*3.1. Indoor Propagation Model of Wireless Signal*

When the wireless signal propagates in the indoor environment, it is influenced by the obstacles in the propagation path, which cause reflection and diffraction. After the propagation of different paths, each component reaches the receiving end with different strengths and phases, resulting in a multipath effect [16]. The indoor propagation model of the wireless signal is shown in Figure 1.

**Figure 1.** Indoor propagation model of wireless signal.

According to the Fries transfer formula [17], the receiving power of the receiving antenna can be expressed as:

$$P\_r = \frac{P\_l G\_l G\_r \lambda^2}{\left(4\pi R\right)^2} \tag{1}$$

where *Pt* and *Pr* are the power of transmitting antenna and receiving antenna, respectively; *Gt* and *Gr* are the gain of transmitting antenna and receiving antenna, respectively; and the distance between transmitting antenna and receiving antenna is *R*. λ is the wavelength of electromagnetic wave.

Assuming that the propagation path length of the electromagnetic wave through the interference of static objects is *D*, and the propagation path length through the interference of the human body is *X*, the Fries transfer formula can be rewritten as follows.

$$P\_r = \frac{P\_l G\_l G\_r \lambda^2}{16\pi^2 (R^2 + D^2 + X^2)}\tag{2}$$

In Formula (2), we can see that both *R* and *D* do not change. When people are indoors, *X* will change, resulting in a change in the power of the receiving antenna. At the same time, because the signal phase is a linear function of the distance of the propagation path, the change of the propagation path will also lead to the change of the signal phase [18]. Human behavior changes the strength and phase of the signal, and the CSI describes the loss and fading on the transmission path. When there is a moving target between the transmitting and receiving devices, the wireless signal reflected by the moving target increases the dynamic component of the channel. The fluctuation of the channel corresponds to the motion information of the target one by one. We can get CSI data from the signals collected by the receiving devices. By analyzing the CSI data, we can sense the changes of the external environment. In the next section, we explain the essence of CSI and its mathematical expression [19].

#### *3.2. CSI*

In order to eliminate the adverse effect of a multipath effect on wireless signal transmission, the MSP described in this paper uses orthogonal frequency division multiplexing (OFDM) modulation technology to decompose the data stream to be transmitted into several independent sub-data streams, that is, multiple subcarriers, and then transmits them in parallel, which can effectively eliminate the inter-symbol interference caused by the multipath effect in high-speed data stream transmission. At the same time, OFDM modulation technology can also greatly improve the data transmission efficiency. Because there are multiple subcarriers, each subcarrier channel is independently available, which also increases the amount of data to extract more information [20].

Multiple input multiple output (MIMO) is supported by OFDM modulation technology [21]. The channel model of the MIMO system in the frequency domain can be expressed as

$$Y = HX + N \tag{3}$$

where *Y* represents the receiving signal, *X* represents the transmitting signal, *N* represents the environmental noise, and *H* represents the state matrix of the wireless channel, and its dimensions are *NT* × *NR* × *NC*. *NT*, *NR*, and *NC*, respectively, represent the number of transmitting antennas, receiving antennas, and subcarriers.

CSI is essentially a representation of the frequency response of each subcarrier channel. For each independent subcarrier channel, its frequency response can be expressed as

$$H\_k(f\_k) = \|H\_k(f\_k)\| \mathcal{e}^{\text{jarg}(H\_k(f\_k))} \left(1 \le k \le N\_{\mathbb{C}}\right) \tag{4}$$

where *fk* represents the center frequency of the Kth subcarrier, ||*Hk*(*fk*)|| represents the CSI amplitude information of the Kth subcarrier, and *arg*(*Hk*(*fk*)) represents the CSI phase information of the Kth subcarrier.

After continuous data collection over a period of time, CSI data can be obtained through the channel estimation formula [22].

$$
\hat{H} \approx \frac{Y}{X} \tag{5}
$$

*3.3. MSP*

The MSP independently developed in this paper works in C-band (4.8 GHz). It is a highly customizable platform that can adapt to different application scenarios. MSP consists of omnidirectional antenna, industrial personal computer, absorbing material, frequency converter, and other related facilities. The use of absorbing materials is mainly to shield the surrounding environment from interference. The main function of MSP is to obtain the CSI of the wireless channel. By analyzing the CSI data, the behavior of patients can be monitored.

MSP uses OFDM technology. Its essence is an OFDM transceiver system, and its functional block diagram for obtaining CSI is shown in Figure 2.

**Figure 2.** Block diagram of microwave sensing platform (MSP) to obtain channel state information (CSI) data.

In Figure 2, *<sup>d</sup>*(*k*) is converted to N parallel data {*x*0, *<sup>x</sup>*<sup>1</sup> , ... , *xN*−1} through serial–parallel conversion. These data can be regarded as N data in the frequency domain. A set of time domain data {*s*0, *s*<sup>1</sup> , ... , *sN*−1} obtained after the inverse discrete Fourier transform (IDFT) is an OFDM symbol. After adding a cyclic prefix to an OFDM symbol, the OFDM symbols are transmitted on the wireless multipath channel after parallel–serial conversion and digital–analog conversion. At the receiving end, the reverse work is performed: analog–digital conversion, parallel–serial conversion, removing cyclic prefix, and fast Fourier transform (FFT). The training sequence after FFT is used to perform channel estimation according to Equation (5), and CSI data can be obtained.
