# Integrated Sensing and Communication Using Random Padded OTFS with Reduced Interferences
## 7 Simulation Results  
### Sinc Extrapolation-Based Data-to-Data Interference Reduction Only  
At the very beginning of the simulation section, we present our sinc extrapolation-based interference reduction results, based on Equation (20). For the test, we used the regular RP-OTFS, i.e., without repetition of pilot carriers, but half of the data carriers of the DD grid are inactive, i.e., filled with zeros. We simulate the influence of the transmission channel with fractional delays with respect to the DD grid, as described in Section 4. After that, we estimated the channel and compensated the CIR oscillations by sinc extrapolating. The part of the grid with zeros was used to estimate the magnitude of the remaining interference. We estimated the dependence of root-mean-square (RMS) of the signal to interference and noise ratio (SINR) on the SNR of the signal before applying the channel, for different numbers of reflections. The reflection coefficient had a normal distribution with the same variance as active data cells, delays had a uniform distribution in the range of \(0\ldots L-2\), and the Doppler was also distributed uniformly in the range of \(-0.3\cdot N\ldots 0.3\cdot N\). The other parameters of the grid had the following values: \(M=32\), \(N=128\), \(L=8\). The results of the simulation are shown in Figure 13.  
It is clearly seen in Figure 13 that for high SNR, the sinc extrapolation-based interference reduction algorithm is saturated, which results from the error of estimation of the parameter of the sinc function. Also, in the algorithm we use, we assume that the fractional part of the delay equals 0.5 (coefficient 0.5 in (20)), which is also a source of inaccuracy. We do not know the real delay, so we choose the value in the middle of the possible fractional delay interval. In the following part of this section, we will estimate by simulation the BER for different application scenarios of regular RP-OTFS without pilot repetition and ZP-OTFS. The OTFS parameters (common for RP and ZP) are given in Table 3. \(M\) and \(N\) were reduced to speed up the simulation. \begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**Speed**} & \multirow{2}{*}{\(N\)} & \multirow{2}{*}{\(M\)} & \multicolumn{2}{c}{**Velocity [m/s]**} & \multicolumn{2}{c}{**Range [m]**} \\ \cline{3-6}  & & & **Resolution** & **Max/Min** & **Resolution** & **Max/Min** \\ \hline A & 128 & 512 & 2.65 & \(\pm\)170 & 3 & 384 \\ \hline B & 128 & 2048 & 0.47 & \(\pm\)30 & 3 & 1534 \\ \hline C & 128 & 65,536 & 0.01 & \(\pm\)0.64 & 3 & 49,152 \\ \hline \end{tabular}
\end{table} 
Table 2: The parameter of the RP-OTFS-based radar (70 GHz, BW 100 MHz, \(L=\frac{M}{4}\)). The OFDM waveform simulation was added to the simulation as a baseline. The length of the OFDM symbol was \(M-L\), the length of the CP was \(L\). \(L\) pilots were evenly distributed inside the OFDM symbol. In this case, it was 16 data carriers and 8 pilots per one OFDM symbol. The first scenario assumes that there is only one path with zero Doppler and 10 randomly scattered fractional reflections. The zero Doppler path is assumed to be the main propagation path, and the receiver is perfectly synchronized to it (no time delay in this path). In this scenario, we fix the number of reflections, but we change the variance of the magnitudes of the CIR coefficients. The variances are normalized to the power of the main propagation path (zero Doppler path). As in the previous case, the CIR coefficients have a normal distribution and zero mean. The delays and Doppler are uniformly distributed in the same range as in the previous case. The results of the simulation without and with the data carrier interference reduction algorithm are presented in Figures 14 and 15, respectively. In this scenario, we used only sinc extrapolating-based data-to-data interference compensation; no pilot repetition is applied. In the figures, one can see that OFDM is inefficient in such a strong Doppler environment.