Spatial reuse in wireless LAN networks

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Khaldoun Al Agha, Laurent Viennot

To cite this version:

Khaldoun Al Agha, Laurent Viennot. Spatial reuse in wireless LAN networks. Personal Wireless Communications (IFIP PWC’2001), Aug 2001, Lappeenranta, Finland. pp.209-222. �inria-00471698�

KhaldounAl Agha

LRI

UniversitedeParis-Sud11b^at490

91405OrsayCedex, Frane

Khaldoun.Alaghalri.fr

Laurent Viennot

INRIA-Hiperom

DomainedeVolueau{B.P.105

78153Le ChesnayCedex, FRANCE

Laurent.Viennotinria.fr

Abstrat Theabsene of aradio arrierreuse patterninwireless LANsystems

neessities to apply aollision avoidane mehanisminorderto man-

age all ollisions that anprodueon the mediumsharing. Previous

studiesonerningellularradionetworksareingeneralfousedonthe

basisoffrequenyellpartition. Were-investigatethisfrequenyreuse

topifor wirelessLANswhere allnodes usethe samehannelandare

randomly plaed. Several measurementsare presentedto omputeall

radioparametersinaloalradionetwork. Then,theoretialstudyand

simulationresultsareintroduedtodeduethedistanethatpermitsa

ompletearrierreusebyusingaarriersensemehanism.

Keywords: WirelessLAN,Propagationmodel,CSMA

Introdution

Channelutilizationinwirelessloalareanetworksis,ingeneral,based

onthe same arrierfrequeny. No reusefator orfrequenyplanning is

dened. All users tune on the same hanneland try to transmit data.

However,ollisionbetweenommuniationsofnearbyusersouldappear

frequently. Toavoidollisions,severaltehniquesexistlikeCarrierSense

xedinorderto managethemediumsharing. Eahuserhasto estimate

thesignal ofneighboringusers. When thenumberof neighboringusers

isrelativelyhigh,theuseravoidstotransmitandwaitsforanothersilent

period. TheCSMAthresholdthat,indiatestoauserwhenthenumber

of interfering signalsis high,represents the key of the system apaity

inradioLANnetworks.

InLuentWaveLAN,threethresholdlevelsaredened: low,medium,

and high [2℄. When the signal measured bythe user is lower than the

threshold, the user an transmit. A human intervention is needed to

modifythethresholdbetweenlow, medium,and high. InHiperlan1[3,

4,5℄,thesystemdenesanadaptivethresholdthatisxedasafuntion

ofthetraÆload. When thetraÆis highthevalueof thethresholdis

bigger.

An adaptive threshold is ruialin a wireless radio whilethe apa-

ity of the system and the ommuniation quality depends diretly of

this threshold. Our approah in this paper onsists in omputing the

maximumdistane fromatransmitterthatguaranteesanon-interfering

ommuniationinparallelwithothertransmittingnodes. This distane

permitsto adapt thethresholdinawireless LAN.

Ontheotherhand, varyingthesignalpowerinan ad-honetwork[6℄

is needed to reah neighbors in order to root all pakets orretly to

thedestination. Thissignalpowervariationisorrelatedwithourreuse

distane. A maximumsignal powerpermitsto reah a farnode butall

nodes inthe transmitter neighboringarea an not transmit and on the

ontrary, a minimum signal power allows arrier reuse but neessities

more paketrouting.

This paperis organized as follows: Setion 2 shows results obtained

with a set of measurements and simulation,while Setion 3 presents a

theoretialstudyofthereusedistane. Insetion4,aspatialreusewith

and withoutarriersenseis simulated.

1. LAN RADIO TRANSMISSION:

MEASUREMENTS AND MODELING

The arrier reuse in loal radio networks depends strongly on the

environment harateristis. Path loss and slow fading eets dene

thereusefator in LANenvironment. Basially,forloalradiosystem,

thesame arrieris reused every where and has a dierent employment

omparingwithaellularsystemlikeGSM[7,8℄. Consequently,allusers

an use the same frequeny band without any onstraints. However,

thehighinterferene levelproduedbyother user ommuniationsin a

losed area prevents a ontinuous utilization of the used arrier. The

Table1 Environmentharateristivalues.

Measurement environment Linearorrelation oeÆient b(dB))

Corner-oÆe 0.95 4.63 -11.45

Corner-wall 0.98 2.86 -40.09

OÆe-oÆe 0.997 3.99 -38.53

Corridor-moving 0.998 2.87 -40.89

Road 0.88 2.31 -31.75

Roadwith ars 0.94 2.35 -36.60

Allpoints(indoor) 0.99 2.67 -44.24

arriersensetehniqueresolvesthis onstraint and permitsall users to

sharethe mediumavoidingalmost all ollisions.

Inthissetion,wetrytoomputeparametersthatmodelsignalprop-

agation. MeasurementparametersarearriedoutbyusingLuentWave

LAN Cards (IEEE 802.11) in dierent ases inluding indoor environ-

ment (oÆes, orridors, inside buildings, et.) and external buildings

environment (roads between buildings with many hurdles). These re-

sults are ompared with simulation results. In fat, the propagation

modelonsidereduses asreeived signalpower[7, 8℄:

P

tr K

R

10

10

(1.1)

whereP

tr

isthetransmittedpower,Kisaonstant,isrelatedtothelog

normalshadowingeet witha standarddeviationthattakesvaluesup

to12dB. Anormaldistributionisusedforvalues. Risthetransmitter

to reeiver distaneand is thepower attenuationexponent.

The idea is to use one Wave LAN transmitter and reeiver and to

ompute a very high quantity of reeived signal power. Then, a lin-

ear orrelation between all points permits to alulate omponents of

the line equation y = ax +b; where a is equal to and b is a

onstant (in dB). Indeed, mapping the Equation 1.1 in dB implies:

E[10log(reeived power)℄ = 10logR+KP

tr

. Table 1 gives values

of the linear orrelation applied on measurement les. The orrelation

oeÆient indiateshowtruevaluesarelosedto theomputedorrela-

tionline. ThisoeÆient hasto bevery lose to 1inorder to exhibit a

highorrelationquality. Eah lineof Table1 onsistsofa measurement

Corner-oÆe: transmitter behindtheorridorornerand reeiver

is movingfrom oÆe to oÆein thesame building;

Corner-wall: transmitter behind the orridor orner and reeiver

behind allwallsinthebuilding;

OÆe-oÆe: transmitter inan oÆe and reeiver is moving from

oÆe to oÆeinthesame building(ineahoÆe,about200mea-

sures aretaken movingaround);

Corridor-moving: transmitter behind the orridor orner and re-

eiver is turning during measures in eah oÆe entrane of the

building.

Road: transmitterand reeiverare ona roadwithoutars;

Road with ars: transmitter and reeiver moving around ars

parked on theroad.

(a) Computingof attenuation om-

ponents: =2:67and b= 44:24;

(reeived signal power versus dis-

tane).

(b)Slowfadingomponentmeasure-

ment;standarddeviation=5.03.

Figure1 Allindoor values.

Figure1.apresentsmeansignalpowermeasurementsomparedtothe

linear orrelation line. All measurements are very lose to the orrela-

tion line. Deviations from themean value areshownin Figure 1.band

omparedto thePDF(ProbabilityDistributionFuntion)ofthenormal

distributionwiththesamestandarddeviation. Thehistogramrepresents

This represents a disrete analog of the PDF. Basially, we an ob-

servethat allvaluestendto form anormaldistributionsilhouettewhile

respeting the same standard deviation issued from the measurement

values. Notethat valuesare measuredinseveral indoorenvironments.

(a) Computingofattenuation om-

ponents: =3:99and b= 38:53;

(reeived signal power versus dis-

tane).

(b)Slowfadingomponentmeasure-

ment;standarddeviation=3.86.

Figure2 MeasurementinbuildingoÆesonly.

Inorder tozoomintovaluesandtoestimatea better standarddevia-

tionofthelog-normalshadowing,weshowonlyvaluesthatmeasuredin

thesame environment onditions. Figures 2.aand 2.bdepitonlymea-

surements arried in an oÆe-oÆe (referred to Table 1) environment.

Clearly,one an see that valuesare more oherent and the form of the

histogram is ideally similarto the PDF of thenormal distributionand

showtherelevaneofthe model.

After doing measurements and omputing all simulation model pa-

rameters,theideaonsistsinreportingallthesevaluesinthesimulation

modelandompareresultswithmeasurements. Allindoorenvironment

values areplotted inFigure 3.a (see Table 1 also). The shadowinglog-

normal standard deviation is estimated to 5dB. Figure 3.a illustrates

measurementvaluesandsimulationresultsforthereeivedsignalpower.

We an observe that the path loss attenuation and the deviation from

the mean value are very similar. This onlusion onrms the validity

of the log-normal distribution for the shadowing modeling or the slow

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

0 10 20 30 40 50 60 70 80

Throughput

C/I in dB

transmitter receiver

(a)Systemthroughput (Mbps)ver-

susC=I(dB)ratio.

-110 -100 -90 -80 -70 -60 -50 -40 -30

0 2 4 6 8 10 12 14 16 18

Signal power (dB)

Distance from transmitter (log) measurement

simulation

(b)Reeivedsignalpower.

Figure3 Throughputmeasurementsandaomparisonbetweensimulationandmea-

surements.

Finally, the system throughput (at transmitter and reeiver) is ex-

hibitedin Figure 3.a asa funtion of the reeived C=I ratio. Measure-

ments weremade byusingaUDP (UserDatagram Protool) stream of

1Kbytes pakets. Reall that the maximum throughput supported by

Wave LANards is supposedto be2Mbps (in atheoretial way!). The

guresuggeststhattheminimumC=I ratiorequiredto maintainahigh

throughputshouldbeabout15dB. Thisvaluewillbeusedlatertoom-

pute the reuse distane in our radiomodel. Also, the transmitter and

reeiver throughput are very approximately equal to eah other when

theC=I isbiggerthan15dB. Thisisduetothehighqualityoftheradio

ommuniation. Inthe other ase, below15dB,Figure 3.a displays the

dierene between throughput at the reeiver and the transmitter end

point (due to paket loss). Evidently, when the bit error rate is high

(smallC=I),there-transmissionprotool willreduethebit rate.

In short, by doing an important number of measurements, we om-

pute all indoor environment harateristis in order to determine the

reusedistane andthemaximumnumberofpossiblesimultaneousom-

2. SPATIAL REUSE MODELING AND

ANALYSIS

In time multiplexed ellularnetworks[7, 8℄spatialreuse is generally

onsideredin termof frequeny patternalloation. We onsider here a

simpler model whih is still onsistent with the ellular approah. We

want to haraterize themaximumdistane between atransmitter and

a reeiver (allowing a good transmission) aording to the density of

simultaneous transmitters. This setion isdevotedto give a simplean-

alyti analysis of the triangular mesh. It will be used as a referene

foromparingthesimulation results. The lassialtriangularmeshis a

basiexamplewheretransmittersareregularlyand denselyplaed. We

haraterize a density of simultaneous transmitters in a LL square

by theinter-node distane of thetriangular meshwith same number of

transmittersthat t inthe square. If N is the number of transmitters,

thenwe have N = L

D

L

D p

3=2 .

Inellularnetworks[7,8℄,frequenyreusepatternisingeneralbased

onafrequenyreusedistaneDproportionaltotheradiusR oftheell

[7℄. Typially,D =3R orD=3:46R for lassialGSM reusepatterns.

We are going to estimate thisfator for the triangular meshsupposing

thatno shadow fadingeet ours.

Figure4 (a)A ratioD=R thatguarantees goodspatial reuseina triangularmesh

withQ=15dBaordingtotheattenuationoeÆient. (b)Asharperlowerbound

on the minimum ratio D=R aording to L=D for = 3 (upper urve), = 3:5

(middleurve)and=4(lowerurve).

A suÆient ondition for getting a good transmission between the

transmittingnode and thereeiveris:

K P

tr

R

QB where B=

X

K P

tr

Distane (e)

Let H

n

denotes the hexagon with transmitters at distane nD from

thesouretransmitter(thereare6n suh transmitters;theirdistane is

greaterthannD p

3=2). Bypartitioningthesumaordingtoonentri

hexagons, we obtain:

B= L=D

X

n=1 X

e2H

n K

P

tr

Distane (e)

L=D

X

n=1 6nK

P

tr

(nD p

3=2)

6KP

tr

(D p

3=2)

( 1)

where(s)= P

1

n=1 1

n s

isthe famouszeta funtionof Riemann. A suÆ-

ient onditionforgood spatialreuseforthetriangularmeshis thus:

D

R

2

p

3

(6Q( 1)) 1=

Note that this inequality is obtained by summing up to innity. It

is possible to get a sharper estimation by onsidering nite sums. See

Figure4foranillustration. NotiethattheD=Rratioonvergesrapidly

asthesystemsizeinreases.

3. SPATIAL REUSE SIMULATION

After presenting measurements that provideradio parameters and a

theoretial studythat givesan ideaaboutthe D=Rratio(D is thedis-

tane between two transmitters as dened in Setion 3 and R is the

maximumdistane fromatransmitterthatguarantees agoodtransmis-

sion),thepaperproposestoexeutesimulationsinordertondtheD=R

ratio as a funtion of dierent parameters: system size, silene CSMA

threshold, and nodes distribution (randomly or triangular). First,

simulations are exeuted without any arrier sense and then by using

a CSMA mehanism. The CSMA mehanism denes a silene CSMA

threshold: if a node needs to transmit, it should listenother user sig-

nals. Ifthesum ofthese signalsisbelowthe threshold,itan transmit.

Otherwise, it waits for a more silent period. The simulation model of

Equation1.1 istaken.

Figures5.aand5.bompareD=Rversussystemsizefordierentval-

uesof intriangularandrandomongurationrespetively. Note that

thestandarddeviationofthelog-normalshadowingdistributionisxed

to5dB. Thenumberoftransmittingnodesisequalto50andno CSMA

protool is applied. In the simulation,a reeiver is plaedrandomly in

a disk of radius R entered on eah transmitter. Then, R is inreased

(we start with 1 meter) untilthe overall of failed ommuniations (e.g.

C=I <15dB)reahes5%. Asdepited inFigures5.aand 5.b,when the

2 3 4 5 6 7 8 9

20 40 60 80 100 120 140 160 180 200

D/R

System size alpha=3 (mean)

alpha=3.5 (mean) alpha=4 (mean) alpha=4

(a)Triangularonguration.

2 4 6 8 10 12 14 16 18 20 22 24

20 40 60 80 100 120 140 160 180 200

D/R

System size alpha=3 (mean)

alpha=3.5 (mean) alpha=4 (mean) alpha=4

(b)Randomonguration.

Figure5 Sileneareasizeversussystemsize;simulationwithoutCSMA.

highand all reeived power isunder 15dB (the numberoftransmitting

nodes is relatively high ompared to the system size). Consequently,

theradius is equalto 1 and theD=R (D depends on system size) rises

aordingtothesystemsize. WhenthesystemsizebeomessuÆiently

big, the D=R reahes a stable value and shows thebiggest radius that

guaranteesaommuniationindependentlyofthesystemsize. Thissta-

blevaluevaries asa funtionof. Indeed, byvarying with thesame

shadowing(here standard deviation isxed to 5), we observe a smaller

D=Rwhen isequalto 4(astrongpathlossattenuation). Inaddition,

inatriangular onguration, allvalues(whenvarying) arevery lose

to thetheoretial study illustratedin Figure 4. In fat, resultsjoin the

reuse fator idea in a ellular ontext beause all base stations are, in

general, plaed in a triangular onguration. On the other side, in an

ad-ho ontext when nodes are plaed randomly, the D=R mean ratio

onverges also to a stablevalue whihis lessinterestingthanthe trian-

gular onguration value. Moreover, values an be far from the mean

value. Indeed, random plaing provides a damaging eet on the value

ofR (see Figure.5.b).

In a CSMA ontext, simulations are aomplished by plaing a re-

eiver nearby eah transmitter (randomly plaed in the disk of radius

R ). Twoasesareonsidered: 1000nodesaredistributedonatriangular

meshor randomly. CSMA mehanism isapplied, e.g. we an transmit

a message only if the summation of other signals is inferior than the

3 4 5 6 7 8 9 10

-95 -90 -85 -80 -75 -70 -65 -60 -55 -50

D/R

CSMA threshold alpha=3 (mean)

alpha=3.5 (mean) alpha=4 (mean) alpha=4

(a)Triangularonguration.

3 4 5 6 7 8 9 10

-95 -90 -85 -80 -75 -70 -65 -60 -55 -50

D/R

CSMA threshold alpha=3 (mean)

alpha=3.5 (mean) alpha=4 (mean) alpha=4

(b)Randomonguration.

Figure6 Silene areasizeversusCSMAthreshold;simulationwithCSMA.

the distane R is inreased as long as 95% of user ommuniations is

above 15dB as before. Figures 6.a and 6.b depit simulations results

andexhibitsD=Raordingto thesileneCSMAthresholdforasystem

size of 200m. Results speify that D=R reahes a stable value after a

ertain threshold and depending, solely, on . Figures indiates also

that randomand triangular onguration are equivalent. In short, the

useof a arriersensemehanism reduesthe damagingeet produed

whentransmittersare plaedrandomly.

Finally, when omparing to a non-CSMA onguration, we observe

thatthevalueof thesileneCSMAthresholdinoursimulationisabout

75dB when 50 simultaneous transmissions is permitted in the sys-

tem(toreah 350transmitting nodesinthesystem,a 55dB threshold

is needed). A suitable threshold for spatial reuse seems to be around

70dB beause it oers small deviations to the mean of D=R values

(seeFigure 6). Inaddition,thisvalue onludesthesmallestD=Rratio

whilemaintaining thesame systemsize.

4. CONCLUSION

Wehaverstshowntherelevaneofalassialradiomodelintheon-

text ofwirelessLANs byomparingvariousmeasurementsfrom Luent

IEEE 802.11 Wave LAN ards (over 2500 signal power measurements)

withanalytialanalysisandsimulations. Moreover,wemodelthespatial

lularradio networks) to wireless LANs whih seems espeially relevant

whena CSMA tehniqueis usedto avoidollisions.

Interesting future work resides in the study of self adaptive CSMA

thresholdtuningpoliies asproposedin theHiperlan1 norm [3℄. Suh

poliiesmayallowto getbetterspatialreuse. Anotherinterestingstudy

onerns ad-ho networks [6℄. A key point resides in nding a good

tradeobetweenspatialreuse and the number of transmissions needed

torouteeahpaket. OurstudiesouldleadtoaCSMAthresholdpoliy

allowingto reah thisgoal:::

Ontheotherhand,ourmodelingisertainlyagoodbasisforenvision-

ingqualityof servieinwireless LANs. Indeed, itallows to model,in a

simple,waythesharing of thepoint-to-point radiolinks: two transmis-

sionsareindependentifthedistanebetweentransmittersisatleastD.

Wean, forexample,designasimplebandwidthreservationprotool: a

node an reserve some bandwidthb ifb plusthe sumof all theurrent

bandwidthreservations of thenodes at distane at most D isless than

themaximumbandwidthavailableon thearrier.

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