The quality of vital signs parameters extraction is affected by many factors. For the non-contact measurement system, the vertical distance R between the radar and the chest, the relative angle between the main beam direction of the transmitting antenna and the body surface, and the interference distribution around the test environment are the three most important factors. Considering the practical application requirements of radar sensors, the test environment is a laboratory with narrow space, which is similar to the ward environment.
3.1. Measurement of Heart Rate and Respiratory Rate
Eight male volunteers with a height of about 1.75 m and a weight of about 65 kg were selected as test objects. During the test, the person about to be tested sat in the chair at a distance of approximately 1.0 m in front of the radar; the heart position of the chest kept a basically vertical relationship with the main beam direction of the radar-transmitting antenna. The heart rate and respiratory rate were measured in the experiment. At the same time, the electrocardiogram (ECG), photoplethysmographic (PPG) pulse wave and respiratory signals measured by the JRTYL-GT6800-10 cardiovascular monitor were compared to verify the correctness of the results.
Figure 5 shows the schematic diagram of the respiratory rate and heart rate measurement experiment.
The measurement system samples the in-phase (I) and quadrature (Q) IF signals through the acquisition card and uploads them to the computer via universal serial bus (USB), after which the IF digital signal I + j × Q corresponding to each FMCW pulse is FFT transformed to obtain the spectrum of the IF signal (range FFT), as shown in
Figure 6.
It can be seen that the IF signals obtained by using narrow beam antenna have no clutter interference. By selecting the spectrum peak corresponding to the human target we are concerned about, and then calculating the phase θ by using the real part and imaginary part of the frequency corresponding to the peak point of the spectrum, we can thus obtain a phase sequence θ(
n) (
n = 1, 2…, N) corresponding to the FMCW pulse. The chest displacement caused by breathing is sometimes greater than
, so the phase sequence has a jump problem. For each pair of adjacent phase values (θ(m),θ(m + 1)), if θ(m + 1) − θ(m) > 180°, it indicates that θ(m + 1) > 0 and θ(m) < 0, θ(m + 1) = θ(m + 1) − 360°; if θ(m + 1) − θ(m) < −180°, which indicates that θ(m + 1) < 0, θ(m) > 0 and θ(m + 1) = θ(m + 1) + 360°. The phase jump process is shown in
Figure 7, where the direction indicated by the green arrow is the correct direction in which the phase angle θ changes [
17].
After the phase sequence is compensated by the jump,
Figure 8a shows the phase sequence changing with time. It can be seen that the phase sequence is a composite signal composed of heartbeat signal and respiratory signal, and the respiratory signal is much stronger than the heartbeat signal. From the demodulated signal, it is easy to read out the respiratory waveform because its peak and trough are very obvious, but it is impossible to observe every heartbeat signal clearly. Due to uncontrollable factors such as system noise in radar itself, the signal quality changes greatly and is unreliable. In order to obtain the respiratory and heartbeat frequencies, we first applied FFT to the phase data. The spectrum is shown in
Figure 8b. The five significant peaks represent different meanings respectively. The frequency of the highest peak is 0.26 Hz, which represents the respiratory rate. The third peak represents the second harmonic of respiratory wave, and the last peak of 1.23 Hz represents the heart rate. The first peak represents the frequency of phase sequence data bias line change caused by different breath depth, which is 0.05 Hz. We can see this from the time–domain waveform in
Figure 8a. In addition, the spectrum also includes the third and fourth harmonics of respiration and other clutter spectra. Sometimes their amplitude is close to the heart rate, which easily interferes with the judgment of heart rate. From the comparison of the FFT calculation value and the results of JRTYL-GT6800-10, it can be seen that the clutter has a cumulative effect with the increase in acquisition time and merely by using the FFT algorithm to evaluate heart rate, the probability of identifying respiratory harmonic or clutter spectrum value as the heart rate is high, which hinders the practical process of vital signs monitoring radar.
Through analyzing the phase sequence data, we found that the time domain waveform of the respiratory signal was relatively clear, and that there was a big difference in time length between different respiratory cycles. The frequency obtained by the FFT algorithm cannot fully reflect the characteristics of respiratory signals. Therefore, we used a Gaussian low-pass smoothing filter to extract the respiratory signal, and then determined the duration of each breath by looking for the waveform peak in the time domain. The filtered respiratory signal waveform is shown in
Figure 9a. Taking the time difference between adjacent peaks in the waveform
as abscissa and 60/
as ordinate, the curve of respiratory rate (times/min) changing with time is drawn as shown in
Figure 9b. Compared with the respiratory rate displayed by the JRTYL-GT6800-10 cardiovascular monitor, the error was within ±2 times/min except for individual scatter points, which was caused by the difference of the time domain waveform feature extraction standards between the two instruments.
The respiratory rate test results of eight volunteers are shown in
Table 1, which represents the average ± standard deviation of frequency. According to reference [
7], the accuracy
p of respiratory rate measurement results is defined as the percentage of time when the error between the detected respiratory rate and the reference frequency is within the range of ±10%. The results showed that the accuracy rate of all subjects was above 90%.
3.2. Average Heart Rate Measurement
From the time domain waveform of heartbeat signal, it can be seen that it is a kind of non-stationary quasi-periodic signal, and the spectrum of respiratory harmonic and clutter sometimes fall into the band range of heartbeat [
18]. Additionally, the signal strength is greater than the fundamental frequency signal of heartbeat signal. Therefore, we used an adaptive notch filter (ANF) to remove respiratory harmonics to improve the accuracy of heart rate detection. The basic principle of an adaptive notch filter is to take the orthogonal signal of a certain center frequency as the reference signal, use the linear combination of the orthogonal signal to track the input signal, and continuously adjust the weight coefficient of the linear combination through the residual error of each step, thus separating the linear correlation part of the input signal with the reference signal and achieving the effect of a narrow band notch. Compared with the conventional digital filter, the ANF has narrow stop band and fast attenuation in band. With two outputs: filter output (y output) and notch output (e output), this device can realize narrow band notch. When the interference or useful signal is a single frequency signal, the adaptive notch filter has good filtering effect [
19]. In this paper, the basic principle of the ANF, the structure of which is shown in
Figure 10, is to take the orthogonal signal of respiratory harmonic frequency as the reference signal, use the linear combination of the orthogonal signal to track the input signal, and continuously adjust the weight coefficient of the linear combination through the residual error of each step, thus separating the linear correlation part of the input signal with the reference signal and achieving the effect of filtering respiratory harmonic.
Since the amplitudes of the second and third harmonics of the respiratory signal were large, especially the third harmonic, whose amplitude and frequency were close to those of the heartbeat signal, we obtained the respiratory signal frequency f
RR through the spectrum peak, by using cos(2π × 2f
RRt) and cos(2π × 3f
RRt) as the initial signals, and then using the least mean square (LMS) adaptive iteration to approach the harmonic signal. After filtering out the harmonics, the heartbeat signal was converted to the frequency domain, and the heartbeat frequency was obtained by searching for the peak value in the frequency domain. In order to evaluate the accuracy of the harmonic cancellation algorithm based on the adaptive notch filter, the Doppler radar detection device and photoelectric pulse sensor designed above were used to simultaneously collect human heartbeat information. Additionally, the experimental results were accurately calculated through the pulse wave signal. The pulse sensor can obtain the pulse waveform by collecting the changing information of light transmittance at the end of the finger. This waveform is of high quality and it is convenient to extract the heart rate information, as a consequence of which the heart rate extraction result can be used as the heart rate reference. To reduce the cumulative effect caused by the increase in clutter time length, the short-term phase data of T = 4096 × 0.0056 s, i.e., 22.94 s, were taken as a calculation unit, and the phase signal was filtered by the adaptive notch filter each time it moved forward for 1 s. Additionally, the frequency corresponding to the highest peak point was found in the heart rate range of the filtered FFT spectrum according to some prior knowledge. The upper part of
Figure 11 shows the FFT spectrum of the phase signal without the adaptive notch filter processing. It was observed that the second and third harmonic amplitudes of respiration were high. Nevertheless, the peak of the heartbeat spectrum lies between two larger respiratory harmonic peaks. If the peak method is used to estimate the heart rate, the estimated heart rate is 0.78 Hz, which is actually the third harmonic frequency of breathing. The lower part of
Figure 11 shows the FFT spectrum of the phase signal processed by the adaptive notch filter, from which it can be seen that the harmonic of the respiratory signal was suppressed, the frequency value of heartbeat signal was significantly higher than that of the respiratory harmonic, and thus the accuracy of heart rate detection was improved. As the heart rate of normal people is between 45–180 bpm, that is, the frequency is between 0.75–3 Hz, the peak value of a respiratory wave below 0.7 Hz is not within our detection range and will not affect the monitoring accuracy of heart rate.
As the phase sampling rate was 178 Hz, the FFT frequency resolution of 4096 sampling points was 0.0435 Hz. When the frequency of signal was not a positive integer multiple of FFT frequency resolution
, the spectrum leakage caused by the FFT “fence effect” greatly reduced the accuracy of frequency estimation. For example, for a heart rate assessment in 60 s, the maximum error could be 1.3 bpm. Therefore, we modified the heart rate obtained by the FFT by the adjacent element proportion of spectrum peak method [
20]. The specific method is shown in reference [
20]. Finally, the heart rate obtained was as follows:
where
k0 represents the frequency sequence number corresponding to the peak value of center rate of the FFT spectrum, and
X(
k0 − 1) and
X(
k0 + 1), respectively, represent the amplitude of the left and right sides of the heart rate peak of the FFT spectrum. Considering the standard of actual heart rate measurements, when the difference between the heart rate results obtained by the Doppler radar and the pulse signal reference are less than or equal to 2 bpm (beats per minute), the heart rate extraction result can be confirmed to be correct. At the same time, the beat error rate per minute is taken as the accuracy index of the method. The error rate is expressed as follows:
where HR
ref is the heart rate obtained from the number of peaks in the pulse wave, and HR
radar is the heart rate obtained from the raw phase data through the ANF and FFT algorithm and frequency correction by using radar sensor. In
Figure 12, after being processed by an extraction algorithm with the Doppler radar signal and PPG reference signal, respectively, the heart rate detection results of a volunteer whose heart beats too fast were compared, where the heart rate average was 22.94 s. It can be seen that although the heart rate differed from one subject to another, this method can detect the heart rate more accurately.
The heart rate test results of eight volunteers were continuously counted as shown in
Table 2, which represented the average ± standard deviation of frequency. The statistical results show that the accuracy rate of all subjects is higher than 90.54%.
3.3. Short-Term Heart Rate Estimation
As heart rate changes continuously with time in a certain range, real-time heart rate measurement plays an important role in the evaluation of arrhythmia and other pathological states. Although the improved FFT algorithm can estimate the average heart rate with long-time phase data, for the raw phase sequence data with low signal-to-noise ratio, short-time frequency estimation by means of FFT algorithm will face the problem of a high error rate of heart rate measurement results. According to the analyses in
Section 3.2, the raw phase sequence data were mainly composed of the respiratory signal, heartbeat signal, radar system noise and environmental clutter. As a narrow beam lens antenna was used in biological radar, the proportion of environmental clutter was low and thus can be ignored. Therefore, when extracting the heartbeat signal, we only needed to separate and remove the respiratory signal and radar system noise. Since the frequency range of respiratory harmonics and part of the noise coincide with that of the heartbeat signal, it was difficult to remove the noise effectively by means of traditional filtering methods. A Fast-ICA algorithm can well estimate the original signals which were statistically independent and mixed by unknown factors from the observed signals [
21]. Therefore, we used the method based on the combination of CEEMDAN and Fast-ICA algorithm to separate the heartbeat signal and evaluate the short-term heart rate in the time domain.
From the raw phase sequence data in
Figure 8, we can see that the waveform contour of the respiratory signal is obvious, so we use the method of taking the middle line of the upper and lower envelope lines of the raw phase sequence data waveform to remove the respiratory fundamental wave.
Figure 13 is the schematic diagram of obtaining the raw phase sequence data envelope.
By subtracting the middle line of the upper and lower envelope from the raw phase sequence data, the phase signal mainly composed of the heartbeat signal, radar system noise and residual respiratory harmonics can be obtained, whose signal waveform is shown in
Figure 14.
Since the preprocessed heartbeat signal with noise is a single channel signal and the Fast-ICA algorithm cannot solve the underdetermined problem, that is, the number of input signals must be greater than or equal to the number of sources, we first adaptively decomposed the signal into multi-dimensional intrinsic mode function (IMF) to meet the requirements of blind source separation (BSS) for positive or over-determined signals. Then, independent component analysis (ICA) was performed on the reconstructed IMF to extract the heartbeat signal. As an improved method for empirical mode decomposition (EMD) and ensemble empirical mode decomposition (EEMD), on the basis of EEMD, CEEMDAN overcomes the problem that EEMD lost with the integrity of decomposition and produces a reconstruction error by adding white noise adaptively. At the same time, CEEMDAN makes it possible for signals to be evenly distributed in the whole frequency band and have continuity in different scales, thus reducing the modal aliasing effect [
22]. From the decomposition results of CEEMDAN, it can be seen that the phase sequence data after removing the respiratory fundamental wave can be decomposed into about 15 IMFs. An FIR band-pass filter with a pass-band of 0.8–3 Hz was used to filter the raw phase sequence data to obtain the heartbeat signal with clutter. A correlation calculation can then be conducted with the heartbeat signal and those IMFs, respectively, and then the IMF with the largest correlation coefficient can be identified as the heartbeat signal. However, from the waveform of the heartbeat signal, it can be found that there still exists mode aliasing, which mainly occurs between adjacent IMFs. In order to suppress the mode aliasing effect and improve the accuracy of heart rate monitoring, the IMF signals decomposed by CEEMDAN were divided into three groups. More specifically, the heartbeat signal and its two adjacent IMFs were divided into one group; the heartbeat signal was a single channel signal; the adjacent IMF whose frequency was higher than that of the heartbeat signal was treated as a channel signal; the adjacent IMF whose frequency was lower than that of the heartbeat signal was treated as a channel signal; those IMFs whose frequencies were higher than that of the IMF adjacent to the heartbeat signal added up to form noise; those IMFs whose frequencies were lower than that of the IMF adjacent to the heartbeat signal added up to form other low-frequency clutter. Then Fast-ICA was performed on the three channels according to different weights to obtain the heartbeat signal with the suppressed mode aliasing effect. The classification results after CEEMDAN and Fast-ICA are shown in
Figure 15. It can be seen that the combination of CEEMDAN and Fast-ICA can effectively separate the heartbeat signal and radar system noise.
As the separated heartbeat signal has the problem of an unstable waveform, it is easy to make mistakes when directly searching the peak in the time domain. Therefore, the sinusoidal curve fitting method was adopted to reconstruct the heartbeat signal and thus improve the accuracy of the heart rate. The short-term heart rate can be worked out by conducting the sinusoidal curve fitting to the heart signal obtained after separation by taking every 3 s as a segment and finding the peak value of the fitting curve. The curve fitting results of the 3-s heartbeat signal are shown in
Figure 16.
We detected the peak value of the heartbeat signal after curve fitting and then calculated the heart rate.
Figure 17 shows the short-term heart rate detection results of a volunteer, from which it can be seen that the heart rate measurement results obtained by means of the above algorithm can reflect how the heart rate changes with time.
Compared with the traditional FIR-type band-pass filter, the CEEMDAN and Fast-ICA algorithm have stronger adaptability, and the time–domain waveform of the heartbeat signal was also more stable, which helps to improve the accuracy of short-term heart rate monitoring. However, its shortcomings are also obvious, and its computational complexity is much higher than that of a band-pass filter. According to the short-term heart rate measurement results of five volunteers, the accuracy of the measurement error within ±2 bpm was 87.88%, 84.85%, 87.88%, 84.85%, 90.91%, 81.82%, 84.85%, 81.82%. These experimental results verify the effectiveness of the short-term heart rate extraction algorithm, and the algorithm can track the changing heart rate. However, due to the large amount of calculations, the short-term heart rate measurement results have a time delay of about 100 s. In the whole process of the algorithm, the delay of CEEMDAN and Fast-ICA play a leading role, which determines the delay of the whole algorithm; while other computing time can be ignored for the total delay.