# Short-Range Noncontact Sensors for Healthcare and Other Emerging Applications: A Review
## 2 Working Principle of CW Doppler Radar
### Theory  
The fundamental mechanism using single-tone CW radar for noncontact vital sign detection is shown in Figure 1. An unmodulated RF signal \(T(t)\) is generated by the waveform generator and transmitted via Tx antenna to the subject with a nominal distance of \(d_{o}\) away:  
\[T\left(t\right)=A_{T}\cdot cos\left(2\pi ft+\theta\left(t\right)\right) \tag{1}\]  
where \(f\) is the carrier frequency, \(A_{T}\) is the power amplitude, and \(\theta\left(t\right)\) is the phase noise from the waveform generator. The subject's chest wall movement, which is induced by the respiration and heartbeat, modulates the RF signal and reflects part of the signal back to the radar. The signal received at radar Rx antenna is [8]:  
\[R\left(t\right)\approx A_{R}\cdot cos\left[2\pi ft-4\pi d_{o}/\lambda-4\pi x \left(t\right)/\lambda+\theta\left(t-2d_{o}/c\right)\right], \tag{2}\]  
where \(A_{R}\) is the received power, \(\lambda\) is the carrier wavelength, \(c\) is the speed of light in free space, \(x\left(t\right)\) is the chest wall movement including respiration and heartbeat, and \(\theta\left(t-2d_{o}/c\right)\) is the phase noise with a delay of \(2d_{o}/c\). As shown in Figure 1, the radar transceiver is a coherent structure that transmitter and receiver share the same signal source. That said, the same Tx signal is used as local oscillator (LO) signal to down-convert \(R\left(t\right)\) to baseband \(B\left(t\right)\):  
\[B\left(t\right)=cos\left[\theta_{o}+4\pi x\left(t\right)/\lambda+\Delta\theta \left(t\right)\right] \tag{3}\]  
where \(\theta_{o}=4\pi d_{o}/\lambda+\sigma\) is the summation of phase shift from the nominal distance \(d_{o}\) and at the reflection surface, \(\Delta\theta\left(t\right)=\theta\left(t\right)-\theta\left(t-2d_{o}/c\right)\) is the residual phase noise. Since both Tx and LO signals come from the same signal source, and they have the same phase noise characteristics [8]. In short range applications, the phase noise of the backscattered signal received by radar is strongly correlated with that of the LO signal. Therefore, phase noise from backscattering can be cancelled out by mixing with the LO signal so that the residual phase \(\Delta\theta\left(t\right)\) in Equation (3) is usually negligible [34]. The range correlation effect makes it possible to cross over phase noise boundary to design high-sensitivity Doppler radar [8]. Due to the coherent nature and the fact that no spectral information is needed, a free running voltage controlled oscillator (VCO) is sufficient for Doppler radar. The waveform generator used in CW Doppler radar does not have to be circuitry based on strict frequency synthesis, such as phase-locked loop (PLL) or direct digital synthesizer (DDS), which dramatically reduces the complexity of the radar hardware system. The receiver structure shown in Figure 1 is direct-conversion homodyne. However, it is imperative to point out that other transceiver architectures are also being used in Doppler radar [24; 49; 50; 51] and each of them has both advantages and disadvantages. For example, the zero-IF homodyne architecture  
Figure 1: Simplified block diagram of CW/FMCW radar sensor and the mechanism of noncontact vital sign detection. WG: waveform generator. allows high level of integration but it has strong dc offset at mixer output [61]; digital IF receiver makes it possible to completely eliminate \(I/Q\) mismatch at the cost of higher speed analog-to-digital converter (ADC) [24]. The selection of radar architecture is driven by specific applications and should be pondered over both hardware complexity and system performance specifications. Besides the radar architecture, the choice of carrier frequency is also of vital importance. People may infer from Equation (3) that the phase modulation is in inverse proportion to the carrier wavelength, so that the higher the frequency and better the detection sensitivity.