# Effective PSCCH Searching for 5G-NR V2X Sidelink Communications
## 3 Proposed Effective PSCCH Searching
### Proposed Effective PSCCH Searching Based on Correlation
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Symbol** & **Designation** & \
\begin{tabular}{c} **Rows of Blind** \\ **Algorithm** \\ \end{tabular} &
\begin{tabular}{c} **Rows of Proposed** \\ **Algorithm** \\ \end{tabular} \\ \hline \(T_{corr}\) & Compute correlation & 3 & 3 \\ \(T_{fmax}\) & Find the maximum correlation & - & 4 \\ \(T_{sort}\) & Sort the maximum correlations & - & 7 \\ \(T_{gpair}\) & Get the pair \((n,i)\) & - & 9–10 \\ \(T_{rem}\) & Remain processing & 4–14 & 11–21 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Runtime definitions. Since \(T_{fmax}\), \(T_{gpair}\) and \(T_{sort}\) are much lower than \(T_{corr}\) or \(T_{rem}\), then \(T_{2}\approx 3N_{subCh}^{SL}T_{corr}+T_{rem}\). Therefore, the Proposed algorithm has a clear advantage over the Blind algorithm when \(T_{2}<T_{1}\Leftrightarrow T_{corr}<T_{rem}\), which is generally true, since \(T_{rem}\) includes CP-OFDM demodulation, PSCCH channel estimation, MMSE equalization, and the SCI/PSCCH decoding. For instance, in a machine with Intel(R) Core(TM) i7-10750H CPU @ 2.60 GHz and 16.0 GB of RAM, we obtain for the scenario of Results section with \(N_{subCh}^{SL}=5\), the values \(T_{corr}=20,285\,\upmu\)s, \(T_{fmax}=34\,\upmu\)s, \(T_{sort}=9\,\upmu\)s, \(T_{gpair}=6\,\upmu\)s, and \(T_{rem}=96,543\,\upmu\)s. Then, from (9) and (10) we have \(T_{1}=934,624\,\upmu\)s and \(T_{2}=401,343\,\upmu\)s.

## 4 Results

In this section, we compare the performance of the Blind and Proposed algorithms. For that, we assume a scenario where \(N_{subChSize}^{SL}=10\), \(N_{PSCCH}=10\), \(T_{PSCCH}=3\), \(N_{PSSCH}=1\), \(N_{RX}=16\) and \(N_{rx}=16\). The PSCCH is transmitted in a subchannel \(n\in\{0,\ldots,N_{subCh}^{SL}-1\}\) selected randomly, and associated to DMRS with a random index \(i\in\{0,1,2\}\). We tested with \(N_{RB}^{SL}=50\) and \(N_{RB}^{SL}=100\), therefore \(N_{subCh}^{SL}=N_{RB}^{SL}/N_{subChSize}^{SL}\) is 5 or 10. Finally, the results were obtained on a machine with Intel(R) Core(TM) i7-10750H CPU @ 2.60 GHz and 16.0 GB of RAM. Figure 5 shows the comparision of the SCI BLER performance for Blind and Proposed algorithms. For both cases, almost all blocks failed to decode until \(\text{SNR}=-18\,\text{dB}\) and almost all blocks were successful when decoding above \(\text{SNR}=-12\,\text{dB}\). So, there was a significant improvement going from \(-18\) to \(-12\,\text{dB}\). Moreover, we can observe that the performance obtained for the two algorithms almost overlaps. Figure 6 shows the throughput obtained for both algorithms. As we can see, the throughput is very low until \(\text{SNR}=-12\,\text{dB}\) and it is almost 100% when above \(\text{SNR}=-8\,\text{dB}\). Therefore, we also have a sudden performance improvement, although this only occurs for slightly higher SNR, when comparing with the results in Figure 5. The throughput obtained for the two algorithms practically overlaps. Figure 5: SCI BLER. Figure 7 shows the average number of attempts for the Blind and Proposed algorithms, for \(N_{RB}^{SL}=50\) and \(N_{RB}^{SL}=100\) (\(N_{subCh}^{SL}=5\) and \(N_{subCh}^{SL}=10\), respectively). As mentioned above, for low SNR, \(E_{1}=E_{2}=3N_{subCh}^{SL}\). Then, for \(N_{RB}^{SL}=50\) we have \(E_{1}=E_{2}=15\), and for \(N_{RB}^{SL}=100\) we have \(E_{1}=E_{2}=30\), which is validated in Figure 7. Moreover, for high SNR, \(E_{1}=\frac{1}{2}(3N_{subCh}^{SL}+1)\) and \(E_{2}=1\). Then, for \(N_{RB}^{SL}=50\) we have \(E_{1}=8\), and for \(N_{RB}^{SL}=100\) we have \(E_{1}=15.5\), which is also validated in Figure 7. As shown in Figures 5 and 6, the same performance in terms of BLER and throughput was achieved, but with a much lower number of attempts to decode the PSCCH at it can be seen in Figure 7. Similar to Figure 5, almost all attempts failed until \(\text{SNR}=-18\,\text{dB}\) and the best performance is achieved above \(\text{SNR}=-12\,\text{dB}\). Figure 6: Throughput for PSSCH. Figure 7: Average number of attempts. Figure 8 shows the runtime measures for PSCCH search/decoding.