Spatial BackoffContention Resolution for Wireless Networks

Technical Report

March 2006

Xue YangCommunications Technology Lab

Corporate Technology GroupIntel Corporation

2111 N.E. 25th AveHillsboro, OR 97124

Email: xue.yang@intel.com

Nitin VaidyaUniversity of Illinois at Urbana-Champaign

Department of Electrical and Computer Engineering,and Coordinated Science Laboratory

1308 West Main StreetUrbana, IL 61801

Email: nhv@uiuc.edu

Abstract— Traditional medium access control (MAC) protocolsutilize temporal mechanisms such asaccess probability or backoffinterval adaptation for contention resolution. They typically takethe set of competing nodes as a given, and address the problemofadapting each node’s channel access behavior to the given channelcontention level. This is a temporal approach for contentionresolution, which aims to separate transmissions from differentnodes in time to achieve successful transmissions.

We explore an alternative approach for wireless networks—named “spatial backoff”—that adapts the “space” occupiedby the transmissions. Each transmission in a wireless networkcompetes for a certain space. By adapting the space occupiedby transmissions, the set of “locally” competing nodes, andthus,the channel contention level, can be adjusted to reach a suitablelevel. There are different ways to realize spatial backoff.In thispaper, we propose a dynamic spatial backoff algorithm usingthejoint control of carrier sense threshold and transmission rate.Our results suggest that spatial backoff can lead to a substantialgain in channel utilization.

I. I NTRODUCTION

Past studies on contention-based medium access control(MAC) protocols have often taken a temporal approach. Thatis, when two nodes are competing for a common channel, theirchannel accesses are separated in time to ensure successfultransmissions. For example, nodes A and B in Figure 1 com-pete for the channel access. Since their transmissions interferewith each other, A and B’s transmissions are separated intime using temporal contention resolution. Such a temporalapproach typically takes the set of competing nodes as a given,and addresses the problem of adapting each node’s channelaccess behavior (e.g., channel access probability, or backoffinterval) to the given channel contention level.

In this paper, we explore an alternative contention resolutionapproach for wireless networks—named “spatial backoff”—that adapts the space occupied by transmissions. Observethat transmissions in wireless networks compete for space aswell, since wireless nodes communicate over air and there is

significant interference among nodes that are spatially closeto each other. We consider each transmission as occupyingcertain part of the space. Intuitively, node B is said to bewithin the space occupied by a transmission from node A, ifa concurrent transmission from node B will prevent reliablereception of A’s transmission. Thus, the space occupied bya transmission depends on the signal level at the intendedreceiver as well as interference that may be posed by othernodes. It should be noted that our proposed protocol does notrely on knowledge of the space occupied by a transmission.

As shown in Figure 1, for the sake of illustration, we usea shaded circular area to represent the space occupied by atransmission. In practice, however, the occupied space is notnecessarily circular.1 Nodes A and B’s transmissions in Figure1 cannot overlap in time because they are within each other’soccupied space. On the other hand, if small enough spacesare occupied by nodes A and B’s transmissions, as shown inFigure 2, the two transmissions can be separated in space andthey both can proceed successfully at the same time.

We refer to the space occupied by a transmission as the“contending region” around the transmitter. It should be notedthat contending region is a property of a transmission, al-though we may often associate the contending region withthe transmitter for the sake of brevity. Figure 3 illustratesthe contending regionω aroundS for a transmission fromnode S to node D.2 Transmissions by nodes located withinthe contending region ofS (e.g., S4, S5, S6, S7) willcause erroneous reception of the transmissions from S to D.Therefore, node S has to compete for the channelin timedimensionwith the nodes in its contending regionω. We referto such contention as “local channel contention” of nodeS.

1In general, the interference that may be posed by other nodesdependson the protocol parameters. The interference tolerance level of a transmissiondepends on the transmission power, rate, and etc.

2Again, the area is shown circular only for the sake of illustration.

Fig. 1. Temporal contention resolution.

Fig. 2. Spatial contention resolution.

Nodes outside of the contending region ofS (e.g.,S1, S2, S3)may have their transmissions overlapped in time with nodeSas long as the SINR requirements of these transmissions canbe satisfied. By using spatial backoff, the size of contendingregionω can be adapted (as elaborated later). As a result, thelocal channel contention of each node can be adjusted to asuitable level, such that the local contention can be resolvedefficiently using temporal contention resolution mechanisms.At the same time, by possibly allowing more concurrenttransmissions, the space can also be utilized more efficiently.Consequently, spatial backoff can help to improve the channelutilization, and thus, the network aggregate throughput.

Fig. 3. Contending region.

The rest of this paper is organized as follows. In Section II,we discuss how spatial backoff affects throughput. Proposeddynamic spatial backoff algorithm is discussed in Section III,

and its performance is evaluated in Section IV. Section Vsummarizes the related work. We present conclusions andfuture directions in Section VI.

II. SPATIAL BACKOFF AFFECTSTHROUGHPUT

A. Adapting CS threshold and transmission rate

The space occupied by a node while competing for channelaccess depends on many factors such as its transmission power,transmission rate, and also the interference caused by othertransmissions. Different approaches can be designed to adjustthe contending regionω. We consider a MAC protocol basedon Carrier Sense Multiple Access (CSMA) as an example.Carrier sensing refers to listening to the physical mediumto detect ongoing transmissions. Only if the received signalstrength detected at a node is below aCarrier Sense (CS)ThresholdCSth may the node access the wireless channel.Given a fixed transmission power used by other nodes, a nodewill transmit more aggressively using a higher CS threshold,as the example in Figure 4 illustrates. The horizontal axis inFigure 4 represents the distance from node A; the verticalaxis represents the signal strength of A’s transmissions; andthe curve plots the received signal strength versus distance forA’s transmissions. When node D uses CS thresholdCS1, D isrequired to defer its transmissions whenever A is transmitting,which implies that D has to compete for the channel accessin time with node A. On the other hand, when a higher CSthresholdCS2 is used, node D is allowed to transmit to C atthe same time when A is transmitting to B.

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Fig. 4. Larger CS threshold and lower rate lead to smaller contending region.

Note that increasing the CS threshold (with a fixed trans-mission power) allows transmitters to be closer to each otherand causes more interference. In the example of Figure 4, ifD uses CS thresholdCS2 instead ofCS1, the transmissionfrom A to B will encounter a larger interference due to theconcurrent transmission from node D. As we know, the qualityof a communication link depends on the interference at thereceiver caused by other transmissions; the higher the signal-to-interference-and-noise-ratio (SINR), the higher the rate atwhich packets can be transmitted reliably. To account for theincrease of interference when using a larger CS threshold, thetransmission rate often needs to be reduced. In essence, as theabove discussion suggests, a larger CS threshold and a lowertransmission rate lead to a smaller contending region. Thus,

spatial adaptation of contending region can be achieved usingthe joint control of CS threshold and transmission rate.

For the ease of argument, we assume for now that all nodesin the network use the same CS threshold and transmissionrate. However, our protocol allows each node to choose theseparameters independently, as elaborated later. For a giventransmission from some node S to another node D, for futurereference, we defineconcurrenttransmissions as other trans-missions that can overlap in time with theS-to-D transmissionwithout causing unreliable reception atD. We also definesimultaneoustransmissions as those transmissions from nodeswithin the contending region of nodeS, which start shortlybefore or after the start ofS-to-D transmission and causeerroneous reception atD. Notice that carrier sensing cannothelp prevent simultaneous transmissions that start withinashort time interval, due to the delay required for carrier sensing(which includes the propagation delay). From the perspectiveof MAC layer, the aggregate throughput for a given networkdepends on the medium access efficiency in resolving the localchannel contention, the number of concurrent transmissionsin the network, and the transmission rate between each trans-mitter/receiver pair. It is straightforward to see that a smallercontending region allows more concurrent transmissions inthenetwork, at the price of lowering transmission rates. A lessstraightforward, yet important, observation is that a smallercontending region can also help to improve the mediumaccess efficiency in resolving the local channel contention. Weelaborate on this observation below.

• A smaller contending region can reduce the collisionprobability when resolving the local contention.Consider the transmissions from S to D in Figure 3. Thereare two primary sources of interference for receiver D.One type of interference comes from other concurrenttransmitters outside the contending regionω (e.g., trans-mittersS1, S2, andS3), which may transmit even whenS is transmitting because the detected signal strengthfrom S’s transmission is below their CS threshold. Theother type of interference comes from what we usuallyrefer to ascollisions, when the simultaneous transmissionattempts from transmitters inside the contending regionoccur. Such events can happen, for example, when nodesS4, S5, S6, S7 start their transmissions close enough tothe start time of nodeS’s transmission.By reducing the transmission rate when using a smallercontending region, the interference from concurrent trans-missions outside the contending region can be taken intoaccount. However, such adaptation cannot address theinterference from simultaneous transmissions inside thecontending region effectively. This is because simultane-ous transmissions may be from a node that is arbitrarilyclose to the receiver; for instance, nodeS5 is very closeto the receiver nodeD in our example in Figure 3.Therefore, local channel contention inside the contendingregion has to be resolved in time domain. When usingtemporal MAC protocols (e.g., IEEE 802.11 DCF) toresolve the local channel contention, the probability of

simultaneous transmissions (i.e., collision probability)often increases rapidly with the number of competingnodes, which, in turn, is a non-decreasing function of thecontending region. As such, a smaller contending regioncan result in a smaller number of locally competing nodesand can lower the collision probability. The tradeoff hereis that transmission rate decreases due to the increasedinterference from outside contending region when thecontending region is reduced.

• A smaller contending region can reduce the “rate-independent” MAC overhead when resolving the localcontention.We define rate-independent overheadof the MACprotocol as the overhead, by which the channel timeconsumed is independent of the transmission rate usedfor data packets [1]. For example, the duration of inter-frame spaces (DIFS, SIFS, EIFS, etc.) in IEEE 802.11DCF is fixed regardless of the transmission rate used fordata; hence, they are rate-independent overheads. LetPl

(in bits) be the packet payload size,T (in seconds) be thechannel time consumed by the rate-independent overheadassociated with each transmission, andR (in bits persecond) be the transmission rate. Adopting a simplifiedmodel, it can be readily shown that TR

Pl+TRfraction

of channel capacity is wasted in the rate-independentoverhead. Therefore, the smaller the rateR, the smallerthe channel wastage in rate-independent overhead.As we have discussed before, when using a smallercontending region, the transmission rate often needs tobe reduced to account for the increased interferencefrom outside the contending region. As a result of thelowered transmission rate, the channel wastage in rate-independent overhead can be reduced. This observationis also made by Yang et al. in [2], although that paperdoes not present a protocol utilizing the observation.

To summarize, a larger CS threshold and a lower trans-mission rate lead to a smaller contending region. By using alarger CS threshold to bring concurrent transmitters closer toeach other, the MAC efficiency in resolving the local channelcontention can be improved, due to the reduced number oflocally competing nodes and the reduced rate-independentoverhead. At the same time, since a lower transmission ratecan tolerate more interference at the receiver given a receivedsignal strength, more concurrent transmissions can proceedreliably. The price paid to gain above benefits is the reducedtransmission rate. Such a tradeoff implies that there exists op-timal CS threshold and transmission rate which can maximizethe aggregate throughput for a given network. Intuitively,anetwork with a larger transmitter density will prefer a smallercontending region for the transmissions. Here the transmitterdensity is defined as the number of transmitter/receiver pairsin the area covered by the maximum transmission range. Withthe increase of transmitter density, the benefit of reducedlocal channel contention resulting from a smaller contending

region becomes more significant, and more transmitters areavailable to exploit the improved spatial reuse. Hence largerCS threshold and lower rate are generally preferable fornetworks with denser traffic patterns.

To provide a better understanding of the impact of CSthreshold and transmission rate on the aggregate throughput,we now present some simulation results for random networks,obtained using a modified ns-2 simulator. We modified theinterference model in ns-2 version 2.26 such that the inter-ference from all concurrent/simultaneous transmissions areaccumulated to properly evaluate SINR at a receiver. Thephysical layer characteristics follow the specifications of IEEE802.11a, with transmission rates at 54, 36, 18, and 9 Mbps.We assume that transmissions at a certain rate are successful ifthe corresponding SINR threshold is met. The SINR thresholdused are listed in Table I [3]. The MAC protocol follows thespecifications of IEEE 802.11 DCF, but with the contentionwindow size CW fixed at 31 (i.e., exponential backoff isdisabled). RTS and CTS transmissions are disabled so thatwe can focus on the impact of CS threshold. Two-ray groundradio propagation model, which models the large scale pathloss, is used in the simulations.

TABLE I

Rates (Mbps) SINR (dB) Rates (Mbps) SINR (dB)54 24.56 36 18.8018 10.79 9 7.78

In addition to adequate SINR, the received signal needsto be above a certainreceived signal thresholdRXth forreliable reception to occur. The value ofRXth thus limitsthe maximum transmission range. In all our simulations, weuse identicalRXth and transmit power levels at all nodessuch that the receive power level at 35 meter distance is equalto RXth under the two-ray ground radio propagation model.Four randomly generated networks with increasing transmitterdensity are simulated. More specifically, in a 300 m× 300 marea, 8, 11, 16 and 40 transmitter/receiver pairs are randomlyplaced, as shown in Figures 5(a), (b), (c), and (d), respectively.As we are interested in the maximum achievable aggregatethroughput, all flows are constantly backlogged. The payloadpacket size is 512 bytes. All results presented in Section IIare averaged over 20 simulation runs, and the 99% confidenceinterval for the presented results are less than 1% of the meanvalues.

In the simulations of this section, all transmitters use thesame static CS threshold and transmission rate. We refer tothis as “static scheme”. Various combinations of CS thresholdand transmission rate are evaluated. The static scheme helpsdetermine the optimal performance when using a static andidentical combination of rate and CS threshold at every node.The aggregate throughput over all flows is presented in Figure6. In each plot of Figure 6, four different curves correspondtofour different transmission rates used; the horizontal axis rep-resentsβ = CSth

RXth

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Fig. 5. Random topologies with increasing transmitter density.

the value of CS threshold (CSth); the vertical axis representsthe aggregate throughput of all the flows in the unit of Mbps.We refer toβ = CSth

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as the “normalized” CS threshold.As we can see in Figure 6(a), when there are only eight

flows, it is best to transmit at the highest available rate of 54Mbps and useβ = −22 dB. However, when the number offlows increases to 11 in Figure 6(b), the maximum aggregatethroughput is obtained when the rate is set to 36 Mbps andβ= −14 dB. Observe that in Figure 6(b), the peak throughputobtained using rate 54 Mbps is 28% lower than the maximumthroughput. Thus, the rate that was optimal in the previous caseis significantly sub-optimal for 11 flows. Further increasing thenumber of flows to 16, as shown in Figure 6(c), the maximumthroughput is now achieved when the transmission rate is setto 18 Mbps andβ = −10 dB; the peak throughput obtainedwhen using both rate 36 Mbps and rate 54 Mbps are nowmuch worse than the maximum throughput. When increasingthe number of flows to 40 in Figure 6(d), the maximumthroughput point remains at rate 18 Mbps andβ = −10 dB;this is because the SINR thresholds of rates 18 Mbps and 9Mbps are relatively close (see table I). In the topologies wehave simulated, the slightly improved spatial reuse when using9 Mbps is not sufficient to compensate the halved transmissionrate (from 18 Mbps to 9 Mbps).

The optimal CS threshold and transmission rate depend onthe transmitter density in the network, and more generally,onthe traffic patterns in the network. It is important to use theappropriate values for both CS threshold and transmission rate,otherwise the aggregate throughput may suffer a significantloss. Additionally, note that in above simulations, we haveforced all transmitters to use the same CS threshold andtransmission rate. In general, different source nodes mayview the network conditions differently, depending on theirneighborhood. A good choice of CS threshold for one sourcenode may not be good for others. Ideally, we would likeeach node to make its own decision on the values of CS

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Fig. 6. Aggregate throughput in random topologies (payloadsize: 512 bytes).

threshold and transmission rate to be used. Allowing eachnode to independently choose its parameters also alleviatesthe overhead occurred in global coordination. Because of theabove reasons, distributed algorithms that allow each nodeto dynamically search for the appropriate CS threshold andtransmission rate are desired. One such algorithm, which wename asdynamic spatial backoffalgorithm, is presented inSection III.

B. Adapting transmission power and rate

The joint adaptation of CS threshold and transmission ratecan help control the size of the contending region, and thus,realize spatial backoff as discussed above. There exist otherways as well. For example, it is possible to use the jointadaptation of transmission power and rate, as the example inFigure 7 shows. Assume node A is transmitting to B usingpowerP2. With a fixed CS thresholdCS, node D has to deferits transmissions whenever A is transmitting, since the signalstrength from A’s transmissions at D is higher thanCS. As aresult, nodes A and D have to compete for the channel accessin time. On the other hand, if A uses a lower transmissionpowerP1, node D can transmit to C at the same time whenA is transmitting, although they may both have to transmit atlower rates. Therefore, a lower transmission power and a lowertransmission rate lead to a smaller contending region; andspatial backoff can also be realized using the joint adaptationof transmission power and rate. In this paper, we focus oninvestigating spatial backoff algorithms that control theCSthreshold and transmission rate, assuming that transmission

AB

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CS

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Fig. 7. Lower power and lower rate lead to smaller contendingregion.

power is fixed. Note that reducing transmission power atMAC layer may affect the connectivity, and the resultinginteraction between MAC and routing layers adds complexityto the spatial backoff problem. We delay the joint control oftransmission power, rate and CS threshold to our future work.

III. D YNAMIC SPATIAL BACKOFF ALGORITHM

The goal of the spatial backoff algorithm is to allow eachnode to search the two-dimensional space defined by theCSthresholdand thetransmission rateto determine the suitablevalues of these parameters. Note that when multiple flows orig-inate from a single source node, this node may use a differentcombination of rate and CS threshold for each of its receivers.In this paper, we often associate these parameters with thesource node for simplifying the description. However, it shouldbe noted that these parameters are per flow basis. Ideally, we

would like to find the optimal operating point for each nodesuch that the network aggregate throughput can be maximized.Note that the optimal operating point for different nodes canbe different, depending on their neighborhood. The difficultyin the optimization problem is that aggregate throughputis a global metric. Aggregate throughput not only dependson the local contention resolution efficiency experienced byeach individual node, but also depends on the transmissionrates used by various transmitter/receiver pairs and the totalnumber of concurrent transmissions in the network. In otherwords, for a transmitter to reach the optimal operating pointthat maximizes the aggregate throughput, it has to gatherinformation from other transmitters in the network. Due tothe dynamic nature of wireless networks and the substantialcost associated with obtaining global information, we are moreinterested in devising a distributed algorithm that enables eachnode to make decisions based on its local information. On theother hand, by using only local information, it is not alwayspossible to find the optimal operating point, as we demonstrateusing the example below.

Consider the first scenario in Figure 8(a). There are twoflows, one from node 1 to 1R and the other from node 2 to2R. The topology is symmetric for nodes 1 and 2. Assume thatthere are two “non-trivially different” CS threshold values,cs1 and cs2, that nodes 1 and 2 can use. By “non-triviallydifferent,” we mean that the interference will change wheneverCS threshold changes. Without loss of generality, assumecs1 < cs2. By usingcs1, suppose that node 1 will defer whennode 2 is transmitting, and vice-versa. As a result, nodes 1and 2 can transmit alternately at the same rate, say,R1, if theyboth usecs1. On the other hand, when usingcs2, suppose thatnode 1 will transmit even though node 2 is transmitting. Asthe network is symmetric, nodes 1 and 2 can both transmitconcurrently at some rateR2 if they both usecs2. AssumingR2 < R1

2 , in this scenario, the optimal CS threshold for node1 is cs1 in order to maximize the aggregate throughput.

Now we consider the second scenario in Figure 8(b), whichonly differs from Figure 8(a) in node 2R’s location. In thisscenario, node 2R is moved away from the interfering node 1.As a result, node 2 can transmit to node 2R at a higher rate,sayR3 (R3 > R2), when nodes 1 and 2 transmit concurrently.At the same time, the transmission rate of node 1 remains atR2 when nodes 1 and 2 transmit concurrently. Node 2R canbe placed close enough to node 2 such that the conditionR3+R2 > R1 is satisfied, whereR1 is the aggregate throughputwhen nodes 1 and 2 transmit alternately usingcs1. As such, inFigure 8(b), the optimal CS threshold for node 1 to maximizethe aggregate throughput iscs2.

The two scenarios in Figures 8(a) and 8(b) cannot bedifferentiated from the local viewpoint of node 1. In bothcases, node 1 gets to transmit at rateR1 when usingcs1,and gets to transmit at rateR2 when usingcs2. Limited bythe local information, it is not possible for node 1 to find theoptimal CS threshold for both scenarios.

Using the above example, we argue that, limited by the localinformation only, it is not always possible for an individual

source node to find the optimal operating point to maximizethe aggregate throughput. As such, the goal of our work is todesign a simple mechanism that can be easily incorporated intoexisting MAC protocols to take advantage of spatial backoffand to improve aggregate throughput. We do not make claimsregarding the optimality of the proposed dynamic spatialbackoff algorithm in this paper. As the above example shows,no local optimal algorithm based only on local informationexists. However, as our results in the next section suggest,our protocol is able to achieve good performance in typicalnetwork topologies.

A. Protocol Description

Our dynamic spatial backoff algorithm allows each sourcenode to search for an operating point with appropriate valuesof CS threshold and transmission rate for itself, in order toimprove the throughput. Given the possible range of CS thresh-old3 and the multiple levels of transmission rate supportedby a wireless transceiver, a naive exhaustive search in thetwo dimensional space can lead to poor performance. This isbecause of the potentially large number of operating points, asignificant fraction of them not being desired ones. Therefore,the design of our dynamic spatial backoff algorithm includesreducing the search space, and then incorporating suitablesearch rules.

1) Reducing the search space:Suppose that each node mayuse one of availableK rates. We represent them using anarray Rate[], where Rate[j] > Rate[i] if j > i (i, j ∈

[1, ..., K]). In order to reduce the cost of searching over thetwo-dimensional space of rate and CS threshold values, foreach available transmission rate, we identify the smallestCSthreshold that may be used in conjunction with that rate. Inparticular, letCS[i] be the smallest CS threshold that may beused in conjunction withRate[i]. How should we determinethe suitable value forCS[i]? While many different approachesmay be devised for this, we use the approach described below.

When some nodeS transmits to another nodeD using afixed transmission rate, two reasons (other than the collisionsdue to simultaneous transmissions from nodes within thecontending region) can cause an erroneous reception at nodeD:

(i) The first reason is that CS threshold used by nodeSmay be too large. The interference atD is proportional tothe detected signal strength at nodeS (this is because thesignal detected at nodeS can also propagate to nodeD butpossibly with a different channel gain). Thus, increasing theCS threshold used by nodeS will allow node S to starttransmitting even if nodeD is experiencing a higher levelof interference when the transmission fromS begins, andvice-versa. Thus, transmission failure occurring with larger CSthreshold used by nodeS may imply thatS has over-estimatedthe interference tolerance level of nodeD.

(ii) The second reason for error may be due to the largeinterference from other transmitters, which begin transmitting

3The minimum CS threshold is constrained by the radio sensitivity.

1 1R 2R 2

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Fig. 8. The optimal CS threshold for node 1 is different for two different network settings.

after nodeS has started its transmission. Carrier sensingat nodeS cannot help to detect this type of interference,since carrier sensing is performed before a node begins itstransmission.

We consider an interference limited environment. As definedpreviously,RXth is the lower bound on the received powerlevel for the receiver to be able to decode the signal. Thus, ifSINR[i] is the SINR threshold for rateRate[i], interferenceless than or equal to RXth

SINR[i] shall not affect the correctreception at rateRate[i], if the received power level is morethan RXth. Secondly, observe that when nodeS uses a CSthreshold, say,PCS , it will transmit when the detected signalstrength is not higher thanPCS . Although the interference atreceiverD will not be identical to that atS, we usePCS

as an approximate estimate on the interference posed to nodeD when the transmission fromS starts. We defineCS[i] asfollows.

CS[i] =RXth

SINR[i](1)

Above discussions suggest that, when using a CS thresholdless than or equal toCS[i] to transmit at rateRate[i], itis not likely that nodeS will over-estimate the interferencetolerance level at nodeD. In other words, if a transmission atrateRate[i] using a CS threshold larger thanCS[i] fails, thenthe cause may be that the used CS threshold is too large. Onthe other hand, if a transmission at rateRate[i] usingCS[i]fails, there is not much benefit in reducing the CS thresholdfurther. Since for a higher rate, the SINR threshold is higher,it follows that CS[j] > CS[i] if j < i (i, j ∈ [1, ..., K]). Asshown in Figure 10, our dynamic spatial backoff algorithmsearches the subspace above or on the diagonal line for thebest combination ofRate[] andCS[] for each node (we willelaborate on the search process). That is, our algorithm limitseach node to use one of the availableK rates, and for eachsuch rateRate[i], the choice of CS threshold is limited toCS[j], j ≤ i. It should be noted that the search rules describedbelow is independent of the manner in which the values ofCS[i] above are determined.

2) Search rules:With K transmission rates available, wedefine “rate level” as a number from1 to K such that ratelevel 1 is the lowest transmission rateRate[1], and rate levelK is the highest rateRate[K]. In addition to rate arrayRate[]and CS threshold arrayCS[], each node also maintains anindex variableRindex and an index arrayCSindex[]. Rindex

represents the array index of transmission rate (i.e., transmis-sion rate equals toRate[Rindex]), whereRindex ∈ [1, ..., K].Given theRindex, there is an associated CS threshold array

index CSindex[Rindex] that is dynamically adjusted. At anygiven time, a node will transmit at rateRate[Rindex] usingthe associated CS thresholdCS[CSindex[Rindex]]. The datastructure is illustrated in Figure 9.

Rindex

Rate CSindex CS

Fig. 9. Data structure of dynamic spatial backoff.

Initially, at each node,Rindex = 1 andCSindex[i] = i (1 ≤

i ≤ K). Thus, each node starts from using the transmissionrateRate[1] and the CS thresholdCS[CSindex[1]] = CS[1].A node will take different actions, depending on whetherits past transmissions have beensuccessesor failures. Wedelay our discussions on the conditions, under which a nodeconsiders its transmissions assuccessesor failures, to the latterpart of this section. The actions of each node onsuccessesor failures are governed by the 4 rules below. For each rule,we also provide our motivation behind the rule. Note that, inthe following text, “diagonal line” refers to the diagonal inFigure 10.

• Rule 1: When transmissions are successful, the nodewill increase its transmission rate by one level unless thehighest transmission rate is already in use, i.e.,Rindex =min(Rindex +1, K). If this results in a rate increase, theCS threshold associated with the old rate will be associ-ated with the new rate, i.e., using the newRindex value,we performCSindex[Rindex] := CSindex[Rindex − 1].Motivation for Rule 1:Successful transmissions indicatethat interference is small enough that the SINR thresholdof current rate is met. Following two actions may possiblybe taken by the node, each of which attempts to increasethroughput by exploiting any remaining interference mar-gin at the receiver. One possibility is to transmit at ahigher rate, and the other is to transmit more aggressivelyby increasing the CS threshold. However, if we allowa node with successful transmissions to increase its CSthreshold, the successful node will become more andmore aggressive and consume more and more channelresource, potentially starving other nodes. In view ofthis, in our dynamic spatial backoff algorithm, a nodeincreases its transmission rate when transmissions havebeen successful, as elaborated earlier in this paragraph.

• Rule 2: When transmissions fail and the operat-ing point is above the diagonal line, the CS thresh-old associated with current transmission rate will bedecreased by updating theCSindex. In particular, weperform CSindex[Rindex] := min(CSindex[Rindex] +1, Rindex). Note that, for the operating point to be onor above the diagonal in Figure 10, we must have thatCSindex[Rindex] ≤ Rindex.Motivation for Rule 2:Recall thatCS[j] > CS[i] if j < i(i, j ∈ [1, ..., K]). As we discussed in Section III-A.1,when transmitting at rateRate[Rindex] using CS thresh-old larger thanCS[Rindex], the cause of transmissionfailures may be that the transmitter has chosen CS thresh-old too large, over-estimating the interference tolerancelevel of the receiver. By reducing the CS threshold, thenode will transmit more conservatively, which may help itimprove its transmission success probability at the currentrate.

• Rule 3: When transmissions fail and the operatingpoint is on the diagonal line, the node will decreaseits transmission rate by one level unless the lowest rateis already in use, i.e.,Rindex := max(Rindex − 1, 1).At the same time, the CS threshold associated with thereduced rate will be applied (CS threshold will increase);that is, the CS threshold will beCS[CSindex[Rindex]]using the new value ofRindex.Motivation for Rule 3:Suppose that a node’s transmissionfail at rateRate[Rindex] and CS thresholdCS[Rindex],which is one of the diagonal points. In this case, the CSthreshold used is already the lowest threshold deemedreasonable for the chosen rate. As the discussion inSection III-A.1 suggests, in this case, the cause of trans-mission failures is likely to be that the other nodeshave been transmitting more aggressively, and excessiveinterference occurs due to transmissions that begin afterthe node has started its own transmission. Therefore,continuing to decrease its CS threshold will not help thenode to improve its transmission success probability. Onthe other hand, by reducing the transmission rate andusing the larger CS threshold associated with the reducedrate, the node can improve its success probability and gainmore chances to access the channel. Recall that a largerCS threshold and a lower rate lead to a smaller contendingregion, which can result in the improved local contentionresolution efficiency and better spatial reuse.

• Rule 4: Avoid starvation when probing small CSthreshold. Notice that, following the above rules, a nodehas to suffer transmission failures before its CS thresholdcan be increased. It could happen that, when using asmall CS threshold, a node becomes so conservative intransmitting that it no longer has sufficient chances toaccess the channel. The transmission successes or failuresof a node cannot be observed if the node does not transmitat all; as a result, the unsuitable small CS threshold canbe retained and the node can lose its chances to accessthe channel. To improve on such an undesirable situation,

in our proposed algorithm, each backlogged node keepstrack of whether or not it has made any transmissionattempt during a certain time periodTtimeout. If no suchtransmission attempts are made, andRindex > 1, then thetransmission rate of the node will be reduced by one level(i.e., Rindex = Rindex − 1), and CS threshold associatedwith the reduced rate, namely,CS[CSindex[Rindex]], willbe used.

Figure 10 illustrates how the proposed dynamic algorithmprobes the two-dimensional space. We elaborate on the searchprocess using an example below. In the example, when wemention that a node operates at the point (x,y), we mean thatthe node uses CS thresholdx and transmits at ratey. Assumethat transmissions of a node have been successful startingfrom the point (CS[1], Rate[1]). Following rule 1 mentionedabove, the node increases its rate and moves to the point(CS[1], Rate[2]). Assume that the transmissions continue tobe successful and the node keeps on increasing its transmissionrate until it reaches the point (CS[1], Rate[K−1]). The nodethen encounters transmission failures at (CS[1], Rate[K−1])becauseCS[1] is too large for rateRate[K − 1]. Followingrule 2, the node decreases its CS threshold and moves to thepoint (CS[2], Rate[K − 1]). As the node transmits more con-servatively now, let us pretend that its transmissions becomesuccessful again. The node again increases its transmissionrate perrule 1 and moves to (CS[2], Rate[K]). At this point,the node starts to suffer transmission failures, which causesit to move to (CS[3], Rate[K]) according torule 2. Supposethat the node continues to fail and eventually it reaches thepoint (CS[K], Rate[K]). Transmission failures at (CS[K],Rate[K]) cause the node to reduces its rate toRate[K − 1],following rule 3 mentioned above. While reducing the rateto Rate[K − 1], sinceCS[2] is associated withRate[K − 1]from prior search process, the node returns back to the point(CS[2], Rate[K − 1]) directly.

Rate

CS Threshold

CS[1] CS[2] CS[3] CS[K]Rate[1]

Rate[2]

Rate[3]

Rate[K]

Rate[K-1]

CS[K-1]

……

…

decreasing CS threshold

incr

easi

ng

rate

Fig. 10. Search space of the dynamic spatial backoff algorithm.

In our dynamic spatial backoff algorithm, nodes adjust theirCS threshold and transmission rate based on whether theirpast transmissions have been successes or failures. In general,the conditions under which a node considers its transmissions

as successes or failures can be defined in many ways. Thecondition currently used in our algorithm is as follows. Wehave two additional arraysS[i] and F [i] (i ∈ [1, ..., K]);and their elements are initialized toSinitial and Finitial,respectively. A node will consider its transmissions at rateRindex as successful if it has hadS[Rindex] consecutivesuccessful transmissions. On the other hand, a node will con-sider its transmissions fail if it sufferedF [Rindex] consecutivetransmission failures.4 To avoid the performance loss due tofrequent unsuccessful probing, the values ofS[] andF [] canbe adjusted dynamically. Intuitively, if a node can transmit atthe rate levelRindex successfully with high probability, but itfails often at the rate levelRindex +1, we would like the nodeto probe the rate levelRindex + 1 less frequently. Therefore,if the total number of successful transmissions for a sourcenode at rate levelRindex + 1 is less than a certain thresholdSth, S[Rindex] will be increased by 1 when the node returnsfrom the rate levelRindex +1 to Rindex; otherwise,S[Rindex]will be reset to the default initial valueSinitial. From anotherperspective, if a node can transmit successfully at the ratelevel Rindex with high probability, we would like the nodeto fall back to the lower transmission rates less frequently.Hence, if the total number of successful transmissions at ratelevel Rindex is more than a thresholdFth, F [Rindex] will beincreased by 1 every time when the node falls back to a lowertransmission rate; otherwise,F [Rindex] will be reset to thedefault initial valueFinitial .

Intuitively, using the proposed algorithm, a source node islikely to oscillate around a point where, given the interferencepresent in the network, it can transmit with a high successprobability using the highest possible transmission rate andcorrespondingly the largest suitable CS threshold. We use theexample in Figure 11 to illustrate this. Assume that there are 4available transmission rates (i.e.,K = 4) and we consider twonodes, node 1 and node 2, in a certain network. Suppose thepoint (CS[2], Rate[3]), which we called point A, is the bestoperating point for both nodes 1 and 2, and they have stayedthere for a relatively long duration. Then, node 1 begins toprobe point B afterS[3] consecutive successful transmissions.Since point B has higher rate and higher SINR threshold, node1 may suffer transmission failures, and thus, move to pointC (trajectory 1 of Figure 11(a)). When usingCS[3], node 1transmits more conservatively, which in turn, can reduce theinterference to node 2’s transmissions. As a result, node 2may also move to point B after it has hadS[3] consecutivesuccessful transmissions (trajectory 1 of Figure 11(b)). If node1 continues to suffer transmission failures at rateRate[4], or itis starved as a result of using a smaller CS threshold than node2, node 1 will end up with going back to point A (trajectory2 of Figure 11(a)). Once node 1 goes back to point A andusesCS[2], node 2 will encounter larger interference. As wepreviously assume point A is the best operating point for bothnodes 1 and 2, node 2 will likely suffer transmission failures at

4Alternatively, we can also define the success or failure conditions in termsof the percentage of successful transmissions over a certain time period.

rateRate[4], and will thus move back to point A, following thetrajectory 2 of Figure 11(b). As the above example illustrates,a node may not always stabilize at one particular operatingpoint, but we anticipate that nodes will tend to oscillate closeto their appropriate operating points.

Rate

CS Threshold

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incr

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(b) Trajectory of node 2

Fig. 11. Interactions between two source nodes

IV. PERFORMANCE EVALUATION

We simulated our dynamic spatial backoff algorithm usinga modified ns-2 simulator. Simulation settings are similar tostatic simulations presented in Section II. As a reminder, thephysical layer follows the specifications of IEEE 802.11a andfour transmission rates (i.e., 54, 36, 18, 9 Mbps) are used.To distinguish the effects of spatial backoff from temporalbackoff, exponential backoff of IEEE 802.11 DCF is disabledand a constant contention window size (i.e., 31) is applied.All flows are constantly backlogged. The rate arrayRate[],and the CS threshold arrayCS[] derived from equation 1, arelisted in Table II. More specifically, given a rateRate[i], wehave10 log CS[i]

RXth

= −10 logSINR[i], whereSINR[i] valuesare based on Table I. Other parameters used by our dynamicspatial backoff algorithm are as follows:Sinitial = 10, Sth =20, Finitial = 3, andFth = 100, Ttimeout = 0.1 second.

TABLE II

Index Rate[Index] SINR[Index]CS[Index]

RXth

1 9 Mbps 7.78 dB −7.78 dB2 18 Mbps 10.79 dB −10.79 dB3 36 Mbps 18.80 dB −18.80 dB4 54 Mbps 24.56 dB −24.56 dB

To show how our spatial backoff algorithm performs dif-ferently from the conventional rate control algorithm, we alsoimplemented the Automatic Rate Fallback (ARF) algorithm[4] with a slight modification. The ARF algorithm is im-plemented as follows. When transmitting at rate levelK,a source node will increase its rate uponS[K] consecutivesuccessful transmissions, and will decrease its rate uponF [K]consecutive transmission failures. We allow the values ofS[K]and F [K] to be adjusted dynamically, in order to avoid theperformance loss due to frequent unsuccessful probing. TheS[] andF [] update algorithm we used for ARF is the same asthat for the dynamic spatial backoff algorithm, as described inSection III-A. Simply put, if rate levelK turns out to be the

most suitable rate level for a node, thenS[K] and F [K] ofthis node will be increased over time. As a result, this nodewill probe other rate levels less and less frequently.

The four plots in Figure 12 correspond to the four randomtopologies in Figure 5, respectively. In each plot, the horizontalaxis represents the normalized CS thresholdβ = CSth

RXth

in dB;the vertical axis represents the aggregate throughput in the unitof Mbps. Results of our dynamic spatial backoff, ARF ratecontrol, and static simulations from Section II are presented.Recall that in static simulations, all source nodes use the sametransmission rate and CS threshold. The throughput of ARF ismeasured when all source nodes use the same CS threshold,but vary their rates independently; various CS threshold valuesare evaluated for ARF.

We observe the results for the topology with 8 flowsin Figure 12(a). Each static simulation curve represents theaggregate throughput when using a specified transmission rateand various CS threshold values. Also shown are the curvesfor the ARF scheme and our dynamic spatial backoff. Thecurves for dynamic spatial backoff are flat, since the schemedoes not depend on the value ofβ = CSth/RXth on thehorizontal axis of the graphs. Note that in each plot in Figure12, the 99% confidence interval of the dynamic spatial backoffalgorithm is shown by the two dashed lines that are above andbelow the average. As we can see, the performance of ARFapproximately follows the envelop of four static simulationcurves. In other words, if we know what is the suitable CSthreshold for a given network and we use this CS threshold,ARF can perform well by controlling the rate alone. On theother hand, if an inappropriate CS threshold is used, theperformance of ARF can be poor. In general, no single CSthreshold performs close to optimal for all networks; henceARF cannot perform well in all networks. Using our dynamicspatial backoff algorithm, on the other hand, each sourcenode dynamically searches for the appropriate combinationof transmission rate and CS threshold, which helps to achievegood aggregate throughput for any given network. As shownin Figure 12(a), the maximum aggregate throughput from thestatic simulations is 28.4 Mbps, while the average aggregatethroughput using our dynamic spatial backoff is 28.9 Mbps.

The results for the topology with 11 flows are shown inFigure 12(b). In this topology, the static maximum aggregatethroughput is 41.9 Mbps, while the average aggregate through-put of our dynamic spatial backoff is 36.2 Mbps. Although thethroughput of dynamic spatial backoff algorithm is 13% lowerthan the static optimal point, dynamic spatial backoff achievesthis performance without a priori knowing the optimal CSthreshold and transmission rate. For the topology with 16flows, as shown in Figure 12(c), the static maximum aggregatethroughput is 44.2 Mbps; and the average aggregate throughputof dynamic spatial backoff is 40.6 Mbps. For the topology with40 flows, the static maximum aggregate throughput is 54.5Mbps, while the average aggregate throughput of dynamicspatial backoff is 54.8 Mbps, as shown in Figure 12(d).More topologies have been simulated, and the results are notpresented here for conciseness. Our results indicate that the

proposed dynamic spatial backoff algorithm is able to achieveperformance close to the static optimal point. Moreover, un-like the static scheme, the proposed dynamic spatial backoffalgorithm achieves this performance without having to a prioridetermine the optimal CS threshold and transmission rate.

We plot the traces of CS threshold and transmission ratein Figure 13, for one source node in the topology with40 flows. The horizontal axis represents the simulation time(in seconds); the vertical axis represents the normalized CSthresholdβ, and transmission rate, in Figures 13(a) and 13(b),respectively. Each dot in the plots indicates a transmissionattempt (the transmission may or may not be successful). Aswe can see, normalized CS threshold of this node oscillatesbetween−7.78 dB and−10.79 dB; transmission rate of thisnode stays at18 Mbps most of the time. Notice from Figure12(d) that, in static simulations, both points (−7.78 dB, 18Mbps) and (−10.79 dB, 18 Mbps) have throughput close tothe static optimal. Using our dynamic spatial backoff, mostnodes use−7.78 dB or−10.79 dB as their CS threshold. Somenodes are able to transmit at rate36 Mbps successfully, whileothers use18 Mbps or 9 Mbps, depending on the channelcondition around each individual node. Our dynamic spatialbackoff algorithm allows each node to choose the appropriatecombination of rate and CS threshold based on its own channelcondition, while static simulations enforce the same rate andCS threshold for all nodes. This explains why our dynamicspatial backoff algorithm achieves slightly higher throughputthan the static optimal point in Figures 12(a) and 12(d).

Table III lists the throughput of each individual flow fromthe random topology with 40 flows, for both our dynamicspatial backoff algorithm and the optimal point of staticsimulations. As we can see, dynamic spatial backoff doesnot starve any individual flow while improving the aggregatethroughput. However, in some cases, we do observe that someflow, like flow 14 in Table III, has relatively fewer chancesthan others to access the channel successfully. To explainthe reason behind this, we plot the traces of CS thresholdand transmission rate used by the source node of flow 14 inFigure 14. We observe that this node has been trying veryhard to access the channel by using the largest CS thresholdand by transmitting at the lowest rate. This node cannot geta chance to access the channel when a smaller CS thresholdis used; and it cannot transmit successfully at a higher ratebecause of the large interference from neighboring nodes.Figure 14 provides an evidence, showing that our dynamicspatial backoff algorithm has helped a node to make the bestefforts it can locally do to access the channel and transmitsuccessfully. The reason that flow 14 does not get successfultransmissions very often is due to the asymmetric natureof the topology. We use the simple asymmetric topology inFigure 8(b) to explain this behavior. There, since transmissionsfrom node 1 cause little interference at node 2R, node 2 canalways transmit to node 2R successfully at high rate usinglarge CS threshold. However, aggressive transmissions fromnode 2 cause significant interference to the flow from node1 to node 1R. There is nothing node 1 can locally do to

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(a) Throughput with 8 flows

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(d) Throughput with 40 flows

Fig. 12. Aggregate throughput of random topologies (payload size: 512 bytes).

0

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β=

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Fig. 13. Traces of one typical node in the random topology with 40 flows.

help itself, except by transmitting at a low rate and using alarge CS threshold. Flow 14 in Figure 14 encounters a similarsituation. The above problem caused by asymmetric topologiescan be alleviated by introducing a certain level of coordinationamong interfering nodes. However, the appropriate level ofcoordination needs to be carefully investigated to minimizethe throughput degradation, which is part of our future work.

V. RELATED WORK

Studies on medium access control to address the channelcontention have been conducted extensively in the time do-main for the past decades. Temporal contention resolutiontypically takes the set of competing nodes as a given, andaddresses the issue on how to separate transmissions fromcompeting nodes in time to achieve successful transmissions.Numerous methods have been proposed in the past to achieve

the temporal separation of transmissions while reducing theoverhead introducing by medium access control. Examples ofsuch proposals include [5]–[10]. In this paper, we proposespatial backoff as an alternative approach for wireless networksto address the channel contention. As a result of using spatialbackoff, transmissions from competing nodes can also beseparated in space to achieve successful transmissions.

Physical carrier sensing provides an effective way to controlthe interference and the amount of spatial reuse in the network.Guo et al. [11] have noticed the impact of CS threshold onthe aggregate throughput. Assuming that the transmission rateis fixed for a given network, Zhu et al. [12], [13] proposed analgorithm that dynamically adjusts the CS threshold to improvespatial reuse and aggregate throughput. Given SINR thresholdof the fixed transmission rate, the algorithm in [12], [13]

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β=

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th/R

Xth

(dB

)

(a) Trace of CS threshold

9

18

36

54

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Tra

nsm

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ate

(Mbp

s)

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(b) Trace of transmission rate

Fig. 14. Traces of flow 14 in the random topology with 40 flows.

TABLE III

THROUGHPUT OF EACH INDIVIDUAL FLOW IN THE RANDOM TOPOLOGY

WITH 40 FLOWS (IN KBPS).

Dynamic spatial backoff Static optimal pointflow thr flow thr flow thr flow thr

0 402.5 20 642.4 0 474.6 20 535.31 1804.9 21 823.4 1 1957.8 21 626.52 1477.1 22 2004.1 2 935.2 22 2096.13 1004.5 23 925.2 3 956.7 23 973.04 909.7 24 1282.1 4 781.8 24 1302.75 2002.1 25 580.8 5 1557.3 25 354.96 931.1 26 1490.3 6 949.6 26 1441.77 1686.3 27 454.7 7 1426.6 27 1164.78 390.5 28 2178.9 8 646.0 28 1971.69 1143.3 29 3197.5 9 1353.7 29 2620.7

10 802.3 30 1111.2 10 1232.7 30 607.911 1003.0 31 805.5 11 2453.0 31 655.112 504.4 32 1709.5 12 715.0 32 1414.213 2848.7 33 142.1 13 1618.7 33 329.014 74.3 34 2042.9 14 504.7 34 2752.915 1338.7 35 729.7 15 1935.4 35 670.116 4110.5 36 561.1 16 3762.3 36 743.917 4984.3 37 999.6 17 3864.8 37 1144.418 716.9 38 1050.8 18 472.7 38 994.719 2183.5 39 1737.6 19 1952.2 39 2550.4

Sum 54788.0 Sum 54500.6

essentially searches the largest CS threshold that can satisfythe SINR threshold for all transmitter/receiver pairs. However,as we discussed in Section II, by reducing the transmission rateand using a even larger CS threshold, we can further improvethe spatial reuse and the local channel contention resolutionefficiency. The algorithm in [12], [13] is unable to exploit suchbenefits by adjusting CS threshold alone. Other works that aimto improve the spatial reuse by adjusting CS threshold include[14] by Vasan et al. and [15] by Nadeem et al. The commonlimitation of the above works is that a fixed transmissionrate is assumed. Yang et al. [2] have analytically shown, foruniformly distributed dense networks that, to maximize theaggregate throughput, the optimal CS threshold increases andthe optimal transmission rate decreases with the increase oftransmitter density. However, [2] does not provide a protocolthat utilizes the above observation.

There also exist some rate control algorithms [4], [16],[17], which aim to adapt the transmission rate based on

channel conditions. The major difference between rate controlalgorithms and our spatial backoff algorithm is as follows.Given the CS threshold used by each node, suppose there area total ofm transmission attempts that overlap in time. Assumethat, using a high transmission rate, onlym1 (m1 < m)transmissions can succeed. Also suppose that, using a lowtransmission rate, allm transmissions can succeed. Moreover,due to the increased interference tolerance level at the lowrate,potentially m2 (m2 > m) transmissions can succeed. Ratecontrol algorithms can only increase the number of successfultransmissions fromm1 to m, while spatial backoff algorithmcan increase the number fromm1 to m2 via the joint controlof rate and CS threshold.

As discussed in Section II-B, we can also realize the spatialbackoff by controlling transmission power and transmissionrate. Prior work has proposed power control protocols toimprove spatial reuse, by introducing new transmissions with-out interrupting existing transmissions [18], [19]. Fuemmeleret al. [20] have explored the joint control of transmissionpower and CS threshold to reduce collisions. Existing workon topology control has addressed the issues on finding theappropriate transmission power each node should use; theobjective is to maintain network connectivity while reducingenergy consumption and improving network capacity [21]–[26]. However, the problem of realizing spatial backoff usingthe joint control of power and rate remains open, and will beexplored in our future work.

VI. CONCLUSIONS ANDFUTURE WORK

The study of medium access control has mostly followedthe temporal dimension approach in the past. In this paper,we propose spatial backoff as an alternative approach toaddress medium access control along the spatial dimension.We propose a dynamic spatial backoff algorithm that jointlycontrols CS threshold and transmission rate. The results wepresent in this paper demonstrate that the proposed spatialbackoff algorithm can adapt to a give network and achieve ahigh level of performance. Some topics for further researchareas follows: (a) Potentially, all three parameters—transmissionpower, CS threshold, and transmission rate—can be jointlycontrolled to adjust the space occupied by transmissions. Workis needed to determine appropriate ways to realize such ajoint control. (b) In this paper, we showed the benefits of

spatial backoff without using temporal contention resolutionadaptation. Future work is needed to identify appropriatestrategies to integrate the temporal and the spatial approaches.(c) The impact of traffic and channel variations over time needsto be further investigated. We have obtained some results onthe impact of channel variations, and they suggest that thespatial backoff approach can work well in this case as well.

ACKNOWLEDGMENTS

This work was performed when Xue Yang was with Univer-sity of Illinois at Urbana-Champaign. This research was sup-ported in part by US Army Research Office grant W911NF-05-1-0246, NSF grant ANI-0125859, and Vodafone GraduateFellowship.

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