## 4 Simulation Results
### Computational Complexity Performance  
In this simulation, we will focus on the computational complexity performance of the proposed STPAP algorithm and the existing STPAP algorithm based on the criterions in [30; 31] since they have the similar processing flow. As for the existing STPAP algorithm based on the PM criterion in [29], its processing flow is different form the MVDR-based criterion because it is unnecessary to estimate DOAs of the desired GNSS signals, due to which it has the lowest computational complexity and thus it is meaningless considering this algorithm in this section. Figure 11: Output C/N\({}_{0}\) performance comparison between the proposed STPAP algorithm and the STPAP algorithms based on the criterions in [29; 30; 31] when there are interferences with the same polarization mode: (**a**) one interference; (**b**) two interferences; (**c**) three interferences; (**d**) four interferences. The number of addition and multiplication can be adopted to measure the computational complexity. Using the proposed adaptive iterative algorithm described in Section 3.2 to implement the proposed STPAP algorithm and the existing STPAP algorithm based on the criterions in [30; 31], the number of addition and multiplication that consumed in each iteration can be shown in Table 3. It is noticed that \(J\) GNSS satellites can be processed at once with only one adaptive filter using the proposed STPAP algorithm and the existing STPAP algorithm based on the criterion in [31], while \(J\) adaptive filters are required using the existing STPAP algorithm in [30]. Thus, it should be taken into consideration when calculating the computational complexity. Moreover, when the desired GNSS satellites change, the metrics \(T\) and \(V\) in (24) are required to be recalculated. Since the update frequency of the desired GNSS satellites is not so fast with regard to the iterative convergence progress, we can assume that the desired GNSS satellites will not change during an iterative period as shown in Figure 3, due to which the calculation amount of \(T\) and \(V\) can be ignored for simplicity. Moreover, one can obtain that the computational complexity of the proposed STPAP algorithm is almost equal to that of the existing STPAP algorithm based on the criterion in [31] with the assumption that the calculation amount of \(T\) and \(V\) can be ignored. As depicted in Figures 12 and 13, it can be seen that the number of addition and multiplication that used in the proposed STPAP algorithm and the existing STPAP algorithm in [31] are always less than that of the existing STPAP algorithm based on the criterion in [30] when there are different tap number and element number. The results indicate that the proposed STPAP beamforming algorithm has a lower computational complexity than the traditional STPAP algorithm based on the MVDR-CSS criterion in [30]. \begin{table}
\begin{tabular}{l c c} \hline \hline
**Criterion** & **Addition Number** & **Multiplication Number** \\ \hline Proposed STPAP algorithm & \(8M^{2}K^{2}\) & \(12M^{2}K^{2}+2 MK\) \\ The existing algorithm in [30] & \(8M^{2}K^{2}J\) & \(12M^{2}K^{2}J+2 MKJ\) \\ The existing algorithm in [31] & \(8M^{2}K^{2}\) & \(12M^{2}K^{2}+2 MK\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Computational complexity. Figure 12: Computational complexity of the proposed STPAP beamforming algorithm and the STPAP algorithms based on the criterions in [30; 31] when \(J=2\): (**a**) addition number; (**b**) multiplication number. From the results in the simulation, we can make a conclusion that the proposed STPAP beamforming algorithm based on the MVDR-CMS criterion can effectively reduce the computational complexity and meanwhile keep the output C/N\({}_{0}\) performance close to that of the traditional STPAP algorithm based on the MVDR-CSS criterion in [30] when the parameter \(J\) is fixed as 2 or 3.