# Short-Range Noncontact Sensors for Healthcare and Other Emerging Applications: A Review
## 3 Recent Technical Advancements
### Signal Distortion Analysis and Compensation  
Another challenge in Doppler radar sensing is the signal distortion while measuring subjects that are moving slowly. The signal pattern of the slow motions is often distorted. Homodyne receiver architecture with quadrature \(I/Q\) has been widely used for radar sensing, to avoid the null point problem and leverage the benefit of the range correlation effect [67]. However, due to circuit imperfections and clutter reflections from surrounding stationary objects, the homodyne receiver suffers from DC offset. AC coupling after mixer output is commonly used, probably the simplest way, to remove DC offset. The AC coupled baseband essentially has high pass characteristics, which results in signal distortion when the target motion has a very low frequency or a stationary moment [67]. For example, Figure 8 shows the distorted \(I/Q\) trajectory, which is due to AC coupling. As radar sensing is based on nonlinear phase modulation, the radar measured signal at baseband output can be expanded as Bessel function. For instance, a single tone sinusoidal movement \(x\left(t\right)=m\cdot sin\left(\omega t\right)\), where \(m\) is the amplitude and \(\omega\) is the movement frequency, can be expressed as:  
\[B\left(t\right)=\sum_{n=-\infty}^{n=\infty}J_{n}\left(\frac{4\pi m}{\lambda} \right)\cdot cos\left(n\omega t+\varphi\right) \tag{12}\]  
where \(\varphi\) is the total residual phase, \(\lambda\) is the wavelength, \(J_{n}\left(x\right)\) is the \(n\)th order Bessel function of the first kind. As can be seen in Equation (12), even for an ideal Doppler radar detecting a single-tone sinusoidal movement, harmonics will be created at the baseband output. If the target movement is slow or has stationary moment so that it falls into the stop-band of the active high-pass filter, the harmonics would be subject to different degrees of attenuation, owing to the slope characteristics of the high-pass filter. Therefore, signal distortion may happen due to the loss of the inherent spectrum  
Figure 8: Signal distortion happens due to AC coupling. The trajectory is not an ideal arch but shows a ribbon-like shape in the \(I/Q\) plane. Figure 7: Setup of radar sensing with random body movement using a radar-camera hybrid system. characteristics, which shows as a ribbon-like shape in the \(I/Q\) plane. As discussed in the second section, DC calibration needs to be carried out before \(I/Q\) signals can be combined to perform arctangent demodulation to recover the motion information in the phase. However, the distorted ribbon trajectory challenges the calibration algorithm to find the accurate DC offset values as well as the center of the arch [67]. Moreover, the signal distortion may impact the demodulation accuracy because the length of the \(I/Q\) trajectory is strictly related to the magnitude of vibration [58]. To eliminate the signal distortion, a straightforward method is to avoid using the AC coupled baseband structure and employ the DC coupled architecture for radar hardware [61; 66]. The DC coupled baseband is all-pass architecture, not like high-pass in AC coupling, so that all the harmonics from nonlinear phase modulation will undergo the same degree of attenuation or amplification, which ensures no signal distortion. To employ DC coupling, hardware modifications need to be made in order that the DC offset at mixer output will not saturate the following stages. Figure 9 shows the block diagram of the DC coupled Doppler radar system, as proposed in [61]. The radar system was designed with adaptive DC tuning stages including RF coarse-tuning and baseband fine-tuning. As we know, a major part of the DC offset is from direct coupling from the transmitter to receiver resulting in the mixer self-mixing.