## 3 Neighbor Verification through Low-Power Beacons
### Whispering Rate and Tx Power  
Lowering the Tx power of whispers helps filter the messages from remote roadside attackers and reduce the channel utilization incurred by the whispers. But the Tx power set too low can render the BMS from even close neighbors not trusted. Therefore, we should find an appropriate Tx power. As to the channel utilization, another parameter that affects it is the whispering rate. To find appropriate whispering Tx power and frequency to be used for the rest of this paper, let us consider two highway driving scenarios depicted in Figure 3. There are four lanes on the simulated road. The BSM Tx power is set to 23 dBm, and the messaging rate to 10 Hz. On the other hand, the Tx power of whispers is varied between 7 and 10 dBm, and the messaging rate between 6 and 8 Hz. The channel model is set to two-ray ground. The physical layer transmission rate is set to 6 Mbps for the most robust delivery [32].  
Figure 3: Highway driving simulation scenarios (**a**) poor visibility (**b**) blocked line of sight.  
In (a), vehicles move at 80 km/h in the rainy road condition, where the road surface friction coefficient is 0.3 [33]. The headway distance between vehicles on the same lane is set to 100 m. In this case, the host vehicle \(V\) cannot detect the stopped vehicle \(X\) due to poor visibility. In (b), vehicles move at 120 km/h on dry road where the friction coefficient is 0.8. The headway distance between vehicles on the same lane is set to 50 m. There is a vehicle between \(V\) and the stopped vehicle \(X\). The stopped vehicle warns approaching vehicles through BSMs. Other vehicles check the distance to the stationary vehicle at the moment of receiving the first BSM that passes the whisper check. In (b), the intervening vehicle changes lanes to evade \(Y\). The human reaction time typically ranges from 0.7 s to 1.5 s [34]. In this paper, we set it to 1 s. When vehicles move at 80 km/h on a rainy road or 120 km/h on a dry road, the braking distances based on our assumptions are 104.5 m and 102.8 m, respectively. Given these parameters, we compute the distance \(d\) between the host vehicle and the stopped vehicle when a whisper checked the first BSM from the stopped vehicle arrives at the host vehicle. Based on \(d\), Figure 4 shows the probabilities in the two scenarios that the host vehicle collides with the stopped vehicle as it could not stop in time. The collision depends on the message delivery loss ratio and latency experienced by the BSM from the stopped vehicle. Now, given the success probability of the forged message delivery, the vehicle collision takes place if  
\[d+v_{f}\cdot\frac{v}{|a|}<v\cdot\left(1+\frac{v}{|a|}\right)+\frac{v^{2}}{2a},\]  
where \(d\) is the headway distance to the front vehicle \(U\), \(v_{f}\) is the speed of \(U\), \(v\) is the speed of the host vehicle \(V\), \(a\) is the maximum deceleration.  
Let \(d_{ca}\) denote the distance between the BSM sender and the receiver at which the collision probability is less than 5%. In (a), the message reception is possible at distances \(d>d_{ca}\) at 9 dBm and 7 or 8 Hz. In (b), all three messaging rates qualify at 9 dBm. For this reason, we will assume in the rest  
Figure 4: Vehicle collision probabilities as functions of messaging rate and Tx power  
of this paper that the whisper Tx power is set to 9 dBm, and the whispering frequency to 7 Hz. Note that these numbers are only used as rough guidelines to demonstrate the potential of the proposed approach. If need be, they will be refined in future work.