Jmming-Resistnt ollbortive Brodcst In Wireless Networks, Prt II: Multihop Networks Ling Xio Ximen University, hin 361005 Emil: lxio@xmu.edu.cn Huiyu Di N Stte University, Rleigh, N 27695 Emil: huiyu di@ncsu.edu Peng Ning N Stte University, Rleigh, N 27695 Emil: pning@ncsu.edu Abstrct We propose in [1] collbortive brodcst scheme for wireless networks, which pplies the Uncoordinted Frequency Hopping UFH) technique to counterct jmming nd exploits node coopertion to enhnce brodcst efficiency. In this scheme, some nodes tht lredy obtin the brodcst messge re selected to rely the messge to other nodes. In this pper, we ext the study to the generlized multihop network scenrios, nd provide solutions for importnt relted issues, such s the rely node selection, multiple ccess control, rely chnnel selection nd pcket scheduling. We lso study the sptil nd frequency chnnel) diversity provided by the collbortive brodcst. Simultion results show tht the collbortive brodcst chieves low brodcst dely, with low energy consumption nd smll computtionl overhed in multihop networks. I. INTRODUTION Jmming-resistnt brodcst is importnt for mny sfetycriticl pplictions such s emergency lert brodcst nd nvigtion signl dissemintion, nd is criticl for the distribution of importnt informtion such s the public key nd system control informtion in wireless systems. As mentioned in Prt I [1], nti-jmming communiction without preshredkeys hs been recognized recently [2] [11], leding to series of promising reserch efforts, including Uncoordinted FH UFH) [5] [8] techniques. In UFH [5], messge is divided into multiple short pckets, nd ech pcket is trnsmitted over rndomly selected chnnel, indepent of ech other nd only known to the ser. Such rpid chnnel switching over lrge frequency rnge effectively thwrts the jmming ttempts. On the down side, ech pcket hs to be sent multiple times, due to the low rte of successful reception resulting from the uncoordinted chnnel selection between the ser nd the legitimte receivers. To this, BMA scheme ws proposed to improve the communiction efficiency by combining ersure coding nd one-wy uthentictor bsed on biliner mps [6]. Some dditionl efficient pcket verifiction methods were proposed in [8]. In [7], the USD-FH scheme ws proposed to further improve the efficiency nd robustness, where the The work is prtly supported by NSF No.61001072), the Nturl Science Foundtion of Fujin Province of hin No.2010J01347), SRF for ROS, SEM, nd Tsinghu-Qulcomm reserch center. The work by Di nd Ning is supported by the US Ntionl Science Foundtion under grnts NS- 1016260 nd by the US Army Reserch Office under grnt W911NF-08-1- 0105 mnged by NSU Secure Open Systems Inititive SOSI). The contents of this pper do not necessrily reflect the position or the policies of the U.S. Government. hopping pttern is conveyed through UFH to llow messge trnsmission through coordinted FH. Despite ll these efforts, the UFH-bsed nti-jmming communictions still need to improve the communiction efficiency nd re vulnerble to powerful responsive jmmers [7]. To further enhnce the communiction efficiency, we propose collbortive brodcst scheme to exploit the node coopertion for single-hop wireless networks [1]. As ll nodes in the network expect the sme messge, it is nturl nd convenient to use set of nodes tht lredy receive the messge to help brodcst it. We design two strtegies for rely chnnel selection: Rndom Rely hnnel selection RR) nd Sttic Rely hnnel selection StR). In RR, ech rely node rndomly nd indepently selects one out of chnnels for the trnsmission of ech pcket. For the StR strtegy, the relys tke fixed non-overlpping chnnels through the messge brodcst process for the trnsmission of ll pckets). For exmple, ech rely my select chnnel bsed on its prtil) ID modulo some prime number nd ) so tht no overlpping is incurred. Both strtegies re menble to distributed implementtion nd hve good sclbility, s ech rely node indepently performs the strtegy disregrding the other rely nodes. In this pper, we ext our study to the multihop networks, where nodes tht hve successfully received the messge serve s relys to help forwrd the brodcst messge over multiple chnnels. In this wy, both the source node nd rely nodes s the messge simultneously t multiple chnnels over vrious geogrphicl regions. Thus the receivers hve lrger opportunity to receive the messge ginst jmming, compred to the brodcst without coopertion. In the multihop setting, besides spectrl chnnel) diversity, we cn further explore sptil diversity to fcilitte relible messge brodcst to much wider geogrphic re. Unless the jmmers re powerful enough to simultneously block ll the chnnels cross the whole geogrphic re, which is not prcticl in most multihop rdio networks, there is lwys chnce for the brodcst messge to rech nodes outside the fully jmmed region, which lter rely the messge to more nodes in the network. ompred to [1], we consider more generl jmming model, where ech jmmer, no mtter how powerful she is, cn no longer jm ll nodes s in the single-hop scenrio. While it is sufficient to consider just one powerful jmmer with combined jmming cpbility in the frequency domin in [1],
here we further introduce the concept of jmming rdius nd consider multiple jmmers distributed in the re. In ddition, we ddress the networking issues tht re lrgely ignored in the single-hop cse, including multiple ccess control, pcket scheduling nd determintion of trnsmission durtion, nd provide suite of solutions menble to distributed implementtion. The reminder of the pper is orgnized s follows. We formulte the system model in Section II, nd discuss some importnt issues for the collbortive brodcst in the multihop wireless networks in Section III. We present our collbortive brodcst protocols in Section IV, nd evlute their ntijmming performnce in Section V. Finlly, we conclude in Section VI. II. PROBLEM FORMULATION We consider nti-jmming brodcst in multihop rdio network, where the trnsmit power of the source node is not high enough to rech the whole network or it is too costly to do so. Suppose the source node locted t the center of disk re brodcsts messge to N identicl rndomly locted nodes with disk rdius R. All these nodes re ssumed to employ common communiction rnge D. Thus it tkes t lest R/D hops for the messge to rech to the frthest node. We suppose ech node trnsmit or receive) simultneously cross set of c m or c n ) chnnels selected from orthogonl chnnels, where is typiclly lrge number for strong jmming resistnce. In this pper, we ssume c m = c n = 1 for simplicity. Our results cn be esily exted to the multichnnel cses. The brodcst messge is divided into M short pckets, ech of which cn be trnsmitted over one time slot hop) with durtion t p. onsider common pth-loss model [12], where the trnsmitted signl power for ech node including the source) stisfies P T = D/R) γ P MAX, with γ s the pth loss exponent nd P MAX s the power required for the trnsmitted signl to successfully cover the whole disk re with rdius R. For simplicity, we ssume tht the minimum energy for node to trnsmit pcket E t is proportionl to P T, neglecting the energy cost on the signl processing in the bsebnd nd IF bnd, nd tht the minimum energy to receive pcket, E r, is constnt. In our study, we consider the most powerful jmming [5], [6], responsive-sweep, where jmmer conducts both non-responsive nd responsive jmming indepently nd simultneously. The corresponding jmming probbility for single source without rely) is given in [1] by p J = n s s + n J J. 1) The nlysis bsed on the responsive-sweep jmming provides lower bound for the brodcst performnce, nd most conclusions cn be esily dpted for other jmming types. We lso consider smrt jmming for the StR-bsed protocol, where ech jmmer knows the StR rely chnnel selection strtegy nd the fixed rely chnnels in its communiction M Number of pckets consisted in the messge to be sent N Number of nodes to receive the messge Number of chnnels in the system R Rdius of the re of interests D Averge coverge rdius for ech node n Node density = ND 2 /R 2 ) P T Trnsmit power Number of slots tht ech node trnsmits p Probbility tht receiver successfully receives pcket p hnnel ccessing probbility J Number of jmmers p J Probbility for chnnel to be jmmed J Number of chnnels concurrently blocked by jmmer s Number of chnnels concurrently sensed by jmmer n J Number of jmming cycles in slot n s Number of sensing cycles in slot D c Jmming rdius P J Jmming power ρ Normlized jmming power = P J /P T ) TABLE I SUMMARY OF NOTATIONS. region. It is in the interest of the smrt jmmer to first jm the fixed nd known rely chnnels, insted of the remining chnnels tht crry out pcket with less probbility. Note tht this effort is solely limited by the physicl jmming cpbility of the jmmer i.e., n J J ), while the sensing cpbility of the jmmer does not help. If power supply permits, the smrt jmmer then continues to ttck the non-rely chnnels using the responsive-sweep strtegy, to prevent successful reception from the source. lerly this mixed jmming strtegy is even more powerful thn the responsive-sweep jmming for the StR-bsed coopertive brodcst. Let P J denote the jmming power, with corresponding jmming rdius D c, nd ρ = P J /P T = D c /D) γ denote the normlized jmming power compred to legitimte node. The nottion summry is listed in Tble I. III. MULTIHOP BROADAST STRATEGIES We consider conveying messge consisting of M pckets to N nodes through collbortive brodcst in multihop wireless network, for both RR nd StR strtegies. ompred with the single-hop oriented work in [1], relizing collbortive brodcst incurs more chllenges in the multihop setting. In this section, we discuss severl importnt issues concerning multiple ccess control MA), pcket scheduling, trnsmission durtion control, nd power control. Then in the following sections, we will introduce our brodcst protocols nd evlute their performnce. A. MA In the collbortive brodcst, the source node nd rely nodes concurrently s pckets over wireless medi. Without pproprite MA mechnism, this multiple ccess might result in trnsmission confliction, pcket loss nd energy wste, especilly when idel coordintion is not vilble. In this work we consider the slotted Aloh scheme for the ese of distributed implementtion, nd investigte the optiml probbility tht trnsmitter ss pcket to the rdio medi during time slot, for both the RR nd StR rely strtegy.
Through our discussion, we ssume lrge greter thn 100 s in typicl frequency hopping system) to provide strong jmming resistnce. In ddition, the lrgest number of one-hop neighboring nodes Υ) is ssumed to be less thn, which is resonble for most typicl wireless d hoc networks. As to the coordintion mong the source nd rely nodes, we consider two scenrios: synchronous nd synchronous. In the former cse, ll trnsmitting nodes in the neighborhood re perfectly synchronized both in time nd in trnsmission content, so no interference is incurred when two more more relys select the sme chnnel. The ltter is more relistic, ssuming tht collision occurs when two relys hop to the sme chnnel due to difference in rrivl time or trnsmitted pckets). First, we consider the RR strtegy, where ech trnsmitter rndomly selects chnnel nd ss pcket on it with the ccess probbility p. Lemm 3.1: If > Υ, the successful pcket reception rte of RR is mximized by p = 1. Proof: Assume tht in the neighborhood of receiver there re m relys, with m Υ, ech trnsmitting with probbility p on rndomly selected chnnel ccording to the RR strtegy. In the synchronous cse, receiver cn successfully receive pcket if t lest one of the m trnsmitters re working on its selected receiving chnnel nd the chnnel is unblocked. The successful pcket reception rte is given by p RR,syn = p RR,syn 1 = mp 1 p 1 ) m ) 1 p J ), 2) which monotoniclly rises with p. As the ccess probbility p [0, 1], p = 1 mximizes p RR,syn. In the synchronous cse, receiver cn successfully receive pcket if exctly one trnsmitter is ccessing the receiving chnnel. Thus successful pcket reception rte in the synchronous cse becomes 1 p 1 ) m 1 1 p J ). 3) Its derivtive with respect to p is p RR,syn p = m 1 p J) 1 p ) m 2 1 p m ). 4) Hence p = min /m, 1) mximizes p RR,syn, s p [0, 1] nd 1. Bsed on the ssumption tht > Υ m, we hve tht p = 1 mximizes p RR,syn. Remrk: By 2) nd 3), both p RR,syn nd p RR,syn monotoniclly increse with m, which indictes tht node coopertion helps reduce the verge brodcst dely. Moreover, since is usully lrge number, the reltive difference between p RR,syn nd p RR,syn is very smll, implying the robustness of RR ginst rely synchroniztion error. Next, we consider the StR strtegy, where ech rely selects fixed non-overlpping chnnel ccording to its node ID while the source node still follows the UFH pproch. As the known rely chnnels provide much lrger trnsmission probbility thn others, it is in the jmmers interest to first block them. Menwhile, smrt receiver cn lso tke dvntge of these fixed rely chnnels unless ll of them re jmmed. Under such strong jmming, receiver cn then switch bck to the whole chnnels. Hence in our scheme, ech receiver first rndomly selects one of these known rely chnnels. If it finds out tht ll the rely chnnels re jmmed, it switches to the mode where it rndomly selects one out of chnnels. Once it comes cross cler rely chnnel, the receiver restricts itself to the rely chnnels gin. The ltter cse hppen s smrt jmmers my just sp enough energy to spoof the receivers wy, insted of continuously jmming the sttic rely chnnels. Lemm 3.2: The successful pcket reception rte of StR is mximized by p = 1. The proof is similr to tht to Lemm 3.1. Note tht the source node cn only rech the first hop nodes, while the trnsmission to ll the other nodes completely relies on the rely nodes. Under the coopertive brodcst, unless ll the chnnels re simultneously jmmed cross the whole re covered by the source node, some nodes in the first hop cn receive the messge with lrge chnce, nd then s it to the other nodes. The bove nlysis cn be esily dpted for the non-first-hop nodes. B. Pcket Scheduling As the source nd rely nodes cooperte to brodcst multiple pckets of the brodcst messge, it is necessry to determine when to strt the trnsmission nd wht to s. We consider two strtegies to decide the beginning of the rely mode: The first one is messge-bsed, where ech node strts relying fter successfully receiving ll the M pckets within the brodcst messge. The second one is pcket-bsed, where ech node relys pcket right fter receiving it, during the next time slots ssigned to s this pcket. In this scheme, the node needs to switch bck nd forth between the relying mode nd receiving mode. The former strtegy is convenient to implement, without requiring idel timing nd synchroniztion. On the other hnd, the ltter strtegy my led to fster brodcst, but it requires perfect timing nd fst switching between the trnsmission mode nd the receiving mode to void the pcket lost. As these requirements re nontrivil to chieve in existing wireless networks, we choose the messge-bsed strtegy for convenience, t the expense of slightly slower brodcst speed. Once strting to rely, ech node ss the M pckets in sequence, nd then periodiclly repets this process before the of the trnsmission which will be further discussed below). It is pprent tht the minimum brodcst dely for receiver to successfully obtin these pckets is M slots, while mostly the dely is much lrger thn M due to lck of coordintion between the trnsmitters nd receivers.. ontrol of Trnsmission Durtion In our collbortive brodcst, ech trnsmitter, either the source node or rely node, stops sing pckets once receiving the Acknowledgements AKs) from ll of its neighboring
nodes or reching the mximum trnsmission durtion, whichever comes first. The limit on the trnsmission durtion is set to del with the possible loss of the AK signl due to the deep fding of wireless chnnels or the trnsmission confliction of multiple AK signls. Ech AK signl, including the messge ID, receiver ID nd time stmp, is sent on fixed nd known chnnel by node right fter successfully obtining ll M pckets. In this wy, ech AK signl is sent t time rnging between the M-th slot nd the -th, deping on the dely of the messge to the node from the source or rely node. As we will see, the trnsmission dely for messge to 100-node network is usully s lrge s severl thousnd time slots, during which the 100 AK signls re sent t rndom time. onsequently, the probbility for node to simultneously receive multiple AK signls from its neighbors is smll. Moreover, even if some of the AK signls re lost, the node cn still stop the trnsmission fter the trnsmission limit, nd the system still works well. By integrting the AK mechnism in the trnsmission durtion control, only provides the upper bound of the trnsmission time in cse the AK signls re lost. We set is the verge time used for ll the receivers within the neighboring re to receive the brodcst messge from the trnsmitter. The verge dely is used here, since it is chllenging to predict the exct vlue in prcticl wireless networks. For simplicity, ssume tht trnsmitter periodiclly brodcsts M pckets to n identicl nd indepent nodes within its communiction rnge. It is cler tht the probbility for ll these receivers to obtin the pckets during the first m slots is 1 1 p ) m ) Mn. Hence the verge brodcst dely over this single hop in terms of time slots is αtvg hop, where the coefficient α > 0 nd Tvg hop T hop vg = M m=0 [ 1 1 1 p ) m ) Mn]. 5) Assuming uniform node plcement, we hve the verge number of the nodes within the rech of one hop, n = D 2 N/R 2. Hence the trnsmission durtion cn be tken s [ ] = αm 1 1 1 p ) m ) D2 NM R 2. 6) m=0 By integrting the AK mechnism in the trnsmission durtion control, the brodcst performnce is not sensitive to the specific vlue of α. Simultion results hve shown tht α = 0.5 2 is good choice, with stble brodcst dely nd energy consumption performnce. IV. BROADAST PROTOOL After discussing some key issues in the previous section, we now present two nti-jmming collbortive brodcst protocols for multihop wireless networks, bsed on the RR nd StR strtegies, respectively. It is ssumed tht ech node knows the node IDs of its neighbors, i.e., legitimte nodes within its direct communiction rdius, nd performs distributed lgorithm Algorithm 1 or 2) to receive nd/or trnsmit messge consisting of M pckets. A. RR-bsed Brodcst In the RR-bsed protocol, ech node other thn the source node first enters the receiving mode. In this mode, node indepently nd rndomly selects one out of chnnels nd listens, nd switches to nother rndomly selected chnnel fter one or severl time slots to counterct jmming. This process repets until the node successfully receives ll M pckets. while The node hs not received ll M pckets yet do hid = n integer rndomly selected from [1,] ; Listen to the hid-th chnnel; S AK Messge ID, Node ID, Time Stmp); Eq. 6) ; for i 1 to do if hs not received AKs from ll its neighbors yet then hid = n integer rndomly selected in [1,] ; S pcket on the hid-th chnnel; Stop the trnsmission immeditely Algorithm 1: RR version of the nti-jmming collbortive brodcst protocol Next, the node ss n AK signl to inform its neighbors bout its successful reception of the messge, nd then enters the trnsmission mode. The AK signl contining the messge ID, node ID nd time stmp, is sent on fixed nd known chnnel. The trnsmission mode of different nodes strts t different time e.g., the source node enters this mode from the very beginning while node t the edge of the network my never enter the trnsmission mode). In the trnsmission mode, ech node rndomly selects chnnel out of the chnnels nd ss pcket. In order to del with the possible loss of AK signls due to chnnel fding or jmming, we introduce timeout mechnism, where ech trnsmission stops fter slots, given by Eq. 6), even without receiving enough AK signls. The node repets this process to s ll M pckets in sequence, until it receives ll the AK signls from its neighbors, or time slots elpse, whichever comes first. B. StR-bsed Brodcst In the StR-bsed protocol, ech node relys the messge on fixed chnnel, ssumed distinctly relted to its node ID. Ech node is ssumed to know the rely chnnels tht its neighbors my use. As mentioned in Section III-A, in order to counterct smrt jmming, ech node hs two receiving modes, bsed on whether ny rely chnnel is not blocked: If tht is true, the node is focused on the rely chnnels by rndomly selecting one of the potentil rely chnnels in the neighborhood; otherwise, the node rndomly selects one out of ll the chnnels.
F lglerrelyhnnel=true; while The node hs not received ll M pckets yet do if F lglerrelyhnnel=true then hid=n integer rndomly selected from the rely chnnel set in its neighborhood; hid = n integer rndomly selected from [1,]; Listen to the hid-th chnnel; if F lglerrelyhnnel=true then if All recent R p pckets re jmmed then F lglerrelyhnnel=flse; if The hid-th chnnel is unblocked rely chnnel then F lglerrelyhnnel=true; S AK Messge ID, Node ID, Time Stmp); Eq. 6) ; hid = n integer derived from its Node ID ; for i 1 to do if hs not received AKs from ll its neighbors yet then S pcket on the hid-th chnnel; Stop the trnsmission immeditely Algorithm 2: StR version of the nti-jmming collbortive brodcst protocol orrespondingly, the StR protocol uses such sttus flg tht is set to be true t the beginning, nd then updtes it ccording to the R checking results of the recent pckets. When working on the rely chnnels, the receiver chnges the flg to be flse, if filing to receive ll the recent R p pckets, which mens tht ll these rely chnnels re very likely to be jmmed. The prmeter R p is the ctul number of neighboring nodes, or the verge neighboring nodes n if the former is unknown. When coming cross cler rely chnnel, the node sets the flg to be true nd focuses on the rely chnnels gin. Next, like the RR-bsed protocol, the node lso ss n AK signl to its neighbors before entering to the trnsmission mode. Then the node ss the pckets on fixed chnnel corresponding to the prtil node ID modulo. The trnsmission durtion is lso determined by timer of length nd the reception of the AK signls from its neighbors. V. PERFORMANE EVALUATION We evlute the performnce of the proposed collbortive brodcst, where messge consisting of M = 7 pckets is brodcst to N = 100 nodes over = 128 chnnels ginst J jmmers with normlized jmming power ρ = 2, with the RR-bsed strtegy or the StR-bsed strtegy. We clculte the overll brodcst dely, defined s the time durtion from the beginning of brodcst till the time when ll the nodes in the network successfully receive the entire messge, nd the corresponding overll energy consumption, defined s the sum of the trnsmit nd the receive energy consumed by ll the N + 1 legitimte nodes during this process. The energy consumption for node to s nd to receive pcket re set s E t = D γ nd E r = 0.1, respectively. Figure 1 presents the RR performnce in solid curves nd the StR performnce in dshed curves, ginst J = 0 to 20 jmmers described in different colors. We consider both the responsive-sweep jmming nd the smrt jmming specificlly trgeting the StR-bsed protocol in dshed dot curves). It is shown tht both schemes consume smll energy nd brodcst dely, compred to the existing jmming-resistnt FH schemes. For exmple, the verge brodcst delys of StR nd RR re less thn 900 nd 1100 slots, respectively, for the brodcst of 7 pckets to 100 nodes ginst one sweepresponsive jmmer with normlized jmming power 2, when the node density N/R 2 100 for N = 100 nd D = 1. In this cse, ech node/jmmer cn pproximtely cover the whole network, s ssumed in the BMA [6]. The performnce of our scheme, especilly the StR version, is better thn tht of BMA for single receiving node even without jmming e.g., BMA tkes pproximtely 2000 slots to s messge of 7 pckets to single node [6]). It lso confirms tht the smrt jmming cn ttck StR more efficiently, especilly when the number of jmmers is lrge. But even in this cse, the StR strtegy still outperforms the RR in most cses. It cn lso be seen from Figure 1 tht the brodcst dely nd energy performnce of RR improves with the node density N/R 2, for given N, while the performnce of StR degrdes with it when ttcked by lrge number of strong smrt jmmers. Next, we study the performnce ginst widebnd jmmers tht concurrently ttck multiple chnnels. Assume limittion on the totl energy consumption of jmmer, i.e., widebnd jmmer cn increse the number of simultneously ttcked chnnels t the expense of smller jmming rdius. We consider 3-hop wireless network with n = 20, D = 1 nd N = 100. It is shown in Fig. 2 tht the protocol cn well resist ten jmmers ech concurrently blocking J 40 chnnels with ρ = 2. The StR strtegy cn provide stronger jmming resistnce thn the RR strtegy, even under the smrt jmming focused on the rely chnnels. Moreover, for the RR strtegy, when there re 10 jmmers ech simultneously blocking ll the chnnels with ρ = 2, only 28 out of 100 nodes re jmmed nd the remining 82 nodes cn still successfully receive ll the pckets. ontrst to the intuition, even when ll the chnnels re simultneously jmmed J = ) by the widebnd jmmers, the collbortive brodcst still prtly survives, thnks to the sptil diversity vilble in multihop networks. Finlly, the number of jmmed nodes is mximizes t J = 63, which cn be theoreticlly determined s n s s )/n J. It is shown in Eq. 1) tht responsive-sweep jmmer cn simultneously jm p J = n s s + n J J chnnels. All the nodes in its jmming re re blocked when p J =, or J = n s s )/n J. Afterwrds, the jmming probbility no longer further increses with J, while the number of nodes
Overll brodcst dely Slot) Overll brodcst Energy 2600 2400 2200 2000 1800 1600 1400 1200 1000 J=0,RR J=1,RR J=10,RR J=20,RR J=0,StR J=1,StR J=10,StR J=20,StR J=0,StR,SJ J=1,StR,SJ J=10,StR,SJ J=20,StR,SJ 800 20 40 60 80 100 120 Network density, N/R 2 5.5 5 4.5 4 3.5 3 2.5 2 1.5 6 x 104 ) Averge brodcst dely J=0,RR J=1,RR J=10,RR J=20,RR J=0,StR J=1,StR J=10,StR J=20,StR J=0,StR,SJ J=1,StR,SJ J=10,StR,SJ J=20,StR,SJ 1 20 40 60 80 100 120 Network density, N/R 2 b) Averge energy consumption Fig. 1. Brodcst performnce vs. node density N/R 2, for the brodcst of M = 7 pckets to N = 100 nodes with chnging network rdius R nd signl coverge rdius D = 1, ginst J responsive-sweep jmmers or smrt jmmers SJs). in its covering re reduces with the shrinking of the jmming rdius. Number of jmmed nodes 40 35 30 25 20 15 10 5 J=1,RR J=5,RR J=10,RR J=1,StR J=5,StR J=10,StR J=1,StR,SJ J=5,StR,SJ J=10,StR,SJ 0 0 20 40 60 80 100 120 Number of chnnels concurrently jmmed, J Fig. 2. Averge number of jmmed nodes by J responsive-sweep jmmers ech of which concurrently blocks J jmming chnnels with ρ = 2, in brodcst to N = 100 nodes over = 128 chnnels, with n = 20 nd D = 1. VI. ONLUSION We hve proposed distributed collbortive brodcst protocol tht exploits the uncoordinted frequency hopping technique nd node coopertion to counterct jmming in multihop wireless networks. With coopertion from rely nodes, this scheme provides sptil nd frequency chnnel) diversities to resist jmming nd enhnce communiction efficiency. Unless ll the chnnels cross the whole geogrphic re re simultneously jmmed, the collbortive brodcst cn lwys exploit the white re not being jmmed or white chnnels in the jmmed geogrphic re. Simultion results show tht the collbortive brodcst is robust ginst responsive smrt jmmers specilly trgeting the collbortive relying strtegies. Tke the brodcst in 3-hop network to 100 nodes for exmple, the protocol cn well resist ten responsive-sweep jmmers ech simultneously blocking 40 chnnels with double jmming power ρ = 2). Even when ech jmmer blocks ll = 128 chnnels t the sme time, only 28 nodes re jmmed nd more thn 70% of the nodes cn still receive the brodcst messge. By exploiting the sptil distribution of the multihop wireless networks, this coopertive brodcst scheme cn efficiently improve the communiction efficiency ginst jmming, compred to most existing ntijmming brodcst schemes, including BMA. REFERENES [1] L. Xio, H. Di, nd N. Peng, Jmming-resistnt collbortive brodcst in wireless networks, prt I: Singlehop networks, in Proc. IEEE Globecom 2011, to pper. [2] L. Bird, W. Bhn, M. ollins, M. rlisle, nd S. Butler, Keyless jm resistnce, in Proc. IEEE Informtion Assurnce nd Security Workshop, 2007, pp. 143 150. [3]. Popper, M. Strsser, nd S. pkun, Jmming-resistnt brodcst communiction without shred key, in Proc. USENIX Security Symposium, 2009. [4] Y. Liu, P. Ning, H. Di, nd A. Liu, Rndomized differentil DSSS: jmming-resistnt wireless brodcst communiction, in Proc. IEEE Infocom, 2010. [5] M. Strsser, S. pkun,. Popper, nd M. glj, Jmming-resistnt key estblishment using uncoordinted frequency hopping, in Proc. IEEE symposium on security nd privcy, 2008. [6] M. Strsser,. Popper, nd S. pkun, Efficient uncoordinted FHSS nti-jmming communiction, in Proc. MobiHoc, 2009. [7] A. Liu, P. Ning, H. Di, Y. Liu, nd. Wng, USD-FH: Jmmingresistnt wireless communiction using frequency hopping with uncoordinted seed disclosure, in Proc. 7th IEEE Interntionl onference on Mobile Ad-hoc nd Sensor Systems, 2010. [8] D. Slter, P. Tgue, R. Poovrn, nd B. Mtt, A coding-theoretic pproch for efficient messge verifiction over insecure chnnels, in Proc. AM onference on Wireless Network Security WiSec 09), 2009. [9] T. Jin, G. Noubir, nd B. Thp, Zero pre-shred secret key estblishment in the presence of jmmers, in Proc. AM interntionl symposium on Mobile d hoc networking nd computing, 2009. [10] L. Lzos md S. Liu nd M. Krunz, Mitigting control-chnnel jmming ttcks in multi-chnnel d hoc networks, in Proc. AM WiSec, 2009. [11] A. Liu, P. Ning, H. Di, Y. Liu, nd. Wng, Defing DSSSbsed brodcst communiction ginst insider jmmers vi delyed seed-disclosure, in Proc. IEEE Annul omputer Security Applictions onference ASA), 2010. [12] A. Goldsmith, Wireless ommunictions, chpter 3, mbridge University Press, 2005.