**2. Preliminaries**

In this section, the measured signal is analyzed to verify the multi-location issue mentioned above. Firstly, the signal metric leveraged in Wi-Fi-based HAR is introduced. Then, the influence of location variations on Wi-Fi signals is investigated to reveal the encountered challenges. More importantly, both amplitude and phase information are presented.

#### *2.1. Channel State Information*

Wi-Fi-based HAR leverages the impact of human movements on the propagation of the wireless signal for sensing. In a Multiple Input Multiple Output (MIMO) and Orthogonal Frequency Division Multiplexing (OFDM) wireless communication system, this process can be described by the fine-grained CSI, which represents the state of the communication link between the transmitter (TX) and the receiver (RX).

Letting *y* and *x* denote the received signal and transmitted signal, the relation between them can be modeled as:

$$y = H\mathbf{x} + \mathbf{n} \tag{1}$$

where *n* is the noise vector and *H* is the CSI channel matrix which is made up of complex numbers, namely *H*=*HR* + *iHI*. For the *s*-th subcarrier between the *i*-th transmitting antenna and the *j*-th receiving antenna, it is given by

$$H\_{ij}^{\mathbf{s}} = \left\| H\_{ij}^{\mathbf{s}} \right\| e^{j \angle H\_{ij}^{\mathbf{s}}}, \mathbf{s} \in [1, N\_{\mathbf{s}}], i \in [1, N\_{\mathbf{t}}], j \in [1, N\_{\mathbf{r}}] \tag{2}$$

where *H*<sup>s</sup>*ij* and ∠ *H*s*ij* denote amplitude and phase, respectively. *Nt* and *Nr* stand for the number of antennas at the TX and RX. And *i* and *j* are the indices of TX and RX antennas. *Ns* is the number of subcarriers for each pair of transceiver antenna.

#### *2.2. Problem Analysis*

To demonstrate the challenge of multi-location HAR using Wi-Fi signals, the CSI amplitudes of the activities at the same and distinct locations are analyzed and presented in Figures 1 and 2. The horizontal axis represents the frame length, and the ordinate indicates the amplitude of CSI. The dataset will be presented in more detail in Section 4. As demonstrated in Figure 1, each subgraph depicts a kind of activity. The two curves in each subgraph represent two samples of the same activity. The measured signals for the same action at a fixed location seem to have similar waveforms. In the left figures of Figure 1, the variation trends of the two samples are different to some extent, which is because there are slight differences in the amplitude, speed, and starting position of each movement performed by the volunteers, resulting in differences among different samples of the same activity. Therefore, in the process of activity recognition, it is necessary to extract similar feature patterns between different samples of the same action that represent the changing trend of the activity itself as much as possible. Furthermore, it can be observed that diverse human activities will generate different characteristic patterns in the received signals at the same location. These are the foundation of wireless sensing. However, the measured signals for the same activity possess varying CSI amplitudes at different locations. As illustrated in Figure 2, five curves correspond to the same activity at five different locations. As can be seen, although it is relatively easy to identify the types of human activities by interpreting the CSI patterns at a single location, it may not be possible to ensure good classification accuracy for multi-location sensing.

**Figure 1.** CSI amplitude of four different activities at the same location.

In addition to the amplitude of CSI, the phase of the activity is also analyzed and shown in Figure 3. As can be seen, the phase can also reflect the characteristics of the activity. Therefore, both amplitude and phase should be utilized effectively. According to the above observation, just in terms of amplitude and phase, apart from the types of activities, the location variations can also obviously affect signal transmission. Therefore, both kinds of information should be strongly integrated, which can provide more accurate representative features so as to achieve multi-location sensing with limited data.

**Figure 2.** CSI amplitude of the same activity at five different locations.

**Figure 3.** CSI phase of the same activity at five different locations.

### **3. System Model**

## *3.1. Overview*

In this part, the framework of the multi-location human activity recognition system is introduced, as shown in Figure 4. First of all, the Wi-Fi communication system is set up to collect CSI data in the Wi-Fi environment. The details will be described in Section 4. Then, feature extraction is carried out on CSI samples that are affected by human activities, and activity categories are distinguished according to the differences in features to realize human activity recognition.

To meet the requirement of high accuracy multi-location human activity recognition, a sensing method based on AP-DCN was proposed. High-accuracy multi-location sensing depends on adequate activity data from various positions. When data samples are restricted, sufficient activity information should be mined from the limited data. According to the above analysis, both the amplitude and phase of the Wi-Fi signal carry information related to human activities. Compared with the real-valued deep learning method based on the single amplitude or phase, the deep complex network simulates complex space computation through real-number space computation and can extract richer feature information. AP-DCN is designed to fully mine human activity information in amplitude and phase of CSI by using the complex convolution operation.

In some application scenarios, besides the lack of data samples, there is also the problem of unbalanced sample numbers provided at different positions. Therefore, a multi-

location human activity perception method based on transfer learning named DCN-TL is proposed to transfer the common features of human activities learned from some locations with sufficient activity data to other locations with insufficient data so as to alleviate the impact of unbalanced data samples and limited sample number.

**Figure 4.** The framework of multi-location human activity recognition system.
