Improved Beetle Antennae Algorithm Based on Localization for Jamming Attack in Wireless Sensor Networks

When checking and sensing external communication data, wireless sensor networks are susceptible to interfering signals with different frequencies. In order to track the location of the jamming attack point and deploy security defense mechanism, a minimum covered circle jamming attack localization algorithm based on the improved beetle antennae search algorithm is proposed. By comparing the different nodes, the relative coordinates of jamming points which are taken as the initial position of the beetle are determined, judging the fitness values of left and right antennae. Meanwhile, by introducing adaptive step size strategy and adjusting the flight distance, the position of beetle is updated to avoid falling into local extremum. Combining with the characteristics of fast convergence of beetle antennae search algorithm, the optimal solution is found. Using this algorithm, the minimum radius of the circle covered by the jammed nodes and the position of the center of the circle are solved, and the location of the jammer is realized. Simulation results show that, the proposed algorithm is more efficient than the existing algorithm with regard to runtime complexity. The proposed algorithm also excels at lowering the error rate and increasing position performance in different distribution types of networks with different nodes densities and other external factors, the proposed algorithm has lower error rate, better positioning performance in different distribution types of networks with different node densities and other external factors. The runtime complexity of the algorithm is small and the error range is uniform, proving the effectiveness of the algorithm.


I. INTRODUCTION
Wireless Sensor Networks (WSN) are a type of wireless network formed by self-organization and widely used in civil and military fields [1]- [4]. Distributed wireless sensor node groups are an important part of wireless sensor networks. The nodes with sensing and communication functions are deployed in or near the monitoring area responsible for collecting and transmitting data between sensors. Due to the exposed nature of wireless links, one critical security issue facing WSNs is jamming attacks targeting signal transmission. Jamming attacks are a special type of denial of service (DoS) attacks where malicious nodes interfere with normal co mmunication among legitimate nodes by sending out interference signals. During the process of data transmission, wireless sensors are susceptible to jamming signals with different frequencies, which may greatly endanger the integrity and confidentiality of the transmitted data, eventually impacting the normal operation of network transmission [5]. The jamming attacks can cause a variety of adverse consequences on the sensor networks within their radiation range. Therefore, when jammers appear, how to quickly detect and accurately locate their attack locations has become an urgent issue to be solved.
A traditional countermeasure for jamming attack is to use the physical layer technology to find the location of jamming sources and implement the security mechanism, such as VOLUME XX, 2021 direct sequence spread spectrum (DSSS) [6]. However, this method usually comes with high cost and consumes large amounts of power, bandwidth, and storage resources. Researchers also proposed some jamming avoidance strategies to defend against attack signals, such as channel surfing and slot channel [7], but these strategies often cause high computational complexity and need the support of corresponding hardware equipment, resulting in more communication overhead and additional resource investment.
Seeking a method that can not only precisely locate where the jamming attack source is, but also save energy consumption, is currently an emerging research field. Rantna, et al proposed a neuro fuzzy disengagement scheme to prevent interference attacks in a WSN, ensuring data transmission by separating the malicious nodes. This method has high throughput and packet delivery ratio (PDR), low latency, but high overhead [8]. Recently, Hu et al, proposed centroid localization (CL), CL algorithm is an algorithm that calculates the centroid of the polygon composed of anchor nodes sending information as the coordinate position of unknown nodes, but the positioning accuracy is low [9].
In this paper, a novel algorithm based on range-free positioning is proposed to locate the single jamming source through the minimu m coverage of the disturbed nodes in the sensor network. The objective of the research is to improve location accuracy and reduce computational complexity. The proposed algorithm is based on the beetle antennae optimization algorithm that beetle uses its two antennae to search the surrounding environment and move quickly to find the target solution. The rapid convergence of the beetle antennae optimization algorithm is combined with the accurate advantages of the minimu m coverage circle to determine the center of the minimu m coverage circle that can cover all disturbed nodes in the interference boundary. The algorithm assumes that there is a jamming boundary among specific nodes in the target network to analyze the distribution characteristics of nodes near the jamming area, consequently constructing a virtual node set on the jamming boundary. Using the minimu m circle coverage algorithm of curve fitting, the estimated position of the jamming source is found as the initial position of the beetle; then the fitness values of the two antennae of the beetle are compared to determine the updated position. Next, according to the coverage of the jamming range to different types of nodes, some new virtual points are constructed and these points are then refitted and corrected. Meanwhile, the step size of the beetle position is dynamically adjusted to make the beetle moving forward to a more accurate interference source, and eventually the center position and radius of the jamming range are obtained. The simulation results show that the proposed algorithm has good positioning time consumption and positioning accuracy in different distribution types of networks and different node densities.
The main contributions of this study are as follows: ① a single jamming source localization algorithm is proposed based on the swarm intelligence optimization algorithm; ② the traditional beetle antennae algorithm is improved by step size adaptation to overcome the defect where the beetle ma y fall into the local extreme value during position update; ③ Experimental simulation shows that the positioning accuracy of the algorithm is higher than that of the existing mainstream algorithms, and the algorithm also maintains good results in time complexity and positioning errors with different node distribution types and different node densities.
The remainder of the paper is organized as follows. Section 2 provides an introduction to minimu m covered circle (MCC), Beetle Antennae Search, and the improved algorithm of Beetle Antennae Search (IBAS). Section 3 explains in detail how IBAS works with the specific steps of minimu m covered circle. In Section 4, we present the simulation and the results about jamming localization in wireless sensor networks. We will conclude our paper with final remarks in Section 5.

II. MODEL AND ALGORITHM
Jammer positioning issue has always been a hot topic in the field of wireless sensor networks. Attackers would block the normal communication of a WSN by deploying jamming sources in the network and performing radio frequency (RF) interference within their radiation range. Because the jamming signal is gradually weakened by factors such as surroundings and terrain during transmission, whether a sensor is being attacked by jamming can be determined according to the change of its communication state. Chowdiry [10] describes how the attackers rely on the detailed knowledge of the network and how the network relies on the detailed knowledge of the attackers, such as interference probability, so that it can be detected. P. Poplip [11] describes the effects of a jamming attack in a mobile dedicated environment where the jammer uses radio waves to interrupt the signals in and out of the mobile nodes. G. Pavani [12] has proposed the packet hiding methods to prevent selective interference attacks and an improved version of anti-interference attack methods. The key to ensure the complete operation of the network is to determine the location of the jamming attack point timely and accurately by the disturbed nodes and remove the impact of the jamming attack.
According to different parameters used, the positioning algorith ms can be classified into ranging based positioning and range-free positioning [13]. The ranging-based me thod works by locating jammers according to the received communicat ion parameter attributes, including received signal strength (RSS) [14], frequency difference of arrival (FDOA), time d ifference of arrival (TDOA) [15], acceptance rate [16] and their joint positioning technology [17]- [18]. This method is relatively accurate in measuring the coordinates of jamming sources, but the errors in the actual co mmunication signal collection process may affect the accuracy of positioning results. The ranging position in VOLUME XX, 2021 algorith m needs to measure the signal strength, arrival time difference and other attributes between network nodes, and estimate the jamming source based on the measured values. Because the communication capability of the node under jamming attack has been partially destroyed and additional hardware overhead is required, the ranging positioning algorith m is not suitable for the determination of jamming attack point.
The range-free method analyzes the location distribution characteristics of target network nodes and uses geometric calculation technology for location. The implementation method is co mparat ively simp le, but the calculat ion error may fluctuate dramatically under various conditions. Virtual Force Iterative Localization [19] (VFIL) , a rangefree method, creates a circular jamming coverage using the centroid position and estimated jamming rad ius calculated by the CL algorith m. It uses the position of the interfered nodes and other nodes in the coverage to adjust the jamming coverage repeatedly until the final conditions are met. Cheng [20] et al have proposed a Double Circle Localization algorith m (DCL), wh ich uses the minimu m circu mscribed circle and the maximu m inscribed circle of the disturbed node to estimate the coordinates of the jamming source. The research based on range-free algorith ms only need the positions of certain nodes and do not require distance, angle and other information between nodes. The methods have been proved effective in determining the appro ximate jamming point location, and reduce the overhead of power consumption and computing cost [21]. Ho wever, the main problem of range-free algorith m lies in the major location erro r in high-density WSNs. In recent years, many researchers have tried to combine range-free algorith ms with signal ranging to propose new location algorithms. The positioning is extended to mobile jamming sources, directional jamming sources, and multip le jamming sources [22]. In addition, researchers also introduced optimization [23]- [24] or clustering algorithm [25] for positioning.
In this paper, an imp roved beetle antennae minimu m coverage location algorith m (IBAS) for range independent single interference source attack is proposed. The goal is to implement positioning in an intuitive way on the premise of less available parameters, so the algorithm could have improved accuracy and stability. Due to the impact of terrain, obstacles and other factors on the interference and communicat ion signals in practical applications, the node signal coverage may vary significantly in different scenarios. In order to facilitate the analysis and comparison of algorith ms, this paper mainly considers the deployment of network nodes under relatively flat terrain, and the coverage of interference is simplified to a circular area with the interference source as the center [26]- [27].

A. THE MINIMUM COVERED CIRCLE PROBLEM
The problem of min imu m covered circle was posed by Sylvester in 1857, which is an impo rtant analysis problem in mathematical applicat ion to find the min imu m c ircle that can cover a set of points on the plane. For a given set of points on a plane { } {( , )} , if there is a circle C so that all points i P are in the circle or on the circu mference, then circle C is the covering circle of the plane point set. A mong all covering circles, the covering circle with the smallest radius is called the minimu m covered circle of the point set. At present, one me thod to solve the minimu m covered circle problem involves the concept of -shell [28] in co mputational geometry, and the determination of  value is the challenge of this algorithm. Cutting-Plane method [29] is also used to solve the minimu m covered circle problem, but this method suffers low calculat ion speed. Some intelligent optimization algorith ms, such as the genetic algorith m can also be used to solve the min imu m circle covering problem, but the algorith m is co mp lex and the solution accuracy is relat ively low [30]. Th is paper seeks to solve the problem of minimu m covered circle based on the imp roved beetle antennae algorithm.
To solve the problem of minimu m covered circle given the point set {} i P on a plane, the key is the determination of the center and radius of the circle. Therefo re, the solution of the min imu m covered circle problem is equivalent to finding the extreme value of the objective function, and the objective function is the fitness function. The objective function can be expressed as follows: Where, ( , ) ab is the center of the minimu m covering circle and r is the radius of the minimum covered circle.

B. BEETLE ANTENNAE ALGORITHM AND ITS IMPROVEMENT
In this sub-section, the traditional Beetle Antennae Search algorith m is introduced first and then the imp roved algorithm of Beetle Antennae Search is presented.

1) BEETLE ANTENNAE ALGORITHM
Beetle Antennae Search (BAS) [31] is a heuristic optimization algorithm proposed by Jiang and Li in 2018. The idea behind this algorith m is that, odors of prey are equivalent to a function, whose values are corresponding to different points in the space. The two antennae of beetles are able to collect the smell values of two points near themselves, so the beetles can find the point with the most distinguished smell. The specific location of prey is equivalent to the maximu m point of the objective function, and the beetle moves towards the location with the distinguished odor step by step. Different fro m other optimization algorithms, BAS requires only one individual, that is, one beetle, which greatly reduces the amount of computation. Therefore, the process of beetle foraging is the optimization process of beetle antennae algorithm. The specific steps are as follows: 1). Set initial position direction vector of beetle: Where () rands is the random function and Dim is the dimension of space. Selection of step factor step : the initial step can be as large as possible, preferably equivalent to the maximu m length of the independent variable. Eq. (3) is used in each iteration: The value range of decline factor eta is between [0,1] , usually taken as 0.95 eta  ; t is the current nu mber of iterations and n is the total number of iterations. 2). Calculate the position coordinates of left and right antennae of a beetle: , then the beetle moves to the left; on the contrary, the beetle moves to the right. Next position update formula: Where, step represents the step size factor of t th  times iterations. In this paper, set the initial beetle step size 1 step  and () sign be the symbolic function to return the positive and negative of the parameter value.

2) IMPROVED BEETLE ANTENNAE ALGORITHM
According to the principle of trad itional beetle antennae algorith m, two primary parameters affecting the performance of the algorith m are the step size of the beetle's position update and its moving flight direction. In order to achieve a better optimization effect in locating the jamming source, and to overcome the disadvantage of the traditional beetle antennae algorith m, which is the tendency to fall into local ext reme value when updating the position, we adopted a dynamic adaptive strategy to calculate the step size o f the beetle. According to Eq. (3), the step size of beetles decreases linearly. The larger the step size step , the stronger the global search ability; the smaller the step size step , the stronger the local search ability of the beetle. In addition, BAS algorith m has the disadvantage of slow convergence speed in the later stage. In order to ensure the calculation efficiency and overcome the above problems, so that the step size of beetle position update can be dynamically adjusted, Eq. (3) is changed as the step size of Eq. (6) to improve the performance of the algorith m [32], where max step is the init ial step size of beetle, and the length is 1.
Where, temp is used as the compensation value to enable step to accurately search in a s mall range in the later stage. Generally, temp is in the range of [0,2] . After verificat ion, 1.5 temp  is taken in this paper. In the early stage of algorith m optimizat ion, beetle expands the search range in the solution space and quickly optimizes with a large step factor; In the later stage of algorith m optimizat ion, after the search solution stabilizes, we let the beetle adopt the small step length factor in order to make the optimizat ion mo re accurate. In order to mo re intuitively represent the length change of the two step updates, we use MATLA B to draw the change of each step length of the original step and the dynamically adjusted step as shown in Figure 1: It can be seen from Figure 1 that the step size of the typical beetle antennae algorithm changes uniformly every time. The beetle is easy to fall into local optimizat ion due to its step size exp loration within a certain range, resulting in solution errors. The step size adaptive strategy is introduced allo wing the optimized BAS algorith m to search in a wide range of space at the beginning of search. When iterating half way through, the step length shortens quickly, which narrows the search range. In the later stage of iteration, the speed of step length shortening slows down, which increases its global search ability and improves the search accuracy. The main steps of the IBAS can be su mmarized in the pseudo code shown in Algorithm 1 below: _ fbest store = the fitness of the best value; 12. return _ fbest store ;

C. JAMMING LOCATION MODEL
When a jamming attack occurs in wireless sensor networks, an approximately circular jamming range centered at the jamming source will be generated. The sensor nodes within the jamming range are affected so that they are not able to transmit normal informat ion with the nodes outside the jamming range. Although the signals from the communicat ion nodes at the edge of the jamming range are weakened during the attack, these nodes can still transmit some info rmation with nodes being outside the range [33], so as to obtain the location of these disturbed nodes. Quickly finding the jamming source through these nodes and adopting the corresponding security mechanism are key to recover the normal co mmun ication of wireless sensor networks.
The target network is based on the following assumptions: it has a total of N nodes, which are arranged in a * LL rectangular area according to certain distribution characteristics, and the communication distance between nodes is d .Node types include jamming source, undisturbed nodes, edge nodes and disturbed nodes. The edge nodes are the target network nodes at the edge of the jamming range that carry out some normal co mmun ication. The jamming attack model of wireless sensor networks is depicted in Figure 2: We used packet send ratio (PSR) to distinguish the different nodes. The general calculat ion formu la of PSR as follows: where n represents the number of messages to be sent by the node and m represents the number of messages sent successfully. This paper implements this model in the following ways. In the normal operation state, the sensor nodes can obtain their own location information, send message data to adjacent nodes periodically while receiving ACK reply simultaneously. When under the influence of the jamming, the disturbed nodes will not be able to receive or send out data; therefore, causing some unsuccessfully sent messages, that is, As shown in Table 1, the computational complexity of Centroid Localization (CL) algorithm and weighted-CL algorithm is relatively low, but the positioning accuracy is also low, which could easily lead to unsatisfying positioning results; whereas the location based on signal strength and the minimu m covered circle algorithms have strengthened the positioning accuracy, but the positioning times is high, so these algorithms are unable to provide real-time determination of the location of jamming attack. Furthermore, the minimu m covered circle algorithm is not sensitive to node density, indicating that the algorithm may have good or bad positioning effects as node density varies. The minimum covered circle algorithm based on the improved beetle antennae algorithm (IBAS) proposed in this paper has high computational complexity, but combined with the characteristics of rapid convergence and optimization of beetle antennae, the positioning time of the algorithm remains fast with better real-time performance. The IBAS algorithm is able to estimate the position of the jamming source more accurately with the minimu m covered circle positioning and it also resolves the problem that the minimum covered circle is not sensitive to node density.

III. SPECIFIC STEPS OF MINIMUM COVERED CIRCLE WITH IBAS
According to the signal jamming attack model of wireless sensor networks, the steps of determining the jamming source attack location based on the minimu m covered circle of the IBAS proposed in this paper are as follows:

IV. JAMMING LOCATION IN WIRELESS SENSOR NETWORKS
For the perfo rmance of the algorithm, the test examples in reference [30] and. Reference [34]- [36] are co mpared to genetic algorithm (GA ) and minimu m covered circle algorith m (M CC). The reason to compare with the classical genetic algorith m is because the design idea of genetic algorith m is relat ively simp le to imp lement and the robustness of the algorithm can solve the minimu m coverage; MCC algorithm is a co mmon method to solve the minimu m circle of a group of point sets on the covering plane. The algorithm can locate the center of the minimu m covered circle with high calculation accuracy. Co mparing these two methods with the algorith m in th is paper has proved that the min imu m covered circle based on IBAS has better performance. The algorithm runs for 5 times and the maximu m nu mber of iterations is 300 times. Each t ime, record the center coordinates of the circle solved, the minimu m radius of the covered circle, the number of iterations for optimal value and the running time.
Firstly, the test is carried out fro m the lo w-density nodes. Case 1 uses 12 nodes. Table 2 shows the point set tested by case 1, and Table 3 presents the test results of IBAS algorith m and the co mparison results of genetic algorith m. Figure 5 shows the minimu m coverage result of IBAS algorith m, and Figure 6 demonstrates its convergence effect.   According to the data of example 1, it can be concluded that in the case of low-density nodes, when compared to the classical optimizat ion algorithm genetic algorithm, the minimu m coverage rad ius obtained by IBAS algorith m is more accurate than genetic algorith m, reaching 14.7086. In terms of the number of iterations, IBAS algorith m needs to run 24 times to solve the optimal value. The genetic algorith m needs 87 times at most; In terms of test time, the shortest running time of IBAS algorith m is 0.041848 second. The good performance is attributed to the rapid convergence of BAS algorithm. The experiment results prove that IBAS algorith m operates well in lo w-density nodes.

B. CASE 2. 32POINTS SIMULATION
After identifying the algorithm has good optimization effect in low-density WSNs, we then test the performance of the algorithm in high density WSNs. This test is compared with the classical minimu m covered circle algorithm (MCC), and the test results are shown in Table 4 with the position information of 32 coordinate points in test example 2. Table  5 shows the average results of IBAS algorithm running for 10 times and the comparison results with other algorithms. Figure 7 shows the coverage of IBAS algorithm tested in 32 nodes. Figure 8 is the convergence effect diagram of algorithm execution.  According to the test results of case 2, the algorithm continues to show good performance in high-density node distribution. The running time is obviously higher than that of MCC algorith m and can obtain the optimal solution in about 110 iterations. The radius of the locating point at the center of the circle is shorter than that in reference [34]- [36], which shows that IBAS algorithm is more accurate. The shortening of the radius of the covering circle makes the positioning of the center of the circle mo re accurate. These results are also reflected in Table 5. Through the analysis of the above two examples, it is known that in the five simulat ion experiments with 12 nodes sets in case 1, the radius of the min imu m coverage issue obtained by IBAS algorith m is shortened by 4.64* 10 -3 , and the location origin is more accurate. The algorith m can find the optimal solution in an average of 65 times iterations, and the number of iterat ions is at least 22 times less than that of the genetic algorith m. In the test simu lation time, the IBAS algorith m shows good time performance; In the 32 nodes sets in example 2, the difference between the radius of the min imu m coverage point solved using the improved beetle antennae algorithm and the results in reference [34]- [35] is not significant, but the difference is nearly 3mm shorter than the results found in reference [36]; In terms of running time, the simulation t ime of IBAS is the shortest, which is 0.05s shorter than that in reference [34] and one order of magnitude shorter than that in reference [36]. These two examp les can fu rther prove the accuracy of this algorithm for solving the min imu m coverage problem in short running time and better accuracy, and thus provide support to the idea of using this algorithm for attack location in wireless sensor networks. Figure 9 shows a square wireless sensor network area with the size o f 1000m* 1000m simulated by MATLA B. The center coordinates of the square wireless sensor network area are (500,500), the coordinates of the lower left corner are (0, 0) and the coordinates of the upper right corner are (1000,1000). The sensor network nodes are randomly assigned within the boundary of this area. Set the center point (500,500) as the jamming attack point and the 375 units length as the interference radius, then all the points within the circle in Figure 9 are the interfered nodes. The sensor network nodes are randomly assigned within the boundary of the area. The simu lation experiment compares the incremental algorith m and MCC   algorithm in reference [37]. Tab le 6 shows the jamming attack location determined by 10 times simulation tests after 600 sensor nodes are placed in the area. It can be seen fro m table 6 that under the 10 times of simu lations, the location of the jamming source is mo re accurate, and the radius length of the containment coverage circle is shorter, up to 370.2199. While the results of the incremental method and MCC   algorith m fluctuate greatly, between 375-397, indicat ing that the imp roved beetle antennae algorithm in this paper is more stable and more accurate. In order to further verify the effectiveness of the IBAS algorith m in solving the min imu m coverage jamming location accuracy of wireless sensor networks and shortening the location time, the location erro r and root mean standard deviation [38] (RM SD) are co mpared as an evaluation index o f jamming attack location. The evaluation formula is as follows:

C. CASE 3. JAMMING LOCATION IN WIRELESS SENSOR NETWORKS
Formula. (9) is the root mean standard deviation, which is the mean value of the sum of squares of the jamming attack source location error, and can reflect the deviation between the algorithm test result and the actual result. Where k is the total number of points. The comparison diagram of positioning error is shown in Figure 10.
According to the data in Table 6, root mean standard deviation of the incremental method is 10.6137, roo t mean standard deviation of the MCC   algorith m is 11.6340, and the root mean standard deviation of the minimu m coverage algorith m based on the IBAS algorith m is 5.4294. It can be seen fro m the co mparison of Figure 10, the difference of the positioning error for solving the jamming attack positioning problem using the min imu m coverage of the IBAS algorith m is s maller than that of the other t wo algorith ms. In 10 t imes simulat ion tests, the maximu m error of the incremental method reaches about 17.7; the maximu m error of the MCC   algorith m is about 20; and the maximu m error of this algorith m is about 11.5. The error fluctuation is more gentle than other algorith ms. Therefore, the deviation between the results of the proposed algorith m and the actual results is small, which further proves the effectiveness of solving the jamming attack location problem in wireless sensor networks based on the minimu m coverage of the improved beetle antennae algorithm.
In order to exp lore the external environ ment and other factors affecting attack location, the perfo rmance of each algorith m under different conditions is analyzed and compared by changing the distribution type, node density (number) of the target network nodes.

1) INSPECTION INDEX
In the simulation experiment, the mean absolute error (MAE) and cumulative distribution function (CDF) are selected to evaluate the error between the test result and the actual value. The calculation formula is as follows: Where, n represents the number of tests, ( , ) ii xy represents the jamming source coordinates estimated in the t th  times test, and ( , ) xy represents the position of the actual jamming source.
() CDF x represents the sum of the probability that the error of all results is not greater than a .

2) INFLUENCE OF NODES DISTRBUTION
The existing research on mu lti-hop wireless networks primarily adopts uniform distribution and Poisson point process distribution [39] (PPP) to construct simu lation networks. Poisson point process is a counting process. The randomly sampled points obey uniform distribution in the range, and the distance between sample points obeys exponential distribution. Poisson point process distribution formula is as follows: Where,  is a g iven parameter, wh ich can be called density; B represents the mathematical reg ion, that is, twodimensional plane space. Then the number of random points () N B n  in reg ion B obeys Poisson distribution. At present, the existing research also has different construction methods for uniformly distributed networks, including the following two methods: ①Within the range of regional coordinates, N coordinates are generated, which are subject to the characteristics of random distribution. The point distribution generated in this way is more common. However, the randomness of node distribution is stronger, and the positioning calculation is relatively d ifficult.
Moreover, if the number of points is too small, there may be only one or even no disturbed points in the jamming area. Therefore, the minimu m number of nodes selected in this experiment is 100. ②Div ide the target area into N grids of equal size, and then put a node at random in each g rid. In doing so, the nodes distribution is rather regular and easy to locate and calculate, but the actual application may be limited.
In our study, we use the above two methods to generate uniform d istribution network and Poisson point process distribution for different types of distribution networks. For the sake of d istinction, the network generated by ① is called uniform network and the network generated by ② is called bisection network. Figure 11 shows three different distribution types of networks. Firstly, the effects in different nodes distribution networks are co mpared. In the test examp le, the jamming radius is set as 50 rm  , the number of nodes is 300 n  , and the coordinate position of the jamming source in the center (150,150) of the sensor network. The CDF curve of each positioning algorithm in the three types of sensor distribution networks is shown in Figure 12: The experimental results show that the improved beetle antennae algorith m is superior to other algorith ms in three different types of network nodes distribution. In the uniform distributed network, the calculation accuracy of attack location error is the best. Because the node distribution of b isection network is fairly regular, the jamming source tends to be in the center, so the calculation accuracy of the improved beetle antennae algorithm decreases slightly. In the distribution of PPP network, due to the relatively dense distribution of nodes in a certain range, the improved beetle antennae algorith m is still not uniformly distributed, and the calculat ion accuracy of the network is high, but still better than other algorithms.

3) INFLUENCE OF NODES DENSITY
In the above test, the jamming attack location of different network node distribution types is analyzed. The density of sensor network nodes is also an important factor affecting the location calculation. The positioning time efficiency and error results when the sensor network nodes increase exponentially are analy zed next. Similarly, the incremental method, MCC   algorith m and CL algorith m are used for comparison. The jamming radius is set as 50 rm  , and the number of wireless sensor network nodes is gradually increased from 100 to 1000. Figure 13 shows the time consumption comparison of the four algorith ms. Figure 14 and Figure 15 are co mparison diagram of the average error of the radius of the four algorith ms in 10 times simu lation tests in a uniformly distributed network. The closer the numerical value is to the zero point, the smaller the error is. As can be seen fro m Figure 13, with the mult iple increase of sensor network nodes, the time consumption of locating jamming attack points by incremental method and CL method increases significantly. The MCC   algorith m and improved beetle antennae algorithm are less affected by the increase of nodes, and the time increases slightly. The time spent by the improved beetle antennae algorithm in locating the jamming attack source is shorter than that of the MCC   algorith m, at about 122ms. The time consumed by the incremental method is about 2 times that of the algorithm, about 1.3 times that of the MCC   algorith m, and about 2.2 t imes that of the CL algorith m. According to the theory, with the increase of node density, the accuracy of positioning error increases. As seen from Figure 14 and Figure 15, the MAE of the algorith m increases with the increase of the node density of the sensor network. Th is is because under different node densities, the setting of the number of iterat ions of the test example remained consistent at 300. The increase of node density will inevitably lead to the increase of time and complexity of the calculation process, so that the error of positioning calculation of all algorith ms increases gradually under the condition of less iterations. However, under the condition of 200-1000 node density, the IBAS algorithm proposed in this paper has better performance, positioning accuracy and low error. At the same time, Figure 14 shows that when the node density is 100, the value of IBAS algorith m is at the highest, because the calculation result is positive in Formu la. (7). In the simu lation test, i) the jamming attack source located by IBAS is mo re accurate, ii) the measured actual point position is more accurate than other algorithms; iii) the positioning position is at a certain distance from the set circle point, wh ich increases the value of MAE. In conclusion, IBAS algorith m has good performance in network distribution with different node density.
Under the condition of unifo rm node distribution, the comparison CDF diagram o f different algorith m errors for different node densities (100-1000) is shown in Figure 16. According to Figure 16, we can intuitively see the difference of cumu lative distribution of solution results of different algorithms under different node densities. The four algorith ms are relat ively the same in cumu lative distribution. When the number o f nodes is small, the error range of the four algorith ms is small. IBAS algorith m has less error than the other three algorithms, and the error range is relatively uniform. When the number of nodes increases to 600 n  , the error range of the four algorith ms increases, IBAS algorith m still maintains good solution performance, and the error of MCC   algorithm is better than CL algorithm and incremental method.

4) INFLUENCE OF ATTACK SOURCE ON JAMMING RADIUS
The jamming range of attack source of sensor network node is another important factor affecting location calculat ion. The following analy zes the impact of different jamming ranges on attack location in sensor network nodes. Figure 17 and Figure 18 show the test results of the change of jamming radius in a uniform node distribution network. When   :30m-70m). VOLUME XX, 2021 caused by the jamming signal of the attack source is simu lated. In the case of location calcu lation, the jamming source center is selected as (500,500) to verify the node in the case of jamming intensity. According to the multivariate standard Gaussian distribution, a total o f 300 sensor nodes are generated. Co mb ined with the IBAS algorith m these nodes are simu lated and tested to locate the location of the jamming source. The algorith m runs 10 t imes. Take the coordinate point deviation as the inspection standard: The test results are as follows in Figure 20 and Figure 21. Based on the test results, for the positioning test of the interference signal generated by the attack source affecting the nodes with different degrees of interference intensity, the improved beetle antennae algorithm still has good positioning ability. The positioning deviation is uniform and has high positioning accuracy in all 10 tests. The result further verifies the effectiveness of the imp roved minimu m coverage method proposed in this paper. The comprehensive statistical analysis of the algorith m is shown in Table 7. According to the statistical results in Table 7, the improved beetle antennae minimu m coverage attack location algorith m is performing well in locating wireless sensor network attack location, and the location error range is mo re accurate than other algorith ms in different types of network node distribution; In high-density nodes, the positioning time is nearly 30ms shorter than other algorith ms, and the positioning error is still less. Under different jamming radius, the accuracy of IBAS algorithm is nearly 0.1 unit better than that of other algorith ms when the jamming radius is 30m. When the jamming radius is 50m, the accuracy is at least 0.1 unit higher. When the jamming radius is 70m, the accuracy is nearly 0.2 units higher. Through comparat ive analysis, we have proved the improved beetle antennae minimu m coverage algorith m is an effective solution fo r locating the attack source pro mptly when the interference signal occurs in the wireless sensor.

V. CONCLUSION AND FUTURE WORK
In order to more accurately determine the location of a jamming attack source in wireless sensor networks, we have proposed the IBAS algorithm that is able to perform the radius search of jamming signals and locating the position of jamming attack sources taking advantage of fast convergence of individual search of the o rig inal beetle antennae algorithm. We performed a series of simu lation tests to verify the effectiveness of the IBAS algorith m. In test 1 with 12 points set, when compared with the genetic algorith m, the IBA S algorith m has faster convergence speed, the simulat ion time is shortened to 0.041848s, and the minimu m coverage radius is further shortened to 14.7086. In case 2 with 32 points set, the result show that IBAS algorithm still has the capability to cover all points and the min imu m coverage rad ius. These two examples provide the proof for the effect iveness of the algorith m as a solution to localizing the jamming source in wireless sensor networks.
In addition, we have also tested the performance of the IBAS algorith m with different node distribution types, with the increased number of nodes, with low-density and highdensity nodes, with different interference radius of the sources, and with different interference signal strength. We compared the perfo rmance with some tradit ional methods for solving the same problems including incremental method and centroid location method. The IBAS algorithm shows faster positioning speed and more accurate positioning, which provides a solution for quickly finding the location of a jamming source and taking defense measures in time when sensor network nodes are being attacked by interference signals. The trad itional centroid localization algorith m has lo wer co mputational comp lexity than the IBAS algorith m, which is what we still need to overcome and improve.
For further research objectives , we will firstly extend our solution to tackling the problem involving mu ltip le jamming sources i.e., to locate the jamming sources when mu ltip le jamming sources are in the presence. Secondly, with the continuous development of engineering technology, the attack jamming source may not appear in a plane. How to establish a positioning model in three-d imensional or even high-dimensional space to find its location is another area that needs us to explore and study.