# Short-Range Noncontact Sensors for Healthcare and Other Emerging Applications: A Review
## 2 Working Principle of CW Doppler Radar
### Demodulation Techniques  
As can been seen from Equation (3), the movement information \(x\left(t\right)\) is nonlinearly modulated inside the cosine function. Special techniques are required to recover the actual movement information from nonlinear phase modulation. * Small Angle Approximation  
In vital sign detection, the displacement of respiration and heartbeat is very small compared to the carrier wavelength. If \(\theta_{o}\) is an odd multiple of \(\pi/2\), the radar baseband output, as shown in Equation (3), can be linearly approximated as:  
\[B\left(t\right)\approx 4\pi x\left(t\right)/\lambda+\Delta\theta\left(t\right) \tag{4}\]  
This is the optimum detection case since the baseband output is linearly proportional to the time-varying motion displacement \(x\left(t\right)\). However, as \(\theta_{o}\) is a function of the distance to the target, there exist situations where \(\theta_{o}\) happen to be an even multiple of \(\pi/2\). In this case, the baseband output is no longer in proportion to \(x\left(t\right)\) and a \"null point\" occurs [65]. The \"null point\" issue not only means weak baseband output but also means inaccurate measurement results [55]. As the \"null point\" depends on \(\theta_{o}\), which is determined by the target distance, the issue happens in an orderly fashion every \(\pi/4\) from the radar. To overcome the null point issue, several effective approaches have been proposed. A frequency tuning technique was developed to adjust the \"null points\" distribution along the path away from radar [65]. It works by utilizing double sideband transmission in such a way that the null points from one sideband the optimum points from the other sideband can overlap each other, as shown below in Figure 2.  
Figure 2: Frequency tuning using double sideband transmission to overcome the null point issue in Doppler radar detection. \(\lambda_{1}\) is is the wavelength of one sideband and \(\lambda_{2}\) is that of the other. The frequency tuning technique needs hardware tuning to achieve good detection accuracy, which is not very convenient. Another approach to solve the null point issue was proposed in [8] using a quadrature receiver. The quadrature \(I/Q\) channels ensure that there is always one channel that is not in the null detection point, without any need to tune the hardware. Unlike the one in Figure 1 which is a single channel receiver, Figure 3 shows the bock diagram of the quadrature receiver with \(I/Q\) channels. Theoretically, the two \(I/Q\) channels at receiver baseband output are:  
\[B_{I}\left(t\right)=cos\left[\theta_{o}+4\pi x\left(t\right)/\lambda+\Delta \theta\left(t\right)\right] \tag{5}\]  
\[B_{Q}\left(t\right)=sin\left[\theta_{o}+4\pi x\left(t\right)/\lambda+\Delta \theta\left(t\right)\right] \tag{6}\]  
When \(\theta_{o}\) is an odd multiple of \(\pi/2\), the \(I\) channel signal will be at the optimum point while the \(Q\) channel will be at the null point. Similarly, when \(\theta_{o}\) is an even multiple of \(\pi/2\), the \(I\) channel will become a null point while the \(Q\) channel will be at the optimum point. Therefore, there is always one channel that is not at null point, ensuring good detection accuracy. In small angle approximation, the worst case is that \(\theta_{o}\) is an integral multiple of \(\pi/4\). In this case, none of the \(I/Q\) channels is at the optimum detection point. * Arctangent demodulation  
Small angle approximation is linear demodulation that only applies to small displacement. Arctangent demodulation is widely used as a nonlinear demodulation approach to precisely recover the full phase information from the nonlinear sinusoidal signal [55]. The actual \(I/Q\) signals are not the ideal sinusoidal signals as shown in Equations (5) and (6). In the practical radar system, the RF signal received at receiver front-end is amplified, filtered, converted directly to baseband \(I/Q\) signals, and then further boosted by the baseband amplifier.