A Novel Wireless Power Transfer-Based Weighed Clustering Cooperative Spectrum Sensing Method for Cognitive Sensor Networks

In a cognitive sensor network (CSN), the wastage of sensing time and energy is a challenge to cooperative spectrum sensing, when the number of cooperative cognitive nodes (CNs) becomes very large. In this paper, a novel wireless power transfer (WPT)-based weighed clustering cooperative spectrum sensing model is proposed, which divides all the CNs into several clusters, and then selects the most favorable CNs as the cluster heads and allows the common CNs to transfer the received radio frequency (RF) energy of the primary node (PN) to the cluster heads, in order to supply the electrical energy needed for sensing and cooperation. A joint resource optimization is formulated to maximize the spectrum access probability of the CSN, through jointly allocating sensing time and clustering number. According to the resource optimization results, a clustering algorithm is proposed. The simulation results have shown that compared to the traditional model, the cluster heads of the proposed model can achieve more transmission power and there exists optimal sensing time and clustering number to maximize the spectrum access probability.

interconnecting wires, through installing a RF energy-conversion circuit that converts the collected electromagnetic energy to the electrical energy for supplying the system operations [20]. In [21], the authors consider a stochastic-geometry model in which PNs and CNs are distributed as independent homogeneous Poisson point processes and communicate with their intended receivers at fixed distances; each PN is associated with a guard zone to protect its intended receiver from CN interference, and at the same time delivers RF energy to CNs located in its transferring zone. However, the transferred energy can be used only for CN transmission but not for spectrum sensing. Most of the research work on spectrum sensing focuses on using the received signal energy to sense frequency spectrum, but the energy cannot be utilized to supply the sensing operation, thus yielding both energy consumption and sensing cost. The contributions of the paper can be listed as follows: (1) The paper firstly combines WPT and spectrum sensing and proposes a novel WPT-based weighed clustering spectrum sensing, in which the common CNs of each cluster receive the RF energy of the PN signal that is then transferred to the cluster head, in order to supply the energy consumption of sensing and cooperation of the cluster head. (2) In our proposed model, fewer nodes will participate in cooperative spectrum sensing, thus the energy and time used for spectrum sensing may decrease greatly. Moreover, the common CNs may transfer the received wireless power to the cooperative nodes, thus the transmission power of the cooperative nodes can be guaranteed. (3) A joint resource optimization problem is formulated to maximize the spectrum access probability of the CSN through jointly optimizing sensing time and clustering number. With the solutions of the proposed optimization problem, the CSN can obtain larger spectrum access probability while guaranteeing the spectrum sensing performance.
The rest of this paper is organized as follows: In Section 2, both energy detection and weighed cooperative spectrum sensing are introduced. WPT-based clustering cooperative spectrum sensing and the joint resource optimization problem are presented in Section 3. Following this, the clustering algorithm is described in Section 4. Simulations and discussions are provided in Section 5 and the conclusions are finally drawn in Section 6.

Spectrum Sensing Models
Common notation as summarized in Table 1 is used throughout this paper.

Energy Detection
In CSN, each CN finds it difficult to obtain any prior information of the PN signal, thus energy detection is used to sense the PN without needing any information about the detected signal. By comparing the energy statistic of the PN signal to a properly set decision threshold, energy detection declares the presence of the PN when the energy statistic is above the threshold, while deciding the absence of the PN when the energy statistic is below the threshold. Owing to its operating principle that measures the signal energy, the energy detection performance is independent on any prior information of the detected signal. The detected signal i y received by the CN i is given by a binary hypothesis problem as follows [22]: where M is given by M = τfs. From Equation (1), the energy statistic of i y is given as follows: Since y(1), y (2)

Weighed Cooperative Spectrum Sensing
If the PN is experiencing severe fading and shadowing conditions, the energy detection performance can be greatly decreased. One of the ways to improve spectrum sensing reliability is through cooperative spectrum sensing. Cooperative spectrum sensing is done by combining all the energy statistics from the local sensing of the CNs and performing energy detection to make a final decision at the fusion center. The performance of cooperative spectrum sensing is improved by achieving a sensing diversity gain that is provided by the different sensing paths from multiple CNs. Even though one node has failed to detect the presence of PN, the other nodes may also help to detect the PN.
In centralized cooperative spectrum sensing, a fusion center combines the collected local sensing information of all the cooperative CNs and decides which channel should be used. Then the decision is broadcast to all the CNs. The centralized cooperative spectrum sensing can control the cooperative CNs effectively, collect enough spectrum sensing information and thus greatly improve the sensing performance. In distributed cooperative spectrum sensing, the CNs exchange their sensing information mutually and each CN only maximizes its own spectrum sensing performance, thus both information share degree and spectrum sensing performance are very low [23]. Moreover, without the management of a fusion center, the sensing information will be exchanged frequently among the CNs and thus the sensing time may be very long. Hence, in this paper we adopt centralized cooperative spectrum sensing to obtain more sharing information.
The frame structure of cooperative spectrum sensing-based CSN is divided into local sensing time, cooperative time and transmission time, as shown in Figure 1 [24]. In the local sensing time, each CN senses to obtain the local energy statistic of the PN, and in the corresponding time slot of the cooperative time, the CN forwards its energy statistic to the fusion center through a public control channel. An aggregate energy statistic is obtained by combining all the local energy statistics at the fusion center, which is then compared to a set threshold to get the final decision on the presence of the PN. If the PN is determined to be absent, the CSN will transmit data in the transmission time.
The weighed cooperative spectrum sensing is shown in Figure 2. Supposing that there are k CNs in the cooperative spectrum sensing, from Equation (2), the combined energy statistic is given as follows: where i  satisfies  If the reporting channel to the fusion center is perfect, substituting Equation (5) into Equation (4), the cooperative probabilities of false alarm and detection are given as follows: ( 1) The cooperative missed detection probability is given by Q m = 1− Q d . Q d is often set fixedly according to the interference sufferance of the PN, and we try to decrease f Q for improving the spectrum access of the CSN. From Equation (6), f Q is related with Q d as follows:  to minimize f Q as follows: where the maximum is achieved when = /√∑ 2 =1 for i = 1, 2, …, k. Substituting Equation (8) into Equation (7), the minimal false alarm probability is given as follows: . However, if the reporting channel to the fusion center is in fading, from Equation (6), the cooperative probabilities of false alarm and detection are given as follows: In a Rayleigh fading channel, the probability density function (PDF) of the sensing SNR of CNi is given as follows: where  is the average SNR of all the CNs. Thus the average cooperative detection probability is given as follows:

Wireless Power Transfer (WPT)
WPT generally refers to the transmissions of electrical energy from a power source to one or more electrical loads without any interconnecting wires. WPT can be realized by installing an energy-conversion circuit in the RF front end of a wireless communication system, as shown in Figure 3 [15]. The wireless power receiver acquires the alternating current (AC) signal from the wireless power transmitter and passes the AC signal through a band-pass filter to ensure that it is correctly matched to the rectifying circuit. Then the AC signal is converted to the direct current (DC) signal through a rectifying circuit that involves some number of diodes and capacitors. The DC voltage is finally obtained after filtering out the fundamental and harmonic signals from the DC signal through a low-pass filter. However, some of the signal energy may be reradiated to the outside environment in the energy-conversion process, thus we assume that 01    is the electromagnetism-to-electricity conversion efficiency, which is determined by the element characters of the energy-conversion circuit.

Clustering Cooperative Spectrum Sensing
From Figure 1, it is seen that the cooperative time will be prolonged as the cooperative nodes increases, which yields to shorten the transmission time greatly. In addition, one node, whose path to the fusion center is in fading, may forward false sensing information to the fusion center, thus the cooperative sensing performance is degraded. Hence, to guarantee the transmission quality of the CSN, only some of the CNs with better single sensing performance can be chosen to cooperatively sense the PN. In this paper, WPT-based clustering cooperative spectrum sensing is proposed, in which all the CNs are divided into several clusters, the favorable cluster heads are selected to perform weighed cooperative spectrum sensing and the common CNs of each cluster transfer the RF energy received from the PN signal to the corresponding cluster head, as shown in Figure 4. Since we select the nodes whose mutual distances are nearest as one cluster, the path loss between the common CN and the cluster head is so less that it can be ignored. With the number of the CNs D and the number of the cluster heads (i.e., clustering number) K, the number of CNs in each cluster is / L D K    . The CN can access the PN spectrum both in the absence of the PN with accurate detection and in the presence of the PN with missed detection. Hence, the spectrum access probability of the CN is given as follows: When the PN is present, the common CN can receive the transferred energy of the PN signal in the sensing time, cooperative time and transmission time. Hence, the transferred PN energy of the common CN in cluster i is given as follows: Each common CN uses the transferred PN energy to drive the power amplifier to generate the RF signal that is transferred to the cluster head in the cooperative time. Then the cluster head receives the RF energy of L − 1 CN signals and converts the RF energy to the electrical energy again. Suppose that the electricity-to-electromagnetism conversion efficiency is 0 < η < 1 that is decided by the element characters of the power amplifier. From Equations (14) and (15), the aggregate transferred energy of the cluster head is given as follows: where with 1 d Q  , the maximum transferred energy is given by: In the traditional clustering cooperative spectrum sensing [12,13], the information transmission power of each cluster head is given as follows: where e p is the sensing power and c p is the cooperative power. However, in the WPT-based clustering cooperative spectrum sensing, the information transmission power of each cluster head is given as follows: ,max 0 where obviously, we have ′ > . In the proposed model, to guarantee that all the initial energy is used for data transmission of the cluster head, we let ̂, ≥ + , thus the transmission power of the cluster head is not less than that of the common CNs. From Equation (17), the expected power level of the transferred energy is given as follows [25]: Thus the distance range of wireless power transfer is given by: where L is the path loss factor, GT is the transmit antenna gain, GR is the receive antenna gain and λ is the wavelength emitted.

Cooperative Overhead and Wireless Power Transfer Antenna
The cooperative overhead of WPT-based clustering cooperative spectrum sensing happens in the clustering process and sensing process. In the clustering process, the fusion center firstly broadcasts the clustering information to all the cluster heads in the inter-cluster broadcasting slot with the length of 1  , then to avoid mutual interference, the cluster heads broadcast the beacon to their corresponding cluster nodes in K special inner-cluster broadcasting slots with the length of 2  , and finally each common CN joins the corresponding cluster according to its received beacon in the grouping slot with the length of 3  . In the sensing process, each common SU transfers its received PN energy to the corresponding cluster head in the energy transfer slot with the length of 4  , then to avoid information conflicts, the cluster heads send their sensing information to the fusion center in K special reporting slots with the length of 5  . Thus the total cooperative time overhead is given as follows: from which, the average cooperative time overhead of each SU is given by: Since both the common CN and cluster head must transfer and receive the RF energy, the WPT antennas adopted by them are often the rectifying antenna that converts RF energy to electrical power, whose structure is shown in Figure 5.
As shown in Figure 1, in the local sensing time, the common CNs transfer RF energy while the cluster heads perform energy detection; in the cooperative time, since each cluster head only uses one of k slots to report the sensing information to the fusion center, it can receive the RF energy of the common CNs in the other k − 1 slots. Moreover, the cluster head cannot receive the transferred energy in the sensing time because of spectrum sensing, thus it can only receive energy in the transmission slot if the presence of the PN is detected accurately. Accordingly, the cluster head receives the transferred CN energy and PN energy in the cooperative slot and transmission slot, respectively. The transferred energy can be used in the transmission slot for increasing the transmission energy and compensating the sensing consumption, thus the transmission power of the cluster head can be improved.

Joint Resource Optimization
Our goal is to maximize the spectrum access probability of the CSN by jointly optimizing sensing time  and the clustering number K, subject to the constraints that the detection probability is above the lower limit of detection performance and the aggregated transferred energy of the cluster head can supply the electrical energy dissipated in the cooperative spectrum sensing. This optimization problem is given as follows: where α is the lower limit of detection probability and is the minimum transmission power of the CN. From Equation (7), Q f and Q d have the same monotonicity and therefore PAcc improves as Q d decreases, i.e., PAcc achieves the maximum only if Q d = α. Substituting Q d = α and Equation (9) (16) and (26) into Equation (25) and noting that the least transferred energy of the cluster head must satisfy the constraint: where ({ } =1 ) = √ ∑ 2 =1 and φ = P(H1)(1 -α). Substituting Equation (16)  We use the alternating direction optimization (ADO) to solve Equation (28). We formulate two sub-optimization problems about one of the two variables and k by fixing the other variable with an initial value, respectively, and obtain the optimal solution through optimizing these two sub-optimization problems alternately until both of and k are convergent [26]. Firstly, we initialize where is any integer within interval (0, min( , N)) and select the K0 where we have used the fact that Q(x) is a decreasing function and upper bounded by 1. Equation (32) means that PAcc(τ) increases when τ is small and decreases when τ approaches T', thus there is a maximum point within interval (0, T'), which can be obtained through using the half searching algorithm. Then Since ≥ ( ) and ≥ , with given ≥ 0 , the optimal solution to Equation (30) is obtained as follows: The second sub-optimization problem is how to find an optimal K for maximizing with the initialization = 0 = * ( 0 ). From Equation (28), this sub-optimization problem is given as follows: Since K is an integer, it is not computationally expensive to search through K from ψ(τ0) to min ( ′′ , ). The optimal solution to Equation (35) is calculated as follows: Based on ADO and half searching, we obtain the jointly optimal solution to Equation (25) using the Algorithm 1 through alternately optimizing Equations (30) and (35). Hence, the maximum spectrum access probability is given by ( * , * ). must collect some information from each CN such as the distances from the fusion center and PN. Based on the distance information, the fusion center assigns the cluster head for each cluster through the clustering algorithm and then broadcasts the clustering information to all the CNs. The message broadcast by the fusion center includes the ID of the elected cluster head, the sensing time and the cooperative time.
Here, we adopt K-center clustering method to divide D CNs into K clusters and choose K reference nodes as the initial cluster heads. The selection of the reference nodes must focus on improving the sensing performance (i.e., the distance from the PN is short) and decreasing the cooperative overhead (i.e., the distance from the fusion center is short). The reference nodes are seen as K initial clusters and the other CNs are gathered into the nearest cluster around them. The clustering algorithm is described in Algorithm 2, where we define that s is the coordinate of node s, the coordinate of the cluster center is until: all the CNs in each cluster are not changed.

Simulations and Discussion
In 27774 0 E = 10 μJ, the electromagnetism-to-electricity conversion efficiency is 0.5   and the electricity-toelectromagnetism conversion efficiency is  = 0.5. Figure 6 compares the false alarm probability f Q of weighed and unweighed cooperative spectrum sensing with different detection probability d Q and the clustering number K = 1, 3, 5, 10. It is seen that f Q of weighed cooperative spectrum sensing is lower than that of unweighed cooperative spectrum sensing, because the local sensing performance of each CN is different and the weighed cooperative spectrum sensing may improve the combined weight of the accurate sensing information while decreasing that of the false sensing information, based on the sensing SNR. f Q decreases as K increases, which indicates that the cooperative sensing performance improves as the cooperative nodes increase. It is seen that f Q increases as d Q improves, yielding to decrease the spectrum access of the CN. Thus to improve the spectrum access, d Q must acquire its lower bound. It is also seen that when K = 1, f Q of weighed sensing approaches that of unweighed sensing, because if the clustering number K = 1, there is only one cluster head to perform spectrum sensing and thus the weighed combination has no any function on improving the sensing performance.  Figure 7a,b compare the detection probability with different clustering number in a perfect channel and a Rayleigh fading channel, respectively. It is seen that the detection probability of clustering cooperative sensing is nearly same as that of the cooperative sensing without clustering in a perfect channel, because the spectrum sensing performance of each cluster head is good enough and increasing the clustering number will not improve the sensing performance too much. However, the detection probability of clustering cooperative sensing can obviously improve as the clustering number increases in a Rayleigh fading channel. Hence, we should note that the clustering cooperative spectrum sensing can only improve the sensing performance if the CN is in fading mode. Figure 8 compares  detection probability m Q of the traditional and WPT-based clustering cooperative spectrum sensing. It is seen that m Q of the WPT-based clustering sensing is a little larger, because the common CNs transfer wireless power instead of sensing information to the cluster head in the WPT-based clustering sensing and the combined information at the fusion center is less comprehensive. However, in the WPT-based clustering sensing, we just select the nodes with better sensing performance as the cluster heads and thus the cooperative sensing performance may approach that of the traditional clustering sensing.   It is seen that the minimum  reduces with the decreasing of K, because the cluster nodes may increase and transfer more wireless power to the cluster head. Figure 10a,b compare the detection probability and the proportion of cooperative CNs of different spectrum sensing methods: the proposed WPT-based weighed clustering cooperative spectrum sensing and the cooperative spectrum sensing with penalty-based weight adjustment mechanism (PWAM) [27], respectively. It is seen that the detection probability of the proposed WPT-based clustering cooperative sensing is a little lower than that of the PWAM-based cooperative sensing, but the proportion of cooperative CNs in the proposed sensing model may decrease greatly as SNR increases, because we only select a few favorable cluster heads to perform cooperative spectrum sensing.   Figure 11 compares BER of the reporting information with different clustering number. It is seen that BER decreases as the clustering number increases, because more favorable cluster heads are chosen to report sensing information to the fusion center. Figure 12 compares the information transmission power t p of the cluster heads in the traditional clustering cooperative spectrum sensing [12] and the proposed WPT-based clustering cooperative spectrum sensing, with different sensing time  . It is seen that t p of WPT-based cooperative spectrum sensing is larger. t p of the traditional clustering sensing decreases as  increases, because the dissipative sensing power increases with  . However, t p of the WPT-based clustering sensing improves with  , because the transferred PN energy also increases with  .     Figure 13 indicates the spectrum access probability with different sensing time τ and clustering number K. It is seen that there indeed exists an optimal set of τ and K that maximizes , and when τ = 1.2 ms and K = 10, the maximum = 0.3632. Figure 14 shows versus K = 1, 5, 10, 15 with different τ, where the convex curve of proves the convex optimization of Equation (30). firstly increases and then decreases as τ increases, because the sensing performance improves while the transmission time decreases and therefore there is a tradeoff between sensing and transmission. The maximum of K = 15 is larger than that of K = 1 but smaller than that of K = 10, because the sensing performance improves while the cooperative overhead increases as K increases and therefore there is also a tradeoff between sensing and cooperation. Figure 15 compares the theoretical and practical maximum versus the sampling frequency fs = 1, 2, 3 kHz, with different detection probability Q d . The practical maximum is obtained by the proposed joint optimization algorithm. It is seen that the practical maximum accords with the theoretical maximum.

Transmission Performance Comparison
decreases as Q d increases, because Q f increases as Q f , which decreases the spectrum access of the CN.    increases but decreases as K increases, because more RF energy of the PN signal will be transferred if the PN is present for a longer time, however less common CNs will transfer energy to the cluster head if the number of the cluster nodes decreases.

Conclusions
In this paper, a WPT-based weighed clustering cooperative spectrum sensing model is proposed to improve sensing performance while decreasing both cooperative overhead and energy consumption. In order to supply the electrical power for sensing and cooperation of the cluster head, the RF energy of the PN signal is converted by the common CNs of each cluster and transferred to the corresponding cluster heads. Through jointly optimizing sensing time and clustering number, the spectrum access probability of the CSN is maximized. The simulation results have shown that compared to the traditional model, the cluster head of the proposed model can achieve more transmission power and there indeed exists an optimal set of sensing times and clustering numbers that maximizes the spectrum access probability.