# An Analytical Model for Interference Alignment in Broadcast Assisted VANETs
## 5 Simulations
### Analysis of IA Simulation  
In our simulation, _hcount_ is set to 6 to limit the number of hops in data routing. Then we analyze simulation results based on V2V, I2V and V2I cases. **Case Study for V2V communication:** As shown in Figure 11, we select some vehicles as example. The communication sessions of selected vehicles are listed in Table 2 and routes of some sessions are listed in Table 3. From Table 3, we find that only 5 sessions adopt direct communication. And vehicle 6 and 54 contribute most routing tasks. It is because that vehicle 54 is closer to base station than any other vehicles in the same cluster and vehicle 6 is located in the center of its cluster. Figure 11: Example of \(V\rightleftharpoons V\) Communication Simulation Result. Figure 10: \(\sigma\)-Clustering Algorithm According to path loss and location. The hop counts are shown in Table 4 with different size of experiments. The 5-hop routing only occurs when there are 30 vehicles in this road since the distribution of these cars is sparser. The percentage of different hop counts are shown in Figure 12. With the vehicle density increasing, the percentage of two hops is increased and the direct communication is reduced, which means the information would be propagated through assisted transmission instead of directly communication under the condition with more vehicles. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{1}{c}{**Number of Vehicle**} & \multicolumn{1}{c}{**Number of Hops**} & **1** & **2** & **3** & **4** & **5** \\ \hline
30 & & 24 & 18 & 12 & 12 & 16 \\
40 & & 52 & 25 & 12 & 21 & 0 \\
50 & & 66 & 43 & 19 & 20 & 0 \\
60 & & 71 & 74 & 28 & 23 & 0 \\
70 & & 83 & 76 & 41 & 44 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Number of Route Hops for \(V\rightleftharpoons V\) as The Number of Vehicles Increases. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**SRC** & **DES 1** & **DES 2** & **DES 3** & **DES 4** & **DES 5** \\ \hline
24 & 6 & 65 & 70 & & \\ \hline
6 & 24 & 34 & 42 & 50 &  
**Case Study for IA in V2I Communication:** During the 20 th time slot, vehicle 21, 31, 39, 47, 59, 68 broadcast message as shown in Figure 15. Vehicle 31, 68 and 59 broadcast to base station that will take up 3 antennas of the base station. However, the base station is also in the interference range of vehicle 39 and 47. Therefore, in order to receive intended messages from 31, 68 and 59, the interference caused by 39 and 47 will be aligned together to save 1 degree of communication freedom. **Case Study for Data-driven Assisted Transmission:** We draw an example of data routing path as shown in Figure 16. The route table is shown in Table 6:  
As shown in Figure 16, during 1 st slot, the base station initiates a broadcast and vehicle 54 receives the message from base station. At time slot 15, vehicle 54 broadcasts to its surrounding vehicles. Since vehicle 65, 24 and 6 are out of the base station's communication range, the session from base station is relayed by vehicle 54. At time slot 16, vehicle 6 center on the cluster broadcasts messages to surrounding vehicles. In this time slot, vehicle 6 relays message sent from vehicle 54 at time slot 15. To make full use of channel resources, during time slot 16, vehicles 43, 16 and 62 are assigned to send messages to base station simultaneously and vehicle 33 broadcasts to surrounding vehicles. Figure 14: Sessions Uploading from Vehicles out of Base Station Communication Range. Figure 15: Example of IA in 20 th Time Slot. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Src** & **Des** & **Routes** & **Src** & **Des** & **Routes** \\ \hline
70 & 65 & 54 & 70 & 14 & 54, 6 \\
70 & 24 & 54 & 70 & 50 & 54, 6 \\
70 & 6 & 54 & 70 & 4 & 54, 6 \\
70 & 39 & 54, 6 & 70 & 34 & 54, 6 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Proportions of Different Hops in Routes of \(V\rightleftharpoons V\). Figure 16: An Example of \(I\to V\) Session Routes from Base Station to Vehicles out of Vommunication Range.