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Abstract

In vehicular ad hoc network, wireless jamming attacks are easy to be launched in the control channel and can cause serious influence on the network performance which may cause further safety accidents. In order to address the issue of wireless jamming attacks, a new technique which localizes the jamming attackers and prevents vehicles from jamming through human intervention is proposed. In this article, we propose a range-free approach to localize the source of the attacker and determine the number of jamming attackers. The data set is the locating information and the jamming detection information associated with each vehicle. Then, we formulate the problem of determining the number of attackers as a multiclass detection problem. We define the incorrectly classified area and use it to measure the distance between samples and centroids in fuzzy c-means algorithm. We further determine the number of jamming attackers through the coverage rate of beaconing circles and utilize weight-based fuzzy c-means to classify the data set. When the data set is classified as acceptable, we further explore the means of using particle swarm optimization algorithm to calculate the positional coordinates of each attacker. We simulate our techniques in MATLAB, and both urban traffic area and open area are considered in our simulation. The experimental results suggest that the proposed algorithm can achieve high precision when determining the number of attackers while the result of the classified performance is always satisfying. Our localization results lead to higher accuracy than other existing solutions. Also, when the data set is limited, the chances of taking accurate localization are higher than other measures.

Keywords

Vehicular ad hoc network jamming attack localization of multiple jamming attackers fuzzy c-means particle swarm optimization

Introduction

Vehicular ad hoc network (VANET) is a type of self-organized peer-to-peer (P2P) wireless network formed by on-board units (OBU; e.g. vehicles) and roadside units (RSU). As shown in Figure 1(a), OBU is used to communicate with other vehicles or RSUs, and RSUs are used to connect with application servers and trust authorities. The communication between vehicles is called vehicle-to-vehicle (V2V), and the communication between OBUs and RSUs is called vehicle-to-roadside (V2R). VANET is developed to perform the public safety applications; such applications can save lives and improve traffic flow by transmitting safety-related messages. Moreover, the VANET can also provide some commercial and entertainment service to meet the demand of the drivers for both convenience and comfort purposes. In 1999, US Federal Communication Commission (FCC) allocated a bandwidth of 75 MHz spectrum at 5.9 GHz, usually referred to as the dedicated short-range communications (DSRC). The DSRC radio technology has been standardized on the definition of the media access control (MAC) and physical layer protocols as IEEE 802.11p by the IEEE 1609 working group. Figure 1(b) shows that the DSRC spectrum has been divided into seven 10-MHz wide channels. Channel 178 is the control channel where all common safety messages are exchanged in it. It is important to point out that Channel 178 is generally restricted to safety communications only. Other non-safety usage in control channel is limited to occasional advertisements of private applications from the service channels which are insignificant to overall channel load.

Figure 1.

(a) Architecture of VANET and (b) 5.9-GHz DSRC band plan.

Due to the openness of the wireless transmission medium, wireless communications are vulnerable to malicious injection of jamming. Certain low-cost jamming devices can be easily purchased by the adversaries, which can be used on the commonly available platforms in order to launch attacks with little efforts. Such attacks are known as the Denial-of-Service (DoS) attacks. The DoS attack can eliminate the network capacity to execute its normal function¹ by affecting its throughput, network load, end-to-end delay.² In VANET, the control channel is generally restricted to exchange specific messages only. The messages like traffic information messages, general safety-related messages, and liability-related messages are transmitted in the channel. Traffic information messages are used to disseminate traffic conditions in a given region, and they affect public safety by preventing potential accidents from traffic congestion; general safety-related messages are used by public safety applications such as cooperative driving and collision avoidance; liability-related messages are exchanged in liability-related situations such as accidents. The control channel is a shared wireless medium, and its communication technologies are publicly accessible. The adversaries can easily observe the V2R or V2V communications; then they launch simple DoS attacks against wireless networks by injecting false messages. Also, the adversaries are able to use the well-known communication rules as basis to launch DoS attacks in this channel. The effects of this DoS attack are twofold: on the side of the transmitters, it renders the medium busy resulting in large back-off times; while on the side of the receivers, it dramatically decreases the signal-to-noise ratio (SNR) resulting in a large number of packet collisions. Under this attack, the common safety messages are disabled because they will not be sent to the receivers in time. The consequences of such attacks will cause some city-wide chaotic traffic problems like traffic congestions, traffic disturbances, and traffic accidents. According to the study of Xu et al.,³ jammer can be categorized as follows:

Constant jammer. The constant jammer continually emits the radio signal. It can be implemented on a normal wireless device or a waveform generator. It continuously sends out random bits to the channel without following any MAC layer etiquette. While the control channel is being occupied at all the time under the attack, a constant jammer can effectively prevent legitimate vehicles from sending safety messages.

Deceptive jammer. The deceptive jammer constantly injects regular packets to the channel without any gaps between subsequent packet transmissions. As a result, normal vehicles will be deceived as receiving a legitimate packet, and they will be duped to remain in the receiving state without doing anything else.

Random jammer. The random jammer alternates between sleeping and jamming. It will enter into a “sleep” mode after jamming for a period of time and resume jamming after the resting period. During its jamming phase, it can act either like a constant jammer or a deceptive jammer.

Reactive jammer. The three models discussed above are active jammers in the sense that they try to block the channel irrespective of the traffic pattern. For the reactive jammer, it stays quiet when the channel is idle but starts transmitting radio signals as soon as it senses activity on the channel.

The methods to detect the jamming problems have been widely researched by scholars and professions.^4–10 In addition to these solutions toward the jamming problems, different strategies and techniques which counter the attacks from adversaries, including frequency-hopping spread spectrum (FHSS) and direct-sequence spread spectrum (DSSS), ultra-wide band (UWB) technology, antenna polarization, and directional transmission methods, have been developed through time.¹¹ But, these solutions overwhelmingly rely on cryptography, which means the mechanism of key establishment must be decided by consensus in advance. As a result, when the shared key is revealed to the adversaries, the solutions may become useless. Another weakness is that when the additional infrastructural overhead is too big, it is impossible to be used as OBU.

Recently, new approaches which utilize localizing algorithm associated with range-based properties to combat attackers in wireless networks have been proposed.^12–18 But in VANET, errors can often be masked through fault tolerance, redundancy, aggregation, or by other means. In certain situation, the additional cost of hardware required by the range-based solutions may be inappropriate in relation to the required location precision. Because of the high mobility and large scale of vehicles in VANET, an alternate range-free solution toward the problem of jammer localization is needed. We focus on using the range-free algorithms to find the location of the jamming attacker in VANET. Such solutions can be effective by eliminating the attackers from the network and guiding the routing protocol to avoid the jammed region. The vehicles record their locating information and combine the information with if-jammed signal in every fixed time interval. The collected information of each vehicle is transmitted to the RSU when the vehicle moves into the communication range of this RSU. Then, RSUs forward their collected information to the application server. At last, the application sever localizes jammers using corresponding algorithms.

The main contributions of our work are as follows: we use the incorrectly classified negative area to measure the distance between samples and centroids in fuzzy c-means (FCM) algorithm, then use the weight-based FCM to classify the data set. We provide two new definitions named Beaconing circle and Coverage rate. We also determine the number of adversaries using the Coverage rate of Beaconing circles; we use particle swarm optimization (PSO) algorithm to find the minimum cover circle in each classified cluster gained from the weight-based FCM. Moreover, the weight-based PSO algorithm is invited to deal with the partly distributed data set; we finally propose a general-purpose localization framework to perform jamming source positioning in VANET.

In weight-based FCM, the calculation formula of the distances between points and centers was redefined with incorrectly classified negative area. At the same time, the possibility of the point being classified into incorrect cluster went down. We then applied the Beaconing circle and Coverage rate to evaluate the performance of classification when the cluster number was confirmed. We further formulated the problem of determining the number of attackers as an automated segmentation of the input data set, and the algorithm iterated with the increasing cluster number until an acceptable classified performance was obtained.

Moreover, we utilized the clusters returned by weight-based FCM to further localize multiple adversaries. We also used minimum cover circle to define the evaluation function in PSO. Then, the PSO-based localization algorithms were developed to calculate more accurate coordinates of jamming attacker in each cluster. As we demonstrated through our experiments in MATLAB, our approach is highly effective in finding and localizing multiple attackers in VANET.

Furthermore, we proposed a general-purpose localization framework to perform multiple jamming source positioning. This framework could combine varieties of technologies like jamming detection, jamming source location, and jamming countermeasure. It is designed with fully distributed functionality while easy to be deployed in practical applications.

The rest of the article is organized as follows: we place our work in the context of related research in section “Related work.” Our network assumption is presented in section “Network assumptions.” We provide our theoretical analysis and describe how to determine the number of attackers in section “Determining the number of attackers and classifying the data set.” We formulate the problem of localizing the jamming attacker as an optimization problem of using PSO algorithm in section “Locating the jammer source.” In section “General-purpose localization framework of positioning multiple jammer,” we present the general-purpose localization framework to perform multiple jamming source positioning. Finally, we conclude our work in section “Conclusion.”

Related work

The jamming attacks were first studied and concluded by Xu et al.;³ they have divided the elementary jammers into four types according to their different jamming characteristics, that is, constant jammer, deceptive jammer, random jammer, and reactive jammer. And the elementary jammers always interfere transmission signal at physical layer. Then, a lot of intelligent jammers were proposed in the following researches.^19–21 Unlike the elementary jammers, the intelligent jammers focus on the MAC layer; they sense the channel at first and inject some jamming signal until the related packets have been transmitted in the channel, that is, request to send/clear to send (RTS/CTS) frame jammer, DATA frame jammer, ACK frame jammer.

The traditional approaches to prevent the DoS are to use the sophisticated physical layer technologies such as FHSS and DSSS, UWB technology, antenna polarization, and directional transmission methods.¹¹ A similarity is that all the traditional approaches use the cryptographic-based authentications and key management schemes as basis for further decoding.^22–24 A secure and efficient key management (SEKM) framework is studied by Wu et al.²² SEKM builds a public key infrastructure (PKI) by applying a secret sharing scheme and an underlying multicast server group. A key management mechanism with periodic key refresh and host revocation is implemented to prevent the compromise of authentication keys in the study of Wool.²³ An authentication framework for hierarchical ad hoc sensor networks is proposed in the study of Bohge and Trappe.²⁴ However, the cryptographic authentication may not be always applicable in VANET because of the additional infrastructural overhead and computational power. Since the communication rules in VANET are open while the key is easily exposed to attackers, it makes even harder at certain situation to apply the solutions.

The localization techniques have been researched widely by scholars and professions. The signal processing–based localization techniques have been studied in the earlier literatures. Various approaches which use the advanced signal processing techniques have been proposed in order to locate the jamming attackers.²⁵ These techniques are all operated at the physical layer. In addition, they require special and additional infrastructures to achieve their goals. The VANET may be used everywhere in the city, yet the jamming attack also may be launched anywhere. A large number of additional hardware is needed to widely deploy such techniques, and the high cost which brings a heavy burden to the governments is unacceptable. Dealing with the ranging methodology, range-based algorithms involve distance estimation using the measurements of various physical properties such as received signal strength (RSS),^12,13 time of arrival (TOA),¹⁴ time difference of arrival (TDOA), and direction of arrival (DOA).¹⁵ RSS-based techniques require the measurements of RSS at various positions (landmarks) to form a signal map. Some well-known approaches belonging to this category are the (weighted) centroid¹⁶ and trilateration¹⁷ approaches. In the study of Bahl and Padmanabhan,¹² a radio direction and ranging (RADAR)-gridded algorithm is proposed; it uses an interpolated signal map which is built from a set of averaged RSS readings with known locations. The nearest neighbor will be returned as the estimated location when an observed RSS reading with an unknown location is given. In the study of Elnahrawy et al.,¹³ an area-based probability estimated method is studied. Such method utilizes an interpolated signal map while the experimental area is divided into a regular grid of equal-sized tiles. RSS readings are used to compute the probability of the existence of the attackers at each tile through Bayes’ rule. The tile which has the maximal probability will be returned as the estimated result. In the study of Madigan et al.,¹⁸ Bayesian networks localization is proposed, and it is a multilateration algorithm that encodes the signal-to-distance propagation model into the Bayesian graphical model for localization. Through Markov chain Monte Carlo (MCMC) simulation, belief network (BN) returns the sampling distribution of the possible location coordinates as the localization result. All of these RSS-based schemes require landmarks to measure the RSS values at different positions. And a set of previously collected measurements, including coordinates and the corresponding RSS values, are required in order to apply the algorithms to identify the positions of attackers. In a slightly different context, Pelechrinis et al.²⁶ use gradient descent minimization to get the position which has minimal packet delivery ratio (PDR), and this position is taken as the estimated result.

In the study of Bulusu et al.,²⁷ a heterogeneous network which contains powerful nodes with established location information is considered as being useful. In this work, anchors beacon their positions to neighbors that keep an account of all received beacons. Using this proximity information, a simple centroid localization (CL) model is applied to estimate the location of the listening nodes. An enhanced version of CL is known as the weighed CL,²⁸ which adds weight values into the procedure of estimating the targeted node position. Liu et al.²⁹ proposed the virtual force iterative localization (VFIL) algorithm which performs better than CL and weighted centroid localization (WCL) in terms of the localization accuracy. VFIL first estimates the jammer’s location using traditional coarse localization scheme such as CL, and then iteratively localizes the jammer by defining a virtual force. Cheng et al.³⁰ further uses basic geometric concepts to improve the performance of VFIL. Also, a rudimentary system based on SNR measurements and bifurcation points is provided by the same researcher.³¹ All of the methods can be used to locate the jammer. However, the localization accuracy of above range-free solutions is unsatisfactory. When the testbed is partly distributed, all the approaches will generate the wrong results.

The works in the previous studies^32–34 are most closely related to ours. Yang et al.³² propose the cluster-based mechanisms to determine the number of spoofing attackers. In addition, some range-based localization algorithms are also used for localizing the adversaries like RADAR-gridded, area-based probability, and Bayesian networks. In his work, the cluster-based mechanism uses the merge energy and partition energy³⁵ to determine the number of the attackers. The relationship between these two energies indicates the divisible state when the system is composed of $k$ clusters. The estimated number of attackers is obtained from $k$ when the system stays at a stable equilibrium state. He et al.³³ propose a range-free Area-based Point-In-Triangulation Test (APIT) scheme in a heterogeneous network which includes anchors equipped with high-powered transmitters and global positioning system (GPS). APIT isolate the environment into triangular regions between beaconing nodes so that the node can estimate its location by narrowing down the triangular region in which it can potentially reside. Sun et al.³⁴ propose minimum-covering-circle-based (MCCL) jammer localization algorithm in wireless sensor network (WSN). He uses the plane geometry knowledge to form an approximate jammed region. As a result, the center of the jammed region is treated as the estimated position of the jammer. But, this approach is inappropriate when the testbed is non-uniformly or partly distributed.

All techniques mentioned above focus on WSN. Compared to WSN, VANET has a larger number of nodes which are the mobile vehicles and jamming attackers which locate at anywhere on the whole urban traffic map of a city are needed to be concerned. Some effective range-based solutions of jammer localization in WSN have two requirements in common: the sensor nodes are static while the RSS values at various positions can be measured. However, the city-wide applied region of VANET is too big to deploy these techniques. In such case, it is feasible and significant for some methods to utilize their own characteristics to localize the jamming attackers. Our work differs from the previous studies in that we use the locating information and if-jammed information gathered by vehicles without any additional infrastructure. Furthermore, our work is novel because it uses big data–based range-free solutions to determine the number of jamming attackers and localize their positions. An iteration-based mechanism is invited to determine the number of attackers with higher accuracy. The PSO-based localization algorithm works well with non-uniformly distributed data set, and the weight-based PSO can make an effective estimation even when the data set is partly distributed.

Network assumptions

Network model

We consider a VANET within an open map as well as an urban traffic map. The open area means that any pairwise coordinate $(x, y)$ is accessible for vehicles, while the urban traffic map means that the vehicles can only run on the road. Our main reasons of choosing the open map are based on the following two points: First, in our view, vehicles can not only run on the road but also be driven into the residential areas for parking needs; Second, we believe that bicycles and motorcycles should be included in VANET with the development of VANET. Based on these two reasons, the real traffic map can be considered as an open area. Also, we assume that each vehicle knows its position all the time. This is a reasonable assumption as most vehicles are equipped with GPS receivers. Additionally, the movement of each vehicle can be considered as a Markov process: when the time interval is close to zero, the time-varying trajectory of a vehicle can be approximately considered as many segmental straight lines, and the vehicle moves uniformly on the line in every time interval. Hence, the location of a vehicle at $t + 1$ can be expressed as $X_{t + 1} = X_{t} + \vec{v} Δ t$ , where $X_{t}$ is the location at $t$ , $\vec{v}$ represents the velocity vector, and $Δ t$ represents the time interval. This equation indicates that the location of a vehicle at $t + 1$ can be calculated through its location at $t$ and a directional shift. In another word, when the location at $t$ is known, the location of a vehicle at $t + 1$ is only related to its location at $t$ but not related to its location at any previous time. It obviously tallies with the definition of Markov process. In our work, the unknown parameter $\vec{v}$ can be easily calculated using the engine revolution and the readings of on-board gravity sensor. This method is also widely used in some navigation systems, it means the vehicles are not necessary to calculate their locations using GPS signal all the time. They only need to use the GPS signal to calibrate their locations after a period of time. As a result, we only need to ensure that the sampling time is multiples of $Δ t$ , and the positions of each vehicle can be gathered correctly even when the GPS signal is also interfered. We focus on localizing the jammers after some jammed regions have been detected. So, we do not consider the process of detecting jamming attack (a lot of researches are focused on this technique^4–10).

Jamming model

As shown in Figure 2, vehicles can perceive two different categories under jamming condition: jammed and unaffected-jammed. That is because vehicles under unaffected-jammed can use control channel to broadcast and receive messages as usual. This fact is important for our future research of anti-jamming techniques once the jamming regions and sources are confirmed. The unaffected-jammed regions are also necessary for the algorithms like WCL,²⁸ MCCL.³⁴ Both of the algorithms are used to compare with our proposed algorithm. Thus, the vehicles record a triple $(x, y, if - jammed)$ in every fixed time interval, where $x$ and $y$ are represented as certain coordinates and the if-jammed signal equal 1 under jamming condition, otherwise the if-jammed signal equal 0. Furthermore, we assume a static jammer which has an isotropic effect, in other words, the jammed region can be modeled as a circular region centered at the jammer’s location.

Figure 2.

Jamming model.

Determining the number of attackers and classifying the data set

The inaccurate estimation of the attacker number and unsatisfactory segmentation of data set will eventually result in failure in localizing the multiple adversaries. To address this issue, we use a weight-based FCM model. We first define the beaconing circle and the coverage rate. Then, we further use them to design a evolutional procedure to determine the attacker number and classify the data set.

The data set gathered from vehicles can be seen as $S = {s_{i}}, i = 1, 2, 3, . . ., m$ , where $s_{i}$ is ith three-dimensional sample, $m$ is the total number of samples. The data set has been divided into two sets through the if-jammed value; they are expressed as $X = {x_{k}}, k = 1, 2, 3, . . ., p$ and $Y = {y_{j}}, j = 1, 2, 3, . . ., n$ , respectively, where $x_{k}$ is a two-dimensional (2D) sample representing the coordinates of the kth point in jammed region, and $y_{j}$ is a 2D sample representing the coordinates of the jth point in no-jammed region and $m = p + n$ . It is a clustering process which maps each instance $s_{i}$ to one element of the set ${X, Y}$ , and the if-jammed signal is used as class label. The confusion matrix and common performance metrics that can be calculated are shown in Figure 3. It is obvious that this classifier makes perfect clustering that the true-positive rate is 1 and the false-positive rate is 0. Then, the mission of determining the number of attackers and classifying the data set converts to find some circle regions which include all elements of $X$ and no element of $Y$ . The reason is that any element of Y will increase the fp rate if it is included in the jammed regions. It also indicates that some no-jammed areas are placed in jammed region.

Figure 3.

Confusion matrix and common performance metrics of clustering $S$ to $X$ and $Y$ .

Weight-based FCM

FCM clustering is a typical unsupervised pattern recognition method which has been successfully applied to feature analysis, clustering, and classifier designs in the fields such as astronomy, geology, medical imaging, target recognition, and image segmentation. This method was initially developed and improved by Dunn³⁶ and Bezdek,³⁷ respectively. As a “fuzzy” version of k-means clustering algorithm, each point is assigned with a degree of belonging to clusters, as in fuzzy logic, rather than completely belonging to just one cluster. Being used in our work, FCM algorithm separates the input 2D data set into clusters by grouping the similar points. A successful clustering can be achieved by iteratively minimizing an objective function which is based on measuring the distance of every sample to the clustering centroid in the feature domain.

FCM algorithm generates fuzzy partitions and prototypes for any set of numerical data. In our work, the jammed region consists of many jammed points, and every point has the positional characteristic that it locates closer to its own jamming source than the other sources. Hence, FCM algorithm is useful in this situation, and we use the FCM algorithm to perform a series of clustering processes to $X = {x_{i}}$ at $c = 1, 2, 3, . . .$ . And the cth clustering yields $c$ clusters. We use $C_{j} = {x_{1}^{j}, x_{2}^{j}, . . ., x_{l}^{j}}$ to represent the jth cluster, $j = 1, 2, . . ., c$ , where $l = | C_{j} |$ . The objective function of FCM algorithm can be described as follows

{\begin{matrix} J_{FCM} = \sum_{j = 1}^{p} \sum_{i = 1}^{c} μ_{ij}^{m} d_{ij}^{2} \\ \sum_{i = 1}^{c} μ_{ij} = 1, \forall j = 1, 2, 3, . . ., p \end{matrix}

(1)

where $μ_{ij} \in [0, 1]$ represents the membership degree of point $x_{j}$ in the ith cluster, $a_{i}$ is the centroid of cluster $i$ , $m > 1$ is the fuzzy index which controls the fuzziness of the resulting partition, and $d_{ij}$ is the distance between point $x_{j}$ to centroid $a_{i}$

d_{ij} = | | x_{j} - a_{i} | | = \sqrt{{(x_{j 1} - a_{i 1})}^{2} + {(x_{j 2} - a_{i 2})}^{2}}

(2)

Mostly, the Euclidean distance in equation (2) is used as the similarity metric of the distance between sample and centroid. However, such method is not suitable in our work, since the classification rules in our work are not only defined by spatial distance but also the spatial distribution of $X$ and $Y$ . Because we must ensure that little or no-jammed areas are included in the jammed regions through the clustering process.

We must redefine the distance using distribution of $Y$ ; as shown in Figure 4, we divide the map into $m \times n$ unit regions. Every unit region is marked if there is a $y_{i}$ located in it. In Figure 4, $\bar{OB}$ represents the segment between any point $B$ in the circle or on it and the centroid $O$ . It is easy to prove that the rectangle which has the diagonal $BO$ is covered by this circle. Thus, if the rectangle generated by $x_{j}$ and $a_{i}$ covers any marked unit region, it means this jammed point is not produced by jammer $a_{i}$ . As a result, it is clear that the point $x_{j}$ obviously locates outside the circle whose centroid is $a_{i}$ . In this condition, a weight value $W$ is added in equation (2), where $W$ is much bigger than the Euclidean distance between $x_{j}$ and $a_{i}$ . New function is shown as follows

d_{ij} = {\begin{matrix} | | x_{j} - a_{i} | | + W & if marked region included \\ | | x_{j} - a_{i} | | & otherwise \end{matrix}

(3)

Figure 4.

Use marked unit regions to weight the distance between sample and cluster centroid.

The membership functions and cluster centroids update as shown, respectively, in equations (4) and (5)

μ_{ij} = {[\sum_{k = 1}^{c} {(\frac{| | x_{j} - a_{i} | |}{| | x_{j} - a_{k} | |})}^{\frac{2}{m - 1}}]}^{- 1}; 1 \leq j \leq p, 1 \leq i \leq c

(4)

a_{i} = \frac{\sum_{j = 1}^{p} μ_{ij}^{m} x_{j}}{\sum_{j = 1}^{p} μ_{ij}^{m}}; 1 \leq i \leq c

(5)

The general procedure of weight-based FCM algorithm is shown as following:

Determine value of $c$ , $m$ , and converging error $ε$ (in this article, $ε = 0.0001$ ). Randomly choose an initial membership matrix $u^{(0)}$ with the constraint of equation (1). Then, at step $k, k = 1, 2, 3, . . ., LMAX$ ;

Compute every distance $d_{ij}$ between sample $x_{j}, j = 1, 2, 3, . . ., p$ and $a_{i}^{(k)}, i = 1, 2, 3, . . ., c$ with equation (3);

Compute cluster centroids $a_{i}^{(k)}, i = 1, 2, 3, . . ., c$ with equation (5);

Compute an updated membership matrix $u^{(k + 1)} = [μ_{ij}^{(k + 1)}]_{c \times p}$ with equation (4);

Compare $J^{(k)}$ to $J^{(k + 1)}$ . If the changes are less than $ε$ , stop. Otherwise, set $u^{(k)} = u^{(k + 1)}$ and return to step 2.

Beaconing circle and coverage rate

The movement of vehicles can be considered as a continuous Markov process. It means when a vehicle moves from inside the circle $O$ to outside in $Δ t$ , if this outside point $C$ is recorded, the circle $O_{beaconing}$ composed by point $O$ as the center and $\bar{OC}$ as the radius is infinitely close to the circle $O$ . A system is called at state $k$ when it is composed of $k$ clusters which form the whole data set. Two definitions are given as follows:

Definition 1 (Beaconing circle)

When a system arrives at state $k$ , the beaconing radius $r_{i}$ of $C_{i}, i = 1, 2, 3, . . ., k$ can be seen as the minimal value among the Euclidean distances between the centroid $a_{i}$ and $y_{j}, j = 1, 2, 3, . . ., n$ , and the beaconing circle of $C_{i}$ is in a circle with the center $a_{i}$ and radius $r_{i}$ .

Definition 2 (Coverage rate)

At state $k$ of a system, the coverage number $n_{i}, i = 1, 2, 3, . . ., k$ of cluster $C_{i}$ is the number of members which locate in the beaconing circle of $C_{i}$ . And the coverage rate at state $k$ is defined as $CR (k)$ which is the ratio of $\sum_{i = 1}^{k} n_{i}$ to $| X |$ , where $| X |$ is the total number of elements in $X$ .

In our work, if every point in $X$ is assigned to the right cluster through a weight-based FCM, the beaconing circle of each cluster must include its all points. In this condition, the coverage rate can reach 100% while the cluster center can be seen as the jammer location similarly. Otherwise, in one of the clusters, there must be a point of $Y$ existing near its cluster center. Such situation will make the beaconing circle too small to cover its points in all, while the coverage rate at this state will get lower.

System evolution

As mentioned above, when the coverage rate reaches closer to 100% at state $k$ , the clustering results are closer to the physical truth. Thus, the coverage rate can be used as the threshold to evaluate the performance at state $k$ . In consideration of the potential errors produced by weight-based FCM (the clustering centroid is near the real circle center but not equal to it), we suggest our system at a stable equilibrium state, as long as the coverage rate reaches upper 90% at state $k$ . The stable equilibrium condition is $CR (k) \geq 0.9$ . Otherwise, we call the system as an unstable state. The unstable condition is $CR (k) < 0.9$ . An iterative algorithm can be obtained from beaconing circle and coverage rate, and the corresponding evolution procedure is designed as follows: as shown in Algorithm 1, a system goes to new states in succession until it reaches a stable equilibrium state, and the coverage rate determine the next state whether the system will go to.

Algorithm 1 Algorithm for determining the number of attackers and classifying data set
1: initialize clustering number $k = 1$ ,2: input data set: $X$ , $Y$ ;3: repeat4: $CR (k) = 0$ , $k = k + 1$ , $CoverNum = 0$ ;5: $Weight - basedFCM (X, k)$ ;6: for $i = 1$ ; $i < k$ ; $i + +$ do7: $r_{i} = min_{y_{j} \in Y} {\| \| y_{j} - a_{i} \| \|}$ ;8: for all $x_{n}^{i}$ in $C_{i}$ do9: if $\| \| x_{n}^{i} - a_{i} \| \| \leq r_{i}$ then10: $CoverNum = CoverNum + 1$ ;11: end if12: end for13: end for14: $CR (k) = \frac{CoverNum}{\| X \|}$ 15: until $CR (k) \geq 0.9$ 16: $NumOfAttackers = k$ , $C_{i}, i = 1, 2, . . ., k$ is the classified data set;

Algorithm 1 Algorithm for determining the number of attackers and classifying data set

1: initialize clustering number

k = 1

,2: input data set:

X

Y

;3: repeat4:

CR (k) = 0

k = k + 1

CoverNum = 0

;5:

Weight - basedFCM (X, k)

;6: for

i = 1

;

i < k

;

i + +

do7:

r_{i} = min_{y_{j} \in Y} {| | y_{j} - a_{i} | |}

;8: for all

x_{n}^{i}

C_{i}

do9: if

| | x_{n}^{i} - a_{i} | | \leq r_{i}

then10:

CoverNum = CoverNum + 1

;11: end if12: end for13: end for14:

CR (k) = \frac{CoverNum}{| X |}

15: until

CR (k) \geq 0.9

16:

NumOfAttackers = k

C_{i}, i = 1, 2, . . ., k

is the classified data set;

Experimental evaluation

The following experiments are to evaluate whether the proposed method can find out the correct number $k$ of jamming attackers and give the most appropriate classification of data set $X$ . Also, we conduct several comparative experiments in order to evaluate the performance of our proposed method.

Experimental environment

We implemented our approach in MATLAB. Both the open map and the urban traffic map were used. As being in the $500 \times 500$ open map, vehicles followed Markov movement. The urban traffic map was generated by the Simulation of Urban Mobility (SUMO) simulator. The map is a part of the area from Shanghai, one of the biggest cities in China as shown in Figure 5. Vehicles were only allowed on road and must choose a random direction at each corner. The weight-based FCM algorithm used fuzzy index $m = 2$ and $Δ t = 1$ . The results indicate that there are three different types of scenarios. The main focus of the first scenario is to test the correctness and the accuracy of our estimated method. In this scenario, we test every coverage rate when the possible number of attackers changes from 2 to 5. Also, we make a comparison with the energy-based two-cluster analysis method which was proposed in the study of Wang et al.³⁵ The second scenario compares the proposed weight-based FCM algorithm with the traditional FCM algorithm, k-means, and partitioning around medoid (PAM) through the receiver operating characteristic (ROC) graphs.³⁸ The third scenario shows the ROC confusion matrix and hit rate of the clustering results generated by weight-based FCM.

Figure 5.

Urban traffic map used in our work.

Validity and comparative experiments of attackers estimated method

In this article, when the coverage rate is greater than 90% at state $k$ , we proposed to use this $k$ as the estimated value of the number of jamming attackers. The correctness of our method is validated by the relational graph of the coverage rate and the possible number of attackers. Both open map and urban traffic map were chosen as part of the samples in this experiment. Four cases (the actual number of jamming attackers changes from 2 to 5) were implemented on each map, and the coverage rate was calculated at different number of attackers in each case. All cases were run 10 times with different vehicle number, simulation time, and jamming range. The coverage rate at different number of attackers was the mean value of these 10 experiments. Figure 6 presents the experimental results, where the x-axis represents the system state or the data set is classified into how many clusters, the y-axis represents the coverage rate of beaconing circles at each system state. It can be seen that the coverage rate gets greater than 90% only when the system state $k$ is equal to the actual number of jamming attackers. So, our method can obtain the appropriate estimation of attacker number. However, this coverage rate is not the greatest one. The evident shows that the coverage rate can reach 100% if each point $x_{i}$ in $X$ is classified as one independent cluster. In the other word, we use a local extremum to estimate the attacker number to make sure a satisfying result is obtained.

Figure 6.

Coverage rate at different estimated number of attackers according to the number of actual attackers: (a) two actual attackers, (b) three actual attackers, (c) four actual attackers, and (d) five actual attackers.

In order to evaluate the performance of our method, we introduce another common multiclass detection method which can be obtained by classifying a data set.³⁵ This method studies two closest clusters after a clustering process, and it provides a pair of evaluation criteria at different estimated number $k$ ; they are merge energy $E_{m} (k)$ and partition energy $E_{p} (k)$ . $E_{m} (k) < E_{p} (k)$ means these two clusters can be further divided, and the estimated number can go to $k + i (i \geq 1)$ through partitioning process; $E_{m} (k) > E_{p} (k)$ means these two clusters can merge into one cluster, and the estimated number can be back to $k - 1$ through merging process. Thus, an evolutive model of estimating the possible number is concluded as follows: $k$ starts at $k = 1$ ; the mission is to find the appropriate $k$ which makes $E_{p} (k - 1) > E_{m} (k - 1)$ , $E_{p} (k) < E_{m} (k)$ , and $E_{p} (k + i) < E_{m} (k + i) (i \geq 1)$ with the increasing value of $k$ . This method can also perform correctly in our research, yet it is important to point out that its runtime is multiple of our proposed method as shown in Figure 7, where the x-axis represents the actual number of jamming attackers, the y-axis represents the runtime of each estimated method. The reason is that our method stops after the coverage rate reaches over 90%. But, when $E_{p} (k - 1) > E_{m} (k - 1), E_{p} (k) < E_{m} (k)$ as a stop criterion is generated by the energy-based method, the method must continue to make several clusterings to ensure that there is no existing $i$ which makes $E_{p} (k + i) > E_{m} (k + i)$ . In another word, the energy-based method has a little chance to fail in local optimum. Due to the longer runtime, energy-based method is hard to be applied in some real-time requirements, and it is also inappropriate to process the bigger data set which is collected by nodes in VANET. However, the energy-based method is a more generalized method, and it can solve almost all the multiclass detection problems. The reason why our method can work better is that it follows the geographic features of jamming attackers and the mobile features of vehicles.

Figure 7.

Comparison graph of runtime between energy-based estimation and coverage rate–based estimation.

Comparison of weight-based FCM and other clustering algorithms

The most important technique of determining multiple jamming attackers is how to correctly classify the data set which has been collected. Some widely used algorithms can be divided into five different types: the partition-based, the hierarchy-based, the density-based, the grid-based, and the neural network–based clustering algorithms. In our research, the data set we chose is 2D which contains a large number of positions. Our goal is to get the correct partition on the data set (jammed points which are interfered by the same jammer must be classified into one cluster) as fast as possible using these clustering algorithms. Although the hierarchy-based and density-based algorithms do not need to assign the cluster number in advance, their qualities of clustering results are always poor. Using these two types of algorithms, some critical points are always misclassified into an individual cluster, and it makes our estimation method failure. The grid-based algorithms are always used in data search because of its high efficiency. Yet, the gird structures are built with many attributes, and it is inoperative in our work. The reason is that we only consider the positional attribute in our work. Finally, the efficiency of neural network–based algorithm is too low to be accepted. Based on these facts, we choose the partition-based clustering algorithms in our work; some popular partition-based algorithms such as k-means, PAM, and traditional FCM are performed to make a comparison with our proposed weight-based FCM in this experiment.

Due to the city-wide applied range of VANET, the data set used in our work is very big. This feature requires the clustering algorithms must perform efficiently. Hence, our first experiment was implemented to evaluate the runtime of each clustering algorithm. We considered six cases with different number of actual jamming attackers which changes from 2 to 7. And in every case, the data set is generated by vehicles with the fixed vehicle number, simulation time, and jamming range. Then, we used k-means, PAM, FCM, and weight-based FCM algorithms to classify the data set in each case, respectively, and the runtime of each algorithm in each case was recorded. The relationship between runtime and the cluster number is shown in Figure 8, where the x-axis represents the cluster number, the y-axis represents the runtime of each algorithm. We can observe that the k-means algorithm gets the shortest runtime in each case, and the PAM algorithm always performs with longest time which increases rapidly. The reason is that the k-means algorithm traverse all points in the corresponding data set only once in every iteration, and its computational complexity is $O (i * n)$ , where $i$ is the iteration number. Similarly, the FCM and the weight-based FCM algorithms have to traverse the points twice for building additional fuzzy matrix, and their computational complexity is $O (2 * i * n)$ , where $i$ is the iteration number. Yet, the weight-based FCM algorithm takes more iterations than the FCM algorithm. Finally, the PAM algorithm is a modified version of k-means algorithm, and it searches the point which has the minimal sum of the distances to the other points in each cluster; then, the algorithm uses this point to update the position of cluster centroid. Therefore, the computational complexity of PAM algorithm is $O (i * n^{2})$ , where $i$ is the iteration number.

Figure 8.

The runtime of k-means, PAM, FCM, and weight-based FCM at each cluster number.

When two jammed regions are located very close to each other, the k-means, PAM, and FCM will classify some points into a wrong cluster because they do not consider the point set $Y$ which consists of no-jammed points. In order to prove that weight-based FCM is useful in this condition, we did a comparative experiment. In this experiment, we located two different jammers closely on map and kept the vehicle number $n = 60$ , simulation time $t = 200$ . Then we used k-means, PAM, FCM, and weight-based FCM algorithms to classify the generated data set $X$ ; we ran them 10 times, respectively. The ROC graph is shown in Figure 9, where the x-axis represents the false-positive rate at each run, and the y-axis represents the true-positive rate at each run. We can see that weight-based FCM always get the higher tp rate and the lower fp rate. The results reach the perfect classification six times, where tp rate equals 1 and fp rate equals 0. The other four times, weight-based FCM leads to a local optimal, little points are misclassified, but we can find out and delete them with our proposed weighted distance in equation (3). It is important for using PSO algorithm to localize the jammer source (it will be introduced in next section). Because, even if one point is misclassified, the localization error will grow to an unacceptable value.

Figure 9.

ROC graphs obtained by k-means, PAM, FCM, and weight-based FCM when there exists two close attackers on map.

It can be seen from above experiments that our proposed weight-based FCM is the best choice for dealing with the clustering problem in VANET. It can achieve the most accurate classification with an acceptable runtime.

Performance experiments of weight-based FCM

As mentioned above, if one $x_{i}$ in $X$ is misclassified, the estimated accuracy of jammer location will be seriously affected. Thus, the accuracy of clustering is a significant standard to demonstrate the effectiveness of the weight-based FCM algorithm. In this experiment, both open map and urban traffic map were selected. The actual number of jamming attackers was three, and four during the experiment. Corresponding to the actual number, the data $X$ gathered from vehicles were classified into three, and four clusters using weight-based FCM, respectively. We used $n$ to represent the vehicle number we have deployed and $t$ to represent the simulation time. $n \times t$ is an important parameter which is used to change the size of the collected data set ${X, Y}$ . With the different values of $n$ and $t$ , the multiclass ROC matrixes and the true-/false-positive rates computed through the clustering results are shown in Tables 1 and 2. The ROC matrix is a very practical and intuitive way of seeing such a distribution. These matrixes can be illustrated with the following example: there are three actual jamming attackers on open map, and data set ${X, Y}$ is generated by $n = 40, t = 200$ . From this data set $X$ , the sum of one column represents that the data size belongs to each class (actual attacker). In another word, 565 elements in $X$ are of class “1,” 469 elements in $X$ are of class “2,” and 708 elements in $X$ are of class “3”; the sum of one row represents the data size of a class which is classified by weight-based FCM. The value of ath row and bth column $(a, b = 1, 2, 3, a \neq b)$ represents the number of elements in class $b$ that have been misclassified into class $a$ . It is clear that all elements in X are correctly classified through our proposed weight-based FCM algorithm. It can also prove that our method is effective, while it always achieves a perfect precision.

Table 1.

The multiclass ROC matrixes and the true-/false-positive rates obtained by weight-based FCM with three actual attackers.

Open map
		n = 40, t = 200			n = 60, t = 200			n = 80, t = 200
		Actual			Actual			Actual
		1	2	3	1	2	3	1	2	3
Predicted	1	565	0	0	715	0	0	749	0	0
	2	0	469	0	0	543	0	0	639	0
	3	0	0	708	0	0	842	0	0	1129
tp rate (%)		100	100	100	100	100	100	100	100	100
fp rate		0	0	0	0	0	0	0	0	0
Urban traffic map
		n = 60, t = 300			n = 90, t = 300			n = 120, t = 300
		Actual			Actual			Actual
		1	2	3	1	2	3	1	2	3
Predicted	1	81	0	0	88	0	0	107	0	0
	2	0	363	0	0	397	0	0	601	0
	3	0	0	137	0	0	172	0	0	259
tp rate (%)		100	100	100	100	100	100	100	100	100
fp rate		0	0	0	0	0	0	0	0	0

ROC: receiver operating characteristics; FCM: fuzzy c-means.

Table 2.

The multiclass ROC matrixes and the true-/false-positive rates obtained by weight-based FCM with four actual attackers.

Open map
		n = 40, t = 200				n = 60, t = 200				n = 80, t = 200
		Actual				Actual				Actual
		1	2	3	4	1	2	3	4	1	2	3	4
Predicted	1	374	0	0	0	517	0	0	0	704	0	0	0
	2	0	186	0	0	0	192	0	0	0	309	0	0
	3	0	0	89	0	0	0	134	0	0	0	203	0
	4	0	0	0	253	0	0	0	382	0	0	0	514
tp rate (%)		100	100	100	100	100	100	100	100	100	100	100	100
fp rate		0	0	0	0	0	0	0	0	0	0	0	0
Urban traffic map
		n = 60, t = 300				n = 90, t = 300				n = 120, t = 300
		Actual				Actual				Actual
		1	2	3	4	1	2	3	4	1	2	3	4
Predicted	1	110	0	0	0	176	0	0	0	235	0	0	0
	2	0	141	0	0	0	195	0	0	0	281	0	0
	3	0	0	315	0	0	0	424	0	0	0	710	0
	4	0	0	0	83	0	0	0	97	0	0	0	134
tp rate (%)		100	100	100	100	100	100	100	100	100	100	100	100
fp rate		0	0	0	0	0	0	0	0	0	0	0	0

ROC: receiver operating characteristics; FCM: fuzzy c-means.

Locating the jammer source

In the last section, the point set $X$ is classified into $k$ clusters, but the cluster centers obtained from weight-based FCM are not precise enough. A new approach which can estimate the coordinates of jammer in each classified cluster is needed. We formulate this problem of localizing the jammer source as an optimalization problem. It can generally be described as the point set $C_{j}$ is given; we need to produce the minimum circle area which can cover all the points in $C_{j}$ . To address this optimalization problem, we use PSO algorithm.

PSO algorithm

There are two insights of a process of optimization using swarm particles:³⁹ First, being assumed as particles in space, the points will tend to move toward and influence one another, with the objective of seeking agreement with their neighbors; second, the space in which the particles move is heterogeneous with respect to evaluation: some regions are better than others. Some points in the parameter space result in greater fitness than others. With this architecture, the process of finding better regions can be viewed as solving the problems of optimization. As a typical method for the implementation of swarm intelligence (SI), the PSO algorithm^39,40 is inspired by social behavior of bird flocking or fish schooling. PSO is a population-based stochastic optimization technique and also a popular and robust strategy for some optimization problems.⁴¹ PSO algorithm suggests that individuals moving through a socio-cognitive space should be influenced by their own previous behaviors and by the successes of their neighbors. As the system is dynamic, each individual is presumed to be moving at all times. The direction of movement is a function of the current position and velocity, the location of the previous best success of individual, and the best position found by any member of the neighborhoods. It has been shown in equation (6)

{\begin{matrix} {\vec{v}}_{i}^{(t)} = {\vec{v}}_{i}^{(t - 1)} + φ_{1} (p_{l} - {\vec{x}}_{i}^{(t - 1)}) + φ_{2} (p_{g} - {\vec{x}}_{i}^{(t - 1)}) \\ {x_{i}}^{(t)} = {x_{i}}^{(t - 1)} + {\vec{v}}_{i}^{(t)} \end{matrix}

(6)

In equation (6), $x_{i}$ is the algebraic symbol of the position of a particle $i$ ; ${\vec{v}}_{i}$ is called for velocity, and it is a vector that is added to the position coordinates in order to move the particles through iteration; $φ_{1}$ and $φ_{2}$ are the effective parameters; $p_{l}$ is the best solution of particle $i$ in advance; $p_{g}$ is the best solution of all particles in advance.

System evolution

When the point set $C_{j}$ is given, we assume any point $a$ ( $a$ has the same dimensionality with $x_{i}$ in $X$ , and it represents a position on map) on open map or urban traffic map as the circle center. Under this premise, the area of minimal covering circle can be expressed as equation (7), where $x_{i}^{j}$ is the ith element in $C_{j}$ , $| C_{j} |$ is the total number of elements in $C_{j}$ , and $| | x_{i}^{j} - a | |$ is the Euclidean distance between point $x_{i}^{j}$ and circle center $a$

S_{a} = max {π | | x_{i}^{j} - a | |^{2}}, i = 1, 2, 3, . . ., | C_{j} |

(7)

Then, the problem of using $C_{j}$ to locate the jammer source can be seen as a strategy to find the most appropriate $a$ with minimal $S_{a}$ . It is clear to find that every point on map is a potential solution toward the optimal $a$ . PSO algorithm is qualified to solve this problem as its swarm particles scan all potential solutions. With the use of PSO algorithm, the task becomes a process of searching the minimum value of $S_{a}$ at the optimal circle center $a$ in equation (8)

S_{optimal} = min_{a \in D} {S_{a}}, D is the set of all points on map

(8)

In order to use PSO algorithm to obtain the minimum value of $S_{a}$ , it is necessary to determine the self-optimal circle center $p_{l}$ and the global optimal circle center $p_{g}$ . If we use $n$ particles to search the best solution of circle center $a_{optimal}$ , every particle denotes a potential solution of $a_{optimal}$ ; so, the particle $h$ is represented as $a_{h}$ , and $S_{a_{h}}$ represents the area at $a_{h}$ , where $h = 1, 2, 3, . . ., n$ . Then, the self-optimal circle center of particle $h$ named $p_{hl}$ can be defined easily as the value of $a_{h}$ when the minimum $S_{a_{h}}$ in the previous iterations is obtained. And the global optimal circle center $p_{g}$ is defined as the value of $p_{hl}$ when the minimum $S_{p_{hl}}$ in the previous iterations is obtained.

PSO algorithm can be consequently taken into consideration as a mean for looking for the most appropriate circle center by the following equation

{\begin{matrix} {\vec{v}}_{h}^{(t)} = {\vec{v}}_{h}^{(t - 1)} + {\vec{φ}}_{1} (p_{hl} - {a_{h}}^{(t - 1)}) + φ_{2} (p_{g} - {\vec{a}}_{h}^{(t - 1)}) \\ {a_{h}}^{(t)} = {a_{h}}^{(t - 1)} + {\vec{v}}_{h}^{(t)} \end{matrix}

(9)

When using PSO algorithm to find the extremum of a function, it will fall in a stable state after several iterations. Moreover, almost all particles are equal to the global optimal centroid $p_{g}$ . That means all potential solutions reach an agreement. Then, the criteria for stopping iterations of algorithm can be defined as equation (10), where $a_{h} (k)$ is the value of $a_{h}$ at kth iteration. The details of PSO algorithm are presented in Algorithm 2

V_{stop} = \frac{\sum_{h = 1}^{n} (a_{h} (k) - p_{g})}{n} < ε

(10)

Algorithm 2 Algorithm for locating the jammer source
1: Import particle size $n$ , initialize particle value $a_{h} (0)$ ;2: input data set: $C_{j}$ , iteration number $m = 1$ ;3: for $h = 1$ ; $h < n$ ; $h + +$ do4: $p_{hl} = a_{h} (0)$ , $S_{p_{hl}} = S_{a_{h}} (0)$ 5: end for6: $p_{g} = p_{kl}$ , where $S_{p_{kl}} = min_{h \in [1, n]} {S_{p_{hl}}}$ 7: repeat8: for $h = 1$ ; $h < n$ ; $h + +$ do9: Calculate ${\vec{v}}_{h} (m)$ and $a_{h} (m)$ 10: for all $x_{i}^{j}$ in $C_{j}$ do11: $d_{i} = \| \| x_{i}^{j} - a_{h} (m) \| \|$ 12: $S_{a_{h}} (m) = π (max {d_{i}})^{2}$ 13: end for14: if $S_{a_{h}} (m) \leq S_{p_{hl}}$ then15: $p_{hl} = a_{h} (m)$ ;16: end if17: end for18: for $h = 1$ ; $h < n$ ; $h + +$ do19: if $S_{p_{hl}} \leq S_{p_{g}}$ then20: $p_{g} = p_{hl}$ ;21: end if22: end for23: $m = m + 1$ 24: until $V_{stop} < ε$ 25: $Jammerlocation = p_{g}$ ;

Algorithm 2 Algorithm for locating the jammer source

1: Import particle size

n

, initialize particle value

a_{h} (0)

;2: input data set:

C_{j}

, iteration number

m = 1

;3: for

h = 1

;

h < n

;

h + +

do4:

p_{hl} = a_{h} (0)

S_{p_{hl}} = S_{a_{h}} (0)

5: end for6:

p_{g} = p_{kl}

, where

S_{p_{kl}} = min_{h \in [1, n]} {S_{p_{hl}}}

7: repeat8: for

h = 1

;

h < n

;

h + +

do9: Calculate

{\vec{v}}_{h} (m)

and

a_{h} (m)

10: for all

x_{i}^{j}

C_{j}

do11:

d_{i} = | | x_{i}^{j} - a_{h} (m) | |

12:

S_{a_{h}} (m) = π (max {d_{i}})^{2}

13: end for14: if

S_{a_{h}} (m) \leq S_{p_{hl}}

then15:

p_{hl} = a_{h} (m)

;16: end if17: end for18: for

h = 1

;

h < n

;

h + +

do19: if

S_{p_{hl}} \leq S_{p_{g}}

then20:

p_{g} = p_{hl}

;21: end if22: end for23:

m = m + 1

24: until

V_{stop} < ε

25:

Jammerlocation = p_{g}

;

In addition, as shown in Figure 10, sometimes the distribution of the points in $C_{j}$ is partial. This situation often appears in urban traffic maps than the open map because the vehicles are placed on road strictly and the existence of inaccessible areas. It will lead to a local optimization and result in an incorrect localization. In another word, the differences among the points in $C_{j}$ are insufficient to lead the particles to move toward a more appropriate position. To avoid the local optimization, the beaconing circle is used as a threshold, and the optimal solution is to find the minimum covering circle area of $C_{j}$ which is close to its beaconing circle. The beaconing circle area of $C_{j}$ is shown in equation (11), where $a$ is still the potential solution, and $| Y |$ is the total number of elements in $Y$ . In this condition, we use PSO algorithm to search the minimum value of $| S_{beconing} - S_{a} |$ instead of $S_{a}$ . We call it weight-based PSO. It is important to point out that weight-based PSO algorithm is different from PSO algorithm: the weight-based PSO uses the absolute value of $S_{beconing} - S_{a}$ , when the weight-based PSO algorithm is performed to find the circle which is closest to the beaconing circle, some different values of $a$ will reach the same evaluation value of $| S_{beconing} - S_{a} |$ . The reason is that there exists two potential solutions $a_{1}, a_{2}$ which make $S_{beconing} - S_{a_{1}} = S_{a_{2}} - S_{beconing}$ . The particles are not sure that which one is better to agree with; they will oscillate between $a_{1}$ and $a_{2}$ . Therefore, they cannot converge to a point $a_{optimal}$ . Instead, the distance between $a_{1}$ and $a_{2}$ can be used as the acceptable error, and many pairs of $a_{1}, a_{2}$ form an area which can be seen as a circle range with the center $a_{optimal}$ . And the weight-based PSO converges to this region. Hence, the error generated by weight-based PSO is larger than PSO when $C_{j}$ is not partly distributed. It is only developed to address the localization problems with partly distributed $C_{j}$

S_{beaconing} = min {π | | y_{i} - a | |^{2}}, i = 1, 2, 3, . . ., | Y |

(11)

Figure 10.

Situation of the point set $C_{j}$ is partly distributed.

Experimental evaluation

The following experiments are to evaluate the effectiveness of locating jammer with PSO algorithm and make comparisons with some existing range-free and range-based location algorithms.

Experimental environment

We implemented our approach in MATLAB as well. The maps, motion model of vehicles we used in this section are the identical ones that we used in the last section. The particle size $m = 50$ , simulation time $t = 200$ , and the PSO effective parameters $ε = 0.1, φ_{1} = 0.0001 \times rand (1)$ , and $φ_{2} = 0.0003 \times rand (1)$ , where $rand (1)$ represents a random number from $0$ to $1$ , and it will make the trajectory of every particle as the sine wave. The localization errors have been defined as the following: the Euclidean distance between the estimated location of the jammer and the true location of the jammer in the network. And the localization error can be seen as an important metric to evaluate the accuracy of our PSO algorithm in comparison to the others. The results show three different scenarios. The first two scenarios evaluate the performance of locating the jammer using CL,²⁷ WCL,²⁸ MCCL,³⁴ and PSO. However, in first scenario, we show how to vary parameters like jammer’s transmission range and vehicle number can affect the performance of locating jammer; The second scenario shows weight-based PSO works well when $C_{j}$ is partly distributed. In the last scenario, we analyze the strengths and weaknesses of each localization method, and we further compare our proposed method to a well-known range-based localization method.

Validity experiments of PSO algorithm

When the particle size is determined, the only input data is $C_{j}$ . So, the distribution of $C_{j}$ and the number of members $| C_{j} |$ are worthy of researching. In this experiment, we consider the impact of $| C_{j} |$ on the accuracy of locating a jammer. Because the simulation time is fixed, $| C_{j} |$ only increases with the vehicle number $n$ and jammer’s transmission range $R$ .

First, we consider the impact of jammer’s transmission range. We kept vehicle number the same ( $n = 30$ on open map and $n = 60$ on urban traffic map), but jammer’s transmission range has been changing during four standard values 30, 50, 100, and 150 ft. Each location algorithm was used to obtain the estimated position of the jammer, and the jammer with the same transmission range was deployed at 30 different locations. The situation indicates that each algorithm ran 30 times. We provide a view of cumulative distribution function (CDF) curves for the generated results in Figures 11 and 12, where the x-axis represents the localization errors, and the y-axis represents the percentage values of CDF. The CDF curves indicate the probability of the localization errors produced by our experiments are less than a fixed value of localization error.

Figure 11.

CDF curves with different jammer’s transmission range when vehicle number is fixed on open map: (a) transmission range R = 30 ft, (b) transmission range R = 50 ft, (c) transmission range R = 100 ft, and (d) transmission range R = 150 ft.

Figure 12.

CDF curves with different jammer’s transmission range when vehicle number is fixed on urban traffic map: (a) transmission range R = 30 ft, (b) transmission range R = 50 ft, (c) transmission range R = 100 ft, and (d) transmission range R = 150 ft.

Figure 11 shows the performances of four different localization algorithms in the scenario of an open map. Figure 12 shows the same performance in the scenario of an urban traffic map. In general, we observe that PSO algorithm always has the highest precision, while the errors generated by PSO are stable and almost less than 1 in all cases. Furthermore, as the jammer’s transmission range increases, the localization error becomes smaller. It indicates that the PSO algorithm is sensitive to the transmission range. The reason is when the jammer’s transmission range becomes larger, the jammed area grows larger as well. And more jammed points will be detected and added in $C_{j}$ . That means, the more points in the circle will join into the estimation process. In addition, the localization errors generated with open map are lower than the same errors generated with urban traffic map. The reason is that the urban traffic map has inaccessible areas which makes the detected jammed points only distribute on some fixed roads in this circle; Finally, when the transmission range $R$ is small, for example, when R=30 ft, the errors are unstable. Such situation is also caused by the non-uniform distribution of $C_{j}$ . In fact, the localization error is significantly impacted by the detected points whether or not to locate in most areas of the jammed circle. More different areas indicate that the diversity of particles is significantly bigger, and it is important for PSO to reach the best decision through a process of evolution. Larger $| C_{j} |$ simply means detected points has a big chance to be located in more areas.

Second, we consider the impact of vehicle number. The transmission range of the jammer was fixed at 50 ft. The vehicle number was varied from 20, 30, 50 on open map and 40, 60, 100 on urban traffic map. The reason we chose these numbers is because the urban traffic map is bigger than the open map in our simulation. Each localization algorithm was run 30 times to obtain the estimated positions of different jammers. The experimental results are shown in Figures 13 and 14, where the x-axis represents the localization errors, and the y-axis represents the percentage values of CDF.

Figure 13.

CDF curves with different vehicle number when the transmission range is fixed on open map: (a) vehicle number n = 20, (b) vehicle number n = 30, and (c) vehicle number n = 50.

Figure 14.

CDF curves with different vehicle number when the transmission range is fixed on urban traffic map: (a) vehicle number n = 40, (b) Vehicle number n = 60, and (c) vehicle number n = 100.

As shown in Figures 13 and 14, we observe that PSO algorithm still achieves the best localization accuracy, and it is sensitive to the number of vehicles. The larger the number is, the better the localization accuracy is. The reason is that more vehicles are used in the experiment, so more jammed points are recorded by them. As mentioned above, larger vehicle number also leads to a big chance to get more different areas in the jammed circle so that it can improve the localization accuracy.

Validity experiments of weight-based PSO algorithm

We have introduced the applied scene of weight-based PSO above. In this experiment, we created a corresponding jammed region which allows vehicles to access partial areas. We implemented our experiment only on open map. The transmission range of the jammer was fixed at 100 ft, while the vehicle number was fixed at 50. Each localization algorithm was ran 30 times to obtain the estimated positions of different jammers. Figure 15 shows the experimental results, where the x-axis represents the localization errors, and the y-axis represents the percentage values of CDF. Overall, we observe that all the other algorithms fail into an unacceptable lower precision except weight-based PSO. Because it is performed to find the circle which does not include any element of $Y$ , it means no-jammed points are not allowed to be located in a jammed circle. However, the errors are also a little high; it clearly validates that weight-based PSO algorithm is only suitable for special situations.

Figure 15.

CDF curves with different localization algorithms when $n = 50, R = 100 ft$ , and $C_{j}$ is partly distributed.

Comparison and analysis

In VANET, compared to the signal processing–based localization techniques, RSS-based localization techniques and some existing range-free-based techniques, the PSO-based range-free localization algorithm we proposed has several advantages. The advantages can be described as follows:

Compared to the signal processing–based localization techniques, our method is software based which operates at application layer instead of physical layer. Our method does not rely on the additional infrastructure like ultrasound, infrared, or laser. This feature can significantly reduce the cost of jammer localization when there are many jamming attackers on the bigger concerned map.

Compared to the RSS-based techniques mentioned in section “Related work,” our method does not rely on the RSS measurements at various positions. Instead, our method is a self-diagnosed method because it uses the normal nodes in VANET to collect information, and the collected information is processed by the server. When RSS-based techniques are used to localize jamming attackers, at least three landmarks are required to monitor RSS values in jammed region. On one hand, the trilateration algorithm is the only method which can be used in the situation of three landmarks, yet the accuracy of this algorithm is lower than the other methods. On the other hand, the concerned map in VANET is always at a big scale (a city-wide traffic map), and the landmarks are required to be uniformly located with a high density on the map. The project of deploying such a large number of landmarks is unpractical, despite the fact that in some cases, certain RSUs can be reused as landmarks. Furthermore, all the existing RSS-based methods focus on the wireless networks whose nodes are static, which means the RSS readings of empty load are easy to measure through an overall management. However, in VANET, vehicles are mobile nodes, and they have complete autonomy. Also, their movement is unpredictable. Thus, the RSS measurements can be seriously interfered by vehicles. As a result, the localization accuracy is unsatisfactory.

Compared to the existing range-free techniques, our proposed method is based on geometric covering. And PSO-based solution is an evolutive model, and it indicates that if the diversity of reference positions is greater, the obtained results are more precise. Moreover, our proposed weight-based PSO algorithm also performs well in jammer localization when the data set is partly distributed. The reason is that the mobile nodes are considered in our research; due to the continuity of motion, we use the beaconing circle to lead the particles to move toward the best solution. In addition, the computational complexity of our method is $O (k * i * n)$ , where $k$ is the particle size, $i$ is the iteration number, and $n$ is the number of reference positions. In VANET, the collected information seems much greater than the used particle size and iteration number in our experiment. So, the computational complexity is approximately equal to $O (n)$ , and it is a linear complexity.

The comparative experiments between the existing range-free solutions and our proposed solution have been implemented and discussed in previous sections. To further illustrate our viewpoints, a RSS-based method which uses trilateration localization algorithm is simulated in this section. We use three landmarks to measure RSS values. The transmission range of jammer is 50 ft, and the shadowing model is used to evaluate the distance between jammer and landmarks as shown in equation (12), where $i, j = 1, 2, 3$ and $i \neq j$ ; $P L_{i}$ represents the path loss at ith landmark; $P_{J}$ is the transmit power of jammer; $P_{r_{i}}$ and $P_{r_{j}}$ represent the RSS readings at ith and jth landmark, respectively; the term $P L_{0}$ represents the path loss at a known reference distance $d_{0}$ ; $d_{i}$ and $d_{j}$ represent the distances between the jammer and $i, j th$ landmark; $λ$ is the path loss exponent; $X_{σ}$ is the shadow fading which follows zero-mean Gaussian distribution with $σ$ standard deviation.⁴² Hence, the position of jammer $(x_{J}, y_{J})$ can be computed with the positions of landmarks. Whether or not the RSS values can be interfered by vehicles were considered in our experiment, and all algorithms were run 30 times. The CDF-based comparison graph of RSS-based trilateration algorithm and our proposed method is shown in Figure 16, where x-axis represents the localization error and y-axis represents the values of CDF. We can observe that our proposed method performs better than trilateration algorithm, and the localization error generated by the trilateration algorithm is too big to accept when there exists an interference

{\begin{matrix} P L_{i} = P_{J} - P_{r_{i}} = P L_{0} + 10 λ \log_{10} (d_{i} / d_{0}) + X_{σ} \\ 10 λ \log_{10} (d_{i} / d_{j}) = P_{r_{j}} - P_{r_{i}} \end{matrix}

(12)

Figure 16.

Comparison graph of RSS-based trilateration algorithm and PSO algorithm.

General-purpose localization framework of positioning multiple jammer

VANET is different from other wireless networks. It is a self-organized P2P wireless network. It has several features compared to WSN: first, the node size and applied regions of VANET are much bigger, the hardware-based methods are hard to be deployed; second, nodes in VANET are more powerful on energy and computational ability, and most of them have an on-board GPS receiver. But, nodes in WSN are always energy constrained and computational ability constrained, and the positional information only can be computed with sensor data without any calibration; Third, every node in VANET has complete autonomy, and they are uncontrolled and unpredictable. All nodes can be used as information collectors instead of processors, and the RSUs can be easily reused as repeater stations; Fourth, the control channel of VANET is completely accessible for any user; some interference avoidance algorithms are not useful. Based on these facts, we have proposed a general-purpose localization framework to perform real-time jammer positioning. This framework is designed with fully distributed functionality, and it is easy to be deployed in real world. It is built around all components in VANET: OBUs, RSUs, and server. The framework architecture is identical as it has been shown in Figure 1. During the localization process, the following steps will take place:

The vehicles record their own GPS information and combine them with the if-jammed signal in every fixed time interval.

Vehicles transmit their recorded information to the RSU when vehicles enter the coverage communication range of this RSU.

RSU forwards its collected information to the application server.

Application sever use weight-based FCM and PSO algorithms to localize multiple jamming attackers.

If there is a need to use certain anti-jamming methods, the server can transmit the jammer location and the jamming range to vehicles through RSUs. These results can help vehicles to take corresponding measures in jammed region and further reduce the energy use.

Conclusion

In this article, we proposed to use a range-free solution to localize multiple jamming attackers in VANET. Vehicles only need to record their positions and if-jammed signal in every fixed time interval. This method does not rely on cryptography and additional hardware infrastructures as the basis. We formulate the problem of localizing multiple jamming attackers as a process of determining cluster number, classifying data, and searching circle center on the data set which consists of the information collected by vehicles. First, we provide two new definitions of Beaconing circle and Coverage rate, and we give a theoretical analysis of using them for determining the number of attackers; Then, we provide a weighted distance to improve FCM algorithm named weight-based FCM and use it for clustering the collected data set. Furthermore, we use PSO algorithm to localize the jammer source in each classified cluster, and a weight-based PSO algorithm is also developed to estimate the jammer location in the partly distributed data set. Finally, we provide a useful general-purpose localization framework to apply our approach in practical applications.

To validate our approach, we conducted many simulation experiments in MATLAB associated with the data set generated by the SUMO simulator. The experimental results provide strong evidence of the effectiveness of our proposed approach. We discover that the Coverage rate can determine the number of adversaries correctly, and weight-based FCM always performs an accurate classification which is better than the other clustering algorithms. We also observe that PSO can always achieve a higher precision than the other existing range-free algorithms, while weight-based PSO can still make a more effective estimation when the distribution of data set is partial.

Footnotes

Acknowledgements

The authors would like to thank the anonymous reviewers for helpful comments. L.P. and X.C. contributed equally to this work and share first authorship.

Academic Editor: Zhipeng Cai

Declaration of cconflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported in part by the National Natural Science Foundation of China under grant nos 61171173, 60932003, 61271220, and 61864068. This work was also supported in part by “Security in Internet of things” which is a subproject of Project Xuguangqi.

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Localization of multiple jamming attackers in vehicular ad hoc network

Abstract

Keywords

Introduction

Related work

Network assumptions

Network model

Jamming model

Determining the number of attackers and classifying the data set

Weight-based FCM

Beaconing circle and coverage rate

Definition 1 (Beaconing circle)

Definition 2 (Coverage rate)

System evolution

Experimental evaluation

Experimental environment

Validity and comparative experiments of attackers estimated method

Comparison of weight-based FCM and other clustering algorithms

Performance experiments of weight-based FCM

Locating the jammer source

PSO algorithm

System evolution

Experimental evaluation

Experimental environment

Validity experiments of PSO algorithm

Validity experiments of weight-based PSO algorithm

Comparison and analysis

General-purpose localization framework of positioning multiple jammer

Conclusion

Footnotes

Acknowledgements

Declaration of cconflicting interests

Funding

References