# Analysis of Multi-Antenna GNSS Receiver Performance under Jamming Attacks
## 3 Simulation Results and Discussion
### Tracking Domain Analysis  
In this section, tracking performance in terms of carrier Doppler estimation, C/N\({}_{0}\) and Phase Lock Indicator (PLI) is evaluated. The C/N\({}_{0}\) is computed using narrow band power and wide band power of the prompt correlation values and PLI is computed using prompt in-phase and quadrature-phase values [29]. Initially, the signal affected by interference from the reference antenna of the array was processed and the corresponding results are discussed in subsequent sections. Since PRN 6 and PRN 16 are more affected by CW interference, these two PRNs are used to analyze tracking performance of the array-based receiver. The tracking outputs of PRN 6 for the single antenna case affected by CW interference after beamforming for the first 20 s are shown in Figure 5 where 'Single Antenna' corresponds to the tracking outputs of the reference antenna of the array in the presence of interference. For the initial 15 s, there was no interference; as mentioned earlier, PM was performed from the beginning of the data and MPDR was performed after 10 s.  
Figure 4: Multi-antenna signal simulation set-up and sky plot of the simulated GPS satellites and interference (INT) source. Let us first consider the initial 15 s of data without interference. After MPDR beamforming, a C/N\({}_{0}\) gain of 7.5 dB is observed. As six antenna elements were used, a gain of 7.7 dB [\(10\times\log_{10}\)(number of antennas)] is expected and one can observe the same with MPDR beamforming. With PM, a gain of 1.5 dB is observed; in this case, since there is no constraint on for the satellite signal AOA, the gain depends on the beampattern, which in turn depends on the interference direction and array geometry. Now consider the data affected by interference (after 15 s) in Figure 5. As soon as interference is injected, the C/N\({}_{0}\) values of the single antenna drops by about 8 dB. However, the same C/N\({}_{0}\) as that without interference was maintained through MPDR and PM methods. This ensured successful mitigation of the interference. If one considers the C/N\({}_{0}\) gain in the presence of interference, MPDR was able to deliver nearly 15.5 dB with respect to the single antenna. The gain observed from PM was 9.5 dB. As shown in Figure 5, Doppler errors increase and PLI degrades for the single antenna case after interference. However, MPDR and PM were able to provide the same performance as that for the interference-free case. To compute the carrier Doppler errors shown in Figure 5, the Doppler values obtained from the reference antenna with clean data were used as reference. The carrier tracking performance of PRN 6 for chirp and BWGN scenarios for the first 60 s are shown in Figures 6 and 7. MPDR was able to provide 15.5 dB of gain even in the presence of chirp and BWGN interference. PM was able to provide 9.5 dB of gain in the presence of the same interference. The Doppler error variance is lower after beamforming; this can be clearly observed in Figure 7 in the presence of BWGN interference. The receiver was able to maintain PLI values of 0.99 after beamforming in all interference scenarios, indicating reliable tracking of the carrier phase. The performance results of different PRNs in terms of Root-Mean-Square (RMS) Doppler errors, C/N\({}_{0}\) gain, and mean PLI for chirp interference are listed in Table 2. These values were computed using the tracking outputs in the presence of interference. For computing Root-Mean-Square Error (RMSE) Doppler errors, the Doppler values obtained from the reference antenna with clean data were used as true values. The tracking performance results of different PRNs in the presence of CW and BWGN jammers are provided in Appendix A for the CW jammer in Table 11 and those for BWGN in Table 12. It can be observed that compared to single antenna results, RMS Doppler errors are reduced for both beamformers for all simulation scenarios. MPDR RMS Doppler errors were lower by 0.1 Hz as compared to PM, a relative improvement of 25%.