## 5 Experimental Results
### Preliminary Results
#### 5.2.2 PER as a Function of the Distance  
Besides the data rate, the distance between communicating nodes in the system has a major impact on the performance of the X-NETAD dissemination protocol. Even if the IF protocol assigns higher rebroadcasting probabilities to the farthest nodes, packet loss probability is an increasing function of the distance. Propagation losses affect all packets, depending on a multitude of factors (e.g., fading, shadowing, absorption, multipath interference, distance). Unlike other factors that are strictly related to the surrounding environment, one can estimate the impact of the distance between sender and receiver nodes through the _Friis_ transmission formula [32]:  
\[\frac{P_{\mathrm{r}}}{P_{\mathrm{t}}}\propto\left(\frac{\lambda}{d}\right)^{n} \tag{3}\]  
where \(P_{\mathrm{t}}\) represents the transmission power (dimension: [mW]); \(P_{\mathrm{r}}\) is the received power [dimension: (mW)], \(\lambda\) is the wavelength [dimension: (m)]; \(d\) is the distance between receiver and sender [dimension: (m)]; and \(n\) is an experimental coefficient that can vary (typically, it lies in the range \([2,4]\)--\(n=2\) for free space transmission). Equation (3) relates the received power with the transmission power and has an impact on the average number of packets received by a node in our system, because IEEE 802.11-compliant devices have a maximum transmission power (\(32\) mW). Therefore, the longer the distance between the nodes, the higher the probability that a packet is lost. The _Friis_ formula gives a characterization of the average received power due to propagation losses over an ideal channel, but does not take into account all the space-time fluctuations, due to phenomena, like _fading_, _shadowing_ or _Doppler_ effects. Despite these limitations, Equation (3) remains a useful tool for understanding the impact that propagation losses have on the application performance.  
In order to better understand the impact of the transmission distance on the PER, we carry out trials in an ideal static scenario, where the wireless propagation can be considered as in free space. We employ two smartphones, configured to send a stream of \(100\) UDP packets--each packet with an application-level payload equal to \(100\) bytes--on the WiFi interface. For each run, we repeat 100 times the transmission of the packet stream, and the experimental PER is computed by averaging over the total number of packets sent. Test devices are fixed at a height of about \(1.5\) m from the ground, in order to avoid as much as possible ground absorptions and reflections--moreover, this value represents, also, the approximate height of a smartphone positioned in a vehicle. We considered different distances between the smartphones. The transmit power is set to the maximum allowed level (\(32\) mW) and the data rate to \(11\) Mb/s, as indicated in Subsection 5.2.1.  
As expected, according to the experimental results shown in Figure 8, the PER is an increasing function of the inter-node distance. Furthermore, the shape of the experimental curve appears to be approximately linear. According to the results in Figure 8, it emerges that for \(d=60\) m, the PER is equal to \(0.054\). We consider this value of \(d\) as the experimental transmission range, \(z\), inside the IF PAF defined in Equation (1)--this experimental value is lower than the open space transmission range claimed by the IEEE 802.11 standard [31]. Note that, with respect to the tests performed in Subsection 5.2.1, the PER in Figure 8 is much lower, because in this case, the test are carried out in more favorable conditions (almost free space).