# An Analytical Model for Interference Alignment in Broadcast Assisted VANETs
## 2 System Model
### Research Scenario in VANETs and the Symbol System  
As shown in Figure 1, the entire VANETs scheduling time can be divided into several time frames. Every frame is taken as one scheduling period containing several equal interval Time Slots (TS) based on TDMA. Each vehicle transmits data during the assigned TS. However, before the scheduling period, the base station sends the status of the entire network and TS scheduling scheme to each vehicle to avoid communication collision.  
* In this scenario, both V2V and V2I communication fashion are coexisting simultaneously.
* In this scenario, the vehicle speed is relatively low and SD could be updated timely.
* Due to the buildings and other architectures, CSI amongst vehicles with base station varies a lot, which should be solved first of all.  
In this road section, there is one base station and several vehicles, denoted by \(I\) and \(V\) respectively in this paper as shown in Figure 2.  
Figure 1: Contents of Scheduling Time.  
Figure 2: Typical VANETs Scenario.  
Symbol \(I\to V\) indicates base station broadcasts message to vehicle and \(V\to I\) indicates vehicles upload information to Base Station. Vehicle communicates with each other denoted as \(V\rightleftharpoons V\). Other symbols in this paper are listed in Table 1. To simply formulas, we use \(i=1:N\) to represent \(1\leq i\leq N\), in which \(i\) is integer.  
\begin{table}
\begin{tabular}{c l} \hline \hline \multicolumn{1}{c}{**Symbol**} & \multicolumn{1}{c}{**Remark**} \\ \hline \(N\) & Number of terminals in network including vehicles and \\  & base station \\ \hline \(F\) & Number of communication times \\ \hline \(St\) & ID of Base station \\ \hline \(Src=\{Src_{1},Src_{2}...Src_{F}\}\) & Set of sources \\ \hline \(Des=\{Des_{1},Des_{2}...Des_{F}\}\) & Set of destinations \\ \hline \(Ts=\{t_{1},t_{2}...t_{K}\}\) & Set of Scheduling time slots \\ \hline \(K\) & Number of time slots \\ \hline \(N_{a}(i)\) & Number of antennas equipped on terminal \(i\) \\ \hline \(IL(i,j)\) & Symbol of interference status between \(i\) and \(j\) (0 means \(j\) is out of interference range of \(i\)) \\ \hline \(L(i,j)\) & Symbol of connectivity between \(i\) and \(j\) (0 means \(j\) is out of \\  & communicate range of \(i\)) \\ \hline \(C(i)\) & Set of vehicles in cluster \(i\) \\ \hline \(\lambda_{\ i,j}(t)\) & Number of communication session vehicle \(i\) sends to vehicle \(j\) \\  & during the same time slot \(t\) \\ \hline \(il_{i,j}(t)\) & Number of interference caused by \(i\) to \(j\) during time slot \(t\) \\ \hline \(al_{i,j}(t)\) & Number of interference caused by \(i\) to \(j\) which could be aligned \\  & during time slot \(t\) \\ \hline \(\delta^{\ i}_{\ T}(t)\) & Sending state of vehicle \(i\) at time slot \(t\) (0 means that vehicle \(i\) is \\  & not broadcasting during time slot \(t\)) \\ \hline \(\delta^{\ i}_{\ R}(t)\) & Receiving state of vehicle \(i\) at time slot \(t\) (0 means that vehicle \(i\) is \\  & not receiving during time slot \(t\)) \\ \hline \(hcount\) & Threshold value of max hops \\ \hline \(rot_{i,j}(f)\) & Integer value indicates whether vehicle \(i\) relays data to \(j\) for \\  & session \(f\) (1 means that \(i\) and \(j\) take part in relaying for session \(f\) ) \\ \hline \(TU(t)\) & Integer value indicates whether time slot \(t\) is assigned to any \\  & vehicles (0 means that there is no vehicle sends data during time \\  & slot \(t\), 1 means that at least one vehicle sends data to others) \\ \hline \(PTU\) & Proportion of the time slots allocated \\ \hline \hline \end{tabular}
\end{table}
Table 1: SYMBOLS and NOTATION.