Restricting passive attacks in 6G vehicular networks: a physical layer security perspective

Modern wireless technologies confirm the massive connectivity with sufficient data rate in intelligent transportation systems. Passive attacks may compromise the user’s transmission with increased amenities. Physical layer security can protect transmissions. The paper investigates outage probability (OP) and secrecy outage probability (SOP) for 6G enabled vehicular networks with passive eavesdroppers. The work considers the vehicular to infrastructure scenario with re configurable intelligent surfaces (RIS) instead of power-hungry roadside units. The vehicles and passive eavesdroppers are equipped with dual antennas. Specifically, for 6G vehicular networks, this work presents the analytical expressions for the received signal-to-noise ratio (SNR). We derive first-order secrecy metrics, such as outage probability and secrecy outage probability, from SNR expressions. We have derived SNR expressions for two initial receiver locations (near and far from the legitimate). Due to their robustness towards road parameters and signal parameters, the developed expressions aid in designing and simulating secrecy systems. We conclude that RIS can be more effective than regular access points because no major fluctuations have been observed in secrecy metrics under the influence of RIS.


Introduction
The services like infotainment, multimedia, driver assistance, route assistance, and lane changing alert needs to have secure transmissions of alert messages, and safety messages. To broadcast such an important information between the nodes, and to withstand over active or passive eavesdropping attacks, physical layer security (PLS) appears an an alternative to enhance the wireless security [1]. From the information theoretic perspective, PLS and its involved metrics have been highlighted in [2]. 6G communications are expected to boost coverage and data rates while also allowing users to connect with one another from anywhere. It is intended to use unusual communication networks to access various sorts of data and transfer them via better radio frequency (RF) networks, allowing for a novel communication experience with virtual existence and involvement from anywhere [3]. The large proliferation of connections in future 6G networks would, without a doubt, create security and privacy concerns. Given the anticipated technological, architectural, and application-specific developments in future 6G networks, a need for PLS for 6G networks for one of its primary relevant networks, such as vehicle networks, has arisen [4].

Related works
PLS is a promising way to resist the eavesdropping and thus it is highly effective for infotainment and multimedia services in intelligent transportation systems. Moreover, it is true that maintaining the security and privacy in a wireless communications is a challenging task at design and simulation perspective. The several approaches have been considered to tackle the designing and simulation task of the secret and private communications systems over noisy fading channels. The approaches are categorised into classical methods and an information theoretic methods.
The classical approach focuses on derivations of the analytical expressions of performance metric related to physical layer security (PLS) while information theoretic methods focuses on the fundamental limits of the performance metrics [2]. Several works have been proposed in literature that focuses on finding secrey performance metrics considering 6G network components in [5][6][7]. In addition to that, for vehicular communications, the in depth survey has been provided in [8] which includes the importance of communication security required for vehicle users. Furthermore, the works in [9,10] focuses on to improve the secrecy performance in wireless networks. Several underlay CR scheme is also provided. Recently, the works [11][12][13][14][15][16][17][18] focuses on various aspects of secrecy performance including the vehicular networks. For underlay CR systems, the work in [19] has proposed the analytical model of secrecy outage probability for single input multiple output (SIMO) systems. Furthermore, PLS for multiple-input multiple-output (MIMO) systems has been analyzed considering Nakagami-m fading under optimal, sub-optimal, and transmit antenna selection scheme [20]. Several studies look into two vehicular network system models: one with vehicle-to-vehicle communication and a RIS based access point as the source, and the other as a vehicular adhoc network (VANET) with a RIS-based relay mounted on a building [21][22][23] (Table 1).
Due to their ease of deployment and variable configuration, RIS-based technologies can be targeted for mobile nodes in vehicle networks. They can be deployed in a variety of shapes, locations, and sizes, ranging from tens to hundreds of cells. Furthermore, existing RIS-related literature has revealed that most RIS-enabled applications are built with the RIS acting as a reflector, as the primary benefit of using a RIS is to control the radio environment for transmissions via smart reflections. Other research, on the other hand, have used the RIS as a signal transmitter (or access point) or as a signal receiver.

Motivations and novelty
Although several prior research [3,4,[21][22][23] assumed quasi static node positions for simplicity of analysis, the mobility effect of nodes has been proven to impair the performance of vehicular nodes. However, it has recently been demonstrated that adopting a real-time tuneable RIS can successfully mitigate rapid changes in received signal strength caused by the doppler effect. Given that the existing research on RIS assisted PLS for non-vehicular applications has only revealed some preliminary simulation findings, there is a need for precise analytical analysis to quickly determine PLS parameters. None of the existing work shows the impact of mobility on received signal-tonoise ratio (SNR) by considering RIS and derived the first order secrecy metrics like outage probability (OP) and secrecy outage probability (SOP) that depends on the road, and vehicle parameters (like road width, length and velocity) as well as signal parameters (instantaneous SNR, and number of receiving branches). Therefore, this research attempts to fill the research gap by contributing in PLS for 6G vehicular networks ( Table 2).

Contributions
Based on the aforementioned motivations, the contributions of this work can be summarised as under: 1. The statistical knowledge in terms of probability distribution function (PDF) of received signal-to-noise ratio (SNR) is derived under the impact of mobility for 6G vehicular networks. Two different initial position of the legitimate receiver has been considered to show the impact of road width on signal strength. The legitimate and eavesdropper nodes' distances are taken into account (from the RIS), as well as realistic fading scenarios for base stations and vehicular mobile nodes. 2. The analytical closed form expression has been derived for the outage probability (OP )secrecy outage probability (SOP). The impact of fading parameters of generalised K fading has been highlighted. Moreover, the impact of velocity on the performance of SOP along with the fading parameters has been covered. The PLS analysis is carried out by examining and deriving expressions for the system's OP and SOP. The developed formulas make it simple to investigate important system parameters.

System model
This section represents the network scenario considered for analyse the eavesdropping. The received signal at the legitimate transmitter, and eavesdropper has been provided. The 6G channel model is also described using RIS. Moreover, to represent the impact of vehicle velocity, the mobility model is also provided as a function of path loss and fading model (Table 3).

Network model with legitimate receiver and eavesdropper
The urban road scenario is shown in Fig. 1. we consider a RIS enabled vehicular network consisting of one legitimate transmitter (P), RIS equipped on building (S), and one legitimate receiver (R) in the presence of one eavesdropper (E). The legitimate receiver begins the journey from Point A towards Point D. In between that, the passive eavesdropper (E) tries to observe the transmission occurring between S and P through R. Each legitimate receiver contains the dual antenna with at least spacing grater than of k=2. For the particular scenario, the the vehicle user may not exceed the speed limit beyond 60 km/h and there is at least 100 m distance between legitimate receiver and eavesdropper. The width of the road b is 30 m. The length of the road c is 4 km. The distance of the RIS from the legitimate receiver a is 500 m.

6G channel model
In addition to the traditional channel features discussed in [24], two additional properties, namely dual mobility and absolute time of arrival, are also relevant in the control channel of cars and moveable robots in vehicular networks. Scenarios for the IIoT The dual mobility model should be used in 3GPP TR 37.885, according to the revised proposal in [25]. The LoS path's Doppler shift can be written as follows: In general, the channel model can be represented as the sum of a random phasor with a log-normal distribution and a Rayleigh phasor.
where u is the received signal at S. z is log normally distributed, and w is Rayleigh distributed. In this scenario, the signal amplitude's probability density function (PDF) is as follows: where p b ðrÞ is the PDF of mobile fading, and p w ðrÞ is the PDF of weather impairments. Rain, clouds, and tropospheric scintillation are among the meteorological phenomena supported by this model. Azimuth angle relative to the driving direction of the mobile terminal was shown to affect channel statistics in [24], in addition to the environment type and satellite height. Furthermore, an imagebased state estimation method was used to propose a statistical land mobile satellite channel model for variable elevation and azimuth angles.

Signal model at legitimate receiver
The received signal vector in the main channel at time slot l is given by [19]: where the main channel vector between transmit antenna and receive antenna is The instantaneous SNR in the main channel is calculated by combining the subset of receive antennas with the highest SNRs at R is given as.
The received signal at the eavesdropper's channel at time slot t is given by: The h is modelled as a function of distance between legitimate transmitter and eavesdropper as follows [18]: where g x is the channel gain modelled generalised K fading as a function of Nakagami-m channel. d x is the distribution of distance between S and R. a is the path loss component.

Preliminaries PDF of fading and distance distributions
The fading amplitude at R, which is a random variable (RV) with a KG distribution, has a PDF of [26]: where k and m are the parameters for shaping the distribution; The modified bessel function is given as K kÀm . For K ! 1 it reduces to dynamic Nakagami-m which is suitable for 5G and beyond vehicular networks. It is clear that a higher density is associated with a lower average velocity. In thick traffic, the speed distribution can be stated as [27]: When the R is at the nearer edge of the road from S, the PDF of distance is given as [27]: When the R is at the far edge of the road from S, the PDF of distance is given as [27]: Àarcsin where h ¼ a þ b, the total distance with addition of road width and distance of S from edge from Fig. 1.

Derivations of signal-to-noise ratio under mobility for 6G vehicular networks
This section mainly delivers the analytical expressions of SNR under impact of mobility for 6G vehicular networks. The joint PDF is obtained by solving the chain of the integration. From (7), it can be seen that the resultant PDF can be obtained by the ratio of two distributions. In that particular direction, the cumulative density function (CDF) can be represented as: By substituting (8) and (10) in (12), the foundation integral of the CDF of received SNR when R is near to S can be written as: Similarly, by substituting (8) and (11) in (12),the foundation integral of the CDF of received SNR when R is far to S can be written as: We simplify the (15) for evaluating the inner integral, and keeping the constant outside, the integration can be rewritten as: Similarly, we simplify the (16) for evaluating the inner integral, and keeping the constant outside, the integration can be rewritten as: It can be seen from the above expression that the special integral rules are helpful to obtain the solution from [28]. Therefore, we use the following identity and compare the inner integral terms to solve the limits which is further expresses as: By simplifying (15) further and taking differentiation, the PDF of received SNR when R is near to the S is expressed as: By simplifying (16) further and taking differentiation, the PDF of received SNR when R is far to the S is expressed as: where k is the dual branches. In this section, the Secrecy Outage Probability is derived for a considered network model in Fig. 1. The Secrecy Outage Probability is given as: By substituting the integrals of (15) and (18) in (22) the integral term for the SOP for 6G vehicular networks when R is near to S is given as: For the further analysis of above integral, let The SOP which is given (23) can be solved by altering the bounds and solving the integral in MATHEMATICA software using the particular integral rules provided in [29] as well as stripping constants out of the integral and identifying certain operations. The solution reduces in terms of the Lauricella hypergeometric function is represented as F 1 . Similarly, the SOP for 6G vehicular networks when R is far to S is given as: The solutions of integral (23) and (24) results in the SOP expressions depended upon the location of legitimate receiver from RIS. The SOP when R is near to S is given as (23), and when R is far to S is given as (24). where in (23), K u is defined as Kummer's solution provided in [29] in which z 1 , z 2 , z 3 are Cð2L À 1Þ, threshould SNR(k) at R, and instantaneous SNR (c) at R respectively. where in (24), l 1 , l 2 , l 3 is expressed as m 2LÀ1 , mc, k respectively. See Appendix A. h

Outage probability for 6G vehicular networks
In this section, we derive the closed-form expression of OP for 6G vehicular networks. The OP determines the minimum information rate on which the successful communication can happen. It also implies that if the certain code rate is not suitable for the transmission, the possibility of eavesdropping can occur. The mathematical expression of OP can be written as follows: From above expression, it can be noticed that the OP is the continuous summation over a region limited to its threshold value. By substituting (18) in (29), and represent the variable in terms of r the integral when R is near to S can be represented as: Similarly, by substituting (19) in (26), and represent the variable in terms of r the integral when R is near to S can be represented as (26). On further solving of the integrals in (27) and (28), the OP can be obtained as (31). In which is the balance parameter.

Numerical results
In this section, we present and discuss some of the outcomes produced from the paper's mathematical expressions. The effect of important parameters on the system's secrecy performance is then investigated. The monte-carlo simulations has been conducted using MATLAB software over 10 10 times. For the Nakagami-m channel, we use method highlighted in [26], and 6G channels samples are generated with the help of [4]. For all the simulations, the road parameters are considered as c ¼ 4 km, m ¼ 4, b ¼ 30 m, a ¼ 500 m, k ¼ 2, R S ¼ 1 mbps. The velocity of the vehicle is considered up to 40 kmph. We consider the RIS ranges upto 100 m with various angles. However, for achieving the maximum bandwidth, antenna placement should be as accurate as possible. The simulations validates the analytical expressions and its convergence with respect to the code rate, SNR, and velocity of the vehicle. To show the impact of velocity in SNR, and as well as in simulations, we create the functions of the analytical expressions of received SNR and create the samples of it. Figure 2 shows the plots of OP against SNR for 6G vehicular networks. The vehicle speed is considered upto 40 kmph. It can be seen from the Fig. that the distance of the vehicle from RIS can make a significant impact on the OP under the impact of velocity. However, it can be compensated by considering the best possible fading parameter. For example m ¼ 4 and higher which results in line-of-sight communication. It can be also seen that if the eavesdropper and legitimate receiver have the similar speed, then the whomsoever fading link is under the deep fade can be intruded. This implies that under the passive attack, in which the identity of the eavesdropper is not known, the fading parameter should be considered as high as possible. The OP decreases with the increasing SNR due to the increasing strength of the transmitted signal towards legitimate receiver. It also confirms that the impact of the non linear medium parameter not only affect the OP but also affect the rapid decrements of the OP. We also validate the performance of OP with shape preserving interpolate which is useful to take confidence on the obtained simulations and its shape with respect to the considered parameter. In this case, we obtain the similar curve of the OP against SNR that decreases with the increasing SNR. Figure 3 shows the plots of SOP against SNR for 6G vehicular networks. The vehicle speed is considered upto 40 kmph. It can be seen from the figure that the distance of the vehicle from RIS can make a significant impact on the SOP under the impact of velocity. The far the distance the more chances of being intruded. Here, in this case, the increment in the velocity does not make any impact on the increment on the SOP from 20 to 30 km. This implies that the SOP is a function of the distance from RIS. Provided that the eavesdropper has sufficient rate and even higher rate than legitimate receiver, the results suggest the probability of the system being in outage at any point of communications. It can be seen from the result that the higher the rate at eavesdropper, the more chance is occurred of information interruption. Figure 6 is the important result in terms of the placement of RIS from the primary transmitter to vehicle users. It can be seen that the angle towards the vehicle side should be under 50 degree in order to achieve full line of sight communication under maximum power transmission. This is also validated by plotting the 7th order polynomial of the secrecy metric. This also implies that out grater than 50 degree beam width, there is a null chance to have the establishment of the link. This implies an important requirement that to cover the 360 degree of area with 100 percent probability of link establishment, we need to increase the RIS slabs. From the result it can be seen that under proper alignment of the RIS, the coverage act as a secondary concern. Figure 7 highlights the important of the carried analysis with the proof of polynomial degree. The correlation coefficient of the RIS angle has been plotted against SNR. It can be seen that the higher order polynomial often increase the computational requirement but provides the accurate link establishment over SNR. This makes the system private and less vulnerable to the passive attacks because at the high the order of the polynomial, the need of high power occurs at eavesdropper side. Moreover, the impact of the initial position of R from RIS as: As we can notice from the simulations of OP and SOP, the initial position of R when its nearer, the possibility of random scatters is less and thus resulting in a sufficient   Angle from P against RIS angle to vehicle establishment of the link with OP less than 0.4. It implies that the at the particular location, the need of increasing the transmission code rate is less. The impact of the velocity as: The higher the velocity of the receiver side, the greater the fluctuation of the signal-to-noise ratio (SNR). Signal reconstruction at the receiver will result in inaccurate approximations to the original transmitted signal. As a result, taking into account the higher velocity has a direct impact on signal reconstruction during processing. As a result, the higher the velocity of nodes, the worse the fading set of circumstances, which increases the chance of being intruded.

Conclusions and future scope
In this research, the outage probability, as well as the secrecy outage probability as crucial metrics for PLS of a wireless vehicle communication network, were studied. We investigated two scenarios for vehicular networks based on RIS technology. Several analytical formulas have been developed in order to determine the signal-to-noise ratio at various receiver positions. This study shows that there is a possibility of improving the secrecy metrics of a vehicle network. This is done by altering the source power, the distance to the eavesdropper, and the number of RIS cells. In addition to these findings, it has also been demonstrated that RIS-based vehicular networks can be developed by assessing the size and placement of RISs (in terms of the number of RIS cells) in order to enhance their performance. In addition to that this work can be further evaluated under the impact of interference from users, and dense traffic conditions.

Appendix A: Derivation of Secrecy Outage Probability
In this section we evaluate the internal terms of the integral to derive the Secrecy Outage Probability over RIS assisted Nakagami-m channel for vehicular networks. The integral terms can be expressed as after taking the constants outside of the integral and performing some mathematical manipulations to identify the special integral rule from [29].
By keeping the constants outside and solving the integral we have the series containing the Gamma function CðÁÞ ð Þ as: The (33) further reduced to the identity given in [28, Section 8] from which (23) is obtained. Similarly, by substituting (13) in (22), the Secrecy Outage Probability is achieved for Nakagami-m fading as (27).
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