# Deterministic Propagation Modeling for Intelligent Vehicle Communication in Smart Cities
## 4 Statistical Analysis  
The fading channel in vehicular environments could be a combination of different fading channel types that changes over distance, time, and mobility. Different fading models have been proposed and utilized in literature as Gamma, Lognormal, Rician [23], Rayleigh, Nakagami, Weibull, composite fading models as Weibull-Gamma [36], Nakagami-Lognormal, K distribution (mixture of Rayleigh and Gamma), mixtures of Gamma distributions [37], etc. In this multipath environment, identification of some statistical fading model able to fit and characterize the fading level of this urban scenario is required, as well as the adoption of a descriptive statistic to measure it. To validate the closeness of the theoretical distribution (Gamma, Lognormal, Weibull, etc.) function to the empirical distribution function (RSS 3D-RL) we used the Anderson-Darling (AD) test, which was another common test along with Kolmogorov-Smirnov(K-S), Cramer-von Mises (C-vM), Chi_Square(C-S), etc. We evaluate the Goodness-of-fit (GOF) for nonparametric data sets. The AD statistic provides robustness and flexibility compared to other GOF measures because it gives more weight to the tail of the distribution, and it has been employed to quantify the difference between the observed and expected values [38], as a type of divergence or discrepancy measurement. In applications such as Cognitive Radio, a proposed AD sensing has much higher sensitivity to detect a transmission signal than energy detector-based sensing, especially for small samples [39]; however, in applications such as hydrological statistics, the results show most powerful GOF results for K-S and C-S test than AD [40]. On the other hand, one of the descriptive statistics to measure data variability is the squared coefficient of variation (SCV) defined as [41]:  
\[\mathrm{SCV}=\frac{\mathrm{Var}}{\mu^{2}}=\frac{\mathrm{E}((\mathrm{x}-\mu)^{2 })}{\mu^{2}}=\frac{\mathrm{E}\big{(}\mathrm{x}^{2}\big{)}}{\left(\mathrm{E}( \mathrm{x})\right)^{2}}-1 \tag{6}\]  
where x is a random variable and E (\(\cdot\)) is expectation operator. According [42], for a given distribution of strength, \(a\), of a received signal, the amount of fading (AF) is defined by the ratio of the variance of the received energy to the square of the mean of the received energy as follows:  
\[\mathrm{AF}=\frac{\mathrm{Var}\big{(}\mathrm{a}^{2}\big{)}}{\left(\mathrm{E}( \mathrm{a}^{2})\right)^{2}} \tag{7}\]  
According to Equations (6) and (7), the SCV of received signal power characterizes the amount of fading (AF) of signal power and will be used in this section to describe the data variability and AF. Figure 14 depicts the TX1-RSS Cumulative Distribution Function (CDF) along the AV2 (refer to Figure 9b) and its statistical comparison with theoretical distributions widely used in the description of multipath fading environments. Complementary to this, Table 4 summarizes: (a) the 3D-RL data Squared Coefficient of Variation (SCV) a statistical measure of the data dispersion level; (b) the GOF between the theoretical distributions and the 3D-RL data using the AD test with 5.0% for a significance  
Figure 13: Doppler Spread (B\({}_{\mathrm{D}}\)) for TX1: (**a**) velocity of 40 km\(/\)h, (**b**) velocity of 60 km\(/\)h.  
level of the hypothesis (H\({}_{0}\)) test; and (c) the input parameter (shape) for the tested distributions. The TX1-RSS coverage area along AV2 was divided into 6 segments: S1 to S3 (left to TX1) and S4 to S6 (right to TX1) where S1 is symmetric and equidistant with S6, S2 with S5 and S3 with S4. This kind of segmentation was chosen for three reasons: (a) to consistently identify the statistical differences between symmetric and equidistant areas (spatial considerations) to TX1; (b) because of reasonable balance between a maximum segment-length and a significant statistical fit when compared with theoretical distributions; and (c) to organize the data into homogeneous segments, avoiding as much as possible extreme 3D-RL RSS values.