On Multicast Capacity and Delay in Cognitive Radio Mobile Ad-hoc Networks

Transcription

1 On Multicast Caacity and Delay in Cognitive Radio Mobile Ad-hoc Networks Jinbei Zhang, Yixuan Li, Zhuotao Liu, Fan Wu, Feng Yang, Xinbing Wang Det of Electronic Engineering Det of Comuter Science and Engineering Shanghai Jiao Tong University, China Abstract In this aer, we focus on the caacity and delay tradeoff for multicast traffic attern in Cognitive Radio (CR Mobile Ad-hoc Networks (MANET In our system model, the rimary network consisting of n rimary nodes, overlas with the secondary network consisting of m secondary nodes in a unit square Assume that all nodes move according to an iid mobility model and each rimary node serves as a source that multicasts its ackets to k rimary destination nodes whereas each secondary source node multicasts its ackets to k s secondary destination nodes Under the cell artitioned network model, we study the caacity and delay for the rimary networks under two communication schemes: Non-cooerative Scheme and Cooerative Scheme The communication attern considered for the secondary network is Cooerative Scheme Given that m = n β (β >, we show that er-node caacity O(/k and O(/k s are achievable for the rimary network and the secondary network, with average delay Θ(n log k and Θ(m log k s, resectively Moreover, to reduce the average delay in the secondary network, we emloy a Redundancy Scheme and rove that a er-node caacity O(/k s m log ks is achievable with average delay Θ( m log k s We find that the fundamental delay-caacity tradeoff in the secondary network is delay/caacity O(mk s log k s under both cooerative scheme and redundancy scheme Index Terms Cognitive Radio, Caacity Scaling, Network Delay I INTRODUCTION Since the seminal work by Guta and Kumar [], the study of the caacity of wireless networks has received great attention It is shown that the er-node caacity is Θ(/ n log n for unicast traffic attern, where n is the number of nodes in the network [] Comared with the unicast traffic attern where ackets are sent from a source node to another destination node, the multicast traffic attern exhibits the following roerty: ackets from source nodes are delivered to multile destination nodes where some links can be shared by different destinations Therefore, the multicast traffic attern consumes less satial and frequency resource required to establish communication among all the destinations Comared to the caacity scaling in static network models, mobility has been leveraged to imrove the caacity bounds In [], Grossglauser et al demonstrated that the er-node caacity Θ( is achievable under indeendent and identically distributed (iid mobility model However, one significant erformance metric in wireless networks, other than the throughut, is under-studied in [], eg, the communication delay This motivated later research to exlore the relationshi between delay and throughut In [3], Neely et al studied the caacity-delay tradeoff in cell artitioned MANET by introducing the redundancy scheme which reduced delay by sacrificing caacity They develoed communication schemes to achieve er-node caacity Θ(, Θ( n and Θ( n log n with average delay Θ(n, Θ( n and Θ(log n, resectively, which imlies that the caacity-delay tradeoff has the characteristics delay caacity that > O(n Later on, the caacity-delay tradeoff for unicast networks was thoroughly studied using various mobility models such as the random walk model [4], the random way oint mobility model [5] and the constrained mobility model [6], [7] For the multicast traffic attern, Li et al [8] studied the caacity in static networks where each node sends messages to k destinations Based on the interference model, they demonstrated that the er-node caacity is Θ( kn log n if k = O( n n log n whereas the er-node caacity is Θ( log n when k = Ω( n log n This result can be seen as a generalization of two different traffic atterns: unicast [] and broadcast [9] Some relevant works can also be found in [0]-[4] In [5], Wang et al studied the caacity and delay tradeoff in cell artitioned MANET under a multicast traffic attern They roved that the er-node caacity and delay are O(/k and Θ(n log k resectively if no redundant relay nodes are used, and O(/k n log k and Θ( n log k resectively otherwise All the aforementioned results focus only on the throughut scaling and delay analysis for a stand-alone network Recently, the ever-growing demand for frequency resources has motivated the study of cognitive radio (CR networks to efficiently utilize the idle sectrum in the time and sace domain CR networks consist of two different networks: rimary network and secondary network In CR networks, rimary users have a higher riority when accessing the sectrum, while secondary users oortunistically access the licensed sectrum without deteriorating the erformance of rimary users Secifically, the secondary network can have vacuum sace to transmit when rimary users are idle Also, secondary nodes within the interference range of any rimary nodes that are transmitting or receiving messages cannot have sectrum oortunities to transmit Different from the stand-alone network, the interaction between rimary and secondary users have to be considered when studying the throughut and delay scaling

2 results in CR networks Previous analysis for stand-alone networks is therefore not directly alicable to CR networks The study of caacity and delay scaling laws for both the rimary and secondary network is a relatively new and challenging field In [6] and [7], the authors investigated the caacity scaling of a homogeneous cognitive networks for unicast traffic by introducing a reservation region around rimary receivers Wang et al [8] extended the CR network caacity scaling analysis to multicast traffic atterns under the Gaussian channel model Interestingly, all these works showed that both the rimary and secondary networks can achieve similar or the same erformance bounds as if they can essentially be regarded stand-alone networks when the secondary network has a higher density than the rimary one Note that existing works mainly focus on static CR networks and, to the best of our knowledge, the erformance of mobile CR networks has not been investigated before Motivated by the fact that mobility can dramatically enhance the throughut in stand-alone networks, we are interested in its imact on CR networks: What throughut and delay scaling law can be achieved under a multicast traffic attern in Cognitive Radio Mobile Ad-hoc Networks (CR MANET? What is the delay and caacity tradeoff characteristic in CR MANET? In this aer, we first adot a non-cooerative scheme to investigate the achievable er-node caacity and delay for the rimary network, where one source is suosed to send messages to k destinations We then consider the cooerative mode to give a unified resentation of the routing scheme Next, we focus on the caacity and delay analysis for the secondary network under a cooerative scheme and a redundancy scheme, resectively Finally, we introduce a destination oriented redundancy scheme 3 to efficiently utilize the network resources in the secondary network The major contributions of this aer are as follows: We investigate the imact of mobility model for both the rimary network and the secondary network Transmission queues are emloyed to analyze the caacity and delay for CR MANET Our results show that mobility can significantly enhance the caacity erformance for both the rimary and secondary networks This aer is a nontrivial generalization of revious work since we directly study the caacity and delay under a multicast traffic attern Different with the mobility model studied in [9] and [0], where the rimary nodes are static and only the secondary nodes have mobility, our model assumes that both the rimary and secondary networks can have mobility Our results can be secialized to the unicast and broadcast traffic by setting the number of destinations to be and n for the rimary network ( and m for the secondary network, resectively A non-cooerative scheme means that destinations cannot act as relays within the same multicast grou Otherwise, it is called a cooerative scheme Redundancy scheme means that there can be multile nodes acting as relays for a acket 3 Destination oriented redundancy scheme means that every destination that has received a acket can act as a relay for the acket We show that both the rimary network and the secondary network can achieve the same throughut as the otimal one established for a stand-alone MANET in [5], if the number of secondary users m is larger than that of rimary users n scaled by m = n β (β > Secifically, under the cooerative scheme, the er-node caacity O(/k and O(/k s are achievable for the rimary network and the secondary network, with average delay Θ(n log k and Θ(m log k s, resectively We introduce redundancy into the secondary network and rove that the tight bound of transmission delay can be reduced to Θ( m log k s with an achievable er-node caacity O(/k s m log ks if there are redundant relay nodes Moreover, we also roosed destination oriented redundancy scheme to utilize wireless resources efficiently in ractical oeration We find that the fundamental caacity-delay tradeoff in the secondary network is characterized by delay/caacity O(mk s log k s under both the cooerative scheme and the redundancy scheme The rest of the aer is organized as follows In section II, we introduce our network model and the main definitions In section III, we resent the communication schedules for both the rimary and the secondary network In sections IV and V, we give our main results of caacity and delay in the rimary network and secondary network, resectively Finally, we conclude this aer in section VI II NETWORK MODEL Cell Partitioned Network Model: Our network model is based on the model used in [3] Consider a unit square with a co-existing rimary network and secondary network, where the two networks share the same sace, time and frequency domain but with different riorities in accessing the sectrum The rimary nodes and secondary nodes are distributed according to a Homogeneous Poisson Process (HPP of density n and m, resectively We assume that n and m satisfy m = n β (β >, which indicates that the secondary network has a higher density than the rimary network It can be roved [] that the total numbers of rimary nodes and secondary nodes within the unit area are of order Θ(n and Θ(m, resectively For simlicity, we will assume that there are n mobile rimary nodes and m mobile secondary nodes distributed over the square throughout the aer We further divide the rimary network into w = Θ(n non-overlaing cells with equal area Θ( n and divide the secondary network into c = Θ(m non-overlaing cells with equal area Θ( m as illustrated in Figure The node density τ is n w for the rimary network and τ s is m c for the secondary network Therefore, both τ and τ s are of constant order Θ( Traffic Pattern: In a multicast traffic attern, we assume that there are a set V = {v, v,, v n } of mobile rimary nodes and another set V s = {vs, vs,, vs m } of mobile secondary nodes in the unit square For each multicast grou in the rimary network, there is a source node v i V and k destinations that are randomly and indeendently chosen Multicast grous in the secondary network can be similarly defined

3 3 Active secondary cells Θ( n { Primary cells Θ ( m { Inactive secondary cells Fig Illustration of cell artitioned network model: the blue rimary cells reresent the active cells where a air of rimary nodes in a cell (denoted by green sots are transmitting No sectrum oortunities will be available for secondary nodes located in the region of active rimary cells Thus we color the secondary cells blue to indicate that they are inactive due to the resence of active rimary cells All the secondary nodes in the inactive secondary cells will buffer their ackets without transmitting Mobility Model: Assuming that time is slotted, we adot the ideal iid fast mobility model The initial osition of each node (rimary or secondary is equally likely to be in any of the (rimary or secondary cells indeendent of the other nodes ositions At the beginning of the next time slot, nodes can roam to a new cell randomly in the network Since we adot the fast mobility model, the time it takes for a node to move from one cell to another has negligible delay Under the mobility model, ackets are carried by the nodes (either the source or relay nodes until they reach their corresonding destination nodes Interference: In CR MANET, there are three kinds of interference: inter-cell interference, intra-cell interference and inter-network interference To avoid intra-cell interference, we assume that each cell (rimary or secondary allows at most one transmission during a time slot In order to mitigate inter-rimary-cell interference, neighboring rimary cells have to transmit over orthogonal frequency bands and four bands are enough for the whole rimary network to ensure this condition [3] The inter-secondary-cell interference can be avoided by adoting a -TDMA 4 schedule for the secondary network Since the rimary nodes have higher riority in using the sectrum, the secondary network has to oerate without causing severe interference to the rimary network To limit the inter-network interference, no sectrum oortunities will be available for a secondary node if it resides in the region of an active rimary cell If a secondary node roams to an inactive secondary cell at a time slot, it will buffer its ackets without transmitting Caacity: We assume that the exogenous rate of ackets to each rimary and secondary source node are both a Bernoulli rocess with rate λ and λ s ackets er slot, resectively The network is stable when there exists a scheduling olicy to ensure that the acket queue for each node will not aroach 4 The TDMA scheme can also be 9-TDMA or 6-TDMA schemes, which is used for concurrently transmissions and since we focus on scaling erformance, the constant will not affect our results infinity as time aroaches infinity and each acket can be delivered to its k (k = k for the rimary network and k = k s for the secondary network distinct destinations We define λ and λ s as the achievable er-node caacity for the rimary network and the secondary network, resectively For other stochastic arrival rocess with the same average rate, the analysis can be treated similarly and the throughut will not change [3] Delay: In the multicast communication attern, the delay in the rimary (secondary network D (D s is defined as the time interval between the time that the acket dearts from the rimary (secondary source node, and the time that it arrives at all the k (k s destination nodes Transmission Queues: We analyze the communication delay using queueing theory For both the rimary network and the secondary network, ackets are transmitted through sourceto-destination queues, source-to-relay queues and relay-todestination queues according to their secific communication schemes Knuth Notation: Given two functions f(n > 0, g(n > 0: f(n = o(g(n means lim n f(n/g(n = 0; f(n = O(g(n means lim n su f(n/g(n < ; f(n = ω(g(n is equivalent to g(n = o(f(n; f(n = Ω(g(n is equivalent to g(n = O(f(n; f(n = Θ(g(n means f(n = O(g(n and g(n = O(f(n The key notations used in this aer are listed in the following table Notation n (m w (c τ (τ s k (k s λ (λ s D (D s TABLE I NOTATIONS Definition The number of rimary (secondary nodes The number of rimary (secondary cells The node density of each rimary (secondary cell The number of rimary (secondary destinations The throughut of rimary (secondary nodes The delay of rimary (secondary ackets III COMMUNICATION SCHEME In this section, we will introduce the communication schemes for both the rimary network and the secondary network Since the rimary network has a higher riority, it is oblivious to the existence of the secondary network The secondary network adatively chooses to transmit based on the given rimary transmission scheme A Communication Scheme for the Primary Network In the rimary network, we assume that the ackets are delivered using at most two hos The source node either sends ackets directly to all the destinations or to one of the relays Then the relay will forward the acket to all the corresonding destinations Each cell becomes active when at least one successful transmission can haen In the following, we consider two schemes: non-cooerative scheme and cooerative scheme Non-cooerative Scheme:

4 4 For an active cell containing at least two rimary nodes, the transmissions are conducted in the following way If at least one rimary source-destination air can be found in the cell, then randomly ick one air to finish the communication If no source-destination air can be found in the cell, erform the following two schedules with equal robability: Source-to-Relay Transmission: Randomly ick one source node as the sender If at least one normal relay node 5 is available for the source node in the same cell, ick the relay node as the receiver to finish the transmission Relay-to-Destination Transmission: If one relay n- ode, carrying a acket destined for a rimary destination node, can be found in one cell and at least one corresonding ristine rimary destination node 6 stays within the same cell, ick the relay node as the sender and one of these ristine destination nodes as the receiver to finish the transmission 3 If neither of the above two items can be satisfied, no transmission will take lace in this cell A acket will be discarded whenever all its k rimary destinations have received it 7 Cooerative Scheme: According to the revious scheme, one rimary destination node cannot serve as a relay for other destinations within the same multicast grou That is to say, a certain destination node either receives ackets from corresonding source node or acts as a relay for other multicast grous However, under the cooerative scheme, we will no longer discriminate between the destination nodes and normal relay nodes The first node that the source delivers its acket to will be treated as a relay node irresective of whether it is a destination node or not Once a destination node is chosen as a relay node, it can send ackets to other destination nodes (ossibly within the same multicast grou or not Under the cooerative scheme for the rimary network, the following two transmission atterns haen with equal robability: Source-to-Relay Transmission: If one rimary source node can be found in the cell and one relay node is available in the same cell, ick the source node as the sender and one relay node as the receiver to finish the transmission Relay-to-Destination Transmission: If one relay node, carrying a acket destined for rimary destination n- odes, can be found in this cell and meanwhile at least one corresonding ristine rimary destination node resides within the same cell, ick the relay node as the 5 For a certain multicast grou, all nodes in the area excet for those destination nodes within this multicast grou can be treated as normal relay nodes for this multicast grou 6 A ristine rimary destination node reresents a destination node which has not received the desired acket, that the relay node is carrying This is the same when we call a node as a ristine secondary destination node 7 The acknowledge information can be delivered when the source and destinations have transmission oortunities Since this information size is very small comared to the acket size, its cost can be neglected sender and one destination node as the receiver to finish the transmission If neither of the above two items mentioned can be satisfied, no transmission will take lace in this cell B Communication Scheme for the Secondary Network Primary nodes have riority to access the channel Secondary nodes should choose their action based on the activity of rimary nodes When rimary nodes is transmitting in some rimary cells, secondary nodes inside would kee silent When rimary nodes is silent, secondary nodes may transmit, when it will not cause severer interference to rimary nodes Since the density of secondary nodes is larger than that of rimary nodes in order sense, the communication range emloyed by the secondary nodes can be much smaller than that of rimary nodes Therefore, the interference that secondary nodes cause can be tolerable for rimary nodes if we schedule aroriately And the schemes analyzed in Section V are all based on this main intuition From the caacity analysis for the rimary network in section IV, we find that the cooerative scheme can achieve better erformance than the non-cooerative scheme Therefore, we only consider the cooerative scheme for the secondary network without considering the non-cooerative scheme further The cooerative scheme in the secondary network is similar to that in the rimary network Note that in the cooerative scheme, only one relay node is used for sending a single acket For the secondary network, we further roose a redundancy scheme in order to reduce the delay, which allows more than one relay to be used for delivering a single acket Then, we imrove the redundancy scheme by avoiding the use of additional nodes other than the destination nodes which have received ackets to serve as relays This is referred to as destination oriented redundancy scheme In this way, we are able to better utilize network resources under this scheme This communication schedule will be discussed in more details later on in section V IV CAPACITY AND DELAY ANALYSIS FOR THE PRIMARY NETWORK In this section, we will study the caacity and delay tradeoff in the rimary network Denote the robability that there are at least two rimary nodes in one cell by, which is given by = ( ( n w n w ( w n = ( w n n w ( w n ( + τ e τ Denote the robability of finding a source-destination air in the rimary network by To get, we need to model the rimary nodes as mutually exclusive grous according to the following definition Definition : {k + }-groued Primary Network: For each source node v i V in the rimary network, we ut it and its k destination nodes into a grou, denoted by G i

5 5 n Then we will have 8 k + grous over the whole rimary network We also assume that G i G j =, for i j, and n i, j [, k + ] Note that in the {k + }-groued rimary network, each node within G i can be a source node or destination node Thus, any two nodes from the same grou are a sourcedestination air However, for any randomly chosen two nodes from different grous, they cannot be viewed as a sourcedestination air Then, we get = [( ( k + w k+ + w ( n ] w k k+ = ( w nk k+ ( + k n n k+ { e τ e τ = 0, if k = o(n; ( + τ e τ, if k = Θ(n A Caacity and Delay Analysis of the Non-cooerative Scheme In this subsection, we will study the achievable caacity and communication delay in the rimary network when destination nodes cannot relay ackets to other destination nodes within the same multicast grou Our main results are resented in the following Theorem : In a cell-artitioned network with overlaing n rimary nodes and m secondary nodes, the achievable er-node caacity for the rimary network under the noncooerative scheme is λ = O(/k with an average delay E[D ] = Θ(n log k Proof: In each time slot, a new acket arrives at a rimary source node v i in the grou G i with rate λ Denote the rate that the acket is transmitted to a rimary destination node or handed over to a relay node by R and, resectively Then we have = R + Since the transmission of the source-to-relay and the relayto-destination have equal robability, is also equal to the rate at which the relay nodes are sending ackets to the rimary destinations Thus, in every time slot, the total rate of transmission oortunities over the rimary network is n(r + Meanwhile, a transmission occurs in any given cell with robability Hence we obtain w = n(r + ( Similarly, since is the robability that a rimary sourcedestination air can communicate with each other in one cell, we have w = nr ( Combining Equations ( and (, we have R = τ ; = ( τ Then we obtain that the total service rate for one rimary source queue is = ( + τ 8 Here we assume that n is divisible by k + Now, we will deal with the traffic delay for the rimary network using queueing theory techniques similar to [3][5] There are two ossible routing strategies for a rimary acket to reach its destination: the -ho source-to-destination ath and the -ho source-relay-destination ath For the first strategy, the source will transmit the acket to all the k destinations directly and the delay consists of only the queueing delay at the source For the second strategy, the acket will first sent to a relay and the relay will transmit the acket to all the k destinations Hence, delay is comosed of the queueing delays at both the source and the relay nodes If one acket is directly sent from the source node to destination nodes, it will wait at the source for a time eriod D s d before the source can find its corresonding destinations to forward this acket Since a source node transmits ackets to k destinations for multicast traffic, we assume that there are k identical coies of the acket in the buffer of the source node Thus, we can model a source queue as a set of k sub-queues, in which each sub-queue is intended for one destination Since the rate of each sub-queue is assumed to be the same, and the transmission scheme is randomly oerated for every sub-queue, the k sub-queues can be seen as indeendent source-destination routings, as illustrated in Figure Source λ Packet 3 k P j k kλ 3 k P j k Destination Destination Destination 3 Destination k Destination k O λ sub Fig Illustration of the source-to-destination transmission rocess in the rimary network under the non-cooerative scheme Denote the delay in each routing by D j s d Then we have D s d = max {D j s d } j k To calculate the delay in this scenario, we first obtain the inut and outut rate for each source-to-destination sub-queue in the following lemma Lemma : Each source-to-destination sub-queue is a M/M/ queue corresonding to one destination node with inut rate λ i sub = λr λ and service rate λ o o sub = R k Proof: It is clear that the robability that the acket will be sent directly from the source to the destination is R Hence, the inut rate of each sub-queue is λ i sub = λ s d = λ R λ o The outut rate of each sub-queue is equal to the communication rate of a source-to-destination air λ o sub = R k because

6 6 the k destinations are equally likely to get the acket directly from the source Thus, the exected queueing time for each sub-queue is λ o sub λi sub To obtain the maximum exected queueing time for all the sub-queues, we first introduce the following lemma [5] Lemma : Suose X, X,, X k are continuous iid exonential random variables with exectation of /a Denote X max = max{x, X,, X k }, then { Θ(/a, k = E{X max } = Θ(log k/a, k > Therefore, we can conclude that ( Θ D s d = ( log k Θ R k λ R R k λ R, k =, k > (3 On the other hand, if the acket is transmitted through a relay node, the relay node will hold the acket and transmit the acket to all destinations We denote the delay from source to relay by Ds r and the delay from relay to destination by D r d Then we have the following lemma Lemma 3: In the first hase of the -ho routing strategy under the non-cooerative scheme, the exected delay before a rimary source node can find a normal relay node to send a R acket is equal to /( λ λ o Proof: The robability that a acket is handed over by a relay in the rimary network is λ Thus, for a source node o with inut rate λ, the rate that the ackets will be delivered R to a relay is λ λ Also note that the available service rate for o a source to a relay is Therefore we conclude this lemma Next, we will calculate the delay in the second hase D r d Note that the robability that the acket is sent to a relay node is i R s r = (n k, because all these n k rimary nodes outside the grou G i are equally likely to be chosen as a relay under the non-cooerative scheme Then the inut rate for a relay-to-destination queue in the rimary network λ i r is λ i r = λ i s r = λ (n k Hence, similar to the revious discussion, we can model this rocess as a acket transmitted through k indeendent sub-queues and each destination is associated with one fixed sub-queue, as shown in Figure 3 Thus, using the same technique as in the revious analysis, the inut rate of one sub-queue is k λ i r and the outut rate is n k because one rimary node can relay ackets for all the other n k nodes excet the k + nodes in its grou Therefore, the exected queueing time for each sub-queue in the relay node is By Lemma, we can obtain n k k λ i r ( Θ D R r d =, k = n k k λ i r ( (4 Θ, k > log k n k kλi r Relay i i λ r Packet Pj P j 3 k P j k i kλr i k 3 n k Destination Destination n k Destination k Fig 3 Illustration of the relay-to-destination transmission rocess in the rimary network under the non-cooerative scheme Combining Lemma, Lemma and Equation (4, we can obtain that the total exected delay for the rimary network under multicast traffic (k > is E[D ] = R D s d + λ o (Ds r + D r d = R ( log k Θ + R k λ R ( ( log k R λ + Θ n k k λ i r = ( log k log k λ o Θ + k λ λ n k kλi r Note that λ i r = (n k Since the inut rate of a stable queue must be smaller than its outut rate, we have k > λ λ ; o R > λ λ ; o n k > k λ i r = kλr λ o(n k The constraint of the above three inequalities allows the er-node caacity λ = O(/k and delay E[D ] = Θ(k log k = Θ(n log k This concludes the roof of Theorem Note that while the network erformance remains almost the same when k varies, the transmission flow goes through different aths To give a more simlified and elegant routing scheme, we further assume that each destination can also act as a relay for the other destinations in the same grou, and we call this as the cooerative scheme in the following subsection B Caacity and Delay Analysis of the Cooerative Scheme In this subsection, we utilize the cooeration among destinations within the same multicast grou and show that the routing scheme can be resented in a unified form while keeing the erformance remain the same Under the cooerative scheme, ackets can be transmitted only through the -ho source-to-relay-to-destination attern The difference from the revious subsection is that the relay node for each acket is selected from n nodes rather than from n k (5

7 7 nodes Our main results under this scenario are resented in the following theorem Theorem : In a cell-artitioned network with overlaing n rimary nodes and m secondary nodes, the achievable ernode caacity for the rimary network is λ = O(/k with average delay E[D ] = Θ(n log k under the cooerative scheme Proof: The roof is similar as that of Theorem To avoid confusion, we will adot the same mathematical symbols as the revious subsection Since only the -ho source-torelay-to-destination attern is available under the cooerative scheme, we have = = τ For the source-to-relay delay Ds r, we have the following lemma Lemma 4: In the first hase of -ho routing strategy under the cooerative scheme, the exected delay before a rimary source node can find a relay node to send a acket is D s r = λ (6 Proof: The roof is quite similar to that of Lemma 3 and we omit it here Now we will discuss the delay in the second hase D r d Under the cooerative scheme, when destination nodes can serve as relay nodes for any multicast grou, the inut rate for a relay-to-destination queue λ i r is λ i r = λ n If a destination node is chosen as a relay node, then it only needs to transmit ackets to the remaining k destination nodes Otherwise, a normal relay node must send ackets to all the k destination nodes It is clear that whether k or k destination nodes that are suosed to receive the acket makes no difference to the delay in an order sense Therefore, we assume that a relay node has to relay ackets for k destination nodes regardless of whether it is a destination node or not Hence, using the same technique as the revious subsection, we have that the inut rate for a sub-queue is k λ i r and the outut rate is R n Therefore, the exected queueing time for each sub-queue in the relay node is n k λ i r According to Lemma, we can obtain D r d = ( Θ ( Θ n kλi r log k n kλi r, k =, k > (7 Combining Equations (6 and (7, we have that the total exected delay under multicast traffic (k > is E[D ] = Ds r + D r d ( log k = R λ + Θ n k λ i r From Equation (8, it is clear that the following two inequalities should hold: { λ < ; k λ i r λk n < R n (8 From the above two inequalities, it is easy to see that the er-node caacity O(/k is achievable under the cooerative scheme regardless of the order of k Note that the exected delay E[D ] is still in the order of Θ(n log k, which imlies that cooerative schemes use a simlified algorithm while keeing a same erformance as non-cooerative schemes V CAPACITY AND DELAY ANALYSIS FOR THE SECONDARY NETWORK In this section, we will discuss the caacity and delay tradeoff in the secondary network Unlike the scheme in the rimary network, a node in the secondary network can only oortunistically transmit whenever it is outside the region of active rimary cells For these active secondary cells, we adot a -TDMA scheme to avoid interference In the following, we first analyze the exected caacity and delay under the cooerative scheme We then introduce the redundancy scheme and destination oriented redundancy scheme to hel reduce the delay and efficiently utilize the network resources for the secondary network A Caacity and Delay Analysis of the Cooerative Scheme The following lemma indicates that, with the communication schemes defined reviously, the secondary nodes (whether source nodes or relay nodes have oortunities to deliver their ackets Later we rove that the whole secondary network aears to have the same caacity and delay erformance as a stand-alone MANET in the order sense Lemma 5: With the roosed communication scheme, the following two results hold: In each time slot, a constant fraction of the secondary cells is outside the region of active rimary cells, which can be scheduled successfully for transmission Each individual secondary cell has a constant robability for sectrum access to transmit Proof: Let c q (n be the fraction of rimary cells with q nodes ( q 0 According to Lemma in [], c q (n = e /q! wh Then e 06 fraction of the rimary cells contains at least two rimary nodes wh This imlies that the remaining fraction of rimary cells may not be active and this allows the secondary nodes access to the sectrum for transmitting Thus, we conclude the first art of the lemma The above art imlies a constant transmission oortunity for the overall secondary cells We have to further consider the transmission oortunity of each individual secondary cell Recall that the secondary network adots a -TDMA scheme with adjacent-neighbor communication In each rimary time slot, we have a comlete secondary TDMA frame in our communication scheme Each active secondary cell will be assigned with at least one active secondary TDMA slot within each secondary frame This comletes the roof Lemma 6: The total service rate for a secondary source queue is λ o s = 3 τ s, where 3 ( + τ s e τ s Proof: Denote the robability that there are at least two secondary nodes in one cell by 3 Then we have 3 = ( c m ( m c ( c m ( + τ s e τ s

8 8 Similar to the cooerative scheme in the rimary network, ackets are transmitted only through the -ho source-relaydestination aths under the cooerative scheme in the secondary network Since the transmission for source-to-relay and relay-to-destination have equal robability, λ o s is also equal to the rate at which the relay nodes are sending ackets to the secondary destinations Thus, in every time slot, the total rate of transmission oortunities over the secondary network is mλ o s Meanwhile, a transmission occurs in any given cell with robability 3 Hence, we obtain c 3 = mλ o s (9 Therefore, the total service rate for a secondary source queue is λ o s = 3 τ s Our results on achievable er-node caacity and transmission delay are given in the following Theorem 3: In a cell-artitioned network with overlaing n rimary nodes and m secondary nodes, the achievable ernode caacity for the secondary network under the cooerative scheme is λ s = O(/k s with average delay E[D s ] = Θ(m log k s Proof: For the -ho source-relay-destination communication strategy, both the queueing time at the secondary source node and relay node are accounted for in the delay We denote the delay in first hase (from a secondary source node to a relay node by Ds r s and delay in second hase (from a relay node to all the k s secondary destination nodes by Dr d s Then, similar to Lemma 3 in revious section, we have the following lemma Lemma 7: In the first hase of the cooerative scheme in the secondary network, the exected delay for a secondary source to send one acket to a relay node equals c, 3 λ s where c (0 < c < is a constant Proof of Lemma 7: Since a secondary frame is divided into sub-frames, the transmission rate for a secondary cell decreases by a factor of Moreover, according to Lemma 5, there is a constant fraction of secondary cells in the unit area that can access the sectrum Here we use the constant c to reresent the overall likelihood that the secondary cells will be successfully scheduled during one second Therefore, the inut rate and outut rate for a secondary source-to-relay queue are λ s and c λ0 s, with average delay c λ 0 s λ s Now, we need to get the delay in the second hase Dr d s Note that a secondary node relays a acket from a secondary λ s m source node with rate λ i s = because all the secondary nodes are equally likely to be chosen as a relay For a relayto-destination sub-queue, there will be k s or k s sources, deending on whether the relay is also a destination for the acket Let us regard the inut rate for a relay-to-destination sub-queue to be k s λ i s c λ o s The outut rate of one sub-queue is (m because one secondary node can relay ackets destined for all the other m nodes with equal robability Therefore, the exected queueing time for each sub-queue in the relay node By Lemma, we can obtain is c λ o s (m ksλi s ( Θ Dr d s = ( Θ c λ o s (m ksλi s log k s c λ o s (m k sλ i s, k s =, k s > (0 Combining Lemma 6 and Equation (0, we have the total exected delay for the secondary network under multicast traffic (k s > as E[D s ] = Ds r s + Dr d s ( = c + Θ λ0 s λ s log k s c λ o s (m k sλ i s ( To make sure that the number of ackets waiting to be transmitted in each queue does not increase to infinity with time, the following two constraints must be satisfied { λs < c λ0 s; c λ o s (m > k sλ i s From the above two inequalities, we obtain λ s < c λ o s k s Thus, the er-node caacity λ s = O(/k s and average delay E[D s ] = Θ(m log k s are achievable for the secondary network Note that in our system model and communication scheme, the rimary network and secondary network achieve er-node caacity O(/k and O(/k s, resectively Therefore, the co-existence and mutual interference do not affect throughut scaling for cognitive networks B Caacity and Delay Analysis of the Redundancy Scheme In this art, we will discuss the caacity and delay tradeoff when more than one secondary node can serve as a relay, ie, the redundancy scheme, for the secondary network Intuitively, the time needed for a acket to reach its destinations can be reduced by reeatedly sending this acket to many other secondary nodes, ie, using more than one node as a relay In this way, the chances that some node carrying an original or dulicate version of the acket finds a destination will increase Thus, it is suosed that adoting the redundancy scheme can reduce communication delay although this may not hel to imrove the network throughut Previous works [3] and [5] have also introduced the redundancy scheme for a stand-alone ad hoc network in which the source node sends ackets to more than one relay node In CR networks, the redundancy scheme is also alicable for both the rimary network and the secondary network However, considering that secondary nodes suffer from a larger average-delay than the rimary nodes, we shall introduce this redundancy scheme to the secondary network to hel effectively reduce its end-to-end delay Here, we first show the lower bound of the average delay, which is given in the following Theorem 4: In a cell-artitioned network with overlaing n rimary nodes and m secondary nodes, no communication scheme with redundancy can achieve an average delay lower than O( m log k s for the secondary network

9 9 Proof: We rove this result by considering an ideal situation where the secondary network has only a single secondary source node that sends a acket to k s destinations The otimal scheme for the source is to send dulicate versions of the acket whenever it meets any node that has never received the acket before These nodes then act as relays to transmit the acket to the destinations once they enter the same cell as the destinations During the time slots {,,, i}, let ϑ j be the total number of intermediate relay nodes at the beginning of time slot j ( j i Clearly, ϑ ϑ ϑ i since the number of relays is non-decreasing over time Note that a relay can only be generated by the secondary source node, hence at most one node can be a new relay in every time slot Thus, ϑ i i for all i Furthermore, denote the robability that a destination node can meet at least one relay node during time slots {,,, i} by (i, we have (i = i ( c ϑ j j= ( c i However, a destination node that encounters a relay does not necessarily ensure the transmission can be scheduled since the secondary cell in which they meet may not be active during that slot Similar to revious discussion in Lemma 7, c a constant should be factored in Hence, the robability that a destination node can successfully receive a acket from a relay during time slots {,,, i} is c (i / Then, we have Let i = P r(d s i ( c (i k s m log k s τ s ( c ( ( ks c i ks ( c k s ( e τ s i m k s and k s, we obtain that P r(d s i ( c k s ( e log k s k s = ( c ks ( k s ks c e ( Therefore, the average delay in the secondary network with redundancy satisfies E[D s ] E{D s D s i}p r(d s i ( c m log ks (3 e τ s as both m and k s aroach infinity, which concludes the theorem To achieve the above lower bound of the average delay, we roose the following redundancy scheme for the secondary network Redundancy Scheme: For an active secondary cell containing at least two secondary nodes, the following two transmission atterns have with equal robability: Source-to-Relay Transmission: Randomly choose a secondary node as the source node to transmit and one other secondary node as the receiver If the source node has forwarded the dulicate of the acket to at least m log k s distinct relays (ossibly be some of the destinations, the acket is removed from the buffer of source node Relay-to-Destination Transmission: If one relay node, carrying a acket destined for secondary destination nodes, can be found in the cell and meanwhile at least one corresonding ristine secondary destination node resides within the same cell, ick the relay node as the sender and the destination node as the receiver to finish the transmission A acket will be removed when all its k s destinations have received it We now state the following result Theorem 5: In a cell-artitioned network with overlaing n rimary nodes and m secondary nodes, the achievable ernode caacity for the secondary network is O(/k s m log ks with an average delay E[D s ] = O( m log k s under the redundancy scheme Proof: Under the redundancy scheme, the exected time required for a certain acket to reach its corresonding k s destinations E[D s ] is less than E[Ds] + E[Ds], where E[Ds] reresents the exected time required to distribute the dulicates to m log k s different nodes, and E[Ds] is the exected time required to reach all the k s destinations given that m log ks relays are holding the acket We then derived uer bounds on E[Ds] and E[Ds], resectively E[Ds] bound: During the time interval from to Ds, there are at least m m log k s secondary nodes that do not have the acket Hence, in every time slot, the robability that at least one of these nodes is located in the same cell as the source is at least ( c m m log k s At every time slot in the duration Ds, a source node can deliver a dulicate acket to a new node with robability of at least given by c α α ( ( m log c m ks, where α is the robability that the source is selected to be the transmitting node in the cell, and α is the robability that this source is chosen to oerate the source-to-relay transmission which is equal to / According to Lemma 6 in [3], α /( + τ s Thus, c e τ s 4 + τ s as m aroaches infinity The average time for a dulicate acket to reach a new relay is uer bounded by / Since there are m log k s dulicates to be transmitted, in the worst case, m log k s of these times are required Therefore, E[Ds] is uer bounded by m log ks / Hence, we have E[D s] c 4+τ s e τ s m log ks E[Ds] bound: At every time slot in the duration of Ds, there are at least m log k s nodes holding the dulicates of the acket The robability that at least one other node is in the same cell as the destination is ( c m Each time slot, a destination node can successfully receive a dulicate

10 0 acket from one of these relay nodes with robability of at least given by = c β β β 3 ( ( c m, where β is the robability that the destination is selected from all the other nodes in the same cell to be the receiver, β is the robability that the sender is chosen to oerate the relay-to-destination transmission which is equal to /, and β 3 reresents the ossibility that the sender is one of these m log ks nodes ossessing a dulicate acket intended for the destination Similarly, we have β /( + τ s and β 3 = m log ks /(m log k s /m Thus, c e τs log ks /m 4 + τ s as m aroaches infinity The average time that a single destination node receives a dulicate acket destined for it is uer bounded by / The time needed for all the k s destination nodes to receive the acket is the maximum of them Using Lemma 9, E[Ds] is uer bounded by log k s / Hence, we have E[Ds] 4+τ s c e m log τs ks Finally, according to Lemma in [3], the total delay can be uer bounded by E[D s ] = O( m log k s and we obtain an achievable er-node caacity O(/k s m log ks Theorem 6: In a cell-artitioned network with overlaing n rimary nodes and m secondary nodes, the achievable ernode caacity for the secondary network is O(/k s m log ks with average delay E[D s ] = Θ( m log k s under the redundancy scheme Proof: This can be directly obtained by combining Theorem 4 and Theorem 5 C Caacity and Delay Analysis of Destination Oriented Redundancy Scheme The above mentioned redundancy scheme can effectively reduce the end-to-end delay However, the shortcoming is that reeatedly sending one acket to more than one relay node can consume more network resources and increase the interference level To account for this, we imrove the original redundancy scheme and roose a novel redundancy scheme, named the Destination Oriented Redundancy Scheme, which not only reduces delay but also better utilizes the network resources Destination Oriented Redundancy Scheme: For an active secondary cell containing at least two secondary nodes, the following two transmission atterns have equal robability Source-to-Relay Transmission: Choose the first node that the secondary source node meets as a relay irresective of whether it is a destination node or not Pick the source node as the sender and the relay node as the receiver to finish the transmission Relay-to-Destination Transmission: If one relay node, carrying a acket destined for secondary destination nodes, can be found in this cell and meanwhile at least one corresonding ristine secondary destination node resides within the same cell, ick the relay node as the sender and the destination node as the receiver to finish the transmission For the destination nodes which have received the acket, they can also serve as relay nodes to conduct the relay-to-destination transmission In the above mentioned scheme, to reduce the delay by bringing in redundancy, we allow the destination nodes who have received the message to erform as relay nodes Note that at most one node besides the source and k s destinations is chosen as a relay, hence we do not introduce extra relay nodes to relay the acket, utilizing the network resources more efficiently With this new redundancy scheme, we show that the lower bound of communication delay for secondary network is O( m log k s if we allow only one transmission in one time slot However, if we assume that all the available transmissions among different active cells can be conducted in one time slot, we rove that the lower bound of communication delay is O( m log k s k s Formally, we define these two communication atterns as Destination Oriented Solo-redundancy Scheme (use Solo-redundancy Scheme for short and Destination Oriented Ensemble-redundancy Scheme (use Ensemble-redundancy Scheme for short, resectively Definition : Solo-redundancy Scheme refers to the scheme when at most one destination node within the same multicast grou is allowed to receive ackets in one time slot, even though there may be more than one active cell in which a acket from a certain source secondary node can be sent to a ristine secondary destination node Whereas the Ensemble-redundancy Scheme allows all the available transmissions within the same multicast grou among different active cells to be conducted in one time slot Theorem 7: When k s = Ω( m log k s, the lower bound of communication delay in the secondary network under the destination oriented redundancy scheme is B Ω( m log k s if we adot the solo-redundancy scheme m log ks B Ω( k s if we adot the ensemble-redundancy scheme Proof: We start with the roof of the first item in Theorem 7 Suose during the time slots {,,, i}, there are ψ i (ψ i k s destination nodes that have received the acket Denote the number of destination nodes who have received the message in time slot j ( j i by ψ j It is clear that ψ ψ ψ i Furthermore, denote the robability that one destination node has not received the acket during the time slots {,,, i} by Then satisfies = i ( c ψ j j= = ( c i j= ψj ( c iψi ( c i ( since ψ i i under solo redundancy scheme

11 Then we have P r(d s i [ c ( ] (k s ψ i ( c (ks ψ i [ ( ] c i (k s ψ i ( c (ks ψ i i ( e τ s m (k s ψ i (4 m log k We choose i = s τ s Substituting the value of i into Equation (4, we obtain that ( c (ks ψ i P r(d s i ( e log k s (k s ψ i ( c (ks ψ i = ( (k s ψ i k s e Therefore, the exected communication delay in the secondary network under solo-redundancy scheme satisfies E[D s ] = E{D s D s i}p r(d s i + E{D s D s < i}p r(d s < i E{D s D s i}p r(d s i ( e m log ks Ω( m log k s τ s Thus, we rove the first claim in Theorem 7 Next we rove the second claim In this scenario, we have that satisfies = Then we have i ( c ψ j j= = ( c i j= ψ j ( c iψi ( c ik s P r(d s i = ( since ψ i k s is always satisfied (5 ( c (ks ψ i ( (ks ψi ( c (ks ψ i [ ( c ik s ] (k s ψ i ( c (ks ψ i ( e τ iks s m (k s ψ i (6 m log ks Here, we choose i = τ sk s Substituting that value into Equation (6, we obtain P r(d s i c (k s ψ i ( e log k s (k s ψ i e Hence, the exected communication delay in the secondary network under ensemble-redundancy scheme satisfies E[D s ] E{D s D s i}p r(d s i ( e m log k s τ s k s Ω( m log k s k s Note that under ensemble-redundancy scheme, more transmissions are allowed in one time slot comared to soloredundancy scheme, thus the delay in ensemble-redundancy scheme should be smaller than that in the solo-redundancy scheme corresondingly Therefore, the two delay lower bounds B and B should satisfy B > B, which is in consistence with our results VI CONCLUSION AND DISCUSSION A Comarison with Previous Work Comared with the multicast caacity of static CR networks develoed in [8], we find that the caacity erformance is better when nodes are mobile Also, different with the artial mobility model studied in [9] and [0], which requires the rimary nodes to be static and only the secondary nodes are allowed to move, our model allows both the rimary and secondary networks to be mobile Moreover, comared with the results of CR network under unicast traffic in [0], we find that the caacity diminishes by a factor of /k and /k s for the rimary network and the secondary network resectively under the cooerative scheme, as shown in Table II This is because we need to forward a acket to k rimary destinations (or k s secondary destinations Particularly, if k = Θ( and k s = Θ(, our results can be secialized to the unicast traffic; if k = Θ(n and k s = Θ(m, our results can be secialized to the broadcast traffic Caacity Delay TABLE II COMPARISONS Unicast, Static Unicast, Mobile Multicast, Mobile, nk mks,, k k s nk, mk s n, m n log k, m log k s Furthermore, we find that although redundancy can reduce the transmission delay in the secondary network, it will lead to a decrease in the caacity The tradeoff between the delay and caacity always satisfies delay/caacity O(mk s log k s under both the cooerative scheme and the redundancy scheme in the secondary network However, if we schedule the transmission in the secondary network by multile unicast from source to k s destinations, the caacity will diminish by a factor of k s and the delay will increase by a factor of k s, which indicates that the delay-caacity tradeoff becomes delay/caacity O(mks in CR MANET This demonstrates that our tradeoff is better than that of directly extending the tradeoff for unicast to multicast B Rationality of System Model In our system model, we consider an ideal iid fast mobility model, which allows nodes to choose new locations every timeslot from overall cells in the network Actual mobility maybe better characterized by Brownian motion or Random Walk mobility model, where nodes mobility is limited However, analysis under the ideal iid mobility model rovides a significant insight on caacity and delay erformance in the

12 limit of infinite mobility [3] Under the iid mobility model, all the nodes locations can not be redicted from time to time, hence the communication schemes are required to be more robust and adatable Comared with other communication schemes, our schemes need less current and future information about users locations In addition, it has been roven in [3] that the network caacity and delay using an iid mobility model is equivalent to the caacity and delay of the networks using other random mobility models under given constraints C Future Work In this work, we have achieved a harmonious co-existence of the rimary network and the secondary network by assuming rimary nodes confine their interference to one cell For a more general and ractical network, we can introduce a guard zone to limit the interference received by rimary and secondary nodes The analysis of caacity and delay under this network model will be considered in future work Additionally, the er-node caacity under the destination oriented redundancy scheme in CR MANET remains unknown VII ACKNOWLEDGMENT This work was artially suorted by NSF China (No630,679,600,64805; China Ministry of Education Doctor Program (No ; Shanghai Basic Research Key Project (JC40500, JC40500; Shanghai International Cooeration Project: (No REFERENCES [] P Guta, P R Kumar, The Caacity of Wireless Networks, IEEE Transactions on Information Theory, vol 46, no, , Mar 000 [] M Grossglauser, D Tse, Mobility Increases the Caacity of Ad Hoc Wireless Networks, IEEE/ACM Transactions on Networking, vol 0, no 4, , Aug 00 [3] M J Neely, E Modiano, Caacity and Delay Tradeoffs for Ad-Hoc Mobile Networks, IEEE Transactions on Information Theory, vol 5, no 6, June 005 [4] X Lin, G Sharma, R Mazumdar, N Shroff, Degenerate Delay- Caacity Trade-offs in Ad Hoc Networks with Brownian Mobility, IEEE/ACM Transactions on Networking, vol 5, no 6, , June 006 [5] G Sharma, R Mazumdar, Scaling Laws for Caacity and Delay in Wireless Ad Hoc Networks with Random Mobility, in Proc of IEEE International Conference on Communications, Paris, June 004 [6] J Mammen, D Shah, Throughut and Delay in Random Wireless Networks with Restricted Mobility, IEEE Transactions on Information Theory, vol 53, no 3, 08-6, Mar 007 [7] M Garetto, E Leonardi, Restricted Mobility Imroves Delay- Throughut Trade-offs in Mobile Ad-Hoc Networks, IEEE Transactions on Information Theory, vol56, no0, , Oct 00 [8] X-Y Li, S-J Tang, O Frieder Multicast Caacity for Large Scale Wireless Ad Hoc Networks, in Proc of ACM Mobicom 08, San Francisco, CA, USA, Set 008 [9] A Keshavarz-Haddad, V Ribeiro, R Riedi, Broadcast Caacity in Multiho Wireless Networks, in Proc of ACM MobiCom 06, Los Angeles, CA, USA, Set 006 [0] L Ying, S Yang, R Srikant, Otimal Delay-Throughut Trade-Offs in Mobile Ad Hoc Networks, IEEE Transactions on Information Theory, vol 54, no 9, Set 008 [] G Sharma, R R Mazumdar, N B Shroff, Delay and Caacity Trade-offs in Mobile Ad Hoc Networks: A Global Persective, in Proc of IEEE INFOCOM 06, Bar, Sain, Ar 006 [] S Zhou, Lei Ying, On Delay Constrained Multicast Caacity of Large-Scale Mobile Ad-Hoc Networks, in Proc of IEEE INFOCOM 0, San Diego, CA, 00 [3] H Luo, H Tao, H Ma, SK Das, Data Fusion with Desired Reliability in Wireless Sensor Networks, IEEE Transactions on Parallel and Distributed Systems, vol, no 3, 50-53, Mar 0 [4] C Wang, H Ma, Y He, S Xiong, Adative Aroximate Data Collection for Wireless Sensor Networks, IEEE Transactions on Parallel and Distributed Systems, vol3, no6, , June 0 [5] X Wang, W Huang, S Wang, J Zhang, C Hu, Delay and Caacity Tradeoff Analysis for MotionCast, IEEE/ACM Transactions on Networking, vol 9, no 5, , Oct 0 [6] S Jeon, N Devroye, M Vu, S Chung, V Tarokh, Cognitive Networks Achieve Throughut Scaling of a Homogeneous Network, IEEE Transactions on Information Theory, vol57, no8, , Aug 0 [7] C Yin, L Gao, S Cui, Scaling Laws for Overlaid Wireless Networks: A Cognitive Radio Network vs a Primary Network, IEEE/ACM Transactions on Networking, vol 8, no 4, 37-39, Aug 00 [8] C Wang, X-Y Li, S Tang, C Jiang, Multicast Caacity Scaling for Cognitive Networks: General Extended Primary Network, in Proc of IEEE MASS 0, San Francisco, CA, Nov 00 [9] Y Li, X Wang, X Tian, X Liu, Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users, in Proc of IEEE INFOCOM, Orlando, USA, Mar 0 [0] L Gao, R Zhang, C Yin, S Cui, Throughut and Delay Scaling in Suortive Two-Tier Networks, IEEE Journal on Selected Areas in Communications, vol 30, no, Feb 0 [] J Zhang, L Fu, X Wang, Asymtotic Analysis on Secrecy Caacity in Large-Scale Wireless Networks, IEEE/ACM Transactions on Networking, vol, no, 66-79, Feb 04 [] A E Gamal, J Mammen, B Prabhakar, D Shah, Throughutdelay trade-offi n wireless networks, in Proc of IEEE INFO- COM 04, Hong Kong, Mar 004 Jinbei Zhang received his B E degree in Electronic Engineering from Xidian University, Xi an, China, in 00, and is currently ursuing the PhD degree in electronic engineering at Shanghai Jiao Tong University, Shanghai, China His current research interests include network security, caacity scaling law and mobility models in wireless networks

13 3 Yixuan Li received her BE degree from the Deartment of Electronic Engineering, Shanghai Jiao Tong University, Shanghai, China, in 03 Currently, she is ursuing the PhD degree at Cornell University, Ithaca, NY, USA Her research interests are in the area of network science, social media and machine learning For more information, lease visit htt://wwwcscornelledu/~yli Zhuotao Liu received BS degree from the Deartment of Electrical Engineering, Shanghai Jiaotong University, 0 Currently, he is ursuing PhD in Deartment of Electrical and Comuter Engineering in University of Illinois at Urbana-Chamaign His research interest includes data centering networking, software defined networking, security and rivacy in the Internet and wireless networks Fan Wu is an associate rofessor in the Deartment of Comuter Science and Engineering, Shanghai Jiao Tong University He received his BS in Comuter Science from Nanjing University in 004, and PhD in Comuter Science and Engineering from the State University of New York at Buffalo in 009 He has visited the University of Illinois at UrbanaChamaign (UIUC as a Post Doc Research Associate His research interests include wireless networking and mobile comuting, algorithmic game theory and its alications, and rivacy reservation He has ublished more than 80 eer-reviewed aers in leading technical journals and conference roceedings He is a receit of China National Natural Science Fund for Outstanding Young Scientists, CCF-Intel Young Faculty Researcher Program Award, CCF-Tencent Rhinoceros bird Oen Fund, and Pujiang Scholar He has served as the chair of CCF YOCSEF Shanghai, on the editorial board of Elsevier Comuter Communications, and as the member of technical rogram committees of more than 40 academic conferences For more information, lease visit htt://wwwcssjtueducn/~fwu/ Yang Feng received his PhD degree in Information and Communication from Shanghai Jiao Tong University Since 008, he has been on the faculty at Shanghai Jiao Tong University, where he is an associate rofessor of Deartment of electronic engineering His research interest include wireless video communication, multiho communication He take art in the rogramme of Beyond 3G Wireless Communication Testing System and in charge of system design By now he is the PI of some national rojects, including the National High Technology Research and Develoment Program of China (863 Program, National Natural Science Foundation of China Xinbing Wang received the BS degree (with hons from the Deartment of Automation, Shanghai Jiaotong University, Shanghai, China, in 998, and the MS degree from the Deartment of Comuter Science and Technology, Tsinghua University, Beijing, China, in 00 He received the PhD degree, major in the Deartment of electrical and Comuter Engineering, minor in the Deartment of Mathematics, North Carolina State University, Raleigh, in 006 Currently, he is a faculty member in the Deartment of Electronic Engineering, Shanghai Jiaotong University, Shanghai, China His research interests include scaling law of wireless networks and cognitive radio Dr Wang has been an associate editor for IEEE Transactions on Mobile Comuting, and the member of the Technical Program Committees of several conferences including ACM MobiCom 0, ACM MobiHoc 0, IEEE INFOCOM