An effective dynamic spectrum access algorithm for multi-hop cognitive wireless networks

Computer Networks 84 (2015) 1–16

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An effective dynamic spectrum access algorithm for multi-hop cognitive wireless networks Dingde Jiang∗, Yuanting Wang, Chunping Yao, Yang Han College of Information Science and Engineering, Northeastern University, Shenyang 110819, China

a r t i c l e

i n f o

Article history: Received 26 May 2014 Revised 1 April 2015 Accepted 6 April 2015 Available online 12 April 2015 Keywords: Dynamic spectrum access Channel allocation Statistical distribution Multihop cognitive wireless networks Channel switch

a b s t r a c t Spectrum utilization, as a current hot research topic, has been paid extensive attention to in cognitive wireless networks. However, due to the complexities and dynamic properties in wireless networks, how to enhance effectively the spectrum utilization is still the main challenge to encounter at present. In this paper, we propose an effective dynamic spectrum access algorithm to improve the spectrum utilization and reliable communication in the multi-hop cognitive wireless network. Considering the inherent nature of licensed users, we adopt the Pareto distribution to model their behaviors. Accordingly, cognitive users can accurately sense the white spectrum. Different from the general dynamic spectrum access, we exploit the acknowledge information to provide the reliable transportation of data packets in multi-hop cognitive wireless networks. Moreover, to achieve the high spectrum utilization, we use the graph theory to perform the reasonable channel allocations. The time and frequency division multiplexing technologies are adopted to propose our practical strategies of channel allocations and switches. Consequently, we can solve the problems of channels sensing, channel allocations, channel accesses and channel switches. Simulation results indicate that the algorithm proposed can effectively reduce the overhead of channel sensing and switching, and improve the spectrum utilization. © 2015 Elsevier B.V. All rights reserved.

1. Introduction With wireless technologies advancing and new service appearing rapidly, the wireless communications are expected to be applied more extensively. This requires more wireless spectrum resource. However, most of the allocated spectrums are not made full use of. This has led to a massive waste of spectrum resource. According to FCC’s investigation, 70% of the allocated spectrums are not exploited sufficiently [1]. The traditional static spectrum allocation policy is not capable of efficiently improving spectrum utilization. It has become a research hotspot how to effectively raise the utilization of the scarce spectrum resource [2–4]. A feasible and practical spectrum allocation scheme is critical to decide

∗

Corresponding author. Tel.: +86 24 83684219. E-mail address: [email protected] (D. Jiang).

http://dx.doi.org/10.1016/j.comnet.2015.04.003 1389-1286/© 2015 Elsevier B.V. All rights reserved.

whether the current spectrums can be utilized efficiently. This has drawn more attention from network researchers and operators [5–7]. Due to dynamic characteristics of spectrum availability, cognitive users must be able to track environmental information and to capture these variations. Cognitive users need to seek for new spectrum access opportunities selfadaptively if the licensed users appear or the current spectrum environment deteriorates [8–10]. Moreover, cognitive users must guarantee the normal activities of licensed users when accessing the network. At the same time, cognitive users should quickly monitor the spectrum resources’ availability. It should also restrain the interference on other cognitive users when there only exist limited access opportunities. In such a case, the overall utility of cognitive system can be maximized [11–13]. Thereby, a flexible spectrum access approach is significantly important to use the allocated spectrum resources efficiently.

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This paper, which takes advantage of graph coloring theory and the combined frequency-division and time-division multiplexing technologies, proposes an effective dynamic spectrum access algorithm (for short GFTDSA) to improve the spectrum utilization as well as network performance. As mentioned by current studies, network traffic holds the selfsimilarity and heavy-tailed distribution properties. What’s more, the non-voice traffic, which has become the main network behavior, is now increasing gradually in new 3G and 4G networks [14–16]. The characteristic of heavy-tailed distribution of network traffic is dominant. Network traffic reflects the inherent nature of licensed users. Pareto distribution can precisely describe the self-similarity and heavy-tailed distribution features of network traffic and users’ behaviors. First, this paper divides each channel into several independent time slots. The idle status of channels is supposed to follow Pareto distribution. Then we exploit Bayes formula to solve the problem of channel sensing and channel access. In the meanwhile, we use graph coloring theory to perform dynamic channels allocation. Although traditional graph coloring theory can reduce the collision probability between licensed users and cognitive users, it often lowers the channel utilization. Especially when the licensed users and cognitive users are close to each other, the cognitive users are not often able to effectively use the channels of licensed users. Therefore, we propose to combine graph coloring model with the channel allocation scheme to improve the utilization of channels. By abstracting the available channels and the interference condition between users as a binary matrix, we allocate dynamically the channel resources to cognitive users from a global point of view. As a result, we can improve the utilization of channels and network performance more effectively while avoiding the interference on licensed users. We also combine the frequency division and time division multiplexing technologies with graph coloring theory. Accordingly, the graph coloring theory is exploited to carry out the frequency division and time division-based channel allocation. The spectrum utilization of networks can be further improved. We can make sure that the cognitive users can get approximate channels through our channel allocation and switch strategies. Simulation results indicate that the algorithm proposed can not only allocate the channels better and hold the higher spectrum utilization, but also it can achieve better network performance and lower channel switch overhead. The rest of this paper is organized as follows. Related work is introduced in Section 2. Section 3 describes system model. Our method is derived in Section 4. Section 5 presents in detail the simulation results and analysis. We conclude our work in Section 6. 2. Related work Dynamic spectrum access is currently a hot research problem. This has attracted extensive attention from network researchers. Xue et al. [2] proposed a dynamic switch scheme based on the hypothesis of the idle time slot probability. This scheme reduced the switch frequency and improved the channel utilization. However it did not consider the channel allocation problem. Zhang et al. [3] brought forward a joint admission control and energy distribution algorithm. This algorithm built a joint admission control and energy

distribution scheme. Xing et al. [22] studied the QoS and interference constraint for dynamic spectrum access. But authors in [3,22] did not consider the case of multiple licensed users and multiple cognitive users. This needs to get all channel information among all licensed users and cognitive users for the centralized power control. This means that plenty of cooperation between licensed users and cognitive network is needed. Some studies have adopted the distributed scheme to realize cooperation and resource sharing. The adaptive spectrum allocation was studied by bargaining with the local union [5–10]. The distributed schemes can achieve the best tradeoff between fairness and efficiency in the cooperative game. However, they have high computation complexity. Hoang et al. [11] put forward the hybrid distribution/centralized control algorithm with two stages. Cognitive users first updated power adaptively until the moment that the interference on licensed user had achieved the upper limit that they could bear (or the transmission power upper limit of cognitive users). The second stage exploits bilateral maximum weighted matching to solve the channel allocation problem. However, this method allocated each channel only to one cognitive user. Each cognitive user could only occupy at most one channel. Authors in [12–16], respectively, proposed the network coding model, probability density model, integer nonlinear programming model, game model and learning model. Only if dynamic spectrum access succeeds in solving the problems of channel allocation, channel access and channel switch, it can largely improve spectrum utilization. In dynamic spectrum access process, the channel allocation method should be able to adapt the dynamic change of licensed users for channel usage in the real-time way. When all cognitive users are competing for limited channel resources, we should consider to maximize the efficiency of cognitive networks. In the process of dynamic spectrum access, the traditional channel allocation methods cannot meet the communication requirement of cognitive users since the random distribution of cognitive users and the competition for channels among different cognitive users and licensed users adds time-space complexity of the network topology. Consequently, the usage of spectrum resources become complicated. The existing researches on spectrum allocation methods include graph theory, game theory, microeconomics theory and so on. The graph theory method models the spectrum allocation as a graph coloring problem. It can solve spectrum utilization, fairness, and throughout problem in cognitive networks via optimization scheme [17]. The game theory constructs the behaviors between cognitive users into a game model. Then it uses the game to make the optimal resource allocation [18]. Microeconomics theory makes use of its auction theory to realize spectrum lease [19,20]. These existing researches show that the spectrum allocation mainly has the following several key problems [21], namely NP optimization problem under the nonlinear interference restraints, system fast convergence problem, consistency problem that whether the simulation assumptions accord with real situations, and computation problem that network scale has larger impact on the computation, convergence and convergence rate. When licensed users do not use their licensed spectrum at some certain time, cognitive users can exploit it to communicate with each other. When licensed users are to use their

D. Jiang et al. / Computer Networks 84 (2015) 1–16

licensed spectrum, cognitive users should exit immediately and find a new idle spectrum to proceed with their communications. This requires cognitive users to perform the appropriate channel access and channel switch processes. These are very important to implement the successful dynamic spectrum access. Cognitive users are able to perceive and localize those unused spectrums dynamically. They make use of these spectrums to communicate while not affecting licensed users’ normal activities. Therefore, when the spectrum sensing information is not ideal enough, we should not only minimize the influence of cognitive users on licensed users, but also maximize the spectrum utilization of the entire network as well as guarantee the fairness among cognitive users. Additionally, the Markov model [23,24] and partiallyobservable Markov model [25,26] were used to study the suitable models describing the behaviors of licensed users in order to track and predict the status of spectrum usage. The access statistics was exploited to maximize the spectrum utilization and avoid the collision among cognitive users [27]. There are also many research topics about MAC protocol design for cognitive wireless technologies [28,29]. In addition, there are some studies on transmission power control in dynamic spectrum access [30]. Huang et al. [31] proposed an optimal sensing-transmission structure to access cognitive networks. However, it is still difficult to construct a reasonable and effective dynamic spectrum access; guaranteeing the robustness of dynamic spectrum access is also a large challenge due to the dynamic change in the wireless network.

3. System model In this paper, we discuss the multi-hop communication among multiple pairs of licensed users and cognitive users. The system model is shown in Fig. 1. In this system model, multiple pairs of licensed users transfer information via a base station while multiple pairs of cognitive users carry out the multi-hop communication with each other via multiple intermediate nodes. Licensed users are p = {p1 , p2 , . . . , pN , pd } with pd representing base station and cognitive users are s = {s1 , s2 , . . . , sK } . There are N available channels C = {c1 , c2 , . . . , cN } with each channel being used by different licensed users and each channel is divided into Imax time slots. There is the interference on corresponding licensed users when different cognitive users communicate with each other. Similarly, there exists interference on cognitive users when different licensed users communicate with each other. In this system model, we take into account how to maximize spectrum efficiency on the condition that cognitive users do not affect the normal communication of licensed users. In our system model, the transmitting terminals of cognitive users use directional antenna to send the signal. The receiving terminals use omni-directional antenna to receive the signal. Both the transmitting terminal and receiving terminal of licensed users use omni-directional antenna to send and receive signals. The transmission model of information transfer among licensed users and cognitive users can be expressed as the following equation:

Ppbu Gbpu ,pd Rpd

≥

 n∈N n=u

Ppbn Gbpn ,pd +

 k∈K

Psbk Gbsk ,pd + Npd ,

(1)

3

where Npd denotes thermal noise, b represents the channels used by licensed users and b  C, Ppbu is the transmission power of licensed users, Gbpu ,pd is the received power gain of receiving terminal pd aiming at transmitting terminal pu of licensed users, Rpd denotes the SINR at the receiver pd of licensed users, Ppbn denotes the transmission power of other licensed users using the same channel b, Gbpn ,pd is the received power gain of receiving terminal pd of licensed users aiming at transmitting terminal pn which use the same channel b, Psbk means the transmission power of other cognitive users sk using the same channel b, and Gbsk ,pd is the received power gain of receiving terminal pd of licensed users aiming at transmitting terminal sk of cognitive users which use the same channel b. Eq. (1) represents the transmission model in the case of the normal communication between licensed user pu and base station pd . The information transmission model among cognitive users can be expressed as:

  Pscu Gcsu ,sv ≥ Pscn Gcsn ,sv + Ppc k Gcpk ,sv + Nsv , Rsv n∈K n=u

(2)

k∈N

where Nsv denotes thermal (or ambient) noise, c denotes the channels used by cognitive users with c  C, Pscu represents the transmission power of cognitive users, Gcsu ,sv is the received power gain of receiving terminal sv aiming at transmitting terminal su of cognitive users, Rsv denotes the SINR at the receiver sv of cognitive users, Gcsn ,sv is the received power gain of receiving terminal sv aiming at transmitting terminal sn using the same channel c of cognitive users, Ppc k represents the transmission power of other cognitive users using the same channel c, and Gcpk ,sv is the received power gain of receiving terminal sv of cognitive users aiming at transmitting terminal pK of licensed users which use the same channel c. Eq. (2) expresses the transmission model in the case of the normal communication between cognitive user su and cognitive user sv . In our system model, as mentioned in [32], we give the reserved small time slot to exchange the information of the channel allocation. At the same time, we also use this time slot as the channel to send sensing information. We use this channel to synchronize cognitive users. For the channel allocation, current methods have the centralized and distributed ways. In our system model, we use the centralized way via the reserved small time slot to transmit the channel sensing result of each cognitive user to the center node of cognitive users. Then the center node calculate the channel allocation scheme for each cognitive user node according to the method proposed below. In our system model, we take into account the information share and cooperation between the licensed user and the cognitive user. When sending data packets, the licensed user does not consider whether the cognitive user uses the channel. The cognitive user must exploit the method presented in the following to identify whether the licensed user is to utilize the channel. If the cognitive user ensures that the licensed user is to use the channel, it must stop the data transmission on the channel or switch to the other channel available to continue the communication process. However, the licensed users cooperate the channel sensing process of cognitive users. The licensed and cognitive users forward the information related with the channel sensing to the center

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Fig. 1. System model.

node via the reserved small time slot. In our system model, cognitive users exploit the sensing-then-transmitting way to access the network. 4. Dynamic spectrum access: GFTDSA We will discuss our dynamic spectrum access algorithm GFTDSA proposed in this paper in this section. Now the spectrum sensing, channel allocation, and channel switch for multi-channels and multi-time slots are discussed in detail. 4.1. Joint sensing of multi-channels and multi-time slots In the circumstance that there are multiple pairs of licensed users and cognitive users, the system model shown in Fig. 1 allocates different licensed spectrum to each licensed user. When cognitive users are sensing the spectrum, the sensing result is either busy or idle. Ideally, the sensing result of all the cognitive users can correctly reflect the state of each licensed channel in different time slots. We consider the detection ability of cognitive users using false detection probability and detection probability. In this paper, we assume that the false detection probability and detection probability of cognitive users si (i = 1, 2, . . . , K) are α f, i and α d, i , respectively. Under the condition of multi-channels and multi-users, we come up with the joint sensing strategy to determine the state of each licensed channel in different time slots. When the cognitive users jointly detect the idle time slots, each cognitive user can send data. And there exist two results of success and failure for the data transmission activities. As mentioned in [31], when cognitive users succeed in sending data, the ACK signal is fed back to transmitting terminal from receiving terminal of cognitive users, and NACK while failing. For cognitive user si (i = 1, 2, . . . , K), we use μi and ν i to describe this kind of circumstance, where μi means the conditional probability of receiving NACK when cognitive user si does not conflict with licensed users, ν i means the probability of receiving NACK when cognitive user si conflicts with licensed users. Assume μi = 0, ν i = 1 in an ideal case. In

general, for cognitive user si , the interference from licensed users can influence the performance of its receiving terminal, and thus let μi  ν i and 0  μi  ν i  1. In the condition that there are multiple pairs of licensed users and cognitive users, we need to consider α f, i , α d, i and μi , ν i of cognitive users si . We combine the frequency-division technologies with the time-division ones together to improve the spectrum utilization given the utilization status of channels in different time slots. Here the duration of sensing and data transmission of cognitive users are fixed, equaling to be tS and tT , respectively. By adjusting the parameters α f, i , α d, i , μi , and ν i , the spectrum detection result and collision sensing result can be obtained in both ideal and non-ideal circumstances. As mentioned in [31], when α f, i is zero (namely without sensing errors), the ideal sensing results are simulated, or otherwise we implement the non-ideal sensing. According to these parameters, each cognitive user can acquire the following messages: the status of licensed users, the status of cognitive users, the utility function value, and the maximum time available. The status of licensed users is used to describe the idle or busy case of licensed users after cognitive users sense channels or send data. The status of cognitive users denotes the result of channels sensing or data transmission of cognitive users. The utility function value represents the channel idle threshold for cognitive users to send data. The maximum time available characterizes the maximum time that cognitive users can take to use the channel while not affecting licensed users. The behaviors of licensed users are often described by the exponential distribution, Markovian process, geometric distribution [37–40]. As mentioned in [34,35], the traffic load embodies the behaviors of licensed users while the latter has an important impact on the former. In [31], authors used the uniform distribution to model the idle status of licensed users. In [34], authors performed a series of measurements to analyze the behaviors of licensed users and the distribution of their idle periods. They have found that the uniform distribution can be used to model the active periods of licensed users. However, as mentioned in [34], because of the heavytail behavior of their idle periods, the generalized Pareto

D. Jiang et al. / Computer Networks 84 (2015) 1–16

5

independent from cognitive users and the idle condition of time slots of channels are totally up to licensed users. So the assumption that the idle time slots of channels obey Pareto distribution is practical. Licensed users can use the channels without considering the behaviors of cognitive users. Their utilization of licensed channels is different in different time slots and changes over time. Let t be the time elapsed since the state change of licensed users from busy to idle and assume them to be idle at moment t [31]. Then, after cognitive users have sensed channels, we can, according to Eqs. (3) and (4), obtain the below idle probability of the licensed user pj (j = 1, 2, . . . , N):

ζj,tS = Fig. 2. Users’ behavior pattern in the mobile cellular network. (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.)

distribution can be exploited to characterize the idle status of licensed users. In our simulation, we use the Pareto process to both the active and idle statuses of channels. Additionally, we also exploit the uniform process to characterize the active status of channels while use the Pareto process to describe the idle status of channels. We find that the latter holds the better performance than the former. More importantly, in [35], author used the real measured data to describe the behaviors of users in the mobile Internet. They have also found that the size of the file browsing by mobile users follows the Pareto distribution. In this paper, we use the on/off model to model the licensed user behaviors. To characterize and validate the idle/busy status process led by licensed user behaviors in the system model, we use data sets of call detail records over 5 months, with several million users, several hundred million lines of data records from a nationwide mobile cellular network [36]. Our analyzed results show that in the on/off model, we find that most of channels are idle. At the same time, we find that for the idle and busy channels, their usage follows the Pareto process over time as indicated in Fig. 2, where the blue curve denotes the channel usage pattern in the mobile cellular network while the red line represents the fitting one. Shafiq et al. also found the similar distribution for Internet traffic in the mobile cellular network [33]. Hence, we use the Pareto process to characterize the active and idle statuses of channels. The idle time τ of channel cj can be described as:

⎧ ⎪ ⎨pj (τ ) = hj ηhj τ −hj −1 ,  η hj ⎪ ⎩Fj (τ ) = 1 − .

0<η≤τ



Imax − t + 1 Imax − t + tS + 1

hj

.

(5)

After cognitive users have sent data, we can attain the idle probability of the licensed user pj as follows:

ζj,tT =



Imax − t + 1 Imax − t + tT + 1

hj

,

(6)

where S and T represent sensing behavior and transmission behavior of cognitive users, respectively, Imax means the number of time slots, and tS denotes the duration for cognitive users to send data. Eqs. (5) and (6) indicate that the idle state of channels in each time slot has nothing to do with cognitive users. Therefore, when licensed users use channels, they need not consider the cognitive users’ activities. Define the conditional probability of the idle state of the licensed user pj at moment t as ς j, t (j = 1, 2, . . . , N), and then we can have the following Theorem 1. Theorem 1. If the conditional probability that the licensed user pj is idle at moment t is ς j, t , then the joint probability that cognitive users sense the licensed user pj to be idle during the duration tS is as follows:

S Pj,t+t S

 K  ⎧ K ⎪ S ⎪ ς ζ ( 1 − α ) (1 − αf,i )ςj,t ζj,tS ⎪ j,t j,t f,i ⎪ ⎪ i=1 i=1 ⎪

 ⎪   ⎪ ⎪ ⎪ ⎪ + (1 − αd,i ) 1 − ςj,t ζj,tS , S=I ⎨

  =  K K ⎪ ⎪ ⎪ ςj,t ζj,tS αf,i αf,i ςj,t ζj,tS ⎪ ⎪ ⎪ i=1 i=1  ⎪ ⎪   ⎪ ⎪ ⎪ ⎩ + αd,i 1 − ςj,t ζj,tS , S=B

(7)

(3) (4)

where j = 1, 2, . . . , N; I and B denote idle and busy. The proof of Theorem 1 is available in Appendix A.

Eqs. (3) and (4) denote the probability density function and cumulative distribution function of Pareto distribution, respectively. hj is the tail index of Pareto distribution corresponding to channel cj and η is the minimum value among all possible values of the random time variable τ . In cognitive wireless networks, the behaviors of licensed users are

According to Eq. (7), we can acquire the state sensing information of cognitive users about channel cj at moment t + tS . All cognitive users have the same detection ability. That is, the false detection probability and detection probability of all cognitive users are α f and α d , respectively, thus Eq. (7) can

τ

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D. Jiang et al. / Computer Networks 84 (2015) 1–16

be turned into:

S Pj,t+t = S

⎧ S S K ⎪ ⎪ [ςj,t ζj,t (1 − αf ) ]/{[(1 − αf )ςj,t ζj,t ⎪   ⎪ ⎪ ⎨ + (1 − αd ) 1 − ςj,t ζj,tS ]K }, ⎪ [ςj,t ζj,tS (αf )K ]/{[αf ςj,t ζj,tS ⎪ ⎪ ⎪ ⎪ ⎩ + αd (1 − ςj,t ζj,tS )]K }.

and

S=I

(8)

(13)

Theorem 2. If the conditional probability that the licensed user pj is idle at moment t is ς j, t , then we can acquire the probability that licensed user pj is idle during the period of tT after cognitive user si uses channel cj to send data:

 K ⎧ K  ⎪ T ⎪ ς ζ ( 1 − μ ) (1 − μi )ςj,t ζj,tT ⎪ j,t i j,t ⎪ ⎪ i=1 i=1

⎪ ⎪ ⎪   ⎪ ⎨ , T=A + (1 − νi ) 1 − ςj,t ζj,tT =

 ⎪ ⎪ K   ⎪ ⎪ ⎪ ςj,t ζj,tT μi ςj,t ζj,tT μi ςj,t ζj,tT ⎪ ⎪ ⎪ i=1 ⎪   ⎩ + νi 1 − ςj,t ζj,tT , T = N

i

i

(9)

T + ν (1 − ς ζ T ). We collision with licensed users is μi ςj,t ζj,t i j,t j,t define the following utility function:

υ=T

(14)

i tmax = min(σi : ζj,tT < ζj,Tδi , ∀t > σi )

(15)

Based on the above discussion, according to the datasending probability threshold and the collision probability threshold of each cognitive user, we can acquire the available time slot matrix M = {muv }N × L of all channels in cognitive wireless networks, where muv = 0 denotes that channel cu is not available in the vth time slot, or otherwise available; N is the number of channels and L is the number of time slots. The available time slot matrix can be expressed as an available time slot graph shown in Fig. 3 where the black and white rectangles represent the available and unavailable time slots of channels, respectively. According to the time slot graph shown in Fig. 3, we can carry out the following channel allocation and switch to improve the spectrum efficiency of cognitive users and to guarantee their normal communication. 4.2. Highly-efficient channel allocation strategy

υ=S (10)

where ϕ is a reward factor and φ denotes a punishment factor. According to Eq. (10), cognitive users will be rewarded if they successfully send data and will be punished if having collision with licensed users. The utility value will be 0 if cognitive users do not send data. The maximum ideal utility function of cognitive users at moment t is defined as: (11)

where ς j (namely the probability threshold) is the value of ς j, t at moment t which is satisfied with the maximum utility value ω(t, ς ), and the definition of ρ (t, ς j ) and θ (t, ς j ) is

ρ(t, ςj )     S=I = [(1 − αf )ςj,t ζj,tS + (1 − αd ) 1 − ςj,t ζj,tS ]ω t + tS , Pj,t+t S     S=B + [αf ςj,t ζj,tS + αd 1 − ςj,t ζj,tS ]ω t + tS , Pj,t+t S

ζj,Tδi

i

φ − (1 − μi )ϕ = (νi − μi )ϕ + φ

Thus we can obtain the maximum duration for cognitive user si to send data as follows:

Like the single-channel, single-user circumstance, since the probability that licensed user pj is idle at moment t is ς j, t , then the probability that pj is still idle after cognitive T . The probauser si have sent data lasting for tT is ςj,t ζj,t bility that cognitive user si successfully send data and receive the feedback signal ACK from the receiving terminal is (1 − μi )ςj,t ζj,tT + (1 − νi )(1 − ςj,t ζj,tT ) and the probability of the

ω(t, ςj ) = max{ρ(t, ςj ), θ (t, ςj )}

where I represents idle, B denotes busy, A means ACK, and N indicates NACK. Since the performance of licensed users should be protected as much as possible, not all time can be made use of by cognitive users. To meet this condition, the duration for cognitive users to send data is bound to meet the maximum transmission period of time δ i . This makes sure that there exist a minimum value ζj,Tδ . Cognitive users are to stop sending T < ζ T . ζ T can be expressed as data when ζj,t j,δ j,δ

where j = 1, 2, . . . , N, i = 1, 2, . . . , K, A and N mean ACK and NACK. The proof of Theorem 2 is available in Appendix B.

⎧  [ϕ (1 − μi )ςj,t ζj,tT + (1 − νi ) ⎪ ⎪ ⎪   ⎪  ⎨ 1 − ςj,t ζj,tT + φ μi ςj,t ζj,tT t ωij (υ) =   ⎪ + νi 1 − ςj,t ζj,tT ]tT , ⎪ ⎪ ⎪ ⎩ 0,

    T=N + [μi ςj,t ζj,tT + νi 1 − ςj,t ζj,tT ]sω t + tT , Pj,t+t + ωijt (υ) T

S=B

Similarly, we have the following Theorem 2 as to the data transmission situation of cognitive users.

T Pj,t+t T

θ (t, ςj )     T=A = [(1 − μi )ςj,t ζj,tT + (1 − νi ) 1 − ςj,t ζj,tT ]ω t + tT , Pj,t+t T

(12)

According to the above spectrum sensing result, we discuss the highly-efficient allocation strategy. In cognitive wireless networks, each channel is completely orthogonal in the spectrum and cognitive users can use multi-channels at the same time. However, it will lead to collision and interference when there are several cognitive users within certain range to use the same channel. Generally, we assume that all cognitive users have fixed location and the network topology will not have change in one sensing period, and then we can abstract the whole cognitive network into a graph G = (s, EI , VU ) in which the graph coloring model is used to model the process of channel allocation. In G = (s, EI , VU ), s denotes the node set of K cognitive users, which is s = {s1 , s2 , . . . , sK }; EI is the edge between two nodes meaning the interference relationship; VU represents the available channels for cognitive users and the utilization value of each channel. Besides, we define the available channel matrix to be V = {vij |vij  (0, 1)}K × N where vij = 1 represents that cognitive user si can use channel cj for i = 1, 2, . . . , K and j = 1, 2, . . . , N. The utility matrix is

D. Jiang et al. / Computer Networks 84 (2015) 1–16

7

Fig. 3. Available time slot graph.

U = {uij }K × N with uij denoting the reward of cognitive user si when it successfully makes use of channel cj ; the rewards will be different if the location of cognitive users are different even though they use the same channel. The channel utility matrix is VU = {vij × uij }K × N . The interference matrix is I = {iikj |iikj  (0, 1)}K × K × N , where iikj = 1 means that it will result in interference when cognitive user si and sk use channel cj in the meantime. The channel allocation matrix is B = {bij |bij  (0, 1)}K × N , where bij = 1 means that channel cj is allocated to cognitive user si . All elements of B meet the following conditions:



bij bkj = 1

∀si , sk ∈ S,

iikj = 0 ck ∈ C

(16)

Unlike previous construction method of available channel matrix, we take into account the distance between licensed users and cognitive users and the available time slot matrix M, where M is obtained based on the above joint sensing result in the case of multi-channels and multi-time slots. By calculating the distance between licensed users and cognitive users, the available channel matrix V is formed according to this distance and the available time slot matrix M. The larger the distance is, the smaller the interference between each other becomes. The available channel considered now is built on the distance between licensed users and cognitive users without considering how active the licensed user are when using the channels. Based on the distance between licensed users and cognitive users, the utility matrix U and channel utility matrix VU are built. The larger the distance, the higher the utility value that the cognitive users utilize channels. We think that using utility value U can have cognitive users choose primarily the channels used by those licensed users which have larger distance from them to protect the performance of licensed users. However, the utility value defined based on traditional graph theory is not complete, since whether the channels can be used by cognitive users or not is not only depend on the distance, but also the idle condition of channels. We will build interference matrix I according to Eqs. (1) and (2). Based on the above available channel matrix V, utility matrix U, channel utility matrix VU and interference matrix I, to take advantage of graph coloring theory to calculate

channel allocation matrix B, we consider the following channel allocation strategies: Strategy B.1: Take no account of the correlation between channels they use and time slots they occupy when the distance between licensed users and cognitive users is larger than a given threshold (generally having relatively long distance). But take that correlation into consideration while the distance is smaller than a given threshold (generally having relatively short distance). That is, when licensed users are far from cognitive users, both licensed and cognitive users can share the channels at any time slot without considering interference between each other. It then can allocate shared channels to corresponding licensed users and cognitive users when performing the graph coloring so as to raise channel utilization ratio. When they are closer to each other, the interference between each other has to be considered. The constraints expressed by Eqs. (1) and (2) have to be satisfied when licensed users and cognitive users want to share channels at any time slot. At this point, the graph coloring will be performed mainly based on interference matrix to find suitable channel allocation matrix. Strategy B.2: Take account of the correlation between channels they use and time slots they occupy when the distance between licensed users and cognitive users is larger than a given threshold (having relatively long distance); take that correlation into consideration as well when the distance is smaller than a given threshold (having relatively short distance). That is, no matter how large the distance is, the interference has to be considered. The constraints expressed by Eqs. (1) and (2) have to be satisfied when licensed users and cognitive users want to share channels at any time slot. At this point, the graph coloring will be performed mainly based on interference matrix to find suitable channel allocation matrix. Strategy B.3: Take account of the correlation between channels they use and time slots they occupy when the distance between licensed users and cognitive users is larger than a given threshold (having relatively long distance). Take no account of that correlation into when the distance is smaller than a given threshold (having relatively short distance). That is, when licensed users are far from cognitive users, both users are expected to communicate with each other via as large coverage range as possible and the

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D. Jiang et al. / Computer Networks 84 (2015) 1–16

interference has to be considered. The constraints expressed by Eqs. (1) and (2) have to be satisfied when licensed users and cognitive users want to share channels at any time slot. At this point, the graph coloring will be performed mainly based on interference matrix to find suitable channel allocation matrix. And when they are closer to each other, both licensed and cognitive users are expected to communicate with each other via as small coverage range as possible and the interference can be neglected. They can share the channels at any time slot without considering the interference between them. At this point, the graph coloring can be performed to allocate shared channels to corresponding licensed and cognitive users and then enhance channel utilization ratio at the same time. Strategy B.4: Take no account of the correlation between channels they use and time slots they occupy when the distance between licensed users and cognitive users is larger than a given threshold (having relatively long distance). Take no account of that correlation as well when the distance is smaller than a given threshold (having relatively short distance). That is, when licensed users are far from cognitive users, both licensed and cognitive users can share the channels at any time slot without considering the interference between each other. At this point, the graph coloring can be performed to allocate shared channels to corresponding licensed and cognitive users and then add channel utilization ratio at the same time. And when they are closer to each other, both licensed and cognitive users are expected to communicate with each other via as small coverage range as possible and the interference can be neglected. They can share the channels at any time slot without considering interference between each other and the graph coloring can also be performed to allocate shared channels to corresponding licensed and cognitive users and then raise channel utilization ratio at the same time. Our Strategy B has the different advantage. Strategy B.1 can improve and raise the channel utilization which the following simulations will demonstrate this. Strategy B.2 takes into account the interference at any case when allocating the channel. Although Strategy B.2 can meet the practice, it can result in the lower channel utilization due to the consideration of unnecessary inference. Strategy B.3 can simplify the channel allocation process while it can lead to the lower channel utility. Strategy B.4 can more effectively assign the channel to the cognitive user via the simplest way, which the following simulations are also to validate this conclusion. Thereby, the different strategies hold the different advantage. They can obtain the different results of channel allocations, which we will verify in the below simulation section. We can acquire valid channel allocation matrix according to above allocation strategies until now and the pseudo code of specific algorithm about channel allocation is shown in Algorithm 1. Based on the channel allocation algorithm discussed above, we take advantage of channel sensing and graph coloring algorithm to gain the channel allocation matrix. Thus cognitive users can access the cognitive network successfully and communicate normally. In the next, we are to discuss the channel switch scheme based on frequency- and timedivision multiplexing in the circumstances of multi-channels and multi-users.

Algorithm 1 Effective channel allocation. Input: location information of licensed users and cognitive users; interference matrix I; available channel matrix V; utility matrix U; Output: channel assignment matrix B; Set: channel m = 1 Procedure: % assign the channel to labeled cognitive users; for m = 1, 2, 3, . . . , M while vn,m (:, m) = 0 % assign channel m to cognitive user n; k=N  in,k,m + 1); labeln = max un,m /( m∈vn

k=1

An,m = 1; % update the channel assignment matrix B; vn,m = 0; % update available channel matrix V; un,m = 0; % update utility matrix U; for k = 1, 2, . . . , N % based on I find cognitive users nk interference with cognitive users n; find In,k,m =1; uk,m = 0; % update available channel matrix V; vk,m = 0; % update utility matrix U; end end end

4.3. Fast channel switch scheme In cognitive wireless networks, licensed users can occupy and exit their licensed channels anytime without the interference from cognitive users, while the cognitive users may be interrupted during communication since they have to guarantee the performance of licensed users, especially their random needs. Here, we consider fast channel switch scheme for dynamic spectrum access and exploit the reserved small time slot to send the information independently to update allocation matrix B. Just as discussed above, define t to be the time passing since licensed user change from busy to idle and assume the idle time slot of licensed user to obey Pareto distribution expressed in Eq. (3). If the period of time needed for cognitive users si to send data at current moment t is tTi , then si need to make judgments based on Eq. (15) each time they switch channels:



tS + tT − t < tTi tS +

i tmax

−t <

(17)

tTi

(18)

At the same time we can acquire the following function i for sending data: according to tTi and the maximum time tmax i g(i, j, t) = tS + tmax − t − tTi

(19)

We obtain the following available transmission time slot matrix by putting g(i, j, t) of all cognitive users in descending order:

G(t) = [g(i1 , j1 , t), g(i2 , j2 , t), . . . , g(iK , jK , t)]

(20)

D. Jiang et al. / Computer Networks 84 (2015) 1–16

9

Fig. 4. Fast channel switch scheme.

where si1 , si2 , . . . , siK ∈ s , cj1 , cj2 , . . . , cjK ∈ C, and g(i1 , j1 , t)  g(i2 , j2 , t)    g(iK , jK , t). Then we calculate the following function based on Eqs. (5)–(9) for channel cj :

⎧  S ς ζ S + Pj,t+t tS ⎪ ⎪ S ⎪ j,t j,t ⎪ ⎪ ⎪ ⎪ + ςj,t ζj,tT tT + g(i, j, t) ⎪ ⎪ ⎪   ⎪ ⎨ K  T f (j, t) = Pj,i,t+tT , if cj is used ⎪ ⎪ i=1 ⎪ ⎪   ⎪ ⎪ S ⎪ tS ⎪ ςj,t ζj,tS + Pj,t+t ⎪ S ⎪ ⎪ ⎩ + ςj,t ζj,tT tT , or

(21) (22)

where i = 1, 2, . . . , K and j = 1, 2, . . . , N. We then get the following idle channel matrix by putting all f(j, t) in descending order:

F (t) = [f (j1 , t), f (j2 , t), . . . , f (jN , t)]

(23)

where f(j1 , t)  f(j2 , t)    f(jN , t) and cj1 , cj2 , . . . , cjN ∈ C. If cognitive user si uses channel cj at current moment t to send data, then we will consider the following strategies for channel switch scheme according to Eqs. (17)–(23): Strategy C.1: If Eqs. (17) and (18) hold, carry out the following steps: i > tT , go to Step 6. Step 1: If tmax i ≤ tT , let z = 1. Step 2: If tmax Step 3: According to Eq. (23), choose f(jz , t). If j = jz , go to Step 6. Step 4: According to the channel allocation matrix B, identify whether channel cjz is occupied. If not occupied, switch to channel cjz , update matrix B via the reserved small time slot, and then go to Step 6. Step 5: In terms of Eq. (20), select g(i, jz , t). If g(i, jz , t) > 0, switch to channel cjz , update channel allocation matrix B via the reserved small time. Or otherwise let z = z + 1 and go to Step 3. Step 6: Proceed with data transmission in the next period.

Strategy C.2: If Eq. (17) holds while Eq. (18) does not hold, i > tT . Not perform the channel switch process and contmax tinue data transmission in the next period. Strategy C.3: If Eq. (18) holds while Eq. (17) does not hold, i ≤ tT . Perform the process from Step 2 to Step 6 in Strattmax egy C.1. Strategy C.4: If Eqs. (17) and (18) do not hold, not perform the channel switch process and continue data transmission in the next period. Strategy C has the following advantage: by considering the different conditions, we can faster determine whether the cognitive user needs to perform the channel switch process. Accordingly, we can quickly make the corresponding decision. Our fast channel switch scheme can be expressed by Fig. 4. According to the fast channel switch scheme, each time it will switch to remaining channel with the most available time slots. Once cognitive users success in switching channel, it will finish sending data or there are not available to send any more. The pseudocode of specific algorithm for the fast channel switch scheme is shown in Algorithm 2. Now, based on the above discussion, we come up with the steps of our algorithm GFTDSA as follows: Step 1: Obtain the available time slot matrix of all channels according to the data transmission probability threshold and collision probability threshold according to expressed in Eqs. (7)–(15). Step 2: According to Algorithm 1, carry out the channel allocation for cognitive users, and make them access to the cognitive network. Step 3: According to Algorithm 2, perform the fast channel switch and make sure that the cognitive users can realize dynamic access. Our algorithms are performed by the center node of cognitive users while the channel sensing process is carried out by individual cognitive user. When sending data packets, licensed users do not consider cognitive users’ behaviors while cognitive users’ activities cannot affect licensed users’ normal

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D. Jiang et al. / Computer Networks 84 (2015) 1–16

Algorithm 2 Fast channel switching. Input: M the number of channels; Tend the maximum time slots for cognitive user occupancy; Ai,t (M × Tend ) the result of channel allocation; Pa the number of packets cognitive users want to transmit; % Ai,t is the channel state; % Ai,t = 1 presents channel i can access at time t. Output: the amount of packets cognitive users transmit Tr; Set: initialize t = 1; % while cognitive user has available channel % and residual packets is above 0, cognitive user % could send messages;  while ( Am,t (:,t) = 0 &&Nsu = 0) % if cognitive user begin to transmit or the % current channel couldn’t use; if (t == 1||Am,t == 0) % if current channel couldn’t use, % cognitive user must switch channel; if (Am,t == 0) t = t + 1; end % if next time slot channel is available;  if ( Am,t (:,t) = 0) % find the channel mi which have most % idle time slots; for i = 1 : M T end CM,T (i,:) I(i) = t=t

end % assign channel mi with the most idle % time slot to cognitive users; mi ← max (I(i)) and Ai,t = 0; end else According to Eq. (11) update Nsu ; t = t + 1; end end % the number of packets that cognitive % users transmit; Tr=Pa−Nsu ;

communications. All cognitive users cooperate each other and send the channel sensing results to the center node. At the same time, licensed users also cooperate the sensing process so that cognitive users can correctly detect the distance. Then the center node calculates the channel allocation matrix via the centralized way and send it to all cognitive users to share the channel status information. The channel switch process is similar to this. Our method works as follows. First, licensed users and cognitive users are randomly distributed in the field. According to the sensing method, cognitive users start sensing the

channel status. Second, in the reserved time slot, the sensing results for channels are sent to the center node. The center node calculates the available time slot and attains the available time slot graph. Third, the center node performs the channel allocation according to the channel allocation strategies. At the same time, it also calculates the channel switch according to the channel switch strategies. Consequently, the channel allocation matrix is obtained. Finally, the center node sends an available channel to each cognitive user. Then cognitive make the normal communication. As mentioned above, the process is repeated. The overhead of our method includes the channel allocation computation overhead and channel switch computation overhead. For the channel allocation, if there are n cognitive users and m licensed channels, the maximum computation overhead of four allocation strategies is O(n × m). For the channel switch, the maximum computation overhead of four switch strategies is O(n). Therefore, our method holds the lower overhead. 5. Numerical experiments To verify the proposed algorithm GFTDSA in this paper, we adopt a network of 1000m × 1000m with the number of cognitive users increasing from 2 to 10. In this network, there are 10 channels for licensed users to use and the licensed users are located randomly. In the time division multiplexing model, we let reward factor ϕ = 1, punishment factor φ = 20, sensing period tS = 5, data sending duration tT = 30 , maximum time slots Imax = 1000 , and initialize μi = 0 as well as ν i = 1 (where i = 1, 2, . . . , K) for all cognitive users. In general, we assume that all cognitive users have the same detection ability, that is, the false detection probability and detection probability of all cognitive users are α f = 0 and α d = 1 in ideal circumstance while α f = 0.2 and α d = 0.85 in non-ideal circumstance. Because this method in [31] proposed the ACK/NACK acknowledge mechanism to improve the spectrum utilization in the cognitive wireless network with the single licensed user and the single cognitive user, we call it the ACK/NACK-based dynamic spectrum access algorithm (for short ACKDSA). Next, we are going to discuss and compare the performance of GFTDSA and ACKDSA. 5.1. Transmission probability threshold We now discuss the spectrum sensing ability of GFTDSA. We simulate the influence on spectrum sensing performance when the Pareto tail index hj of all channels cj (j = 1, 2, . . . , N) are different. Without loss of generality, we suppose the Pareto tail index of all channels to be the same h and here its values are 0.1, 0.5, 1.0, and 1.5, respectively. We will compare GFTDSA with ACKDSA in detail. Fig. 5 plots the graph of transmission probability threshold for GFTDSA. We can find that the transmission probability threshold of GFTDSA are the same as ACKDSA when h = 1 in Fig. 5. In contrast to ACKDSA, when h < 1, the transmission threshold of GFTDSA decreases and the transmission probability of cognitive users increases. Contrarily, when h > 1, the transmission threshold of GFTDSA increases and the transmission probability of cognitive users decreases. Fig. 5 tells us that GFTDSA can describe the real distribution of network traffic more accurately when h < 1 and it possesses the higher spectrum sensing performance.

D. Jiang et al. / Computer Networks 84 (2015) 1–16

11

1.00 h = 0.1

0.85

GFTDSA: t = 30

h = 0.5

0.80

GFTDSA: tS = 5

h = 1.0

0.75

h = 1.5

0.70

ACKDSA: t = 5

0.65

ACKDSA: tS = 1

j j

GFTDSA: t = 1

j j

0.90

Utility value

Transmission propability threshold

0.95

S

0.85

S

ACKDSA: tS = 30 S

0.60 0.55 0.50 0.45

0.80

0.40 0.35

0.75

0.70

0.30

0

100

200

300

400

500 time

600

700

800

900

1000

0

2

4

6

8 10 12 Punishment factor

14

16

18

20

Fig. 7. Impact of punishment factor on utility value in ideal condition.

Fig. 5. Transmission probability threshold.

0.90 GFTDSA: tS = 30

0.85

GFTDSA: t = 5

1.000

S

0.995

0.80

GFTDSA: t = 1

0.75

ACKDSA: tS = 30

S

Throughput

Transmission probability threshold

ACKDSA: t = 5 S

0.70

0.990 0.985 0.980

ACKDSA: tS = 1

0.65 0.60 0.55

0.975

0.50 GFTDSA: t = 30 S

0.970

0.45

GFTDSA: tS = 5 GFTDSA: t = 1

0.40

ACKDSA: tS = 30

0.35

S

0.965

ACKDSA: t = 5

0.960

S

ACKDSA: tS = 1 0.955

0

100

200

300

400

500 time

600

700

800

900

1000

Fig. 6. Impact of sensing period on transmission probability threshold.

In order to portray the spectrum detection performance of GFTDSA, we discuss the threshold probability under different sensing periods. Fig. 6 depicts the influence of sensing period on transmission probability threshold. Here, the simulation parameters are h = 0.5, ϕ = 5, φ = 10, α f = 0.1, α d = 0.9, μi = 0.1, and ν i = 0.3 for i = 1, 2, . . . , K. Fig. 6 implies that the larger sensing period tS is , the smaller the transmission threshold is. Moreover, the larger tS is, the smaller the times and the accuracy of spectrum sensing are. From Fig. 6, we can also figure out that GFTDSA has the higher transmission probability threshold comparing with ACKDSA under the different sensing period tS . Therefore, comparing with ACKDSA, GFTDSA has higher spectrum utilization and thus can provide more access opportunities and longer communication period for cognitive users. In addition, we can figure out that GFTDSA has more steady variation and smaller fluctuation on transmission probability threshold. 5.2. Utility value and throughput We now discuss the impact of collision punishment factor on utility value and throughout with GFTDSA in ideal and non-ideal circumstances respectively. Fig. 7 shows the relationship between the punishment factor and the maximum

0

2

4

6

8 10 12 Punishment factor

14

16

18

20

Fig. 8. Impact of punishment factor on throughput in ideal condition.

average utility value, as well as the relationship between the punishment factor and throughout in ideal circumstance, respectively. And here, we define the maximum average utility value to be the ratio of the maximum utility value during the period of Imax corresponding to each punishment factor to Imax . From Figs. 7 and 8, we can see that with the increase of the punishment factor φ , the costs of collision between cognitive users increase, the threshold increases and the collision probability decreases. The chances for cognitive users to communicate decrease as well and so do the transmission probability and the throughout and utility value of cognitive users. Besides, when the spectrum sensing period tS rises, the time used for cognitive users to send data shortens correspondingly. Thus this is to result in the increase in collision probability when licensed users and cognitive users send data, and further lead to the decrease in throughput and utility value of cognitive users. Figs. 7 and 8 also state that GFTDSA has higher utility value and more throughout comparing with ACKDSA. Figs. 9 and 10 show the relationship between the punishment factor and the maximum average utility value, as well as the relationship between punishment factor and throughout, respectively, in non-ideal circumstance. We can see from Figs. 9 and 10 that with the increase of the punishment factor φ , the utility value and throughout of cognitive users lower. Similar to the situation in the ideal circumstance, this is

12

D. Jiang et al. / Computer Networks 84 (2015) 1–16 1 0.9

GFTDSA: vi = 0.1

0.8

GFTDSA: vi = 1.0

Number of available channels

8

ACKDSA: v = 0.1 i

0.7 Utility value

Strategy B.1 Strategy B.2 Strategy B.3 Strategy B.4

9

GFTDSA: vi = 0.5

ACKDSA: vi = 0.5 ACKDSA: v = 1.0

0.6

i

0.5 0.4 0.3

7

6

5

4

0.2

3

0.1 0

0

2

4

6

8 10 12 Punishment factor

14

16

18

2

20

Fig. 9. Impact of punishment factor on utility value in non-ideal condition.

Percentage of cognitive users with available channels

0.8

GFTDSA: vi = 1.0

i

ACKDSA: vi = 0.1

Thoughtput

0.7

ACKDSA: vi = 0.5 ACKDSA: vi = 1.0

0.6 0.5 0.4 0.3 0.2 0.1 0

0

2

4

6

8 10 12 Punishment factor

14

16

18

3

4

5 6 7 Number of cognitive users

8

9

10

1.00

GFTDSA: vi = 0.1 GFTDSA: v = 0.5

2

Fig. 11. Impact of allocation strategies on number of available channels.

1 0.9

1

20

Strategy B.1 Strategy B.2 Strategy B.3 Strategy B.4

0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55

1

2

3

4

5 6 7 Number of cognitive users

8

9

10

Fig. 10. Impact of punishment factor on throughput in non-ideal condition. Fig. 12. Percentage of cognitive users with available channels to all cognitive users.

because that when φ rises, the threshold rises and the transmission probability of cognitive users drops. The chance for cognitive users to communicate is then reduced, thus leading to the decrease in their utility value and throughout. The larger the feedback information ν is, the more collision between licensed users and cognitive users we can avoid. Therefore the collision rate can be reduced and the utility value and throughout of cognitive users can be raised. Figs. 9 and 10 reflect this situation precisely. So we can see that GFTDSA has higher utility value and more throughout comparing with ACKDSA in non-ideal circumstance. And this further demonstrates that GFTDSA has better performance. 5.3. Impact of channel allocation strategies We now discuss the influence of different channel allocation statistics on GFTDSA’s performance. Fig. 11 shows the average number of available channels for each user under different strategies corresponding to the different number of cognitive users. We can see from Fig. 11 that Strategy B.3 can upgrade the number of available channels of cognitive users remarkably while Strategy B.4 lowers that. It is because that when the distance between licensed user and cognitive user is large, it will not cause interfere on licensed users when cognitive users use the channels. In such a case, the active

situation of licensed users to use channels can be neglected. And thus it can add the number of available channels of cognitive users. When the users are closer to each other, due to taking the active situation of licensed users into consideration, we can make use of those channels which cannot be used before. Thereby the number of available channels of cognitive users is increased. Strategy B.4 is just on the contrary. Fig. 12 shows the percentage of cognitive users which can hold the available channel and send data among all cognitive users under different channel allocation strategies. When the number of cognitive users is far less than the number of channels, all cognitive users can have the chance to utilize the channels. The percentages of four strategies are not completely the same, but different. This indicates that diverse channel allocation strategies have different impact on the performance of GFTDSA. Among all the strategies, Strategy B.1 can make cognitive users hold more available channels. 5.4. Impact of collision probability threshold Figs. 13–15 plot out the impact of the collision probability threshold on the performance of GFTDSA and ACKDSA, where the collision probability threshold rc is 0.19 and 0.22. Only if the collision probability of cognitive users is lower

D. Jiang et al. / Computer Networks 84 (2015) 1–16 60

13

1.00

GFTDSA: rc = 0.22

55

ACKDSA: rc = 0.22

50

0.95

GFTDSA: r = 0.19 c

Times of channel switch

45

Percentage of time slot utilization

ACKDSA: r = 0.19 c

40 35 30 25 20 15 10

0.90 GFTDSA: r = 0.22 c

0.85

ACKDSA: r = 0.22 c

GFTDSA: r = 0.19 c

ACKDSA: r = 0.19

0.80

c

0.75

0.70

5 0

0.65

1

2

3

4 5 6 7 Number of cognitive uesers

8

9

10

Fig. 13. Impact of collision probability thresholds on channel switch performance.

GFTDSA: r = 0.22 c

Times of spectrum sensing

ACKDSA: rc = 0.22

6.5

GFTDSA: r = 0.19

6.0

ACKDSA: rc = 0.19

2

3

4

5 6 7 Number of cognitive users

8

9

10

Fig. 15. Impact of collision probability thresholds on time slot utilization.

cognitive networks is. This explains that the more cognitive users can make full of the idle time slots of the silenced networks. Moreover, the larger collision probability threshold can provide cognitive users with the more access opportunity. Fig. 15 also illustrates that the curves of percentage of time slot utilization of ACKDSA stay below those of GFTDSA. GFTDSA possesses the much larger time slot utilization than ACKDSA. This further illuminates that in contrast to ACKDSA, GFDSA holds the better performance.

7.5 7.0

1

c

5.5 5.0 4.5 4.0 3.5

6. Conclusion

3.0 2.5 2 1.5

1

2

3

4

5 6 7 Number of cognitive users

8

9

10

Fig. 14. Impact of collision probability thresholds on spectrum sensing.

than rc , they cannot affect the normal activity of licensed users. The larger the collision probability threshold, the larger licensed users can bear the collision between them and cognitive users. And thus cognitive users can have more opportunity to make use of the channel. In the result, the times of spectrum sensing, the times of channel switch, and percentage of time slot utilization can remarkably be improved. Figs. 13 and 14 tell us that when the number of cognitive users increases, the times of channel switch and spectrum sensing of two algorithms become larger and larger. With the addition of the collision probability threshold, they dramatically rise. More importantly, from Figs. 13 and 14, we can easily find that the curves of the times of channel switch and spectrum sensing of GFTDSA are over those of ACKDSA. This demonstrates us that although the situation get worse and worse (namely both the number of cognitive users and the collision probability threshold turn large), GFTDSA always hold the lower times of spectrum sensing and channel switch comparing with ACKDSA. This indicates that GFTDSA is to exhibit the better performance of dynamic spectrum access. Fig. 15 shows that the larger the number of cognitive users and the collision probability threshold of GFTDSA and ACKDSA become, the higher their time slot utilization of

This paper studies dynamic spectrum access in multi-hop cognitive wireless networks with multiple licensed users and multiple cognitive users. We proposes an effective algorithm to enhance spectrum utilizations and reliable communications between licensed users and cognitive users. Different previous method, according to the nature of network traffic and licensed users’ behaviors, we exploit the Pareto distribution to characterize the activities of licensed users. The spectrum sensing method is presented to detect the idle and busy status of channels in the cognitive network with multiple licensed users and multiple cognitive users. The acknowledge information is used to provide the reliable communication in multi-hop cognitive wireless networks. By abstracting the available channels in the system and the interference condition between users as a binary matrix, we allocate dynamically the channel resources from a global point of view. Based on the graph theory, we use the time and frequency division multiplexing technologies to bring forth the channel allocation strategies and switch mechanism. Simulation results indicate that the algorithm proposed can effectively reduce the times of channel sensing and switch and improve the spectrum utilization. Acknowledgments This work was supported in part by the National Natural Science Foundation of China (no. 61071124), the Program for New Century Excellent Talents in University (no. NCET11-0075), the Fundamental Research Funds for the Central Universities (nos. N120804004, N130504003), and the State

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D. Jiang et al. / Computer Networks 84 (2015) 1–16

Scholarship Fund (201208210013). The authors wish to thank the reviewers for their helpful comments. Appendix A. The proof of Theorem 1

and st st P (sst 1 (t + tS ) = B, s2 (t + tS ) = B, . . . , sK (t + tS ) = B)

=

K  



αf,i ςj,t ζj,tS + αd,i (1 − ςj,t ζj,tS )

(28)

i=1

Proof: Because the idle condition probability of licensed user pj at the time t is ς j, t , the probability that licensed user pj is still idle after cognitive user si keeps up sensing for the S , namely duration tS become ςj,t ζj,t

According to Eqs. (24)–(28), the probability that the spectrum sensing result of cognitive users is idle and licensed users also stay idle can be denoted as follows:

  S P pst j (t + tS ) = I = ςj,t ζj,t ,

st st P (pst j (t + tS ) = I|s1 (t + tS ) = I, . . . , sK (t + tS ) = I)

(24)

(t + tS ) denotes the status of licensed user pj at the where pst j moment t + tS . According to discussion in this paper, we can attain the following equation:

  st P sst i (t + tS ) = B|pj (t + tS ) = I = αf,i ,

(25)

where sst (t + tS ) represents the status of cognitive user si at i the time t + tS . And then we can obtain the below equation:

  st P sst i (t + tS ) = I|pj (t + tS ) = I = 1 − αf,i .

((P(sst1 (t + tS ) = I, . . . , sstK (t + tS ) st = I|pst j (t + tS ) = I))/P (s1 (t + tS ) = I, =

st sst 2 (t + tS ) = I, . . . , sK (t + tS ) = I))

P (pst j (t + tS ) = I)  K  K   S = ςj,t ζj,t (1 − αf,i ) [(1 − αf,i )ςj,t ζj,tS i=1

  + (1 − αd,i ) 1 − ςj,t ζj,tS ]

× P (pst j (t + tS ) = I)

st st P (pst j (t + tS ) = I|s1 (t + tS ) = B, . . . , sK (t + tS ) = B)

st + P (sst i (t + tS ) = I|pj (t + tS ) = B)

st = {[P (sst 1 (t + tS ) = B, . . . , sK (t + tS )

× P (pst j (t + tS ) = B)

st = B|pst j (t + tS ) = I)]/[P (s1 (t + tS ) = B, st sst 2 (t + tS ) = B, . . . , sK (t + tS ) = B)]}

= (1 − αf,i )ςj,t ζj,tS + (1 − αd,i )(1 − ςj,t ζj,tS ) and st st P (sst i (t + tS ) = B) = P (si (t + tS ) = B|pj (t + tS ) = I)

=

st × P (pst j (t + tS ) = I) + P (si (t + tS )

= B|

pst j

=

P (pst j (t + tS ) = I)   K K  

ςj,t ζj,tS

αf,i

i=1

α ς ζ + αd,i (1 − ς ζ ) S j,t j,t

The proof is concluded. Due to the independence of spectrum sensing among cognitive users, then the below equation holds: st st P (sst 1 (t + tS ) = I, s2 (t + tS ) = I, . . . , sK (t + tS ) = I)

= P(

(t + tS ) = I)P(   P sst K (t + tS ) = I

sst 1

sst 2

(t + tS ) = I) · · ·

= B, . . . , sst K (t + tS ) = B)     = P sst ( t + tS ) = B P sst 1 2 (t + tS ) = B · · ·

  st P sst ijr (t + tS ) = N |pj (t + tS ) = I = μi ,

Further, we can derive out the below equation:

=

K  

(t + tS ) =

(t + tS ) = I) 

(1 − αf,i )ςj,t ζj,tS + (1 − αd,i )(1 − ςj,t ζj,tS )

i=1

Appendix B. The proof of Theorem 2

(31)

According to the discussion in this paper, we can attaint the below equation:

P (sst K (t + tS ) = B)

(t + tS ) =

(30)



  T P pst j (t + tS ) = I = ςj,t ζj,t .

st P (sst 1 (t + tS ) = B, s2 (t + tS )

I, . . . , sst K



Proof. According to the discussion in this paper, we know that the idle condition probability of licensed user pj at the time t is ς j, t . After cognitive user si keeps up sending data with channel cj for the duration tT , the idle probability of pj T , namely is ςj,t ζj,t

and

I, sst 2

[αf,i ςj,t ζj,tS

i=1

  + αd,i 1 − ςj,t ζj,tS ]

(t + tS ) = B)P( (t + tS ) = B) pst j

S f,i j,t j,t

(29)

Likewise, the probability that the spectrum sensing result of cognitive users is busy while licensed users in fact stay idle can be described as:

st st P (sst i (t + tS ) = I) = P (si (t + tS ) = I|pj (t + tS ) = I)

P(



(26)

Additionally, we can also get the following equation:

sst 1

i=1

(27)

(32)

(t + tS ) denotes the status that cognitive user si uses where sst ijr channel cj to receive the signals ACK and NACK at the moment t + tS . Then we can deduce the below equation:   st P sst ijr (t + tS ) = A|pj (t + tS ) = I = 1 − μi .

(33)

D. Jiang et al. / Computer Networks 84 (2015) 1–16



Additionally, we can also derive the below equation:

=

st P (sst ijr (t + tS ) = A) = P (sijr (t + tS )

= (1 − μi )ςj,t ζj,tT + (1 − νi )(1 − ςj,t ζj,tT )

(t + tS ) = N) = P( (t + tS )

+ P(

(t + tS ) = I)P( (t + tS ) = I)

=μς

(t + tS ) = B| (t + tS ) = B)P( (t + tS ) = B) pst j

pst j

ζ + νi (1 − ς ζ )

T i j,t j,t

st = [P (sst 1j1 r (t + tS ) = N, . . . , sKjK r (t + tS ) st = N|pst j (t + tS ) = I)]/[P (s1j1 r (t + tS ) = N,

T j,t j,t

st sst 2j2 r (t + tS ) = N, . . . , sKjK r (t + tS ) = N )]

Due to the independence in which cognitive users send data, we can obtain the below equation:

P(

sst 1j1 r

(t + tS ) =

sst KjK r

A, sst 2j2 r

=

(t + tS ) = A, . . . ,

st P (sst 1j1 r (t + tS ) = N, s2j2 r (t + tS ) = N, . . . ,

sst KjK r (t + tS ) = N ) st = P (sst 1j1 r (t + tS ) = N )P (s2j2 r (t + tS ) = N ) · · ·

P (sst KjK r (t + tS ) = N ) Further, we can derive the following equation:

 st P sst 1j1 r (t + tS ) = A, s2j2 r (t + tS ) = A, . . . ,  sst KjK r (t + tS ) = A K 





((1 − μi )ςj,t ζj,tT + (1 − νi ) 1 − ςj,t ζj,tT ) ,

(34)

i=1

and st P (sst 1j1 r (t + tS ) = N, s2j2 r (t + tS ) = N, . . . ,

sst KjK r (t + tS ) = N ) 



(μi ςj,t ζj,tT + νi 1 − ςj,t ζj,tT ) .

(35)

i=1

According to Eqs. (29)–(33), the probability that cognitive users receive ACK while licensed users is idle can be denoted as follows: st P (pst j (t + tS ) = I|s1j1 r (t + tS ) = A, . . . ,

sst KjK r (t + tS ) = A) st = [P (sst 1j1 r (t + tS ) = A, . . . , sKjK r (t + tS ) st = A|pst j (t + tS ) = I)]/[P (s1j1 r (t + tS ) = A, st sst 2j2 r (t + tS ) = A, . . . , sKjK r (t + tS ) = A)]

P (pst j (t + tS ) = I)

μi





μi ςj,t ζj,tT + νi 1 − ςj,t ζj,tT



i=1



References

and

K 

ςj,t ζj,tT

The proof is concluded.

P (sst KjK r (t + tS ) = A)

=

P (pst j (t + tS ) = I) 

  K K  i=1

(t + tS ) = A)

st = P (sst 1j1 r (t + tS ) = A)P (s2j2 r (t + tS ) = A) · · ·

=

i=1

sst KjK r (t + tS ) = N )

pst j

sst ijr

(1 − μi )ςj,t ζj,tT

st P (pst j (t + tS ) = I|s1j1 r (t + tS ) = N, . . . ,

sst ijr

= B|

 T



Likewise, t the probability that cognitive users receive NACK while licensed users is idle can be denoted as follows:

and

pst j

(1 − μi )

 + (1 − νi ) 1 − ςj,t ζj,t

st = A|pst j (t + tS ) = B)P (pj (t + tS ) = B)

P(

  K

K  i=1

st st = A|pst j (t + tS ) = I)P (pj (t + tS ) = I) + P (sijr (t + tS )

sst ijr

ςj,t ζj,tT

15

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[39] M. Wellens, J. Riihijarvi, P. Mahonen, Modeling primary system activity in dynamic spectrum access networks by aggregated ON/OFFprocesses, in: Proceedings of SECON Workshops’09, 2009, pp. 1–6. [40] Y. Liang, K. Chen, G.Y. Li, P. Mahonen, Cognitive radio networking and communications: an overview, IEEE Trans. Vehicular Technol. 60 (7) (2011) 3386–3407. Dingde Jiang received the Ph.D. degree in communication and information systems from School of Communication and Information Engineering, University of Electronic Science and Technology of China, Chengdu, China, in 2009. He is an associate professor in College of Information Science and Engineering, Northeastern University, Shenyang, China. His research interests include energy-efficient networks, cognitive networks, network measurement, network security, Internet traffic engineering, and performance analysis. He is a member of IEEE and IEICE. Yuanting Wang received B.Sc. in College of Electronic and Information Engineering, Northeastern University at Qinhuangdao, China, in 2011. He is currently a Master in Communication and Information System, Northeastern University, China. His research interests include energy-efficient networks.

Chunping Yao received B.Sc. in College of Information Science and Engineering, Northeastern University, Hainan, China, in 2011. He is currently a Master in Communication and Information System, Northeastern University, China. His research interests include cognitive radio network and cooperation communication.

Yang Han received B.Sc. in College of Information Science and Engineering, Hainan University, Hainan, China, in 2010. He is currently a Master in Communication and Information System, Northeastern University, China. His research interests include cognitive radio network and cooperation communication.