## 1 Introduction
However, in such cases, measurement accuracy depends on the precision of the mechanical system, which includes components such as motors, metal arms, and reflectors in a complex structure. Consequently, scale errors may arise, which are difficult to isolate. To mitigate such scale errors, some studies employed optical laser displacement sensors as reference sensors for radar measurements [13]. When two sensors (i.e., radar and laser sensor) are used, precise alignment between the sensors and target (e.g., a reflector) is critical, as even a slight angular misalignment can introduce micrometer-scale errors. To resolve alignment issues, an experimental apparatus was developed in which both sensors were linearly aligned on a mechanical linear slider system to minimize misalignment caused by angular offsets [14]. Additionally, the setup was built on a solid granite slab to isolate it from environmental influences. This configuration achieved an accuracy of \(\pm\)4.5 \(\upmu\)m while other limitations, such as thermal expansion and mechanical alignment errors, were also addressed. Furthermore, another study controlled environmental factors such as air temperature, relative humidity, air pressure, and carbon dioxide concentration to improve radar measurement accuracy, achieving \(\pm\)0.1 \(\upmu\)m accuracy, which reached the limit of reference laser sensor accuracy of \(\pm\)0.4 \(\upmu\)m [15]. Further improvements in measurement accuracy require an alternative setup beyond the limitations of the reference laser sensor. Moreover, previous studies did not fully examine MMIC phase accuracy and precision due to circuit characteristics. In FMCW radar-based vibration monitoring, the phase characteristics of beat signals between consecutive FMCW chirps are directly linked to displacement accuracy and precision [16]. Therefore, phase accuracy and precision are critical parameters for radar sensors in detecting small displacements. This study aims to address the gap in precise micrometer-scale displacement measurement using FMCW radar through controlled experiments with enhanced methodologies. Unlike previous studies, this research employs a novel loopback waveguide testing method to provide a stable radar target free from environmental influences. Two experiments were conducted to evaluate the radar system's phase accuracy and precision. The first experiment focused on fundamental phase measurements using a loopback waveguide to evaluate the inherent phase accuracy and precision of the MMIC, independent of environmental factors. The second experiment measured actual displacements in free space using an industrial vibration shaker, which enables precise displacement control and is widely used in the development of commercial industrial products. The methodologies and findings presented in this paper contribute to the advancement of next-generation sensing technologies, establishing a new standard for precision in vibration monitoring using FMCW radar. This paper is organized as follows: Section 2 introduces the radar signal processing algorithm for machine vibration and small displacement sensing. Section 3 details the experimental setup for phase accuracy and precision measurements. Section 4 presents the results of the two experiments, followed by a discussion in Section 5. Finally, Section 6 concludes this paper.