Performance Analysis for Cooperative Jamming and Artiﬁcial Noise Aided Secure Transmission Scheme in Vehicular Communication Network

Vehicular communication has emerged as a supporting technique for improving road traﬃc safety and eﬃciency in the intelligent transportation system (ITS). However, the wireless vehicular communication links may suﬀer from an eavesdropping threat due to the wireless broadcasting nature and high-mobility of vehicles. In practice, artiﬁcial noise (AN) assisted beamforming scheme can be utilized for ﬁghting against multiple malicious eavesdroppers. Unfortunately, channel estimation errors caused by the high-mobility of vehicles may lead to noise leakage at the legitimate receiver, thus resulting signiﬁcant loss in the secrecy performance. In this paper, a joint cooperative jamming and AN aided secure transmission scheme is proposed in vehicular communication network by considering the imperfect channel state information(CSI). In this scheme, cooperative jammers are utilized for further enhancing physical layer security. We derive the closed-form expressions of the connection and secrecy outage probabilities in the presence of AN leakage and signal oﬀset using a stochastic geometry approach. Furthermore, the proposed scheme is capable of maximizing the secrecy throughput in terms of relative vehicular velocity for balancing both the reliability and security of the legitimate link. We further comprehensively analyze the eﬀect of key system parameters on secrecy performance through asymptotic analysis. Finally, the eﬀectiveness of the proposed scheme is validated by numerical results.


Introduction
Vehicular communication is believed as a emerging technology to improve the road safety, transport efficiency and driving experience in the intelligent transportation system (ITS) and future autonomous transport system [1,2]. Messages can be disseminated quickly by exploiting the paradigm of vehicle-to-infrastructure (V2I) and vehicle-to-vehicle (V2V) communications in vehicular network [3]. However, due to the broadcast nature of wireless medium, malicious vehicles may eavesdrop or jam the vehicular communication links for their own profit, which can threaten driving safety and jeopardize ITS efficiency [4,5]. Therefore, the information security is a key issue in the development applications of vehicular network [3,4,5]. This motivates the research on vehicular communication from the perspective of communication security [6].  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53  54  55  56  57  58  59  60  61  62  63  64  65 for the proposed scheme are providesd by MATLAB in Section V. Finally, the conclusions are drawn in Section VI.
Notations: We use bold lowercase and uppercase letters to denote column vectors and matrices, respectively. I n denotes the n × n identity matrix. P r {·}, · , |·|, and (·) T denote probability, Euclidean norm, absolute value, and transpose, respectively. exp (λ), T (N, λ) and CN µ, σ 2 denote exponential distribution with parameter λ, gamma distribution with parameters N and λ, and circularly symmetric complex Gaussian distribution with mean µ and variance σ 2 , respectively. L (·) denotes the Laplace transforms of a random variable. Finally, C m×n denotes the m × n complex number domain.
1 System Model Figure 1 Joint CJ and AN aided secure transmission model. Legends: Alice aims to transmit confidential message to Bob, in the presence of randomly located passive eavesdropper Eves trying to capture the confidential information. In addition, there also exist cooperative jammers (Charlies) emit interference signals to confuse Eves.
As shown in Fig. 1, we consider a joint CJ and AN aided secure transmission model in vehicular communication network, where a vehicle (Alice) aims to transmit confidential message to another legitimate vehicle (Bob), in the presence of randomly located passive eavesdropper vehicles (Eves) trying to capture the confidential information. In addition, there also exist cooperative jammers (Charlies) emit interference signals to confuse Eves. Note here Charlies act as pure cooperative jammers without information forwarding [25]. The sets of Eves and Charlies are defined as K = {1, 2, . . . , K} and C = {1, 2, . . . , C}. For convenience, we refer to the k-th Eve as E k and the c-th Charlie as C c . We assume that each Charlie and Alice are equipped with N c and N a antennas, respectively. Each Eve and Bob are all equipped with single antenna [26]. Without loss of generality, the spatial locations of Eves and Charlies are denoted as characterized by two independent homogeneous Poisson Point Processes (PPPs) Φ e and Φ c with the intensities λ e and λ c over the two-dimensional plane, respectively.
All the communication links undergo a standard path-loss characterized by the exponent α and the channels are quasi-static Rayleigh fading, where the fading coefficients are assumed to vary from one block to another, while keeping constant during a transmission block for simplicity [18,28]. All fast fading channels from Alice to Bob and E k are denoted by h a,b ∈ C Na and h e,k ∈ C Na , respectively, and those from Charlie to Bob and E k are denoted by h c,b ∈ C Nc and h c,k ∈ C Nc . We assume Bob estimates the intended channel with estimation errors [16]. In this case, we use a first-order Gauss-Markov model to depict the fast fading variation [29], the exact intended channel h a,b can be modeled as where the estimated value h a,b ∼ CN 0, ρ 2 I Na is independent of the channel estimation errors e a,b ∼ CN 0, (1 − ρ 2 )I Na . We consider ρ ∈ [0, 1] as channel estimation accuracy [16]. Note that ρ = 0 indicates that no CSI is obtained at all ,   1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53  54  55  56  57  58  59  60  61  62  63  64  65 while ρ = 1 means a perfect channel estimation. For the Jakes' fading model, ρ is given by ρ = J 0 (2πf d T ) , where J 0 (·) is the zero-order Bessel function of the first kind, T is the block duration time, and f d = νf c /c is the maximum Doppler frequency with c = 3 × 10 8 m/s, ν being the relative vehicular velocity, and f c being the carrier frequency [16]. For simplicity, the CSI of Charlies and Eves are available [28]. Specifically, we assume that h e,k ∼ CN (0, I Na ) and h c,k ∼ CN (0, I Nc ).

Secure Transmission Scheme
For confusing Eves while ensuring a secure transmission, Alice adopts the ANaided beamforming transmission strategy to emit confidential information along with AN. Let [w a , W a ] constitute an orthogonal basis, where w a = h * a,b / h a,b is the beamforming precoding vector with h a,b being the estimate of channel h a,b , and W a ∈ C Na×Na−1 denotes an AN beamforming matrix onto the null-space of h a,b , i.e., h H a,b W a = 0. The AN-aided transmitted signal vector s a can be formulated as where θ ∈ [0, 1] is the ratio of information-bearing signal power to Alice' total transmit power P a . Note that θ = 1 indicates the secrecy beamforming without AN, and θ = 0 denotes that the confidential information transmission is suppressed.
x ∼ CN (0, 1) indicates the secret message for Bob. z a ∈ C Na−1 is an AN vector with distribution CN (0, I Na−1 ). Concurrently, the zero-forcing technique is utilized at Charlies. These external jamming signals generated by Charlies will further enhance security performance [25]. The jamming signal s c at each Charlie should be properly designed to jam Eves while eliminating the additional interference at Bob. Therefore, s c can be design as where P c denotes the transmit power of each Charlie. T c ∈ C Nc×(Nc−1) constitutes an orthonormal basis for the null-space of h c,b , i.e., T c is a Gaussian jamming signals vector. Alice and Charlies simultaneously transmit confidential and jamming signals. The received signals at Bob and E k can be respectively expressed as where d a,b , d e,k and d c,k denote the propagation distance from Alice to Bob, from Alice to the E k , and from the C c to the E k , respectively. n b ∼ CN 0, σ 2 b and n k ∼ CN 0, σ 2 e are independent variables denoting the terminal Gaussian noises .   1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53  54  55  56  57  58  59  60  61  62  63 64 65 According to (4)-(5), the signal-to-interference-plus-noise ratios (SINRs) at Bob and E k can be given by where P a θ e ab w a 2 and P a (1−θ) e a,b W a 2 /(N a − 1) denote signal offset caused by the channel estimation error and AN leakage, which give rise to a serious reduction in security performance. According to stochastic knowledge, we obtain that . The SINRs γ b and γ e,k are changed dynamically by channel estimation accuracy ρ and power allocation ratio θ. As such, capacities of the k-th eavesdropper link and the legitimate link can be expressed as In consideration of the non-colluding scenario, the maximal eavesdropping capacity depends on the maximal capacity among all the Eves, i.e., C E = max k∈Φ E {C e,k }.

Secrecy Performance Analysis
In this section, secrecy throughput is introduced as a crucial performance metric for evaluating the reliability-security rate of the legitimate link (bps/Hz) [16,32,33]. Adopting Wyner' wiretap encoding scheme [14], we use R b and R s to denote the transmitted codeword rate and secrecy rate, respectively. Furthermore, the redundant information rate R e =R b −R s is used to provide secrecy against Eves. Therefore, the secrecy throughput T can be given by where the P top denotes the connection outage probability (COP) and P sop denotes the secrecy outage probability (SOP).

Secrecy Outage Probability (SOP)
A secrecy outage inevitably occurs when the capacity of the equivalent wiretap link exceeds the redundant information rate, i.e., C E < R e . Therefore, the SOP P sop is given by β Re = 2 Re − 1, and (a) is obtained by utilizing the probability generating functional (PGFL) of PPP [33]: According to [36], the CDF ofγ e,k is expressed as: Thus, for the SOP of the E k , we have Pr γ e,k > I e,k β Re d α e,k |Φ c = (1 + β Re Φ) where s = . Therefore, by substituting (16) into (15), we can obtain: Pr γ e,k > I e,k d α e,k |Φ c = (1 + β Re Φ) 1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53  54  55  56  57  58  59  60  61  62  63  64  65 By plugging (17) into (13), we can obtain the SOP as shown in (18) Pr γ e,k > I e,k d α e,k |Φ c rdr) Paθ . In especial, the thermal noise can be neglected in the interference-limited network [37], i.e., σ 2 e = 0. We can further obtain the simple expression of SOP, i.e., P int sop , as follows: From (19), it is easily observed that the expression of SOP is inversely proportional to the cooperative jammer density λ c . Therefore, the secrecy performance can be enhanced by increasing λ c . In contrast, we can easily obtain that the P int sop is an increasing function with respect to the eavesdropper density λ e . In addition, the P int sop increases as the power allocation ratio θ increases. This is due to the fact that a higher θ denotes a lower power allocated to the AN for confusing Eves.

Secrecy Throughput
Using the definition given by (9), we can obtain a closed-form expression for the secrecy throughput in the interference-limited network, as shown in (20).

Numerical Simulation Results and Discussions
In this section, several numerical results are provided to verify the theoretical analysis. In particular, the effects of key system parameters such as: the number of transmit antennas N a and N c , the relative vehicular velocity v, the ratio of λ c /λ e , and the power allocation ratio θ, on security performance are presented in the figures below. Unless otherwise stated, the following main simulation parameters are adopted [27]: P c = P v = 30 dBm, α = 4, and N a = N c = 4. Additionally, R b = 5 bps/Hz, R e = 3 bps/Hz, and ρ = 1  We observed that as the parameter θ increases, the P cop is always decreasing for different number of antennas N a . The results match the analytical expression in (12) very well. Furthermore, by fixing the parameter θ unchanged, adding transmit antennas can be to the benefit of decreasing the COP. It is because that increasing the transmit power of the information-bearing signal or adding antennas is beneficial to improve connection performance.   3 presents the COP of legitimate link P cop versus the relative vehicular velocity v for different transmitted codeword rate R b . It is shown that increasing the parameter R b will weaken the connection performance of the legitimate link. Furthermore, the connection performance can be weakened significantly when the relative vehicular velocity v increases. It is due to the fact that channel estimation errors caused by high-mobility of vehicles in dynamic vehicular network may lead to noise leakage at the legitimate receiver, thus resulting significant loss in the connection performance.   Fig. 4, it is observed that the SOP P sop declines rapidly at fist and then tends to stabilization with increasing the number of antennas N from all considered jammer power. It is because that when the parameter N becomes large, increasing the number of antennas is conducive to improving secrecy performance. However, when the parameter N becomes sufficiently large, there also exists secrecy performance floor phenomenon. Hence, the result confirms the accuracy of our asymptotic analysis at high N in (25). Furthermore, one can readily observe that increasing the power of cooperative jammer can be also beneficial to enhance secrecy performance in Fig. 4.  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53  54  55  56  57  58  59  60  61  62  63 64 65 Figure 5 The SOP versus power allocation ratio θ for different density ratio. Legends:(λc = 0.1λe, λc = 0.5λe, λc = λe, λc = 5λe). Fig. 5 shows the relationship between the SOP and the power allocation ratio θ for different density ratio of cooperative jammers and Eves. We can observe that the SOP P sop increases as the parameter θ increases. This is because that a higher θ denotes a lower transmission power allocated to the AN for confusing Eves. Furthermore, the SOP P sop is shown to decrease with the increase of the density ratio of cooperative jammers and Eves. It is because that when the density ratio increases, more cooperative interference signals can be used for guaranteeing security.   6 shows the secrecy throughput versus power allocation ratio θ for different density ratio of cooperative jammers and Eves. As shown in Fig. 6, it is observed that the security throughput rises at first and then decrease as the power allocation ratio θ increases. This implies that there exists an optimum θ * for maximizing security throughput. This is due to that the power allocation ratio has a reliability-security tradeoff. A smaller θ stands for allowing more transmission power allocated to AN signal, which obtains a higher security performance while impairing the reliability performance. Conversely, a larger θ stands for allowing more power allocated to information-bearing signal, which obtains a higher reliability performance while impairing the security performance. This reveals that selecting an appropriate θ can improve the secrecy throughput. Furthermore, the tendency that the secrecy throughput declines as the density ratio decreases can be observed in Fig. 6, which can be attributed to the increasing SOP. The result is consistent with Fig. 2 and   where λ c = 10λ e , θ = 0.6. For a given jammer power P c , it can be noticed that the secrecy throughput decreases as the relative vehicular velocity v increases, which implies that the imperfect CSI caused by high-mobility of vehicles is not conducive to enhancing the secrecy throughput performance. Furthermore, as the power of cooperative jammer increases, a prominent increase in the security throughput can be observed. As expected, the joint CJ and AN aided secure transmission scheme always outperforms the without CJ transmission scheme. This means that the cooperative jammers are utilized for further enhancing physical layer security.

CONCLUSION
In this paper, a joint CJ and AN aided secure transmission scheme with imperfect CSI has been investigated in vehicular communication network. In this scheme, the closed-form expressions of the COP and the SOP have been provided. We have quantified the secrecy throughput performance for maintaining the reliability-security tradeoff of the legitimate link. Meanwhile, there exists an optimal solution of power allocation that yields the maximum security throughput under different relative vehicular velocity. Furthermore, the performance of the proposed scheme has been demonstrated by numerical results. More importantly, our results indicated that the cooperative jammers can be utilized for further enhancing physical layer security, which will be to the benefit of the information security in vehicular communication network.