# Routing and data diffusion in VANETs -- Signal disturbance

January 30, 2018

Small-scale fading refers to the effect of the multi-path of the wave. It occurs when the interaction between the signal and the obstacle produces a split of the current signal with a different speed and strength. Such effects can be modeled by some statistical laws. The Rayleigh model describes an environment with several multi-paths that have the same strength. Such models are used to describe environments where the signal is highly disturbed. The amplitude of the received signal z can be described by the Rayleigh distribution defined by equation [3.9].

with 2σ2 the root mean square of the received signal and the assumption that each path is uniformly distributed [−π,π]. An environment wherein the strength of a path is higher than others can be described with a Rice distribution. The amplitude of the received signal, z, can be described with the Rice distribution defined in equation [3.10].

where I0 is the Bessel function (zero order) and A the amplitude of the predominant path. The strength of the predominant path and others ratio is determined by K = A2/2σ2 describing the fading degree. Regarding K, the Rice distribution can model a Rayleigh if K = 0 and a Gaussian distribution when K → ∞.

3.2.2.4. Doppler

The motion of an emitter and a receiver produces a frequency shift of the incoming electromagnetic waves. It results in an offset in the carrier frequency as depicted in Figure 3.4, where two observers A and B are looking for a vehicle going to B direction. A typical scenario is the sound emitted by a moving car with an observer behind it and an observer in front of the car. For A observer, the sound frequency is higher than the frequency measured at the car, whereas the frequency at B is lower than that measured at the car.

Figure 3.4. Illustration of the Doppler effect

The resulting frequency fr observed when a source emits at a frequency of f is computed as follows:

where c is the celerity of the wave, vs the velocity of the source and vr the velocity of the observer. Regarding the motion of the source, vs and vr are positive if the receiver is moving towards the source and the receiver is moving away from the receiver, respectively. Under three assumptions, the antenna of the receiver is omnidirectional, the radio wave is propagated horizontally and the angle of receiving radio waves is uniformly distributed, the Doppler effect can be described by a Jakes model, wherein the normalized Jakes Doppler power spectrum is given by:

where fd is the maximum Doppler frequency.

3.2.2.5. A note on praxis measurements

In a theoretical manner, a link between two entities is considered as enabled or lost. In praxis, such a vision is too simplistic. As depicted in Figure 3.6, the signal affected by a path loss, shadowing and a fast-fading effect cannot be easily considered as enabled or lost. [ZAM 07] have demonstrated with their channel model that a link is characterized by three phases (Figure 3.5). First, the connected region where the link has a high packet reception ratio. Second, the transitional region, wherein the link is considered as unreliable and the packet ratio is fluctuated. Third, the disconnected region, where the link has a low packet reception ratio.

Figure 3.5. The three regions of the link quality

In Figure 3.6, the signal affected only by a Friss model shows a disconnection at 2000 m. With realistic propagation models, the good region of the link extends to 700 m, at which point the transitional region is then extended to around 1500 m, and consequently at the end, the list is then considered to be disconnected.

click for larger image

Figure 3.6. Attenuation, shadowing, fast fading effect: power reception over distance with two ray ground, shadowing, Rice (K = 2) and Doppler model

It is important for performance evaluations to test data delivery solutions under realistic propagation conditions. That is why [ABB 15] have designed a realistic propagation model from real measurements. Its effectiveness was investigated and confirmed by [HIL 17].

The next installment of this series looks at VANET routing protocols and their related mechanisms.

Frédéric Drouhin is an Assistant Professor in the Laboratoire Modélisation Intelligence Processus Systèmes (MIPS) at the Université de Haute Alsace.

Sébastien Bindel is an Associate Professor in the Département Réseaux et Télécommunications at Université de Haute-Alsace.

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