*3.1. Influence of Reference Channel Interference on DPI and MPI Suppression*

To suppress DPI and MPI, an adaptive filtering algorithm was adopted [22–24]. The direct wave signal received on the reference channels is used as reference signals to cancel the DPI and MPI on the monitoring channels. The specific suppression principle is shown in Figure 3, where *X*ref(*n*) is the direct wave signal of the reference channel, *X*s(*n*) is the mixed signal received by the monitoring channel, and *W*(*n*) is the coefficient of the filter. The algorithm is able to adjust the filter coefficients adaptively to minimize the output error *e*(*n*) of the filter, and *e*(*n*) also gives the signal for the monitoring channel after interference suppression, which is obtained by

$$
\varepsilon(n) = X\_{\delta}(n) - \mathcal{W}^H(n-1) X\_{ref}(n). \tag{3}
$$

From Figure 3, reference signals are required in this method. The reference signal is used to cancel the DPI and MPI in the monitoring channel, and is also used as a reference signal for time-frequency two-dimensional correlation with the echo signal in the monitoring channel. Therefore, the reference signal is very important throughout the process. This section analyzes the influence of reference channel noise and interference signals on the direct wave multipath suppression. In Figure 4, the DPI and MPI suppression are performed by using the algorithm in Figure 3, and the monitoring channel signal and the reference signal after suppression are used as fuzzy functions, and the DPI and MPI

inhibition effects are judged by observing whether or not there is a peak corresponding to the echo on the time delay-Doppler spectrum.

**Figure 3.** The suppression methods of DPI and MPI.

First, set the monitoring channel to include both the target echo and DPI and MPI. The reference channel only has the reference signal and noise corresponding to the target echo. There are no other GPS interference signals. The parameter settings are shown in Table 1. The DPI and MPI suppression effects are assessed by observing whether there is a peak corresponding to the echo on the delay-Doppler spectrum, which are shown in Figures 4 and 5. As can be seen from Figure 4, when the SNR of the reference signal is −15 dB, after using this reference signal to perform DPI and MPI suppression on the monitoring channel, the interference peak in the delay-Doppler spectrum is still strong, making the peak corresponding to the target echo invisible. When the SNR of the reference signal is 5 dB, after the suppression of the direct wave, it can be seen from Figure 5 that, although the interference peaks of DPI and MPI still exist, the peak of the echo can be seen in the delay-Doppler spectrum. If the SNR is gradually increased, DPI and MPI can be completely suppressed. Therefore, it can be concluded that the noise of the reference channel has a great influence on the suppression process of DPI and MPI.

**Table 1.** Parameter setting.


Second, set the echo channel to include the target echo plus DPI and MPI. In this case, only the reference signal and other GPS interference signals are in the reference channel. The parameter settings are shown in Table 2.



**Figure 4.** The influence of reference channel SNR on interference suppression process with SNR = −15 dB.

**Figure 5.** The influence of reference channel SNR on interference suppression process with SNR = 5 dB.

As can be seen from Figure 6, when the power of the interference signal in the reference channel is −110 dBm, that is, the signal-to-interference ratio (SIR) is 10 dB, the peak corresponding to the target is still invisible after interference suppression, and the DPI and MPI suppression methods fail in this scenario. As can be seen from Figure 7, when the power of the interference signal in the reference channel is reduced to −140 dBm and the SIR is 30 dB, the peak corresponding to the target can be seen after interference suppression, but the interference is still not eliminated. Therefore, it can be concluded that, under normal circumstances, the reference channel inevitably receives signals from multiple GPS satellites as co-channel interference, and it has a great influence on the suppression process of DPI and MPI.

**Figure 6.** The influence of reference channel SIR on DPI and MPI suppression with SNR = 10 dB.

**Figure 7.** The influence of reference channel SIR on DPI and MPI suppression with SNR = 30 dB.

Based on the above analysis, the noise and interference signals in the reference channel have a great influence on DPI and MPI suppression. The traditional external source detection system does not process the reference channel signal and uses it directly as a reference signal for the DPI and MPI interference suppression algorithms. In order to correctly detect the echo signal, the GPS reference signal of the reference channel must be purified and separated.
