A Novel Sensing Nodes and Decision Node Selection ... - IEEE Xplore

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IEEE SENSORS JOURNAL, VOL. 13, NO. 5, MAY 2013

A Novel Sensing Nodes and Decision Node Selection Method for Energy Efficiency of Cooperative Spectrum Sensing in Cognitive Sensor Networks Maryam Najimi, Ataollah Ebrahimzadeh, S. Mehdi Hosseini Andargoli, and Afshin Fallahi

Abstract— In this paper, we address the problem of sensor selection for energy efficient spectrum sensing in cognitive sensor networks. We consider minimizing energy consumption and improving spectrum sensing performance simultaneously. For this purpose, we employ the energy detector for spectrum sensing and formulate the problem of sensor selection in order to achieve energy efficiency in spectrum sensing while reducing complexity. Due to the NP-complete nature of the problem, we simplify the problem to a more tractable form through mapping assignment indices from integer to the real domain. Based on the standard optimization techniques, the optimal conditions are obtained and a closed-form equation is expressed to determine the priority of nodes for spectrum sensing. In the next step, to save more energy, the decision node (DN) selection procedure is proposed to address the problem of direct transmissions to fusion center. Then, the problem of joint sensing node selection and DN selection is analyzed and an efficient solution is extracted based on the convex optimization framework. The novelty of the proposed work is to address the selection of the best sensing nodes while minimizing energy consumption. Simulation results show that significant energy is saved due to the proposed schemes in different scenarios. Index Terms— Cognitive wireless sensor networks, cooperative spectrum sensing, detection and false alarm probabilities, fusion center.

I. I NTRODUCTION

O

VER the last decades, wireless technologies have grown rapidly. Given the limitations of the natural frequency spectrum, it is obvious that the current static frequency allocation schemes cannot support numerous emerging wireless services. Cognitive radio arises to be a solution to the spectral congestion problem by providing opportunities for unlicensed users (secondary users) to utilize the unused portions of the licensed spectrum bands [1], [2]. As an intelligent wireless communication system, a cognitive radio is aware of the radio frequency environment. It selects the communication parameters (such as carrier frequency, bandwidth and transmission power) to optimize the spectrum usage. One of the most critical components of the cognitive radio technology is spectrum Manuscript received November 5, 2012; accepted January 4, 2013. Date of publication January 17, 2013; date of current version March 27, 2013. The associate editor coordinating the review of this paper and approving it for publication was Prof. Paul P. Sotiriadis. M. Najimi, A. Ebrahimzadeh, and S. M. H. Andargoli are with the Faculty of Electrical and Computer Engineering, Babol University of Technology, Babol 47148-71167, Iran (e-mail: [email protected]; [email protected]; [email protected]). A. Fallahi is with RighTel, Tehran, Iran (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JSEN.2013.2240900

sensing. In fact, spectrum sensing is employed to identify the spectrum holes. On the other hand, with spectrum sensing of a radio channel, the occupancy status of the channel for cognitive sensors is determined. In this way, if the secondary users know that channel is idle, then transmission can be done in that channel in order to avoid interference with primary users. Thus, reliable determination of the idle channels is a critical problem. Attenuation impairments such as shadowing and fading can lead to unreliable detection of the spectrum holes by sensor nodes and degrade the primary network’s performance. It has been shown that cooperative spectrum sensing using several cognitive sensors performs better than when only one node participates in spectrum sensing. In cooperative spectrum sensing, different users share their results and decide on the status of the channel. [3]–[6] show that the sensing performance can be improved significantly if cooperative spectrum sensing is used. In [7] it is considered that increasing the number of cooperating users can decrease the required detector sensitivity and the sensing time significantly. However, it should be noted that as the number of cooperating users increases, the communication overhead will also increase in terms of exchanged messages and processing overhead. On the other hand, increasing the number of sensing nodes does not change the detection performance significantly. According to [13], it is not necessary for all secondary users to cooperate in the network to achieve the optimum performance, and secondary users with the highest primary user’s signal-to-noise ratio (SNR) are participated in spectrum sensing. In [14] the detection performance for spectrum sensing in cognitive radio networks in low SNR is investigated. But both of these works have no analytical expressions for their problems. Another issue is sensor nodes, which are employed for spectrum sensing, operate under limited energy budgets. Typically, they are powered through batteries, which must be either replaced or recharged (e.g., using solar power) when depleted. For some nodes, neither option is possible, that is, they will simply be discarded once their energy source is depleted. In this paper, we consider the problem of minimizing energy consumption in cooperative spectrum sensing for a cognitive wireless sensor network which comprises of a fusion center (FC) and cognitive sensors for channel sensing in a specific duration. FC makes the final decision about the occupancy of the channel using a fusion rule. We use the energy detector because of its simple implementation and independency of

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NAJIMI et al.: A NOVEL SENSING NODES AND DN SELECTION METHOD

having prior knowledge about the primary user signal for channel sensing. With this technique, the energy received on a licensed band is measured. Whenever the level exceeds a predefined threshold, it would be interpreted as detecting primary user’s transmission; otherwise a spectrum hole is confirmed. The assumption is that signal-to noise-ratio (SNR) and distance between each node and FC are known. We propose a saving energy method in cooperative spectrum sensing by selecting the sensing nodes, which satisfy the constraints on the detection performance and help to decrease energy consumption. In our approach, we consider an on/off scheme, in which some sensors turn off their radios. Therefore, such nodes don’t sense the corresponding channel. One of the other schemes is censoring, which means when one sensor has useful information, sends its results to FC. This method is shown to be very effective in saving energy [8], [9]–[12]. In [15] a combination of sleeping and censoring schemes is applied and its goal is to minimize energy consumption with constraints on the detection performance by choosing the sleeping and censoring design parameters. In fact, in [15] only the number of sensing nodes is determined without giving which nodes are sensing. Furthermore, SNR in [15] is the same for all cognitive sensors, which is not a real assumption and only apply to simplify the problem. Moreover, this assumption implies that the probability of detection for all sensors is the same, which is not true due to the different distances between each node and primary user. Our contribution in this paper is as follows: 1) We formulate the problem of minimizing energy consumption in cooperative spectrum sensing under the constraints on the false alarm and the probability of detection by sensing nodes selection when SNR and distances between each node and FC are known. 2) The optimum solution of this problem is based on the exhaustive search algorithm which cannot be applied in practice due to its high computational complexity. The problem becomes easier through mapping the integer assignment indices to the equivalent real values. Then, it is solved analytically based on the convex optimization framework. 3) After obtaining the optimal conditions based on Karush– Kuhn–Tucker (KKT) conditions, an iterative algorithm is proposed to search the optimum nodes selection strategy. 4) To achieve more energy efficiency, the problem of joint sensing nodes and decision node selection is formulated. Two solutions for this problem are exhaustive search and combining sensing node selection solution with all decision node states. Both of the methods, are complex, so again, similar to the first problem, we convert the problem to more tractable form through mapping integer assignment indices to real values. Then, the optimal conditions are extracted using KKT conditions. An iterative algorithm is proposed which can find the best decision node and sensing nodes simultaneously. 5) The numerical results have been used to analyze the proposed algorithm in finding the solution, energy consumption and detection performance in different conditions.

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Fig. 1.

Cooperative spectrum sensing configuration.

The rest of the paper is organized as follows. In Section II, we describe the system model and formulate the global false alarm and the probability of detection in the energy detection. Expression of the sensor selection problem is then derived in Section III. In Section IV, we analyze how to solve the first problem using the analytical algorithms. In Section V, our modified algorithm is proposed. We declare the second problem of finding the best decision node and corresponding sensors selection and solving this problem using an iterative algorithm in Section VI and Section VII. We present numerical and simulation results to show the energy savings obtained by the proposed scheme in Section VIII. Conclusions are drawn in Section IX. II. S YSTEM M ODEL We consider a network with N cognitive sensors and an FC as it is shown in Fig. 1. We use T to denote the frame duration. We assume that all cognitive sensors have the same spectrum sensing duration, and we use δ, 0 < δ < T to denote the spectrum sensing time of the cognitive sensors. We assume that fs is the sampling frequency of the received signal from primary user for the cognitive user j , ∀ j ∈ N. δ is a multiple of 1/ f s , thus the number of samples is δ f s . Each sensing node based on its observation, Xj [k], k = 1, 2, . . . , δ f s decides on the channel status. Each observation sample has two hypotheses. Hypothesis H1 , means the primary user is active and hypothesis H0, means the primary user is inactive in using the channel. H1 : X j [k] = s j [k] + u j [k]

(1)

H0 : X j [k] = u j [k]

(2)

where s j [k] is the primary user’s signal at the j th sensor and is assumed to be a random process with zero mean and variance σs2j . The noise, u j [k] is a Gaussian, independent and identically distributed (i.i.d) random process with zero mean and variance σu2 . Our assumption is that s j [k] and u j [k] are independent processes. We denote γ j as the received signalto-noise ratio (SNR) of the primary user measured at the j th sensor under the hypothesis H1 .

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IEEE SENSORS JOURNAL, VOL. 13, NO. 5, MAY 2013

In channel sensing, the probability of detection, Pd , and the probability of false alarm, P f , are defined as the probabilities of detecting a primary user under H1 and H0 , respectively. So, with these probabilities, a cognitive sensor can determine if channel is busy or idle. The higher Pd protects a primary user transmission from the interference with the secondary user transmission and lower P f provides the opportunity of using idle channel for secondary users. Therefore, it is desirable for the network to have a high Pd and a low P f . The decision rule which is applied by the energy detector for the sensor j is as follows  δ fs 1  2 H1 D j = 0 if H0 X j k ≷ H0  : (3) Ej = δ fs D j = 1 if H1 k=1 where  is the detection threshold for all the cognitive sensors and D j is the decision made by node j . Therefore, each user sends one bit to inform the FC about its decision of presence (“1”) or absence (“0”) of the primary user signal. Under H0 the test static E j is a random variable whose probability density function (PDF) is a chi-square distribution with 2δ f s degrees of freedom and under H1, E j distribution is a noncentral chi-square distribution with 2δ f s degrees of freedom and a non-centrality parameter 2γ j , respectively. Using central limit theorem, for a large 2δ f s , the PDF of E j can be approximated by a Gaussian distribution. For a chosen threshold  the probability of false alarm in the j th cognitive sensor is given by [13]        −1 δ fs (4) P f j = P E j > |H0 = Q σu2 where Q is the complementary distribution function of the standard Gaussian. Also, under hypothesis H1, the probability of detection of the cognitive sensor j is [13]   

   δ fs . − γj − 1 Pd j = P E j > |H1 = Q σu2 2γ j + 1 (5) In [16] and [17] it is shown that deep fading and shadowing degrade the detection performance. Cooperative spectrum sensing is considered as a solution for this problem, where several cognitive sensors decide about a channel and send their results to the FC. Then, FC makes the final decision for that channel based on a decision rule to combine results of the cognitive sensors [18]. For simplicity, we assume that OR rule is used. That is, if one of the sensors reports that there is an active primary user, then the final decision declares that the channel is busy. We assume that the decisions made by each cognitive radio in the same channel are independent. The Pd and P f of the final decision are presented as follows, respectively: P f (δ) = 1 −

N

(1 − P f j (δ))

(6)

(1 − Pd j (δ)).

(7)

j =1

Pd (δ) = 1 −

N j =1

In [7] and [13], it is shown that it is not necessary for all nodes to participate in spectrum sensing. In our algorithm, some nodes with higher probabilities of detection and less distances from the FC are selected for spectrum sensing. Therefore, we can modify (6) and (7) to the following formulas: P f (δ) = 1 −

N

(1 − ρ j P f j (δ))

(8)

(1 − ρ j Pd j (δ))

(9)

j =1

Pd (δ) = 1 −

N j =1

where ρ j ∈ {0, 1} is the assignment index and it denotes “1” for sensing and “0” for not sensing the spectrum by the cognitive sensor. Therefore, we should determine which sensors sense the spectrum. III. S ENSOR S ELECTION IN S PECTRUM S ENSING The average energy consumption in spectrum sensing has two main parts: first, the energy consumed for sensing the channel and making a decision about the status of the channel and energy consumption for signal processing like modulation type, signal shaping, etc. It is denoted by Cs j . Second, energy consumption for transmitting one reliable decision bit to the FC, it is denoted by Ctj [15]. Therefore, the total energy consumed for cooperative spectrum sensing is given by CT =

N 

ρ j (Cs j +Ctj ).

(10)

j =1

Due to similarity of nodes, we assume Cs j is the same for all sensors and it is shown with Cs . Ctj is used to derive the radio electronics and the power amplification. It should be noted that the power attenuation depends on the distance between the transmitter and receiver, and in order to satisfy a given receiver sensitivity level, power amplification is required, then Ctj is as follows [19], [20].   Ctj d j = Ct-elec + eamp d j 2 (11) where Ct-elec is the transmitter electronics energy and eamp is the required amplification and d j is the distance between the j th node and FC. In order to formulate our problem, we need to consider final probability of detection and false alarm and their constraints. Pd (δ) and P f (δ) are denoted by global probability of detection and false alarm, respectively. The constraints on these probabilities are: P f (δ) < α and Pd (δ) > β. It is desirable to have higher probability of detection and lower probability of false alarm. Our goal is to determine which sensors sense the spectrum so that C T in (10) is minimized subject to the constraints P f (δ) < α and Pd (δ) > β. Smaller α and bigger β means higher opportunities of utilizing the spectrum and to decrease the interference of the secondary user transmission with the primary user activity, respectively. On the other hand, these conditions help the network to improve the detection

NAJIMI et al.: A NOVEL SENSING NODES AND DN SELECTION METHOD

performance meanwhile minimize total energy consumption in spectrum sensing. Therefore, we have minρ j C T =

N 

ρ j (Cs j + Ctj )

s.t. P f ≤ α, Pd ≥ β. (12)

j =1

IV. P ROBLEM A NALYSIS

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To reduce the complexity in finding a solution for (16), we assume ρ j is a continuous parameter so that ρ j ∈ [0, 1]. It is similar to the time-sharing parameter in [21] and represents the priority of the sensor node j for sensing. Then, ρ j s for the nodes with the higher priority are denoted by “1” and for other nodes are denoted by “0”. Therefore (16) is stated as follows:

First, it is better to change the constraint P f (δ) < α to another format. By substituting (4) and (5) in (8) and (9), we have    N    −1 δ fs 1 − ρj Q (13) P f (δ) = 1 − σu2 j =1   

N  δ fs − γj − 1 1 − ρj Q Pd (δ) = 1 − . σu2 2γ j + 1

minρ j C T =

s.t.

n

minρ j C T =

N  j =1

1−

N j =1

ρ j (Cs j + Ctj )

s.t.

N 

ρj = M

(17-1)

1−

N

(1 − Pd j (δ)) ≥ β

(17-2)

j =1

ρ j ∈ [0, 1].

(17-3)

Since, ∂C T /∂ρ j > 0 and ∂Pd /∂ρ j > 0 and ∂Pf /∂ρ j > 0, and also ∂C2 T /∂ρ j 2 = 0 and ∂P2d /∂ρ j 2 = 0 and ∂P2f /∂ρ j 2 = 0, so our problem in (17) has a conic form. This can be solved systematically as a convex optimization problem [22] where the constraints are convex with respect to ρ j . Finally, we solve the resulting convex problem to find the minimum C T and its corresponding parameter ρ j for each node. First, we use the Lagrangian function as follows: ⎛ ⎞ N N     L(ρj , λ, η) = ρ j Cs + Ctj −λ (Pd − β)+η ⎝ ρ j − M⎠ j =1

ρj = M

j =1

(1 − ρ j P d j (δ)) ≥ β ρ j ∈ {0, 1}.

N  j =1

(14)

where M is the maximum numberof the cognitive sensors which sense the spectrum and n = Nj=1 ρ j is the number of sensing nodes. Then, we rewrite it as follows:

ρ j (Cs j + Ctj )

j =1

j =1

We see that, P f (δ) is not dependent on the γ j and using (13), the upper limit for the number of sensing nodes is obtained as ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ln(1 − α) ⎣    √  ⎦ = M (15) n≤ ln 1 − Q σ2 − 1 δ fs

N 

(16)

Here, our goal is to minimize the total energy incurred by the cognitive sensor network to perform spectrum sensing while maintaining a global detection performance by determining the nodes which sense the spectrum. Note that sometimes there is no answer, i.e., the channel condition between every sensor node and primary user is bad and sensors have low Pd j s, so even with the selection of M sensors for sensing, the constraint Pd (δ) > β is not satisfied. As said before, ρ j is a discrete parameter and (16) becomes NP-complete. The optimum solution for such problem is to apply an exhaustive algorithm, in which, we should  search  M N examine all states to find the best answer which j =1 j consumes the lowest energy and also satisfies Pd > β. However, for large values of N, exhaustive search algorithm is very complex with the order of O(N!), which has an exponential complexity of N. Then, we search for more tractable form of the problem to find the solutions which have rational complexity and can be near optimal, and meanwhile can be applied in realistic situations. In fact, the complexity of the problem (16) comes from the integer nature of the assignment indices, ρ j . In this way, solution for these problems is gained through the exhaustive search algorithms that are very complex.

j =1

(18) where η and λ are the Lagrangian multipliers for (17-1) and (17-2) constraints, respectively. Then, Karush–Kuhn–Tucker (KKT) conditions reveal that   ∂L = Cs + Ctj + η − λPd j (1 − ρk Pdk ) = 0 ∂ρ j k = j

∀ j ∈ {0, 1, 2, . . . , N} .

(19)

Therefore, there are N equations and N unknown ρ j s, and solving these equations is difficult; however, our goal is to determine the priority of the sensor nodes for spectrum sensing and the quantity of ρ j s is not very important. Instead, the ratio of ρj /ρi for any pair of sensors should be compared and the sensor nodes with higher priority are selected. Therefore, by using (18) and (19), we have ∂L = (Cs + Cti ) + η − λPdi (1 − ρk Pdk ) = 0 (20) ∂ρi k =i

and

  ∂L = Cs + Ctj + η − λPd j (1 − ρk Pdk ) = 0. ∂ρ j

(21)

k = j

Hence, using (20) and (21), we obtain   (Cs + Cti ) + η  − λPdi 1 − ρ j Pd j = 0 (1 − ρ P ) k dk k =i, j     Cs + Ctj + η  − λPd j 1 − ρi Pdi = 0. k =i, j (1 − ρk Pdk )

(22) (23)

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Then, we have (Cs + Cti ) + η  − λPdi = −λPdi ρ j Pd j k =i, j (1 − ρk Pdk )   Cs + Ctj + η  − λPd j = −λPd j ρi Pdi . k =i, j (1 − ρk Pdk )

(24)

(25)

Therefore, the ratio is obtained as follows  Cs + Cti + η − λPdi kN= j,i (1 − ρk Pdk ) ρj =  ρi Cs + Ctj + η − λPd j kN= j,i (1 − ρk Pdk ) = cost(i )/cost( j ).

(26)

ρ j /ρi is related to the inverse ratio of the following cost function: cost(i ) = Cs + Cti + η − λPdi

N

(1 − ρk Pdk ).

(27)

k = j,i

This states that each sensor node with the smaller cost function as defined in (27) has the higher priority in spectrum sensing. To determine the priority of sensor nodes, cost function in (27) is calculated for all of them and then sorted in ascending order. The first M sensors with the highest priority are selected as spectrum sensing candidates. The next step is to determine the optimum λ and select the cognitive sensors for spectrum sensing out of the M sensors from the previous step. We assume that η is the same for all sensors and it can be omitted from the cost function. Also, we consider ρ j /ρi for only two nodes (i.e., the other sensors are not selected yet). Therefore (27) can be simplified as

Algorithm 1 EESS Algorithm λmin = 0 λmax = ζ (a large enough number) ε is a small number While (abs(λmin − λmax ) > ε) λ = (λmin + λmax )/2 number of sensing nodes(n) =0 Compute cost ( j ) = Cs +Ctj − λPd j for every node While (select n sensor with higher priority< M) Compute Pd If Pd > β, break, end n =n+1 end compute C T for all sensing nodes if Pd > β λmax = λ Else if Pd < β λmin = λ End end

in (28) for all sensors are calculated and sorted in ascending order, then the sensors with the highest priority are selected until the global Pd > β is satisfied and the number of selected nodes becomes less than M. Then, λ is updated according to the computedPd and searching space is halved and algorithm is repeated again. This iterative algorithm ends when the accuracy of λ becomes smaller than ε. ε declares the resolution of our algorithm. Note that in each iteration, for obtaining the cost( j ) = Cs + Ctj − λPd j (28) optimal, if Pd > β, then λ is decreased and if Pd < β, then λ is increased. It means that our algorithm converges to the complimentary slackness conditions imply that optimal λ which satisfies Pd = β. Our proposed algorithm  ⎧ has the linear complexity with the order of O(N), because (29-1) λ = 0, Pd > β ⎪ ⎪ ⎪ in each iteration, cost functions for all sensors are computed. λ (Pd − β) = 0 → ⎨ λ = 0, Pd = β (29-2) The order of iterations is (log2 (λmax − λmin )/ε). Pesudo code   ⎪   η = 0, ρ j < M (29-3) for Energy Efficient Sensor Selection (EESS) algorithm is ⎪ ⎪  ρj − M = 0 → ⎩η η = 0, ρ j = M. (29-4) shown below. In order to limit the search space of optimal λ, we try to We note that the proposed algorithm is not affected by find λmax , so that it is guaranteed 0 < λoptimal < λmax . λmax (29-3) and (29-4). In other words, the nodes should be selected is obtained when priorities of selecting sensors are determined so that one of these conditions is satisfied. It means that if the according to their Pd j s. We sort Pd j s of all nodes, then the number of sensing nodes is considered less than M, then first relation between cost functions of two nodes becomes condition becomes true and if maximum number of sensing 2 nodes equals M, then the second condition is satisfied. In the eamp d j − λmax Pd j < eamp d 2j −1 − λmax Pd j −1 next step, we should determine optimal λ. λ can be a positive ∀ j ∈ {0, 1, 2, . . . , N} . (30) nonzero parameter or a zero parameter. Lemma 1: The optimum λ is a positive and non zero Hence, eamp (d 2j − d 2j −1) parameter and then Pd = β. . (31) λmax > Proof: If λ = 0 is the optimal, then due to (29-1), (Pdjmax − Pd j −1max ) Pd > β is satisfied. We also know that Pd , P f and It means that, λmax should be selected according to (31) C T are the increasing functions of ρ j s. Therefore, we can such that a suitable searching space is considered to find a decrease ρ j s so that Pd = β is satisfied. Under this reducdesirable answer. tion, we have smaller P f and C T which leads to a more desirable answer. This way, λ is selected so that Pd = β V. M ODIFIED EESS A LGORITHM is satisfied. It is equal to (29-2) condition. In order to find the optimum λ we use an iterative bisection In EESS algorithm, at each iteration and by updating λ, the algorithm. We search through the algorithm to satisfy the opti- sensors are selected according to the cost function in (28). mal conditions stated before. At each iteration, cost functions This means that the nodes with the lowest cost functions,

NAJIMI et al.: A NOVEL SENSING NODES AND DN SELECTION METHOD

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energy consumption becomes CT =

N 

ρi

N 

πj (Ct-elec + eamp ((x i − x j )2

j =1

i=1

+(yi − y j )2 + d j 2 )).

(32)

πj is the DN selection index and can be “1” or “0”. It indicates that a sensor node is selected as DN (“1”) or not (“0”), respectively. x i and yi show the location of the i th sensor node and d j is the distance between node j and the FC. Our new problem can be formulated as follows: min C T ρi ,π j

s.t.

N 

ρj = M

j=1

Fig. 2.

Sending decision of sensing nodes to DN.

1−

N

(1 − ρ j Pd j (δ)) = β

j =1

which satisfy the constraint on Pd , are selected for spectrum sensing. However, by reducing λ, there are possibilities that the total energy consumption increases compared to the pervious iteration. This is due to the fact that the distance between each node and FC becomes more important than its Pdi . Therefore, in order to satisfy the constraint Pd > β, more nodes may be selected and then more energy is consumed. The reason for this is because of mapping ρj from continuous space to discrete space. While reducing λ with continuous ρj s has very small impact on the number of sensing nodes, in discrete space the number of nodes increases suddenly. To solve this problem, our algorithm is modified such that the last iteration with the minimum CT that satisfies Pd > β is taken as the best solution and the algorithm ends. In other words, instead of taking the final outcome of the iterative algorithm, we also search for the previous outcomes that satisfy Pd > β.

VI. S ELECTING D ECISION N ODE (DN) FOR I MPROVING E NERGY C ONSUMPTION In EESS algorithm, it is possible that some sensing nodes are located in far distances from the FC. Therefore, energy consumption for reporting results increases. In our system model one solution for saving energy is that, every sensor node sends its spectrum sensing result to a decision node (DN) for that licensed frequency band when the sensing time δ expires. DN is a node among all sensors as it is indicated in Fig. 2. DN will combine the sensing results of the selected sensor nodes which sense the channel and will determine the status (i.e., busy or idle) of the channel and then DN will send the final decision to the FC. We assume that the DN decides about the channel status based on a decision fusion rule to combine the sensing results of the cognitive sensors [5]. For simplicity, we assume that OR rule is used again. Then, the new problem is how to select a DN for making a final decision about the channel status and corresponding sensing nodes. Then, total

ρj ∈ {0, 1} πj ∈ {0, 1} N 

πj = 1

j=1 N 

ρ j πj = 0.

(33)

j =1

In (33) the last constraint indicates that one sensor can not be selected as DN and sensing node simultaneously. VII. S ENSING N ODES AND D ECISION N ODE S ELECTION P ROBLEM A NALYSIS One solution for (33) is an exhaustive search algorithm. It means there are N possible candidates for DN selection scheme. The sensing nodes selections are tested for all n < M combination of remaining sensors; The number of possible states is determined according to (34), in which the optimum solution is the state that leads to minimum energy consumption and satisfies Pd > β.  M   N −1 N . (34) j j =1

But, this method has a high complexity with the order of O(N!), we therefore look for a solution to find DN with less complexity. One solution is that, for each sensor as DN, the sensing nodes are selected by MEESS algorithm which has been proposed in Section IV. Although, this scheme has less complexity than the exhaustive search with the order of O(N 2 ), we search for the solutions with linear complexity. Table 1 shows the complexity of different algorithms. Again because ρj and πj are discrete parameters and the problem is NP-complete, at first, ρj and πj are considered as continuous parameters, and then after solving the problem, ρj and πj are mapped to the discrete parameters. In this case, the last condition in (33) is removed, but in selecting DN,

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TABLE I

DN selection is obtained using the following cost function:

C OMPLEXITY OF THE A LGORITHMS Algorithms

The order of the complexity

Exhaustive Search in Sensing Node Selection

Exhaustive Search in Selection

O(N !)

O(N !)

MEESS DN O(N )

ρi ,π j

ρj = M

j =1

1−

N

(1 − ρ j Pd j (δ)) = β

j =1

π j ∈ [0, 1] π j = 1.

(35)

j =1

According to the conic form of C T , we can use the convex optimization algorithms for solving (35), therefore, Lagrangian function is given by ⎛ ⎞ ⎛ ⎞ N N   L = CT + η ⎝ ρ j − M⎠ − λ (Pd − β) + ⎝ π j − 1⎠ j =1

j=1

⎛ ⎞ N  −υ ⎝ ρ j πj − 0 ⎠

(36)

j =1

and KKT conditions imply that  ∂L = Cs +π j (Ct-elec + eamp ((x i − x j )2 + (yi − y j )2 ∂ρi j =1 ⎛ ⎞ N  +d j 2 )) − λPdi + η − ω ⎝ π j − 1⎠ − υπj = 0 (37) N

j =1

∂L = ∂πj

N 

(40)

where the node with minimum cost_DN is selected as DN. Again complimentary slackness conditions for this problem reveal that ⎧  ⎪ λ = 0, Pd > β ⎪ ⎪ λ (Pd − β) = 0 → ⎪ ⎪ ⎪ λ = 0, Pd = β ⎪ ⎪  ⎪  ⎪ ⎪   η = 0, ρ j < M ⎪ ⎪ → ρj − M = 0  ⎪ ⎨η η = 0, ρ j = M     ⎪ ω = 0, Nj=1 π j = 1 ⎪ N ⎪ ω N π − 1 = 0 → ⎪ j =1 j ⎪ ⎪ ω  = 0, ⎪ j =1 π j = 1 ⎪  ⎪ ⎪   ⎪ N υ = 0, ρ j πj = 0 ⎪ ⎪ ⎪ j =1 ρ j πj − 0 = 0 → ⎩υ υ = 0, ρ π = 0. j j

ρ j ∈ [0, 1] N 

ρ j (Ct-elec + eamp ((x i − x j )2

i=1

min C T N 

N 

+(yi − y j )2 + d j 2 ))

we note that one node cannot be a DN and sensing node simultaneously, so we have

s.t.

cost_DN( j ) =

ρi Ct-elec + eamp ((x i − x j )2 + (y i − y j )2

i=1

+d j ) + ω − υρ j = 0. 2

(38)

Due to (37) and similar to Section IV, priority of each node for spectrum sensing can be computed based on a cost function as follows: cost(i, j ) = Cs + Ct-elec + eamp ((x i − x j )2 +(yi − y j )2 + d j 2 ) − λPdi

(39)

where cost (i, j ) denotes the cost function of node i when node j is selected as DN. According to (39) the priority for

(41) The first and second conditions are similar to (29-1) and  (29-2) but in the third condition Nj=1 π j = 1 is true because in each iteration we have only one DN, therefore sum of DNs becomes one. In the fourth condition, one node cannot be both sensing node and DN so ρ j πj = 0 is a true condition. ω and υ are the same for all sensors, then priority is not affected by them. Pesudo code for MEESS algorithm for selecting DN is shown below. In order to select DN, all sensors can be a DN candidate. Then, we use modified EESS (MEESS) algorithm similar to the first problem and in each iteration by updating λ, for every node as DN candidate, (39) is computed and the minimum number of sensors for sensing the spectrum is determined to satisfy the constraint on Pd . Then, every sensor with minimum cost in (40) is selected as a DN and goes to the next iteration. In this algorithm, in each iteration by updating λ, DN is also selected, so its complexity is much less than the exhaustive search algorithm in combination with MEESS in which for every node as DN candidate, updating λ and sensing nodes selection are also done which is more complex. VIII. N UMERICAL AND S IMULATION R ESULTS We consider a network of cognitive sensors changing from five to fifty in quantity. The aim is to find the sensing sensors and the best location of DN with respect to the constraints on probability of false alarm and probability of detection. Simulation results are shown for α = 0.1 and β = 0.9 and also obtained for α = 0.05 and β = 0.95. Every simulation result in this section is averaged over 1000 realizations. We use the 2.4 GHz IEEE 802.15.4/ZigBee as the communication technology for our cognitive sensors which have to cooperate with each other to sense the spectrum [15], [23]. For the numerical analysis, we consider our sensors located in a square field with a length of 100 m, where nodes are uniformly distributed and the FC is located in the center. We model the wireless channel between the cognitive sensor and the FC using a free-space path loss model and wireless channel

NAJIMI et al.: A NOVEL SENSING NODES AND DN SELECTION METHOD

Algorithm 2 MEESS algorithm with selecting DN λmin = 0 λmax = ζ (a large enough number) ε is a small number while (abs(λmin − λmax ) > ε) do λ = (λmin + λmax )/2 while ( j < N) do number of sensing nodes= 0 Compute cost(i, j ) = Cs + Ct-elec + eamp ((x i − x j )2 + (yi − y j )2 + (x i − x j )2 + (yi − y j )2 + d j 2 ) − λPdi , for node i and decision node(DN) j while (number of sensing nodes< M) do Compute Pd if Pd > β then break end if end while compute C T for all sensing nodes and decision node (DN) j cost_DN( j ) =

N 

ρ j (Ct-elec + eamp ((x i − x j )2

i=1

+(yi − y j )2 + d j 2 )) end while Sort(cost_DN ( j )), select minimum cost_DN ( j ) and j as DN if (λ is less than previous iteration) & (C T for DN > C T in previous iteration), then break, end if if Pd > β then λmax = λ else if Pd < β then λmin = λ end if end while

between every cognitive sensor and primary user has a model as follows: −l j H j = 10 20 .g j (42) where gj is a Gaussian random process with zero mean and unit variance accounting to Raleigh fast fading and Lj has two components  d 4π f  pj c L j = 20 log (43) + nj c where the first part is path loss component based on free-space path loss (FPL) model which involves dp j that is the distance of each node from primary user and fc is our working frequency that is denoted to be 2.4 GHz, and c is the speed of light. The second part is a real Gaussian random variable with zero mean and standard deviation 3 according to large scale log-normal shadowing [24], [25]. Considering the fact that the typical circuit power consumption of ZigBee is approximately 40 mW, the energy consumed

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for listening is approximately 40 nJ. The processing energy related to the signal processing part in the transmit mode for a data rate of 250 kb/s, a voltage of 2.1 V, and current of 17.4 mA is approximately 150 nJ/bit. Since we use one bit per decision, the sensing energy of each cognitive sensor is Cs = 190 nJ [26], [27]. Assuming a data rate of 250 kb/s and a transmit power of 20 mW, Ct-elec = 80 nJ. The eamp to satisfy a receiver sensitivity of −90 dBm is 40.4 pJ/m 2 [15]. We also select decision threshold () as a multiple of the noise power. We compare our proposed algorithm with the following algorithms. 1) Minimum energy algorithm (MEA): in this algorithm, sensors are sorted in ascending order according to their distances from the FC and nodes with minimum distances are selected for sensing the channel so that Pd > β is satisfied. Number of sensing nodes is less than M. If MEA can find the nodes which satisfy Pd > β constraint, then its answer is near optimal due to selecting the nodes with minimum distances from the FC. 2) Maximum detection probability algorithm (MDPA): in this algorithm, sensors are sorted according to their Pd j s in descending order. Therefore, the nodes with the maximum Pd j are selected, so that the number of selected nodes is less than M and Pd > β constraint is satisfied. MDPA finds the solution for the algorithm if any solution exists. 3) Random sensor selection algorithm (RSSA): in this algorithm, sensors are randomly selected for spectrum sensing, so that the number of selecting nodes is less than M. This algorithm has the minimum complexity to find the solution for our problem. A. Sensing Node Selection Simulation In Fig. 3 successful percent of finding solution for different algorithms that satisfy Pd > β are shown. This metric for every algorithm shows the ability of the algorithms in finding the answer when the problem constraints are satisfied. It is illustrated that MEESS algorithm is in accordance with MDPA algorithm, means that if there is a solution for the problem, then our proposed algorithm can find it. On the other hand, it is possible for MEA and RSSA to find no answer for the problem while it has a solution. Fig. 4 shows the average energy consumed for every algorithm in different number of nodes. All algorithms are compared when MEA algorithm finds a solution, because when MEA has a solution, i.e., the channel condition is good and MEA is near optimal. It is shown that MEESS has less energy consumption than MEA. MEA selects the nodes only according to their distances from the FC and it is possible to select the sensors with lower Pdi s. In order to reach Pd > β constraint, MEA needs more nodes, and then energy consumption increases, while MEESS in selecting nodes considers the distances between nodes and FC and their Pd j s together. Therefore, it has a better solution than MEA. MEA overlaps with EESS; because in EESS, number of sensing nodes is not considered and the distance

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30

100

MEESS EESS RSSA MDPA MEA

99.5 A verage num ber of sensing nodes

successfl percent of finding solution

25 99 98.5 98 97.5 97 MEESS EESS RSSA MEA MDPA

96.5 96 95.5

10

0 5

10

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25 30 Number of nodes

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40

45

50

5

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25 30 Number of nodes

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Fig. 5. Average number of sensing nodes for different number of nodes for α = 0.1 and β = 0.9.

340

100

MEESS EESS RSSA MDPA MEA

320

99.5 successfl percent of finding solution

330

E nergy in nJ

15

5

Fig. 3. Successful percent for finding solution in different number of nodes for α = 0.1 and β = 0.9.

310

300

290

280

270

20

99 98.5 98 97.5 97 MEESS EESS RSSA MEA MDPA

96.5 96 95.5

5

10

15

20

25 30 Number of nodes

35

40

45

50

Fig. 4. Energy consumed for different number of nodes for α = 0.1 and β = 0.9.

between each node and the FC becomes more important than its probability of detection. Hence, EESS algorithm consumes the same energy similar to MEA. In all algorithms, when the number of nodes increases, network consumes less energy in spectrum sensing because nodes become closer to each other. In Fig. 5 the average number of sensing nodes for different algorithms is shown. It is clear MDPA uses the minimum number of nodes. Our algorithm and MEA are very close to MDPA. This shows our algorithm consumes minimum energy while maintaining Pd > β constriant. RSSA algorithm has the maximum number of sensing nodes. The results are also obtained for α = 0.05 and β = 0.95. It means that we consider more difficult conditions for algorithms to select sensing nodes. In fact, by reducing

5

10

15

20

25 30 Number of nodes

35

40

45

50

Fig. 6. Successful percent for finding solution in different number of nodes for α = 0.05 and β = 0.

α, maximum number of sensing nodes is decreased while by increasing β, more nodes should sense the spectrum so that the energy consumption increased. Fig. 6 shows successful percent of finding answer for different algorithms. It can be shown that MEESS can follow the solutions for our problem. Small α provides more opportunities for secondary users to employ the idle channel while large β decreases the interference of the secondary user transmission with the primary user activity. In comparison with Fig. 3, it shows that the successful percent of finding answer is reduced for smaller number of nodes. In Fig. 7, MEESS consumes less energy than all other algorithms, even less than MEA. It is shown that, with selection of less α and more β, energy consumption for smaller number of sensor nodes increases because more nodes should be selected

NAJIMI et al.: A NOVEL SENSING NODES AND DN SELECTION METHOD

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340 MEESS EESS RSSA MDPA MEA

330

E nergy in nJ

320

310

300

290

280

Fig. 7. β = 0.

5

10

15

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25 30 Number of nodes

35

40

45

50

Fig. 8.

Energy consumed for different number of nodes for α = 0.05 and

to satisfy the constraint on Pd . It is important to note that our solution is not dependent on the selection of α and β. On the other hand, our algorithm can find the near optimal answer which consumes less energy in spectrum sensing while obtaining Pd > β constriant, in different conditions of the channel between each node and primary user. The proof of optimality of the proposed MEESS algorithm is very hard, because of integer nature of the primary problem, but in comparison with MDPA algorithm and MEA algorithm, it can be concluded that 1) This algorithm notably finds the solution for the problem even in bad channel conditions (in these conditions, the MDPA solution is optimum), while energy consumption of the proposed algorithm is less than MEA algorithm (i.e., in good channel conditions MEA is near optimal). On the other hand, MEESS algorithm is optimal in the extreme limit.

FCDNS algorithm to select DN.

300 MEESS without DN selection ESMEESS MEESS with DN selection FCDNS

295

290 E nergy in nJ

270

285

280

275

270

5

10

15

20

25 30 Number of nodes

35

40

45

50

Fig. 9. Energy consumed for different number of sensor nodes for α = 0.1 and β = 0.9.

B. Decision Node and Sensing Nodes Selection Simulation In this section, we investigate the performance of the decision node (DN) and sensing nodes selection together in minimizing the total energy consumed. We compare the energy consumption in different algorithms. 1) MEESS algorithm without using DN selection. 2) MEESS algorithm using DN selection. 3) Exhaustive search algorithm in combination with MEESS (ESMEESS). 4) Four clusters for DN selection (FCDNS) algorithm: in this algorithm, the environment is divided into four squares and four nodes nearest to the middle of the squares are candidates as DNs. MEESS algorithm is done for every DN candidate, then one DN candidate which makes less energy consumption, is considered as the final DN as it is shown in Fig. 8.

In Fig. 9 the average energy consumption for different number of nodes in different algorithms is shown. It is clear that MEESS using DN selection can help to reduce energy consumption in spectrum sensing. MEESS using DN and ESMEESS algorithms are close to each other but our algorithm is simpler than ESMEESS algorithm, because it has less complexity. FCDNS algorithm also has much less energy consumption than MEESS without DN selection. Fig. 10 shows DN selection in the scenarios in which network has different dimensions. Our MEESS algorithm with DN selection consumes less energy than MEESS algorithm in different environments. This difference increases specially in large dimensions and shows that selecting DN and sending results to the FC using DN is very effective in saving energy.

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-7

750 3.05

650

Convergence Analysis of the our Proposed Algorithm

MEESS without DN selection ESMEESS FCDNS MEES•S with DN selection

700

E nergy in nJ

600 550 500 450 400 350 300 250 50

100

150

200 250 300 350 Different environment

400

450

500

Fig. 10. Energy consumption for different environments for α = 0.1 and β = 0.9.

x 10

MEESS 3

2.95

2.9

2.85

2.8

2.75

2.7

0

10

Fig. 12.

20

30 40 Number of iterartions

50

60

Convergence of MEESS for different iterations.

288

IX. C ONCLUSION

ESMEESS MEESS with DN selection FCDNS

286 284

E nergy in nJ

282 280 278 276 274 272 270 50

100

Fig. 11.

150

200 250 300 350 Different environment

400

450

500

Energy consumption in different environments.

In this case, our algorithm is very close to ESMEESS algorithm again. Fig. 11 is the focused version of Fig. 10. It is obvious that in large environments, the difference between FCDNS and ESMEESS algorithms becomes greater. However, simulation results show that we can use a simple clustering scheme similar to FCDNS to select DN, which can save energy significantly, because the difference between ESMEESS and FCDNS is 13 nJ in the worst state. Fig. 12 shows the convergence analysis for our proposed algorithm in finding the answer for different iterations. Note that the convergence is evaluated according to the energy consumption for the steps that reach the optimal λ. It is clear, in the 28t h iteration, energy consumption is fixed and minimum its value is obtained.

Under heavily faded environments, a faded primary signal may become extremely weak when it reaches the detector that could be declared as a spectrum white space incorrectly. This could eventually lead to causing harmful interference to the primary system if the secondary users transmit on this frequency. Therefore, Cooperation among cognitive sensors in spectrum sensing is essential for mitigating the effects of shadowing and fading, and consequently, accurate sensing. However, by increasing the number of users, we spend a lot of energy on observation, processing and transmission. Moreover, increasing the number of users for spectrum sensing does not improve the detection performance of the system linearly. Hence, it is not necessary to exploit all the users all the time for spectrum sensing. In this work, we presented an energy-efficient spectrum sensing technique based on on/off mode and finding the best location of DN policies. Our goal was to minimize the total energy consumption in spectrum sensing subject to a global detection performance constraint by determining the sensors which sense the spectrum. We obtained a closed-form equation and optimal conditions due to KKT to reduce energy consumption and satisfy Pd > β while having a linear complexity. We solved our problems using convex optimization methods. Our solution is independent from the distribution of Pd and can be applied to any fusion rule like AND and “k-out-of-N” nodes. R EFERENCES [1] J. Mitola and G. Q. Maguire, “Cognitive radio: Making software radios more personal,” IEEE Pers. Commun. Mag., vol. 6, no. 4, pp. 13–18, Aug. 1999. [2] Notice of Proposed Rule Making and Order: Facilitating Opportunities for Flexible, Efficient, and Reliable Spectrum Use Employing Cognitive Radio Technologies, FCC Standard 03-108, Feb. 2005. [3] A. Ghasemi and E. S. Sousa, “Collaborative spectrum sensing for opportunistic access in fading environments,” in Proc. IEEE 1st Symp. Dynamic Spectr. Access Netw., Nov. 2005, pp. 131–136.

NAJIMI et al.: A NOVEL SENSING NODES AND DN SELECTION METHOD

[4] E. Visotsky, S. Kuffner, and R. Peterson, “On collaborative detection of TV transmissions in support of dynamic spetrum sharing,” in Proc. IEEE 1st Symp. Dynamic Spectr. Access Netw., Nov. 2005, pp. 338–345. [5] S. M. Mishra, A. Sahai, and R. W. Brodersen, “Cooperative sensing among cognitive radios,” in Proc. IEEE Int. Conf. Commun., vol. 4. Jun. 2006, pp. 1658–1663. [6] A. Ghasemi and E. S. Sousa, “Impact of user collaboration on the performance of opportunistic spectrum access,” in Proc. IEEE Veh. Technol. Conf., Sep. 2006, pp. 1–6. [7] A. Ghasemi and S. Sousa, “Spectrum sensing in cognitive radio networks: Requirements, challenges and design trade-offs,” IEEE Commun. Mag., vol. 46, no. 4, pp. 32–39, Apr. 2008. [8] C. Sun, W. Zhang, and K. B. Letaief, “Cooperative spectrum sensing for cognitive radios under bandwidth constraints,” in Proc. IEEE Wireless Commun. Netw. Conf., Mar. 2007, pp. 1–5. [9] S. Appadwedula, V. V. Veeravalli, and D. L. Jones, “Decentralized detection with censoring sensors,” IEEE Trans. Signal Process., vol. 56, no. 4, pp. 1362–1373, Apr. 2008. [10] S. Appadwedula, V. V. Veeravalli, and D. L. Jones, “Energy-efficient detection in sensor networks,” IEEE J. Sel. Areas Commun., vol. 23, no. 4, pp. 693–702, Apr. 2005. [11] S. Appadwedula, V. V. Veeravalli, and D. L. Jones, “Robust and locallyoptimum decentralized detection with censoring sensors,” in Proc. IEEE Inf. Fusion Conf., vol. 1. Jul. 2002, pp. 56–63. [12] C. Rago, P. Willett, and Y. Bar-Shalom, “Censoring sensors: A lowcommunication-rate scheme for distributed detection,” IEEE Trans. Aerosp. Electron. Syst., vol. 32, no. 2, pp. 554–568, Apr. 1996. [13] E. Peh and Y. Ch. Liang, “Optimization for cooperative sensing in cognitive radio networks,” in Proc. IEEE Commun. Society, Wireless Commun. Netw. Conf., Mar. 2007, pp. 27–32. [14] S. Atapattu, C. Tellambura, and H. Jiang, “Spectrum sensing via energy detector in low SNR,” in Proc. IEEE Int. Commun. Conf. Commun. Soc., Jun. 2011, pp. 1–5. [15] S. Maleki, A. Pandharipande, and G. Leus, “Energy-efficient distributed spectrum sensing for cognitive sensor networks,” IEEE Sensors J., vol. 11, no. 3, pp. 565–573, Mar. 2011. [16] I. F. Akyildiz, B. F. Lo, and R. Balakrishnan, “Cooperative spectrum sensing in cognitive radio networks: A survey,” Elsevier Phys. Commun., vol. 4, no. 1, pp. 40–62, Mar. 2011. [17] G. Ganesan and Y. Li, “Agility improvement through cooperative diversity in cognitive radio,” in Proc. IEEE Global Telecommun. Conf., Dec. 2005, pp. 2509–2513. [18] Y.-C. Liang, Y. Zeng, E. C. Peh, and A. T. Hoang, “Sensing-throughput tradeoff for cognitive radio networks,” IEEE Trans. Wireless Commun., vol. 7, no. 4, pp. 1326–1337, Apr. 2008. [19] W. Heinzelman, A. P. Chandrakasan, and H. Balakrishnan, “An application-specific protocol architecture for wireless microsensor,” IEEE Trans. Wireless Netw., vol. 1, no. 4, pp. 660–670, Oct. 2002. [20] J. Ammer and J. Rabacy, “The energy-per-useful-bit metric for evaluating and optimizing sensor network physical layers,” in Proc. IEEE Int. Workshop Wireless Ad-Hoc Sensor Netw., vol. 2. Sep. 2006, pp. 695–700. [21] B. Yang, K. B. Letaief, and R. S. Cheng, Z. Cao, “Timing recovery for ofdm transmission,” IEEE J. Sel. Areas Commun., vol. 18, no. 11, pp. 2278–2291, Nov. 2000. [22] S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge, U.K.: Cambridge Univ. Press, 2004. [23] Part 15.4:Wireless Medium Access Control (MAC) and Physical Layer(PHY) Specifications for Low-Rate Wireless Personal Area Networks(WPANs), IEEE Standard 802.15.4, 2006. [24] B. Sklar, “Rayleigh fading channels in mobile digital communication systems part1:Characterization,” IEEE Commun. Mag., vol. 35, no. 7, pp. 90–100, Jul. 1997. [25] Y. Ma, D. I. Kim, and Z. Wu, “Optimization of ofdm-based cellular cognitive radio networks,” IEEE Trans. Commun., vol. 58, no. 8, pp. 2265–2276, Aug. 2010.

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[26] S. Maleki, A. Pandharipande, and G. Leus, “Energy-efficient distributed spectrum sensing for cognitive sensor networks,” in Proc. 35th Annu. Conf. IEEE Ind. Electron. Soc., Nov. 2009, pp. 2642–2646. [27] S. Maleki, A. Pandharipande, and G. Leus, “Energy efficient distributed spectrum sensing with convex optimization,” in Proc. 3rd Int. Workshop Comput. Adv. Multi-Sensor Adapt. Process., Nov. 2009, pp. 396–399.

Maryam Najimi received the B.Sc. degree in electronics from Sistan and Baluchestan University, Zahedan, Iran, in 2004, and the M.Sc. degree in telecommunication systems engineering from the K. N. Toosi University of Technology, Tehran, Iran. She is currently pursuing the Ph.D. degree in communications at the Babol University of Technology, Babol, Iran. Her current research interests include spectrum sensing in wireless cognitive sensor networks.

Ataollah Ebrahimzadeh received the Ph.D. degree in electrical engineering from Ferdosi University, Mashhad, Iran in 2007. He is currently an Associate Professor with the Faculty of Electrical and Computer Engineering, Babol University of Technology, Babol, Iran. He has authored or co-authored more than 50 papers in international journals and conferences. His current research interests include signal processing and artificial intelligence. Dr. Ebrahimzadeh is a reviewer of international conferences and journals.

Seyed Mehdi Hosseini Andargoli received the B.Sc. degree in electronics engineering from Shahed university, Tehran, Iran, in 2004, and the M.Sc. and Ph.D. degrees in telecommunication systems engineering from the K. N. Toosi University of Technology, Tehran, in 2009 and 2011, respectively. He is currently an Assistant Professor with the Department of Electrical and Computer Engineering, Babol Noshirvani University of technology, Babol, Iran. His current research interests include resource allocation of cellular networks, cognitive radio networks, relay networks, sensor networks, optimization, and MIMO-OFDM systems.

Afshin Fallahi received the B.Sc. degree from the University of Tehran, Tehran, Iran, the M.Sc. degree from Tarbiat Modares University, Tehran, and the Ph.D. degree from the University of Manitoba, Winnipeg, Canada, in 1996, 1999, and 2008, respectively, all in electrical engineering. His current research interests include modeling, analysis, and optimization of wireless networks.