the track is approximately4.3km and it introduces a good variety of different RSSmeasurement distributions. Notice that although the shape ofthe track is similar to the real life track, the surroundingcellular network is entirely different, apart from predefinedstatistical similarities. To model variations in the RSS values

Figure 4. Distribution of Nhear in the learning stage

Figure 5. Distribution of Nhear in the positioning stage

1 2 3 4 5 6 7 8 9 100

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Figure 6. Cumulative user positioning error for synthetic model and real lifemeasurements

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Synthetic model (mean and standard deviation over 100 trials)Real life data

observed by the user terminal (orientation loss, body loss, etc.),white Gaussian noise with standard deviation of 1 is added ontop of the synthetic model based RSS values.

In Fig. 4 and Fig. 5 the distributions of Nhear for the learningstage data and the positioning stage data are compared betweenreal life measurements and the synthetic model over onesimulation trial. It can be seen that the synthetic model matchesrather well to the real life data. However, more interesting iscomparison of user positioning accuracy between the syntheticmodel and the real life measurements. Thus, the cumulativedistribution of user position error for both of the cases is shownin Fig. 6, where the solid blue curve shows both the mean andthe standard deviation of the results over 100 trials (i.e.approximately 68% of the results are within the error bars). Theresults are noticeably close to each other, especially taking intoaccount the simple modeling structure compared to thecomplexity of real life network design. This clearly shows thatthe positioning performance can be adequately dimensionedand approximated with relatively simple computer simulations.

V. CONCLUSION

In this paper we developed a stochastic cellular networkmodel for approximating network based user positioningperformance. The model was constructed based on empiricalstudies which included statistical analysis of radio environmentparameters, design of network topology and BS sectoring, andmodeling of a stochastic approach of deciding how many cellIDs can be heard at a time. It was shown by simulations thatthe constructed model has very similar position errordistribution with the real life scenario. Although the syntheticmodel enables adequate approximation of the positioningperformance, it cannot replace real life measurements.However, using the proposed model, the research can be easily

extended to different radio environment scenarios withoutperforming extensive measurement campaigns. In addition, themodel can be used in the problem dimensioning, and thereforehelp in planning of measurement campaigns.

ACKNOWLEDGMENT

This research was partly funded by Nokia Inc. and by theAcademy of Finland, which are gratefully acknowledged. Theauthors are grateful to Dr. Tech. Lauri Wirola and Dr. Tech.Jari Syrjärinne for their support and advice.

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