Interference-Aware Routing Ram a Krishna

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Interference-Aware Routingin Wireless Multihop Networks

Georgios Parissidis, Student Member, IEEE, Merkourios Karaliopoulos, Member, IEEE,

Thrasyvoulos Spyropoulos, Member, IEEE, and Bernhard Plattner, Fellow, IEEE

AbstractInterference is an inherent characteristic of wireless (multihop) communications. Adding interference-awareness to

important control functions, e.g., routing, could significantly enhance the overall network performance. Despite some initial efforts, it is

not yet clearly understood how to best capture the effects of interference in routing protocol design. Most existing proposals aim at

inferring its effect by actively probing the link. However, active probe measurements impose an overhead and may often misrepresent

the link quality due to their interaction with other networking functions. Therefore, in this paper we follow a different approach and:

1) propose a simple yet accurate analytical model for the effect of interference on data reception probability, based only on passive

measurements and information locally available at the node; 2) use this model to design an efficient interference-aware routing

protocol that performs as well as probing-based protocols, yet avoids all pitfalls related to active probe measurements. To validate

our proposal, we have performed experiments in a real testbed, setup in our indoor office environment. We show that the analytical

predictions of our interference model exhibit good match with both experimental results as well as more complicated analytical models

proposed in related literature. Furthermore, we demonstrate that a simple probeless routing protocol based on our model performs at

least as good as well-known probe-based routing protocols in a large set of experiments including both intraflow and interflowinterference.

Index TermsWireless networks, interference model, interference-aware routing, routing metric.

1 INTRODUCTION

THE standardization of Wireless Local Area Networks(WLANs) [1] opened the way to wireless networkaccess provision without the need for wired infrastructure.The IEEE 802.11 ad hoc mode, in particular, enabled the

intercommunication of mobile, battery-powered devicesand opened the way to a revolutionary method ofcommunication that departs from the well-establishedinfrastructure-based network access paradigm. In this newparadigm, messages are routed (relayed) over multiplewireless (mesh) hops to reach their destination.

Yet, within this paradigm, interference becomes a majorimpact factor on the network efficiency and performance.Due to the broadcast nature of the medium and the complex-ity of wireless propagation phenomena, it is inherentlydifficult to spatially partition the wireless medium intoclearly disjoint links as in the case of wired networks. Thiscombined with the random access mechanism (implemented

by a carrier sense function) of the 802.11 MAC protocol givesrise to nodes that do transmit while they shouldnt (hiddennodes), but also nodes that do not transmit while they could(exposed nodes). Both phenomena result in significantreductionoftheinformationdeliverycapacityofthenetwork.

Adding interference-awareness to routing decisions cantherefore enhance significantly the network performance.

Jain et al. in [2] show that under ideal interference-awarerouting, the data delivery capability of the network can besignificantly improved with respect to shortest-path rout-ing, even under nonoptimal MAC scheduling. There have

been efforts to capture the effect of interference in thedesign of routing metrics (see, e.g., [3], [4], [5]) that canserve as alternatives to minimum hop count; nevertheless,their common feature is that they are based on activelymeasuring (probing) the link. Such measurement-basedapproaches have three major disadvantages. First, the activemeasurements impose additional data overhead on thenetwork. Second, part of the node radio resources is spenton probe transmissions, which may be a concern for energy-constrained nodes. Third, the achievable accuracy andreliability of the measurements can sometimes be low,either because the estimation of small or moderate errorrates would need a large number of sample measurements

or due to the various interactions between the activemeasurement packets and other packets in the network.These considerations motivate a different approach,

which is to pose and try to answer the following questions:how well can we estimate interference and predict thesuccess probability of transmitting a message over a linkwithout resorting to measurements and probing, but ratherby exploiting only information that is locally available to thenode? Can an interference-aware routing metric based on asimple analytical model achieve similar performance toprobing-based schemes?

To this end, we first develop an analytical model toestimate the probability that a transmission destined to a

node is successful in the presence of interference. Startingfrom the simple physical (Signal-to-Interference and Noise-Ratio (SINR)) model [6], we introduce the concepts ofinterference zones that aim at quantifying the effect of

716 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 10, NO. 5, MAY 2011

. The authors are with the Computer Engineering and Networks Laboratory,Swiss Federal Institute of Technology in Zurich (ETHZ), Gloriastrasse 35,8092 Zurich, Switzerland.E-mail: {parissid, karaliopoulos, spyropoulos, plattner}@tik.ee.ethz.ch.

Manuscript received 27 Aug. 2008; revised 13 Aug. 2009; accepted 1 July2010; published online 19 Oct. 2010.For information on obtaining reprints of this article, please send e-mail to:[email protected], and reference IEEECS Log Number TMC-2008-08-0344.Digital Object Identifier no. 10.1109/TMC.2010.205.

1536-1233/11/$26.00 2011 IEEE Published by the IEEE CS, CASS, ComSoc, IES, & SPS


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cumulative interference by concurrently transmittingnodes, such as hidden nodes and nodes outside the sensingrange. Furthermore, to also capture the carrier sensefunction common to many real MAC protocols, we includein our model a very simple and generic MAC model, whichensures that nodes within range of the transmitting sourcedefer from transmitting. Accounting for both these effects,we derive an analytical expression for the probability ofsuccessful reception in the presence of interference, as afunction of the node degree, node transmission probability,radio propagation environment, and network card recep-tion sensitivity. Compared to probe-based approaches, theadvantage of this derivation is that all model inputs can beavailable (or estimated) locally to the node; for example,information regarding a nodes degree can be extractedfrom the routing layer at no additional cost in terms ofcommunication overhead. Finally, compared to other, morecomplex analytical models of wireless interference [7], [8],our model does not require prior measurements and canscale up to large number of nodes.

It is important to note here that our analytical modeldoes not aim to capture the exact working details of arealistic 802.11 protocol (e.g., Distributed CoordinationFunction of 802.11 [1]), and unavoidably makes someassumptions with respect to real propagation phenomena,in order to ensure it remains simple enough to be utilized as ahandy interference-aware routing metric. This is the real goal ofthis work. Nevertheless, to evaluate the effect of ourassumptions in a real world setting, we validate our modelagainst experiments in a real testbed, setup for this purposein our indoor office environment. Despite the generic natureof the model, the experimental results from our IEEE 802.11

testbed show good match with the analytical predictionsand advocate the models utility. What is more, we find thatour model predictions also follow closely those of moreelaborate well-known analytical models [8].

Having confirmed the utility of our model, we nextdefine an interference-aware routing metric that explicitlytakes interference into account via our derivation. Thismetric is generic and could be used by various routingprotocols to estimate link and path weights. Similar tothe Expected Transmission count (ETX) metric [9], ourmetric estimates the number of transmissions (includingretransmissions) required to send a packet over a link.

However, the important difference between the two is that,unlike ETX which measures link quality directly (actively)using small probe packets, our metric tries to predict thelink quality based on information locally available at anode (passively).

Naturally, we are interested in whether and how muchthis lack of direct link measurements deteriorates therouting performance. To evaluate this, we use our testbedto perform two sets of experiments featuring intraflow andinterflow interference and variable settings for transmissionrate and transmit power. In all experiments, our metric iscompared against the minimum hop count and the ETX

metrics, the latter being the first of a whole family of probe- based metrics. In the first set, with one node-pair (dataflow) active at a time, our metric finds more high-throughput paths than ETX and minimum hop count do.

Varying the transmission rate and the transmit power doesnot change the relative performance of the metrics althoughthe absolute throughput values change, as expected. In thesecond set of experiments, we evaluate the three metricswith multiple active node-pairs (flows) simultaneously. Weobserve that our interference-aware routing metric per-forms at least as good as ETX and better than minimum hopcount despite the lack of probing.

Summarizing, the contributions of this paper are thefollowing: 1) we introduce a simple analytical model for theprobability of successful reception that can be calculatedusing information already available at the node and use realtestbed experiments to show that our models predictionsare sufficiently accurate; 2) we then propose an inter-ference-aware routing metric based on our derivation thatrequires no probing to estimate link and path quality, and isshown to perform at least as good as well-known probing-based routing metrics. Our contribution is also methodolo-gical. We demonstrate how a simple model for the radiointerference can yield good results when used for the design

of a higher layer network function, such as interference-aware routing. We definitely do not contest the value ofmore complicated models in general; we do howeverprovide an example where a simple model fares as wellas more complicated models.

The paper is organized as follows: In Section 2, wepresent our analytical derivation for the probability ofsuccessful reception over a link in the presence ofinterference. Numerical results showing the model sensi-tivity to its parameters and their independencies arediscussed in Section 3. In Section 4, we define ourinterference-aware routing metric, and in Section 5, we

present our indoor testbed. The model validation againsttestbed experiments is carried out in Section 6. In the samesection, we compare our model predictions with thosemade by other models. The performance evaluation of ourinterference-aware routing metric is presented in Section 7and we summarize related work in Section 8. We concludethe paper in Section 9, where we discuss how our workcould be applied to multirate networks and support routingmetrics that, besides expected transmission counts, alsotake into account the time devoted to these transmissions.

2 ANALYTICAL INTERFERENCE MODELING

Our analytical model formulation proceeds as follows: First,we derive the link delivery probability Pxi;xj that a transmis-sion from node xi is successfully received at node xj in thepresence of cumulative interference without taking a parti-cular MAC model into account; for example, nodes do notsense the medium before transmitting, as the case is withCSMA. Then, we include a simple enhancement into ourmodel that aims at capturing the effect of carrier sense andcalculate Pxj for the complete model. Finally, we expressthis probability as a function of node degree when networknodes are uniformly distributed in space.

2.1 Physical Model and AssumptionsIn our analysis, the network comprises a set of nodes Xfx1; . . . ; xng located in the euclidean plane. Node transmis-sions may interfere each other and the outcome of an

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individual transmission is determined by the SINR model(for example, see [6]). Under the SINR model, the transmis-sion success depends on the received signal strength (RSS),the interference caused by simultaneously transmittingnodes, and the environmental thermal noise level. Let Pw;ibe the transmit power of node i and T be the set of nodestransmitting at that instant (T X). A transmission from

node xi; i 2 T is successfully received by node xj ifPw;i

jxixj j

NPk2T ;k6i Pw;kjxkxj j ! : 1In (1), jxi xjj denotes the euclidean distance betweennodes xi and xj; N is the ambient noise power level, and isthe path loss exponent, which depends on the environmentand typically ranges from 2 to 5. The SINR model impliesthat a minimum signal-to-interference ratio ofis necessaryfor successful reception. The actual value of primarilyrelates to the specific physical layer design, such as the

deployed modulation, interleaving, and coding schemes, aswell as the receiver hardware.For the sake of analytical tractability, we make the

following set of assumptions:

A1. All nodes have similar receiver chain characteristics:omnidirectional antenna, the same transmit powerand noise floor, and similar physical layer perfor-mance, i.e., Pw;i Pw;j Pw and i j 8i 6 j.This is called the uniform node assumption. Underthis assumption, the node reception range rmax, i.e.,the maximum possible distance between two nodesallowing them to receive each other correctly in the

absence of other node transmissions, is given from

rmax ffiffiffiffiffiffiffiffiffiffiffi

PwN

s: 2

A2. Nodes transmit with equal probability (uniformload assumption). Note that the probability reflectsthe transmission attempt rate, i.e., the rate at whichnodes actually transmit data over the sharedmedium after the traffic shaping at MAC layer,rather than the incoming traffic load at the MAC

layer from higher layers. In general, the parameter and the number of nodes competing for the mediumare coupled with each other instead of varyingindependently. Their exact coupling relationshipdiffers according to the details of the specific MACprotocol. In the IEEE 802.11x suite of protocols, forexample, it is well known that the actual allowedvalues of the transmission probability depend onmany parameters, such as the number of contendingnodes, back-off algorithm, and bandwidth of thewireless medium (see [10], [11] for the protocoloperation under saturation and [12], [13] undernonsaturated conditions1).

In Table 1 we summarize our notation.

2.2 Interference (MAC-Agnostic) Model

We pick an arbitrary sender-receiver pair and evaluate theeffect of cumulative interference from other nodes on datareception. This simple model, sometimes referred to asphysical model [6], has often been used in studies of networkthroughput for ad hoc networks. In our derivation, we drawon it to introduce the concepts of interference zone andinterference area.

Definition 1. An interference zone Aij;m with respect to areceiver node xj is the area, where up to m 1 nodes cantransmit simultaneously, for all possible combinations of nodelocations therein, without resulting in unsuccessful reception atnode xj, in the absence of other transmissions in the network.

Definition 2. An interference area Cij;m with respect to a

receiver node xj is the area beyond which a minimum ofm 1simultaneous transmissions is required to result in unsuccessfulreception at node xj, for all possible transmitting node locations,in the absence of other transmissions in the network.

Lemma 1. Assume that a node xi transmits to another node xjand their distance jxi xjj equals r. Then, a third node xk liesin the interference zone Aij;m of node xj; m 2 f1; 2; 3 . . .g, ifits distance to the node xj; jxk xjj, satisfiesffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffim 1

p r < jxk xjj

ffiffiffiffiffiffiffiffim

p r; m 2 f1; 2; 3 . . .g: 3

Proof. From (1) and assumption A.1, the simultaneous

transmission ofm

nodes will not result in unsuccessfulreception due to interference at node xj, as long as

Pwr

NPmk1;k6i Pwjxkxjj ! ;which results in

Pwr

!Xm

k1;k6i

Pwjxk xjj

!:

The sum on the right-hand side is maximized when thedistance

jxk

xj

j;

8xk

2Aij;m is minimized. Requiring that

Pwr

!Xm

k1;k6i

Pwjxk xjjmin

!;


TABLE 1A Summary of Key Notation

1. In literature related to 802.11 DCF modeling, the transmission attemptrate is denoted either with (e.g., [11]) or with (e.g., [10], [12]).


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we get

Pwr

>m Pw

jxk xjjmin:

Therefore,

jxk xjjmin !ffiffiffiffiffiffiffiffi

mp

r rij;m:In other words, the simultaneous transmission of

m nodes does not result in unsuccessful reception due tointerference at node xj when all m nodes lie at distancegreater than

ffiffiffiffiffiffiffiffim

p r; or, equivalently, at least m 1 nodetransmissions are required to prevent successful datareception if all transmitting nodes lie outside the circlecentered on node xj with radius rij;m, which coincideswith interference area Cij;m. On the other hand, theinterference zone Aij;m is delimited by the intersection ofinterference area Cij;m with the complement of inter-ference area Cj;m1; Cij;m

TCj;m1, namely, interference

zone Aij;m is a circular ring bounded by the circumferenceof two concentric circles with radii rij;mrij;m1, as shown

in Fig. 1. For example, a node xk is located in theinterference zone Aij;2 if its euclidean distance to node xjis

ffiffiffi

p r < jxk xjj ffiffiffiffiffiffi

2p r. tu

The definition of interference zones then allows toapproximate the probability Pxi;xj that a transmission of xidestined to node xj is successful despite interference fromother nodes in the network as a function of the spatialnode distribution.

Let be the probability that a node is transmitting and

M be the number of interference zones Aij;mm 2 f1; 2; 3 . . .gthat are taken into account in the computation of Pxi;xj (M

depends on the spatial node distribution; we discuss howto select proper values of M when nodes are uniformly

distributed in space in Section 2.4.1). Then, Pxi;xj depends

on the number of nodes nAij;m and their exact position in

interference zone Aij;m. In the general case, the nodes maylie anywhere within the interference zones, encumbering aprecise derivation of Pxi;xj ; nevertheless, it is straightfor-ward to derive an upper and a lower bound for theresulting Pxi ;xj by considering two extreme cases regardingthe node positions.

In the first (worst) case, all nAij;m nodes within themth interference zone are assumed to lie at the inner zoneborder at distance rj;m1 from the receiving node xj. In thatcase, successful reception results as long as the numberof transmitting nodes within each one area Cij;mm 2f1; 2; 3 . . .g does not exceed m 1, respectively. Theresulting lower bound PLBxi;xj for the probability of success-ful delivery can then be written

PLBxi;xj 1 nAij;1 XM1

iM0

nAij;MiM

iM1 nAij;MiM

Xmax0;M2iM

iM10

nAij;M1iM1

iM11 nAij;M1iM1

Xmax 0;1PMn3 in i20

nAij;2i2

i2 1 nAij;2i2 :

4In (4), the summation is made from the further away

interference zones toward the inner ones. The number ofactive (transmitting) nodes iM lying in the most remoteinterference zone Aij;M determines the maximum numberof interferers iM1 that can be tolerated from the zoneAij;M1. Their sum in turn sets an upper limit to the numberof interferers iM2 in zone Aij;M2 that would not hinter

correct reception and so on. Under this worst-case scenario,even a single node transmission from the first interferencezone Aij;1 would result in transmission failure.

Of course, in thegeneral case, the m 1 transmissions thatcan be tolerated in interference zone m can be distributed inall possible locations within the zone. The further they arefrom the inner border of the zone, the better the SINRbecomes; and when all of them reach the outer border of thezone, at distance rij;m from the receiver node, it becomesfeasible to accommodate another, mth, transmission, withoutimpeding successful reception. Therefore, an upper boundPUBxi;xj for the link delivery probability is derived when weassume that all n

Aij;m

nodes within the mth interference

zone lie at the outer zone border, namely, at distance rij;mfrom the receiving node xj. Now, the maximum number ofnodes that may be transmitting in each one area Cij;m withoutresulting in unsuccessful transmission is m, respectively, i.e.,one more than in the worst case so that

PUBxi;xj XMiM0

nAij;MiM

iM1 nAij;MiM

Xmax0;M1iMiM10

nAij;M1iM1

iM11 nAij;M1iM1

Xmax 0;1PMn2 in i10

nAij;1i1

i1 1 nAij;1i1 :

5


Fig. 1. Interference zones Aij;m with respect to recipient node xj.


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The summation in (5) is carried out along the same linewith the computation of the lower bound; only now themaximum number of active interferers tolerated in eachzone is one more than before since they are assumed placedin the best possible (most remote) position within theinterference zones.

2.3 MAC-Aware Interference Model

The basic model does not make any assumption aboutthe actual MAC protocol that shapes the offered traffic. Theactual transmission attempt probabilities could be theoutcome of random access or the full backoff process of802.11 DCF operation, with the limitations discussed inassumption A.2. In this section, we take one step further tobring our model closer to CSMA/CA MAC protocols, wherenodes defer when they sense the medium busy (when thereception energy is over the Clear Channel Assessmentthreshold, CCAthr) and schedule their transmissions basedon an exponential backoff algorithm [1]. This mechanismonly partially solves the problem of interfering transmissionsas often nodes within the interference range of the receiverare outside the carrier sense range of the sender (hiddennodes). Our simple enhancement, aiming at preserving thesimplicity of our original model rather than incorporating

the full complexity of CSMA MAC protocols, takes intoaccount the physical carrier sense property (CCAthr) fornodes located in the first interference zone Aij;1. In otherwords, all nodes within the carrier sense range of thetransmitter and inside the first interference zone of thereceiver defer from transmitting.

In Fig. 2, r1 ffiffiffi

p r denotes the radius of interference

zone Aij;1 and

r2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

P wi10CCAthr=10

r

is the senders physical carrier sense range. Hidden nodes

can still exist in the area RH, given by

SRH r21 B; 6

where B is the surface of the intersection between Aij;1and senders physical carrier sensing area (see, forexample, [14])

B r21cos1r2 r21 r22

2 r r1

r22cos1

r2 r22 r212 r r2

12 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffir1 r2 rr1 r2 rr1 r2 rr2 r1 rp :

The two bounds for Pxi ;xj for the complete model resultfrom (4) and (5), when replacing nAij;1 with the expectednumber of nodes in area RH

nAij;1 nRh: 7In the rest of the paper, Pxi ;xj denotes the probability of

successful reception obtained from the MAC-aware model.In Section 4.1, we discuss how we can approximate the

parameter in an IEEE 802.11x protocol, and then, use it inthe computation of Pxi ;xj .

2.4 Probability of Successful Reception under

Uniform Node DistributionIn the general case, Pxi;xj is a function of the network radioload (via ), number of network nodes nAij;m in eachinterference zone Aij;m; 8m 2 f1; 2; 3 . . .g, propagation en-vironment (), and hardware equipment (). We showbelow that, under the assumption of uniform spatial nodedistribution, we can express Pxi;xj as a function of networkdensity and node degree. This is particularly attractive sincethe node degree can be easily obtained locally at each node.

For each node xi, it is possible to define its node degreeand transmission range.

Definition 3. The node degree dxi of a node xi is

dxi xjjP

jxixjj

N! ; xj 2 Xn fxig

( ): 8

In other words, the degree of the node xi equals thenumber of network nodes j j from which xi can success-fully receive a signal in the absence of any interference fromother nodes. In the case of uniform node distribution withnode density equal to , it is easy to see that

dxi rmax2: 9Under the uniform node assumption, the expected

number of nodes in an interference zone Aij;m will beproportional to its surface

EnAij;m r2ffiffiffiffiffiffiffiffiffiffiffiffiffim2

q

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffim 12

q ; 10

where r jxi xjj is the transmitter-receiver distance. Thelatter is always a fraction of the node reception range

r c rmax; 11where 0 < c < 1, a scale factor that depends on the nodedistribution as well as the routing protocol. For example,minimum-hop routing protocols tend to select nodes at the

edge of coverage as next hop, implying a value of c close tounity. On the contrary, protocols that favor reliable overshortest paths will yield smaller values of c. EnAij;m cannow be written as a function of the node degree dxj


Fig. 2. Hidden nodes area RH in the first interference zone Aij;1.


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EnAij;m c2 ffiffiffiffiffiffiffiffiffiffiffiffiffim2

q

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffim 12

q dxj: 12

We can then write the probability Pxi;xj as a function ofthe node degree dxj, if we replace nAij;m in (4) and (5)with the expected number of nodes in interference zoneAij;m; EnAij;m, rounded to the closest integer. For theMAC-aware interference model described in Section 2.3, the

number of nodes in the area RH becomes

nAij;1 nAij;1 SRHr21

: 13

2.4.1 Estimating the Number of Interference Zones, M

Although the number of zones considered in (4) and (5)does not have to be constrained, i.e., M 1, the numericalcomputation of Pxi;xj has to consider a finite number ofzones. To determine M, let us first study how theinterference contribution is spread over different zones.The width of the mth interference zone as a function of the

interference node index m is given by

fm r2m 12 m2; m 2 f1; 2;::Mg: 14It is then straightforward to show that the derivative of

fm isdfm

dm 4r

2

2m 12 m2 < 0; > 2; 15

namely, the width of interference zones for given ;;c isdecreasing with higher m values, and so does the expectednumber of nodes under uniform distribution, as (12)suggests. Therefore, the interference contribution from

different zones decreases as well and becomes negligiblefor some high enough value of m.

In general, M may be selected empirically taking intoaccount the particular network geometry. A more systema-tic approach would be to stop adding interference con-tributions from zones k > m, as soon as the worst-caseinterference from zone m falls below a given threshold; Mwould then equal

M: min mPwr

EnAij;m Pwrij;m1

%

; m 2 f1; 2; 3; . . .g

8 1 is a scaling factor; higher % will result in higherM values and vice versa.

The number of interference zones computed via (16) isplotted in Figs. 3a and 3b. As expected, the number of areasthat needs to be included decreases for shorter transmitter-receiver distances and higher signal attenuation (larger a)values. For example, when % 10; M ranges from 2 to 15 for 5, from 3 to 23 when 4, and from 3 to 33 for 5,as c varies from 0.1 to 0.8, respectively.

2.5 Interference Model Applicability under Node

MobilityAn interesting property of our interference model is that itcan address both static and mobile networks, in contrastwith other models that apply only to static networks [7], [8].

The two bounds for the probability of successful receptionin (4) and (5) allow for arbitrary node distributions in space.Different mobility models can be accommodated as long assteady-state spatial node distributions exist for theirmobility patterns.

For example, our derivation under the assumption that

nodes are uniformly distributed applies directly formobility models widely used in the literature, such as therandom walk and random direction. For these two models,it has been proved that if users are uniformly distributed intheir movement space, they remain so for arbitrary move-ment patterns [15].

In addition, the more generic derivations in (4) and (5)still hold when the node mobility patterns do not give riseto uniform node distribution. Bettstetter et al., for example,have analytically derived the spatial node distribution overa bounded rectangular area for the random waypoint(RWP) mobility model in [16]. Though less straightforward,their result could be the starting point for the derivation of

the number of nodes per interference zone, nAij;m,whenever the RWP model is deemed a valid assumptionfor the node mobility. Only now the resulting distributionof nodes among interference zones is strongly related to theactual position of the transmitter and receiving nodes,rather than simply their distance.

3 NUMERICAL RESULTS

In this section, we provide numerical results for the impactof the five parameters ;;;c, and dxj on the probabilityof successful reception Pxi;xj . Both worst-case (dashed line)and best-case (solid line) bounds, as estimated from (4) and(5) with the MAC-aware interference model adaptations ofSection 2.3, are plotted. In the case of the node degree dxj,it is important to note that we manipulate it by changing therespective node density (see (9)). Obviously, for a givennumber of network nodes, dxj changes with the cardreception threshold, , and path loss exponent, . Yet, sincefrom the MAC perspective it is the number of nodeneighbors that are more relevant, we choose to depict thevarious plots as a function of node degree, even though it isalways implied that the respective degree is determined bychoosing the node density accordingly.

3.1 Impact of the Transmission AttemptProbability,

For fixed ; , the communication range is also fixed. Aslong as c remains fixed, the radii of the interference areas


Fig. 3. Number of interference zones, M, included in the computation ofPxj as a function of the sender-receiver distance scale factor c.(a) 10; dxj 10; % 10. (b) 10; dxj 10; % 15.


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and sizes of interference zones do not change. Underuniform spatial node distribution, the number of nodes ineach zone increases linearly with the node density and thusalso with the node degree, as (12) suggests. On the otherhand, increase of for a given node degree value implies

more communication-active nodes. As a result, highervalues of both node degree and transmission probabilityresult in higher loss probability, as intuitively expected.

Fig. 4a plots the two bounds for the link deliveryprobability Pxi;xj as a function of the node degree forvarious values of the transmission probability . All otherparameters are kept constant; the specific values, i.e., 3:84; 2:5; c 0:5, were chosen so that they matchthe values measured in the testbed and reported in Section6. The decrease of successful reception probability is moredramatic for higher node degree values since the number ofpotential interfering nodes is then higher. One order sizeincrease of , from 0.003 to 0.03 reduces Pxi;xj by approxi-

mately 16 percent for dxj 30, versus less than 4 percentfor dxj 10. The difference between the worst- and best-case bounds is within 10 percent and broadens for highervalues. As a final note, in these examples corresponds toan unsaturated network (see discussion in Section 2.2).

3.2 Impact of the Reception Threshold,

The reception threshold determines when a MAC frame issuccessfully received. It depends on the transmission rate,frequency, and sensitivity of the network card/chipset;higher rates and lower quality network cards require higher values for achieving a given frame error rate. Typicalvalues for , as reported in network card specifications, are

2.5 to 25 [17].Increase of the reception threshold value at a given

environment (constant ) reduces the communicationrange, after (2), increases the widths of interference zones,as (3) suggests, and for given c results in higher concentra-tion of nodes at the first interference zones, see (10). Theresult is increased interference, as shown in Fig. 4b. Therelative reduction on the successful reception probabilityincreases with higher node density, where the concentrationof interfering nodes at the first zones becomes more visible.The relative difference between the upper and lowerbounds obtained under the MAC-aware interference modelstays well below 10 percent.

3.3 Impact of the Path Loss Exponent,

The path loss exponent models the reduction of the radiosignal power as a function of distance from the transmitting

source. Its values depend strongly on the radio propagationenvironment [18]. Combining (2) and (3), we could write forthe radius rij;m of interference area Cij;m

rij;m ffiffiffiffiffiffiffiffiffiffiffim p ffiffiffiffiffiffiffiffiffiffiffiPw

N s ffiffiffiffiffiffiffiffiffiffiffiffiffiffim

Pw

N

r: 17

As increases, the signal attenuation with distance ishigher and the radii of the interference zones decreases.Nodes can be placed closer to the receiver withoutinterfering with the intended signal. The impact of theparameter on Pxi;xj is plotted in Fig. 4c. As with Fig. 4a,higher node degree values amplify the variation of Pxi;xjwith . The margin between the two bounds increases with, reaching a maximum of 11 percent for 5.3.4 Impact of the Sender-Receiver Distance Scale

Factor, c

In our analytical derivation, we express the distance between the sender and receiver nodes as a ratio of themaximum communication range, c rmax. The impact of thesender-receiver distance on the probability of the successfulreception is plotted in Fig. 5. We vary the node degree,while letting all other parameters constant. As with and ,higher network densities magnify the effect of c. Only the


Fig. 4. Probability of successful reception versus node degree (i.e., node density ) for variable ; , and ; solid (dash) lines correspond to the upper(lower) bound values. (a) Variable ; 3:84; 2:5; c 0:5. (b) Variable ; 3:84; 0:02; c 0:5. (c) Variable ; 2:5; 0:04; c 0:5.

Fig. 5. Probability of successful reception versus node degree (i.e., nodedensity ) and sender-receiver distance scale factor c; 2:5; 4; 0:02; solid (dash) lines correspond to the upper (lower) boundvalues.


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latter is more dramatic in absolute terms than the one and have on the probability of successful reception.

Finally, Fig. 5 directly points to the well-known ineffi-ciencies of minimum-hop routing. Minimum-hop routingtends to select few but distant hops when selecting networkroutes. This trend results in more noisy but also, as Fig. 5suggests, more interference-prone links. On the other hand,shorter links may also imply a large number of hops,which can also be detrimental to throughput [6]. This trade-off can be resolved by interference-aware routing, which, asshown in Section 4, is the application targeted by our model.

Overall, the deviation of the two bounds is almostalways upper bounded by 10 percent, most of the times being around 5 percent. Although this deviation is notnegligible, it corresponds to the worst-case possible penaltydue to the uncertainty about node locations within theinterference zones. The uncertainty reduces with the indexof zone, being highest for the first widest interference zone,and to some extent reflects the inaccuracy of localizationtechniques yielding the node positions. In practice, how-

ever, one would weigh these bounds, e.g., taking theiraverage, to come up with a more realistic estimate of Pxi;xj .

4 FROM INTERFERENCE MODELING TOINTERFERENCE-AWARE ROUTING METRIC

The ultimate objective of our interference model is tosupport the routing function. In this section, we describe aninterference-aware routing metric drawing on the modeland explain practical aspects related to its implementation.

4.1 Estimation of Transmission Attempt

Probability The node transmission probability in the analysis ofSection 2 cannot be directly controlled in IEEE 802.11 MAC.In our actual metric implementation using the open sourceMadwifi wireless adapter drivers [19], the traffic load isestimated in real time. We modified the source code of thedrivers similar to [20] to measure the time the wirelessmedium is sensed busy. The percentage of the busy timebttotal (0 bttotal 1) in 1 second time windows isreported to the interference-aware routing metric process.The busy time report includes the percentage of time btxiduring which the medium is sensed busy due to transmis-

sions of sender xi. This information is fed to the estimationof the traffic load induced from interfering nodes to eachsender-receiver pair.

For uniform node distribution, we approximate thetransmission attemptprobability xi;xj forathelink xi xj as

xi;xj bttotal btxi

dxj ; 18

where dxj is the degree of the receiver node xj. Thenode degree dxj is retrieved directly from the routingprotocol state.

Note that to estimate in (18), we resort to the uniform

load contribution assumption over the local neighborhood ofeach node, as if all the interfering traffic load in the sharedmedium is uniformly spread over the neighbors of thereceiver node. In other words, different receiver nodes may

well attribute different estimates to a common neighbor oftheirs depending on the radio load each one senses.

4.2 Calculation of Interference-Aware RoutingMetric

Our interference-aware routing metric borrows essentialdesign properties of the ETX routing metric [9]; we postponea discussion on how could we support other routing metrics,

originally relying on active probing, in the Section 9. ETXestimates the number of transmissions (including retrans-missions) required to send a packet over a link. Let Pxi;xj bethe expected delivery ratio of the sender node xi to receivernode xj and Pxj;xi be the reverse delivery ratio, i.e., theprobability that the acknowledgment packet is transmittedsuccessfully. Then, the probability that a packet is receivedand acknowledged correctly is Pxi;xj Pxj;xi . Assuming thateach attempt to transmit a packet is statistically independentfrom the precedent attempt, individual transmission at-tempts can be viewed as Bernoulli trials and the number ofattempts till the packet is successfully received as a

geometrically distributed variable, GeomPxi;xj Pxj;xi.Therefore, converting the delivery ratios in both directionsto expected number of transmissions (ETXs), the interfer-ence-aware metric value Ixi; xj is

Ixi; xj 1Pxi;xj Pxj ;xi

; 19

where the probability of successful reception Pxi;xj at node xjis given from (4) or (5) or, more generally, some function ofthe two bounds. Note that, besides the independence ofindividual transmission attempts, the use of (19) screens thefollowing assumptions: 1) retransmissions at the MAC layer

are infinitealthough the more realistic case of finiteretransmissions calls for a more elaborate formula, the useof (19) preserves the ordering of paths at the routing layer2

and simplifiesthe respective computations; 2) the probabilityof success in consecutive (re)transmission attempts is thesamethere is experimental evidence that this assumptionisnot accurate under nonsaturated demand in 802.11 networks[22]; 3) the experienced packet loss does not vary (signifi-cantly) with the packet size. We discuss further thisassumption in Section 6.

Our interference-aware metric is generic and can be usedfrom any routing protocol. In our experimental evaluation,

we used the Destination-Sequenced Distance Vector (DSDV)[23] routing protocol. DSDV is a distance-vector protocolusing sequence numbers to ensure up-to-date routing tableinformation. To accommodate our metric in the DSDVimplementation, we extended the DSDV routing table entryto include a field for the probability Pxi;xj .

As routing decisions are made by the sender node xi, thequestion that arises now is how xi estimates the metricvalue Ixi; xj. Whereas the reverse probability of successfulreception at node xi (Pxj;xi ) from xj is estimated locally at xi(see Section 4.1), the forward probability of successfulreception Pxi;xj needs to be communicated to xi from xj. In


2. When the transport layer carries out end-to-end retransmissions, therelative positions of links within the paths should also be taken into accountin optimal path selection, besides the probabilities Pxi ;xj , otherwisesuboptimal paths may emerge [21].


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fact, each node xj advertises its local estimates of Pxi;xj forits neighbor nodes xi; i 6 j.

To avoid additional routing overhead, the messagesupdating the forward probabilities of successful receptionare encapsulated into the triggered routing update messagesof DSDV. Algorithm 1 describes the essential steps tocalculate the interference-aware routing metric at each node.

Algorithm 1. Estimation of the interference-aware routingmetric value Ixi; xj at node i.

Upon packet reception pif p

data packet from neighbor j then

Update variables btxi ; bttotal and calculate xi;xj (18)else

if p routing packet from neighbor i then1. Get the probability of successful reception Pxj;xi andestimate the metric Ixi; xj (4), (5), (13), (19)2. Update the routing table. The routing protocol thenmaintains the routing tables updated

else

Packet not used in the algorithmend if

end if

5 EXPERIMENTATION PLATFORM

We evaluate our interference model and interference-awarerouting metric using testbed experiments. Our TIC-Nettestbed consists of 23 stationary Linux PC nodes equippedwith 802.11a/b/g Atheros cards. The nodes are located atthe second floor of the ETZ building, as illustrated in Fig. 6.The offices have floor-to-ceiling walls made mostly out ofwooden material. All nodes in our testbed communicateusing the IEEE 802.11b. The 802.11b cards during theexperimental evaluation are set to ahdemo mode, aMadwifi driver specific ad-hoc mode, where no manage-

ment packets are sent to maintain connectivity. The RTS/CTS handshake mechanism is disabled in line withthe default behavior for most wireless cards [24], and therate adaptation mechanism is inactive. All experiments are

carried out during weekends or nights to minimizeinterference from external sources.3

5.1 Obtaining Model Inputs

The experimentation results are compared with the analy-tical estimates of the probability of successful receptionPxi;xj under uniform node distribution. The required inputsfor this calculation are the parameters , , and . Theeuclidean distance r between the transmitter and receivernodes can become available through GPS [25] or otherpositioning methods. In our experiments, the node dis-tances are statically given to the routing protocol.

5.1.1 Path Loss Exponent Estimation

The dependence of path loss on is approximated by thelog-distance path loss model (e.g., [18])

PijdBm Pdo dBm 10 logdijdo

; 20

where d0 is a reference distance, dij is the distance betweenthe sender i and the receiver j; PijdBm is the meanreceived signal power in decibel meter, and Pd0 dBm isthe mean received power at a reference distance d0. Weused two nodes to measure the signal strength as a

function of distance in our indoor office environment. Thesignal strength is derived by the RSS values reported bythe cards at various distances. Setting d0 4 m andcarrying out a least-square fit computation, we estimatedPd0 51:12 dBm, 3:84. The measured values and theleast-square fit curve are plotted in Fig. 7b.4

5.1.2 SINR Threshold Estimation

The CMU wireless channel emulator [26] was used toestimate the SINR threshold of our Atheros wireless


Fig. 6. Our wireless mesh network testbed. The 23 802.11a/b/g nodes are distributed in offices all over the floor covering an area of approximately32 79 m2.

3. External interference was caused only by the beacons frames broadcast by the wireless APs (Access Points) installed in the building, which isnegligible compared to the traffic generated from our experiments.

4. The exponent is taken to be the same for all node pairs in the testbedsince all nodes lie within an office environment. At a further level ofaccuracy, these values could be measured separately for different areas inthe floor or even for each single node pair. Note that these measurementsare carried out once and offline.


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cards. In our experiment, two Atheros cards similar to theones in our testbed were connected to the hardwareemulator; one card was sending five thousand 802.11 broadcast packets at 1 Mbps and the other was receivingthem. Note that 802.11 broadcast packets are not subject toMAC retransmissions. Varying the attenuation of the radiosignal through the emulator in increments of 1 dB, we

estimated by measuring the ratio of the correctlydelivered packets as a function of the RSS. The results areplotted in Fig. 7a. Since the noise floor of the Atheros cardswas measured to be approximately 96 dBm, the knee ofthe delivery ratio curve at RSS 92 dBm means that thethreshold value equals 4 or 2.5 dB.

The last parameters required to estimate the probabilityPxi ;xj under uniform node distribution are the number ofinterference zones, M, and expected number of nodes perinterference zone; their values are obtained from (16) and(10), respectively.

6 MODEL VALIDATION VIA TESTBEDEXPERIMENTATION

In this section, we assess the prediction capability of ourinterference model via testbed experimentation. The analy-sis in Section 2 is carried out considering a simple model forthe MAC operation. Real-world MAC protocols bear a largenumber of finer engineering details, which cannot be easilycaptured into a analytical model. Therefore, we resort toexperimentation to get a better understanding of thestrengths and limitations of our analysis in a realisticwireless network environment based on a real MACprotocol, such as the IEEE 802.11b.

6.1 Experimentation Methodology

The wireless network cards are configured to send at1 Mbps with 31.62 mW (15 dBm) of transmit power. Theaverage communication range in our testbed for thistransmit power was measured approximately to 25 m.The sender-receiver pair used in our experimental evalua-tion are nodes 4 and 23, respectively. This is one of the mostfavorably placed node pairs in the testbed in the sense thatwe can selectively include various testbed nodes in ourexperimentation and change the network density whilepreserving their adequately uniform spatial distribution

thereinwe have also tested nodes 3, 10, 11 as sender nodesand moved receiver node 23 within a radius of 2 m aroundthe location shown in Fig. 6, obtaining comparable numbersof interference zones and nodes therein and similar results.

The euclidean distance between nodes 4 and 23 isr 12:5 m, which corresponds to a distance scale factorvalue of c 0:5. All captured traces of this evaluation areavailable in [27].

6.1.1 Distribution of Nodes

For the and values estimated earlier in Section 5, theradii of interference areas for the receiver node 23 usingLemma 1 are: r23;1 15:8 m, r23;2 19 m, r23;3 21:1 m,r23;4 22:8 m, and r23;5 24:1 m. Equation (16) provides thenumber of interference areas that have to be considered and(12) yields the expected number of nodes EAj;m8m 1; 2; 3 . . . M in each interference zone as a function of thedegree of the receiver node 23. We vary the network densityby letting the node degree dxj take values in the interval[5..15] nodes. For each node degree value (scenario), weactivate the respective nodes listed in Table 2.

6.1.2 Traffic Generation

In each experimental scenario, all participating nodes sendIEEE 802.11 broadcast packets at constant bit rate. This iscommon practice in related work [7], [8], [28] since MAC broadcast packets involve no retransmissions or link-layeracknowledgments. We estimate the successful receptionprobability under simultaneous interfering transmissionsmeasuring the ratio of the successfully received packetsover the total number of broadcast packets sent.

In the remainder of the paper, the experimental resultsare compared against the average of the two bounds for Pxi;xj ,as derived in Section 2. Note that, as shown in Figs. 4 and 5,the deviation of two bounds for the testbed parameters and

considered node degree range lies within 10 percent.

6.2 Experimentation Results

The model predictions festig are compared against theexperimental results factualig in Figs. 8a, 8b, and 8c; weplot average values of the successful packet receptions with90 percent confidence intervals. We quantify the accuracy ofour model by computing the root-mean-square error(RMSE), defined over the total number k of predictions asffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

Pesti actuali2

k

s:

There is close match between the two curves in all threefigures. The analytical predictions for the probability ofsuccessful reception match the monotonic change of Pxi;xj


Fig. 7. (a) Packet delivery ratio as a function of signal strength. (b) Signalstrength PijdBm as a function of the distance dij.

TABLE 2Number of Nodes in Each Interference Area Aij;m8m 1; 2 . . . 5


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with the node degree throughout the 5::15 range of nodedegree values for different . This is also reflected in theRMSE values. For 0:005, the RMSE is 0.01 and forhigher 0:04 the RMSE equals 0.02.

To assess how well our model trades simplicity withaccuracy, we compare it with the general model forinterference (GMI) proposed in [8]. The model, whichreflects the state-of-the-art in interference modeling, usesmeasurements to RF-profile the network nodes and links.The RF profiles are then fed into explicit Markovian modelsfor the 802.11 sender and receiver behavior to derive thepacket loss probability. The GMI evaluation in [8] waslimited to five simultaneous broadcast senders. Here, wecompare the predictions of our model and GMI in scenariosof Table 2 involving up to nine simultaneous broadcastsenders under unsaturated traffic demands.

Table 3 illustrates the relative error in prediction, absestiactuali

actuali, for node degree dxj 5::8. In these scenarios,

both models yield comparable accuracy in predicting themeasured probability of successful delivery. Interestingly,our model appears to even outperform GMIfor higher valuesof (i.e., 0:05). Moreover our model features distinctadvantages over GMI; it does not require seed measurements(RFprofiling) andscales better than GMIwithhigh number ofnodes from a computational point of view. In fact, itssimplicity renders it directly applicable to routing, as shown

later in Section 4.A final note on the experimental results concerns the

impact of packet size. The analytical derivation for Pxi;xj isnot packet size aware, namely, it does not take into accountthe packet size transmitted over the medium. We investi-gated the impact of packet size with a set of experiments.For the given , , and c values of our testbed setup, we

simultaneously varied the packet size and packet transmis-sion rate so that they yield the same equivalent node

transmission probability , as estimated in Section 6.1. For

example, the pktsize;rate pairs estimated for 0:04 are128bytes; 20pkts=s, 256bytes; 15pkts=s, 512bytes; 8pkts=s,and 1;024bytes; 4:5pkts=s. Fig. 9a plots Pxi ;xj for all fourscenarios. The deviation between the four combinations

increases with node degree, but remains overall below 0.06.

In fact, the deviation between the curves is comparable to

the confidence intervals for the measured results, suggest-ing that there is no significant change of Pxi;xj with packet

size. Another way to see this is at Fig. 9b, which plots the

Pxi;xj values obtained with two scenarios against each

other. Absolute coincidence of the measured values in the

two cases would align the 2D points along the 45 degree

slope line. Note that according to the 802.11 performance

analysis models (see [9], [10], [11], [12]), the collisionprobability is constant for given transmission attempt

rate in fact, it is a monotonically decreasing function

of in 0; 1. On the other hand, larger packet sizes shouldmake transmissions more prone to errors for given link

quality (Bit Error Rate). For the rest of the evaluation, we

use packet sizes of 128 bytes.

7 INTERFERENCE-AWARE ROUTING METRICPERFORMANCE EVALUATION

The ultimate mission of our interference model is to become

the main building block for the interference-aware metricdescribed in Section 4. In this section, we evaluate theperformance of our interference-aware metric versus the


TABLE 3Relative Error in Prediction

Fig. 8. Analytical model versus testbed experimentation results. The analytical model values are 3:84, 2:5, a nd c 0:5.(a) 0:005; RMSE 0:01. (b) 0:02; RMSE 0:016. (c) 0:04; RMSE 0:019.

Fig. 9. Impact of packet size on Pxi ;xj . (a) Pxi ;xj versus packet size.(b) Scatter plot of Pxi ;xj .


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ETX and minimum hop count (Hop Count) metrics in ourindoor TIK-Net testbed. The minimum hop count repre-sents the alma mater of metrics used by default on mostrouting protocols, whereas the active-probe measurementsof ETX [9], [29] are the base for a whole family of metrics,which are viewed as current state-of-the-art [30]. Notethat the original ETX specification does not explicitly

capture the carrier sense impact (sender-side interference).However, the part of it that is due to the intraflowinterference is taken into account by ETX derivatives likethe Weighted Cumulative Expected Transmission Time(WCETT) [4] and the Metric for Interference and ChannelSwitching (MIA) [5], which explicitly consider the use ofchannels across the network routes. We discuss how ourmodel-driven metric can be extended along these lines inSection 9.

The Click toolkit [31] was used for our experimentation;we implemented our metric on it and relied on the Click- based implementations of the ETX metric and DSDV

routing protocol.

7.1 Experiment Sets

We evaluate our routing metric through two main sets ofexperiments:

. Experiment Set A: One node pair is active at a time,with 20 TIC-Net testbed nodes taking turns intransmitting data, resulting in 20 19 380 differ-ent sender-receiver pairs.

. Experiment Set B: Ten node pairs transmit simulta-neously. The pairs used in this set of experiments arelisted in Table 4; nodes with id i send to nodes with

id 20 i 1 with i1::10. This scenario is mostchallenging since it results in many multihop pathsand much cross-traffic in the network.

In the first set of experiments (set A), we evaluate thecapability of metrics to find high throughput paths in theabsence of interflow interference, i.e., interference fromother flows. In this specific set of experiments, interferenceis mainly due to simultaneous transmissions in multihopforwarding (intraflow interference). In every experiment,each node sends UDP packets at maximum rate for30 seconds. Each round is followed by 20 seconds ofpause to let routing entries converge to the initial state (no

traffic/boot phase). We vary the transmit power Pw (10/18 dBm) and the transmission rate (1/11 Mbps) each timeexecuting 50 rounds. Thus, the total duration of set A is380 50 3 seconds or 15.9 hours testing all three metrics

under a single (Bit_rate, Pw) tuple and approximately

64 hours for all tuples.The second set of experiments (set B) evaluates the

metrics in the presence of interflow interference, with

multiple simultaneously active data flows. In order to

generate a challenging experimental scenario, we selected

node pairs with the largest possible distance at our testbed

(see Table 4 and Fig. 6). Within an experiment round, each

sender node is configured to send 5,000 UDP packets at a

rate of 10 packets per second. The duration of each round is

500 seconds followed by 100 seconds of pause time, thus in

total 600 seconds. We repeat each round 20 times, resulting

in 600 20 3 seconds or 40 hours for the three metricsunder each (Bit_rate, Pw) tuple.

7.2 One Node Pair Active at a Time

Fig. 10a compares the throughput Cumulative Distribution

Functions (CDFs) (in packets per second) of the paths found

for all 380 node pairs by DSDV using the ETX, minimum

hop count, and our interference-aware metric, under

Bit rate 1 Mbps, Pw 18 dBm, and Pkt size 128 B. Inthe figure, there are essentially two areas, above and below,

approximately 150 packets per second. The values abovethis threshold correspond to node pairs that communicate

over a single hop, whereas those smaller or equal to it to

multihop paths. The fastest two-hop path has at most half


TABLE 4Node Pairs Used for the Second Set of Experiments (Set B)

Fig. 10. One node-pair active: Bit rate 1 Mbps, Pw 18 dBm, andPkt size 128 bytes. (a) Throughput CDF (in packets per second) ofpaths found by DSDV using ETX, minimum hop count and ourinterference-aware metric. (b) Throughput histogram (in packets persecond) of paths found by DSDV using ETX, minimum hop count andour interference-aware metric.


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the throughput of a single-hop path due to interferingtransmissions of two consecutive hops [9], [32].

More amenable to discussion is the throughput histo-gram (in packets per second) of the paths found by eachmetric as presented in Fig. 10b. Again, there are two distinctareas in this graph; the one with throughputs correspond-ing to one-hop paths (right side) and that with multihoppaths (left side). The right side suggests that our metricfinds more high throughput one-hop paths than the othertwo metrics, namely, among all node pairs for which one-hop paths were chosen, higher proportion of node pairs liesin the high throughput area than with the other metrics.Likewise, the left side of the graph implies that when ourmetric decides in favor of a multihop path for a node pair,the chances are much higher that this pair will get thehighest throughput possible: our metric finds up to threetimes more multihop paths with high throughput (between125 and 150 packets per second) when compared to ETXand minimum hop count. In other words, our metric tendsto select better paths, which are subject to less intraflowinterference, when the other metrics decide in favor of morelossy links.

One should note that min hop, as expected, and ETX, toa fewer extent, are more aggressive in using one-hop paths.For some small number of flows, this aggressiveness paysoff in that even over lossy one-hop paths they manage toget higher throughput than that they would with the besttwo-hop path. But for the majority of node pairs, it doesnot. Therefore, for many one-hop flows chosen by the minhop count the actual throughput is well less than theexpected >150 value. ETX should not suffer from thisproblem since it relies on active probing for estimating the

link delivery probabilities. Yet, as admitted also in the ETXpaper [9], heavy load causes the MAC protocol to becomeextremely unfair, distorting the probe-based measurements.Thus, ETX might not accurately estimate the link deliveryprobabilities and accordingly result in suboptimal paths.

7.2.1 Effect of Transmit Power

Lower transmit powers reduce the effective node commu-nication range; the network is less connected and nodesrequire more hops to communicate. Furthermore, routingmetrics have fewer paths to select. In that specific set ofexperiments, we decrease the transmit power Pw from 18 to

10 dBm. We also did experiments for very low transmitpower Pw 0 dBm (1 mW); however, the network in thatspecific set of experiments is very sparsely connected and thethroughput of most of the node pairs is very close to zero.

Fig. 11a plots the throughput CDFs for Pw 10 dBm andPkt size 128 bytes. Comparing with the results for Pw 18 dBm (see Fig. 10a), all metrics find paths with relativelylow throughput. Our interference-aware metric finds fewermore than one-hop paths with throughput between 125 and150 packets per second; for Pw 18 dBm, there are almost100 node pairs, whereas for Pw 10 dBm only 65 nodepairs. However, it still finds more paths with high

throughput than both ETX and minimum hop count (abouttwo times more paths with high throughput values).

In summary, the transmit power affects the performanceof the metrics since it directly determines the connectivity of

the network. The advantage of our interference-awaremetric over ETX and minimum hop count is more profoundin densely connected networks (higher transmit power).The gain is smaller in sparsely connected networks becauseavailable paths that can be found from a routing protocolare fewer and there is little margin for differentiation in thedecisions made by the three metrics.

7.2.2 Effect of Transmission Rate

It is known that there is an inherent trade-off between

transmission rate and effective transmission/communica-tion range. Higher transmission rates result in higherthroughput, but can only be supported within lowereffective transmission range, resulting in sparser network.

We repeat our experiments for transmission rate equal to11 Mbps. The sensitivity threshold for the cards used in ourexperimental evaluation, as reported from the manufacturer,are 89 dBm for 1 Mbit per second and 82 dBm for 11 Mbitper second (for 8 percent packet error rate). Fig. 12a showsthe throughput CDFs for Bit rate 11 Mbit per second,Pw 18 dBm, and data packets of Pkt size 128 bytes. Incomparison with the experiments at 1 Mbps (Fig. 10), the

overall throughput increases; 30 percent of pairs achievethroughput over 200 data packets per second for Bit rate 1 Mbit per second, while for 11 Mbit per second therespective value is 60-70 percent for all metrics.


Fig. 11. One node-pair active: Bit rate 1 Mbps, Pw 10 dBm, andPkt size 128 bytes. (a) Throughput CDF (in packets per second) ofpaths found by DSDV using ETX, minimum hop count and ourinterference-aware metric. (b) Throughput histogram (in packets persecond) of paths found by DSDV using ETX, minimum hop count and

our interference-aware metric.


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Looking into the performance of individual metrics,similar to the aforementioned results, the three metrics findapproximately the same number of one-hop routes. The gainof our interference-aware routing metric is on the left half ofthe figure where it finds multihop paths of higher through-put. This can be clearly seen in Fig. 12b where ourinterference-aware metric outperforms ETX and hop countand finds almost three times more high throughput paths(between 500 and 600 packets per second) than ETX andminimum hop count. ETX finds more paths between 200 and300 packets per second, whereas minimum hop count finds

more low-throughput paths (between 0 and 100 packetsper second).

Overall, our results suggest that our interference-awaremetric performs at least as good as ETX and minimum hopcount in almost all experimental scenarios, irrespective oftransmit power and transmission rate settings. Our metricyields performance gain for multihop paths, where intra-flow interference affects the end-to-end throughput. Mini-mum hop count does not account for interference, whereasETX estimates link losses based on probe measurements.Under heavy load, the ETX probe packets may be distorted,resulting in biased measurements.

Note that these experiments are more useful in showingthe dynamics and biases of the different metrics. Theirperformance in realistic scenarios is better reflected in thesecond type of experiments shown in the following, where

multiple flows compete for the medium. There thepenalization of min hop and ETX aggressiveness canbe seen more clearly.

7.3 Multiple Active Node Pairs

In the second set of experiments, we evaluate theperformance of the three routing metrics under multiplesimultaneous data flows. In the results that follow,we estimate the average throughput values as well asthe 95 percent confidence intervals. Fig. 13a compares thethroughput (in packets per second) of each sender-receiverpair (1-10 as illustrated in Table 4) for Bit rate 1 Mbps; Pkt size 128 bytes, and Pw 18 dBm. Generally,our interference-aware metric and ETX achieve higherthroughput when compared with the minimum hopcount. Specifically, for the node pairs 1, 2, 7, 8, and 9,the throughput of our interference-aware metric is higherthan ETX (10 percent on average) and minimum hopcount (30 percent on average). ETX achieves higherthroughput for the node pair 10, while for node pairs 3,4, 5, 6 the throughput is similar to our interference awaremetric. While ETX finds lower but comparable throughputpaths to the interference-aware metric, minimum hopcount achieves consistently the lowest throughput for all

node pairs.Fig. 13b presents the throughput (in packets per second)

for lower transmit power, namely, Pw 10 dBm. Amongthe three metrics, minimum hop count emerges as the most


Fig. 12. One node-pair active: Bit rate 11 Mbps, Pw 18 dBm, andPkt size 128 bytes. (a) Throughput CDF (in packets per second) ofpaths found by DSDV using ETX, minimum hop count and ourinterference-aware metric. (b) Throughput histogram (in packets persecond) of paths found by DSDV using ETX, minimum hop count andour interference-aware metric.

Fig. 13. Multiple node-pairs active: Throughput (in packets per second)of paths found by DSDV using ETX, minimum hop count and ourinterference-aware metric. (a) Bit rate 1 Mbps, Pw 18 dBm, andPkt size 128 bytes. (b) Bit rate 1 Mbps, Pw 10 dBm, and Pkt size 128 bytes.


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sensitive to the transmit power setting. For node pairs 1, 2,

4, and 10, the throughput drops up to 50 percent belowthat obtained with transmit power of 18 dBm. The averageper-pair throughput over all node pairs for the threemetrics is presented in Table 6. Notably, our interference-aware routing metric outperforms ETX and minimum hopcount. We explain why this is the case in the paragraphsthat follow.

7.3.1 Impact of Path Length

Table 5 presents the average path length of all experimentrounds for transmit power Pw equal to 10 and 18 dBm. Tocalculate the average path length, we keep track of the paths

taken by data packets. The minimum hop count features theshortest average path length (3.2 and 3.29) followed by theinterference-aware metric (3.26 and 3.36) and ETX (3.4 and3.56). Similar results are obtained for the average pathlength of each node pair.

The small diversity in path length among the ETX,minimum hop count, and interference-aware metrics doesnot justify the difference in throughput for both experi-mental settings. In other words, since routing metrics selectpaths with approximately equal average length, thereshould be another reason differentiating the performanceof the three metrics.

7.3.2 Load Distribution

We now turn our attention in the distribution of data trafficacross network nodes and paths. In Fig. 14, the traffic load

distribution with the 95 percent confidence intervals of theaverage values is shown. More specifically, the bar chartshows the average number of packets sent and/or receivedper second at each node, i.e., nodes selected from the

routing metrics to forward data traffic. We observe thatrouting metrics favor different nodes for forwarding datatraffic. Nodes 11 and 12 are selected from ETX, while ourinterference-aware metric pushes the traffic to nodes 2, 4,15, 17, and 18. Minimum hop count favors nodes 11 and 12similar to ETX, but with lower data volume.

The total volumes of transferred data for our interference-aware metric and the ETX are approximately equal, asshown in Fig. 15 that plots the per-node sorted average load.The qualitative difference between our interference-awarerouting metric and ETX is that our metric distributes thetraffic over less interfering paths. Nodes 11 and 12 selectedfrom ETX and hop count interfere to each other as they arewithin the transmission of each other. Our interference-aware routing metric distributes the traffic on less interfer-ing nodes (nodes 2, 4, 15, 17, and 18) as the estimation of linkdelivery ratios takes into account the impact of interference.The ETX metric does not directly account for link load sincebroadcast packets sent at low rate (one broadcast packet persecond) may have different loss ratios than the actual packetloss of data packets sent at higher rates.5

Summarizing the comparative performance evaluationof the three metrics, our main findings are:

. Our interference-aware routing metric performs at

least as good as the ETX and clearly better than theminimum hop count in most experimental scenarios,with intraflow interference or without. The perfor-mance improvement over ETX ranges from 5 to11 percent when average values are compared,exceeding 25 percent for individual node pairs. Ofcourse, the size of our testbed is such that it would be surprising to see higher performance differences between non-naive (e.g., hop count) metrics. It isconceivable that in larger testers, giving rise to pathswith even more hops, the performance gap will bemore pronounced.

. Our experimental results suggest that load balancingis the key performance differentiation factor between


TABLE 5Average Path Length over All Rounds

(Bit rate 1 Mbit per Second, Pkt size 128 Bytes)

TABLE 6Average Throughput over All Node Pairs

(Bit rate 1 Mbit per Second, Pkt size 128 Bytes)

Fig. 14. Multiple node-pairs active: Histogram of traffic load (averagenumber of packets sent/received per second) at all nodes forBit rate 1 Mbps, Pw 18 dBm, and Pkt size 128 bytes.

Fig. 15. Multiple node-pairs active: Traffic load (average per secondnumber of packets sent/received per second) sorted for all nodes.Bit rate 1 Mbps, Pw 18 dBm, and Pkt size 128 bytes.

5. The broadcast probing implementation of ETX is the original onedescribed in [3].


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the two metrics. Taking explicitly interference intoaccount, our metric distributes the load amongnetwork nodes better than ETX.

. Although they affect the absolute path throughputvalues achieved by the three metrics, neither thetransmit power nor the transmission rate have asignificant impact on their relative performance.

8 RELATED WORK

Multiple access interference has always been one of the mainconcerns when building wireless networks. Whereas it isquite well explored in infrastructure-based cellular networks(see, for example, [33] and [34]), its characteristics and impactin multihop networks are less thoroughly understood.

Jain et al. in [2] propose the use of conflict graphs fordescribing interference between neighboring nodes. Con-trary to the typical graph semantics, vertices of the graphsare the individual network links(hops) with an edgeconnecting them when the two links interfere. The authors

use this abstraction to compute bounds for the optimalnetwork throughput under ideal interference-aware routingand argue in its favor. Conflict graphs may be eitherunweighted, when they are extracted according to theProtocol Interference Model [6], or weighted, when basedon the Physical Interference Model (SINR) model. Theadvantage of the SINR model is that it can take thecumulative effects of interference due to simultaneoustransmissions into account. It has been used, beyond theexplicit context of conflict graphs, to derive capacity boundsand optimize scheduling alone [35], or jointly schedulingand routing [36]. In our work, we also start from the SINRmodel to derive an interference-aware routing protocol.

The practical estimation of interference, sometimes asinput for determining the edges (and vertices) of the conflictgraph, is addressed in [28] and [7]. Padhye et al. in [28] use broadcast transmissions to derive the Broadcast Interfer-ence Ratio (BIR) as a measure of the interaction betweentwo network hops, whereas Reis et al. combine a simplifiedanalytical model for the CSMA/CA function of 802.11 withfewer measurements (n versus n2 in [28], where n is thenumber of network nodes) to estimate BIR values anddetermine the graph edges [7]. While their model is limitedto two competing broadcast senders, Qiu et al. develop ageneral interference model for arbitrary number of senders

[8]. They build up an N-dimensional discrete-time MarkovChain (MC) for the state of each one of the N nodes, whichmay transmit or idle during a time slot. They usemeasurements and assumptions about the distribution ofwhite noise and interference to derive the transitionprobabilities of this MC and solve it numerically to obtainthe steady-state probabilities and the resulting packet lossprobabilities. It is not therefore straightforward to feed themodel as input to other tasks, such as the design ofinterference-aware metrics. Furthermore, the computationalcomplexity of the model is prohibitive: the state space of theMC grows exponentially and even with state pruning, it is

hard to get results for N > 10 nodes. Both models have asstarting point RSSI measurements that profile the networknodes and become inputs to the analytical model. On thecontrary, our approach is fully analytical and circumvents

the need for measurements and their pitfalls, such as thelimited accuracy of the reported RSSI values and theirinappropriateness for nonstatic networks.

In a different line of work, focusing more on protocolengineering, there is agreement in the research communitythat interference should be an input for routing protocols.Several routing metrics have been proposed to overcomethe inefficiencies of minimum-hop routing in this respect.

They rely on active probing for measuring the path roundtrip time (RTT), ETXs [3], and the WCETT [4] and makingtheir routing decisions. The actual probing may be im-plemented in broadcast mode or, as in [37], in unicast modeand be combined with cooperative and passive measure-ments to better trade accuracy with measurement overhead.It is also possible to further process these measurementstogether with information about the used radio channelsover each link to account for inter- and intraflow inter-ference, as the Metric of Interference and Channel Switch-ing (MIC) does [5]. The main disadvantage of theseapproaches is that their dependence, even to a differentextent, on probe measurements. Active probing calls foradditional capacity and results in unnecessary energywastage. Almost all implementations of probing metricsin routing protocols that we are aware of (DSDV, LQSR,OLSR) do not shut down the probing during no trafficperiods. Consequently, there is a periodic energy overheadpaid by probing based metricsthe small size of the packetis not as much a factor for energy consumption as the factthat something is sent (see, e.g., [38]). On the other hand,probing metrics cannot avoid measurement inaccuraciesand feature limited responsiveness to network nodemobility [3]. On the contrary, our model-based metriccircumvents the need for probe measurements and the

pitfalls related to them, while exhibiting comparableaccuracy with those approaches.

9 CONCLUSIONS

Interference in ad hoc wireless networks is the core subjectof our paper. We derive an analytical expression for the linkdelivery probabilities as a function of the network density,load, propagation environment, and network card hard-ware. The analysis is initially carried out assuming a genericMAC model, which does not take into account anyengineering details of actual protocols, such as the IEEE802.11x suite of protocols. We then extend our analytical

derivation with a simple enhancement to capture the carriersense function of real-world MAC protocols. The predictioncapacity of our analysis is evaluated in a wireless meshnetwork testbed, which was set up particularly with thisobjective. Measurements obtained from the testbed suggestthat our model compares favorably with state-of-the-artinterference models that model explicitly the sender andreceiver operation in 802.11, without requiring RF measure-ments to profile the network nodes.

We then apply this interference model to interference-aware routing. We introduce a routing metric, whichcomputes the expected number of transmissions over a path

relying on the analytical derivation of the link deliveryprobabilities according to our model. The metric is testedunder a large set of experimental scenarios featuring intra-flow and interflow interference and different transmission



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rate and transmits power settings. Without any reliance onactive probe measurements, our metric finds better pathsthan the minimum hop and equally good with the ones thatthe ETX routing metric finds. The reason for this is that ourmetric takes advantage of its interference-awareness to betterdistribute traffic load over the network and mitigates thedetrimental impact of interference on the network through-put. Notably, it does so wasting neither network capacity nornode radio power on probe transmissions making itparticularly attractive for energy constrained nodes.

Throughout this paper, we use the ETX metric ascomparison reference for our metric and the evaluation iscarried out in single-rate networks. This is a deliberatechoice since our model effectively substitutes the black box measurement-based estimate of link delivery prob-abilities, which lies at the core of not only ETX, but a wholefamily of metrics drawing on it; for example, the ETT,WCETT, and MIC metrics discussed in the related worksection. Notably, it is straightforward to expand theapplicability of our work in multirate networks and support

rate-sensitive metrics, such as ETT. The model formulationand the link success probability formulas (4) and (5) wouldthen have to account for the transmission rate of node xi;different rates sij from the transmitter node imply differentthresholds sij for the receiver, which, in turn, determine theradii r

sijij;m and interference zone areas A

sijij;m and, eventually,

the rate-specific link delivery probabilities Psijxi;xj . From the

metric computation point of view, nodes would need to become aware of the rate at which each neighbor nodetransmits to them to locally estimate the link deliveryprobabilities for each link. Such information can becommunicated among nodes with the help of the routing

protocol messages much as the link delivery probabilitiesare in the single-rate network. Awareness of the transmis-sion rate besides the link delivery probabilities would thenenable estimates of expected transmission times to be usedin ETT-like metrics.

Overall, our work is an argument in favor of modelingsimplicity. We do not dispute the general utility of moreelaborate modeling approaches; we do however give anexample, i.e., interference-aware routing, where equallygood results may be obtained with simpler models.

APPENDIX

MODEL FOR NONUNIFORM SEND RATES

The model in Section 2 was derived under the assumptionthat nodes transmit with equal probability over the radiomedium. This assumption can be relaxed, only now moreinformation should be propagated in the network and aclosed-form expression is no longer obtainable for the twobounds of the link delivery probability.

In general, the nonuniform send rates could be the resultof different send rates at the MAC layer or application ratesor both. The SINR threshold s and the reception range rsmaxdepend directly on the transmit rate s of the sender node.

The SINR threshold value then directly determines theradio interference areas Csij;m and the width of theinterference zones through (3). In the general case, eachnode nm;k in the mth interference zone might transmit with

a different transmission probability, m;k. Therefore, thedistribution of transmitting nodes in each interference zoneis that of a sum of binomial random variables withdistributions Sm

Pk Bnm;k; pm;k, where k is the number

of the mth zone node partitions with respect to thetransmission probabilities, 1 k nAij;m; while nm;k !1 with Pk nm;k nAij;m and pm;k m;k are the twoparameters of the corresponding Binomial distribution. Theresulting distribution can be both exactly calculated withrecursive methods and approximated efficiently withdistributions drawn from the Pearson family of continuousdistributions [39].

The lower bound for the link probability of receptionwould then become

PLBxi;xj P rS1 0XM1iM0

P rSM iM

Xmax0;M2iM

iM10

P rSM1 iM1 . . .

Xmax 0;1PMn3 in i20

P rS2 i2:

21

The upper bound ((4) in Section 2) can be computed in asimilar manner.

Note that now the node cannot just be measuringcumulative traffic load in the radio medium, as (18)suggests. It rather has to keep track of the activities of theindividual nodes, which add to the complexity of therouting metric implementation.

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