Millimeter-wave radars can be divided into pulse radars and continuous-wave radars according to the waveforms they transmit.

The waveforms emitted by the millimeter-wave radars we use in the project are frequency-modulated continuous waves (FMCW), as shown in Figure 1. The frequency change linearly with time [2].

Theoretically, the shape of received signal (RX) is the same as the transmitted signal, while there is a time lag between the transmitted signal and the received signal. The time lag is caused by the distance between the radar and target. The radar mixes the TX and RX waves and output the intermediate-frequency signal (IF) S I F ( t ) as follows:

S I F ( t ) = A I F exp { j [ ψ ( t ) + ω ( t ) t ] } , t d < t < T r # (1)

ω ( t ) = 4 π K d ( t ) c # (2)

ψ ( t ) = 4 π d ( t ) λ # (3)

where the A I F , ω ( t ) and ψ ( t ) are the amplitude, frequency and phase of the IF signal. t d is the time lag between TX and RX. K is the increasing rate of frequency of TX which is set to 0.04 GHz/μs. T r is the frequency increasing time which is set to 128 μs. c is the speed of light. d ( t ) is the distance between the radar and target. λ is the wavelength of the radar waveform and it is set to 5 mm.

The detection of human heart rate and breathing frequency can be realized by detecting the movement of the human chest. The combined action of breathing and heart beating makes the human chest rise and fall. When a person breathes smoothly, the breathing will cause the regular rise and fall of the human chest. During the beating process of the heart, the contraction and relaxation of the heart are transmitted to the chest wall to move the chest cavity. Using the high precision of the millimeter-wave radar to capture the tiny displacement of the chest cavity, and extract the frequency information from the displacement information, the monitoring diagram is shown in Figure 2.

When the human body remains as still as possible, the non-contact sensor is used to detect the distance of the chest relative to the sensor. And the simplified calculation formula of d(t) is as follows [3]:

d ( t ) = d 0 + d R + d H = d 0 + A R sin ( 2 π f R t ) + A H sin ( 2 π f H t ) # (4)

In Equation (4), d₀ is the average distance of the human chest relative to the sensor. d_R and d_H are the changing distance of the chest relative to sensor caused by respiration and heartbeat. f_R and f_H are the respiratory rate and heartbeat rate. The general range of A_H is 0.1 - 2 mm, the range of A_R is 3 - 10 mm, the range of f_R is 0.2 - 0.9 Hz, the range of f_H is 0.9 - 2 Hz [4].

When millimeter-wave radar is actually used for monitoring, complex monitoring scenarios will generate noise clutter in radar data. In addition to the human body in the room, static objects such as beds, wardrobes, and walls will reflect radar waves, which will greatly interfere with the monitoring results. A large number of static objects in the scene make the obtained spectrum have strong zero components, which interfere with the display and identification of normal spectrum waves [5]. How to filter out the interference of static furniture on radar data is a key point and difficulty of our algorithm.

In practice, we found that the IF of the obtained intermediate frequency signal is very noisy, and the time domain and frequency domain diagram is shown in Figure 3:

We can find that the signal is mixed with：

1) Linear noise component

2) Low frequency noise component

3) High frequency noise component

Noise sources are from:

1) External DC signal component [6]

2) Local oscillator leakage

3) Nonlinearity of the mixer [7]

According to the modulation and demodulation theory of RF signals, a trigonometric function can decompose the IQ signal as follows:

x ( t ) = I cos ( 2 π f c t ) − Q sin ( 2 π f c t ) # (5)

This project requires reverse demodulation. Our solution is to use carrier demodulation. The flow chart is shown in Figure 4:

Ideally the sinusoidal signal IQ decomposition should be a circle in the complex plane with the center of the circle at the origin of the complex plane. However, the original signal contains a DC bias that deforms the signal, and this component can significantly affect the accuracy of phase extraction in vital signs signal measurements [8]:

ϕ = arctan ( I ( t ) + c 1 R ( t ) + c 2 ) ≠ ψ # (6)

so we use the method of DC offset, which means normalizing the amplitude and translating the center of the circle to the origin as shown in Figure 5.

Empirical Mode Decomposition (EMD) is a new time-frequency analysis method system based on the intrinsic mode function. It jumps out of the traditional Fourier framework and can be used to deal with non-stationary and nonlinear signals. EMD decomposes an unknown signal into a series of signal components and the sum of a remainder, each signal component is completely obtained through the local time scale of the signal, which makes the empirical mode decomposition (EMD) decomposition highly adaptable [9]; In contrast, such as wavelet analysis, the choice of basis function is selected at the beginning, the wavelet basis may be the best globally, but the local may not be, lack of adaptability.

From Figure 6 we can see that the original signal is decomposed into components containing various frequency ranges, including respiration and heartbeat curves.

Millimeter-wave radar can not only measure the target distance, but also measure the target angle according to the arrangement of the receiving antennas. If multi-target health monitoring is to be carried out, some methods proposed by the current research are to detect the target position based on the angle, and cooperate with beam forming technology [10] [11] or beam steering technology [12] to detect the azimuth of each target, and then extract vital signs signals for each target. But these two technologies require multi-transmission and multi-reception radars to obtain multiple sets of data for analysis. The radar used in

the project can only obtain three sets of data with one launch and three receptions, and the receiving antennas are arranged in an L shape. That is to say, the angle detection in the horizontal direction and the vertical direction can only be analyzed based on two sets of data, so we use mathematical methods to improve frequency bandwidth with algorithms. The diagram is shown as Figure 7.

Through the above operations, we can easily find the location of multiple targets on the cloud map as shown in Figure 8.