QoS-Based Sequential Detection Algorithm for Jamming Attacks in VANET

Abstract

As a key component of the future Vehicle-to-anything (V2X) communication technology, Vehicular Ad hoc Network (VANET) has a great potential of enabling real-time traffic safety and efficiency applications for people on roads. Therefore, attacking and misusing such network could cause destructive consequences. Wireless communication in VANET is based on IEEE 802.11p-based DSRC standard. Due to its inherited distributed contention resolution mechanism, the MAC protocol in IEEE 802.11p is more susceptible to jamming attacks. While preventing jamming attacks in VANET is not feasible, due to its unbounded scalability, detecting such attacks is primordial. First we develop optimization methodology for IEEE 802.11p MAC which defines its stability region under normal network conditions, this will allow us to determine detection threshold value to distinguish normal operation and attacks. Second, we implement the sequential detection of change method along with the developed methodology and we propose QoS-based Sequential Detection Algorithm (QoS-SDA). The important performance characteristics of QoS-SDA are accuracy and speed, while jamming attacks are detected with low probability of false alarms. Finally, we provide comprehensive analytical and simulation analyses to prove the validity of the develop methodology and the efficiency of the proposed algorithm.

Appendix: Proof of Lemma 1

Let us define

• CW: The contention window size.

• $P_m (\mu ,\sigma ^{2})$: The distribution of the traffic with mean $\mu$ and variance $\sigma ^{2}$.

• P: The probability of successful transmission.

• $\lambda$: Poisson arrival rate.

• k: The expected number of packets that are successfully transmitted during a time interval l given that it started with the transmission of m packets.

When no constraints (i.e., delay or successful transmission bounds) on the transmitted traffic are imposed, the following definition of throughput is meaningful to capture IEEE 802.11p MAC algorithm stability

$$\begin{aligned} \lambda ^* = \sup \big (\mu :\mu =\alpha \big ) \end{aligned}$$

(7)

Let us define the output rate $\alpha$ such that $\alpha =\frac{1}{n}\sum _{i=1}^{n} \beta _i$, in [15] it has been proven that the output process of IEEE 802.11p under stable conditions tends to follow a Bernoulli distribution. Hence

$$\begin{aligned} \{\beta _i\}_{1}^{n}\sim \text {Brn} = \left\{ \begin{array}{ll} P(\beta _i=1)=P &{} \text {if the } i^{th} \text { slot is a success slot} \\ P(\beta _i=0)=1-P &{} \text {otherwise} \end{array}\right. \end{aligned}$$

(8)

The only parameter of the Bernoulli output in (8) is P. To define P let us consider the following scenario: Let m represents the total number of arrivals (packets) in a time interval l with rate $\mu$. If the contention resolution in IEEE 802.11p, induced only a single successful transmission, then the probability of this event is $P=CW/l$. However, under stable operation of the algorithm this value approaches the input rate i.e., $P = \mu$ and consequently (7) holds.

Now let m to increase and the quantities $\mu$ and $\sigma ^{2}$ in the arrivals’ distribution $P_m$ simultaneously to decreases so that

$$\begin{aligned} m\mu = \lambda \quad \text {for } \lambda >0, m\gg 1 \end{aligned}$$

(9)

the latter expression is the Poisson theorem, then $P_m$ converges in distribution to Poisson process, i.e., $P_m\longrightarrow Pois(\lambda )$. Give Poisson rate $\lambda$ and in the presence of constraints, the expected number of packets transmitted in the first slot of a time interval l is $\lambda CW$ and therefore the fraction of packets that are successfully transmitted S during l is $S = k/\lambda CW$. In [15], recursions for computing the quantity k have been found. In Poisson process, the arrival points in an interval are uniformly distributed. Hence, if a fraction S of the packets are successfully transmitted it means that S is also the fraction of the interval resolved. Therefore, $(k/\lambda CW)CW= k/\lambda$ represents the average portion of the resolved interval, which takes on the average N slots to be resolved. Thus, the algorithm remains stable, even under congestion conditions, whenever it is able to resolve collisions at the rate in which the arrival process progresses in time, that is

$$\begin{aligned} N \leqslant \frac{k}{\lambda } \end{aligned}$$

(10)

(10) defines the maximum value on the input rate $\lambda$ at this specific CW value so that IEEE 802.11p throughput is maximized while the successfully transmuted packets are bounded by S; thus, the statement in Lemma 1 is a consequence of this.