Table Of ContentSafe Carrier Sensing Range in CSMA Network
under Physical Interference Model
Liqun Fu, Soung Chang Liew, Jianwei Huang
Department of Information Engineering
The Chinese University of Hong Kong
Shatin, New Territories, Hong Kong
Email: lqfu6,soung,jwhuang @ie.cuhk.edu.hk
{ }
9
0
0 Abstract—In this paper, we study the setting of carrier- the cumulative interference powers from all the other links
2 sensingrangein802.11networksunderthe(cumulative)physical maystillcorruptthetransmissiononthelinkconcerned.Since
n interference model. Specifically, we identify a carrier-sensing thecollisionisnotduetoaspecific“hidden”node,theconven-
range that will prevent collisions in 802.11 networks due to
a tionalterm of “hiddennodecollision” doesnot quite applyto
carrier-sensingfailureunderthephysicalinterferencemodel.We
J find that the carrier-sensing range required under the physical thissituationthatarisesunderthephysicalinterferencemodel.
3 interference model must be larger than that required under the We define a new term “missed-carrier-sensing collision” to
2 protocol (pairwise)interferencemodel byamultiplicativefactor. describe this phenomenon. Missed-carrier-sensing collisions
Forexample,iftheSINRrequirementis10dB andthepath-loss occur when the transmitter does not sense the transmissions
] exponentis4,thefactoris1.4. Furthermore,given afixedpath-
I of the other links, but the cumulative interference power
N lossexponentof 4, thefactor increasesastheSINRrequirement
increases. However, the limit of the factor is 1.84 as the SINR of all the other concurrent transmissions will interfere the
.
s requirement goes to infinity. transmission on this particular link. This paper is dedicated
c Index Terms—carrier-sensing range, physical interference to the study of the required carrier-sensing range to prevent
[ model, SINR constraints.
missed-carrier-sensingcollisionsin802.11networksunderthe
1 physical interference model.
v I. INTRODUCTION
1
1 In 802.11,carriersensing is designed to preventconcurrent II. SYSTEMMODEL
transmissions that can corrupt each other. The setting of the
6
3 carrier-sensing range is crucial. Too large a carrier-sensing A. Network and Physical Interference Model
. rangewilllimitspatialreuse,whiletoosmallacarrier-sensing
1 We represent a wireless network by a set of directed links
0 range will fail to prevent collisions. = l ,1 i . Let = T ,1 i and
i i
9 To date, most studies on the proper setting of the carrier- L = {R ,1≤ i ≤ |L|}denoteTthe s{et of tr≤ansm≤ittin|Lg|}nodes
i
0 sensing range [1]–[5] are based on the pairwise interference Randth{esetof≤rece≤ivi|nLg|}nodes,respectively.Areceiverdecodes
:
v model (referred to as the protocol interference model in itssignalsuccessfullyif andonlyif thesignal-to-interference-
Xi [6]). For a link under the pairwise interference model, the plus-noise ratio (SINR) requirementat the receiver is abovea
interferences from the other links are considered one by one. certain threshold. We adopt the physical interference model,
r
a If the interference from each of the other links on the link where the interference is the sum total of the powers the
concerned does not cause a collision, then it is assumed receiver receives from all transmitters except its own trans-
that there is no collision overall. In particular, the pairwise mitter.Weassumethatradiosignalpropagationobeysthelog-
interference model does not take into account the cumulative distance path model with path loss exponentα>2. The path
effects of the interferences from the other links. The physical gain G(T ,R ) from transmitting node T to receiving node
i j i
interference model [6], on the other hand, considers the R follows a geometric model
j
cumulative interferences and thus is a more accurate model.
Under the pairwise interference model, hidden-node colli- G(Ti,Rj)=d(Ti,Rj)−α, (1)
sion happens if the transmitters of two links do not carrier
senseeachother,butthetwolinksarecloseenoughtointerfere where d(Ti,Rj) is the Euclidean distance between nodes Ti
with each other. Ref. [5] established the carrier-sensing range and R .
j
requiredtopreventhidden-nodecollisionsin802.11networks In802.11,eachdatatransferonalinkl consistsofaDATA
i
under the pairwise interference model. This resulting carrier- frameintheforwarddirection(fromtransmitterT toreceiver
i
sensing range is too optimistic when the more accurate phys- R ) followedbyanACK frameonthe reversedirection(from
i
ical interference model is considered instead. For a particular R to T ). The data transfer on link l is said to be successful
i i i
link, although the carrier-sensing range is set large enough if and only if both the DATA frame and the ACK frame are
with respect to the interference from each of the other links, correctly received. So under the physical interference model,
2
the conditions for successful transmissions on link l are the conditions (2) and (3), with = = l , are
i ′ ′′ con i
L L L \{ }
satisfied.
P G(T ,R )
i i
· γ0, (DATA frame) (2) In the following analysis, we assume that the background
N + P G(S ,R ) ≥
j i
lj∈L′ · noise power N can be ignored.
P
and
III. SUFFICIENT CONDITION ONSafe-CSRange
P G(R ,T )
N + · P iG(iS ,T ) ≥γ0, (ACK frame) (3) In this section, we will derive a sufficient large value on
j i
lj∈L′′ · the Safe-CSRangethat will preventthe missed-carrier-sensing
P collisions in 802.11.
where P is the transmission power level, N is the average
It is shown in [5] that although the CSRange is sufficient
noise power, and γ0 is the SINR threshold for correct recep-
large for the SINR requirements of all nodes, transmission
tion.WeassumethatallnodesusethesametransmitpowerP
failures can still occur due to the “Receiver-Capture effect”.
andadoptthesameSINRthresholdγ0.Let ′ ( ′′)denotethe
L L Consider two links l and l such that T and T are out of
set of links that transmit concurrently with the DATA (ACK) i j i j
the CSRange, but R is in the CSRange of T . If T transmits
frame on link l . For a link l in or , the interference j i i
i j ′ ′′
L L first,thenR willhavesensedthesignalofT andthedefault
could be either from transmitter T or the receiver R of j i
j j
operation in most 802.11 products is that R will not attempt
link l through the DATA or ACK transmission on link l , j
j j
toreceivethelatersignalfromT ,evenifthesignalfromT is
respectively. So we use the notation S to denote the sender j j
j
stronger. This will cause the transmission on link l to fail. It
of link l , which could be either T or R . j
j j j
is further shown in [5] that no matter how large the CSRange
B. Carrier Sensing in 802.11 is, we can always come up with an example that give rise to
Considerthewirelesslinkset .Ifthereexistsalinkl transmission failures, if the “Receiver-Capture effect” is not
i
L ∈L
such that not both (2) and (3) are satisfied, collision happens. dealtwithproperly.Thiskindofcollisionscanbesolvedwith
In802.11,carriersensingcanbeusedtopreventsimultaneous areceiver“RS(Re-Start)mode”whichcanbeenabledinsome
transmissions that collide. 802.11 products(e.g., Atheros WiFi chips). With RS mode, a
We assume carrier sensing by energy detection. That is, receiver will switch to receive the stronger packet as long as
if the power received from another node is above a power the SINR threshold γ0 for the later link can be satisfied.
threshold P , then a transmitter will not transmit and its With the receiver’s RS mode, we can derive the Safe-
cs
backoff countdown process will be frozen. Given a carrier CSRange that will preventcollisions in 802.11network under
sensing power threshold P , it can be mapped to a carrier- the Physical Interference Model.
cs
sensing range CSRange. Consider two links, l and l . If the Theorem 1: Considerthewirelesslinkset .Thesufficient
i j
L
transmittersT andT cancarrier-sensetheframestransmitted condition on the Safe-CSRange that will prevent collisions in
i j
by each other, simultaneous transmissions by them will be 802.11 network under the Physical Interference Model is:
prevented.That is, if the distance between T and T satisfies
i j
Safe-CSRange=(K+2)dmax, (5)
d(T ,T )<CSRange, (4)
i j
tbheefoDreAhTanAd.frame transmissions on li and lj are prevented lwenhgerthe idnmtahxe=netwmli∈oarLxkd,(aTnid,Ri), which is the maximum link
Setting an appropriate CSRange is crucial to the perfor-
α 1
mance of 802.11 network. If CSRange is too large, spatial 2 1 α
K = 6γ0 1+ . (6)
reuse will be unnecessarily limited. If CSRange is not large √3 α 2
(cid:18) (cid:18) (cid:18) (cid:19) − (cid:19)(cid:19)
enough,the missed-carrier-sensingcollisions may occur. That
Proof: With the receiver’s RS mode, in order to prevent
is a number of transmitters may transmit simultaneously
collisions in 802.11 networks, we only need to show that
because condition (4) is not satisfied by all pairs of the
condition(5) issufficienttosatisfyboththeSIRrequirements
transmitters. However, there may exist one link that not both
(2) and (3) of all the concurrent transmission links.
conditions (2) and (3) are satisfied. In this case, collisions
With the transmitter-side carrier sensing in 802.11, concur-
happenandthecarriersensingfailstopreventsuchcollisions.
rent transmissions can only happen when the transmitters do
We define a Safe CSRange that will prevent the missed-
not carrier sense each other. Let denote the set of links
carrier-sensingcollisionsin802.11networkunderthephysical Lcon
which have concurrent transmissions. Consider any two links
interference model as follows:
l and l in , we have the following inequality:
Definition 1 (Safe-CSRange): Considerthewirelesslinkset i j Lcon
. Let denote a subset of links that are al-
L Lcon ⊆ L d(Tj,Ti) Safe-CSRange=(K+2)dmax. (7)
lowed to transmit concurrently under a CSRange setting. ≥
Let LC(CSRange) = {Lcon} denote all such subsets of Because both the lengths of links li and lj satisfy
links. A CSRange is said to be a Safe-CSRange if for any
con C(CSRange) such that for any link li con, both d(Ti,Ri) dmax, d(Tj,Rj) dmax,
L ∈ L ∈ L ≤ ≤
3
using triangular inequality, we have
d(T ,R ) d(T ,T ) d(T ,R )
j i j i i i
≥ −
(K+2)dmax dmax =(K+1)dmax, (8)
≥ −
Kd
max
T R
d(Rj,Ti)≥d(Ti,Tj)−d(Tj,Rj) id i
max
(K+2)dmax dmax =(K+1)dmax, (9)
≥ −
and also
First layer link
d(R ,R ) d(R ,T ) d(T ,R ) Second layer link
j i i j j j
≥ −
(K+1)dmax dmax =Kdmax. (10) Third layer link
≥ −
We take the most conservative distance Kdmax in our
interference analysis (i.e., we will pack the interference links
Fig.1. Thepackingoftheinterfering linksintheworstcase
in a tightest manner given the CSRange in (5)). Consider any
two links l and l in . The following four inequalities
i j con
L
are satisfied:
d(Ti,Tj) Kdmax, (11) If link lj is the nth layer neighbor link of link li, we have
≥
d(Ti,Rj)≥Kdmax, (12) d(Sj,Ri)≥ √23n·Kdmax. Thus we have
d(Tj,Ri)≥Kdmax, (13) √3 −α 1
d(Ri,Rj)≥Kdmax. (14) Pd−α(Sj,Ri)≤P 2 nKdmax! = √3nK αPd−mαax,
2
Consider any link l in . We will show that the SIR
i Lcon (cid:16) (cid:17)
requirements for both the DATA frame and the ACK frame and there are at most 6n neighbor links in the second layer.
can be satisfied. We first consider the SIR requirement of the Sothecumulativeinterferencepowersatisfiesthefollowing
DATA frame. The SIR at R is: inequality:
i
SIR= Pd−α(Ti,Ri) (15) Pd−α(Sj,Ri)
lj∈LPC,j6=iPd−α(Sj,Ri) lj∈LXC,j6=1i α ∞ 2 α
For the received signal power we consider the worst case 6 + 6n Pd α
−max
that d(Ti,Ri)=dmax. So we have ≤ ·(cid:18)K(cid:19) n = 2 (cid:18)√3nK(cid:19) ·
X
Pd−α(Ti,Ri) P d−mαax. (16) 1 α ∞ 2 α
≥ · =6 1 + n Pdm−αax
Tocalculatethecumulativeinterferencepower,weconsider ·(cid:18)K(cid:19) n = 2 (cid:18)√3n(cid:19) ·
X
the worst case that all the other concurrenttransmission links
α α α
have the densest packing, in which the link lengths of all the =6 1 1 + 2 ∞ n 1 Pd α
−max
other concurrent transmission links are equal to zero. In this · K √3 n ·
(cid:18) (cid:19) (cid:18) (cid:19) n = 2 (cid:18) (cid:19)
case, the links degenerates to nodes. The minimum distance X
betweenbetweenanytwolinksinLconisKdmax.Thedensest =6 1 α 1 + 2 α ∞ 1 Pd α
packing of nodes with minimum distance requirement is the · K √3 nα 1· −max
hexagon packing (as shown in Fig. 1). (cid:18) (cid:19) (cid:18) (cid:19) nX= 2 −
If link l is the first layer neighbor link of link l , we have 1 α 2 α 1
j i 6 1 + Pd−mαax (17)
d(Sj,Ri)≥Kdmax. Thus we have ≤ ·(cid:18)K(cid:19) (cid:18) (cid:18)√3(cid:19) α−2(cid:19)·
Pd α
Pd−α(Sj,Ri)≤P(Kdmax)−α = K1α ·Pd−mαax, = γ−m0ax, (18)
and there are at most 6 neighbor links in the first layer. where (17) follows from a bound on Riemann’s zeta function
If link l is the second layer neighbor link of link l , we and (18) follows from the definition of K in (6).
j i
have d(Sj,Ri) √3Kdmax. Thus we have According to (16) and (18), we find that the SIR of the
≥
DATA frame of link l at the receiver R satisfies:
α 1 i i
Pd−α(Sj,Ri)≤P(cid:16)√3Kdmax(cid:17)− = √3K αPd−mαax, SIR= Pd−Pα(dT−iα,R(Si)j,Ri) ≥ PP·dd−m−mαaxαax =γ0. (19)
and there are at most 12 neighbor links in(cid:0)the se(cid:1)cond layer. lj∈LC,j6=i γ0
P
4
ThismeanstheSIRrequirementofthesuccessfultransmission
2.5
of the DATA frame on link l can be satisfied.
onTlhinekplrioocfasnthbaet stahteisfSieIRd firoelqluoiwremtheentsiomfiltahrepAroCcKedufrreamaes ngepairwise ααα===345
a
above. So for any link l in the concurrent transmission links R
i S
Lofcotnh,ecosuncdciteisosnfu(l5)triasnssumffiiscsiieonntstoosfabtiosfthytihtseSDIARTrAeqaunirdemAeCnKts Safe−C 2
fcroanmdeitsi.oTnh(i5s)miseasnusfftihcaiet,nttogfoerthperrewveitnhtitnhgecreoclleiisvioern’ssRinS8m02o.d1e1, e/physical
g
networks under the physical interference model. an
R
Condition (5) provides a sufficiently large CSRange that CS 1.5
−
preventsmissed-carrier-sensingcollisionsin 802.11networks. afe
S
So there is no need to set a CSRange larger than (5) in order o
ati
to prevent collisions. Setting a larger CSRange than (5) will e r
h
only decrease spatial reuse. T
1
0 200 400 600 800 1000
SIR Requirement γ
IV. COMPARISON OF THESafe-CSRangeWITHTHE 0
PAIRWISE INTERFERENCEMODEL
ThissectioncomparestheSafe-CSRangeunderthephysical Fig.2. AnalyticalresultsoftheratiooftheSafe-CSRangeunderthephysical
interference modeltothatunderthepairwiseinterference model
interference model to that under the pairwise interference
model (derived in [5]). Let Safe-CSRange denote the
pairwise
CSRange that prevents hidden-node collisions under the pair-
wise interference model. Let Safe-CSRange denote the which is also an increasing function of γ0. And the limit of
physical
CSRangethatpreventsmissed-carrier-sensingcollisionsunder the ratio of Safe-CSRangephysical to Safe-CSRangepairwise as γ0
goes to infinity is:
the physicalinterferencemodel. The Safe-CSRange and
pairwise
the Safe-CSRangephysical are: Safe-CSRangephysical 2+ 334γ0 41
lim = lim
Safe-CSRangepairwise = 2+γ0α1 dmax, (20) γ0→∞Safe-CSRangepairwise γ0→∞ 2(cid:0)+γ041(cid:1)
1
Safe-CSRangephysical =((cid:16)K+2)dm(cid:17)ax = 34 4 1.8348 (27)
α 1 3 ≈
2 1 α (cid:18) (cid:19)
= 2+ 6γ0 1+ dmax. (21) Safe-CSRange
(cid:18) (cid:18) (cid:18)√3(cid:19) α−2(cid:19)(cid:19) ! Fig. 2 shows the ratio Safe-CSRangeppahiyrswiciasel as a function of
the SIR requirements γ0. Different curves represent different
For example, if γ0 = 10 and α = 4, which are typical for choices of path loss exponent α.
wireless communications, we have
V. CONCLUSION
Safe-CSRangepairwise =3.78dmax, (22) Thispaperstudiestheproblemofsettingthecarrier-sensing
Safe-CSRangephysical =5.27dmax. (23) range that will prevent missed-carrier-sensing collisions in
802.11 networks under the physical interference model. We
The Safe-CSRangeneedsto be increased by a factor of 1.4 to
establish a sufficient condition for the carrier sensing range.
ensuresuccessfultransmissionsunderthephysicalinterference
We call the minimum carrier sensing range that meets the
model.
condition Safe-CSRange and compare it with that established
Given a fixed path loss exponent α, both Safe-
under the pairwise interference model [5]. We find that for
CSRange and Safe-CSRange will increase when
pairwise physical the typical setting of path-loss exponent α = 4 and SINR
the SIR requirement γ0 increases. This is the case when the
requirementγ0 =10,theSafe-CSRangeneedstobeincreased
separationamonglinksmustbelargertomeettheSIRtargets.
by a factor of 1.4 under the physical interference model. We
For example, if α=4, we have
also find that, given a fixed path-loss exponent α, the factor
Safe-CSRangepairwise = 2+γ014 dmax, (24) increases when the SINR requirement γ0 increases. And the
factor tendsto a constantas the SINR requirementγ0 goesto
(cid:16) (cid:17) 1
34 4 infinity.For example,when the path-lossexponentα=4, the
Safe-CSRangephysical = 2+ 3 γ0 dmax. (25) limit of the factor is 1.84 as the SINR requirementγ0 goesto
(cid:18) (cid:19) !
infinity.
The ratio of Safe-CSRange to Safe-CSRange is
physical pairwise
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