## 3 Feasible Study of Doppler Radar Antenna for Respiration
The results show that the system fidelity factors are very good at all distances and thus the designed slot-type antenna is suitable for Doppler radar applications. Figure 9: Fidelity factor: (**a**) antenna fidelity factor; (**b**) correlation between Tx pulse and Rx pulse at the distance of 11 mm; (**c**) system fidelity factor. Next, we plot the amplitude and phase of the signal returned from the phantom over a distance of 5 to 15 mm at 24.125 GHz in Figure 10. The phase of the returned signal is almost linear, and a displacement of 1 mm corresponds to a phase change of about 0.8 rad. The amplitude of the returned signal fluctuates, since the designed Doppler radar operates in near field. However, human body displacement is only related to the phase information and thus this non-flat amplitude response is not problematic for the Doppler radar. The I/Q data are obtained by mixing the returned signal with the transmitting signal. Figure 11 shows I/Q data corresponding to Figure 10. Although the I/Q trace is not a perfect circle (due to non-flat amplitude response), the phase response is almost linear to displacement, as expected. Until now, we analyze the returned signal from the human body in a stationary position. However, the displacement of the human body is not stationary when breathing and thus the time-varying returned signal must be investigated. In this work, to emulate the movement of the human body in breathing, it is assumed that the displacement of the human body changes linearly with time. In specific, the one exhale time is 2 s and the one inhale time is 2 s and thus respiration is periodic to 4 s, as shown in Figure 6:0 Note that the movement of the human body by actual breathing is complex with respect to time, but the purpose of this work is to investigate the phase-shifted returned signal and thus this linear assumption is appropriate for this work. Figure 6:1 Amplitude and phase of the signal returned from the phantom: (**a**) amplitude; (**b**) phase. Figure 13a shows the I/Q data for the time-varying returned signal and it is observed that the period of I/Q data is 4 s, same as respiration. Next, the converted displacement is calculated by arctangent demodulation. Ideally, the converted displacement of 0 mm (10 mm) corresponds to the distance between the antenna and the object of 5 mm (15 mm). According to Figure 13b, the converted displacement is 0 mm to 9 mm. Note that the difference between maximum and minimum converted displacement (9 mm) is not the same as human body movement (10 mm) since the abdomen of the phantom is not flat and the human body is not perfectly electric conductor (PEC). We also calculate theoretically the converted displacement of a flat PEC in far field. As shown in the Figure 13, the converted displacement in this case is exactly the same as the movement of the human body. It should be noted that the respiration rate is successfully obtained by the near-field Doppler radar, albeit with little discrepancy of displacement. Numerical experiments show that the designed Doppler radar antenna can sense human respiration in near field in electromagnetic aspects. Figure 6:2 I/Q plot. Figure 6:3 Assumed respiration versus time.