# Location Adaptive Motion Recognition Based on Wi-Fi Feature Enhancement
## 3 Enhanced Wi-Fi Features Based on Human Body Speed Distribution
### DFS Estimation Based on Dynamic Signal Amplification Method  
To obtain DFS caused by the movement of the human body between a pair of transmitting and receiving antennas [40], we propose a method to amplify the dynamic signal changes caused by the human body and extract the required DFS from it. According to the Fresnel zone model, the larger the motion amplitude, the greater the signal change, and the easier it is to detect the dynamic path. The signal change is a segment of a sine wave. When the path length change caused by action is small, its phase change is not easily observed. However, the same displacement at different starting positions will cause different signal changes. Therefore, to change the phase difference to amplify the signal, the phase of the static vector can be changed by adding a virtual path to change the phase difference between the dynamic vector and the static vector. The specific process is as follows:  
(A) Search for phase shift. As shown in Figure 1, \(H_{\mathrm{s}}\),\(H_{d}\), \(H_{\mathrm{v}}\) and \(H^{\prime}_{\mathrm{s}}\) are static variable, dynamic variable, virtual variable, and static synthetic variable, respectively, and \(H^{\prime}_{\mathrm{s}}\) is the final variable to be updated. The dynamic and static vector phase difference \(\Delta\theta_{sd}\) can not be obtained directly from the original signal but can be traversed between \(0-2\pi\), and the phase shift with the strongest sensing ability is the best one. (B) Calculate multiple radial quantities. Estimate the static variables approximately by the signal average value periodically. In Figure 2, \(H_{\mathrm{v1}}\) and \(H_{\mathrm{v2}}\) are two virtual paths with different lengths; they and \(H_{\mathrm{s}}\) are combined into different static paths, \(H^{\prime}_{s1}\) and \(H^{\prime}_{s2}\), respectively. It can be observed that although \(H^{\prime}_{s1}\) and \(H^{\prime}_{s2}\) have different lengths, they have the same phase shift, which ensures the same degree of improvement in sensing performance. To simplify the problem, we can set \(|H^{\prime}_{\mathrm{s}}|\)to a value equal to \(|H_{\mathrm{s}}|\), which will not affect the correctness of the result. To date, according to the known parameters, the amplitude of the synthetic static path can be constructed:  
\[|H_{\mathrm{v}}|=\sqrt{|H_{\mathrm{s}}|^{2}+|H^{\prime}_{\mathrm{s}}|^{2}-2|H_ {s}||H^{\prime}_{s}|\cos\omega} \tag{6}\]  
After the amplitude of \(H_{\mathrm{v}}\) is obtained, \(\delta=\arcsin\frac{\sin\omega|H_{\mathrm{v}}|}{|H_{\mathrm{v}}|}\) can be obtained according to \(\frac{|H_{\mathrm{v}}|}{\sin\omega}=\frac{|H^{\prime}_{\mathrm{s}}|}{\sin\delta}\). The phase of virtual path \(H_{\mathrm{v}}\) is \(\theta_{\mathrm{v}}=\theta_{s}+\delta-\pi\), and \(\theta_{s}\) is the phase of static path vector. According to the given \(\omega\), the virtual static vector can finally be obtained as follows:  
\[H_{\mathrm{v}}=|H_{\mathrm{v}}|e^{\beta\theta_{\mathrm{v}}} \tag{7}\]  
(C) Add a composite path. After \(H_{\mathrm{v}}\) is obtained, this path is created by MATLAB and added to the original signal. For the original signal of \(S_{0}=(CSI_{1},CSI_{2},\dots,CSI_{P}))\) with p-CSI samples, the new signal after adding virtual path is \(S=(CSI_{1}+H_{\mathrm{v}},CSI_{2}+H_{\mathrm{v}},\dots,CSI_{P}+H_{\mathrm{v}})\). Figure 1: Diagram without virtual diagram. To date, a new signal with strong dynamic perception ability has been obtained. The DFS caused by the dynamic path can be extracted by time-frequency analysis of this signal, and its symbol is \(f_{D}(t)\), which is related to the change of signal propagation path length \(d(t)\):  
\[f_{D}(t)=-\frac{1}{\lambda}\frac{d}{dt}d(t) \tag{8}\]  
where \(\lambda\) is the signal wavelength.