# Analysis of Multi-Antenna GNSS Receiver Performance under Jamming Attacks
## 3 Simulation Results and Discussion  
The effect of different types of interference sources and array processing approaches are now studied through simulations. Simulations were carried out considering different interference types. In order to evaluate the effect of different kinds of interference and different beamforming methods, it is assumed that only one interference source is present at the time in each simulation scenario. The interference sources considered are Continuous Wave (CW) interference, chirp interference, and band-limited additive white Gaussian noise. The effect of these interference sources on GNSS receiver operation differs due to their spectral characteristics. Therefore, it is of interest to check the performance of the array based receiver under different interference types. Even though the power and the number of interference sources eventually affect beamformer performance, the main goal here is to compare PM and MPDR beamformers for high precision applications.  
The input IF data file for the multi-antenna software simulator was collected using a Spinrent hardware GPS simulator [28] by disabling multipath and atmospheric errors. A static user scenario was used for collecting IF data samples at a 5 MHz sampling rate. The multi-antenna GPS signals were generated using the multi-antenna signal simulator and interference was added later to the clean IF samples. The six-element rectangular antenna array described earlier was considered for the simulations. The interference source was assumed to be static and was added after 15 s in order for the receiver to acquire and track the signals (for the post-correlation beamforming). The multi-antenna signal simulation method and sky plot of the simulated GPS satellites and interference source direction are shown in Figure 4. The characteristics of the interference source are given in Table 1. In all the simulation scenarios, the interference source direction was the same. The C/N\({}_{0}\) values for all PRNs were set to be the same for all the antenna elements (48 dB-Hz).  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Simulation Scenarios** & **Interference Type** & **Interference Characteristics** \\ \hline Scenario 1 & CW interference & The frequency of the CW interference is 500 Hz away from IF (420 kHz). Jammer-to-signal power is assumed to be 30 dB. \\ \hline Scenario 2 & Chirp interference & Chirp signal bandwidth is 11.8 MHz with an interval of 1.7 \(\mu\)s. These values are basically chosen from commercially available in-car jammers. Jammer-to-signal power is 30 dB. \\ \hline Scenario 3 & Band limited white Gaussian noise & White Gaussian noise is generated through the MATLABTM \\  & & awgn() function with a bandwidth of 5 MHz and \\  & & jammer-to-signal power of 30 dB. \\ \hline \hline \end{tabular}
\end{table}
Table 1: Interference sources considered in the simulations and their characteristics.  
The simulated signals were processed using GSNRxTM with the architectures shown in Figures 2 and 3 to generate tracking and measurement parameters. Here, PM was performed from the beginning of the dataset as it was done in the pre-correlation stage. In the case of the MPDR beamformer, the receiver was made to operate with a single antenna for the initial 10 s, after which beamforming was performed before the occurrence of interference. This was done to ensure that the receiver operates in beamforming mode when interference affects the IF samples. In both PM and MPDR approaches, correlator spacing of 0.4 between early and late arms and non-coherent early-minus late discriminators were used. Carrier tracking was performed using a third order Phase Locked Loop (PLL) with a 15 Hz bandwidth.