# Networked Roadside Perception Units for Autonomous Driving
## 5 Evaluation
### Numerical Analysis  
A mathematical evaluation was carried out about the RSPUs' underlying performance with regard to PDR and delay in delivering the messages. To begin with, we undertook a calculation of the throughput of \(CPM_{CAM}\) across IEEE802.11p. In these calculations, Table 1 provides a summary of values, symbols, and variables. The following equation denotes the average interval necessary for sending a \(CPM_{CAM}\) packet through \(t_{cpm}\), a wireless channel:  
\[t_{cpm}=t_{DIFS}+b+t_{send}, \tag{4}\]  
where \(t_{DIFS}\) denotes the interval of distributed interframe space, \(b\) signifies the backoff time, whereas \(t_{send}\) denotes the transmission's duration. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Layer** & **Variable Type** & **Symbol** & **Value** \\ \hline \multirow{4}{*}{MAC} & AIFSN with OCB & \(AIFSN\) & 6 \\  & Slot length of IEEE802.11p & \(slen_{11p}\) & 0.013 ms \\  & SIFS interval & \(t_{SIFS}\) & 0.032 ms \\  & Contention windows size & \(CW\) & 0\(\sim\)15 \\  & Average of CW & \(CW_{ave}\) & 7.5 \\ \hline \multirow{4}{*}{PHY} & Switch time between Tx and Rx & \(t_{switch}\) & 0.001 ms \\  & PLCP preamble duration & \(t_{pre}\) & 0.032 ms \\ \cline{1-1}  & Duration of PLCP Signal & \(t_{sig}\) & 0.008 ms \\ \cline{1-1}  & Symbol interval & \(t_{sym}\) & 8 \(\mu\)s \\ \cline{1-1}  & Number of data bits per symbol & \(N_{DBPS}\) & 144 bits \\ \hline Other & Payload Length of \(CPM_{CAM}\) & \(P_{cpm}\) & 680 bits \\ \hline \hline \end{tabular}
\end{table} 
Table 1: MAC and Physical Layers’ Parameters. Figure 8: Packet delivery ratio \(R_{pd}\) in field experiment. \(t_{DIFS}\), the interval of DIFS, denotes the time for waiting after the channel becomes an ideal state. It is shown by the following equation:  
\[t_{DIFS}=AIFSN\times slen_{11p}+t_{SIFS}. \tag{5}\]  
As far as the AC_BE class is concerned within the EDCA, six is the arbitration interframe space number (\(AIFSN\)) upon the activation of OCB [42]; \(b\), the backoff time denotes the random waiting time that the following equation denotes  
\[b=CW_{ave}\times slen_{11p}, \tag{6}\]  
where the value of \(CW\), the contention window size, is0 \(\sim\) 15 [42]. The average contention windows size (\(CV_{ave}\)) = 7.5; for this reason, \(b=0.0975\) ms.  
A \(CPM_{CAM}\)'s duration of transmission is denoted by the following equation:  
\[ \begin{split} t_{send}&=t_{switch}+t_{pre}+t_{ sig}\\ &\quad+t_{sym}\times ceil(\frac{16+P_{cpm}+6}{N_{DBPS}}),\end{split}  \tag{7}\]  
where \(t_{switch}\) denotes the switch time between Rx and Tx, On the other hand, \(t_{pre}\) refers to the duration of physical layer convergence protocol, or PLCP, \(t_{sig}\) signifies the PLCP signal's total duration, \(N_{DBPS}\) denotes the data bits per symbol of orthogonal frequency-division multiplexing (OFDM), \(t_{sym}\) represents the interval of symbol, whereas \(ceil()\) refers to a function that returns the smallest sized integer equal to or higher than a particular number. In case 18 Mbps is the data rate, the utilization of 16 QAM is specified for the modulation scheme following which the code rate is 3/4. Thus, from Equation 7, \(t_{sym}=\) = 8 \(\upmu\)s and \(N_{DBPS}=\) 144 bits, which implies that \(t_{send}=\) 0.081 ms  
Based on Equation 4, the interval of time (average) required for successful transmission of CPM packet is denoted by \(t_{cpm}=\) 0.2885 ms. On average, a \(CPM_{CAM}\) gets sent across 0.2885 ms, thus implying in an efficacious throughput of CPM on of approximately 2.73 Mbps. Accordingly, it is possible to get the data rate calculated at which the transmitter is capable of broadcasting CPMs without keeping any within the queue. In case all RSPUs, on average, trace ten vehicles, it is also capable of broadcasting messages from nearly 40 adjacent RSPUs. This means that queuing would not commence until RSPU detects over ten vehicles and when messages are being sent by over 40 neighboring RSPUs.