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2006 IEEE Ninth International Symposium on Spread Spectrum Techniques and Applications

On

the

Number of Clusters

in

Channel Model

Keziban Akkaya, Celal Alp Tunc, Defne Aktas and Ayhan Altintas

Department of Electrical and Electronics Engineering, Bilkent University Bilkent, Ankara, Turkey, TR-06800

Email: keziban@ee.bilkent.edu.tr

Abstract- Typically, scatterers in an environment are not spread and rms delay spread (RDS). We use a geometric distributed uniformly but rather observed to occur in clusters. channel model based on

COST259

for an outdoor radio envi-Identification of clusters is an issue under discussion. To this ronment. Note that in the

COST259

model,

NoC is a random

end, we study the effect of number of clusters on channel . . '

model through computer simulations. We focus on a geometric parameter. However, in this paper, fixng a scatterer scenario, stochastic directional channelmodel based on COST259. Fixing we group the scatterers into varying NoC and compute the a scatterer scenario, we calculate root mean square delay and rms angular and delay spreads of the corresponding channel angular spreads when scatterers are grouped into varying num- model.

bers of clusters and study how sensitive these parameters are to

the number of clusters used inthis channel model. II. STRUCTURE OF THE SYSTEM

I. INTRODUCTION We consider a circular cell of radiusRceii where base station

Forthe improvement of existing mobile radiosystems, real- (BS) isplacedat the center of the cell (origin). Mobile station istic channel models arerequired. Inthis work,we concentrate (MS) can be assumed to be located at any point in the cell.

on a geometric stochastic channel model based on COST259 Weassume anumber of scatterers are distributedoverthe cell [1]. Inthis model theraypathsare coming from thescatterers area. These scatterers are groupedinto clusters. Each scatterer distributed in the cell. Number and the density of scatterers inside the cluster represents a single multi-path component. differ according to the environment. From the experimental The geometrical representation is given in Fig. 1.

data, it is observed that scattererstend to occurin groups [2]. Therefore, the scatterers are grouped into clusters. Handling the channelby clustering ofscatterersenablesus toget a more

simplified approach and physically appealing picture.

Clusters ofscatterersinapropagation environmentaretypi- Far

cluster

m

callyidentifiedthroughchannelmeasurements. Toestimate the of scatterers

location of clusters throughout the cell,oneapproach isto use BS

the angle of arrival data from the measurements. The clusters

are then specified according to their contribution to the total R

receivedpower [3].According to measurementresults, cluster cell

locations and parameters such as propagation delays, angles of arrival and departure for the scatterers within each cluster

canbe modeledusing appropriateprobability distribution func-tions. Afterwards, theimpulseresponseof thegeometrybased

stochastic channel model is evaluated using theseparameters

[4]. COST259 is one of the geometric channel models and

its parameters are based on the number and the location of at

tranmoite s.ign

a

lav the bas saion daies

clusters, and the existence ofvisibility regions [5]. Since the athemblsaiowthaprcurdlywihdpns

clusters,and. .

of..visibility.region

sens.

Sitivitye

on the

distance signal

travels. The

delay

is calculated for

clustering

is the basic concept of

modeling,

the sensitivity each scatterer inside each cluster. First, we find thedistances

of the channel model to how the scatterers are grouped into from the cluster center to the base

station

and

mobile station,

clusters~~~~~~~

imo.n.Teefc

is fclseigoikcpct separately. The total path length

iS

the sum of these

distances

is examined in [6]. hile examining the ffect of clustering

(dy).

Then, we find the

corresponding

delay

(Ta)

for this path the analytical expressions for angle and delay spread are

important to characterize the channel [7]. Using angle and as

delay spreads, clusters aredefined within the environment and

n=-(1)

the effect of far clusters on root-mean-square (rms) angular where c is the speed of light. The propagation delay associated

spread anchannel apacity s discussd in [8]

with

the kth scatterer

in

nth

cluster

is given

as Our aim in this study is to investigate the effect of number

of clusters (NoC) used in the channel model on rms angular Tn,1k Tn +

Tadd,m,kc

(2) 0-7803-9780-0/06/$20.00©)2006 IEEE 6

(2)

where

Tadd,m,k

is the additional delay for the corresponding and4 comparethe RDS as a function of NoC for two different scatterer. The additional delay for each scatterer inside the mobile locations andtwo values of total number of scatterers cluster is modeled as aLaplacian distributed random variable (NofSc). For the computation of rms values the results are

with probability density function (pdf) [4]: averaged over 2,000 realizations.

f(Tadd,n,k) = Vexp 2-d Tadd,n,k ) (3) 2000 ScattererGeometry

Therms delay spread is then computed as [9]:

1500

En,k -,

(ZnhkTn,kN

()1000

Nt E 2 500

where N t is the total number ofscatterers. E

0-

~~~x

Since COST259 is adirectional channel model, we needto BS

compute the angle of each multipath component. Firstly, the -500 *

angle between the centerof the cluster and the mobile station is calculated and denoted by -. Then, the angle of arrival

corresponding tothekth scattererin nth cluster is found from -1500- X

[4] as MS

-2000

0rn,k =Yo +CPadd,n,k (5) -2000 -1500 -1000 -500 0 500 1000 1500 20000

x(m)

wherefadd,n,k isthe additional shift inangle of arrival for the (a) The scenario where 200 scatterers are randomly

kth scatterer. This angle is also assumed to have aLaplacian distributed throughout the cell.

distribution. The rms angular spread is computed ina similar

fashion as therms delay spread. 10

The impulse response of the channel is then obtainedas: 9

N, N, 8

H(t, o)

=

E

E [ei

0mk(t

-

Tn,)(-

On,k)]

(6) 7

n=1k=1

where NCdenotes the number of clusters and Ns denotes the -.6 number of thescattererswithin the cluster and

On,k

is thephase 5

shift associated with the {n, k}th scatterer and is modeled as

uniformly distributed.

3-III. THEMETHOD FOR CLUSTERING OF THE SCATTERERS

2-Typically the scatterers are notdistributed uniformly within 1

the cell area. However, it is usually not clear how to group

the scatterers into clusters for a given scenario. -50 0 50 100 150 200 250 We usek-means algorithmtogroup agivensetofscatterers Angle (degree)

into NC clusters [10]. In the k-means algorithm grouping of (b) Delayvsangledistributionfor the scenario

consid-scatterers into NC clusters is based on the relative Euclidean ered

distances of geometric centroids of clusters to each other. In Fig.2. Scatterer scenario. a recent paper, k-means algorithm with a different distance

metric is usedtoidentify clusters frommeasurementdata [11]. From

Figs.

3 and

4,

it is observed that as NoC increases,

In order to study the effect of NoC used in the channel the RDS

quickly

converges tothe

limiting

value. The

limiting

model onchannel statistics wevarythe number of clusters

Nc,

value

corresponds

to the case where each individual scatterer

from 2 to Nst the number of total scatterers, andcompute the is considered a cluster, i.e.,

Nc

=

Nst

It is noted that the

RDS andrms angular spread for each value ofN_. Note that limiting value depends on the number of scatterers (NofSc),

NC= s corresponds to the case where each scatterer is a as shown in Figs. 3 and 4, since the scatterer locations are

cluster itself. different in the two scenarios. However, when NoC is small

(e.g. less than 20), the RDS is more dependent on NoC, since IV. NUMERICALRESULTS path delays of scatterers inside a cluster do not approximate

The scatterer scenario considered is illustrated in Fig. 2 the actual delay values close enough. It should be noted that (a). Radius of the cell (RC) is taken as 2km. Two different most geometric channel models such as C0ST259 assumes

scenarios are considered where the mobile station is located small NoC.

at (0,-500) and (0,-1500), so that the mobile distance from the Results fortherms angular spread are slightly different from base station (MD) is 0.5km and 1.5km, respectively. Figs. 3 RDS. Observing Figs. 5 and 6, it is seen that the rms angular

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1.5 4.5 1.4 -NofSc=100; MD/RC=0.75 4 -NofSc=100; MD/RC=0.75 NofSc=100;MD/RC=0.25 NofSc=100;MD/RC=0.25 1.3

-_______________3_______________5_______

3 1 10.1

~0.

9 0.6 0.5 0.5 0 -0 10 20 30 40 50 60 70 80 90 100 0 10 20 30 40 50 60 70 80 90 100

Numberof Clusters Number of Clusters

Fig. 3. RDS for total number ofscatterers isequalto100. Fig. 5. Rms angleof arrival spreadfor total number of scatterers isequal

to100.

spread

varies

notably

around the

limiting

valueas afunction of

NoC. This variation is more

pronounced

for low NoC values.

45-So the channel is more

dependent

on

clustering compared

to 4 -Nfc20 DR07

the RDS results. This may be due to the fact that in k-means No m ber0of

0.5~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.

algorithm,

clusters are selected based on Euclidean distance

360

metric only. Cluter

2.5__ __ _ _ _

~1.5

1.5

Fig. 4. RDS for totalnumberofscattererNofSc=200; MD/Re=0.75 1

1.4NofSc=200;MD/RCm0.25

1.3

~~~~~~~~~~~~~~~~~~~~~~~~~~~0.5

1.3

0 20 40 60 80 100 120 140 160 180 200

1.1 Numberof Clusters

C0.9tFig. 6. Rms angleofafival spreadfor total number ofscatterers isequal

_to 20 0

0.7-

0.6-study how

sensitivethe

rms

angular spread

is more sensitive to the number of

0 20 40 60 80 100 120 140 160 180 200 clusters used in the channel model. Number of Clusters

ACKNOWLEDGMENT Fig.4. RDS for total number ofscatterers isequalto 200.

This workhas been conducted within NEWCOM Network ofExcellence in Wireless Communications funded

through

the

V. CONCLUSION

European

Community (EC)

6th Framework

Program.

Clustering

ofscatterersisauseful tool for

simulating

mobile RFRNE

radio channels. However, identification of clusters from the REFERENCES

whl h m ea pedlcessahubrof clusters usedctinna geometric-stochasticbaechannel model." 10th T.Fh,AFoic,adEoe,"nfe hneoeleformobil

modrelased,iconvreC0 t2o9 Shimultiong ralesqultsde lyonsraevthat CzchtiRepublic, SeT.LOR2003. Blrd, uolva,Nv 02

(4)

[5] H. Asplund, A.F.Molisch, M. Steinbauer, and N.B.Mehra, "Clustering of scatterers in mobile radio channels - Evaluation and modeling in theCOST259 directional channel model", in Proc. IEEE International Conference on Communications (ICC2002), vol. 2, pp. 901-905, Apr. 2002.

[6] K.H. Li, M.A. Ingram, and A.V. Nguyen, "Impact of clustering in statistical indoor propagation models on link capacity," IEEE Trans. Commun., vol.50,no.4, Apr. 2002.

[7] Y Chen and V.K. Dubey, "A generic channel model in multi-cluster environments," in Proc. IEEE Vehicular Technology Conf., vol. 1,,pp. 217-221, Apr. 2003.

[8] A.F.Molisch,"Effect of farscattererclusters in MIMO outdoor channel models," in Proc. IEEE Vehicular Technology Conference (VTC), vol. 1, pp. 534-538,April 2003.

[9] T.S.Rappaport,Wireless Communications: PrinciplesandPractice,2nd ed., Prentice Hall, 2001.

[10] A.Likas,N. Vlassis, and J.J. Verbeek,"Theglobalk-meansclustering algorithm,"PatternRecognition,vol. 36, pp. 451 -461, 2003. [11] N. Czink, P. Cera, J. Salo, E. Bonek, J.-P. Nuutinen, and J. Ylitalo,

"Improving clustering performance using multipath component distance," Electronics Letters, vol. 42,no.1, 5thJanuary2006.

Şekil

Fig. 4. RDS for total numberofscattererNofSc=200; MD/Re=0.75 1.4NofSc=200; MD/RCm0.25 1

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