Effective Carrier Sensing in CSMA Networks under Cumulative Interference
aa r X i v : . [ c s . N I] D ec Effective Carrier Sensing in CSMA Networks underCumulative Interference
Liqun Fu, Soung Chang Liew, Jianwei Huang
Department of Information EngineeringThe Chinese University of Hong KongShatin, New Territories, Hong KongEmail: { lqfu6,soung,jwhuang } @ie.cuhk.edu.hk Abstract —This paper proposes and investigates the conceptof a safe carrier-sensing range that can guarantee interference-safe (also termed hidden-node-free) transmissions in CSMAnetworks under the cumulative interference model. Comparedwith the safe carrier-sensing range under the commonly assumedbut less realistic pairwise interference model, we show thatthe safe carrier-sensing range required under the cumulativeinterference model is larger by a constant multiplicative factor.For example, if the SINR requirement is dB and the path-loss exponent is , the factor is . . The concept of a safecarrier-sensing range, although amenable to elegant analyticalresults, is inherently not compatible with the conventional power-threshold carrier-sensing mechanism (e.g., that used in IEEE802.11). Specifically, the absolute power sensed by a node in theconventional mechanism does not contain enough informationfor it to derive its distances from other concurrent transmitternodes. We show that, fortunately, a carrier-sensing mechanismcalled Incremental-Power Carrier-Sensing (IPCS) can realizethe carrier-sensing range concept in a simple way. Instead ofmonitoring the absolute detected power, the IPCS mechanismmonitors every increment in the detected power. This meansthat IPCS can separate the detected power of every concurrenttransmitter, and map the power profile to the required distanceinformation. Our extensive simulation results indicate that IPCScan boost spatial reuse and network throughput by more than relative to the conventional carrier-sensing mechanism. Lastbut not least, IPCS not only allows us to implement our safecarrier-sensing range, it also ties up a loose end in many otherprior theoretical works that implicitly assume the use of a carrier-sensing range (safe or otherwise) without an explicit design torealize it. Index Terms —carrier-sensing range, cumulative interferencemodel, CSMA, WiFi, IEEE 802.11, SINR constraints, spatialreuse.
I. I
NTRODUCTION AND O VERVIEW
Due to the broadcast nature of wireless channels, sig-nals transmitted over wireless links can mutually interferewith each other. How to optimize spatial reuse and networkthroughput under such mutual interferences has been an in-tensely studied issue in wireless networking. In particular, it
This work was supported by two Competitive Earmarked Research Grants(Project Number 414507 and Project Number 412308) established under theUniversity Grant Committee of the Hong Kong Special Administrative Region,China, the Direct Grant (Project Number C001-2050398) of The ChineseUniversity of Hong Kong, and the National Key Technology R&D Program(Project Number 2007BAH17B04) established by the Ministry of Science andTechnology of the People’s Republic of China. is desirable to allow as many links as possible to transmittogether in an interference-safe (or collision-free) manner. Theproblem of interference-safe transmissions under the coordina-tion of a centralized TDMA (Time-Division Multiple-Access)scheduler has been well studied (e.g., see [1]–[6]). Lesswell understood is the issue of interference-safe transmissionsunder the coordination of a distributed scheduling protocol.The CSMA (Carrier-Sense Multiple-Access) protocol, suchas IEEE 802.11, is the most widely adopted distributedscheduling protocol in practice. As the growth of 802.11 net-work deployments continues unabated, we are witnessing anincreasing level of mutual interference among transmissions insuch networks. It is critical to establish a rigorous conceptualframework upon which effective solutions to interference-safetransmissions can be constructed.Within this context, this paper has three major contributionslisted as follows (more detailed overview is given in thesucceeding paragraphs):1) We propose the concept of a safe carrier-sensingrange that can guarantee interference-safe transmissionsin CSMA networks under the cumulative interferencemodel .2) We show that the concept is implementable using avery simple Incremental-Power Carrier-Sensing (IPCS)mechanism.3) We demonstrate that implementation of safe carrier-sensing range under IPCS can significantly improvespatial reuse and network throughput as compared to theconventional absolute-power carrier sensing mechanism.Regarding 1), this paper considers the cumulative interfer-ence model (also termed physical interference model in [7]),in which the interference at a receiver node i consists of thecumulative power received from all the other nodes that arecurrently transmitting (except its own transmitter). This modelis known to be more practical and much more difficult toanalyze than the widely studied pairwise interference model(also termed the protocol interference model in [7]) in theliterature. Under the cumulative interference model, a set ofsimultaneously transmitting links are said to be interference-safe if the SINRs (Signal-to-Interference-plus-Noise Ratios) atthe receivers of all these links are above a threshold. Given a set of links L in the network, there are many subsets of links, S ⊂ L , that are interference-safe. The set of all such subsets F = {S | the SINR requirements of all links are satisfied } constitutes the feasible interference-safe state space. For cen-tralized TDMA, all subsets are available for scheduling, anda TDMA schedule is basically a sequence ( S t ) nt =1 whereeach S t ∈ F . For CSMA, because of the random anddistributed nature of the carrier-sensing operations by in-dividual nodes, the simultaneously transmitting links S CS may or may not belong to F . Let F CS = {S CS | simultaneous transmissions of links in S CS are allowed bythe carrier-sensing operation } . The CSMA network is said tobe interference-safe if F CS ⊆ F . This is also the conditionfor the so-called hidden-node free operation [8]. However, thisissue was studied under the context of an idealized pairwiseinterference model [8] rather than the practical cumulativeinterference model of interest here. In this paper, we showthat if the carrier-sensing mechanism can guarantee that thedistance between every pair of transmitters is separated by a safe carrier-sensing range , then F CS ⊆ F can be guaranteedand the CSMA network is interference-safe even under acumulative interference model. We believe that the safe carrier-sensing range established in this paper is a tight upperboundand achieves good spatial reuse. Another issue is how to im-plement the concept of safe carrier-sensing range in practice.This brings us to 2) above. In traditional carrier sensingbased on power threshold (e.g., that of the basic mode in IEEE802.11), the absolute power received is being monitored. Thispower consists of the sum total of powers received from all theother transmitters. It is impossible to infer from this absolutepower the exact separation of the node from each of the othertransmitters. This leads to subpar spatial reuse. Fortunately, weshow that a simple mechanism that monitors the incrementalpower changes over time, IPCS, will enable us to map thepower profile to the required distance information. We believethat this contribution, although simple, is significant in thatit shows that the theoretical concept of safe carrier-sensingrange can be implemented rather easily in practice. It alsoties up a loose end in many other prior theoretical works thatimplicitly assume the use of a carrier-sensing range (safe orotherwise) without an explicit design to realize it. That is,IPCS can be used to implement the required carrier-sensingrange in these works, not just our safe carrier-sensing range here. Without IPCS, and using only the conventional carrier-sensing mechanism, the results in these prior works wouldhave been overly optimistic. Given the implementability ofsafe carrier-sensing range, the next issue is how tight thesimultaneously transmitting nodes can be packed.This brings us to 3) above. In the conventional carriersensing mechanism, in order that the detected absolute poweris below the carrier-sensing power threshold, the separationbetween a newly active transmitter and other existing activetransmitters must increase progressively as the number ofconcurrent transmissions increases. That is, the cost of en-suring interference-safe transmissions becomes progressivelyhigher and higher in the “packing process”. This reduces spatial reuse and the overall network throughput. Fortunately,with IPCS, the required separation between any pair of activetransmitters remains constant as the safe carrier-sensing range which is independent of the number of concurrent transmis-sions. Indeed, our simulation results indicate that compared tothe conventional carrier-sensing mechanism, IPCS mechanismimproves the spatial reuse and the network throughput by morethan . A. Related Work
In the literature, most studies on carrier sensing (e.g., [8]–[13]) are based on the pairwise interference model. For a linkunder the pairwise interference model, the interferences fromthe other links are considered one by one. If the interferencefrom each of the other links on the link concerned does notcause a collision, then it is assumed that there is no collisionoverall. Ref. [8] established the carrier-sensing range requiredto prevent hidden-node collisions in CSMA networks underthe pairwise interference model. The resulting carrier-sensingrange is too optimistic and can not eliminate hidden-nodecollisions if the more accurate cumulative interference modelis adopted instead.A number of recent papers studied the CSMA networksunder the cumulative interference model (e.g., [14]–[17]). Anearlier unpublished technical report of ours [17] derived thesafe carrier-sensing range under the cumulative interferencemodel. The technical report, however, did not include the IPCSrealization presented in this paper. Neither did Ref. [14]–[16]address the implementation of a carrier-sensing range basedon power detection. Ref. [14] studied the asymptotic capacityof large-scale CSMA networks with hidden-node-free designs.The focus of [14] is on “order” result rather than “tight” result.For example, if γ = 10 dB and α = 4 , the safe carrier-sensingrange derived in [14] is . d max . In this paper, we show thatsetting the safe carrier-sensing range to . d max is enoughto prevent hidden-node collisions.The authors in [15], [16] attempted to improve spatial reuseand capacity by tuning the transmit power and the carrier-sensing range. Although the cumulative interference modelis considered in [15], [16], spatial reuse and capacity areanalyzed based on carrier-sensing range. In particular, theyassumed that the transmitters of concurrent transmission linkscan be uniformly packed in the network. As discussed inthis paper, such uniform packing can not be realized usingthe current 802.11 carrier-sensing mechanism. Therefore, theresults in [15], [16] are overly optimistic without an appropri-ate carrier-sensing mechanism. IPCS fills this gap so that thetheoretical results of [15], [16] remain valid. We summarizethe key related models and results in the literature in Table I ∗ .The rest of this paper is organized as follows. Section IIpresents the cumulative interference model and the carriersensing mechanism in the current 802.11 protocol. Section IIIderives the safe carrier-sensing range that successfully prevents ∗ This paper focuses on the incremental-power carrier-sensing (IPCS) mech-anism under the cumulative interference model. But IPCS proposed in thispaper can also deal with the pairwise interference model.
TABLE IS
UMMARY OF THE R ELATED W ORK
InterferenceModels PairwiseInterference Model CumulativeInterference ModelAbsolute powercarrier sensing many (e.g., [8],[10]) [15], [16]Incremental powercarrier sensing
This paper This paper the hidden-node collisions under the cumulative interferencemodel. Section IV presents the IPCS mechanism. Section Vevaluates the performance of IPCS in terms of spatial reuseand network throughput. Section VI concludes this paper.II. S
YSTEM M ODEL
A. Cumulative Interference Model
We represent links in a wireless network by a set of distinctand directed transmitter-receiver pairs L = { l i , ≤ i ≤ |L|} .Let T = { T i , ≤ i ≤ |L|} and R = { R i , ≤ i ≤ |L|} denote the set of transmitter nodes and the set of receivernodes, respectively. A receiver decodes its signal successfullyif and only if the received Signal-to-Interference-plus-NoiseRatio (SINR) is above a certain threshold. We adopt thecumulative interference model, where the interference is thesum of the received powers from all transmitters except its owntransmitter. We assume that radio signal propagation followsthe log-distance path model with path loss exponent α > .The path gain G ( T i , R j ) from transmitter T i to receiver R j follows a geometric model: G ( T i , R j ) = d ( T i , R j ) − α , where d ( T i , R j ) is the Euclidean distance between nodes T i and R j .In 802.11, each packet transmission on a link l i consists of aDATA frame in the forward direction (from T i to R i ) followedby an ACK frame in the reverse direction (from R i to T i ). Thepacket transmission is said to be successful if and only if boththe DATA frame and the ACK frame are received correctly.Let L ′ ( L ′′ ) denote the set of links that transmit concurrentlywith the DATA (ACK) frame on link l i . Under the cumulativeinterference model, a successful transmission on link l i needsto satisfy the following conditions: P t · G ( T i , R i ) N + P l j ∈L ′ P t · G ( S j , R i ) ≥ γ , (DATA frame) (1)and P t · G ( R i , T i ) N + P l j ∈L ′′ P t · G ( S j , T i ) ≥ γ , (ACK frame) (2)where P t is the transmit power, N is the average noise power,and γ is the SINR threshold for correct reception. We assumethat all nodes in the network use the same transmit power P t and adopt the same SINR threshold γ . For a link l j in L ′ or L ′′ , S j represents the sender of link l j , which can be either T j or R j . This is because either DATA or ACK transmissionon link l j will cause interference to link l i . B. Existing Carrier Sensing Mechanism in 802.11
If there exists a link l i ∈ L such that not both (1) and (2)are satisfied, this means there is collision in the network. In802.11, carrier sensing is designed to prevent collision due tosimultaneous transmissions that cause the violation of either(1) or (2). In this paper, we assume carrier sensing by energydetection. Consider a link l i . If transmitter T i senses a power P CS ( T i ) that exceeds a power threshold P th , i.e., P CS ( T i ) > P th , (3)then T i will not transmit and its backoff countdown processwill be frozen. This will prevent the DATA frame transmissionon l i .In most studies of 802.11 networks, the concept of a carrier-sensing range CSR is introduced. The carrier-sensing range
CSR is mapped from the carrier-sensing power threshold P th : CSR = (cid:18) P t P th (cid:19) α . Consider two links, l i and l j . If the distance betweentransmitters T i and T j is no less than the carrier-sensing range,i.e., d ( T i , T j ) ≥ CSR, (4)then T i and T j can not carrier sense each other, and thus caninitiate concurrent transmissions between them. The pairwiserelationship can be generalized to a set of links S CS ⊆ L . Ifthe condition in (4) is satisfied by all pairs of transmitters inset S CS , then all links in S CS can transmit concurrently.Setting an appropriate carrier-sensing range is crucial tothe performance of 802.11 networks. If CSR is too large,spatial reuse will be unnecessarily limited. If
CSR is notlarge enough, then hidden-node collisions may occur. Theunderlying cause of hidden-node collisions are as follows.A number of transmitters transmit simultaneously becausecondition (4) is satisfied by all pairs of the transmitters.However, there is at least one of the links does not satisfyeither (1) or (2). As a result, collisions happen and the carriersensing mechanism is said to have failed in preventing suchcollisions.We now define a safe carrier-sensing range that alwaysprevents the hidden-node collisions in 802.11 networks underthe cumulative interference model.
Definition 1 (Safe-
CSR cumulative ): Let S CS ⊆ L denote asubset of links that are allowed to transmit concurrently undera carrier-sensing range CSR . Let F CS = {S CS } denote allsuch subsets of links in the network. A CSR is said to be a
Safe-
CSR cumulative if for any S CS ∈ F CS and for any link l i ∈S CS , both conditions (1) and (2), with L ′ = L ′′ = S CS \ { l i } ,are satisfied.For analysis simplicity, we assume that the backgroundnoise power N is small compared with interference and thuscan be ignored. We will consider Signal-to-Interference Ratio(SIR) instead of SINR. III. S
AFE C ARRIER - SENSING R ANGE UNDER C UMULATIVE I NTERFERENCE M ODEL
In this section, we derive a sufficient threshold for
Safe-
CSR cumulative . When discussing the hidden-node free design[8], it is required that the receivers are operated with the“RS (Re-Start) mode” (see Appendix A for details). In thefollowing discussion, we also make the same assumption.Ref. [8] studied the safe carrier-sensing range under the pairwise interference model . The threshold is given as follows:
Safe-
CSR pairwise = (cid:16) γ α + 2 (cid:17) d max , (5)where d max = max l i ∈L d ( T i , R i ) is the maximum link length inthe network. However, the pairwise interference model doesnot take into account the cumulative nature of interferencesfrom other links. The threshold given in (5) is overly optimisticand not large enough to prevent hidden-node collisions underthe cumulative interference model , as illustrated by the three-link example in Fig. 1. T R max d T R max d max d T R max d max d DATA DATA ACK l l l Fig. 1. Setting the carrier-sensing range as
Safe-
CSR pairwise is insufficientto prevent hidden-node collisions under the cumulative interference model
In Fig. 1, suppose that the SIR requirement γ = 8 and thepath-loss exponent α = 3 . According to (5), it is enough toset the carrier-sensing range as (cid:16) γ α + 2 (cid:17) d max = 4 d max andthe carrier sensing power threshold P th = P t (4 d max ) − =0 . P t d − . In Fig. 1, there are three links: l , l , and l with the same link length d max . The distance d ( R , R ) equals d max and the distance d ( T , R ) equals d max . Since thedistance d ( T , T ) = 4 d max = (cid:16) γ α + 2 (cid:17) d max , from (4), wefind that T and T can simultaneously initiate transmissionssince they can not carrier sense each other. We can verify thatthe SIR requirements of both DATA and ACK transmissionson l and l are satisfied. This means l and l can indeedsuccessfully transmit simultaneously.Suppose that l wants to initiate a transmission when T is sending a DATA frame to R and R is sending an ACKframe to T . Transmitter T senses a power P CS ( T ) givenby P CS ( T ) = P t · (5 d max ) − + P t · (8 d max ) − = 0 . · P t d − < P th . This means that T can not sense the transmissions on l and l , and can initiate a DATA transmission. However, when allthese three links are active simultaneously, the SIR at R is P t ( d max ) − P t (6 d max ) − + P t (2 d max ) − = 7 . < γ . This means the cumulative interference powers from l and l will corrupt the DATA transmission on l due to theinsufficient SIR at R . This example shows that setting thecarrier-sensing range as in (5) is not sufficient to preventcollisions under the cumulative interference model.We next establish a threshold for Safe-
CSR cumulative so thatthe system will remain safe under cumulative interference.
Theorem 1:
The setting
Safe-
CSR cumulative = ( K + 2) d max , (6)where K = (cid:18) γ (cid:18) (cid:18) √ (cid:19) α α − (cid:19)(cid:19) α . (7)is sufficient to ensure interference-safe transmissions under thecumulative interference model. Proof:
The proof is given in Appendix B.Condition (6) provides a sufficiently large carrier-sensingrange that prevents the hidden-node collisions in CSMAnetworks. Therefore, there is no need to set a
CSR largerthan the value given in (6).Let us compare
Safe-
CSR cumulative with
Safe-
CSR pairwise with different values of γ and α . For example, if γ = 10 and α = 4 , which are typical for wireless communications, Safe-
CSR pairwise = 3 . · d max , Safe-
CSR cumulative = 5 . · d max . Compared with
Safe-
CSR pairwise , Safe-
CSR cumulative needs tobe increased by a factor of . to ensure successful transmis-sions under the cumulative interference model.Given a fixed path-loss exponent α , both Safe-
CSR pairwise and
Safe-
CSR cumulative increase in the SIR requirement γ .This is because the separation among links must be enlargedto meet a larger SIR target. For example, if α = 4 , we have Safe-
CSR pairwise = (cid:16) γ (cid:17) d max , Safe-
CSR cumulative = (cid:18) γ (cid:19) ! d max . The ratio of
Safe-
CSR cumulative to Safe-
CSR pairwise is Safe-
CSR cumulative
Safe-
CSR pairwise = 2 + (cid:0) γ (cid:1) γ , which is an increasing function of γ , and converges to aconstant as γ goes to infinity: lim γ →∞ Safe-
CSR cumulative
Safe-
CSR pairwise = lim γ →∞ (cid:0) γ (cid:1) γ = (cid:18) (cid:19) ≈ . . Fig. 2 shows the ratio
Safe-
CSR cumulative
Safe-
CSR pairwise as a function of the SIRrequirements γ . Different curves represent different choicesof the path-loss exponent α . The ratio Safe-
CSR cumulative
Safe-
CSR pairwise increaseswhen γ increases or α decreases. For each choice of α , the γ T he r a t i o S a f e − C S R c u m u l a t i v e / S a f e − C S R pa i r w i s e α =3 α =4 α =5 Fig. 2. The ratio of
Safe-
CSR cumulative to Safe-
CSR pairwise ratio converges to a constant as γ goes to infinity. This showsthat, compared with the pairwise interference model, the safecarrier-sensing range under the cumulative interference modelwill not increase arbitrarily.IV. A N OVEL C ARRIER S ENSING M ECHANISM
We now discuss the implementation of
Safe-
CSR cumulative .We first describe the difficulty of implementing the safecarrier-sensing range in (6) using the existing physical carrier-sensing mechanism in the current 802.11 protocol. Then,we propose a new Incremental-Power Carrier-Sensing (IPCS)mechanism to resolve this implementation issue.
A. Limitation of Conventional Carrier-Sensing Mechanism
In the current 802.11 MAC protocol, given the safe carrier-sensing range
Safe-
CSR cumulative , the carrier-sensing powerthreshold P th is set as P th = P t · ( Safe-
CSR cumulative ) − α . (8)Before transmitting, a transmitter T i compares the power itsenses, P CS ( T i ) , with the power threshold P th . A key disad-vantage of this approach is that P CS ( T i ) is a cumulative powerfrom all the other nodes that are concurrently transmitting. Thecumulative nature makes it impossible to tell whether P CS ( T i ) is from one particular nearby transmitter or a group of far-offtransmitters [18]. This reduces spatial reuse, as illustrated bythe example in Fig. 3.There are four links in Fig. 3, with Safe-
CSR cumulative setas in (6). In Fig. 3, the distance d ( T , T ) is equal to Safe-
CSR cumulative . From (4), we find that T and T can not carriersense each other, thus they can transmit simultaneously.First, consider the location requirement of the third link l ′ that can have a concurrent transmission with both l and l , assuming that each transmitter can perfectly differentiatethe distances from the other transmitters. Suppose that the - cumulative Safe CSR T max d max d max d R T R ' T ' R max d T R cumulative Safe CSR (cid:66) (cid:184) cumulative
Safe CSR (cid:66) (cid:184) - cumulative Safe CSR - cumulative Safe CSR ' l l l l Fig. 3. Conventional carrier-sensing mechanism will reduce the spatialreuse in 802.11 networks. Link l is placed based on the absolute powersensing mechanism in current 802.11, and link l ′ is placed based on the Safe-
CSR cumulative as enabled by our IPCS mechanism. third link is located on the middle line between l and l . Based on the carrier-sensing range analysis, the require-ments are d ( T ′ , T ) ≥ Safe-
CSR cumulative and d ( T ′ , T ) ≥ Safe-
CSR cumulative . So the third link can be located in the posi-tion of l ′ , shown in Fig. 3. Furthermore, as the number of linksincreases, a tight packing of the concurrent transmitters willresult in a regular equilateral triangle packing with side length Safe-
CSR cumulative . The “consumed area” of each transmitteris a constant given by A = √ Safe-
CSR cumulative .Now, let us consider the location requirement of the thirdlink l under the carrier-sensing mechanism of the current802.11 protocol. In order to have concurrent transmissionswith both l and l , the cumulative power sensed by T dueto transmissions of both links l and l should be no largerthan P th , i.e., P CS ( T ) = P t · d ( T , T ) − α + P t · d ( T , T ) − α = 2 · P t d ( T , T ) − α ≤ P th , where P th is given in equation (8). So the minimum distancerequirement on d ( T , T ) and d ( T , T ) is d ( T , T ) = d ( T , T ) ≥ (cid:18) P t P th (cid:19) α = 2 α · Safe-
CSR cumulative , as shown in Fig. 3. Since α is always greater than , the requirement of the separation between transmit-ters is increased from Safe-
CSR cumulative (i.e., d ( T , T ) ) to α Safe-
CSR cumulative (i.e., d ( T , T ) and d ( T , T ) ). The re-quirement on the separation between transmitters will increaseprogressively as the number of concurrent links increases, andthe corresponding packing of transmitters will be more andmore sparse. As a result, spatial reuse is reduced as the numberof links increases. Another thing to notice is that the order of the transmissionsof links also affects spatial reuse in the conventional carrier-sensing mechanism. Consider the three links, l , l and l inFig. 3 again. If the sequence of transmissions is { l , l , l } ,as discussed above, T , T and T sense a power no greaterthan P th , and thus l , l and l can be active simultaneously.If the sequence of transmissions on these links is { l , l , l } ,however, both T and T sense a power no larger than P th .But the cumulative power sensed by T in this case is P CS ( T ) = P t · d ( T , T ) − α + P t · d ( T , T ) − α = P t (cid:16) α Safe-
CSR cumulative (cid:17) − α + P t ( Safe-
CSR cumulative ) − α = 32 P th > P th . Therefore, T will sense the channel busy and will not initiatethe transmission on l . The spatial reuse is unnecessarilyreduced because there would have been no collisions had T decide to transmit †† . B. Incremental-Power Carrier-Sensing (IPCS) Mechanism
We propose an enhanced physical carrier-sensing mech-anism called Incremental-Power Carrier-Sensing (IPCS) tosolve the issues identified in section IV-A. Specifically, theIPCS mechanism can implement the safe carrier-sensing rangeaccurately by separating the detected powers from multipleconcurrent transmitters.There are two fundamental causes for collisions in a CSMAnetwork. Besides hidden nodes, collisions can also happenwhen the backoff mechanisms of two transmitters count downto zero simultaneously, causing them to transmit together. Notethat for the latter, each of the two transmitters is not awarethat the other transmitter will begin transmission at the sametime. Based on the power that it detects, it could perfectlybe safe for it to transmit together with the existing activetransmitters, only if the other transmitter did not decide tojoin in at the same time. There is no way that the carrier-sensing mechanism can prevent this kind of collisions. Thispaper addresses the hidden-node phenomenon only. To isolatethe second kind of collisions, we will assume in the followingdiscussion of IPCS that no two transmitters will transmitsimultaneous ‡ . Conceptually, we could imagine the randomvariable associated with backoff countdown to be continuousrather than discrete, which means that the starting/ending ofone link’s transmission will coincide with the starting/endingof another link’s transmission with zero probability.The key idea of IPCS is to utilize the whole carrier-sensing power history, not just the carrier-sensing power at oneparticular time. In CSMA networks, each transmitter T i carriersenses the channel except during the time when it transmits †† This corresponds to the exposed-node phenomenon. ‡ Collisions due to simultaneous countdown-to-zero can be tackled by anexponential backoff mechanism in which the transmission probability of eachnode is adjusted in a dynamic way based on the busyness of the network.In WiFi, for example, the countdown window is doubled after each collision.The probability of this kind of collisions can be made small with a properdesign of the backoff mechanism
DATA or receives ACK. The power being sensed increasesif a link starts to transmit, and decreases if a link finishestransmission. As a result, the power sensed by transmitter T i ,denoted by P CSi ( t ) , is a continuous function of time t .In IPCS, instead of checking the absolute power sensed attime t , the transmitter checks increments of power in the pastup to time t . If the packet duration t packet (including bothDATA and ACK frames and the SIFS in between) is a constantfor all links, then it suffices to check the power increments dur-ing the time window [ t − t packet , t ] § . Let { t , t , · · · , t k , · · · } denote the time instances when the power being sensedchanges, and { ∆ P CSi ( t ) , ∆ P CSi ( t ) , · · · , ∆ P CSi ( t k ) , · · · } denote the corresponding increments, respectively. In IPCS,transmitter T i will decide the channel to be idle at time t ifthe following conditions are met: ∆ P CSi ( t k ) ≤ P th , ∀ t k such that t − t packet ≤ t k ≤ t, (9)where P th is the carrier-sensing power threshold determinedaccording to CSR ; otherwise, the channel is deemed to be busy . Since ∆ P CSi ( t k ) is negative if a link stops transmissionat some time t k , we only need to check the instances wherethe power increments are positive.By checking every increment in the detected power, T i canseparate the powers from all concurrent transmitters, and canmap the power profile to the required distance information.In this way, IPCS can ensure the separations between alltransmitters are tight in accordance with Theorem 1. Theorem 2:
If the carrier-sensing power threshold P th inthe IPCS mechanism is set as: P th = P t ( Safe-
CSR cumulative ) − α , (10)where Safe-
CSR cumulative is the safe carrier-sensing range in(6), then it is sufficient to prevent hidden-node collisions underthe cumulative interference model.
Proof:
The proof is given in Appendix C. t t t ( ) CS P t ( ) CS P t ( ) CS P t
Fig. 4. The power sensed by transmitter T ′ as a function of time Let us use Fig. 3 again to show how IPCS can implementthe safe carrier-sensing range successfully. We set the carrier-sensing power threshold P th as in (10). We will show that thelocation requirement of the third link under IPCS is the sameas indicated by the safe carrier-sensing range (location l ′ inFig. 3). The transmitter of the third link will only initiate its § This assumption is used to simplify explanation only. In general, we couldcheck a time window sufficiently large to cover the maximum packet sizeamong all links. transmission when it senses the channel to be idle. Its carrier-sensed power is shown in Fig. 4. Without loss of generality,suppose that link l starts transmission before l . The thirdtransmitter detects two increments in its carrier-sensed powerat time instances t and t which are due to the transmissionsof T and T , respectively. In the IPCS mechanism, the thirdtransmitter will believe that the channel is idle (i.e., it can starta new transmission) if the following is true: ( ∆ P CS ( t ) = P t d ( T ′ , T ) − α ≤ P th , ∆ P CS ( t ) = P t d ( T ′ , T ) − α ≤ P th . (11)Substituting P th in (10) to (11), we find that the requirementsin (11) are equivalent to the following distance requirements: ( d ( T ′ , T ) ≥ Safe-
CSR cumulative ,d ( T ′ , T ) ≥ Safe-
CSR cumulative . So the third link can be located at the position of l ′ , as shownin Fig. 3, instead of far away at the location of l as in theconventional carrier-sensing mechanism.Compared with the conventional carrier-sensing mechanism,the advantages of IPCS are1) IPCS is a pairwise carrier-sensing mechanism. In theIPCS mechanism, the power from each and every con-current link is checked individually. This is equivalent tochecking the separation between every pair of concurrenttransmission links. With IPCS, all the analyses based onthe concept of a carrier-sensing range remain valid.2) IPCS improves spatial reuse and network throughput.In the conventional carrier-sensing mechanism, the linkseparation requirement increases as the number of con-current links increases. In IPCS, however, the linkseparation requirement remains the same. Furthermore,because IPCS is a pairwise mechanism, the order of thetransmissions of links will not affect the spatial reuse.V. S IMULATIONS R ESULTS
We perform simulations to evaluate the relative perfor-mance of IPCS and conventional Carrier Sensing (CS). Inour simulations, the nodes are located within in a squarearea of m × m . The locations of the transmitters aregenerated according to a Poisson point process. The lengthof a link is uniformly distributed between and meters.More specifically, the receiver associated with a transmitteris randomly located between the two concentric circles ofradii m and m centered on the transmitter. We study thesystem performance under different link densities by varyingthe number of links in the square from to in oursimulations.The simulations are carried out based on the 802.11bprotocol. The common physical layer link rate is M bps .The packet size is
Bytes. The minimum and maximumbackoff window CW min and CW max are 31 and 1023, respec-tively. The slot time is µs . The SIFS and DIFS are µs and µs , respectively. The transmit power P t is set as mW .The path-loss exponent α is , the SIR requirement γ is s pa t i a l r eu s e IPCSTraditional CStheorectical result (optimal) 01234567 t h r oughpu t pe r un i t a r ea ( M bp s ) Fig. 5. Spatial reuse and network throughput under IPCS and the conventionalCS mechanisms , and the corresponding Safe-
CSR cumulative equals . m based on (6). That is, the carrier-sensing power threshold P th = P t ( Safe-
CSR cumulative ) − α = 5 . × − mW .In Fig. 5, we plot spatial reuse and network throughputunder IPCS and the conventional CS mechanisms. Simulationresults show that network throughput is proportional to spatialreuse. So we plot these two results in the same figure.We define a “unit area” as the “consumed area” of each“active” transmitter under the tightest packing. Given Safe-
CSR cumulative = 117 . m , according to the carrier-sensingrange analysis, the “unit area” is √ Safe-
CSR cumulative =1 . × m . The x-axis is the average number of links (i.e.,all links, including active and inactive links) per unit area aswe vary the total number of links in the whole square. Thatis, the x-axis corresponds to the link density of the network.The left y-axis is the spatial reuse, or the average “active” linkdensity in the network. The optimal value of the spatial reuseis , which is shown as a dashed line in Fig. 5. The righty-axis is the throughput per unit area.It is clear from Fig. 5 that IPCS outperforms the conven-tional CS. The improvement becomes more significant whenthe network becomes denser. At the densest point in the figure,spatial reuses under IPCS and conventional CS are . and . , respectively. The network throughputs per unit area are . M bps and . M bps , respectively. Using conventionalCS as the base line, the IPCS improves spatial reuse andnetwork throughput by more than .Under the conventional CS, in order to make sure the cu-mulative detected power is no larger than the power threshold P th , the packing of concurrent transmission links will becomemore and more sparse as additional number of links attemptto transmit. Under IPCS, this does not occur. As a result, theimprovement in spatial reuse is more significant as the networkbecomes denser. We also find that when the network becomes denser anddenser, spatial reuse under IPCS becomes very close to thetheoretical result. The small gap is likely due to the fact that alink which could be active concurrently under IPCS does notexist in the given topology. The probability of this happeningdecreases as the network becomes denser.VI. C
ONCLUSION
In this paper, we derive a threshold on the safe carrier-sensing range that is sufficient to prevent hidden-node colli-sions under the cumulative interference model. We show thatthe safe carrier-sensing range required under the cumulativeinterference model is larger than that required under thepairwise interference model by a constant multiplicative factor.We propose a novel carrier-sensing mechanism calledIncremental-Power Carrier-Sensing (IPCS) that can realize thesafe carrier-sensing range concept in a simple way. The IPCSchecks every increment in the detected power so that it canseparate the detected power of every concurrent transmitter,and then maps the power profile to the required distanceinformation. Our simulation results show that IPCS can boostspatial reuse and network throughput by more than relative to the conventional carrier-sensing mechanism in thecurrent 802.11 protocol.One future research direction is to further tighten the safecarrier-sensing range according to the topology information.In this paper, we have assumed a common safe carrier-sensing range for all transmitters. Allowing the carrier-sensingrange to vary from transmitter to transmitter according to thelocal network topological structures may improve spatial reusefurther. In this paper, we have not considered virtual carriersensing (i.e., the RTS/CTS mode in 802.11). Ensuring hidden-node free operation under virtual carrier sensing is rathercomplicated even under the pairwise interference model (see[11] for details.) The study of interference-safe transmissionsfor virtual carrier sensing under the cumulative interferencemodel is a subject for further study.A
PPENDIX AT HE N EED FOR
RS(R E -S TART ) M
ODE
It is shown in [8] that although the carrier-sensing rangeis sufficiently large for the SINR requirements of all nodes,transmission failures can still occur due to the “Receiver-Capture effect”. T R max d T R max d cannot carrier sense each othercan carrier sense each other Fig. 6. Collision due to “Receiver-Capture effect”
Take a two-link case shown in Fig. 6 as an example. InFig. 6, d ( T , T ) > CSR and d ( T , R ) < CSR . So thetransmitters T and T can not carrier-sense each other, but R can sense the signal transmitted from T . Suppose that CSR is set large enough to guarantee the SINR requirements on l and l (both the DATA frames and the ACK frames). If T transmits first, then R will have sensed the signal of T andthe default operation in most 802.11 products is that R willnot attempt to receive the later signal from T , even if thesignal from T is stronger. This will cause the transmissionon link l to fail. It is further shown in [8] that no matterhow large the carrier-sensing range is, we can always comeup with an example that gives rise to transmission failures, ifthe “Receiver-Capture effect” is not dealt with properly. Thiskind of collisions can be solved with a receiver “RS (Re-Start)mode”. With RS mode, a receiver will switch to receive thestronger packet as long as the SINR threshold γ for the laterlink can be satisfied. A PPENDIX BP ROOF OF T HEOREM Proof:
With the receiver’s RS mode, in order to preventhidden-node collisions in 802.11 networks, we only needto show that condition (6) is sufficient to guarantee thesatisfaction of both the SIR requirements (1) and (2) of allthe concurrent transmission links.Let S CS denote a subset of links that are allowed to transmitconcurrently under the Safe-
CSR cumulative setting. Considerany two links l i and l j in S CS , we have d ( T j , T i ) ≥ Safe-
CSR cumulative = ( K + 2) d max . Because both the lengths of links l i and l j satisfy d ( T i , R i ) ≤ d max , d ( T j , R j ) ≤ d max , we have the following based on the triangular inequality d ( T j , R i ) ≥ d ( T j , T i ) − d ( T i , R i ) ≥ ( K + 1) d max ,d ( R j , T i ) ≥ d ( T i , T j ) − d ( T j , R j ) ≥ ( K + 1) d max ,d ( R j , R i ) ≥ d ( R i , T j ) − d ( T j , R j ) ≥ Kd max . We take the most conservative distance Kd max in ourinterference analysis (i.e., we will pack the interference linksin a tightest manner given the Safe-
CSR cumulative in (6)).Consider any two links l i and l j in S CS . The following fourinequalities are satisfied: d ( T i , T j ) ≥ Kd max , d ( T i , R j ) ≥ Kd max ,d ( T j , R i ) ≥ Kd max , d ( R i , R j ) ≥ Kd max . Consider any link l i in S CS . We will show that the SIRrequirements for both the DATA frame and the ACK framecan be satisfied. We first consider the SIR requirement of theDATA frame. The SIR at R i is: SIR = P t d − α ( T i , R i ) P l j ∈S CS ,j = i P t d − α ( S j , R i ) For the received signal power we consider the worst casethat d ( T i , R i ) = d max . So we have P t d − α ( T i , R i ) ≥ P t · d − α max . (12) To calculate the cumulative interference power, we considerthe worst case that all the other concurrent transmission linkshave the densest packing, in which the link lengths of allthe other concurrent transmission links are equal to zero.In this case, the links degenerate to nodes. The minimumdistance between any two links in S CS is Kd max . The densestpacking of nodes with the minimum distance requirement isthe hexagon packing (as shown in Fig. 7).If link l j is the first layer neighbor link of link l i , we have d ( S j , R i ) ≥ Kd max . Thus we have P t d − α ( S j , R i ) ≤ P t ( Kd max ) − α = 1 K α · P t d − α max , and there are at most 6 neighbor links in the first layer.If link l j is the second layer neighbor link of link l i , wehave d ( S j , R i ) ≥ √ Kd max . Thus we have P t d − α ( S j , R i ) ≤ P t (cid:16) √ Kd max (cid:17) − α = 1 (cid:0) √ K (cid:1) α P t d − α max , and there are at most 12 neighbor links in the second layer.If link l j is the n th layer neighbor link of link l i with n ≥ ,we have d ( S j , R i ) ≥ √ n · Kd max . Thus we have P t d − α ( S j , R i ) ≤ P t √ nKd max ! − α = 1 (cid:16) √ nK (cid:17) α P t d − α max , and there are at most n neighbor links in the n th layer.So the cumulative interference power satisfies: X l j ∈S CS ,j = i P t d − α ( S j , R i ) ≤ · (cid:18) K (cid:19) α + ∞ X n =2 n (cid:18) √ nK (cid:19) α ! · P t d − α max =6 · (cid:18) K (cid:19) α ∞ X n =2 n (cid:18) √ n (cid:19) α ! · P t d − α max =6 · (cid:18) K (cid:19) α (cid:18) √ (cid:19) α ∞ X n =2 n (cid:18) n (cid:19) α ! · P t d − α max =6 · (cid:18) K (cid:19) α (cid:18) √ (cid:19) α ∞ X n =2 n α − ! · P t d − α max ≤ · (cid:18) K (cid:19) α (cid:18) (cid:18) √ (cid:19) α α − (cid:19) · P t d − α max (13) = P t d − α max γ , (14)where (13) follows from a bound on Riemann’s zeta functionand (14) follows from the definition of K in (7).According to (12) and (14), we find that the SIR of theDATA frame of link l i at the receiver R i satisfies: SIR = P t d − α ( T i , R i ) P l j ∈S CS ,j = i P t d − α ( S j , R i ) ≥ P t · d − α max P t d − α max γ = γ . This means that the SIR requirement of the successfultransmission of the DATA frame on link l i can be satisfied. First layer link max Kd i T i R max d Second layer linkThird layer link
Fig. 7. The packing of the interfering links in the worst case
The proof that the SIR requirement of the ACK frame onlink l i can be satisfied follows a similar procedure as above.So for any link l i in the concurrent transmission link set S CS ,condition (6) is sufficient to satisfy the SIR requirements of thesuccessful transmissions of both its DATA and ACK frames.This means that, together with the receiver’s RS mode, condi-tion (6) is sufficient for preventing hidden-node collisions inCSMA networks under the cumulative interference model.A PPENDIX CP ROOF OF T HEOREM Proof:
Consider any link l i in the link set L . Transmitter T i will always do carrier sensing except when it transmitsDATA frame or receives ACK frame. We show that condi-tion (10) is sufficient to prevent hidden-node collisions inthe following two situations, which cover all the possibletransmission scenarios:1) Link l i has monitored the channel for at least t packet before its backoff counter reaches zero and it transmits.2) Link l i finishes a transmission; then monitors the chan-nel for less than t packet when its backoff counter reacheszero; then it transmits its next packet.Let us first consider case 1 ) :We show that for the links that are allowed to trans-mit simultaneously, the separation between any pair oftransmitters is no less than the safe carrier-sensing range Safe-
CSR cumulative . We use inductive proof method. Supposethat before l i starts to transmit, there are already M linkstransmitting and they are collectively denoted by the linkset S CS . Without loss of generality, suppose that these M links begin to transmit one by one, according to the order l , l , · · · , l M . For any link l j ∈ S CS , let t j and t ′ j denote thetimes when link l j starts to transmit the DATA frame and theACK frame, respectively. In our inductive proof, by assumption we have d ( T j , T k ) ≥ Safe-
CSR cumulative , ∀ j, k ∈ { , · · · , M } , j = k. (15)We now show that condition (15) will still hold after link l i starts its transmission.Before link l i starts its transmission, transmitter T i monitorsthe channel for a time period of t packet . So T i at leastsenses M increments in the carrier-sensing power P CSi ( t ) that happen at time t , t , · · · , t M when the links in S CS start to transmit their DATA frames. There may also be someincrements in the P CSi ( t ) that happen at t ′ , t ′ , · · · , t ′ M if thelinks in S CS start to transmit the ACK frames before link l i starting it transmission. In the IPCS mechanism, at least thefollowing M inequalities must be satisfied if T i can start itstransmission: ∆ P CSi ( t j ) ≤ P th , for j = 1 , · · · , M. Because ∆ P CSi ( t j ) = P t d ( T i , T j ) − α ,P th = P t ( Safe-
CSR cumulative ) − α , we have d ( T i , T j ) ≥ Safe-
CSR cumulative for j = 1 , · · · , M. Thus, we have shown that the separation between any pairof transmitters in the link set S CS ∪ l i is no less than Safe-
CSR cumulative after link l i starting transmission.Now let us consider case 2 ) :Before starting the transmission of the ( m + 1) th packet,link l i first finishes the transmission of the m th packet (fromtime t i ( m ) to t i ( m ) + t packet ), and waits for a DIFS plusa backoff time (from time t i ( m ) + t packet to t i ( m + 1) ). Let S CS denote the set of links that are transmitting when l i startsthe ( m + 1) th packet at time t i ( m + 1) . Consider any link l j in set S CS . Because the transmission time of every packet inthe network is t packet . We know that the start time t j of theconcurrent transmission on link l j must range from t i ( m ) to t i ( m + 1) , i.e., t i ( m ) < t j < t i ( m + 1) .If t i ( m ) + t packet < t j < t i ( m + 1) , this means t j is inthe DIFS or the backoff time of link l i . During this period,transmitter T i will do carrier sensing. The IPCS mechanismwill make sure that the distance between T i and T j satisfies d ( T i , T j ) ≥ Safe-
CSR cumulative .If t i ( m ) < t j < t i ( m ) + t packet , this means t j falls intothe transmission time of the m th packet of link l i . Duringthe transmission time, T i is not able to do carrier sensingbecause it is in the process of transmitting the DATA frameor receiving the ACK frame. However, the transmitter T j willdo carrier sensing before it starts to transmit at time t j . Thecarrier sensing done by T j can make sure that the distancebetween T i and T j satisfies d ( T i , T j ) ≥ Safe-
CSR cumulative .So for any link l j in S CS , we have d ( T i , T j ) ≥ Safe-
CSR cumulative . R
EFERENCES[1] G. Brar, D. M. Blough, and P. Santi, “Computationally efficient schedul-ing with the physical interference model for throughput improvement inwireless mesh networks”, in Proc. ACM Mobicom , 2006.[2] S. A. Borbash and A. Ephremides, “Wireless link scheduling with powercontrol and SINR constraints”,
IEEE Trans. Information Theory , vol. 52,no. 11, pp. 5106-5111, Nov. 2006.[3] G. Sharma, R.R. Mazumdar, and N.B. Shroff, “On the Complexity ofScheduling in Wireless Networks”, in Proc. ACM Mobicom , 2006.[4] O. Goussevskaia, Y.A. Oswald, and R. Wattenhofer, “Complexity inGeometric SINR”, in Proc. ACM MobiHoc , 2007.[5] T. Moscibroda, R. Wattenhofer, and A. Zollinger, “ Topology ControlMeets SINR: The Scheduling Complexity of Arbitrary Topologies”, inProc. ACM MobiHoc , 2006.[6] K. Jain, J. Padhye, V. Padmanabhan, and L. Qiu, “Impact of interferenceon multi-hop wireless network performance,” in Proc. ACM Mobicom ,2003.[7] P. Gupta and P.R. Kumar, “The Capacity of Wireless Networks,”
IEEETrans. Info. Theory , Vol.46, No. 2, pp. 388-404, 2000.[8] L. B. Jiang and S. C. Liew, “Hidden-node Removal and Its Applicationin Cellular WiFi Networks”,
IEEE Trans. Veh. Technol. , vol. 56, no. 5,Sep. 2007.[9] S. Xu and T. Saadawi, “Does the IEEE 802.11 MAC protocol work wellin multihop wireless ad hoc networks?”
IEEE Commun. Mag. , vol. 39,no. 6, pp. 130-137, Jun. 2001.[10] K. Xu, M. Gerla, and S. Bae, “How effective is the IEEE 802.11RTS/CTS handshake in ad hoc networks?” in Proc. IEEE GLOBECOM ,Nov. 2002.[11] L. B. Jiang and S. C. Liew, “Improving throughput and fairness byreducing exposed and hidden nodes in 802.11 networks”,
IEEE Trans.on Mobile Computing , vol. 7, no. 1, pp. 34-49, Jan. 2008.[12] A. Vasan, R. Ramjee, and T. Woo, “ECHOS–Enhanced capacity 802.11hotspots”, in Proc. IEEE Infocom , Mar. 2005.[13] P. C. Ng and S. C. Liew, “Throughput analysis of IEEE 802.11 multihopad hoc networks”,
IEEE/ACM Transactions on Networking , vol. 15, no.2, pp. 309-322, Apr. 2007.[14] C. K. Chau, M. Chen, and S. C. Liew, “Capacity of Large-scale CSMAWireless Networks”, to appear in ACM Mobicom , 2009.[15] T. S. Kim, H. Lim, and J. C. Hou, “Improving Spatial Reuse throughTuning Transmit Power, Carrier Sense Threshold, and Data Rate inMultihop Wireless Networks”, in Proc. ACM Mobicom , 2006.[16] T. Y. Lin and J. C. Hou, “Interplay of Spatial Reuse and SINR-determined Data Rates in CSMA/CA-based, Multi-hop, Multi-rate Wire-less Networks”, in Proc. IEEE Infocom , 2007.[17] L. Fu, S. C. Liew, and J. Huang, “Safe Carrier Sensing Range in CSMAnetwork under Physical Interference Model”, Technical Report, 2009.http://arxiv.org/abs/0901.3611.[18] K. Jamieson, B. Hull, A. Miu, and H. Balakrishnan, “Understandingthe Real-World Performance of Carrier Sense”,