# Effective PSCCH Searching for 5G-NR V2X Sidelink Communications
## 2 System Model  
In this manuscript, we consider a 5G-NR V2X sidelink system, which uses the Cyclic Prefix-Orthogonal Frequency Division Multiplexing (CP-OFDM)--as the access technique. For the sake of simplicity and, without loss of generality, we consider only two UEs, where the transmitter and receiver UE are equipped with \(N_{tx}\) and \(N_{rx}\) antennas, respectively. The UEs are communicating based on a resource allocation scheme in the Mode 2, Figure 1, i.e., both UEs are out of coverage and have autonomous resource selection. These resources are mapped in time and frequency domains as we can see in Figure 2. The smallest unit in a sidelink (SL) communication is the RE, composed by a subcarrier \(k\), and an OFDM symbol \(l\), where \(N_{RB,SC}^{SL}=12\) subcarriers (SC) are a RB, with a subcarrier spacing equal to \(15\times 2^{\mu}\,\mathrm{kHz}\), and 14 OFDM symbols corresponds to a time slot, \(t_{i}^{SL}\), as presented in Figure 2, with \(0\leq t_{i}^{SL}<10,240\times 2^{\mu}\), \(0\leq i<T_{\max}\), where \(\mu\in\{0,1,2,3,4\}\) defines the 5G-NR numerology [27]. In the time domain, a set of \(2^{\mu}\) slots corresponds to 1 ms. In the frequency domain, we have \(N_{subCls}^{SL}\) subchannels with \(N_{subClsize}^{SL}\) RBs each one, in a total of \(N_{RB}^{SL}=N_{subCls}^{SL}N_{subClsize}^{SL}\) RBs available for sidelink transmissions. Figure 1: System model. The PSCCH is allocated with the corresponding PSSCH in the same slot. To enable low latency and energy efficiency, the PSCCH and PSSCH are time-division-multiplexed [28]. The allocation of PSCCH starts in the second OFDM symbol of the time slot and it can have a duration of \(T_{PSCCH}\in\{2,3\}\) symbols, which are pre-configured. In the frequency domain, the PSCCH starts in the lowest RB of a subchannel, and it can occupy \(N_{PSCCH}\in\{10,12,15,20,25\}\) RBs, where \(N_{PSCCH}\leq N_{subChSize}^{SL}\) is also a pre-configured value [7]. The PSCCH carries the first stage SCI, i.e., the SCI format 1-A, which contains the following information [29]:  
* Priority;
* Frequency resource assignment for the PSSCH;
* Time resource assignment for the PSSCH;
* Resource reservation period;
* DMRS pattern;
* Second stage SCI format;
* Beta offset indicator;
* Number of DMRS port;
* Modulation and coding scheme for the PSSCH;
* Additional Modulation and Coding Scheme (MCS) table indicator;
* Physical Sidelink Feedback Channel (PSFCH) overhead indication;
* Reserved. Therefore, the PSSCH allocation is indicated by the SCI through the frequency resource assignment and time resource assignment fields, in a form of time RIV (TRIV) and frequency RIV (FRIV), respectively, computed as in [27]. The PSSCH allocation in a resource grid is defined in terms of starting subchannel and number of contiguously occupied subchannels. The number of contiguous subchannels occupied by a PSSCH transmission is \(N_{PSSCH}\) and the starting subchannel of the first resource is \(n_{start,0}\), both of which are obtained from FRIV. There are DMRS associated to physical channels to allow the channel estimation. The DMRS associated to PSCCH for subcarrier \(k\) and symbol \(l\) within the slot, \(d_{PSCCH,k,l}^{i}\), used in channel estimation are given by [30],  
\[d_{PSCCH,k,l}^{i}=\beta_{PSCCH}w_{i}\big{(}k^{\prime}\big{)}r_{l}\big{(}3m+k^{ \prime}\big{)}, \tag{1}\]  
where \(k=mN_{RB,SC}^{SL}+4k^{\prime}+1,k^{\prime}=0,1,2\) and \(m=0,1,\ldots\). The amplitude scaling factor \(\beta_{PSCCH}\) is applied to transmit with the power specified in [31], and the quantity \(w_{i}(k^{\prime})\) is given by Table 2, where \(i\in\{0,1,2\}\) shall be randomly selected [30]. Figure 2: Resource grid. Finally, \(r_{l}(u)\), \(u=0,1,\ldots\) is a sequence generated by  
\[r_{l}(u)=\frac{1}{\sqrt{2}}(1-2c(2u))+j\frac{1}{\sqrt{2}}(1-2c(2u+1)), \tag{2}\]  
where \(c(u)\) is a pseudo-random sequence defined in [30].