Leader Election Algorithm for Distributed Ad-hoc Cognitive Radio ...

The 9th Annual IEEE Consumer Communications and Networking Conference - Wireless Consumer Communication and Networking

Leader Election Algorithm for Distributed Ad-Hoc Cognitive Radio Networks O. Olabiyi, A. Annamalai and L. Qian Centre of Excellence for Communication Systems Technology Research Department of Electrical and Computer Engineering Prairie View A&M University, TX 77446 Abstract— Recent development in wireless communication has necessitated a high demand for radio resources. This has led to the development of cognitive radio technology in which radio equipments are now capable of identifying spectrum opportunity in their environment and take advantage of spectrum unused by licensed primary radio users for communication. One of the derivatives of the emerging technology is the ad hoc cognitive radio networks where control of the network resources is distributed among the users. In order to improve co-ordination in ad hoc cognitive radio networks, there is a need for selection of an appropriate leader that will guarantee quality of service (QoS), spectrum allocation and aggregation and synchronization of cognitive radios. In this paper we proposed a novel leader election algorithm that is robust for distributed ad hoc cognitive radio networks. Keywords— cognitive radio, leader election, distributed, algorithm, energy detector

I. INTRODUCTION In the traditional ad hoc cognitive radio systems, the coordination is being distributed among the cognitive radios (CR) which pose great challenge on the networks performance and quality of service (QoS) required for some applications. The QoS provisioning is a major requirement in multimedia content which is expected to dominate most of the internet traffic in the nearest future. Therefore, in order to ensure proper co-ordination of network resources, there is need for having a leader among the radio nodes. Some of the responsibilities of the cluster head include: synchronization of new members, acting as fusion centre for sensing information, maintenance of cluster size and radio resources, handling members’ and own handoff , routing of cluster traffic and management of inter-cluster relationships, maintenance of QoS for nodes with time sensitive applications and the security within the cluster. Several cluster head election algorithms have been proposed in both wireless sensors and cognitive radio system but none has really addressed the election challenges in distributed cognitive radio networks. In wireless sensor networks, several energy efficient algorithms like low-energy adaptive clustering hierarchy (LEACH) [1], cluster head election mechanism using fuzzy logic (CHEF) [2], power-efficient gathering in sensor information system (PEGASIS) methods [3] and energy-efficient chainThis work is supported in part by funding from the US Army Research Office (W911NF-10-1-0087), Air Force Research Laboratory/Clarkson Aerospace, and the National Science Foundation (0931679 & 1040207).

978-1-4244-8790-5/12/$26.00 ©2012 IEEE

cluster routing (ECR) protocol [4] have been proposed. In [5], the authors also introduced an efficient multi-parameter group leader selection schemes for wireless networks while [6] introduced cluster leader selection algorithm in a partially connected sensor network for multi-hop network. While the algorithms proposed in the above and related articles have lots of advantages in clustering, none of them can be applied to the cognitive radio environment without adaptation. This is because they have made inherent assumption that radio frequency channels are always available which is not the case in cognitive radio transmission. Recently, there has also being efforts in developing clustering algorithm for cognitive radio. For example, [7] developed cluster selection algorithm for infrastructure based cognitive radio network. This cannot be applied to ad hoc network as no energy constraint is considered with is the main limitation of ad hoc network. Interestingly, in one of the foremost article on cluster based cooperative sensing [8], the authors alluded to the choice of cluster head based on the number of available channels, a departure from general knowledge in wireless sensor. However, this does not take into consideration the energy efficiency of the choice. This limitation is taken care of in [9] where the author introduced energy efficiency to cluster based spectrum sensing. However, the topology or density of the cognitive radio spatial distribution is not considered as it is inherently assumed that the cluster head is centrally located within the cluster. Lastly in [10], the authors developed a very efficient media access control (MAC) protocol for cluster based cognitive radio network. While the operation of the cluster was discussed it is not clearly stated how the cluster head emerged. In other words, in all the literature reviewed, no publication has yet considered all of the important criteria required for an efficient leader election in the context of distributed ah hoc cognitive radio networks. This is the main contribution of this paper and we have considered a distributive leader or cluster head election based on the available spectrum opportunity, energy and the topology of the network subject to location, energy and QoS constraints. It is worth to mention here that, this work mainly focuses on leader election algorithm and not on the design of the entire MAC layer for cognitive radio networks with the assumption that the network is homogeneous i.e., any CR within the network or sub-network is capable of becoming a leader as long as it meets the election criteria. First, we proposed a novel selection function and show that it has the appropriate properties. We then employ this function in our leader election algorithm.

859

1/ K

f ( E, Z , K ) = ( EZ )

∂f ( E , Z , K ) ∂K

bounded between 0 and 1 i.e. f ( E , Z , K ) = [0,1] as shown in Fig. 1. Fig. 1 illustrates that the SF increases as K and/or EZ product increases. Also, it shows that the change in K results into further increase in EZ. We could also observe that the marginal effect of increment in K reduces at larger values of K. This is shown clearer in Fig. 2 which illustrates the gradient of SF w.r.t K. It could be observed that the gradient reduces with increasing

=−

1 K2

K. 1/ K

( EZ )

However,

the

gradient

ln ( EZ ) is always positive for all values of

K, which shows that f ( E, Z , K ) is a monotonically increasing function between 0 and 1. This indicates that our choice of SF is suitable for our purpose. We shall now consider the actual election leader election algorithm for ad hoc cognitive radio network. 1 0.9 0.8 0.7 0.6 EZ 0.5 0.4 EZ = 0.2 0.3

EZ = 0.4

0.2

EZ = 0.6 EZ = 0.8

0.1 0 0

EZ = 1 2

4 6 Number of Channels K

8

10

Fig.1 Selection factor versus number of available channel for different values of EZ product. 0.4 EZ = EZ = EZ = EZ = EZ =

0.35

(1)

where E = [0,1] is the remaining energy normalized by the maximum energy or battery capacity, Z = [0,1] is the neighborhood factor or cluster density with respect to (w.r.t) the candidate and it the number of the node within the communication range of the candidate normalized by the total number of node in the cluster, N. K = [0, M ] is the number of channels available to the candidate. The product of E and Z agrees with their inverse relationship, i.e. the more the number of nodes within the communication range the lower the remaining energy as there will be more communication energy consumed. K being an exponent ensures that more weight is given to K especially at lower values. Therefore the SF f ( E , Z , K ) is always

of

Selection Factor

II. SYSTEM MODEL AND ALGORITHM Consider a secondary user networks with N CRs and M channels being occupied by the primary users but CRs could use the channels opportunistically. Let i=1…M indicate the channel indices and n=1…N indicate the CR indices. The major concern is to find election criteria function with the following properties: (i) Gives preference to candidate with highest remaining energy (ii) Gives preference to candidate with highest neighborhood factor (highest density) i.e. that contains most number of nodes within its preferred communication range (iii) Gives preference to the candidate with highest average number of vacant channels (iv) Gives equal weight to both remaining energy and neighborhood factor (v) Gives higher weight to the number of channels when number of channel is low to moderate (vi) Reduces the weight on the number of channels when it becomes very large so that remaining energy and neighborhood factor becomes more important then Such objective function or selection factor (SF) that fulfils these properties can be modeled by the function

values

Gradient of Selection Factor wrt K

We later show that our algorithm gives better overall performance than the existing wireless sensor’s algorithms (which consider only energy and topology) and better than existing algorithms in cognitive radio which consider only the number of available channels in each nodes. The remainder of the paper is organized as follows; section I discusses the system model and leader election algorithm. Section II discusses the performance analysis while section III and IV contain the simulation results and concluding remarks respectively

0.3

0.2 0.4 0.6 0.8 1

0.25 0.2 EZ

0.15 0.1 0.05 0 0

2

4 6 Number of Channels K

8

10

Fig.2 Gradient of selection factor versus number of available channels for different values of EZ product.

Leader Election Algorithm The main requirement here is to ensure that the election is not centrally controlled either by the incumbent leader or by a centralized facility. Some articles have considered the selection being done by the incumbent leader. This is not practical because several common network problems can render the incumbent leader inactive in the network before being able to select a successor. Here we proposed an election algorithm that is independent of the current leader but could also be initiated by the current leader. The main purpose of the algorithm is to solve the following equation (2) in a distributed manner.

860

1/ K n

L = arg max ( En Z n )

(2)

n

subject to En > Eth , Z n > Zth , K > K th where Eth is the minimum energy threshold required to be a leader to ensure longer die out time; Zth is the neighborhood factor threshold to ensure communication to at least certain percentage of the nodes; K th is the minimum number of vacant channel required to ensure at least, minimum QoS and control communication from the leader to the cluster members. In addition, these thresholds minimize the number of nodes that participate in the election thereby reducing total energy consumption due to election. The leader election algorithm is shown in Fig. 3. Here we assume that the members of the cluster access the channel in a random fashion. We also assume that there is availability of control channel which is not used by the primary user. The beginning of an election process can be periodic, initiated by the current leader or initiated by sudden loss of the current leader or by a new cluster member. Cluster Head or Leader Election Algorithm 1 2 3 4 5 6 7 8 9 10 11

/* for every election round each node n performs*/ Rand () Broadcast Member_message (ID, with time stamp); while broadcasting ID, perform spectrum sensing end while Listen to the ID broadcast from other nodes; Compute Z from received broadcast information; Compute E from measured current battery level; Compute K from spectrum sensing information; if ( ( E > Eth )& (Z > Z th )& (K > K th )) then 1/ K

Compute SF = ( EZ )

channel. If before a node broadcasts, it hears another node with higher selection factor (chance) than it’s own, it update its leader parameter with the node’s ID. The node with maximum SF values declares itself cluster head (CH) or the leader. The successful cluster head then send CH message to the members. This ends the distributed election procedure. The elected leader however monitors its constraints periodically and once it is falling short, it will initiate another election process. III. PERFORMANCE ANALYSIS Here, we will model different factors considered in the leader election and use the model in our simulation to investigate how different factors affect the success of election process. A. Modelling of Spectrum Availability The spectrum availability in cognitive radio network is not deterministic due to random behavior of primary user transmission and secondary user spectrum sensing error. The spectrum sensing has been shown to be a binary hypothesis testing problem with H 0 : Primary user is absent and H1 : Primary user in operation [11]. Using energy detection with white noise modeled as a zero-mean Gaussian random variable with variance σ w2 , i.e. w( n) = N (0, σ w2 ) and the signal term s(n) , the decision variable, Y under H 0 follows the chi-square distribution with 2u 2 degrees of freedom χ 2u and under H1 follows the non-central chi-

square distribution with 2u degrees of freedom χ 22u (є ) where є is known as the non-centrality parameters. Consequently, the probability of detection Pd and the probability of false alarm P f in an AWGN channel of channel i by the nth CR can be expressed as in (3) and (4) respectively [11]: Pd( n , i ) = Q u ( 2 γ n , i , λ ) (3)

;

n ,i

12 Broadcast Candidate_message (SF); 13 while receiving candidates message from node j 14 if SF < j’s SF 15 myCH = j; 16 SF =j’s SF; 17 end if 18 end while 19 if myCH==me then 20 Broadcast CH_message; 21 end 22 else 23 On receiving CH_Message 24 Select the CH; 25 end if

Pf(n,i ) = Γ(un,i , λ2 ) / Γ(un,i )

(4)

where λ denotes the threshold of the detector, Qu (.,.) is the generalized Marcum Q-function of u-th order, and Γ(.,.) is the upper incomplete gamma function which is defined by the ∞

integral Γ(a, x) = ∫ t a −1e−t dt, u ( n,i ) = Wsiτ sn is sensing window size x

and it is the bandwidth-time product of the sampling system and W si is the bandwidth of channel i , τ sn is the sampling(sensing) time of the node n, and γ n,i is the SNR of primary user signal in channel i measured by node n. The channel is available when the primary user is absent H 0

Fig.3 Cluster head or leader election algorithm

At the beginning of election period, all station broadcast their IDs with time stamps; by this each station is able to estimate the location of other using itself as a reference. Each station checks its neighbourhood factor, number of channels and power constraints. Only nodes that meet the constraints partake in the election. Each potential candidate then broadcast its ID starting with any of the contesting candidates that gets hold of the control

and there is no false alarm or when the primary user is present H1 but was missed by the CR. Therefore, the total channel availability of channel i as perceived by CR n is given by: Cn,i = Pr Yn ,i = H 0 , H 0  + Pr Yn ,i = H 0 , H1 

861

=Pr Yn ,i = H 0 | H 0  Pr  H 0  + Pr Yn ,i = H 0 | H1  Pr [ H1 ]

(

)

(

)

= 1-Pf( n,i ) Pr  H 0  + 1-Pd( n ,i ) Pr [ H1 ]

(5)

If we assume that the actual channel vacancy Pr H 0  is known and denoted by cn ,i . Also using the fact that Pr H 0  + Pr [ H1 ] = 1 ,

We employ the following communication power consumption model used in [7, eq. (2)] for information exchanges between nodes.

(

then (11) becomes

(

( n,i ) f

Cn ,i = 1-P

)

(

( n ,i ) d

cn,i + 1-P

)

(1 − cn,i )

(6)

From the CR perspective, each channel can either be available with probability Cn,i or occupied by the primary user with probability (1 − Cn,i ) , then, the

effective probability that Kn

channels will be available can be modeled by the generalized binomial distribution and is given by, Kn

Pr[k = K n ] =

M

∑ ∏ (C ) ∏ (1 − C ) n,k

k =1,.. Kn k =1

n,k

(7)

k = Kn +1

Assuming equal availability on each channel, we obtain M  K M −K Pr[k = K n ] =   ( Cn ) n (1 − Cn ) n K  n

(8)

Therefore, the average number of channel available to the nth CR is given by K n =MCn (9) =M  1-Pf( n ) cn + 1-Pd( n ) (1 − cn )   

(

)

(

)

B. Effect of PU Activity Here we consider the effect of the primary user transmission behavior on the channel availability. If we assume the expected number of primary user arriving within a particular time interval is µ . If we also assume that the arrival of each PU is independent of the other and there is finite number of arrivals within the time interval. Also, if we assume that the inter arrival time is exponential distributed, the instantaneous number of arrival within any arbitrary interval can be modeled according to the Poisson distribution. Therefore the probability of pn,i arrivals within any interval in channel i within the transmission region of CR n is given by p −µ µ n ,i e (10) n ,i

f ( pn , i ) =

)

v=2 and α 2 = 0.001 pJ / bit / m2 when v=4. The sensing power is also similar to the reception power and it is given by Ps = α12 rS ; where rS is the sensing rate and it is given by rS = 2W where W is the sensing bandwidth of M channels. Substituting all these into (13), we can derive the remaining energy expression and it is given by En = 1 − ET / Em (15) = 1 −  α11 + α 2 d n , j v rCτ t + α12 rCτ r + 2α12 un M  / Em  

(

(

)

D. Modelling of Neighbourhood or Density Factor Here we derive the expressions to determine the fraction of nodes within the preferred communication distance of the potential candidate. Assuming the position of all the N nodes are obtained with reference to node n. Here, we assume this is one dimensional radial distance since it is obtained from the time stamped broadcast from other node j. We define an indicator function which counts the number of nodes within the best communication range and it is given by d n , j ≤ d max   1, I n, j =  (16)  otherwise  0, where d n, j is the computed distance between node n and j; and

d max is the range of QoS service. Therefore the neighborhood factor can be derived as

Zn =

pn ,i !

Eq. (11) shows that the channel availability decreases as the expected number of PUs increases. Substituting into (11) we obtain K n ==M  1-Pf( n ) e− µn + 1-Pd( n ) (1 − e− µn )  (12)  

)

C. Modelling of Remaining Energy Here we provide the modeling of CR energy consumption. We assume that the CR is either transmitting or sensing at any point in time. Therefore, the total energy consumed by CR is the sum of the sensing energy and communication energy given by ET = EC + ES = PCτ C + Psτ s (13)

(14)

where PT is the transmission power consumption and PR is the reception power consumption, v is the path loss exponent , α11 = 145nJ / bit , α12 = 135nJ / bit , α 2 = 10 pJ / bit / m2 when

n ,i

cn,i in (6) can be evaluated from (10) as the probability of no PU arrival within the considered time interval and it is given by −µ (11) cn ,i = f (0) = e n ,i

(

)

PC = PT + PR = α11 + α 2 d n, j v rC + α12 rC

1 N

∑

j

I n, j

(17)

IV. SIMULATION RESULTS In this section we present the simulation result of our algorithm in comparison with popular clustering algorithms in wireless sensor networks. For illustrative purpose we consider, N=50 CRs spread over a space of 50m x 50m. The locations of CR nodes are randomly generated and are uniformly distributed. We assume initial energy of 1J/CR, rCτ t = 1000bits /round, u=5bits/round, Pf is normally distributed between 0-0.2, average number of PU, µ is also uniform random integer between 0-5 , assume the path loss exponent, v=2, γ = 10dB , λ = 10dB , M=10 channels, dmax=25m radius. We consider single cluster here just to illustrate the efficiency of our algorithm. Figure 5 illustrates the result of the election based on the existing algorithms in sensor networks and our proposed algorithm for cognitive radio networks. The LEACH algorithm normally makes the choice of

862

V. CONCLUSIONS We developed a robust leader election algorithm for distributed ad hoc cognitive radio networks using a novel selection criterion that consider the number of available channels, energy and location subject to energy, location and QoS constraint. First we showed the suitability of the criterion and we developed CH election algorithm based on this criteria. We later showed that our algorithm is more efficient than some of the existing algorithm being currently used in sensor networks. More so, it has comparable energy savings!

50 45 40 35 30

K=10 P K=8

25

C L K=3

20 15

REFERENCES

10

[1]

5 0 0

10

20

30

40

[2]

50

Fig.5 Spatial distribution CRs and choice of cluster head selection using different algorithms.

the node closest to the centre of the topology while the CHEF algorithm considers the neighbourhood factor. Interestingly, the two algorithms make the same choice of the CH because of the uniform distribution and single cluster case. In both cases the channel availability was not considered. Due to the random nature of PU activity and consequently channel availability, both LEACH (L) and CHEF (C) algorithm chose a node with only 3 channels. In our algorithm we use the proposed selection factor which also takes into consideration the channel available. The choice is P which has 8 channels but a little bit displaced from the centre. Our algorithm also shows that the node with 10 channels is not good as its position and distribution badly impacts the energy efficiency. In Fig. 6, we investigate the loss in energy due to the location of P compared to both C and L. We found out that there is no appreciable difference in the total communication from the choice of this location. This shows that while our algorithm considered the specific nature of the cognitive radio system, it also has comparable performance as the LEACH and CHEF in terms of energy saving.

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

50

40 Total Remaining Energy (J)

[11]

LEACH CHEF Proposed method

45

35 30 25 20 15 10 5 0

500

1000 1500 2000 No of Simulations

2500

3000

Fig.6 Total remaining energy of 50 CR nodes versus the number of simulation for different algorithms.

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