## 4 Real-Life Signal Analysis
### Target Doppler Rate Estimation  
The obtained data were examined with one of the analyzed estimators in order to verify whether the proposed tool is effective in analyzing real-life signals from PFSR. The recorded waveform was processed using the cross-correlation of the reference and reflected from the target signal. As with the simulation, the object's dimensions can be neglected. This is due to the fact that the available GSM signal bandwidth is \(\sim\)200 kHz, giving a bistatic range resolution of \(\sim\)1500 m. Four cases were considered during which the object examined crossed the baseline between the transmitter and the receiver. During the real-life signal analysis, the following parameters were employed:  
* N = 4096--amount of points in FFT analysis,
* W = 1300--Blackman-Harris window length (in samples),
* H = 1--hop-size (in samples),
* \(f_{\mathrm{s}}=1\) kHz--sampling rate (after decimation). The spectrograms of the analyzed cases are presented in Figure 13.  
Apart from the signal that is caused by the analyzed phenomenon, that is the signal with frequency modulation, additional components are visible on the spectrograms. They arise for several reasons. The first of these is the presence of a significant number of stationary objects in the radar beam. A strong echo from the surface of the earth, trees or buildings creates a strong permanent component at \(f\approx 0\) (Hz), the impact of which can be reduced, as described in Reference [25], for example. The second effect is visible as numerous components with a much higher modulation coefficient. Figure 12: Measurement geometry diagram. T\({}_{\mathrm{x}}\)—GSM transmitter of opportunity, R\({}_{\mathrm{var}}\)—the reference antenna, R\({}_{\mathrm{ss}}\)—the surveillance antenna. Figure 13: Spectrograms of all considered cases. However, these are only visible for a short time. This phenomenon, in turn, arises as a result of the presence of side lobes, which cause the receiving of a signal reflected from a moving object as well as from other objects in space. In addition, there was a highway near the measuring scene, and the cars moving on it are visible in the spectrograms. However, it is possible to distinguish a significant component, which is the echo coming from the analyzed object. For such obtained data, accelerograms, that is a local (instantaneous) CR distribution on the TF plane, were determined. The results for the analyzed cases are shown in Figure 14.  
As can be noticed, similar results were obtained for four measurements which confirmed the repeatability of the results. Although the most significant portion of the signal energy is at the moment of changing the frequency sign (around 0 Hz), it is possible, as in the case of the simulation, to determine the CR for the entire recorded segment. Such information can be extremely useful when determining the trajectory or kinematic parameters of the target. In the case of the previously mentioned solutions [9; 10; 11; 12; 13; 14; 15], only the Doppler rate was determined at the moment when the baseline is crossed. The proposed method therefore extends the spectrum of possibilities, allowing more information to be extracted. For all cases the estimated CR value at the time of \(t_{0}\) is CR\(\in[-0.3,-0.5]\) (Hz/s), which agrees with the actual value. For example in the first case shown in Figures 12(a) and 13(a), it can be observed that the frequency is reduced by less than 30 Hz within 60 s, which gives an estimated value. In fact, it is difficult to reproduce the vehicle's motion perfectly a few times, which resulted in temporary changes in the signal. It can be observed by comparing the 1 st and 2 nd cases (corresponding spectrograms Figure 12(a),b and accelerograms Figure 13(a),b) with 3 rd and 4 th (corresponding spectrograms Figure 12(c),d and accelerograms Figure 13(c),d). For the first two cases the car maintains a constant velocity, while for the other two cases the velocity is not retained in the second phase of the move.