## 3 Radar Micro-Doppler Analysis of Vibrating Structures
### Radar Micro-Doppler from Idling Vehicles  
Radar micro-Doppler refers to the small, time-varying frequency shifts detected by radar as it interacts with a moving object or component. Radar micro-Doppler can capture vibrations from various parts of an idling car, such as the front, back, and left and right doors. These vibrations are a result of the engine, suspension, and the vehicle structure as they transmit forces from the running engine through the chassis, affecting different regions of the vehicle. The specific relationship between radar micro-Doppler and these vibrations depends on the components of the vehicle that are vibrating and how these vibrations  
Figure 1: Basic mechanical state space model of a vehicle.  
are transmitted through the car's structure. For a stationary vehicle (such as an idling car), radar can typically detect vibrations caused by the engine's operation, chassis flexing, suspension dynamics, and passenger and load shifts. The micro-Doppler spectrum reflects these vibrations by showing periodic shifts in frequency corresponding to the oscillations or small movements of the vehicle's parts.  
At the front of the vehicle, the radar micro-Doppler signature will capture the vibrations related to engine-induced vibrations: The front engine block and related components (like the alternator, crankshaft, and pistons) produce cyclic low-frequency vibrations that propagate throughout the vehicle. The front suspension system (e.g., coil springs or shock absorbers) also causes low-frequency vibrations that may be detected, especially when the engine is running. Radar micro-Doppler signature characteristics will show low-frequency cyclic components from the engine as well as high-frequency oscillations resulting from bodywork panel vibration modes.  
At the rear of the vehicle, the radar micro-Doppler spectrum will reflect vibrations from the rear suspension system and the drivetrain. The rear suspension transmits vibrations caused by the engine's power being transferred through the vehicle's chassis, which can cause flexing and oscillations, especially if the vehicle is heavily loaded in the rear. In vehicles with rear-wheel drive, the drivetrain (including axles and differential) can generate low-frequency vibrations that are transmitted through the vehicle's frame to the rear. Radar micro-Doppler signatures will be characterized by low-frequency vibrations from the drivetrain or rear axle and high-frequency components from the engine.  
Radar can also detect the vibrations transmitted through the chassis, including the left and right doors of the vehicle. These vibrations can be caused by chassis flex and passenger-induced vibrations. The vehicle's frame and bodywork (including the left and right doors) transmit vibrations from the engine and suspension systems. These vibrations are typically of low frequency, spreading throughout the vehicle's body and detectable at various positions. The presence of passengers in the front or rear seats will affect the distribution of weight and load, which can alter the vibration characteristics in the vehicle. This can cause additional, often higher-frequency, vibrations in the doors and surrounding areas. Radar micro-Doppler signature characteristics therefore show low-frequency chassis flexing signals and higher-frequency passenger-related vibrations, which can be detected in the doors and the sides of the vehicle.  
Using a 94 GHz radar, the vibration frequency spectrum of a truck was measured at the front bumper and on the roof with the engine idling. The peak frequency for both measurements was close to 32 Hz with a second harmonic at 64 Hz at a level of 20 dB lower [24].