
%Version 2.1 April 2023
% See section 11 of the User Manual for version history
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%                                                                 %%
%% Please do not use \input{...} to include other tex files.       %%
%% Submit your LaTeX manuscript as one .tex document.              %%
%%                                                                 %%
%% All additional figures and files should be attached             %%
%% separately and not embedded in the \TeX\ document itself.       %%
%%                                                                 %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%\documentclass[referee,sn-basic]{sn-jnl}% referee option is meant for double line spacing

%%=======================================================%%
%% to print line numbers in the margin use lineno option %%
%%=======================================================%%

%%\documentclass[lineno,sn-basic]{sn-jnl}% Basic Springer Nature Reference Style/Chemistry Reference Style

%%======================================================%%
%% to compile with pdflatex/xelatex use pdflatex option %%
%%======================================================%%

%%\documentclass[pdflatex,sn-basic]{sn-jnl}% Basic Springer Nature Reference Style/Chemistry Reference Style


%%Note: the following reference styles support Namedate and Numbered referencing. By default the style follows the most common style. To switch between the options you can add or remove �Numbered� in the optional parenthesis. 
%%The option is available for: sn-basic.bst, sn-vancouver.bst, sn-chicago.bst, sn-mathphys.bst. %  
 
%%\documentclass[sn-nature]{sn-jnl}% Style for submissions to Nature Portfolio journals
%%\documentclass[sn-basic]{sn-jnl}% Basic Springer Nature Reference Style/Chemistry Reference Style
\documentclass[sn-mathphys,Numbered]{sn-jnl}% Math and Physical Sciences Reference Style
%%\documentclass[sn-aps]{sn-jnl}% American Physical Society (APS) Reference Style
%%\documentclass[sn-vancouver,Numbered]{sn-jnl}% Vancouver Reference Style
%%\documentclass[sn-apa]{sn-jnl}% APA Reference Style 
%%\documentclass[sn-chicago]{sn-jnl}% Chicago-based Humanities Reference Style
%%\documentclass[default]{sn-jnl}% Default
%%\documentclass[default,iicol]{sn-jnl}% Default with double column layout

%%%% Standard Packages
%%<additional latex packages if required can be included here>

\usepackage{graphicx}%
\usepackage{multirow}%
\usepackage{amsmath,amssymb,amsfonts}%
\usepackage{amsthm}%
\usepackage{mathrsfs}%
\usepackage[title]{appendix}%
\usepackage{xcolor}%
\usepackage{textcomp}%
\usepackage{manyfoot}%
\usepackage{booktabs}%
\usepackage{algorithm}%
\usepackage{algorithmicx}%
\usepackage{algpseudocode}%
\usepackage{listings}%
\usepackage{natbib}%
\usepackage[utf8]{inputenc}%
\usepackage{pdfpages}%
\usepackage{subfigure}%
\usepackage{array}%
\usepackage{amsmath}%
%%%%
%%%%%=============================================================================%%%%
%%%%  Remarks: This template is provided to aid authors with the preparation
%%%%  of original research articles intended for submission to journals published 
%%%%  by Springer Nature. The guidance has been prepared in partnership with 
%%%%  production teams to conform to Springer Nature technical requirements. 
%%%%  Editorial and presentation requirements differ among journal portfolios and 
%%%%  research disciplines. You may find sections in this template are irrelevant 
%%%%  to your work and are empowered to omit any such section if allowed by the 
%%%%  journal you intend to submit to. The submission guidelines and policies 
%%%%  of the journal take precedence. A detailed User Manual is available in the 
%%%%  template package for technical guidance.
%%%%%=============================================================================%%%%
%\jyear{2021}%
%% as per the requirement new theorem styles can be included as shown below
\theoremstyle{thmstyleone}%
\newtheorem{theorem}{Theorem}%  meant for continuous numbers
%%\newtheorem{theorem}{Theorem}[section]% meant for sectionwise numbers
%% optional argument [theorem] produces theorem numbering sequence instead of independent numbers for Proposition
\newtheorem{proposition}[theorem]{Proposition}% 
%%\newtheorem{proposition}{Proposition}% to get separate numbers for theorem and proposition etc.

\theoremstyle{thmstyletwo}%
\newtheorem{example}{Example}%
\newtheorem{remark}{Remark}%

\theoremstyle{thmstylethree}%
\newtheorem{definition}{Definition}%

\raggedbottom
%%\unnumbered% uncomment this for unnumbered level heads

\begin{document}

\title[Article Title]{Research on WiFi human gesture recognition system based on hybrid model of DSC-SGRU}

%%=============================================================%%
%% Prefix	-> \pfx{Dr}
%% GivenName	-> \fnm{Joergen W.}
%% Particle	-> \spfx{van der} -> surname prefix
%% FamilyName	-> \sur{Ploeg}
%% Suffix	-> \sfx{IV}
%% NatureName	-> \tanm{Poet Laureate} -> Title after name
%% Degrees	-> \dgr{MSc, PhD}
%% \author*[1,2]{\pfx{Dr} \fnm{Joergen W.} \spfx{van der} \sur{Ploeg} \sfx{IV} \tanm{Poet Laureate} 
%%                 \dgr{MSc, PhD}}\email{iauthor@gmail.com}
%%=============================================================%%

\author[1,2]{\fnm{Yulang} \sur{He}}\email{0521221006@tute.edu.cn}

\author*[1,2]{\fnm{Zhibiao} \sur{Zhao}}\email{zhaozhibiao@tute.edu.cn}


\author[1,2]{\fnm{Shanshan} \sur{Li}}\email{lishan.6@163.com}
\author[1,2]{\fnm{Zhen} \sur{Li}}\email{2256562546@qq.com}


\affil*[1]{\orgdiv{School of Automation and Electrical Engineering}, \orgname{Tianjin University of Technology and Education}, \orgaddress{\street{Dagu South Road}, \postcode{300222}, \state{Tianjin}, \country{China}}}

\affil[2]{\orgdiv{Tianjin Key Laboratory of Information Sensing and Intelligent Control}, \orgname{Tianjin University of Technology and Education}, \orgaddress{\street{Dagu South Road}, \postcode{300222}, \state{Tianjin}, \country{China}}}



%%==================================%%
%% sample for unstructured abstract %%
%%==================================%%

\abstract{Wi-Fi wireless sensing technology has become a research hotspot in the field of perception, which can realize the intelligent perception of human activities and the surrounding environment. Aiming at the problem that the existing wireless sensing models have a large number of parameters, which makes it difficult to sense in real-time in scenarios with limited computing power, such as mobile devices, a lightweight feature extraction module based on Depthwise Separable Convolution (DSC) mixed with Stacked Gate Recur-rent Unit (SGRU) is proposed as a recognition model. The model first captures the spatial features of human gestures using DSC and keeps the temporal characteristics of the features unchanged, and then learns the spatio-temporal characteristics of the gestures using the SGRU network. The performance of the model is validated using the open source dataset Widar. The results show that the proposed DSC-SGRU model has only 236.891 K parameters with an accuracy of 77.6\%. Compared with existing gesture recognition models, DSC-SGRU greatly reduces the number of parameters of the model with approximate performance.}

%%================================%%
%% Sample for structured abstract %%
%%================================%%

% \abstract{\textbf{Purpose:} The abstract serves both as a general introduction to the topic and as a brief, non-technical summary of the main results and their implications. The abstract must not include subheadings (unless expressly permitted in the journal's Instructions to Authors), equations or citations. As a guide the abstract should not exceed 200 words. Most journals do not set a hard limit however authors are advised to check the author instructions for the journal they are submitting to.
% 
% \textbf{Methods:} The abstract serves both as a general introduction to the topic and as a brief, non-technical summary of the main results and their implications. The abstract must not include subheadings (unless expressly permitted in the journal's Instructions to Authors), equations or citations. As a guide the abstract should not exceed 200 words. Most journals do not set a hard limit however authors are advised to check the author instructions for the journal they are submitting to.
% 
% \textbf{Results:} The abstract serves both as a general introduction to the topic and as a brief, non-technical summary of the main results and their implications. The abstract must not include subheadings (unless expressly permitted in the journal's Instructions to Authors), equations or citations. As a guide the abstract should not exceed 200 words. Most journals do not set a hard limit however authors are advised to check the author instructions for the journal they are submitting to.
% 
% \textbf{Conclusion:} The abstract serves both as a general introduction to the topic and as a brief, non-technical summary of the main results and their implications. The abstract must not include subheadings (unless expressly permitted in the journal's Instructions to Authors), equations or citations. As a guide the abstract should not exceed 200 words. Most journals do not set a hard limit however authors are advised to check the author instructions for the journal they are submitting to.}

\keywords{Wireless sensing, Channel state information, Deeping learning, Gesture recognition, Cross-domain}

%%\pacs[JEL Classification]{D8, H51}

%%\pacs[MSC Classification]{35A01, 65L10, 65L12, 65L20, 65L70}

\maketitle
\section{Introduction}\label{sec1}
In recent years, with the development of information technology, the number of human-computer interaction scenarios has been increasing\cite{bib1}. Gesture, as an important medium of human-computer interaction, has become one of the hotspots of research in academia and industry\cite{bib2}. Currently, gesture recognition is mainly realized by devices such as sensors\cite{bib3,bib4}, cameras\cite{bib5,bib6} , radar\cite{bib7} and Wi-Fi\cite{bib8}. Among them, sensor-based gesture recognition schemes require users to wear sensors, resulting in limited application scenarios; recognition of gestures based on visual sensors such as cameras is susceptible to light and occlusion, which leads to a significant reduction in recognition performance. In addition, visual sensors can cause problems with user privacy leakage; and although higher accuracy can be achieved using radar devices, they are more expensive to deploy. In contrast, using Wi-Fi has a number of advantages. First, Wi-Fi is widely available, greatly reducing deployment costs. Second, Wi-Fi signals are extremely robust to light and can be used as a stable signal source for activity sensing. In addition, Wi-Fi has been successfully applied to environment sensing\cite{bib9}, occupancy detection\cite{bib10}, activity recognition\cite{bib8}, indoor localization\cite{bib11}, crowd counting\cite{bib12}, human gesture recognition\cite{bib13} and human life signal detection\cite{bib16} etc.\par\noindent Wi-Fi based wireless sensing is mainly based on Received Signal Strength Indicator (RSSI)\cite{bib17} and Channel State Information (CSI)\cite{bib8}. However, current research has found that RSSI signals are affected by multipath effects and are not stable enough to recognize subtle changes in the human body.  In contrast, CSI can provide more fine-grained information by capturing signal strength and phase information that contains Orthogonal Frequency-Division Multiplexing (OFDM) subcarriers as well as signal strength and phase information between each pair of transmitter-receiver antennas\cite{bib18}. Currently, CSI information can be obtained from devices equipped with Intel 5300 NICs\cite{bib19}, Atheros AR9590 NICs\cite{bib18}, Nexmon or OpenFWWF\cite{bib21}.\par\noindent Many traditional machine learning techniques have been widely used for gesture recognition. However, methods based on traditional machine learning usually rely on features designed based on expert knowledge\cite{bib22,bib23,bib24}. In recent years, the development of deep learning technology has contributed to the innovation of gesture recognition technology, which has higher accuracy compared to traditional machine learning methods\cite{bib25}. However, deep learning-based approaches face some challenges. With the continuous development of deep learning theories, the number of model parameters increases, leading to higher training and deployment costs of the models, which are prone to overfitting problems, especially for small sample datasets. In addition, wireless signals are susceptible to different domain factors (including noise, system deployment location, environment, and users, etc.), leading to poor generalization of the sensing model to new environments, i.e., the model lacks cross-domain sensing capability\cite{bib41}.\par\noindent To address the problem of large number of deep learning model parameters, KABIR \cite{bib42} et al. proposed CSI-DeepNet, a lightweight gesture recognition system based on heterogeneous deep learning. The system utilizes Feature Attention Blocks (FAs) and Residual Blocks (RBs) of Deeply Separable Convolutional Neural Networks (DS-Conv) for extracting fine-grained features and reduces the complexity using fewer model parameters. While CSI-DeepNet performs well in collecting CSI information for alphanumeric gestures using the low-power System-on-Chip (SoC) ESP-32, the degradation of model performance during cross-domain recognition is not considered. In order to address the impact of scene transformations on perceptual performance, Xiao et al\cite{bib43} proposed WiTeacher, a cross-domain human activity recognition framework based on Mean Teacher. In this framework, a classification loss based on label smoothing is constructed in order to address the feature bias between the source and target domains. Class-target samples are generated by StyleGAN as input data, and the method of labeling dynamically adjusting the corresponding label values is also designed. To improve the robustness of the model, a regularization term based on the relationship between samples is designed so that the distance between two samples remains constant with and without perturbation. The relationship between samples is used to improve the recognition performance. Experiments show that WiTeacher significantly improves the model performance without requiring any annotation data in the target domain. However, WiTeacher makes the whole system bulky due to the design of tags dynamically adjusting the corresponding tag values and the regularization term based on the relationship between the samples. Zhang\cite{bib19} et al. proposed Widar3.0, a gesture recognition system with some cross-domain sensing capability. The key idea of Widar 3.0 is to derive and extract gesture-domain independent features on the Doppler Frequency Shift (DFS) of CSI. A generic perceptual model DNN trained using these features performs well in experiments. The DNN model mainly consists of Convolutional Neural Network (CNN) and GRU. Both WiTeacher and Widar 3.0 aim to recognize gestures across domains, but neither considers model lightweighting.
\par\noindent In this paper, a hybrid DSC-SGRU network model based on deep learning theory is proposed to build a gesture recognition system. First, the CSI-related theories and how gestures affect the change of CSI are described. Second, the BVP information of the gesture dataset is processed and the DSC-SGRU model is built. The model utilizes a lightweight feature extraction module consisting of DSC to capture the spatial features of gesture CSI information without destroying the temporal order of the features. The extracted features are passed through the SGRU module with temporal processing capability to process the temporal information of the gesture. Finally, the comparison experiments of DSC-SGRU with the traditional GRU, MLP, and other combined models demonstrate that high recognition accuracy is achieved with fewer number of parameters and FLOPs.

\section{Related theories}\label{sec2}
\subsection{Channel status information(CSI)}\label{subsec2}
CSI\cite{bib13} describes the channel characteristics of a communication link, responding to how a wireless signal propagates through the physical environment after diffraction, reflection and scattering. For each communication link, CSI describes the multipath phase shift and amplitude attenuation on each subcarrier. Let $f$ denote the carrier frequency, $X(f,t)$ and $Y(f,t)$ be the frequency domain signals at the transmitter and receiver, respectively. The relationship between them is shown in eq. (1):\begin{equation}Y(f,t)=H(f,t)\times X(f,t)+n(f,t)\end{equation}Where $n(f,t)$ denotes the Gaussian white noise and $H(f,t)$ denotes the CSI measurement at time $t$, which can be estimated from $X(f,t)$ and $Y(f,t)$. Each antenna consists of multiple subcarriers. For example, the Intel 5300 NIC has 30 subcarriers for each antenna. The CSI measurements of the $ith$ subcarrier are expressed as shown in Eq. (2): \begin{equation}H_i=I_i+jK_i=|\left.H_i\right|\exp(j\angle H_i)\end{equation}Where $I_{i}$, $K_{i}$ are the in-phase and quadrature components of the subcarrier $i$, respectively. $\left|H_i\right|$ and $\angle H_{i}$ are the amplitude and phase of subcarrier $i$, respectively. Considering that CSI signals propagate in indoor environments with multiple different paths leading to signal components with different arrival times, amplitudes and phases, these different paths can be caused by reflections, refractions, diffractions, etc. $H_{i}$ can be transformed as shown in Eq. (3):\begin{equation}H_{i}=\sum_{q=1}^{Q}r_{q}\cdot e^{-j2\pi f\tau_{q}}\cdot e^{-j2\pi\Delta ft}\end{equation}Where $Q$ is the number of multipath components. $r_q$ denotes the initial phase offset and attenuation of the $qth$ path. $\tau_{a}$ is the propagation delay on the $qth$ link. The phase shift due to the difference $\Delta f$ between the transmitted carrier frequency and the received carrier frequency is denoted by $e^{-j2\pi\Delta ft}$. 
\par\noindent The multipath effect of gestures is shown in Fig. 1, where the user on the left is drawing the capital letter N in the direction of the red arrow. On the right is an environmental obstacle represented by a sofa. The wireless signals emitted by Wi-Fi passing through the gesture and the environment will be picked up by the Wi-Fi receiver. By filtering out the effect of environment, the mapping relationship between gesture and CSI information can be obtained. It is known that the change of CSI caused by gesture movement is represented by the first major path\cite{bib13}. When the gesture changes from moment 0 to moment $t$, the length of the $qth$ path changes from $d_{q}(0)$ to $d_{q}(t)$. $\lambda$ and ${\boldsymbol{v}}_{q}$ denote the wavelength and constant traveling speed for a short period of time, respectively. It can be obtained as $\lambda=c/f$, $d_{q}(t)=d_{q}(0)+v_{q}t$ and $\tau_{q}=d_{q}(t)/c$, where $c$ denotes the speed of light. The phase shift $e^{-j2\pi f\tau_{q}}$ can be rewritten as $e^{-j2\pi d_q(t)/\lambda}$, indicating that the path length varies with wavelength, the phase of the received subcarrier length will be converted to $2\pi $.\begin{figure}[h]%
	\centering
	\includegraphics[width=0.4\textwidth]{fig2.eps}
	\caption{Human gesture multipath effect map}\label{fig2}
\end{figure}
\par \noindent CSI can be decomposed into dynamic CSI and static CSI, whose measurements are defined as $H_{d}(f,t)$ and $H_{_s}(f,t)$, respectively. Static CSI is generated when the CSI signal passes through a static object such as an environmental obstacle, which is usually regarded as a constant. Dynamic CSI is the sum of the paths that change under the influence of moving objects, and is also the key to distinguish different human activities, and its calculation formula is shown in Eq. (4):\begin{equation}
	H_{d}=\sum_{q\in P_{d}}r_{q}\cdot e^{-j2\pi d_{q}(t)/\lambda}
\end{equation}\par\noindent Where $P_{d}$ denotes the sum of dynamic paths affected by the gesture. The CSI information $H_{i}$ of subcarrier $i$ is then transformed as shown in Eq. (5):\begin{equation}\begin{aligned}
	H_{i}& =(H_{d}+H_{s})\cdot e^{-j2\pi\Delta ft}  \\
	&=\Bigg(\sum_{q\in P_{d}}r_{q}\cdot e^{-j2\pi d_{q}\left(t\right)/\lambda}+H_{s}\Bigg)\cdotp e^{-j2\pi\Delta ft}
\end{aligned}\end{equation}Since the power $H_{i}^{2}$ of the CSI is closely related to the length variation of the multipath, in order to solve the phase interference $e^{-j2\pi\Delta ft}$ , the power $H_{i}^{2}$ of the CSI is used instead of $H_{i}$\cite{bib27}, and $H_{i}$ is shown in Eq. (6).\begin{equation}\begin{aligned}
H_{i}^{2}& =|H_{s}|^{2}+\sum_{q\in P_{d}}|r_{q}|^{2}  \\
&+\sum_{q\in P_d}2|H_s\cdot r_q|\cos\left(\frac{2\pi\nu_qt}{\lambda}+\frac{2\pi d_q(0)}{\lambda}+\phi_{sq}\right) \\
&+\sum_{q,s\in Pd,q \neq e}2\Big|r_{q}\cdot r_{e}\Big|\cos\left(\frac{2\pi\big(\nu_{q}-\nu_{e}\big)t}{\lambda}+\frac{2\pi\big(d_{q}(0)-d_{e}(0)\big)}{\lambda}+\phi_{qe}\right)
\end{aligned}\end{equation}Where $[2\pi d_{q}(0)/\lambda]+\phi_{sq}$ and $[2\pi(d_{q}(0)-d_{e}(0))/\lambda]+\phi_{qe}$ are constant values representing the initial phase offset. The frequency of a sine wave is a function of the rate of change of the path length, and since human activity affects the change of the CSI path length, this gives a mapping relationship between human activity and the frequency of the CSI signal. By extracting the features of the CSI signal frequency change it is possible to react to the change in human activity, which shows that it is feasible to use the change in CSI signal for gesture recognition.
\begin{figure}[h]%
\centering
\includegraphics[width=1\textwidth]{fig1.eps}
\caption{Human gesture CSI information collected using an Intel 5300 NIC. A total of four types of gesture data are selected, the first row is amplitude, the second row is phase, and both amplitude and phase are curves consisting of 30 different colored subcarriers.}\label{fig1}
\end{figure}\par\noindent In Figure 2, these magnitude and phase curves consist of 30 subcarriers of different colors. The phase provides spatial information about the signal propagation and the magnitude provides information about the signal strength. Observation of the data in the figure reveals that the variation in amplitude from one gesture to another is large, while the variation in phase is more subtle. Each gesture has characteristics that distinguish it from the others. In summary, different gestures have different patterns, which provides the possibility of using deep learning models for gesture recognition.
\section{Gesture Recognition Model of DSC-SGRU}\label{sec3}
In order to fully exploit the spatio-temporal features about gestures in CSI information, this paper first uses a lightweight feature extraction module consisting of DSC to extract the spatial features of CSI information and keep the temporal features of CSI information unchanged. Then the extracted spatial features are passed into the SGRU to allow the SGRU network to fully learn the temporal features about gestures in the CSI information, which makes the different network modules play their own specialties to do specific tasks.
\subsection{Data preprocessing}\label{subsec2}
 Utilize the largest known open-source dataset on gestures to date, Widar\cite{bib19}, as the data for the model. And its relevant parameters are shown in Table 1.
 \begin{table}[h]
 	\caption{Table 1 Parameters related to the dataset}\label{tab1}%
 	\begin{tabular}{@{}ll@{}}
 		\toprule
 		Name & Widar \\
 		\midrule
 		Collection Tools & Intel 5300 NIC    \\
 		Gesture Category & 22 \\
 		Gesture name & Push\&Pull, Sweep, Clap, Slide and 22 other activities\\
 		data type & BVP   \\
 		data size & (22,20,20)on behalf of (time, x\_velocity,  y\_velocity)    \\
 		Number of training samples & 34926      \\
 		Number of test samples & 8726 \\
 		\botrule
 	\end{tabular}
 	\footnotetext{The brackets H, V stand for horizontal and vertical respectively, e.g. Draw-N(H) and Draw-N(V) stand for drawing N horizontally and vertically respectively}
 \end{table} Widar collects 22 gestures from multiple volunteers in classroom, hall, and office environments, and validates the cross-domain capability of the model by dividing the gesture data from different domains into a training set and a test set, respectively. The raw CSI information of the gestures was processed into Body-coordinate Velocity Profile (BVP). Gesture changes drive body parts to change, and each gesture has its own unique velocity distribution, which is utilized to distinguish different gestures. The BVP information is extracted from the DFS, which theoretically does not contain information about domains unrelated to the gesture, allowing the model trained with the BVP information to have a certain cross-domain perceptual ability. The DFS mainly describes the effect of the target's motion on the signal frequency, which reflects the target's velocity. effect, which reflects the velocity information of the target. Figure 3 shows the DFS diagram of the Push\&Pull gesture, which contains two major DFS components and some minor components caused by the gesture.\begin{figure}[h]%
 	\centering
 	\includegraphics[width=0.5\textwidth]{fig4.eps}
 	\caption{Push\&Pull partial Doppler spectrograms}\label{fig4}
 \end{figure}
 \par\noindent Fig. 4 DFS plot of CSI information collected at six different locations of the gesture Push\&Pull. \begin{figure}[h]%
 	\centering
 	\includegraphics[width=0.9\textwidth]{fig3.eps}
 	\caption{Doppler spectrograms of the Push\&Pull gesture}\label{fig3}
 \end{figure}It can be observed that the DFS obtained for the same type of gesture is different at different WiFi receivers. This indicates that the DFS information is also domain dependent\cite{bib19}. Therefore the model trained directly using DFS information cannot be generalized to different domains.\par\noindent BVP information describes the power distribution over different velocities of the body parts involved in a gesture. Assuming that the person's orientation is in positive axial coordinates, each type of gesture has its own unique velocity distribution in the body coordinate system regardless of domain variations. The BVP information is approximated from the main velocity components using compressed perception \cite{bib19}. In this paper, BVP is used as the training data for the model. The raw data of BVP information is (20, 20, $t$ ), which denotes the 20-dimensional axial velocity component, the 20-dimensional axial velocity component, and the timestamp t, respectively. Fig. 5 illustrates the extracted BVP information features of the Push\&Pull gesture. Since the Push\&Pull gesture has 14 time frames, there are 14 feature maps. By observing these 14 feature maps, domain-independent BVP information features are found to be highly abstract. The model gains the ability to discriminate the gestures by learning these features.\begin{figure}[htbp]
\centering
\subfigure{
	\begin{minipage}[b]{.11\linewidth}
		\centering
		\includegraphics[scale=0.15]{1.eps}
	\end{minipage}
}
\subfigure{
	\begin{minipage}[b]{.11\linewidth}
		\centering
		\includegraphics[scale=0.15]{2.eps}
	\end{minipage}
}
\subfigure{
	\begin{minipage}[b]{.11\linewidth}
		\centering
		\includegraphics[scale=0.15]{3.eps}
	\end{minipage}
}
\subfigure{
	\begin{minipage}[b]{.11\linewidth}
		\centering
		\includegraphics[scale=0.15]{4.eps}
	\end{minipage}
}
\subfigure{
	\begin{minipage}[b]{.11\linewidth}
		\centering
		\includegraphics[scale=0.15]{5.eps}
	\end{minipage}
}
\subfigure{
	\begin{minipage}[b]{.11\linewidth}
		\centering
		\includegraphics[scale=0.15]{6.eps}
	\end{minipage}
}
\subfigure{
	\begin{minipage}[b]{.11\linewidth}
		\centering
		\includegraphics[scale=0.15]{7.eps}
	\end{minipage}
}
\subfigure{
	\begin{minipage}[b]{.11\linewidth}
		\centering
		\includegraphics[scale=0.15]{8.eps}
	\end{minipage}
}
\subfigure{
	\begin{minipage}[b]{.11\linewidth}
		\centering
		\includegraphics[scale=0.15]{9.eps}
	\end{minipage}
}
\subfigure{
	\begin{minipage}[b]{.11\linewidth}
		\centering
		\includegraphics[scale=0.15]{10.eps}
	\end{minipage}
}
\subfigure{
	\begin{minipage}[b]{.11\linewidth}
		\centering
		\includegraphics[scale=0.15]{11.eps}
	\end{minipage}
}
\subfigure{
	\begin{minipage}[b]{.11\linewidth}
		\centering
		\includegraphics[scale=0.15]{12.eps}
	\end{minipage}
}
\subfigure{
	\begin{minipage}[b]{.11\linewidth}
		\centering
		\includegraphics[scale=0.15]{13.eps}
	\end{minipage}
}
\subfigure{
	\begin{minipage}[b]{.11\linewidth}
		\centering
		\includegraphics[scale=0.15]{14.eps}
	\end{minipage}
}
\caption{Push\&Pull Gesture BVP Heatmap}
\end{figure}\par\noindent In order to facilitate the subsequent training of the model, referring to the data processing of Yang et al\cite{bib20}, the timestamps of the gestures are uniformly expanded to 22 frames, and the BVP data of one gesture is processed as (22, 20, 20), which is subsequently downscaled into a CSV file of (22, 400), and the training and test sets are divided according to the ratio of 8:2, in which the distribution of samples of each category in the training set The number of samples in each category in the training set is shown in Figure 6. It is found that there is an imbalance in the individual gesture samples in the Widar dataset. When training deep learning models, sample imbalance may lead to better prediction of the model for most categories and worse prediction for a few categories. In order to solve this problem, in the experiments of this paper, by calculating the weights between the data of different gesture samples, we let the loss function balance the sample imbalance according to the weights, which makes the model pay more attention to the minority category.
\begin{figure}[h]%
	\centering
	\includegraphics[width=0.35\textwidth]{fig6.eps}
	\caption{Number of individual gesture distributions in the training dataset}\label{fig6}
\end{figure}
\subsection{DSC-SGRU model}\label{subsec2}
The BVP data of the gesture is first fed into the lightweight feature extraction module with DSC as the main component for gesture feature extraction. As shown in Fig. 7, the DSC consists of two parts, depthwise convolution and point convolution (PC), respectively. \begin{figure}[h]%
	\centering
	\includegraphics[width=0.7\textwidth]{DSC.eps}
	\caption{The structure of Depthwise Separable Convolution}\label{fig6}
\end{figure}
The 22 frames of the BVP information are used as channels, i.e. , the convolution operation is performed in the channels while keeping the number of channels constant, which is the depthwise convolution. Then pointwise convolution is performed using N convolution kernels of size , respectively. The information from the previous channel is fused and converted into N channel outputs, which is a DSC operation. The gesture features after two DSCs are then subjected to a maximum pooling operation with a kernel of 2. The pooled features are finally fed into the fully connected layer. The relevant parameters of the network are shown in Table 2.
\begin{table}[h]
	\caption{Detailed parameters of the dataset}\label{tab2}%
	\begin{tabular}{@{}ll@{}}
		\toprule
		parameters & numerical value \\
		\midrule
		learning rate & 0.001    \\
		Convolutional kernel size in DSC & $6\times 6$, $3\times 3$ \\
		Training, Test Batch Size & 1024, 64\\
		Dropout rate & 50\%   \\
		optimizer & Adam   \\
		activation function & ReLu      \\
		\botrule
	\end{tabular}
\end{table}
\par\noindent Compared to traditional convolutional neural network CNN, DSC has less number of parameters \cite{bib44}. The reduction in the number of parameters makes the network faster in both training and inference, which is very beneficial for both real-time model identification and large-scale deployment. In addition, the DSC structure makes it easier to avoid overfitting by having a more abstract feature representation. Therefore, DSC can be better generalized to different datasets and tasks. Since DSC can handle spatial features and channel features separately, this allows the model to better capture correlations between different scales and channels, thus improving the model's representational capabilities.\par\noindent  GRU\cite{bib30} is a variant of Recurrent Neural Networks (RNN) based on two gate vectors, including update gate and reset gate. The reset gate is used to forget useless information, while the update gate focuses on passing necessary and useful information from the previous time step to the current time step. A single-layer GRU is a shallow model with weak representational capabilities. Whereas, Stacked GRU (SGRU) consists of multiple GRU units stacked on top of each other and has a stronger characterization capability. By increasing the depth of the network, SGRU can capture different levels of sequence information and thus has the ability to learn complex sequence patterns. The structure of SGRU is shown in Fig. 8\begin{figure}[h]%
\centering
\includegraphics[width=0.3\textwidth]{fig9.eps}
\caption{SGRU struct}\label{fig9}
\end{figure}\par\noindent The update gate, the reset gate, the history hiding state and the final hiding state of the first GRU unit are shown in equations (7), (8), (9) and (10), respectively: \begin{equation}z_{t}^{i}=\sigma\Big(W_{z}^{i}\cdot\Big[h_{t-1}^{i},h_{t}^{i-1}\Big]\Big)
\end{equation}\begin{equation}r_t^i=\sigma\Big(W_r^i\cdot\Big[h_{t-1}^i,h_t^{i-1}\Big]\Big)
\end{equation}\begin{equation}\tilde{h}_t^i=\tanh\Bigl(W^i\cdot\Bigl[r_t^i\odot h_{t-1}^i,h_t^{i-1}\Bigr]\Bigr)
\end{equation}\begin{equation}h_t^i=z_t^i\odot h_{t-1}^i+\left(1-z_t^i\right)\odot h_t^{i-1}
\end{equation}Where the subscript represents the moment $t$, the SGRU output result is shown in equation 11:\begin{equation}\tilde{y}_{las t}=\sigma(W_{o}^{n}h_{o}^{n}+b_{o}^{n})
\end{equation}Where $\tilde{y}_{last}$ is the predicted label of the $ith$ sample, $W_{o}^{n}$ is the output layer weight of the $n$th GRU unit, $b_{o}^{n}$ is the bias of the $nth$ GRU unit, n=2 due to the use of two GRU units.
\par\noindent The overall flow of this paper is shown in Fig. 9.\begin{figure}[h]%
	\centering\includegraphics[width=0.9\textwidth]{fig10.eps}
	\caption{Overall flowchart of the DSC-SGRU model}\label{fig10}
\end{figure} For the original CSI information, it is smoothed and denoised and the domain independent BVP information is extracted from the DFS. The BVP information goes to the feature extraction module. This module consists of two DSC modules, a maximum pooling layer with kernel 2 and a fully connected layer. Each DSC module consists of a DSC, a ReLU activation function, and a Batch Normalization (BN) layer. The fully connected layer consists of two linear layer modules and a Dropout layer. These modules are used to extract spatial features of the gesture. The extracted features are fed into the SGRU module to learn the temporal information of the gesture. The SGRU structure is designed as a stack of two GRU units, where the hidden layer output of the first GRU unit is used as the input of the second GRU unit. This structure enhances the model's characterization and inference ability for long time-series information. Finally, the recognition results are output through the Softmax layer to achieve the classification and recognition of hand gestures. The SGRU module is able to model the input data at different levels, which enhances the model's representational ability and inference ability for long time series information, and makes it better able to capture the long term dependencies between complex sequence information.
\section{Experimentation and Evaluation}\label{sec4}
\subsection{Experimental environment configuration}\label{subsec2}
The experiments in this paper were built on the Ubuntu 18.04 platform. The platform is equipped with two NVIDIA GeForce RTX 3090 graphics cards with a total of 48G RAM. The network model is built under the Pytorch 1.12.1 deep learning framework with CUDA version 11.6. The Adam optimizer is used, which combines the advantages of both AdaGrad and RMSProp optimizers. It has the advantages that the parameter update is not affected by the gradient scaling transformation, the step size of the update is limited to the approximate range of the initial learning rate and the learning rate is automatically adjusted.
\subsection{loss function}\label{subsec2}
In the choice of loss function, Cross Entropy Loss (CEL) is used in this paper. CEL is a commonly used loss function, which is especially suitable for multi-category classification tasks, and can effectively measure the difference between the model prediction and the real label, which helps to accelerate the convergence process of the model. For the problem of sample imbalance, this paper adopts the method of weighted loss function to solve it. When calculating the loss function, the loss of each sample is multiplied by the weight of its corresponding category. Assuming that the loss of the ith sample is $L_{i}$ , the overall loss is calculated as shown in Eq. (12):
\begin{equation}CEL_ {weighted} =-\frac{1}{n} \sum_{i}^{n}w_{i}\times L_{i}
\end{equation}
 Where $\omega _{i}$ is the weight of the category to which the ith sample belongs. The category weight is set as the inverse of the ratio of the number of samples in the category to the total number. Less frequent categories will be given higher weights to balance the sample imbalance in the training process.
 \subsection{Evaluation indicators}\label{subsec2}
 In this paper, we use a combination of Accuracy (Acc), Precision (Pr), F1 score, Recall(Re), Params, and Floating Point Computations per Second (Flops) to evaluate the performance of the model. Among them, Accuracy reflects the test results of the model, Parameter count indicates the total number of weight parameters that can be learned in the model, and Flops is used to evaluate the computational complexity of the model by evaluating the number of floating-point operations performed per second during the training of the model.
  \subsection{Analysis of experimental results}\label{subsec2}
 \par In this paper, comparative experiments are conducted with DSC-SGRU using LeNet, MLP, RNN, LSTM, GRU, CNN-GRU\cite{bib20}, ResNet18, and ResNet50 etc. as the benchmark models to validate the superiority of the proposed model in this paper.
 \subsubsection{Experimental results}
 MLP consists of two hidden layers and ReLu activation function. LeNet consists of 2-dimensional convolution, ReLu activation function and fully connected layer respectively, where the fully connected layer consists of two linear layers and ReLu activation function. GRU network consists of GRU layer and fully connected layer. The numbers in the confusion matrix diagram indicate specific gestures and their correspondences are shown in Table 3.
 \begin{table}[h]
 	\caption{Specific gestures corresponding to confusion matrix numbers}\label{tab1}%
 	\begin{tabular}{@{}llllllll@{}}
 		\toprule
 		Number & Gesture & Number & Gestures & Number & Gestures & Number & Gestures \\
 		\midrule
 		1 & Draw-3    &7&Draw-O(V)  &13& Draw-Z(H) & 19 & Draw-10 \\
 		2 & Draw-N(H) &8&Draw-9     &14& Draw-1    & 20 & Draw-T(H)\\
 		3 & Draw-R(H) &9&Draw-Z(V)  &15& Draw-2    & 21 & Draw-5\\
 		4 & Draw-4    &10&Sweep     &16& Slide     & 22 & Draw-8 \\
 		5 & Draw-6    &11&Push\&Pull&17& Draw-N(V) &  & \\
 		6 & Clap      &12&Draw-7    &18& Draw-O(H) &  & \\
 		\botrule
 	\end{tabular}
 	\footnotetext{The parentheses H and V stand for horizontal and vertical directions, e.g. Draw-N(H) and Draw-N(V) stand for drawing N horizontally and vertically, respectively.}
 \end{table}
 \par\noindent In order to verify the superiority of this paper's model, the experimental results of this paper's model and the traditional neural network are plotted in a confusion matrix as shown in Fig. 10. The test accuracies of the four models are, in descending order, DSC-SGRU, LeNet, MLP, and GRU. The different complexity of the CSI information of each gesture leads to the varying recognition performances of the same model for different gestures. The LeNet model cannot recognize Draw-7 and Draw-10, and has extremely low recognition results for Draw-3 and Draw-O(V). Draw-7 and Draw-10 cannot be recognized, and has extremely low recognition results for Draw-3 and Draw-O(V). However, DSC-SGRU recognizes Draw-7, Draw-3, and Draw-10 with accuracies above 70\%, and only Draw-O(V) with an accuracy of 20\%. MLP fails to recognize gesture Draw-8, and the accuracies of gestures Draw-9, Draw-Z(V), Draw-2, and Draw-10, respectively, are all did not exceed 50\%. Draw-O(V), Draw-9, Draw-1, Draw-2, Draw-N(V), and Draw-5 respectively, the recognition accuracies do not exceed 50\%. In contrast, the DSC-SGRU recognizes gestures Draw-6 and Draw-7 with more than 70\% accuracy. And the recognition accuracy of gestures Draw-4, Draw-9, Draw-1, Draw-2, Draw-N(V) and Draw-5 is above 80\%.
\begin{figure}[htbp]
	\centering
	\subfigure{
		\begin{minipage}[b]{.3\linewidth}
			\centering
			\includegraphics[scale=0.2]{LeNet2.eps}
		\end{minipage}
	}\hspace{1cm} 
	\subfigure{
		\begin{minipage}[b]{.3\linewidth}
			\centering
			\includegraphics[scale=0.2]{MLP1.eps}
		\end{minipage}
	}
	\centering
	\subfigure{
		\begin{minipage}[b]{.3\linewidth}
			\centering
			\includegraphics[scale=0.2]{GRU2.eps}
		\end{minipage}
	}\hspace{1cm} 
	\centering
	\subfigure{
	\begin{minipage}[b]{.3\linewidth}
		\centering
		\includegraphics[scale=0.2]{example3.eps}
	\end{minipage}
	}
	\caption{Training and Loss diagrams for testing the optimal model for accuracy}
\end{figure}
%加LeNet，MLP
\par \noindent In addition to the comparison experiments with traditional neural networks, this paper also explores the effect of different combinations of network modules on gesture recognition results. The models combined in a stacked structure are SRNN, SLSTM, SGRU and SBiGRU. The models combined with feature extraction modules composed of CNNs and networks with temporal processing capabilities (RNN, LSTM, GRU) are CNN-RNN, CNN-LSTM, CNN-GRU, CNN-BiLSTM, CNN-BiGRU, CNN-SLSTM, CNN-SGRU, CNN-SBiLSTM, CNN-SBiGRU. SBiGRU. The models combined with feature extraction module and timing processing module composed of DSC are DSC-RNN, DSC-LSTM, DSC-GRU, DSC-BiLSTM, DSC-BiGRU, DSC-SLSTM, DSC-SGRU, DSC-SBiLSTM, DSC-SBiGRU. In order to compare the experimental rigor, the rest of the combined model is kept the same as the model in this paper, including the training batch, optimizer, and loss function. For example, when constructing the CNN-SBiLSTM model, the spatial features of the gesture are first extracted using the feature extraction module, which is mainly composed of CNN, while keeping the temporal features of the gesture as unchanged as possible. Then, the features extracted by the feature extraction module enter the SBiLSTM module to learn the temporal information of the features, and the SBiLSTM denotes the stacking of two BiLSTMs, and the output of the hidden layer of the previous BiLSTM network serves as the input of the next BiLSTM network. The CNN-SGRU, CNN-SBiGRU, and CNN-SLSTM are constructed with similar ideas. The results of the three models with the best recognition performance among the models combined by the network modules are shown in Fig. 11, respectively. CNN-SBiLSTM has a 50\% probability of misrecognizing Draw-O(V) as Clap and has a 40\% probability of recognizing Draw-7 as Draw-O(H). CNN-SLSTM has a poor recognition result for Draw-7 and has a 40\% probability of will misidentify Draw-10 as Draw-O(H). Both CNN-SBiLSTM and CNN-SLSTM have misidentified Draw-10 as Draw-O(H). This may be due to the similarity between the gesture of Draw-10 and the gesture of Draw-O in the vertical direction. The overall performance of CNN-SBiGRU on the recognition of various types of gestures is relatively balanced, with no cases of inability to recognize or recognition rate lower than 50\%, but the overall recognition accuracy of the model is lower than that of CNN-SLSTM and CNN-SBiLSTM.
 %加CNN-SBiLSTM，CNN-SBiGRU
\begin{figure}[htbp]
	\centering
	\subfigure{
		\begin{minipage}[b]{.3\linewidth}
			\centering
			\includegraphics[width=\linewidth]{example.eps}
		\end{minipage}
	}\hfill
	\subfigure{
		\begin{minipage}[b]{.3\linewidth}
			\centering
			\includegraphics[width=\linewidth]{example1.eps}
		\end{minipage}
	}\hfill
	\subfigure{
		\begin{minipage}[b]{.3\linewidth}
			\centering
			\includegraphics[width=\linewidth]{example2.eps}
		\end{minipage}
	}\hfill
	\caption{Confusion matrix of classification results for three classes of better models}
\end{figure}
\subsubsection{Performance comparison of different models}\label{subsubsec2} 
 \par The training and loss curves of the four better performing models are shown in Fig. 12, and they are similar. The first 200 Epochs converge rapidly and then level off.
 \begin{figure}[htbp]
 	\centering
 	\subfigure{
 		\begin{minipage}[b]{.3\linewidth}
 			\includegraphics[scale=0.9]{Train1.eps}
 		\end{minipage}
 	}\hspace{1cm} 
 	\subfigure{
 		\begin{minipage}[b]{.3\linewidth}
 			\includegraphics[scale=0.9]{Loss.eps}
 		\end{minipage}
 	}
 	\caption{Training and loss diagrams for four performance-optimal models}
 \end{figure}
\par\noindent In order to reduce the impact of chance bias of a single experiment on the model accuracy, three experiments were conducted to evaluate the system performance of the four models with optimal performance, respectively. The experimental results are shown in Fig. 13.\begin{figure}[h]%
	\centering
	\includegraphics[width=0.5\textwidth]{example4.eps}
	\caption{Boxplots of the model's three training results}\label{fig6}
\end{figure} \par\noindent The test accuracy of all four models is above 77\%. Compared with the remaining three models, DSC-SGRU performs more stably with less fluctuation in the training results. In order to verify the reasonableness of selecting two-layer GRU stacking, the model with four-layer GRU stacking is compared with the model with two-layer GRU stacking in this paper for the comparison experiment. As shown in Fig. 14, DSC-SGRU-2 is the experimental curve using two-layer GRU stacking in this paper, and DSC-SGRU-4 is the experimental curve using four-layer GRU stacking. The left graph in Fig. 14 shows the training curve of the model, and the right graph shows the test curve which is tested every 10 Epochs of training. The training accuracy of the 4-layer GRU is significantly higher when the test accuracy is approximated, but this justifies the selection of the 2-layer GRU.
\begin{figure}[htbp]
	\centering
	\subfigure{
		\begin{minipage}[b]{.3\linewidth}
			\includegraphics[scale=0.9]{Test.eps}
		\end{minipage}
	}\hspace{1cm} % 手动指定水平间距
	\subfigure{
		\begin{minipage}[b]{.3\linewidth}
			\includegraphics[scale=0.9]{Test1.eps}
		\end{minipage}
	}
	\caption{Comparison results of 2-layer GRU and 4-layer GRU stacking}
\end{figure}
\par\noindent The experimental results of the remaining benchmark models are shown in Table 4, where S stands for the use of a stacked (Stacked) structure, which in this paper refers to two network (network refers to RNN, LSTM or GRU) structures in tandem, i.e., the output of the hidden layer of the previous network is used as the input of the latter network, and Bi denotes the bi-directional network structure. For example, BiLSTM denotes bidirectional Long and Short-Term Memory(LSTM) recurrent neural network. Compared to other benchmark models, the model DSC-SGRU has the lowest number of parameters and operations with approximate recognition capability.
\begin{table}[h]
	\caption{Comprehensive comparison of detailed data for each type of model}\label{tab1}%
	\begin{tabular}{@{}llllllll@{}}
		\toprule
		Model Name & & Acc(\%) & Pr(\%) & Re(\%)&F1 Score(\%) & FLOPs & Params\\
		\midrule
		MLP        & & 64.2  & 65.2 & 62.9 & 63.0 & 9.145M   & 9.146M \\
		LeNet      & & 71.5  & 70.3 & 68.8 & 68.8 & 3.370M   & 298.838K\\
		RNN        & & 43.2  & 47.9 & 46.5 & 46.4 & 658.944K & 31.254K \\
		LSTM       & & 59.0  & 67.1 & 65.2 & 65.4 & 2.637M   & 120.726M \\
		BLSTM      & & 57.3  & 58.4 & 55.6 & 56.3 & 5.273M   & 240.022K\\
		GRU        & & 58.2  & 59.6 & 59.4 & 58.8 & 1.980M   & 90.902K  \\
		BGRU       & & 54.6  &59.3  & 57.6 & 57.2 & 3.958M   & 180.374K \\
		SRNN       & & 58.7  & 46.1 & 56.3 & 50.2 & 4.168M   & 190.486K  \\
		SLSTM      & & 73.3  & 72.3 & 71.9 & 71.9 & 16.695M  & 757.654K  \\
		SGRU       & & 70.4  & 61.0 & 64.8 & 62.1 & 12.528M  & 568.598K   \\
		SBGRU      & & 71.3  & 71.8 & 71.2 & 70.9 & 15.558M  & 706.326K  \\
		ResNet18   & & 71.3  & 69.7 & 71.5 & 69.7 & 50.524K  & 11.192M \\
		ResNet50   & & 72.9  & 69.5 & 68.6 & 68.6 & 87.005M  & 23.583M  \\
		ResNet101  & & 67.8  & 69.1 & 67.4 & 67.6 & 163.183M & 42.602M   \\
		CNN-RNN    & & 42.0  & 28.3 & 43.4 & 33.5 & 2.163M   & 42.574K   \\
		CNN-LSTM   & & 76.1  & 76.0 & 74.2 & 74.5 & 3.928M   & 117.374K   \\
		CNN-GRU    & & 73.5  & 71.8 & 69.7 & 69.9 & 3.379M   & 92.542K \\
		CNN-BiLSTM & & 76.2  & 77.3 & 75.8 & 76.2 & 6.040M   & 216.654K  \\
		CNN-BiGRU  & & 73.7  & 76.5 & 74.2 & 74.6 & 5.038M   & 167.038K    \\
		\textbf{CNN-SLSTM}  & & \textbf{78.7}$^{2}$  & \textbf{80.8}$^{1}$ & \textbf{78.9}$^{1}$ & \textbf{79.4}$^{1}$ & \textbf{4.062M}$^{15}$   & \textbf{249.470K}$^{18}$  \\
		CNN-SGRU   & & 76.7  & 76.2 & 74.8 & 75.1 & 5.579M   & 191.614K \\
		\textbf{CNN-SBiLSTM}& & \textbf{78.8}$^{1}$  & \textbf{75.9}$^{11}$ & \textbf{74.4}$^{10}$ & \textbf{74.4}$^{11}$ & \textbf{14.877M}$^{25}$  & \textbf{611.966K}$^{23}$\\
		\textbf{CNN-SBiGRU}& & \textbf{78.5}$^{3}$  & \textbf{73.7}$^{14}$ & \textbf{76.9}$^{3}$ & \textbf{77.1}$^{3}$ & \textbf{5.534M}$^{20}$   & \textbf{365.230K}$^{20}$ \\
		DSC-RNN    & & 54.0  & 63.4 & 64.8 & 62.8 & 2.175M   & 91.051K\\
		DSC-LSTM   & & 74.7  & 77.5 & 75.0 & 75.7 & 2.831M   & 116.187K \\
		DSC-GRU    & & 72.4  & 72.0 & 69.0 & 69.4 & 2.282M   & 91.355K  \\
		DSC-BiLSTM & & 74.1  & 75.2 & 72.9 & 73.5 & 5.039M   & 215.515K \\
		DSC-BiGRU  & & 72.4  & 75.3 & 71.3 & 72.7 & 3.940M   & 165.851K  \\
		DSC-SLSTM  & & 76.5  & 76.9 & 75.8 & 76.0 & 13.779M  & 610.799K \\
		\textbf{DSC-SGRU} & & \textbf{77.6}$^{4}$& \textbf{76.7}$^{7}$ & \textbf{75.1}$^{7}$& \textbf{75.5}$^{8}$ & \textbf{3.407M}$^{11}$& \textbf{236.891K}$^{16}$  \\
		DSC-SBiLSTM& & 73.7  & 77.8 & 77.2 & 77.2 & 14.877M  & 611.966K   \\
		DSC-SBiGRU & & 76.1  & 77.2 & 76.6 & 76.4 & 5.534M   & 365.230K  \\
		\botrule& 
	\end{tabular}
	\footnotetext{The parentheses H and V stand for horizontal and vertical directions, e.g. Draw-N(H) and Draw-N(V) stand for drawing N horizontally and vertically, respectively.For the convenience of calculation, FLOPs are the calculated values when the batch size is 1. Precision, accuracy, recall and F1 score are the calculated values when the batch size is 512.}
\end{table}\par\noindent From the results of the comparison experiments in Table 4, it can be seen. Compared with the traditional models MLP, LeNet, DSC-SGRU has higher recognition results and has a lower number of parameters. Due to the use of feature extraction module, the recognition accuracy of DSC-SGRU is also higher compared to the time series model represented by GRU. DSC-SGRU also maintains a superior recognition performance with a reduced number of parameters compared to the ResNet network represented by the residual structure. In the comparison with the models of CNN-SBiLSTM, CNN-SBiGRU and CNN-SLSTM, which are combinations of network modules, although the accuracy of DSC-SGRU is slightly lower than the remaining three models, the number of parameters and FLOPs of the DSC-SGRU model are the lowest. The recognition of the DSC-SGRU compared to the SGRU is better, even though the number of parameters has been increased a little bit, the results are better, which is a function of the feature extraction module. DSC-SGRU shows better performance with about 18\% increase in the number of parameters compared to CNN-SGRU. In the comparison experiments, it is found that the enhancement of the bidirectional structure of the temporal model on the recognition results is weak compared to the increased number of parameters. For example, DSC-SGRU shows an improvement in the recognition results along with a reduction in the number of parameters by about 54\% compared to DSC-SBiGRU, i.e., the bi-directional structure of the network does not substantially improve the performance of the model while increasing the number of parameters of the model. Among the network models with multiple bi-directional structures, only CNN-SBiGRU outperforms CNN-SGRU in terms of recognition accuracy, but the 1.8\% improvement in accuracy is accompanied by an increase in the number of parameters by about 54\%. \par\noindent The DSC-SGRU model has less number of parameters and FLOPs in the model with approximate recognition accuracy. The reduction in FLOPs and number of parameters means that the model can make decisions in less time under the same hardware environment. This saves computational resources. For resource-limited environments, such as mobile devices, the model reduces computation and storage costs and is more energy efficient. Models with a smaller number of parameters also have a lower risk of overfitting and are better able to generalize to new datasets.
\section{Conclusion}\label{sec5}
\par In this paper, a new gesture recognition algorithm based on CSI information is proposed, which is mainly divided into data processing and DSC-SGRU model recognition two major parts, in the data processing process, the BVP data extracted from CSI information will be synthesized into images. The DSC in the DSC-SGRU model will mainly extract the spatial features of the gesture information, and the extracted spatial features are fed into the SGRU network to learn the spatio-temporal features of the gesture, and the experimental results prove the feasibility of the proposed method. Compared with the existing classification and recognition models, the proposed DSC-SGRU model has lower FLOPs and fewer parameters with approximate accuracy that this saves the training cost, computational cost and storage cost of the model. The trained model is more lightweight, which lays the foundation for real-time sensing in scenarios with limited computing power.

 
\section*{Declarations}
Compliance with Ethical Standards
\begin{itemize}
\item Funding \par This work is supported by The National Natural Science Foundation of China (Grant No.62103301), The Fund of Tianjin Natural Science Grant (No.22JCQNJC01100), The Fund of Scientific Research Project of Tianjin Education Commission (Grant No.2020KJ119) ,Tianjin Research Innovation Project for Postgraduate Students (Grant No.2022SKYZ296). The authors thank all anonymous reviewers for their valuable comments.
\item  Conflict of Interest \par  Yulang He, Zhibiao Zhao, Shanshan and Zhen Li declare that they have no conflict of interest. 

\item Ethical and informed consent for data used\par The data used in this study were obtained from an open-source dataset freely available to the public. The data is used in accordance with the terms and conditions set by the provider of the dataset and there are no ethical issues.\item Authors' contributions:\par 
	\begin{tabular}{|c|c|}
		\hline
		Author & contributions \\
		\hline
		Yulang He & Data preprocessing; funding acquisition; writing–original draft\\
		\hline
		Zhibiao Zhao & Conceptualization; formal analysis; investigation; project administration\\
		\hline
		Shanshan Li & formal analysis; funding acquisition; visualization; writing–original draft \\
		\hline
		Zhen Li & Formal analysis; methodology; validation; \\
		\hline
	\end{tabular}
\item Data availability and access:https://drive.google.com/file/d/14vp4D8W0X2bDLpXnpP-U\_VT9PIGkVf\_4/view?usp=drive\_link
\end{itemize}

\bibliography{sn-bibliography}% common bib file
%% if required, the content of .bbl file can be included here once bbl is generated
%%\input sn-article.bbl


\end{document}
