# Motion Compensation for SAA FMCW Radar Based on Specific Switching Scheme
## 3 Simulation and Measurement  
Table 1 shows the numerical and experimental radar parameters. The Bartlett beamformer with 30 dB Chebyshev attenuation is used for DoA estimation in this paper.  
The simulation was conducted without noise to avoid uncertainty. Two point scatterings with identical amplitude were considered as moving targets. Their ranges, velocities, and azimuths were \(\{r_{1}\), \(v_{1}\), \(\theta_{1}\}\) = {30 m, \(-\)100 m/s, \(0^{\circ}\)} and \(\{r_{2}\), \(v_{2}\), \(\theta_{2}\}\) = {40 m, 50 m/s, \(-\)30\({}^{\circ}\)}. Figure 5 shows the phase characteristic curve of SAA with and without compensation. There was significant distortion in the uncompensated phase characteristic due to the motion-induced phase. In contrast, the compensated phase characteristic was in good agreement with the theoretical value, which represents the phase characteristic of the multichannel antenna array. Figure 6 shows the DoA estimation results with and without compensation. The DoA estimations without compensation were \(-\)15\({}^{\circ}\) and \(-\)21\({}^{\circ}\), respectively, deviating from the true angles of the targets. The fluctuation of the side lobes was caused by the nonlinear phase of the first four elements. With compensation, the DoA estimations were \(1^{\circ}\) and \(-\)31.5\({}^{\circ}\), which were close with the actual values. Meanwhile, the side-lobe level was reduced overall. The measurement error is caused by the high-order term of the beat signal. For the received signal of a single element, the phase error introduced by the high-order term can be neglected [16], so this paper and works of the authors of [3; 4] use the simplified signal model represented by Equation (3) for phase analysis. However, in this paper, the received signals of the first three units are used to extract the phase of motion introduction, so that the high-order term causes measurement error.  
\begin{table}
\begin{tabular}{l l l} \hline \hline  & **Simulation** & **Measurement** \\ \hline Operating frequency: \(f\) & 10 GHz & 10.25 GHz \\ Modulation period: \(T\) & 10 \(\upmu\)s & 0.1 ms \\ Sweep bandwidth: \(BW\) & 100 MHz & 100 MHz \\ Number of elements: \(N\) & 32 & 8 \\ Spacing: \(d_{r}\) & 0.5\(\lambda\) & 0.52\(\lambda\) \\ Type of element & Ideal element with cosine pattern & SIW slot array \\ \hline \hline \end{tabular}
\end{table}
Table 1: Radar parameters for simulation and measurement.  
Figure 5: Phase characteristic curve of SAA.  
Figure 7 shows the experimental scenario. The target is the unmanned aerial vehicle (UAV): DJI Phantom 3. It rose vertically at a speed of 3 m/s at a distance of 80 m from the radar. The antenna was placed parallel to the ground to avoid ground clutter. Figure 8 shows the phase characteristic curve of SAA with and without compensation. Without compensation, the phase characteristic had motion-induced distortion. With compensation, the phase characteristic was consistent with the theoretical value. Figure 9 shows the DoA estimation results with and without compensation. Without compensation, the DoA was incorrectly estimated at \(-4.3^{\circ}\). With compensation, the DoA was correctly estimated at \(0^{\circ}\). Note that the side-lobe level deteriorated due to the ambient noise. Additionally, we also used the TISV-based multiparameter estimation algorithm [8] to estimate DoA and obtained the real DoA of UAV at \(0^{\circ}\).