Efficient Transmission-Based Human Behavior Recognition Algorithm

Abstract

In the contemporary field of wireless sensing, passive sensing leveraging channel state information (CSI) has found widespread applications across diverse scenarios, including behavior recognition, keystroke recognition, breath detection, and indoor localization. To ensure optimal sensing performance, wireless devices often collect a substantial number of CSI packets. However, when these packets need to be transmitted to a server or the cloud for time series analysis, the transmission load on the passive sensing system escalates rapidly, thereby impeding the system’s real-time performance. To address this challenge, we introduce the KCS algorithm, a novel compressed sensing (CS) algorithm grounded in K-Singular Value Decomposition (KSVD). The primary objective of the KCS algorithm is to enable the efficient transmission of CSI data. Departing from the use of a universal sparse matrix in traditional CS, the KCS algorithm constructs an overcomplete sparse matrix. This construction not only substantially bolsters the sparse representation capacity but also fine-tunes the compression performance. By doing so, it ensures the secure and efficient transmission of data. We applied the KCS algorithm to human behavior recognition and prediction. The experimental outcomes reveal that even when the volume of CSI data is reduced by 90%, the system still attains an average accuracy of 90%. This showcases the effectiveness of the KCS algorithm in balancing data compression and recognition performance, offering a promising solution for realistic applications where efficient data transmission and accurate sensing are crucial.

1. Introduction

In recent years, the passive sensing system based on Wi-Fi has emerged as a captivating research area, primarily because it eliminates the need for users to carry additional devices [1]. The movement and occlusion of targets within the sensing environment can cause fluctuations in the received signal strength indicator (RSSI) and channel state information (CSI) of wireless signals [2,3,4,5]. By analyzing and processing feature parameters (such as Doppler frequency shift) extracted from RSSI or CSI, the passive sensing system can be employed for diverse sensing applications. Compared to RSSI, CSI collected by wireless devices can reflect the channel frequency response (CFR) of the communication system. Each CSI sampling value at subcarriers of antennas contains both amplitude and phase information, endowing CSI-based sensing with finer granularity, higher robustness, and stability. Additionally, the integration of orthogonal frequency division multiplexing (OFDM) and multiple-input multiple-output (MIMO) technologies holds the promise of further enhancing the accuracy of wireless sensing [6].

However, a significant challenge in CSI-based passive sensing systems is the large volume of CSI packets that need to be collected by wireless devices. While this large-scale data collection is beneficial for improving sensing performance [7,8,9], it leads to a sharp increase in the data volume when transmitting CSI packets to the server for processing. This, in turn, affects the system’s transmission performance. For instance, in a three-by-three Wi-Fi link operating under the IEEE 802.11n protocol, a single CSI packet for all 64 subcarriers collected by the wireless network card amounts to 1152 bytes, while the maximum transmission unit (MTU) in Ethernet is 1500 bytes [10]. In the scenario shown in Figure 1, multiple access points (APs) need to be deployed to cover the whole environment, so as to achieve passive sensing. At the same time, in order to realize real-time sensing, wireless devices must constantly collect CSI data, which brings enormous transmission burdens to the network.

Therefore, it is imperative to compress the CSI data of the passive sensing system. In the existing research, CSI compression is generally aimed at massive multiple-input multiple-output (MIMO) systems, because untimely CSI feedback or large CSI bandwidth overhead will affect the user scheduling, precoding, and power allocation of the base station and further deteriorate the communication performance [11,12]. To address this issue, researchers have explored different CSI compression methods. Early works in the area of massive MIMO systems focused on reducing the CSI feedback burden. For example, some initial attempts involved simple data reduction techniques such as transmitting only a part of the CSI matrix after singular value decomposition. However, as pointed out by [13], these methods often failed to reconstruct the original CSI accurately, limiting their applicability in practical scenarios.

Subsequently, more sophisticated approaches were proposed. Roh et al. [11] introduced a method using SVD and Givens transform to compress CSI data. This approach, while reducing computational complexity, had limitations in terms of compression ratio and signal fidelity. In an effort to improve compression performance, Chang et al. [14] proposed vector quantization and codebook-based methods. Although these methods could capture fine-grained channel information, they required substantial computational resources for codebook construction.

Conversely, the compression method based on curve fitting has been demonstrated to exhibit effective compression ability [15,16], yet its reconstruction accuracy is suboptimal. The field of compressed sensing (CS) [17] has emerged as a synthesis of the advantages inherent in both of these approaches, thus providing the motivation to compress the CSI of commercial Wi-Fi-based passive sensing systems. The theoretical underpinnings of compressed sensing demonstrate that, under certain conditions, a high-dimensional signal can be sparse in a transform matrix, thereby enabling its projection onto a low-dimensional space by a measurement matrix that is independent of the transform matrix. This reconstruction can be achieved with a high probability from a small number of projections by solving an optimization problem. Furthermore, the accuracy of the reconstructed signal is directly proportional to the sparsity of the original signal in the transform matrix [18]. Despite the sparsity of the CSI matrix of a massive MIMO system in a discrete cosine transform (DCT) matrix [19] or a discrete Fourier transform (DFT) matrix [20], the number of antennas and subcarriers in a commercial Wi-Fi system is significantly lower than that of a massive MIMO system. Consequently, the CSI compression method for massive MIMO systems is not applicable to commercial Wi-Fi systems.

In order to address these issues, a methodology was devised with a view to reducing the amount of CSI data for efficient transmission in commercial Wi-Fi systems. Simultaneously, we utilize commercial Wi-Fi devices to collect experimental data and verify the feasibility of the method on the behavior recognition system. The findings demonstrate that the average accuracy of the behavior recognition system exhibits only a marginal decline when the data volume of CSI is significantly diminished. In short, our main contributions are as follows:

• The proposed KCS algorithm enhances compressed sensing performance by constructing an overcomplete sparse matrix through KSVD dictionary learning, which not only improves sparse representation fidelity but also facilitates efficient data transmission and enables effective temporal feature extraction in signal processing applications;
• A behavior recognition model based on a convolutional neural network (CNN) has been developed in order to ascertain the impact of compressing CSI data on sensing performance. The experimental results demonstrate that the behavior recognition system maintains optimal performance when the volume of CSI data is significantly reduced.

2. Related Work

The advent of the intelligent information age has precipitated rapid development in the field of indoor passive sensing technology. Wi-Fi devices are characterized by their low cost, safety, and reliability, and have been extensively deployed. As a common network transmission device, the CSI data of its physical layer can also be used as the signal source of indoor passive sensing. In order to promote the cloud of passive sensing and reduce the burden of sensing data storage and transmission, it is necessary to compress CSI.

In the existing research, CSI compression algorithms are usually used in massive MIMO systems, while there are few CSI compression algorithms for commercial Wi-Fi systems. In massive MIMO systems, users often need to feed CSI data back to the base station (BS) through the feedback link in real time [21]. However, due to the large number of antennas and subcarriers in massive MIMO systems, it is unrealistic to directly feed back CSI data. Therefore, how to effectively reduce the cost of CSI feedback has always been a concern. After singular value decomposition of the original CSI matrix, the method of transmitting only the V matrix after singular value decomposition [22] can reduce a certain amount of CSI data, but it cannot reconstruct the original CSI signal, so it is not suitable for CSI compression of commercial Wi-Fi in passive sensing systems. Roh et al. [11] utilized SVD and Givens transform to express the matrix as angle values and quantized these values to achieve the purpose of compression. Although the computational complexity of this method is low, the CSI compression performance is not strong. Chang et al. [14] applied vector quantization and codebook-based methods to reduce channel state information feedback, but in order to capture fine-grained channel state information, a large number of codebooks must be constructed, which brings additional computational overhead to the passive sensing system. Jiménez et al. [23] employed Huffman codes to quantify CSI to reduce CSI data volume, but it also has the problem of low CSI compression ability. Luo et al. [24] proposed a CSI prediction model based on the convolutional neural network (CNN) and long short-term memory (LSTM), which can predict the channel state information from the historical data of wireless communication systems. However, the model is only suitable for relatively stable environments, and its prediction ability will be greatly reduced due to rich multipaths and drastic changes in CSI in indoor environments. CSIFit [15] is the first algorithm to compress CSI on commercial Wi-Fi systems, which is verified by collecting real-world CSI data. It constructs an analytical expression with only a few undetermined parameters to fit the CSI curve and employs the Levenberg Marquardt (LM) algorithm to solve the parameters in the analytical expression. Because a small number of parameters can recover the original CSI data, CSIFit has a good compression ability. CSIApx [16] optimizes the analytical expression of CSIFit and obtains the complex coefficient of the analytical expression through the mean square error fitting (MSE Fit) algorithm, which further improves the compression ability of CSI. However, these two algorithms are very vulnerable to noise, which degrades the performance of fitting CSI curves and further affects the performance of passive sensing systems. Han et al. [25] utilized compressed sensing technology to compress the CSI of massive MIMO systems. However, the sparse matrix employed in CSI compression in commercial Wi-Fi systems is not suitable for this purpose, due to the significantly lower number of antennas and subcarriers in such systems compared to that of massive MIMO systems. Furthermore, the sparsity of CSI signals in the sparse matrix is not readily apparent. To address these challenges, we have devised the KCS algorithm, a methodology that optimizes the sparse matrix for compressed sensing. This enhancement of sparsity in the CSI signals within the sparse matrix leads to an improvement in the reconstruction accuracy of CSI signals, thereby facilitating superior sensing outcomes. Notably, this approach not only enhances the transmission rate but also ensures the security of data by facilitating the recovery of the original CSI matrix through the sparse dictionary at the server.

3. Preliminaries

In this section, we introduce basic knowledge about CSI and compressed sensing, which together form the basis of this paper.

3.1. Channel State Information

In wireless communication systems, CSI is often used for power allocation and rate adaptation [26]. The signal propagation delay, amplitude attenuation, and phase offset can be reflected by CSI [27]. Now, some commercial devices can obtain CSI values for passive sensing, such as the Linux 802.11n CSI tool [28], Atheros CSI tool [29], and Nexmon CSI tool [30]. Figure 2 shows the format of CSI packet collected by the wireless network card. At the sampling time t, the dimension of the CSI packet is $N_T\times N_R\times N_C$, where $N_T$ is the number of transmit antennas, $N_R$ is the number of receive antennas, and $N_C$ is the number of subcarriers. Since each CSI value is a complex number, the exponential form is expressed as

$$h_k=\left|h_k\right|e^{j{\theta }_k},$$

(1)

where $|h_k|$ and ${\theta }_k$ represent the amplitude and phase of the kth subcarrier, respectively. It can be seen that CSI contains the amplitude and phase information of signals. In the passive sensing system, the movement of the target will cause a change in the signal propagation direction, and then it affects the signal propagation delay, phase offset, and amplitude attenuation, and these changes will be recorded in the CSI information [31,32], so the CSI information can be used to achieve passive sensing.

3.2. Compressed Sensing

The idea of compression can be described as

$$\mathbf{y}=\mathbf{\Phi }\mathbf{h},$$

(2)

where $\mathbf{h}\in R^{N\times 1}$ denotes the original CSI signal, $\mathbf{\Phi }\in R^{M\times N}$ represents the fixed measurement matrix, and $\mathbf{y}\in R^{M\times 1}$ is the compressed CSI signal. As long as $M<N$, the measurement matrix can compress CSI. However, Formula (2) refers to underdetermined equations and there is no definite solution, so $\mathbf{h}$ would not be reconstructed through $\mathbf{y}$ and $\mathbf{\Phi }$ uniquely. Fortunately, the emergence of compressed sensing [33] solves this problem. Formula (2) can be written as

$$\mathbf{y}=\mathbf{\Phi }\mathbf{\Psi }\mathbf{s},$$

(3)

where $\mathbf{\Phi }$ is the sparse matrix, $\mathbf{s}$ is the sparse coefficient, and $\mathbf{h}=\mathbf{\Phi }\mathbf{s}$. According to compressed sensing theory, if the matrix $\mathbf{s}$ is k-sparse in the sparse domain represented by matrix $\mathbf{\Phi }$ and if the sensing matrix $\mathbf{A}$ satisfies the restricted isometry property (RIP) criterion [34], then the sparse coefficient $\mathbf{s}$ can be uniquely recovered from the sensing matrix $\mathbf{A}$ and the measurement value $\mathbf{y}$ with high probability. Subsequently, by multiplying the recovered sparse coefficient $\mathbf{s}$ with $\mathbf{\Psi }$, the original CSI $\mathbf{h}$ can be reconstructed.

4. System Structure

In this section, we illustrate the overall architecture of CSI compression and reconstruction for behavior recognition, as shown in Figure 3. Initially, Wi-Fi devices in radio frequency (RF) link collect a substantial number of CSI packets. Subsequent to down-sampling, the original CSI is compressed and transmitted to the server, whilst the original CSI is utilized to train a sparse dictionary. Then, following the reception of the sparse dictionary and compressed CSI, the server reconstructs the original CSI by employing the orthogonal matching pursuit (OMP) algorithm. Finally, following a series of preprocessing steps, the CSI data are input into a CNN classifier for behavior recognition.

4.1. Down-Sampling

In the process of CSI packet collection, the packet rate is set to 500 Hz. For behavior recognition, the necessity for high packet rates [35] is not as imperative as in certain passive sensing applications, such as indoor tracking [36]. In order to facilitate future expansion of the application, this section has been included. Simultaneously, an elevated packet rate will increase the time taken for training, which requires down-sampling of CSI packets. In this instance, one CSI packet is extracted for every 20 packets, a process which significantly reduces the quantity of CSI data requiring transmission.

4.2. CSI Data Compression

The dimension of a CSI matrix collected by a Wi-Fi device operating under a MIMO-OFDM mechanism is $N_T\times N_R\times N_C$ (the number of transmit antennas is $N_T$, the number of receive antennas is $N_R$, and the number of subcarriers is $N_C$). In order to facilitate the calculation process, it is necessary to transform a single CSI packet into a column vector. This results in the dimensions of the original CSI signal, denoted by $\mathbf{h}$, being reduced to $N_T{N}_R{N}_C\times 1$ prior to compression. For the measurement matrix $\mathbf{\Phi }$, Candes and Tao proved that the independent and identically distributed (IID) Gaussian random matrix satisfies the RIP criterion and can become a universal measurement matrix in CS [37]; that is, the entries ${\varphi }_{ij}\sim {\displaystyle \frac{1}{\sqrt{M}}}N(0,1)$ in matrix $\mathbf{\Phi }$. The CSI compression process in Figure 3 can be expressed as

$$\mathbf{Y}=\mathbf{\Phi }\mathbf{H}=\mathbf{\Phi }\mathbf{\Psi }\mathbf{S},$$

(4)

where $\mathbf{H}\in R^{N_T{N}_R{N}_C\times L}$ and $\mathbf{Y}\in R^{M\times L}$ represent CSI data before and after compression, respectively. $\mathbf{\Phi }\in R^{M\times N_T{N}_R{N}_C}$ is the measurement matrix, $\mathbf{\Psi }\in R^{N_T{N}_R{N}_C\times N_T{N}_R{N}_C}$ is the sparse matrix, and $\mathbf{S}\in R^{N_T{N}_R{N}_C\times L}$ is the sparse coefficient matrix, respectively. L is the number of CSI packets, and M is the number of measurement values. The data volume of CSI in the behavior recognition system exhibits a positive correlation with the parameter M. Specifically, a reduction in M leads to a corresponding decrease in CSI data volume. The CSI compression can reduce ${\displaystyle \frac{N_T{N}_R{N}_C-M}{N_T{N}_R{N}_C}}$ to $100\%$ the amount of CSI data transmission.

4.3. Dictionary Training

For massive MIMO systems, complete sparse matrices (such as the DFT or DCT matrix) have a good sparse representation effect. However, due to the limited number of antennas and subcarriers in indoor Wi-Fi devices, the CSI signal cannot be well represented by sparse matrices, which poses difficulties in recovering the original CSI signal and affects the performance of passive sensing.

In order to enhance the sparsity of $\mathbf{S}$, we propose the KCS algorithm to generate an overcomplete sparse dictionary $\mathbf{D}$ (the number of columns of a matrix is greater than the number of rows of a matrix) for CSI compression in a behavior recognition system and use it to replace $\mathbf{\Psi }$. The reason that the overcomplete sparse dictionary $\mathbf{D}$ can enhance the sparsity of $\mathbf{S}$ is illustrated in Figure 4. Considering the kth column ${\mathbf{s}}_k$ in $\mathbf{S}$, when $\mathbf{D}=\{{\mathbf{d}}_1$, ${\mathbf{d}}_2$, ${\mathbf{d}}_3\}$ and $\mathbf{h}=s_1{\mathbf{d}}_1+s_2{\mathbf{d}}_2+s_3{\mathbf{d}}_3$, the sparse coefficient ${\mathbf{s}}_k$ is $\{s_1,s_2,s_3\}$.

Now, Formula (5) can be written as

$$\mathbf{Y}=\mathbf{\Phi }\mathbf{H}=\mathbf{\Phi }\mathbf{DS},$$

(5)

where $\mathbf{H}$ represents the original CSI, $\mathbf{S}$ is the sparse coefficient matrix, and $\mathbf{D}$ is the sparse dictionary obtained by the KCS algorithm. Then, the specific generation process of the sparse dictionary $\mathbf{D}$ can be described as the optimization problem

$$\begin{array}{cc}\hfill & {\mathbf{D}}^{*}={\mathrm{argmin}\left|\right|\mathbf{H}-\mathbf{DS}\left|\right|}_{\mathrm{F}}^2\hfill \\ & \mathrm{s}.\mathrm{t}.\sum _{i=1}^L\left|\right|{\mathbf{s}}_i{\left|\right|}_0\le K_s,\hfill \end{array}$$

(6)

where $\mathbf{H}=\{{\mathbf{h}}_1,{\mathbf{h}}_2,\dots ,{\mathbf{h}}_L\}$ refers to the total CSI packets collected by Wi-Fi devices for training the sparse dictionary, $\mathbf{D}=\{{\mathbf{d}}_1,{\mathbf{d}}_2,\dots ,{\mathbf{d}}_{\mu N_T{N}_R{N}_C}\}$ is the sparse dictionary, and $\mathbf{S}=\{{\mathbf{s}}_1,{\mathbf{s}}_2,\dots ,{\mathbf{s}}_L\}$ is the sparse coefficient matrix. ${\mathbf{h}}_i$, ${\mathbf{d}}_i$, and ${\mathbf{s}}_i$ are $N_T{N}_R{N}_C\times 1$ vectors. Here, $\mu$ is an overcomplete factor to ensure that the number of columns of the matrix is greater than the number of rows, $K_s$ is a sparsity constraint for $\mathbf{S}$, and $L\gg \mu N_T{N}_R{N}_C$.

The sparse coefficient matrix and the sparse dictionary alternately need to be solved to obtain the optimal sparse dictionary ${\mathbf{D}}^{*}$. The sparse coefficient matrix ${\mathbf{S}}^{*}$ is initialized by randomly selecting $N_T{N}_R{N}_C$ columns from $\mathbf{H}$, denoted by

$$\begin{array}{cc}\hfill & {\mathbf{S}}^{*}=\mathrm{argmin}\left|\right|\mathbf{H}-{\mathbf{DS}\left|\right|}_{\mathrm{F}}^2\hfill \\ \hfill & \mathrm{s}.\mathrm{t}.\sum _{i=1}^L\left|\right|{\mathbf{s}}_i{\left|\right|}_0\le K_s.\hfill \end{array}$$

(7)

When the ith column ${\mathbf{h}}_i$ in $\mathbf{H}$ is selected, the corresponding ${\mathbf{s}}_i$ is obtained by the orthogonal matching pursuit (OMP) algorithm. The current sparse dictionary $\mathbf{D}$ is updated column by column, which is

$$\begin{array}{cc}\hfill {\mathbf{D}}^{*}& =\mathrm{argmin}\left|\right|\mathbf{H}-\sum _{i=1}^{\mu N_T{N}_R{N}_C}{\mathbf{d}}_i{\mathbf{s}}_T^i{\left|\right|}_{\mathrm{F}}^2\hfill \\ \hfill & =\mathrm{argmin}\left|\right|\mathbf{H}-\sum _{i\ne k}^{\mu N_T{N}_R{N}_C}{\mathbf{d}}_i{\mathbf{s}}_T^i-{\mathbf{d}}_k{\mathbf{s}}_T^k{\left|\right|}_{\mathrm{F}}^2\hfill \\ \hfill & =\mathrm{argmin}\left|\right|{\mathbf{E}}_k-{\mathbf{d}}_k{\mathbf{s}}_T^k{\left|\right|}_{\mathrm{F}}^2,\hfill \end{array}$$

(8)

where ${\mathbf{E}}_k=\mathbf{H}-{\sum }_{i\ne k}^{\mu N_T{N}_R{N}_C}{\mathbf{d}}_i{\mathbf{s}}_T^i$ is the residual, and $\left|\right|·{\left|\right|}_{\mathrm{F}}$ is the Frobenius norm. ${\mathbf{d}}_i$ and ${\mathbf{s}}_T^i$ are the ith column of $\mathbf{D}$ and the ith row of $\mathbf{S}$, respectively. In order to ensure that the sparsity of $\mathbf{S}$ is not destroyed in the update process, it is necessary to select the elements which are not 0 in ${\mathbf{s}}_T^k$ to form a new ${\tilde{\mathbf{s}}}_T^k$, and the corresponding column index set ${\mathbf{c}}_k$ is also recorded. The corresponding column of ${\mathbf{E}}_k$ is selected to form a new ${\tilde{\mathbf{E}}}_k$ based on the column index set ${\mathbf{c}}_k$, and then SVD can be performed, which is

$${\tilde{\mathbf{E}}}_k=\mathbf{U}\Sigma {\mathbf{V}}^{\mathrm{T}}.$$

(9)

The column vector ${\mathbf{u}}_{max}$ in the left singular matrix corresponding to the maximum singular value ${\sigma }_{max}$ is assigned to ${\mathbf{d}}_k$, and the product of the maximum singular value ${\sigma }_{max}$ and the transpose of its corresponding row vector ${\mathbf{v}}_{max}$ in the right singular matrix is assigned to ${\tilde{\mathbf{s}}}_T^k$

$$\begin{array}{cc}\hfill {\mathbf{d}}_k& ={\mathbf{u}}_{max},\hfill \\ \hfill {\tilde{\mathbf{s}}}_T^k& ={\sigma }_{max}{\mathbf{v}}_{max}^{\mathrm{T}},\hfill \end{array}$$

(10)

and then ${\tilde{\mathbf{s}}}_T^k$ is updated to the corresponding position in ${\mathbf{s}}_T^k$ by index ${\mathbf{c}}_k$. By iteratively updating $\mathbf{D}$ and $\mathbf{S}$ until $\left|\right|\mathbf{H}-{\mathbf{DS}\left|\right|}_{\mathrm{F}}^2<\epsilon$, the optimal sparse dictionary ${\mathbf{D}}^{*}$ can be obtained, and its explicit steps are described in Algorithm 1.

Algorithm 1 KCS algorithm.

Input:   CSI data $\mathbf{H}$ Output:   Sparse dictionary $\mathbf{D}$   1: Initialization: ${\mathbf{D}}_0={\mathbf{H}}_0$, ${\mathbf{S}}_0=\mathbf{O}$, $j=0$   2: repeat   3:    for $i=1$ to L do   4:        ${\mathbf{s}}_i=\mathrm{OMP}\left({\mathbf{h}}_i,{\mathbf{D}}_j\right)$   5:    end for   6:    for $k=1$ to $\mu N_T{N}_R{N}_C$ do   7:        ${\mathbf{E}}_k=\mathbf{H}-{\sum }_{m\ne k}^{\mu N_T{N}_R{N}_C}{\mathbf{d}}_m{\mathbf{s}}_T^m$   8:        ${\mathbf{c}}_k=\left\{n\right|1\le n\le L,{\mathbf{s}}_T^k\left(n\right)\ne 0\}$   9:        ${\tilde{\mathbf{E}}}_k={\mathbf{E}}_k\left(:,{\mathbf{c}}_k\right)$ 10:        $[\mathbf{U},\Sigma ,\mathbf{V}]=\mathbf{SVD}\left({\tilde{\mathbf{E}}}_k\right)$ 11:        ${\tilde{\mathbf{s}}}_T^k={\sigma }_{max}{\mathbf{v}}_{max}^T$ 12:        $[{\mathbf{d}}_k,{\mathbf{s}}_T^k\left({\mathbf{c}}_k\right)]=[{\mathbf{u}}_{max},{\tilde{\mathbf{s}}}_T^k]$ 13:    end for 14:    $j=j+1$ 15: until halting condition true; 16: return $\mathbf{D}={\mathbf{D}}_j$

The $\mu N_T{N}_R{N}_C$ columns of ${\mathbf{H}}_0$ are initialized randomly selected from $\mathbf{H}$. $\mathbf{O}$ is a zero matrix whose dimension is $N_T{N}_R{N}_C\times L$, and j is the number of iterations. ${\mathbf{c}}_k$ is the column index set of non-zero elements in ${\mathbf{s}}_T^k$, ${\mathbf{E}}_k(:,{\mathbf{c}}_k)$ represents a new matrix formed by taking out the corresponding columns in ${\mathbf{E}}_k$ according to the column index set ${\mathbf{c}}_k$. Here, the halting condition is $\left|\right|\mathbf{H}-{\mathbf{D}}_j{\mathbf{S}}_j\left|\right|<\epsilon$.

4.4. CSI Data Reconstruction

After the server obtains the compressed CSI $\mathbf{Y}$ and sparse dictionary $\mathbf{D}$, it can recover the original CSI $\mathbf{H}$ using convex optimization algorithms or greedy algorithms. Although convex optimization algorithms have high precision in CSI reconstruction, they have higher time complexity compared with greedy algorithms [38], which will introduce additional time overhead. Therefore, we choose the OMP algorithm, a type of greedy algorithm, to reconstruct the original CSI. Compared with other greedy algorithms, it is relatively simple and has excellent performance [39], which is shown in Algorithm 2.

Algorithm 2 OMP algorithm.

Input:   Sensing matrix $\mathbf{A}=\mathbf{\Phi }\mathbf{D}$, sampled vector $\mathbf{y}$ Output:   Sparse coefficient vector $\mathbf{s}$ 1: Initialization: ${\mathbf{s}}_0=\mathbf{0}$, ${\mathbf{r}}_0=\mathbf{y}$, ${\mathbf{\Lambda }}_0=\mathit{\varphi }$, ${\mathit{\mu }}_0=0$, $k=1$ 2: repeat 3:     ${\mu }_{k-1}=\underset{i=1,2,\dots ,N}{argmax}\left|\langle {\mathbf{a}}_i,{\mathbf{r}}_{k-1}\rangle \right|$ 4:     ${\mathbf{\Lambda }}_k={\mathbf{\Lambda }}_{k-1}\cup {\mu }_{k-1}$ 5:     ${\mathbf{s}}_k={{\mathbf{A}}_{{\mathbf{\Lambda }}_k}}^{†}\mathbf{y}$ 6:     ${\mathbf{r}}_k={\mathbf{y}}_k-{{\mathbf{A}}_{\mathbf{\Lambda }}}_k{\mathbf{s}}_k$ 7:     $k=k+1$ 8: until halting condition true; 9: return $\mathbf{s}={\mathbf{s}}_k$

In Algorithm 2, $\mathbf{y}={\mathbf{h}}_i$ and $\mathbf{A}={\mathbf{D}}_j$ are the inputs to the OMP algorithm. In addition, ${\mathbf{s}}_k$, ${\mathbf{r}}_k$, and ${\mathbf{\Lambda }}_k$ are the sparse coefficient, the residual, and the column index set of the kth iteration, respectively. $〈\mathbf{a},\mathbf{b}〉$, $\left|·\right|$, and ${\left(·\right)}^{†}$ represent the vector inner product, the absolute value, and the matrix pseudo inverse, respectively. For the column index set ${\mathbf{\Lambda }}_k\in \left\{1,\dots ,N\right\}$, ${\mathbf{A}}_{{\mathbf{\Lambda }}_k}$ is the submatrix of $\mathbf{A}$ with indices $i\in {\mathbf{\Lambda }}_k$. Here, the halting condition is $∥{\mathbf{r}}_k∥<\epsilon$. After the sparse coefficient vector $\mathbf{S}$ is obtained, the original CSI can be reconstructed: $\mathbf{H}=\mathbf{DS}$.

Through the construction of an overcomplete sparse matrix via KSVD dictionary learning, the KCS algorithm transforms the original CSI data into a sparse representation. This representation retains the essential features necessary for applications such as human behavior recognition. Crucially, an attacker receiving the compressed data and the associated dictionary would find it extremely challenging to reconstruct the original CSI data. The KCS algorithm decomposes the original CSI matrix into a sparse dictionary and sparse coefficients. Without knowledge of the specific dictionary construction process, the sparsity patterns, and the overall compression algorithm, an unauthorized party cannot reverse-engineer the data back to their original form. This is not a form of encryption in the traditional sense, where data are scrambled using cryptographic keys. Instead, it is an algorithm-based security mechanism that is an added value of the KCS algorithm.

4.5. Behavior Recognition

In order to evaluate the efficacy of the CSI compression and reconstruction algorithm, a CNN has been developed for the purpose of behavior recognition in passive sensing. Prior to the input of the reconstructed CSI data into the CNN classifier [40,41,42], it is necessary to undertake preprocessing.

The CSI collected by the wireless network card includes not only the frequency components caused by the movement of torso and limbs but also components such as electromagnetic pulse and burst noise. Due to the slow movement of the human body, the frequency of CSI which can effectively distinguish human behavior is low. The high-frequency components caused by electromagnetic pulse and burst noise will cover or suppress the low-frequency components we need, so it is necessary to filter the original CSI. In this study, the Butterworth low-pass filter is employed for this purpose, with a passband cutoff frequency of

$${\omega }_c={\displaystyle \frac{2\times \pi \times f}{F_s}}$$

(11)

where f is the highest frequency of the CSI signal and $F_s$ is the sampling frequency. In the experiment, frequency components of the CSI signal above 80 Hz are filtered out. Because the Butterworth low-pass filter’s stopband characteristics may still contain residual noise due to its limited attenuation, a weighted moving average (WMA) is introduced to further deal with it [43]

$${\widehat{csi}}_t={\displaystyle \frac{m\times {\widetilde{csi}}_t+(m-1)\times {\widetilde{csi}}_{t-1}+\dots +1\times {\widetilde{csi}}_{t-(m-1)}}{m+(m-1)+\dots +1}}$$

(12)

where t is the sampling time, m is the size of the sliding window, ${\widetilde{csi}}_i$ is the signal after low-pass filtering, and ${\widehat{csi}}_i$ is the signal after WMA filtering.

In order to reduce the irregular fluctuation in the CSI data and enhance the difference between static-state and motion-state CSI data, a first-order difference is applied to the filtered CSI. After applying the first-order difference, the CSI value tends to be stable when there is no action, and it fluctuates significantly when there is action, which is convenient for subsequent data processing. The CSI before and after preprocessing is shown in Figure 5. It can be seen that the preprocessed signal is more conducive to behavior segmentation.

4.6. Classification

In this section, we propose the construction of a CNN for the purpose of behavior recognition. Prior to the input of data into the CNN, it is necessary to extract the initial and final points of the activity. In this instance, the difference in sliding variance of CSI is utilized to extract the initial and final points of CSI activity. Let the CSI sequence be $\mathbf{CSI}=\{{\widehat{csi}}_1,{\widehat{csi}}_2,\dots ,{\widehat{csi}}_L\}$ and ${\widehat{csi}}_i$ be the ith CSI value in the CSI sequence. The sliding variance can be written as

$${\sigma }_i={\displaystyle \frac{{\sum }_{j=1}^m{({\widehat{csi}}_{i+j-1}-\overline{\widehat{csi}})}^2}{m}}$$

(13)

where m is the size of the sliding window, and $\overline{x}$ is the mean value of CSI in the sliding window, i.e., $\overline{\widehat{csi}}={\displaystyle \frac{1}{m}}{\sum }_{j=1}^m{\widehat{csi}}_j$. Algorithm 3 provides the specific process of obtaining the starting and ending points of activities in a CSI sequence.

Algorithm 3 first uses the SV function to compute sliding variance. After obtaining the variance, the starting and ending points of the activity are recorded through threshold comparison. Once the starting and ending points of all activities are obtained, the activity classification model based on CNN will be adopted to classify activities. Here, the CNN is used to avoid complicated feature extraction steps and has strong recognition and classification ability [44,45,46,47], so it is selected as the classifier of our activity classification model.

Table 1. Network architecture of CNN.

No.	Operation	Configuration
1	Input	100 × 30 × 3 (window × subcarriers × antennas)
2	Dropout	0.3
3	Conv	Kernel = 3 × 3 Stride = 1 × 1 FM = 32 BN IReLU
4	Conv	Kernel = 3 × 3 Stride = 1 × 1 FM = 32 BN IReLU
5	Dropout	0.3
6	Pooling	Kernel = 2 × 2 Stride = 2 × 2 averagePooling
7	Conv	Kernel = 3 × 3 Stride = 4 × 2 FM = 64 BN IReLU
8	Conv	Kernel = 3 × 3 Stride = 4 × 2 FM = 64 BN IReLU
9	Dropout	0.5
10	Pooling	Kernel = 2 × 2 Stride = 2 × 2 averagePooling
11	Conv	Kernel = 3 × 3 Stride = 4 × 2 FM = 128 BN IReLU
12	Conv	Kernel = 3 × 3 Stride = 4 × 2 FM = 128 BN IReLU
13	Fc	10
14	Fc	4

shows the network architecture of CNN, where Conv, BN, FM, Pooling, and IReLU stand for the convolution layer, batch normalization, feature maps, the pooling layer, and the activation function, respectively. The input window size was set to 100, and the number of subcarriers and antennas was determined by the wireless network card.

Algorithm 3 Segment algorithm.

Input:  CSI data, sliding window size m, the number of activities N, and the threshold T Output:   The starting and ending points of activities   1: Initialization: $j=1$, $i=1$, ${\mathbf{P}}_{start}=\mathbf{0}$, ${\mathbf{P}}_{end}=\mathbf{0}$   2: repeat   3:     ${\sigma }_i=\mathbf{SV}(\mathbf{CSI},m)$   4:     if ${\mathbf{P}}_{start}\left(j\right)=0$ then   5:         ${\mathbf{P}}_{start}\left(j\right)=i-10({\sigma }_i>T)$   6:     else   7:         ${\mathbf{P}}_{end}\left(j\right)=i+10({\sigma }_i<T)$   8:     end if   9:     if ${\mathbf{P}}_{start}\left(j\right)\ne 0and{\mathbf{P}}_{end}\left(j\right)\ne 0$ then 10:         $j=j+1$ 11:     end if 12:     $i=i+1$ 13: until $j=N$ 14: return ${\mathbf{P}}_{start}, {\mathbf{P}}_{end}$

5. Implementation

This section presents an evaluation of the performance of the algorithms. The experimental settings and scenarios are introduced first, followed by a comparison of the performance of different algorithms. The impact of the experimental environment is then analyzed.

5.1. Experiment Setup

The ProBox23 mini computer is utilized as both the transmitter and receiver, equipped with an Intel 5300 wireless network card manufacted by Intel from US for the purpose of collecting CSI packets. Concurrently, the RF link system operates in 1 × 3 MIMO mode, with the transmitter being equipped with a single omni-directional antenna and the receiver possessing three such antennas. In order to extract the CSI packets collected by the device, it is also necessary to install the open-source CSI tool. The CSI tool runs on a Linux system (Ubuntu 12.04 LTS) and can set the parameters of the working bandwidth, signal power, packet rate, and working mode between wireless transceiver devices. The specific installation steps can be referenced at http://dhalperi.github.io/linux-80211n-csitool/, accessed on 23 September 2023. In the present experiment, the packet rate was set to 500 packets/s and the transmitter power to 15 dBm. As the indoor environment was full of 2.4 G wireless signals (e.g., Bluetooth, ZigBee), the central frequency was set to 5 GHz to mitigate the risk of packet loss due to signal congestion.

5.2. Experiment Scenarios and Data

The collection of CSI packets was undertaken in two experimental scenarios: one in a meeting room and the other in a classroom. Figure 6 shows the floor plan of the experimental areas in different scenes. During CSI packet collection, the transceivers are hung 1.5 m high and 5 m apart. In each experimental scene, four actions (fall, run, sit, and walk) were recorded from five participants (three males and two females), with each action being recorded 30 times. The experiments were conducted using K-fold cross-validation, where $K=4$, and 66.6% of the collected data were used as the training set and 33.3% as the test set.

5.2.1. Impact of CSI Compression on Different Sparse Dictionaries in CS

We conducted experiments on three different sparse dictionaries: DCT, DFT, and KCS. Figure 7 shows the construction time and average recovery error of the different sparse dictionaries. Although the KCS dictionary increased the calculation time, the KCS dictionary only needed to be transferred once, and the server could reuse the KCS dictionary to recover CSI data in the subsequent sensing process. With the increase in passive sensing time, the overhead of KCS dictionary can be ignored.

5.2.2. Impact of Different Overcomplete Factors

In order to facilitate a comparison of the CSI recovery error of different overcomplete factors, a total of nine configurations from one to five were established, with an interval of 0.5. Figure 8 shows the time overhead and the corresponding average CSI recovery error under different overcomplete factors. As shown in Figure 8, when the overcomplete factor $\mu$ increases from 1 to 1.5, the recovery error of KCS decreases from 0.18 to 0.12; when the overcomplete factor $\mu$ increases from 1.5 to 5, the recovery error of KCS increases to a certain extent. Although the error decreases when $\mu =2.5$ or $\mu =4$, it is still higher than when $\mu =1.5$. In addition, with the increase in the overcomplete factor, the time cost of the algorithm will increase to a certain extent. Therefore, the relatively optimal value of 1.5 is selected as the overcomplete factor in the KCS algorithm.

5.2.3. Impact of Different CSI Compression Algorithms

Here, we compare the recovery error and running time of four different CSI compression algorithms, including KCS, CSIFit, CSIApx, and SVD. As shown in Figure 9, the recovery error of KCS in most cases is very small, with a median of 0.095. Although the running time of the KCS algorithm is higher than that of SVD, our recovery error is less than it in most cases. CSIApx has the lowest time complexity, but its recovery error is the highest. Compared with CSIApx, CSIFit increases the time overhead significantly, but the recovery error is only slightly reduced.

5.2.4. Impact of CSI Compression for Activity Recognition

In order to evaluate the impact of CSI data volume on the performance of a behavior recognition system, the CSI data were input into a CNN classifier both before and after compression. This enabled an assessment to be made of the accuracy of behavior recognition. Figure 10 shows the CSI data volume reduction from 0% (no CSI compression) to 99% (maximum compression of CSI). As shown, the accuracy of the behavior recognition system based on the CNN classifier reaches 94.2% without CSI compression. For the KCS algorithm, when the reduction in CSI data volume is less than 50%, the performance of the system remains almost unchanged. With the further reduction in CSI data volume, the recognition accuracy of the system begins to slow down. Even in the extreme case (99% reduction in CSI data volume), the accuracy of the behavior recognition system still remains higher than 70%. For the other three algorithms, when the CSI data volume begins to decrease, the accuracy of behavior recognition also decreases. In extreme cases, the performance of KCS is about 15.2%, 22.6%, and 33.8% higher than that of CSIFit, SVD, and CSIApx, respectively.

5.2.5. Impact of Different Classification Algorithms

In order to compare the performance of different classification algorithms before and after CSI compression, four common classification algorithms were selected for analysis: CNN, KNN, SVM, and Decision Tree. Figure 11 shows the behavior recognition accuracy of the four algorithms under different CSI data volumes. When the reduction in CSI data volume is from 0% to 70%, the accuracy of any classification algorithm is relatively stable; when the reduction in CSI data volume is from 70% to 90%, the recognition accuracy of algorithm has a slight downward trend. In the most extreme case (99% reduction in CSI data volume), the result shows that the accuracy of any algorithm has a steep drop, which is due to the loss of key information caused by too few measurements. Although the classification algorithm based on CNN has the best performance under different CSI data volumes, the compressed CSI maintains a relatively stable performance under different algorithms; that is, the CSI compression has little impact on the subsequent algorithm classification.

5.2.6. Impact of Different Environment

Figure 12 shows the behavior recognition accuracy under different experimental scenes. The CSI compression algorithm has been demonstrated to function effectively in a variety of scenarios. Furthermore, the efficacy of the algorithm in processing CSI data collected from the meeting room is superior to that collected from the classroom. This is attributable to the fact that the classroom structure is more intricate, the multipath is more abundant, and the collected CSI data contain a greater amount of noise.

6. Conclusions

In recent years, the widespread installation of wireless devices has spurred the development of passive sensing technology, enabling more seamless implicit interactions. This paper focuses on devising a behavior recognition system to reduce the volume of CSI data. Our system can achieve a 70% accuracy in behavior recognition even when the CSI data volume is cut by 99%, effectively alleviating the burden of large-scale CSI data transmission in passive sensing.

The KCS algorithm we proposed serves as a practical solution for data compression and time series analysis in wireless sensing systems. By creating an overcomplete sparse matrix, it improves the sparse representation and compression efficiency. This allows for better data transmission while maintaining the recognition performance of the sensing system, offering useful insights for the application of CSI sensing technology in intelligent environment monitoring, health monitoring, and human–computer interaction.

Nonetheless, our approach has limitations. The KCS algorithm’s performance can be affected by complex wireless environments. High levels of interference or low signal-to-noise ratios may disrupt the construction of the overcomplete sparse matrix, resulting in less ideal compression and a drop-in recognition accuracy. Also, although our system works well for common behaviors, accurately recognizing highly variable and complex realistic behaviors remains a challenge. In terms of deployment, although our solution has potential in many realistic applications, such as smart homes and healthcare monitoring, further research is needed to optimize the algorithms for resource-constrained devices, such as low-power IoT devices. Despite these drawbacks, the KCS algorithm’s unique application of KSVD for CSI data compression and the overall system design offer new ideas for the field. Our work contributes to the ongoing research on CSI-based passive sensing and can potentially lead to further improvements in relevant applications.