## 4 Numerical Experiments
### Results  
Signals recorded by the passive radar demonstrator were processed with the passive FSR signal processing chain as presented in Figure 6.  
Figure 4: The cooperative aerial target. Figure 5: Digital multichannel signal recorder. At first, signals from two channels (reference and surveillance) were selected for further calculations. All further computations were performed on the signals' blocks with a 200 ms integration period (which resulted in a velocity resolution equal to 8.13 m/s). Next, a clutter filter was used for removing the reference signal from the surveillance signal [9]. This operation normally significantly reduces target echo power when reaching zero Doppler velocity. In order to limit the scale of this phenomenon, clutter removal filter coefficients were fixed for the time when the target was crossing the baseline [47]. An additional step of signal processing was the removal of direct current (DC) offset, which was achieved by subtracting the mean value from the signal after clutter filtering. The last step of the processing was a multi-stage decimation. According to the simulations carried out, the expected Doppler frequency was not greater than 100 Hz. The input sampling rate of the recorded signals was equal to 8 MHz, so the filtered signal might have been down-sampled a few thousand times without losing valuable information. This step considerably reduced the number of unnecessary subsequent calculations. It should be mentioned that the bistatic range resolution for the processed signal is equal to 37.5 m (this is the size of the first range cell). Next, the signal was transformed into the TF domain using Equation (11) giving the classical signal distributions on the 2D TF plane, as shown in Figure 7. The Doppler history is clearly visible for the entire trajectory, however, some interference related to multipath propagation and clutter removal algorithm are apparent, especially at the point when the waveform changes the frequency sign. Additionally, the clutter cannot be suppressed at this point due to the presence of the useful signal that should not be filtered out. Figure 6: Passive FSR signal processing scheme. Figure 7: The energy distributions of the measured signal obtained using the classical short-time Fourier transform (STFT). The same signal was processed using the concept of energy concentration. The outcomes for this approach are depicted in Figure 8, where the significant concentration was obtained. In such a case, the component extraction and separation are obtainable even in the case of low SNR. Both classical and reassigned distributions were obtained using an 8192-point FFT and the Gaussian window of a standard deviation \(\sigma=0.2\). The shift of the window in consecutive steps the processing was equal to 1 sample in order to provide precise signal representation. Then, in accordance to the approach proposed by [PERSON] et al. (20, 20, 28, 29), the Hough transform was applied to estimate the signal Doppler rate as a straight line on the TF plane composed by the Doppler history of the signal near the zero-intersection point. The results are depicted in Figure 9.  
As can be observed, both the classical and the concentrated distributions allowed the Doppler rate to be estimated. The selected sections of both distributions \(f\in(-20,20)\) Hz, \(t\in(40,60)\) s containing the most important parts of the signal were processed using the Hough transform, which gave results corresponding to the frequency slope at the interesting point. These values were estimated as follows: \(f_{S}=-3.6392\frac{\mathrm{Hz}}{\mathrm{s}}\) for the classical STFT distribution and \(f_{R}=-3.9873\frac{\mathrm{Hz}}{\mathrm{s}}\) for the reassigned spectrogram. Both estimated lines coincide with the Doppler history, and the visual analysis of them does not give an answer as to which of them is more precise. Thus, in order to verify the correctness of the estimate, an additional line was created.