*3.1. Digital Signal Processing*

– The detection accuracies of both the vital signs of the subject and the distance to the subject are determined by how accurately the phase difference is measured in the FSK radar, and they are significantly affected by the *I*/*Q* imbalance and DC offset in the baseband. The *I*/*Q* imbalance in the amplitude and phase caused by the imperfections of the quadrature receiver can be measured by phase shifters and calibrated by the Gram–Schmidt procedure [21]. The phase shifter is used to generate a circle trajectory by varying the phases of the signal on the complex plane, and several other methods can be employed to implement this function. When the target is mechanically moved within a displacement similar to the half wavelength of the operating frequency, baseband signals can draw the circle trajectory on the complex plane as in the case of using the phase shifter [22]. However, an elliptical trajectory is generated owing to the change in the distance to the target, in contrast to the circle trajectory using phase shifters. The elliptical trajectory can be compensated by the data-based

quadrature imbalance compensation technique using the ellipse fitting method [23]. Figure 4a,b present the calibrated *I*/*Q* channels after the imbalance calibration.

**Figure 4.** In-phase/quadrature (I/Q) imbalance calibration on the complex plane using the reference distance and the known periodic movement: (**a**) At the frequency of 2.45 GHz; (**b**) at the frequency of 2.5 GHz.

DC offsets are generated by stationary clutters in the surroundings as well as the imperfection of the hardware configuration of the radar. The FSK radar receives the vector-sum signals reflected from all objects located in the antenna beamwidth [15]. The accuracy of the phase difference can decrease as the measurement distance increases because the DC offsets increase with the amount of clutters received on the radar. The DC offsets on the radar can be eliminated while preserving vital signs, which are located near DC in the frequency domain, using a dynamic DC offset compensation algorithm [24]. Figure 5 presents the baseband *I*/*Q* signals at each frequency measured by the proposed FSK radar on the complex plane. The trajectory at each frequency is a part of each circle on the complex plane, and the DC offset voltage is indicated by the center of the circle by the circle fitting method using the trajectory. The DC offset can be effectively calibrated by this procedure, which is known as the Pratt method, when the circle trajectory is obtained from the measured data [25].

The phase difference in each frequency is extracted by demodulating the calibrated signals. In the proposed FSK radar, the arc-sine demodulation and the complex signal demodulation (CSD) techniques are used for detecting the vital signs of the subject and the distance to the subject, respectively [26,27]. The arc-sine demodulation technique is generally used as a demodulation technique, but is not suitable for distance measurement with the FSK radar, because the measurement error can significantly increase with the decreasing accuracy of the DC offset when accurate circle fitting cannot be realized via either the random body movement or the curved chest wall of the human body. The CSD technique is an appropriate demodulation method in distance measurement of the FSK radar, because an accurate circle fitting process is not mandatory in the CSD, in contrast to the arc-sine demodulation technique [28]. Bandpass filters with cutoff frequencies ranging from 0.8 to 2 Hz and from 0.1 to 0.8 Hz are used after the demodulation process to extract the respiration and heartbeat signals, respectively, in these two techniques. Considering the characteristics of the vital signs, which vary irregularly, FFT with a sliding window of 30 s is performed every 10 s with a measurement time of 90 s. Figure 6 shows the signal processing procedure to obtain the vital signs from the raw data of the proposed radar.

**Figure 5.** Direct-current (DC) offset calibration on the complex plane: (**a**) Uncalibrated signals of each frequency in the baseband; (**b**) Calibrated signals of each frequency based on the Pratt method.

**Figure 6.** Signal processing procedure in the proposed vital-signs detector.
