## 4 Simulation Results
### Effectiveness Validation of the Proposed STPAP Beamforming Algorithm  
#### 4.1.1 Array Pattern in the Joint Space-Time-Polarization Domain  
In this scenario, the effectiveness of the proposed STPAP beamforming algorithm is validated through observing the array pattern in the joint space-time-polarization domain. It is noticed that the array pattern corresponding to the STPAP algorithm are related to the spatial, temporal and polarized parameters and thus it is a four-dimensional data in this simulation, which means that it is difficult to depict the data in only one figure. As a result, if nulls in one domain are supposed to be observed, we have to fix parameters in another two domains. Since the data of the space domain and time domain in the simulation is one-dimensional, the array pattern in the space domain and time domain can be observed together if the polarized parameter has been fixed. Meanwhile, array pattern in the polarization domain can be observed if the spatial and temporal parameters are fixed. In addition, \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Scenario**} & \multirow{2}{*}{**Incident Signal**} & \multirow{2}{*}{**SNR/INR**} & \multirow{2}{*}{**Spatial Parameter**} & \multicolumn{2}{c}{**Polarized Parameter**} \\ \cline{5-6}  & & & & **Amplitude** & **Phase** \\  & & & & **Ratio** & **Difference** \\ \hline \multirow{3}{*}{1} & BD2 B3 (PRN 1) & \(-\)20 dB & 0 & \(\pi/4\) & \(\pi/2\) \\  & BD2 B3 (PRN 2) & \(-\)20 dB & \(-\pi/6\) & \(\pi/4\) & \(\pi/2\) \\  & Wideband interference (EP) & 40 dB & \(\pi/3\) & \(\pi/6\) & \(\pi/3\) \\ \hline \multirow{3}{*}{2} & BD2 B3 (PRN 1) & \(-\)20 dB & \(\pi/36\) & \(\pi/4\) & \(\pi/2\) \\  & BD2 B3 (PRN 2) & \(-\)20 dB & \(\pi/12\) & \(\pi/4\) & \(\pi/2\) \\  & BD2 B3 (PRN 3) & \(-\)20 dB & \(\pi/4\) & \(\pi/4\) & \(\pi/2\) \\  & BD2 B3 (PRN 4) & \(-\)20 dB & \(5\pi/12\) & \(\pi/4\) & \(\pi/2\) \\  & BD2 B3 (PRN 5) & \(-\)20 dB & \(4\pi/9\) & \(\pi/4\) & \(\pi/2\) \\  & BD2 B3 (PRN 6) & \(-\)20 dB & \(17\pi/36\) & \(\pi/4\) & \(\pi/2\) \\  & BD2 B3 (PRN 7) & \(-\)20 dB & \(-\pi/36\) & \(\pi/4\) & \(\pi/2\) \\  & BD2 B3 (PRN 8) & \(-\)20 dB & \(-\pi/12\) & \(\pi/4\) & \(\pi/2\) \\  & BD2 B3 (PRN 9) & \(-\)20 dB & \(-\pi/4\) & \(\pi/4\) & \(\pi/2\) \\  & BD2 B3 (PRN 10) & \(-\)20 dB & \(-5\pi/12\) & \(\pi/4\) & \(\pi/2\) \\  & BD2 B3 (PRN 11) & \(-\)20 dB & \(-4\pi/9\) & \(\pi/4\) & \(\pi/2\) \\  & BD2 B3 (PRN 12) & \(-\)20 dB & \(-17\pi/36\) & \(\pi/4\) & \(\pi/2\) \\  & Wideband interference (HP) & 40 dB & \([-5\pi/36,-7\pi/36]\) & 0 & \(\pi\) \\  & Wideband interference (VP) & 40 dB & \([11\pi/36,13\pi/36]\) & \(\pi/2\) & \(\pi\) \\  & Wideband interference (LHCP) & 40 dB & \([5\pi/36,7\pi/36]\) & \(\pi/4\) & \(-\pi/2\) \\  & Wideband interference (RHCP) & 40 dB & \([-11\pi/36,-13\pi/36]\) & \(\pi/4\) & \(\pi/2\) \\ \hline \multirow{3}{*}{3} & BD2 B3 (PRN 1) & \(-\)20 dB & \(\pi/36\) & \(\pi/4\) & \(\pi/2\) \\  & BD2 B3 (PRN 2) & \(-\)20 dB & \(\pi/12\) & \(\pi/4\) & \(\pi/2\) \\  & BD2 B3 (PRN 3) & \(-\)20 dB & \(\pi/4\) & \(\pi/4\) & \(\pi/2\) \\  & BD2 B3 (PRN 4) & \(-\)20 dB & \(5\pi/12\) & \(\pi/4\) & \(\pi/2\) \\  & BD2 B3 (PRN 5) & \(-\)20 dB & \(4\pi/9\) & \(\pi/4\) & \(\pi/2\) \\  & BD2 B3 (PRN 6) & \(-\)20 dB & \(4\pi/9\) & \(\pi/4\) & \(\pi/2\) \\  & BD2 B3 (PRN 6) & \(-\)20 dB & \(4\pi/9\) & \(\pi/4\) & \(\pi/2\) \\  & BD2 B3 (PRN 6) & \(-\)20 dB & \(4\pi/9\) & \(\pi/4\) & \(\pi/2\) \\  & Wideband interference (RHCP) & 40 dB & \([-5\pi/36,-7\pi/36]\) & \(\pi/4\) & \(\pi/2\) \\  & Wideband interference (RHCP) & 40 dB & \([11\pi/36,13\pi/36]\) & \(\pi/4\) & \(\pi/2\) \\  & Wideband interference (RHCP) & 40 dB & \([5\pi/36,7\pi/36]\) & \(\pi/4\) & \(\pi/2\) \\  & Wideband interference (RHCP) & 40 dB & \([-11\pi/36,-13\pi/36]\) & \(\pi/4\) & \(\pi/2\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulation parameterswe can choose 5.115 MHz as the fixed temporal parameter, which also applies to the next scenario, as all interferences and desired BD2 signals are wideband.