## 3 Feasible Study of Doppler Radar Antenna for Respiration  
In general, quadrature receiver systems are widely used in Doppler radar to detect vital signs, because the performance of single-channel receivers is limited [21]. Two orthogonal output signals of the quadrature receiver system can measure relative phase information. The two signals are represented as the in-phase (I) channel and the quadrature-phase (Q) channel. The magnitude and phase of the I-and Q-channel signals can be displayed via the I/Q plot. Note that the time-varying phase shift is linearly proportional to the displacement caused by human body surface movement. Displacement can be obtained by applying arctangent demodulation to the I and Q signals ratio [22]. Note that we assume that RF and baseband systems are perfect since we focus on the feasibility study of a near-field Doppler radar in terms of antennas and propagation. As a proof of concept, in this work, we consider human respiration. Toward this purpose, let us assume that the Doppler radar antenna is embedded in the ID badge holder. The designed Doppler radar antenna is placed in front of the abdomen of Duke phantom in Simalife. The dielectric properties of human tissues can be found in [23]. The distance between the Doppler radar antenna and the human body is changed from 5 to 15 mm because respiration is accompanied by movement of the upper body surface and its movement is usually about 10 mm [24, 25]. Figure 7 shows a simulation setup of the designed Doppler radar antenna with Duke phantom in Simalife. The pulse signal is excited to analyze the frequency response of the designed Doppler radar with the Duke phantom. The total time  
Figure 5: Simulated and measured S-parameters. Figure 6: Simulated and measured radiation patterns at 24.125 GHz. s spent on simulation is about 5 h by using a DELL T7910 workstation with an NVIDA Tesla K40 GPU accelerator. Figure 8 shows the simulated reflection coefficients. It is observed that that the designed Doppler radar antenna placed at a distance of 5 mm has a reflection coefficient of \(-\)9.2 dB and the rest is less than \(-\)10 dB at 24.125 GHz. In order to accurately analyze the phase information by the Doppler effect, the direct signal from the transmitter must be excluded from the signal received at the receiver. Note that the direct signals can be subtracted from the received signals by the calibration in the actual Doppler radar system. Before proceeding with the Doppler performance, it is worthy to investigate the antenna fidelity factor and the system fidelity factor [26,27]. The fidelity factors can be obtained as follows:  
\[T_{N}(t)=\frac{T(t)}{\left[\int_{-\infty}^{\infty}\left|T(t)\right|^{2}dt \right]^{1/2}} \tag{1}\]  
\[R_{N}(t)=\frac{R(t)}{\left[\int_{-\infty}^{\infty}\left|R(t)\right|^{2}dt \right]^{1/2}} \tag{2}\]  
\[F=\max\int_{-\infty}^{\infty}T_{N}(t)R_{N}(t+\tau)dt \tag{3}\]  
The \(T_{N}(t)\) and \(R_{N}(t)\) are the normalized pulses to compare the shape between the two pulses. The fidelity factor F is the maximum value of the correlation between the normalized pulses. The antenna  
Figure 8: Simulated reflection coefficient of the designed Doppler radar antenna with Duke phantom. Figure 7: Simulation setup of the designed Doppler radar antenna with Duke phantom in Sim4 life. fidelity factor is obtained by calculating with the cross-correlation of the radiated E- field and the input signal. As shown in Figure 9a, the good antenna fidelity factor is observed for all angles. The system-fidelity factor is calculated by the cross-correlation between the transmitted pulse and the received pulse. Figure 9b shows the correlation between the transmitted pulse signal and the received pulse signal at the distance of 11 mm. As shown in the Figure 9b, the maximum value of the correlation is almost one and thus the very high system fidelity is expected. Figure 9c shows the system fidelity versus the distance.