# Evaluation of the Use of Compressed Sensing in Data Harvesting for Vehicular Sensor Networks
## 4 Cs-Vdh
### Enhancement to the Basic Scheme  
If every node inside the RoI transmits its sensed information at the same time, the network will be notably overloaded, and the data communication will be jeopardized in such a way that only a few \begin{table}
\begin{tabular}{|c|c c c|c|} \hline  & \multicolumn{3}{c|}{**Areas**} & **Projection Performed** \\ \cline{2-5}  & 1 & 2 & 3 & 4 & \\ \hline
**Node1** & X & X & & & P1 = A*X1 + B*X2 \\
**Node2** & & X & X & P2 = C*X3 + D*X4 \\ \hline
**Combin.** & X & X & X & **P1+P2** \\ \hline \end{tabular}
\end{table} 
Table 2: CS: the combination of projections is possible because they do not overlap. \begin{table}
\begin{tabular}{|c|c c c|c|} \hline  & \multicolumn{3}{c|}{**Areas**} & **Values** \\ \cline{2-5}  & 1 & 2 & 3 & 4 & \\ \hline
**Node1** & X & X & X & & P1 = A*X2 + B*X2 + C*X3 \\
**Node2** & & X & X & P2 = C*X3 + E*X4 \\ \hline
**Combin.** & **Not possible** & & & \\ \hline \end{tabular}
\end{table} 
Table 3: CS: combination of data not possible because projected data overlap according to the boolean vector. data will arrive in the FC due to the contention, lack of resources, and the likes. Examples such as Mobeyes, and Mobeyes-ODH, were presented in Section 3 which have these problems because nodes immediately respond after receiving the query sent by the FC. This undesired behavior can be mitigated by sorting the different responses in such a way that, instead of having all the nodes sending their sensed information at the same time, they do it gradually. Thus, intermediate nodes can take advantage of traversing packets to introduce their sensed information in them. If the nodes farther from the FC are the first ones in answering with their sensed information, intermediate nodes are more likely to include their information as it is forwarded back to the FC. For our proposal we studied the use of a delay function expressed by the following equation:  
\[y=p_{1}*e^{-e^{\frac{x-p_{2}}{P3}}}, \tag{6}\]  
and whose parameters are \(p_{1}\), \(p_{2}\), and \(p_{3}\). We have used this function because of its flexibility. That is, by varying the values of its parameters, the function can change their shape. Each of the parameters has a purpose in the function:  
* \(p_{1}\): this parameter limits the upper asymptote, that is, the maximum time (TMAX) a node must wait until it sends back its sensed information. * \(p_{2}\): it models the distance from which the answer time decreases exponentially. * \(p_{3}\): finally, \(p_{3}\) models the number of points the slope has. The more points, the less steep the slope will be. Considering an urban scenario like the one of the city of Murcia with \(4*5\ km^{2}\) we made a first analysis of the selected mathematical function by varying its different parameters. Actually, we have used three different sets of parameters that change the response time that the mobile nodes have to depend on their distance as presented in Figure 9 and whose values can be seen in Table 4.  
Figure 9: Representation of three different shapes the proposed delay function can have according to the values for \(p_{1}\), \(p_{2}\) and \(p_{3}\) specified in Table 4.  
Now let us select a set of 10 random points that correspond to mobile nodes positions with different distance to the FC which is placed in the center of the scenario. As we can see in both Table 5 and Figure 10, these positions obtain different delay time depending on the series. Series 1 values provide different delay time to different positions although they are nearby. Nevertheless, series 2 and series 3 provide a similar delay time to nodes located nearby each other. This is caused by the steep slope both series present in the figure having the majority of the represented points in both the maximum delay time, or 0 delay time.