## 3 Experimental Setup
### Phase Performance Test Using Loopback Waveguide  
As described in Section 2, the accuracy and precision of radar sensors are crucial for detecting small displacements. A previous study evaluating the phase performance of FMCW radar employed a measurement method in which radar targets were positioned at arbitrary distances, and phase fluctuations in the IF signal from the target echo received by the radar sensor were analyzed [18]. However, to accurately measure extremely small phase deviations, which are affected by small displacements of the target, both the radar and the target must be securely fixed. Furthermore, completely eliminating noise caused by spatial and environmental vibrations is challenging, as such noise often affects the measurement system. For instance, a previous study [14] observed a 100 Hz noise originating from the measurement equipment.  
Traditionally, the phase characteristics have been measured or calibrated in free space (i.e., over-the-air), where a radar MMIC transmits an FMCW waveform and receives the echo from a fixed target (e.g., a corner reflector). For general-purpose ranging applications, such as sensors for autonomous driving, this is not a critical issue. However, for detecting very small displacements on the micrometer scale, it becomes a significant challenge. The target must remain strictly rigid relative to the MMIC, and isolating the setup from any environmental vibrations is also challenging.  
In this study, we mitigated environmental influences by connecting the transmission and receiving ports with a waveguide, as shown in Figure 6. This waveguide setup simplified the experimental configuration by eliminating the need for vibration-isolation tables to stabilize the radar and target, as well as an anechoic chamber to remove unintended  
\begin{table}
\begin{tabular}{c c} \hline RF frequency (OBW) & 77.1–80.9 GHz (3.8 GHz) \\ \hline Radar type & FMCW \\ \hline Transmitter & 1-ch \\ \hline Receiver & 1-ch \\ \hline Detectable range & 5 m (max.) \\ \hline Field of view & \(\pm 3^{\circ}\) \\ \hline Interface and power & 100 BASE-T (UDP) + PoE \\ \hline \end{tabular}
\end{table}
Table 1: Millimeter-wave FMCW radar sensor system specification.  
Figure 5: Millimeter-wave FMCW radar sensor system. (**a**) System hardware image. (**b**) Measurement software image.  
echoes, thereby facilitating easier measurements. The radar sensor used in this experiment was the miRadar CbM, with the only modification being the replacement of the antenna output and input with a waveguide, while all other configurations remained unchanged.  
Measurements were performed using the FMCW radar profile outlined in Table 2. In this experiment, two pulse repetition time (PRT) profiles were evaluated. Each chirp consisted of 256 ADC samples, and range FFTs were computed with 4096 samples, achieved by zero-padding the original 256 samples to 4096. A single chirp burst comprised 2048 chirps. Measurements were conducted over a 30 s duration, corresponding to approximately 60 bursts per iteration. The experiment was repeated three times, resulting in a total of 583,500 ADC samples collected for analysis under each of the two sensor settings, as summarized in Table 3.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Items** & **Unit** & **Value** \\ \hline RF frequency & GHz & 77.1–80.9 \\ \hline RF occupied bandwidth & MHz & 3800 \\ \hline RF center frequency & GHz & 79.0 \\ \hline FMCW up/down-chirp time & & \\ \hline Long PRT setting & \(\upmu\)s & 200/200 \\ \hline Short PRT setting & \(\upmu\)s & 200/12.5 \\ \hline Chirp count in burst & & 2048 \\ \hline ADC sample in chirp & samples & 256 \\ \hline ADC Fs & MHz & 5 \\ \hline Range FFT point after zero padding & points & 4096 \\ \hline FFT windows & & Hann \\ \hline \hline \end{tabular}
\end{table}
Table 2: FMCW parameters for measurement test.  
Figure 6: Loopback waveguide test setup.