# Detection of Weak Radar Return Signals Based on Pseudo-Time Domain Algorithm
## 3 Experimental Results and Analysis
### Results and Analysis of Outdoor Experiments  
At the position marked in red in the Figure 5, multiple sets of background noise signals were received by a signal reception system. The signal reception system consisted of a loop antenna, Universal Software Radio Peripheral (USRP) X410 (National Instruments, Austin, TX, USA), a computer, and other equipment. The outdoor experiment flowchart is shown in Figure 6.  
The open-loop experiment conducted in the outdoor environment captured all signals received by the transceiver from system startup to shutdown, as illustrated in Figure 7. The acquired time-domain waveform is partitioned into three characteristic segments: initial transient noise, stable external environmental noise, and post-shutdown system noise. Specifically, multiple stable segments from the second phase are selected as experimental background noise. The normalized time-domain waveform of the selected background noise is shown in Figure 8a, with corresponding pseudo-temporal domain representations provided in Figure 8b,c. These pseudo-temporal profiles reveal four distinct peaks from other interference sources, corresponding to spectral components at \(\pm 1\) kHz and \(\pm 15.875\) kHz.  
After adding the reference signal to the background noise to form a \(-30\) dB received signal and normalizing it, the time-domain waveform is shown in Figure 9a, and the pseudo-time-domain waveforms are presented in Figure 9b,c. In Figure 9b, the two peaks of the red reference signal correspond to the spectral positions of the \(10\) kHz signal, which are completely masked by the noise. The denoising comparison of the received signal with an SNR of \(-30\) dB is shown in Figure 10. Figure 10a shows the pseudo-time-domain waveform of the received signal with the reference signal, and Figure 10b shows the pseudo-time-domain waveform of the received signal without the reference signal. From Figure 10a, it can be seen that the peaks at the frequency positions of the pseudo-time-domain waveform of the received signal with the reference signal are significantly larger  
Figure 5: Location of outdoor experiment.  
Figure 6: Flowchart of the outdoor experiment.  
after denoising. From Figure 10b, it can be seen that the peaks at the frequency positions of the pseudo-time-domain waveform of the received signal without the reference signal are much smaller after denoising.  
Through multiple experiments with 1000 sets of signals randomly added in the SNR range from \(-40\) dB to \(-10\) dB, the results obtained using the denoising method presented in this paper are shown in Figure 11. As the SNR increases, the detection accuracy gradually  
Figure 8: The waveform diagrams of the background noise signal, where Figure (**a**) is the time-domain waveform, and Figure (**b,c**) are the pseudo-time-domain waveforms, respectively.  
Figure 7: Time domain diagram of received signal, (**a**) real part, (**b**) imaginary part.  
improves. When the SNR is greater than or equal to \(-25\) dB, the detection rate reaches 100%, and it exceeds 99% at an SNR of \(-28\) dB.  
Figure 10: Waveform diagrams before and after denoising: (**a**) Waveform of the noise signal before and after denoising, (**b**) Waveform of the received signal before and after denoising.  
Figure 9: The time-domain waveform and the pseudo-time-domain waveform of the received signal.  
The comparison between the SNR values that can be processed in this article and other literature is shown in Table 1. In the selection of SNR for detecting radar signals, the minimum SNR value in other literature is \(-20\) dB. The method proposed in this article achieves detection accuracy close to the theoretical limit in simulation experiments at \(SNR=-40\) dB.