Throughput Analysis and Routing Security Discussions of Mobile Access Coordinated Wireless Sensor Networks

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1 Throughput Analyss and Routng Securty Dscussons of Moble Access Coordnated Wreless Sensor Networks Ma Abdelhakm Jan Ren Tongtong L Department of Electrcal & Computer Engneerng, Mchgan State Unversty, East Lansng, MI 48824, USA. Emal: {abdelhak, renjan, tongl}@egr.msu.edu Abstract In ths paper, we analyze the throughput of a novel moble access coordnated wreless sensor network archtecture (MC-WSN) under sngle path and multpath routng. The obtaned throughput expressons hghlght the trade-off between achevng hgh throughput performance and mprovng the network securty strength. The results reveal the mportance of: () mnmzng the number of hops n maxmzng the throughput, and () adoptng routng dversty n combatng malcous attacks and network falure condtons. We control the number of hops n data transmsson through optmal topology desgn and actve network deployment acheved by the moble access pont (MA). To combat routng attacks, we propose a secure routng path selecton approach, and show the mpact of the proposed approach on mprovng the throughput performance under malcous attacks. Index Terms Wreless sensor networks, moble access coordnator, throughput, routng securty. I. INTRODUCTION Wreless sensor network has receved sgnfcant research attentons due to ther paramount mpact on varous crtcal mltary and cvlan applcatons. The adopted archtecture largely mpacts the performance of the network. For example, n random ad-hoc networks, t was shown n [1] that the average throughput of a node vanshes as the number of nodes n the network ncreases. Ths ndcates that for effcent communcatons, the network should not be completely structureless. In [2], throughput of multhop many-to-one network wth unformly deployed nodes and tme dvson multple access (TDMA) protocol s nvestgated, and t was shown that clusterng the network can potentally mprove the throughput. Incorporatng moblty n the network archtecture could mprove the throughput performance. For example, when the network nodes are moble and the packets are splt over multple moble relays, the acheved throughput can be hgher than that of fxed ad-hoc networks [3]. The drawback, though, s hgher energy consumpton, whch s a bg challenge for sensor networks. When the snks or access ponts are moble, lke n Sensor Networks wth Moble Access Ponts (SENMA) [4], the capacty of a node havng a drect communcaton wth the snk s sgnfcantly superor to that of ad-hoc sensor networks. However, snce the sources wat for an access pont s vst, the throughput s lmted by the traversal speed and trajectory length of the access pont. In ths paper, we consder the novel Moble Access Coordnated Wreless Sensor Network Archtecture (MC-WSN). In MC-WSN, multple snks are utlzed for data collecton. There exst a powerful center cluster head () located n the mddle of each cell, and powerful rng cluster heads (s) that are unformly placed on a crcular rng n each cell. Data transmsson goes through smple routng from each sensor to the and/or s. MC-WSN also explots moble access ponts (MAs) to coordnate the network by deployng sensors nodes and cluster heads, rechargng low-power nodes, as well as detectng malcous sensors and replacng them. MAs collects data from the sensors through the and S. The MA can also traverse the cell f the routng paths do not work. The feasblty of ths desgn s supported by the recent advances n unmanned aeral vehcle technology [5]. In ths paper, we extend our prevous work n [6], and calculate the throughput of the MC-WSN. We start by analyzng the throughput from an nformaton theoretc perspectve, then obtan the throughput expressons under both sngle path and multplath routng scenaros. Moreover, we dscuss routng securty n MC-WSN. Sensor networks are vulnerable to malcous attacks that could severely degrade the network performance. Among the dfferent attacks, the compromsaton of authentcated nodes poses serous securty threats. Ths ncludes routng attacks, where malcous nodes can modfy and drop packets that are beng routed to the snk [7]. In ths paper, we propose a secure routng path selecton mechansm to mtgate routng attacks n MC-WSN, and hghlght the nherent securty features of MC-WSN n combatng these attacks. We then dscuss the throughput lmtaton of MC- WSN under routng attacks, and the mprovements acheved through employng the proposed secure routng path selecton approach. II. THE MOBILE ACCESS COORDINATED WIRELESS SENSOR NETWORK (MC-WSN) In ths secton, we descrbe the MC-WSN archtecture, present ts major advantages and features, and dscuss the hop number control. A. Descrpton of the Archtecture In MC-WSN, we assume the network s dvded nto cells each of radus d. Each cell contans a sngle powerful moble /14/$ IEEE 4814

2 access pont (MA) and n unformly deployed sensor nodes (SNs) that are arranged nto K CH clusters. Each cluster s managed by a cluster head (CH), to whch all the cluster members report ther data. CHs then route the data to the MA. A powerful center cluster head () s employed n the mddle of each cell, and K powerful rng cluster heads () are placed on a rng of radus R t. The and s can establsh drect communcaton wth the MA or wth other that are closer to the MA. All nodes wthn a dstance R o from the route ther data to the MA through the. All other nodes route ther data to the MA through the nearest. If a sensor s wthn the MA s coverage range, then drect communcatons can take place. After recevng the data of the sensors, the MA delvers t to a Base Staton (BS). The overall network archtecture s llustrated n Fgure 1. As wll be llustrated later, the number of hops from any sensor to the MA can be lmted to a pre-specfed number through the deployment of and s. Cluster head Moble access Pont Sensor node Base Staton Center cluster head ()/Rng cluster head () Fg. 1. Proposed MC-WSN archtecture. In the proposed MC-WSN archtecture, the MA coordnates the sensor network and resolves the node deployment ssue as well as the energy consumpton problem of wreless sensor networks. More specfcally, the MAs are responsble for () deployng nodes, () replacng and rechargng nodes, () detectng malcous sensors, then removng and replacng them, (v) collectng the nformaton from sensors and delverng t to the BS. The MAs can move on the ground, and can also fly. Each MA traverses ts cell manly for removng the malcous nodes and replacng or rechargng low-energy sensor nodes and cluster heads. It moves physcally for data collecton only n the case when the routng paths do not work. Data transmsson from any SN to the MA goes through smple routng, ether wth the or the s. Let the communcaton range of each sensor node and CH be r c and R c, respectvely. SNs only communcate wth ther correspondng CH, whch then routes ther data to the MA. CHs have larger storage capacty and longer communcaton range than SNs,.e., R c >r c. The man advantages of MC-WSN le n: the multfunctonalty of the moble access, the hop number control through topology desgn, and herarchcal and heterogeneous sensor deployment. MC-WSN has the followng features: Controlled network development and prolonged network lfetme Tme-senstve data transmsson Enhanced network securty Effcent energy consumpton Enhanced network reslence, relablty and scalablty: Due to the actve network deployment feature n the proposed archtecture, we can assume that the nodes are unformly dstrbuted n the network. It s also reasonable to place the powerful s at evenly spaced locatons on the rng R t. Fgure 2 shows an example of the MC-WSN wth four s. Under normal network condtons,.e., wthout malcous attacks, to maxmze the throughput and mnmze the delay of data transmsson from the sensors to the MA, the number of hops needed n routng should be mnmzed. In Secton II-B, we consder topology desgn for hop number mnmzaton. B. Hop Number Mnmzaton In ths subsecton, we obtan the optmal radus R o and the rng radus R t that mnmze the average number of hops from any CH to ts nearest snk. Assumng multple paths are present due to network dversty, ths topology desgn wll ensure that at least one of the paths from any node to a snk has mnmum number of hops,.e., shortest path. Shortest path routng results n hgher throughput performance under normal network condtons as wll be llustrated n Secton III. Note that under shortest path routng, the number of hops s proportonal to the dstance between the source and the snk. To mnmze the number of hops, we desgn the topology such that the average dstance between a cluster head and ts nearest snk s mnmzed. We calculate the average squared dstance between any source and the correspondng snk (/) d 2 accordng to Fg.2, o =0, d t =0, and get the followng result: Proposton 1: Assumng a crcular cell of radus d, to mnmze the number of hops n the MC-WSN archtecture wth one and K s, where K>1, data transmsson should be arranged as follows: (1) The CHs wthn a dstance R o =0.366 d from the center of the cell delver ther data to the MA through the. (2) The CHs at a dstance x from, where R o apple x<d, delver ther data to the MA through the nearest on the rng of radus R t =0.233K sn( K )d. The average number of hops along the shortest path routng can be expressed as N hop = d R c, where R c s the communcaton range of the cluster heads. Note that as K ncreases, d and consequently N hop decrease. On the other hand, f the cell radus d decreases, then also d and N hop decrease. As can be seen, the maxmum number of hops can be lmted to a pre-specfed number through actve deployment of s. 4815

3 d Fg. 2. R o = 2 /K R t R t x R t sn /K (x 2-2xR t cos +R t 2 ) 1/2 MC-WSN wth four powerful s. III. THROUGHPUT ANALYSIS In ths secton, we analyze the throughput of the multhop MC-WSN archtecture. We frst ntroduce the defnton of the throughput n the sngle hop case, then analyze the multhop throughput under both sngle path and multpath routng. A. Bref Overvew As an mportant measure of network performance, throughput s generally defned as the amount of nformaton that can be successfully transmtted over a network, and s largely determned by the network model and transmsson protocols. Exstng work on throughput analyss s versatle [1], [8], [9], ncludng one-hop centralzed cases [8], [9] and ad-hoc cases [1]. There are also research on systems wth moble nodes [3] and systems wth moble access ponts, lke SENMA [4]. In SENMA, as there s a drect lnk between each sensor and the moble snk, the system throughput s sgnfcantly superor to that of ad-hoc sensor networks [4]. In [1], the throughput of random ad-hoc networks s studed. It was shown that the throughput obtaned by each node vanshes as the number of nodes n the network ncreases. More specfcally, for an ad-hoc network contanng n nodes, the throughput obtanable by each node s O( W p n ) bt-meters/sec, where W s the maxmum capacty of each lnk n the network. Note that the sze or densty of an ad-hoc network or a wreless sensor network plays a crtcal role n network performance. Ths result ndcates that for relable and effcent communcatons, the network cannot be completely structureless, but should have a well-defned structure whle mantanng suffcent flexblty. Ths thought has actually been reflected n the mergng of centralzed and ad-hoc networks, leadng to adhoc networks wth structures, known as hybrd networks [10]. As can be seen, the proposed MC-WSN s also an example of hybrd network: t has a herarchcal structure supported by the, s, and CHs; at the same tme, t also allows partally ad-hoc routng for network flexblty and dversty. B. Defnton of the Throughput We start wth the sngle hop case. Assumng node s transmttng to snk k, where k 2{0, 1,...,K}. The throughput =0 of node to snk k, T,k, s defned as the average number of packets per slot that are ntated by node and successfully delvered to the ntended recever k. Defne RS k ( ) as the set of nodes that have ther packets successfully delvered to snk k n slot, where S s the set of nodes scheduled to transmt. P Then, 1 T T,k can be expressed as: T,k =lm T!1 T =1 Pr{ 2 RS k ( )} [11]. Assumng that the packet recepton from slot to slot s an..d process, then the throughput can be formulated usng two bnary flags t k and r k, where tk s a bnary flag ndcatng that node transmts data to snk k and r k s a bnary flag ndcatng that the data of node s successfully receved at the ntended destnaton k ( or ). It follows that: T,k = Pr{r k =1 t k =1}Pr{t k =1}. (1) Note that the transmsson from the powerful / to the MA can be made at hgh-power and hgh-rate. Also, wth the actve network deployment performed by the MA, the data from each sensor to ts CH can be transmtted over a sngle hop usng a collson-free MAC protocol. Thus, we focus on data transmsson from the CH of the orgnatng node to ts correspondng /. In the followng, we analyze T,k from the nformaton theory perspectve, by dscussng the relatonshp between T,k and the mutual nformaton between the packet transmtted from CH and the packet receved at snk k. For each slot, defne X k as the transmtted packet from CH to snk k, where X k = 0 means that node s not transmttng. Let Xk be the non-zero packets of X k, then X k = t k X k [8]. Assumng that snk k receves packets from multple nodes. Defne Y k as the receved vector at snk k, where the th element n Y k s the receved packet from CH. Let r k be the vector whose th element s r k. It has been shown n [8] that the mutual nformaton between X k and Y k can be wrtten as a functon of the throughput of CH to snk k (T,k ) as follows: I(X k, Y k )=I(t k, r k )+H( X k )T,k, (2) where I(x, y) s the mutual nformaton between x and y, and H(x) s the entropy of x. Let I k p = I(X k, Yk )/H( X k), whch s measured n number of packets per slot. In general, T,k apple I k p. Note that t k s bnary,.e., H(t k ) apple 1, whch mples that I(t k, rk ) apple H(t k ) apple 1. As a result, f the packet length gets large,.e., H( X k)!1, then we have T,k ' I k p. From the nformaton theory perceptve, ths shows that: T,k s the average normalzed nformaton (measured n packets per slot) passed through the channel between CH and snk k. C. Multhop Sngle Path Routng Case Consder that CH requres N k hops to reach snk k. N k s based on the network archtecture, topology, and routng scheme. Let the deal or shortest path from CH to snk k be N k! N k 1!... 1! 0, where N k s the source CH and 0 s the snk k. Let t k,h be a bnary flag at hop h, ndcatng that CH h s scheduled to relay a packet of CH 4816

4 to CH h 1 along the route to snk k. Also, let r,h k be a bnary flag ndcatng that the data of CH s successfully receved at CH h 1 along the same route to snk k. It follows that, at each partcular tme slot, we have: Pr{r k,h =1} = Pr{r k,h =1 t k,h =1}Pr{t k,h =1}. (3) Consder that a packet of CH s receved at snk k n slot. Ths mples that there exsts a schedulng slot vector =[ N k 1,..., 1, ], such that all nodes along the routng path from to the snk successfully transmt the packet of node. More specfcally, node h s scheduled to transmt n slot h 1, where x > y, 8x > y and 0 =0. Along slot vector, defne the transmsson flag of CH as t k ( ), such that tk ( ) =[1,..,1] when CH transmts a packet to snk k and the transmsson at the last hop (at CH 1 ) occurs n slot. Note that f the relay at the last hop along the transmsson path from to the snk transmts the packet of node, then t mples that all ntermedate hops were scheduled to transmt n pror slots. That s, we have Pr{t k ( ) =1} = Pr{t k,1( ) =1,...,t k,n k ( N k 1 )=1}. (4) Omt the slot ndex, (4) can be smplfed as: Pr{t k =1} = Pr{t k,1 =1,...,tk =1}.,N k For the throughput calculaton here, we do not consder retransmssons of packets. Assumng that there exsts a schedule such that the source CH and all ts ntermedate relays are assgned tme slots to transmt/forward the source s data, and assumng that the transmssons n all slots are..d, then we can drop the slot ndex from the throughput expresson. In the case when the amplfy-and-forward protocol s adopted n the relayng process, whch mples that r,h k s are ndependent at dfferent hops, t follows from (1) and (3) that: N k Y T,k = Pr{t k =1} Pr{r,h k =1 t k,h =1}. (5) h=1 The probablty of transmsson Pr(t k = 1), depends on the schedulng scheme adopted n the network. When TDMA protocol s used, each node connected to snk k can transmt wth a probablty Pr(t k 1 = 1) N ntf n k, where n k s the number of CHs connected to snk k and N ntf as the mnmum separaton between lnks for bandwdth reuse. That s, when a transmsson s made by a CH, other nodes wthn a dstance of N ntf R c from the transmttng CH should reman slent or use another orthogonal channel. The probablty of successful recepton, under normal network condtons, can be vewed as a condton on the receved sgnal to nterference and nose rato SINR. Assume the SINR threshold for successful recepton s, then we have Pr{r,h k = 1 tk,h = 1} = Pr{SINR h, h 1 > }, 8, h. In structured networks, the assgnment of channels and tme slots can be managed to mnmze the nterference; hence the nterference term becomes neglgble, and we can wrte SINR,j = L,j P N o, where L,j s the dstance between nodes and j, s the path loss exponent, P s the transmtted power, and N o s the nose power. Assumng that the power s exponentally dstrbuted wth mean P for all nodes, then by lettng,h = N o Lh, h 1 we have Pr{SINR h, h 1 > } = Pr{P h >,h } = exp. (6) No P Lh, h From the dscusson above, we get the followng result: Theorem 1: In a multhop MC-WSN network, assumng exponentally dstrbuted transmt powers, the throughput of CH along a predefned sngle routng path to snk k s: 8 9 < N k T,k = Pr{t k =1} exp : apple X = Lh, h 1 ;, (7) h=1 where N k s the number of hops n CH s transmsson, Pr{t k =1} s the probablty that CH and all ts ntermedate relayng nodes are scheduled to transmt the data of CH to snk k, s the path loss exponent of the channel, L x,y s the dstance between nodes x and y, and apple = No P. Remark 1: It can be seen from Theorem 1 that f the hops are equdstant, the throughput wll decrease as the number of hops ncreases. More specfcally, when L h 1, h = L, 8h 2{1, 2,..,N k}, we get T,k / exp{ N k }. It follows that lm N k!1 T,k =0. Ths result justfes our motvaton of lmtng the number of hops n the topology desgn and the and s deployment. D. Multhop Multpath Routng Case In the prevous subsecton, we consdered the case when there s a sngle pre-defned path between a CH and a snk. Note that, n general, the transmsson can go through multpaths due to the exstence of network dversty. Multpath routng would also ncrease the securty strength aganst malcous routng attacks as wll be llustrated n Secton IV. In ths secton, we formulate the throughput for the multpath case. Theorem 2: Let N be the maxmum number of hops from a CH to a snk along any routng path, and N k (p) apple N s the number of hops from CH to snk k along path p. Consder that for each hop number l 2 {1, 2,...,N}, there are P,l possble l-hop paths from CH to the snk(s). Let T ( N k(p) = l, P k = p) be the throughput that can be acheved along one of the l-hop paths from source to snk k assumng the path P k = p. Hence, the throughput of node to snk k can be calculated as: P NX X,l T,k = T ( N k (p) =l, P k = p)pr{p k = p, N k (p) =l} l=1 p=1 Here, l-hop path means a path that conssts of l hops. It s noted that T ( N k = l, P k = p) can be obtaned from Theorem 1 by substtutng N k = l, whch s the number of hops along the partcular path P k = p. The term Pr{P k = p N k = l} depends on the routng protocol. It should be emphaszed that when multple routes are enabled, 1 (8) 4817

5 the utlzed schedulng protocol, and hence P (t k = 1), could be dfferent than that n the sngle routng path case. E. Total Network Throughput The network throughput,, s defned as the average number of packets receved successfully from all clusters per unt tme. Let N k be the set of CHs that transmt to snk k. Followng Theorems 1 and 2, the total throughput of the proposed MC- WSN archtecture wth K s and a can be obtaned as: KX X = = = T,k k=0 2N k KX X k=0 2N k l=1 p=1 KX X k=0 2N k l=1 p=1 P NX X,l T ( N k = l, P k = p) Pr{P k = p N k = l} Pr{N k = l} P NX X,l ( lx h ) p k (p)exp apple L k h, k h 1(p) h=1 Pr{P k = p N k = l} Pr{N k = l}, (9) where n k s the number of nodes connected to snk k, L k h, (p) s the length between CHs k k h 1 h and k h 1 along path p, and p k (p) s the transmsson probablty of CH along path p to snk k. IV. ROUTING SECURITY FOR MC-WSN A. Secure Routng Path Selecton In a multhop routng scheme, a compromsed node along any routng path can launch routng attack by droppng packets or modfyng ther contents as they are beng forwarded to a snk. Routng attacks could not be completely resolved through cryptographc approaches solely. To combat ths type of routng attack, we propose to use multpath dversty n combnaton wth ntegrty check. More specfcally, we propose the followng: Each node establshes multple, preferably dsjont, routes to snk(s). Every packet s transmtted on a randomly selected route. Recall that the probablty that node selects path p to snk k s Pr{P k = p N k (p) =l}, where N k (p) s the correspondng number of hops along the path. Note that the number of hops n any path should be lmted to a pre-specfed number to mprove the network throughput performance as llustrated n the prevous secton. Each transmtted packet has a sequence number, whch s ncluded n the packet header. To ensures that packets have not been modfed by malcous nodes along the routng paths, data ntegrty s checked through a cryptographc keyed Hash functon. Assume that each source shares a secret key wth the snk(s) t communcates wth. A Hash functon uses the shared key to produces a fxed sze fngerprnt for each packet. The keyed Hash functon enables the snk to mmedately verfy data ntegrty. Along wth the sequence number check, the snk can adjust the routng probabltes (Pr{P k = p N k (p) =l}) accordngly, then notfy the correspondng source. More specfcally, we have the followng: () If n p packets receved through routng path p are erroneous (checked through the Hash functon) then Pr{P k = p N k(p) =l} decreases by l. If over multple observaton perods n p or more packets are receved through path p wth no errors, then ths path s consdered relable and Pr{P k = p N k(p) =l} ncreases by h. l and h are the decrement and ncrement step szes, respectvely, and they should be tuned along wth n p to take nto account errors resultng from possble poor envronmental condtons. The tunng of l and h s subject to the constrant that the sum of probablty over all possble paths always equals to 1. After suffcent observatons, only the relable routes wll be chosen for data delvery. Note that h could depend on the number of hops along the path. For example, f two paths have shown to be equally relable, hgher h can be used for the path wth lower number of hops. That s, gven that paths p 1 and p 2 are equally relable, f l 1 <l 2, then choose h1 and h2 such that: Pr{P k1 = p 1 N k1 (p 1 )=l 1 } > Pr{P k2 = p 2 N k2 (p 2 ) = l 2 }. That s, we choose the shortest path for throughput maxmzaton. We would analyze the selecton of optmal l and h from an nformaton theoretc perspectve n future work. () Smlarly, through sequence number check, a packet drop along any of the paths can be detected. The snk consequently decreases the probablty that the source transmts over the correspondng path. The sequence number check can be verfed at the MA, then notfed to the ndvdual snks (/). B. Dscussons on Throughput In ths subsecton, we dscuss the effect of routng attacks on the throughput, then show that the proposed secure routng selecton approach can lead to an mproved performance under malcous attacks. We start wth a sngle routng path case, where CH establshes a sngle path to ts (nearest) snk k,.e., P,l =1. Note that a routng path s sad to be compromsed f one or more nodes along ths path s compromsed. Let an ntermedate node at hop level h be compromsed to drop or manpulate packets that are beng relayed through t. Therefore, the probablty of successful recepton Pr{r,h k =1} =0, and thus, by referrng to (5), the overall throughput of node wll be zero. On the other hand, snce packets routed along a compromsed path wll not reach the snk, then ths means that the average delay per packet s nfnte. In other words, wthout routng dversty, routng attacks can lead to a zero throughput and nfnte delay. Let the number of compromsed paths between node and the snk(s) be P c; hence, there are P b = P,l P c paths 4818

6 that do not nvolve any compromsed nodes. Followng the proposed approach for routng securty, f there s at least one path between a CH and a snk has no compromsed nodes,.e., P b 1, then a non-zero throughput can be guaranteed for the node. Let S b be the set of non-compromsed paths, and Sc be the set of compromsed paths. Therefore, we have: T = X NX X T ( N k (p) =l, Pk = p) k l=1 = X k p2s b,sc Pr{P k = p, N k (p) =l}. NX X T ( N k (p) =l, Pk = p)pr{pk = p, N k (p) =l}. l=1 p2s b (10) From the equaton above, t s clear that to ncrease the throughput, packets should be transmtted through relable paths only by choosng Pr{P k = p N k(p) =l} =08p 2 Sc. Note that Pr{P k = p N k (p) = l} can be regarded as the weght of choosng path p. Therefore, to maxmze the throughput, we need P p2s Pr{P k b = p N k (p) =l} =1. Through the keyed hash functon and sequence number check, the unrelable paths can be detected and the snk updates Pr{P k = p, N k (p) = l} by lowerng the probabltes that P a compromsed path s selected. Eventually, we get: p2s Pr{P k b = p N k (p) = l} = 1, whch mproves the throughput as can be seen n (10). V. SIMULATION RESULT In ths secton, we llustrate the effect of the number of hops and the malcous attacks on the throughput. Three cases are consdered: shortest path routng n the absence of malcous attacks, multpath routng under malcous attacks wth and wthout the secure routng path selecton approach. Assume three paths (p 1,p 2,p 3 ) are avalable, wth number of hops N m, N m +1, N m +2, respectvely, and path p 2 s compromsed. The throughput versus the number of hops N m s plotted n Fgure 3. Wthout the secure route selecton scheme, all paths are selected wth equal probablty. When routng path selecton s utlzed, data s transmtted on the un-compromsed paths p 1 and p 2, wth hgher probablty for the shorter path p 1. Here, Pr{p 1,N m } = 0.8 and Pr{p 3,N m +2} = 0.2. It can be seen that usng secure routng path selecton, the throughput performance under malcous attack s sgnfcantly mproved compared to the case when routng path selecton approach s not adopted. It s also clear that the throughput decreases as the number of hops ncreases. Ths echoes our theoretcal analyss. VI. CONCLUSIONS In ths paper, we analyzed the throughput of the MC- WSN archtecture under sngle path and multpath routng. The obtaned throughput expressons revealed the mpact of the number of hops on the attaned throughput performance, and llustrated the trade-off between throughput effcency and securty strength. It was concluded that the shortest path Throughput 4.5 x No malcous attacks, shortest path routng Under malcous attack, multpath, wthout routng path selecton Under malcous attack, multpath, wth routng path selecton Mnmum number of hops (N m ) Fg. 3. Throughput versus number of hops. Here, SINR = R c P =8dB, N o =5dB, Pr(t k =1)=0.02. routng mproves the throughput. However, under routng attacks, shortest path routng cannot be optmal f compromsed. To combat routng attacks, we presented a secure routng path selecton approach, and showed that t can mprove the network throughput performance. ACKNOWLEDGEMENT Ths research s partally supported by NSF under awards ECCS , CNS and CNS REFERENCES [1] P. Gupta and P. Kumar, The capacty of wreless networks, IEEE Transactons on Informaton Theory, vol. 46, no. 2, pp , Mar [2] E. J. Duarte-Melo and M. Lu, Data-gatherng wreless sensor networks: organzaton and capacty, Computer Networks, vol. 43, no. 4, pp , 2003, wreless Sensor Networks. [Onlne]. 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