## 3 Results of the Simulation  
In order to verify the proposed method simulations were carried out. Two radar scenes were considered in which one or two targets crossed the baseline. The first of the analyzed cases covers the situation presented in Figure 4.  
The continuous wave (CW) transmitter working with the harmonic signal using the carrier frequency \(f_{c}=900\) MHz is 1500 m away from the target trajectory (at the closest point) which, in turn, is 500 m from the receiver. The point target (dimension is neglected) moves with the velocity \(v=10\frac{\text{m}}{\text{s}}\) perpendicularly to the baseline. The TF distribution of the signal energy in the form of a spectrogram is presented in Figure 5. The signal was merged with the white Gaussian noise, for which SNR = 30 dB. This was due to the fact that in the further part of the article covering the real-life signal analysis, waveforms characterized by SNR > 0 dB are considered, and on such conditions the simulations were focused. STFT parameters during the simulations are as follows:  
* N = 1024--amount of points in FFT analysis,
* W = 350--Blackman-Harris window length (in samples),
* H = 1--hop-size (in samples),
* \(f_{\text{s}}=1\) kHz--sampling rate. Figure 4: Radar scene for the 1 st simulation case. Figure 5: Spectrogram of the 1 st simulation case. The spectrogram shows a characteristic curve, typical for a bistatic geometry utilizing the forward scattering phenomenon. The received signal is defined only by the Doppler frequency (due to the fact that the transmitter works with the CW) expressed by Equation (1), the consequence of which is the frequency modulation of the wave. The Doppler rate, in this case, can be considered as the CR described in the previous section and the physical interpretation of both is the same. Thus, the proposed CR estimation methods were employed to verify their usability in such a context. A calculated accelerogram presenting instantaneous CR for each point in the TF plane is depicted in Figure 6.  
By analyzing this distribution, it can be noted that during the crossing of the baseline the target provided a Doppler rate of \(\sim\)\(-1.5\frac{\overline{m}}{\mathrm{s}}\). Additionally, the Doppler rate can be determined for each point for the observation time. This is an advantage of the proposed approach due to the fact that the estimation process automatically provides a set of information about the movement parameters of the target, allowing an unknown trajectory or velocity to be assessed. In comparison to the methods presented in the literature, unique movement signatures are provided by this approach, which allows additional information about the object to be distinguished. For the purpose of validation, the theoretical Doppler rate, as the first order derivative of the \(f_{d}\) given by Equation (1), was compared with the estimated value. This value was read in the maximum point of the spectrogram in each time frame. Because of the amplitude modulation, the estimated value in the minimum of the envelope is distorted, thus additionally results for the constant signal amplitude were plotted. A comparison of the true value and estimated CR for both cases (amplitude modulation and no amplitude modulation) is presented in Figure 7.  
As can be noticed, the estimated Doppler rate (CR) for the constant amplitude signal is similar to the theoretical value. In Figure 7 the blue line overlapped completely with the yellow line, which confirms the convergence of the results of the estimation with the theory. However, because of the fact that the signal has an amplitude locally near or equal to zero, the estimation process returns  
Figure 6: Accelerogram of the 1 st simulation case. Figure 7: Comparison of the true Doppler rate and estimated CR for two amplitude cases. distorted results (see the red line in Figure 7). This is caused by the character of the signal, not by the error of the estimation, which can be seen in the case where the amplitude is constant.