## 4 Simulation Results
### GNSS Signal Tracking Performance Analysis  
The simulation module, which consists of three parts including the signal generation module, array signal processing module, and GNSS tracking module, was used to verify the efficacy of the algorithm. Figure 10 illustrates the simulation module. The signal generation module is used for simulating the array receiver signals. Specifically, the GNSS signal vector, interference signal vector, and noise signal vector were simulated individually, and then combined to form the received signal. On the other hand, the array signal processing module were mainly used for interference suppression, DOA estimation, and beamforming. After array weighting, the GNSS software-defined receiver [27] was used for GNSS signal tracking. In the simulation, one satellite navigation signal and two interference signals were simulated, a uniform line array with eight elements was used, the sampling rate was 6 MHz, and the correlation integration time was 1 ms. The navigation signal was GPS LIC/A  
Figure 10: The flowchart of the simulation model. Figure 9: Tracking results in the scenario of DOA parameter step change: (**a**) DOA tracking results; (**b**) DOA tracking error. signal, the pseudo-code frequency was 1.023 MHz, C/N0 was 45 dBHz, and the DOA parameter was 30\({}^{\circ}\). The interference signal was broadband Gaussian noise interference, the bandwidth was 2.046 MHz, the incidence direction was \(-40^{\circ}\) and \(55^{\circ}\), respectively, and the interference-to-noise-ratios were 50 dB and 55 dB, respectively. The simulation duration was 3 s, which was divided into three stages: the interference was turned off in the first second; the interference was turned on in the second second; and the C/N0 value was turned down to 30 dBHz in the third second. In the software receiver, the performance of the proposed method was compared with the PI and MVDR methods. The PI algorithm is one of the most useful blind adaptive beamformers, and forms nulls in the direction of the jammers. The cost function of PI is as follows:  
\[\min_{\mathbf{w}_{PI}}\mathbf{w}_{PI}^{H}\mathbf{R}\mathbf{w}_{PI}\;s.t.\; \mathbf{w}_{PI}^{H}\delta=1 \tag{23}\]  
where \(\delta=\left[1,0,\cdots,0\right]^{T}\) is an \(N\times 1\) vector. The PI beamformer can be expressed as  
\[\mathbf{w}_{PI}=\frac{\mathbf{R}^{-1}\delta}{\delta^{H}\mathbf{R}^{-1}\delta} \tag{24}\]  
The MVDR cost function is given as  
\[\min_{\mathbf{w}_{MVDR}}\mathbf{w}_{MVDR}^{H}\mathbf{R}\mathbf{w}_{MVDR}\;s.t. \;\mathbf{w}_{MVDR}^{H}\mathbf{a}(\theta)=1 \tag{25}\]  
The solution of Equation (25) is given by  
\[\mathbf{w}_{MVDR}=\frac{\mathbf{R}^{-1}\mathbf{a}(\theta)}{\mathbf{a}^{H}( \theta)\mathbf{R}^{-1}\mathbf{a}(\theta)} \tag{26}\]  
The simulation results are shown in Figures 11-14. Figure 11 gives the normalized array pattern results of the proposed method and the PI method with and without the influence of the interference. It shows that the PI method can achieve an effective suppression of interference, but cannot achieve signal direction enhancement, and may even lead to signal energy loss. In the proposed method, the DOA parameter can be estimated accurately using DiLL, so a blind adaptive beamformer can be constructed to point the beam in the direction of the navigation signals, which can enhance the signal energy, even in the interference scenario. Figure 11: Normalized array patterns of the proposed method, the PI method, and the MVDR method: (**a**) no-interference scenario; (**b**) interference scenario. Figure 12 shows the punctual branch correlation value using the proposed method and the PI and MVDR methods. From the figure, it can be seen that the proposed method and MVDR can both achieve gain in the signal direction, and significantly increase signal energy compared with the PI algorithm.