*3.2. Implemented FSK Radar Module*

For vital-signs and distance measurement, the frequencies of 2.45 and 2.5 GHz are used in the proposed FSK radar, which operates in the 2.45 GHz ISM band. The maximum unambiguous range of the FSK radar is 3 m, which is determined by the frequency difference of 50 MHz. The radar front-end circuit and two patch antennas are implemented on an FR4 printed circuit board (PCB) with a thickness of 1 mm, as shown in Figure 7. The FSK signals with a frequency spacing of 50 MHz and an output power of 15 dBm are generated by an N5183B signal generator manufactured by Keysight Technologies Inc. The FSK operation is realized by using the internal function of the signal generator. The generated signals are divided by a Wilkinson power divider into the reference and transmitting signals. Quadrature signals are generated by a hybrid power divider with a phase difference of 90 ◦ between two outputs. The signal of each frequency is radiated toward the subject and received by the separated patch antennas with a directivity of 5.9 dBi. The received signal is amplified using a low-noise amplifier (LNA) with a power gain of 13.7 dB and noise figure of 5.3 dB. In-phase and quadrature signals in the baseband are generated by mixing the received signals with the reference and filtering them with low pass filters having a cut-off frequency of 80 MHz.

**Figure 7.** Implemented radar module with two patch antennas on an FR4 printed circuit board (PCB).

#### **4. Measurement Results and Discussions**

Figure 8 shows the measurement setup for obtaining both the vital signs and the distance to the subject. The switching time of the two CW frequencies was set as 0.1 s in the generator. The maximum unambiguity range was determined to be 3 m by the frequency space of 50 MHz between the two operating frequencies. By using two low-noise preamplifiers manufactured by Standford Research Systems Inc., the in-phase and quadrature signals from the module were amplified with a voltage gain of 17 dB. Signal conditioning and processing in the digital domain were implemented using NI LabVIEW and MATLAB on a personal computer after quadrature signals were simultaneously obtained with a sampling rate of 1 k samples per second from the DAQ board of NI USB-6009. A range finder (Bosch, Gerlingen, Germany) and a three-electrodes ECG sensor (Vernier Software and Technology, Beaverton, OR, USA.), were used as the reference sensors to measure the accuracies of the distance and vital signs, respectively, of the proposed FSK radar. In the surroundings, there were only fixed clutters; the moving objects (except for the subject) were limited in number. The distance to the subject was measured from 1 to 2.4 m at the intervals of 15 cm, and the vital signs were measured as respiration and

heartbeat per minute for 90 s at each distance. The detection range for the demonstration is determined by considering both the nearfield effect on the radar and the maximum unambiguity range of the FSK radar. The subjects were three males in their twenties who did not suffer from cardiac diseases. They did not consume caffeine, alcohol, or nicotine, which may affect the vital signs, before measurement of the vital signs. Detailed information of the subjects is presented in Table 1.

**Figure 8.** Measurement setup for detecting the distance and vital signs using the proposed FSK radar.


**Table 1.** Information relevant to the subjects.

The single-frequency in-phase signals obtained after the discrimination using the proposed envelope detection method and the signals digitally filtered by the passband from 0.1 to 0.8 Hz are shown in Figure 9. According to the operation of the CW Doppler radar, the phase information for the movement generated by the vital signs is clearly reflected by the raw data. As shown in Figure 9, the respiration is dominant in the raw data because the data are similar to the signal filtered by only the frequency band of the respiration.

The absolute distances measured by using the proposed FSK radar are shown in Figure 10. The initial phase differences in the radar front-end are calibrated with measurement results for the reference distance of 1 m, and the relative distance obtained by the radar is modified to an absolute distance after the calibration. The accuracy of the distance measurement is expressed by the root-mean-square error (*RMSE*) relative to the distance measured by the reference sensor. The *RMSE* in the distance measurement can be expressed as

$$RMSE = \sqrt{\frac{1}{n} \sum\_{i=1}^{n} \left(d\_i - rf\_i\right)^2} \tag{10}$$

where *n* is the number of subjects, *d<sup>i</sup>* is the absolute distance measured using the proposed radar, and *rf<sup>i</sup>* is the reference distance measured using the laser-based range finder. The *RMSE* is ≤0.1 m at a distance of ≤ 1.7 m, corresponding to ≤ 6.6% of the measurement distance. The accuracy is increased with an *RMSE* of 0.3 m at a distance of 1.8–2.4 m, which corresponds to 14.3% or less of the measurement distance. The increase in the measured distance error at the distances of >1.6 m is explained as follows: The phase difference of the FSK radar is determined by the vector sum of the overall signal received through the antenna. When the measurement distance increases, more information resulting from clutters is included in the received signal by the beamwidth of the receiving antenna, and it has an effect on the increase of the measurement error in the phase detection. Additionally, the SNR of the radar decreases as the measurement distance increases. The FSK radar measures the distance using the phase difference obtained from the vector sum of the overall reflected signals, including those from the surface and inside of the human body, while the reference sensor measures the absolute distance to the skin surface of the subject. The uncertainty of the phase difference obtained by the vector sum in the FSK radar results in an intrinsic error in the distance measurement for the human body. Additionally, the switching time of 0.1 s in the FSK radar is sufficiently short to neglect the changes in the vital signs, which occur less than 2 times per second. Considering the uncertainty of the phase difference and the short switching time, the error in the distance measurement of the radar is attributed to the detection accuracy of the phase in the radar. If the phase error of the FSK radar, including the uncertainty, is 5 ◦ in the measurement, the *RMSE* is 0.04 m for the frequency spacing. The distance measurement shows that vital signs obtained for each frequency at different times have a correlation at a similar level of the phase error in the measured distance.

**Figure 9.** Raw and filtered waveforms measured at a distance of 1 m using the proposed radar.

Vital-signs detection using the proposed radar are performed by varying the subjects' position by 1 to 2.4 m at intervals of 0.15 m for a measurement time of 90 s. The respiration rate and heartbeat measured by the proposed radar are presented in the spectrum. The respiration rate per minute shown in Figure 11 for one subject is clearly measured at 12, but the heartbeat per minute (BPM) is not easily obtained in Figure 11 because of the low SNR of the heartbeat signal and the low resolution in the dynamic range to represent the respiration signal. The heartbeat signal may be measured by using high-pass filtering to reduce the respiration signal in the baseband pre-amplifier block, but this method has a limitation in increasing the measurement accuracy because it does not improve the heartbeat SNR itself. Figure 12 shows the frequency spectra of the heartbeat signals measured at a distance of 1 m using the proposed FSK radar. The raw data of the measured heartbeat show that signals due to the respiration and its harmonics might have been generated mostly around the frequency band of the heartbeat signal in the single CW radar operation. It is difficult to identify the frequency peak representing the heartbeat, because there are several peaks in the spectrum obtained at each operating frequency. The noise fluctuation level obtained at each frequency is approximately a quarter of the maximum frequency. However, the cross-correlated signals obtained using the proposed FSK radar exhibit the same frequency peak as those obtained using the reference ECG sensor and both higher SNR and lower noise level compared to those obtained at each frequency. The number of data points in

Figure 10 (based on a comparison between the single frequency and cross-correlated signals) indicates that the frequency resolution can be increased by the cross-correlation.

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**Figure 10.** Measured distance and the root-mean-square error (*RMSE*) in the measurement using the proposed FSK radar with a frequency spacing of 50 MHz and switching time of 0.1 s: (**a**) Subject A; (**b**) Subject B; (**c**) Subject C; (**d**) averaged data.

sed radar are performed by varying the subjects' position

**Figure 11.** Spectra of the vital signals measured at a distance of 1 m using the proposed FSK radar.

**Figure 12.** Spectra of the heartbeat signals measured by the proposed FSK radar at each operating frequency and with cross-correlation. The frequency peak of the cross-correlated signals is almost identical to that of the reference electrocardiogram (ECG) signals.

The measurement accuracy for a subject wearing a contact-type reference ECG sensor is evaluated using the *RMSE* and the SD. The *RMSE* in the heartbeat measurement can be expressed as

$$RMSE = \sqrt{\frac{1}{m} \sum\_{i=1}^{m} \left( h\_i - ECG\_i \right)^2} \tag{11}$$

 = √ ∑(ℎ − ) 2 =1 where *m* is the number of windows, *h<sup>i</sup>* is the heartbeat (BPM) measured using the proposed radar, and *ECG<sup>i</sup>* is the reference BPM measured using the commercialized ECG sensor. The BPM is measured for three subjects using the proposed FSK radar. The heartbeat measurement results in Figure 13 are the *RMSEs* and SDs of the subjects depending on the measurement distance. The results of the proposed

FSK radar typically exhibit a smaller *RMSE* and SD than those measured at individual operating frequencies, i.e., those for the CW Doppler radar. When the measurement distance is increased, both the *RMSE* and SD of the heartbeat measurement increase corresponding to the reduction in the SNR. At a distance of 2.05 m, the accuracy obtained from the cross-correlated signals is similar to that obtained from the single-frequency signals. This indicates that the accuracy improvement due to the cross-correlation for the proposed FSK radar might not be significant when the effect of the low SNR and the uncertainty of the phase measurement increase owing to the increase in distance from the radar. Table 2 presents the average *RMSEs* and SDs for all BPM measurements for each subject. As shown, the cross-correlated signals had small *RMSEs* and SDs for all the subjects. In the proposed FSK radar, the average *RMSEs* and SDs of the heartbeat obtained using the cross-correlation method are improved by 2.42 and 2.36 BPM, respectively, compared to those measured at each frequency. With regard to the operating principle and the procedure, heartbeat measurement with only a single frequency using the proposed radar is identical to that using the CW Doppler radar. The measurement results demonstrate that the proposed FSK radar with the cross-correlation in a single hardware configuration is advantageous for improving the accuracy of vital-signs detection compared to the CW Doppler radar. Table 3 summarizes the performance comparison of the proposed radar with the radars from our previous studies, which were employed for vital-signs detection in similar measurement surroundings.


**Table 2.** Average root-mean-square error (*RMSE*) and standard deviation (SD) of overall heartbeat per minute measured for each subject by using the proposed FSK radar.

<sup>1</sup> The cross-correlation method.

**Table 3.** Performance comparison of the proposed radar with the radars from our previous studies, which were used for vital-signs detection in a similar measurement environment.


<sup>1</sup> Calculated by using the average error of heartrate (BPM) measured in all detectable ranges.

**Figure 13.** Measured accuracies of the signals obtained at each operating frequency and signals processed with the cross-correlation method in the proposed FSK radar depending on the distance to the subjects: (**a**) Root-mean-square error (*RMSE*) of subject A; (**b**) standard deviation (SD) of subject A; (**c**) *RMSE* of subject B; (**d**) SD of subject B; (**e**) *RMSE* of subject C; (**f**) SD of subject C; (**g**) *RMSE* of the averaged data; (**h**) SD of the averaged data.
