# Effective PSCCH Searching for 5G-NR V2X Sidelink Communications
## 3 Proposed Effective PSCCH Searching
### Receiver Model  
The block diagram of the received signal processing is shown in Figure 3. It has three parts: (1) synchronization procedures; (2) obtain control information; and (3) obtain the desired data. The first step of the receiver is to try to synchronize with the transmitter. For that, the receiver knows the possible Sidelink Primary Synchronization Signals (S-PSS), and performs a correlation with the received signal until it finds a significant peak. After finding the S-PSS, the receiver also performs a correlation between known sequences of the S-SSS and the received signal. Taking into account the S-PSS/S-SSS sequences that gave the \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & & & \(i\) & \\ \hline  & & 0 & 1 & 2 \\  & 0 & 1 & 1 & 1 \\ \(k^{\prime}\) & 1 & 1 & \(e^{j\frac{1}{3}\pi}\) & \(e^{-j\frac{1}{3}\pi}\) \\  & 2 & 1 & \(e^{-j\frac{1}{3}\pi}\) & \(e^{j\frac{1}{3}\pi}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The quantity \(w_{i}(k^{\prime})\). Figure 3: Block diagram of the receiver. main correlation peaks, a sidelink identity is obtained, which is then used to try to decode the Master Information Block (MIB). If the MIB is successfully decoded then the receiver proceeds to the next step. Otherwise, the receiver goes back to the beginning and continues trying to synchronize. Once the MIB is obtained, the receiver is ready to search for PSCCHs. As mentioned above, the resource grid is organized into subchannels, and the PSCCH starts in the lowest RB of a subchannel. Moreover, the DMRS associated to PSCCH are computed based on the quantity \(w_{i}(k^{\prime})\), where \(i\in\{0,1,2\}\) shall be randomly selected. Therefore, the receiver needs to search for PSCCHs in different subchannels, and needs to try different indexes \(i\) until they are able to decode the SCI/PSCCH. Thus, only after this, it is possible to get the SCI carried in the PSCCH and extract the desired data, i.e., the Transport Block (TB) from the PSCCH. To proceed with the PSCCH search, an algorithm is needed. To the best of our knowledge the most commonly used algorithm is a blind one, as discussed in [15], whose pseudo-code is presented in the Blind algorithm (Algorithm 1). ```
1 For \(n=0,\ \ldots,\ N_{subCh}^{SL}-1\) do
2 For \(i=1,2,3\) do
3\(\mathbf{c}_{n,i}=\sum\limits_{v=1}^{N_{g}}\text{corr}(\mathbf{s}_{\tau x,v}, \mathbf{d}_{PSCCH}^{nj})\)
4 Compute \(f_{offset}(q_{\text{max}})\), where \(q_{\text{max}}=\underset{q\in\{0,\ldots,Q_{\text{max}}-1\}}{\text{max}}\) \(\mathbf{s}_{\tau x,v}^{gmc}(q)=\mathbf{s}_{\tau x,v}(q+f_{offset})\), \(q=0,\ldots,Q_{\text{max}}-1-f_{offset}\)
6 Perform the CP-OFDM demodulation
7 Extract the PSCCH candidate
8 Perform the PSCCH channel estimation
9 Perform the MMSE equalization
10 Try to decode the PSCCH
11 Try to decode the SCI
12 If SCI decoded with success, then
13 Break
14 End
15 End
```  
**Algorithm 1**Blind Algorithm  
As we can see in the Blind algorithm, we search in all subchannels (line 1), for all indexes \(i\) (line 2) until decode the SCI/PSCCH (lines 1-1). In the PSCCH decoding processing, first we compute the correlation of received signal by each antenna, \(\mathbf{s}_{\tau x,v}=\left[\ \mathbf{s}_{\tau x,v}(0),\ldots,\mathbf{s}_{\tau x,v}(Q_{ \text{max}}-1)\right]^{T}\), \(v=1,\ldots N_{\tau x}\), where \(Q_{\text{max}}\) is the maximum number of samples used in the correlation, with the DMRS, \(\mathbf{d}_{PSCCH}^{nj}=\left[\ \ldots,\ d_{PSCCH,k,l}^{i},\ \ldots\ \right]^{T}\), \(k=nN_{subChSize}^{SL}N_{RB,SC}^{SL}+4k^{\prime}+1\), \(k^{\prime}=0,1,2\), \(l=1,\ldots,T_{PSCCH}\) (line 3). Then, the frame offset, \(f_{offset}(q_{\text{max}})\), is computed using the index number of sample where the correlation peak is stronger (line 4) and a subframe synchronization is completed (line 5).