## 1 Introduction  
Millimeter-wave FMCW radar is emerging as an effective technology for sensing applications, particularly in the field of small displacement measurement, such as respiration detection, vibration detection, or bridge displacement detection [1]. With advancements in integrated semiconductor technology, the performance of millimeter-wave radar sensors has significantly improved recently, enabling their application in critical machine vibration sensing, where detecting extremely small displacements is crucial. Machine vibration sensing, commonly known as condition-based monitoring (CbM), has gained popularity as a proactive maintenance strategy [2]. Traditionally, accelerometers have been used to measure small vibrations [3, 4]. However, as contact-based sensors, accelerometers present certain challenges. For instance, the mass of the sensor itself may alter the vibration characteristics of the target, making it less suitable for specific applications. In such cases, contactless vibration sensing techniques, such as millimeter-wave radar, offer a viable alternative. In the context of machine vibrations related to deterioration, the P-F (Potential Failure-Functional Failure) curve, shown in Figure 1, is widely discussed in the CbM engineering field [5]. The P-F curve tracks machine deterioration through various indicators, including vibration, over the operational period. Detecting vibrations in the early stages of deterioration is crucial, as characteristic changes often emerge during this period [6]. Early detection is essential for timely maintenance. For example, bearing fault monitoring requires detecting high-frequency vibrations, as these serve as critical diagnostic features. A motor rotating at 880 rpm can generate vibrations exceeding 10 kHz in the frequency spectrum [7], which must be detected by sensors. For sinuous vibrations, the displacement (D [mm]) is determined by acceleration (A [g]) and vibration frequency (f [Hz]), as expressed in Equation (1). As the equation indicates, higher vibration frequencies correspond to smaller displacements, necessitating sensor systems capable of detecting extremely small displacement ranges. \[D=\frac{A\times 2\times 10^{3}\times 9.8}{(2\pi f)^{2}} \tag{1}\]  
Among contactless displacement sensing techniques, optical laser sensors are one of the feasible options for precise displacement measurement. Several studies have employed optical laser sensors to measure small displacements. To achieve extreme sensor accuracy, a photonic FMCW radar architecture has been proposed, in which the chirped signal generator and dechirp modulation are implemented using a photonic circuit, while the RF frontend is based on a microwave and millimeter-wave transceiver circuit [8]. Since the photonic circuit offers lower phase noise, higher chirp linearity, and significantly wider bandwidth [9], ultra-high accuracy can be achieved in small displacement measurements, reaching the sub-micron or nanometer range. However, this system requires more complex components and a much higher-speed analog frontend circuit (e.g., a high-speed A/D converter). Furthermore, in condition-based monitoring (CbM) of machines, vibration amplitudes typically range from millimeters to micrometers, making RF-based FMCW radar sufficiently accurate while allowing for a simplified circuit, such as a single integrated  
Figure 1: P-F curve on machine CbM. MMIC. Additionally, RF frontends can operate reliably in harsh and dusty environments, and RF-based circuits offer greater stability under such conditions. As for studies on RF radar sensor accuracy, several studies have validated the accuracy and precision of radar sensors for small vibration or displacement measurements using controlled experimental setups. For instance, mechanical linear sliders or actuators have been used to provide well-defined displacements while radar sensors detect the target's position [10; 11; 12].