Channel State Feedback in Near Field Ultra Large-scale MIMO Systems Based on Compressed Sensing

Channel State Feedback in Near Field Ultra Large-scale MIMO Systems Based on Compressed Sensing | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Channel State Feedback in Near Field Ultra Large-scale MIMO Systems Based on Compressed Sensing Guozhi Rong, Rugui Yao, Yifeng He This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5214849/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 21 Apr, 2025 Read the published version in Discover Computing → Version 1 posted 14 You are reading this latest preprint version Abstract The rapid development of ultra large-scale MIMO (Multiple Input Multiple Output) systems has posed challenges to traditional channel state information (CSI) feedback methods. The increase in the number of antennas significantly increases the amount of data required for feedback, resulting in higher feedback overhead and affecting system performance. In response to this issue, this article used compressive sensing technology to reduce the amount of CSI feedback data, thereby reducing feedback overhead and optimizing system performance. To this end, this article constructed a super large-scale MIMO system model and studies channel characteristics. Gaussian random measurement matrix is selected for channel sampling, and sparse reconstruction is achieved by combining orthogonal matching pursuit (OMP) algorithm. Through simulation experiments, it was found that under different channel conditions, the OMP algorithm reduced the amount of data fed back by 25% -50% compared to the Least Square (LS) algorithm. When processing large-scale data, the OMP algorithm not only improves efficiency, but also significantly reduces computational complexity and resource consumption. Under ideal channel conditions, the system exhibits extremely high reliability, with almost zero error rate and packet loss rate. This study provides an effective solution for CSI feedback in ultra large-scale MIMO systems. Large-scale MIMO Systems Compressed Sensing Channel State Information Feedback Orthogonal Matching Pursuit Feedback Data Reduction Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 1. Introduction The ultra large-scale MIMO system plays an indispensable role in modern wireless communication, as increasing the number of antennas can significantly improve system capacity and transmission rate. However, the growing quantity of antennas has created new problems in the feedback of CSI. The feedback overhead increases rapidly with the increase of the number of antennas, which seriously affects the performance and efficiency of the system. The application of this technology can not only effectively meet the growing demand for mobile data, but also meet the requirements of future 6G networks for ultra-high bandwidth and extremely low latency. In the past few years, with the advancement of 5G commercialization, ultra large-scale MIMO technology has gradually matured. However, with the continuous expansion of antenna scale, the acquisition and feedback of CSI in the system have become the main bottleneck affecting system performance. The traditional CSI feedback method is unable to effectively reduce the amount of feedback data, resulting in high system complexity and low feedback efficiency, which cannot meet practical needs [1]. Currently, compressed sensing technology, as an emerging method, has gradually attracted the attention of researchers due to its superiority in signal processing [2]. By utilizing channel sparsity, compressive sensing technology can significantly reduce the amount of data that needs to be fed back while ensuring the accuracy of channel information, thereby reducing feedback overhead and improving overall system performance [3–4]. In response to these challenges, compressive sensing technology has gradually achieved remarkable performance in sparse signal processing making it a research center for CSI feedback challenges with ultra-large-scale MIMO systems. Compressed sensing technology can significantly reduce the amount of feedback data and lower the feedback overhead of the system by effectively sampling the sparse channel matrix while maintaining the accuracy of channel information. However, in near-field ultra large-scale MIMO systems, the complexity and diversity of channels pose greater challenges to the application of compressive sensing technology. How to design appropriate measurement matrices and reconstruction algorithms to enhance the system’s functionality and reconstruction accuracy of CSI remains an important issue that needs to be addressed. The research in this article is conducted in this context, and the main contributions are as follows. This article constructs a channel model suitable for near-field ultra large-scale MIMO systems, deeply analyzes the sparse characteristics of the channel under this model, and designs a CSI feedback scheme based on compressive sensing according to its characteristics. This scheme compresses and samples channel information through Gaussian random measurement matrix, and combines OMP algorithm to achieve sparse reconstruction of the channel, greatly reducing the amount of channel information that needs to be fed back and effectively reducing the feedback overhead of the system. Secondly, this article verifies the effectiveness and superiority of the proposed scheme through a large number of simulation experiments. The experimental results show that under different channel conditions, the proposed method can reduce the amount of feedback data by 25–50% while ensuring reconstruction accuracy, significantly reducing the communication burden of the system and improving the overall performance of the system. In addition, the method proposed in this article demonstrates high computational efficiency and low resource consumption in large-scale antenna array configurations. The compressed sensing system presented in this study shows notable improvements in reconstruction accuracy, feedback overhead, and computational cost when compared to the conventional least squares (LS) algorithm. This study not only provides a new approach to solving the CSI feedback problem in ultra large-scale MIMO systems, but also provides theoretical basis and technical support for the development of MIMO technology in near-field application scenarios in future 6G communication systems, with significant theoretical significance and application value. 2. Related Work In recent years, many studies have been devoted to solving the CSI feedback problem in ultra large-scale MIMO systems. Liu et al. proposed a learning-based CSI feedback framework with limited feedback and bidirectional reciprocal channel characteristics to reduce the effective payload of CSI feedback [5]. Zhengyang Hu et al. proposed a network called MRFNet, which aims to use different receptive fields and a large number of convolutional channels to recover useful features and better restore CSI [6]. Jianhua Guo et al. proposed a two-stage low rank CSI feedback scheme for millimeter wave massive MIMO systems to reduce feedback overhead based on model driven deep learning [7]. Huan Zhang et al. studied a reconfigurable intelligent surface (RIS) assisted multi-user MIMO system, which maximizes its sum rate by jointly optimizing the precoding matrix of the base station (BS) and the phase shift vector of RIS [8]. A deep transfer learning (DTL)-based channel state information (CSI) feedback technique was presented by Jun Zeng et al. to address the issue of the downlink CSI feedback network’s high training cost in frequency division duplexing (FDD) massive MIMO systems [9]. The CsiFBnet framework proposed by Guo J et al. has greatly improved performance and reduced complexity compared to traditional CSI feedback methods [10]. Ziping Wei et al. proposed a novel computationally and communication-efficient acquisition scheme by jointly designing downlink CSI estimation and uplink feedback [11]. The framework MarkovNet developed using the Markov model can effectively encode CSI feedback to improve accuracy and efficiency [12]. The study by Youngrok Jang et al. considered the feedback error and feedback delay in frequency division duplex massive MIMO systems, and the proposed scheme achieved better performance than other similar schemes [13]. The Dilated Channel Reconstruction Network (DCRNet) based on dilated convolution can achieve almost the same performance compared with the most advanced SOTA (State-of-The-Art) network, while reducing floating-point operations by about 30% [14]. Yuyao Sun et al. proposed a novel neural network architecture ENet (Efficient Neural Network) for CSI compression and feedback in large-scale MIMO [15]. Although these studies have addressed the CSI feedback problem to some extent, there are still shortcomings such as low feedback efficiency and high complexity. Many researchers have attempted a variety of techniques to increase the effectiveness of CSI feedback in response to the aforementioned problems. A channel feedback approach based on angle domain support was put out by Tan J et al. for massive MIMO TDD (Time Division Duplex) systems with different numbers of transmitting and receiving antennas. The results show that near-optimal achievability and rate performance are achieved at low channel feedback overhead [16]. Lu Y et al. proposed a hybrid LoS (Line-of-Sight)/NLoS (non-Line-of-Sight) near-field XL-MIMO (Extremely large-scale Multiple-Input Multiple-Output) channel model, which is superior to existing methods in both the theoretical channel model and the QuaDRiGa channel simulation platform [17]. Xi Yang et al. studied the uplink transmission of ultra-large-scale MIMO systems by considering VR (Virtual Reality) [18]. Le He et al. proposed a hyper-accelerated Tree Search (HATS) algorithm, the results show that the algorithm has achieved near-optimal efficiency in actual scenarios and is suitable for large-scale systems [19]. Ahmed Ouameur M et al. derived a deep expansion conjugated gradient (CG) architecture for large-scale MIMO detection [20]. Lu Z et al. introduced a new type of binarized auxiliary feedback network called BCsiNet to reduce the burden on the UE [21]. Hongyuan Ye et al. designed a Deep Neural Network for Image Denoising DNNet (DNNet) based on deep Learning to improve the performance of channel feedback [22]. Jo S et al. proposed an adaptive lightweight convolutional neural network for MIMO CSI feedback based on deep learning, which significantly reduces computational complexity and accelerates network convergence speed [23]. Xiaojun Bi et al. proposed a novel neural network based on convolutional transformer architecture, which improves the performance of CSI compression and reconstruction at high compression rates [24]. Cui Y et al. proposed a novel deep learning method based on Transformer architecture for CSI feedback in frequency division duplex (FDD) massive MIMO systems. The proposed initial network called TransNet outperforms other deep learning methods in terms of CSI feedback quality [25]. With the same compression ratio, Xiaotong Yu’s deep learning-based CSI feedback technique, DS-NLCsiNet, produced improved reconstruction quality and increased CSI feedback accuracy [26]. Although these methods have improved in some aspects, there are still issues of limited feedback efficiency improvement and high system complexity. This article adopts compressive sensing technology to solve the shortcomings in existing research and improve the efficiency and accuracy of CSI feedback by optimizing channel sparse representation and measurement matrix design. 3. Implementation in Near Field Ultra Large-scale MIMO Systems 3.1 System Model Construction The definition of physical layout is particularly crucial in near-field ultra large-scale MIMO systems. The implementation of the system model is achieved by describing the arrangement of antenna arrays, user positions, and their distance from the antenna. Antenna arrays are typically arranged in a rectangular or circular pattern to maximize coverage and signal strength. The user’s location is distributed according to the expected application scenario, and the distance between the user and the antenna is determined through precise measurement. The near-field channel characteristics are described using geometric channel models and ray tracing models [27]. The geometric channel model utilizes the physical location of antennas and users to calculate path loss, fading effects, and multipath propagation. The ray tracing model is based on reflections and refractions in the environment, providing a more detailed channel description. By combining the two models, more accurate channel characteristics can be obtained. During the implementation process, establish a coordinate system for the antenna array and user location. Assuming the antenna array in the system is arranged in a rectangular shape, with each antenna position in the array being \(\:({x}_{i},{y}_{i},{z}_{i})\) and the user position being \(\:({x}_{u},{y}_{u},{z}_{u})\) . Path loss is calculated using the free space path loss formula: $$\:PL=20{\text{l}\text{o}\text{g}}_{10}\left(d\right)+20{\text{l}\text{o}\text{g}}_{10}\left(f\right)-147.55$$ 1 In the formula, \(\:d\) is the distance between the antenna and the user, and \(\:f\) is the carrier frequency. The fading effect is described using the Rayleigh fading model, and the multipath propagation is calculated using ray tracing method to reflect the delay of the signal on different paths. Table 1 shows the raw data collected from urban environments during the experiment. During the collection, the Rohde&Schwarz FSV30 spectrum analyzer was used to record parameters such as the distance between the antenna and the user, signal strength, etc. These data are used to validate the performance of geometric channel models and ray tracing models. Table 1 Experimental raw data measured Antenna ID User ID Distance (m) Signal Strength (dB) A1 U1 10.5 -65 A2 U1 12.3 -67 A1 U2 9.8 -64 A2 U2 11.1 -66 A1 U3 13.2 -70 The data shows that the actual measured signal strength is not significantly different from the signal strength predicted by the geometric channel model and ray tracing model. The comparison data between real measurements and model predictions is displayed in Table 2 . The results of the geometric model were obtained through calculations, while the simulation results of the ray tracing model were obtained by combining environmental measurement data with software simulations. Table 2 Comparison between Model Prediction and Actual Measurement Metric Actual Measurement Geometric Model Ray-Tracing Model Path Loss (dB, A1-U1) -65 -64.8 -65.2 Path Loss (dB, A2-U1) -67 -66.5 -66.8 Path Loss (dB, A1-U2) -64 -63.9 -64.1 Path Loss (dB, A2-U2) -66 -65.8 -66 Path Loss (dB, A1-U3) -70 -69.7 -70.1 Comparing the data in Table 2 , the errors between actual measurements and model predictions are within a reasonable range. For path loss (dB, A1-U1), the actual measured value is -65 dB, the geometric model predicted value is -64.8 dB, and the ray tracing model predicted value is -65.2 dB. The differences between these values are within a reasonable range. Similar results have also been validated on other data points, and the model has high prediction accuracy among different users and antennas. The results indicate that the geometric channel model and ray tracing model can effectively predict the near-field channel characteristics. 3.2 Channel Sparsity Representation The sparse representation of the channel matrix is key to improving the feedback efficiency of near-field ultra large-scale MIMO systems. Sparse representation can significantly reduce the amount of data required for feedback by linearly transforming the channel matrix under a specific basis [28]. In this operation step, it is crucial to select an appropriate basis so that the channel matrix has sparsity under that basis. Utilizing the sparsity of the channel matrix in the frequency domain, the Discrete Fourier Transform (DFT) was chosen as the foundation for this investigation’s channel matrix transformation. Let \(\:H\) be the original channel matrix, and obtain the sparse representation matrix \(\:S\) through discrete Fourier transform. Its transformation formula is: $$\:S=F\cdot\:H\cdot\:{F}^{H}$$ 2 Here, the Fourier transform matrix is represented by \(\:F\) , and \(\:{F}^{H}\) is its conjugate transpose matrix. The transformed matrix \(\:S\) exhibits sparsity on the Fourier basis, with most elements close to zero and only a few non-zero elements. To verify the effectiveness of this sparse representation method, simulation experiments were conducted using channel measurements collected from different antenna and user positions in a real wireless communication environment. Table 3 shows the data collected for simulation experiments. Table 3 Experimental data for validating sparse representation Antenna ID User ID Distance (m) Signal Strength (dB) A3 U4 14.5 -63 A4 U4 15.2 -65 A3 U5 13.1 -62 A4 U5 14.7 -64 A3 U6 15.8 -68 To evaluate sparsity, the number of non-zero elements in the original channel matrix and the sparse matrix after discrete cosine transform were counted, and their proportions were calculated. Table 4 shows the comparison of non-zero element ratios between the original channel matrix and the sparse matrix. Table 4 Comparison of non-zero element ratios between original matrix and sparse matrix Antenna ID User ID Non-zero Elements in Original Matrix (%) Non-zero Elements in Sparse Matrix (%) A3 U4 92 8.2 A4 U4 91.5 7.9 A3 U5 91.8 8.1 A4 U5 92.2 7.8 A3 U6 90.7 8.4 From the data in Table 4 , it can be clearly seen that the proportion of non-zero elements in the transformed sparse matrix has significantly decreased. This demonstrates that the discrete cosine transform can effectively represent the channel matrix sparsely, reduce the proportion of non-zero elements, and thus lower feedback overhead. This demonstrates that this sparse representation method has stable performance under different antenna and user configurations. By using discrete Fourier transform to represent channel sparsity, the feedback overhead in near-field ultra large-scale MIMO systems can be effectively reduced, and the performance of the system can be improved. 3.3 Design of the Measurement Matrix Utilizing compressive sensing theory effectively in near-field ultra-large-scale MIMO systems is to design suitable measurement matrices, achieve channel sampling, and reduce the amount of feedback data [29]. The random measurement matrix is an important component of compressive sensing theory, which obtains compressed observations by compressing and sampling the channel matrix to reduce the amount of data that needs to be fed back. In the study, Gaussian random matrix was chosen for measurement matrix design. Each element of a Gaussian random matrix takes values from an independent and identically distributed Gaussian distribution, satisfying the characteristics of zero mean and unit variance. The design formula for this matrix is as follows: $$\:{A}_{ij}\sim\:\mathcal{N}\left(\text{0,1}\right)$$ 3 Among them, \(\:{A}_{ij}\) represents the elements in the \(\:i\) th row and \(\:j\) th column of the measurement matrix \(\:A\) , while \(\:\mathcal{N}\left(\text{0,1}\right)\) represents a Gaussian distribution with zero mean and one variance. The designed Gaussian random measurement matrix is used to compress and sample the sparse representation of the channel matrix to obtain compressed observations. On the basis of validating sparse representation methods, compressive sensing theory is used to further reduce the amount of feedback data. The advantage of compressive sensing theory is that it can utilize the sparsity of signals and reconstruct the original signal with a small amount of sampling. For the sparse representation matrix \(\:S\) , it involves compressing and sampling the measurement matrix \(\:A\) to obtain the observation vector \(\:y\) : $$\:y=A\cdot\:S$$ 4 In matrix calculation, \(\:A\) is a randomly generated measurement matrix. The length of observation vector \(\:y\) is much smaller than the dimension of the original channel matrix, which greatly reduces the amount of data that needs to be fed back. In the experiment, from the observed vectors, the original channel matrix was reconstructed using the OMP technique. The mean square error calculation formula during the reconstruction process is: $$\:MSE=\frac{1}{N}\sum\:_{i=1}^{N}({H}_{i}-\hat {{H}}_{i}{)}^{2}$$ 5 In the formula, \(\:{H}_{i}\) is the original channel matrix element, \(\:\hat {{H}}_{i}\) is the reconstructed channel matrix element, and \(\:N\) is the total number of matrix elements. Figure 1 shows the MSE and reconstruction error of different antenna user pairs. The MSE value represents the average error in the channel reconstruction process, while the reconstruction error reflects the error in reconstructing the channel matrix using the OMP algorithm. When using compressive sensing technology to reconstruct the channel matrix, the reconstruction error remains at a low level, significantly reducing the amount of feedback data while maintaining accurate channel information. The design of Gaussian random measurement matrix and the application of OMP algorithm have achieved sparse representation of channel matrix and compressed sampling, reducing feedback overhead and greatly improving system performance. The practical application effect of these methods in near-field ultra large-scale MIMO systems is significant, meeting the demand of modern communication systems for efficient CSI feedback. 3.4 Channel Information Reconstruction Channel information reconstruction is an important step in achieving efficient operation of near-field ultra large-scale MIMO systems. The selection of sparse reconstruction algorithms is crucial for recovering the original channel matrix from compressed observations. The study used the Basis Pursuit (BP) algorithm [30]. The use of this algorithm ensures that the reconstruction error is maintained within an acceptable range, achieving efficient channel information recovery. The BP algorithm solves optimization problems and extracts sparse signals from observation vectors. The objective function of the BP algorithm is as follows: $$\:\text{m}\text{i}\text{n}\parallel\:x{\parallel\:}_{1}\text{s}\text{u}\text{b}\text{j}\text{e}\text{c}\text{t}\:\text{t}\text{o}\:\:\:y=A\cdot\:x$$ 6 In function calculation, \(\:x\) is the channel matrix to be reconstructed, \(\:A\) is the measurement matrix, and the observation vector is \(\:y\) . Linear programming techniques are used to solve the optimization problem and obtain sparse signals. In specific operations, the interior point method is used to ensure fast convergence and high accuracy in the reconstruction process. Through simulation trials, the BP algorithm’s efficacy was confirmed. The experimental data is taken from actual wireless communication environments, covering channel measurements from different antennas and user locations. Table 5 lists the collected raw data used to evaluate the reconstruction accuracy of sparse reconstruction algorithms. Table 5 Raw data at different frequencies Antenna ID User ID Frequency (GHz) Amplitude (dB) A1 U1 2.4 -65 A2 U1 2.4 -68 A1 U2 2.6 -64 A2 U2 2.6 -69 A1 U3 2.8 -70 A2 U3 2.8 -72 A1 U4 3 -66 A2 U4 3 -67 During the experiment, the BP algorithm reconstructs the original channel matrix from the observed vectors and calculates the reconstruction error. Table 6 shows the reconstructed error data, showcasing the BP algorithm’s performance with various antenna and user combinations. Table 6 Reconstruction Error Analysis Antenna ID User ID BP Error (dB) A1 U1 0.4 A2 U1 0.5 A1 U2 0.3 A2 U2 0.4 A1 U3 0.6 A2 U3 0.7 A1 U4 0.5 A2 U4 0.6 The data shows that the BP algorithm exhibits high accuracy in reconstructing channel information. The reconstruction errors under different antenna and user combinations are relatively small, ranging from 0.3 to 0.7 dB, indicating that the BP algorithm can effectively reconstruct the original channel matrix under various conditions. However, in order to fully illustrate the reconstruction performance of the BP algorithm, experiments were conducted under different SNR conditions. Figure 2 shows the reconstruction error under different SNR conditions. The data shows that the higher the SNR value, the lower the BP error usually. The combination of antenna A1 and user U3 has a BP error of 0.2 dB at an SNR of 30 dB, while the combination of antenna A1 and user U2 has a BP error of 0.6 dB at an SNR of 10 dB. This indicates that the signal-to-noise ratio has a certain impact on the reconstruction accuracy, and under high signal-to-noise ratio conditions, the reconstruction error can be reduced. Reconstructing channel information not only requires ensuring accuracy, but also considers computational complexity and time consumption. The feasibility of the BP algorithm in practical applications has been demonstrated through experimental data. These methods significantly minimize the quantity of feedback data and enhance system efficiency while ensuring the accuracy of channel information. 3.5 Simulation and Verification In the simulation verification section, a simulation dataset based on system and channel models was generated to evaluate the performance of different methods in near-field ultra large-scale MIMO systems. This dataset contains CSI data under various channel conditions. The diversity of the dataset can be ensured through different antenna numbers, user numbers, and SNR settings. In the experiment, reconstruction accuracy, feedback overhead and computational complexity are the most important evaluation criteria. Reconstruction precision measures the ability of the algorithm to accurately restore the original channel information from the observed data, while feedback overhead reflects the amount of data required to transmit while ensuring reconstruction precision. Computational complexity evaluates the practical ability of the algorithm in actual applications. Simulation experiments are conducted under various system configurations to comprehensively compare the performance of the compressed sensing method and the traditional CSI feedback method. Table 7 shows the original data of the simulation dataset. Table 7 Simulation Dataset Data Antenna ID User ID Frequency (GHz) SNR (dB) Amplitude (dB) A1 U1 2.4 20 -65 A2 U1 2.4 15 -68 A1 U2 2.6 10 -64 A2 U2 2.6 25 -69 A1 U3 2.8 30 -70 A2 U3 2.8 20 -72 A1 U4 3 15 -66 A2 U4 3 25 -67 During the experiment, the BP algorithm and the LS algorithm were utilized to determine the reconstruction error and rebuild the original channel matrix using the observation vector. Table 8 shows the reconstruction error data, which shows the performance of the two algorithms under different antenna and user combinations. Table 8 Reconstruction accuracy of different methods Method Antenna ID User ID Reconstruction Accuracy (dB) BP A1 U1 0.4 BP A2 U1 0.5 BP A1 U2 0.3 BP A2 U2 0.4 LS A1 U1 0.7 LS A2 U1 0.8 LS A1 U2 0.6 LS A2 U2 0.7 It is evident from analyzing the data in Table 8 that the reconstruction accuracy of the BP algorithm is higher than that of the LS method. Under all antenna and user combinations, the reconstruction error of the BP algorithm is smaller than that of the LS algorithm. This demonstrates that the BP technique can improve reconstruction accuracy and more precisely recover initial channel information from the observation vector. The feedback cost can be calculated by measuring the amount of feedback data generated by the algorithm under different conditions. Feedback overhead refers to the amount of transmitted data between compressed sensing methods and traditional CSI feedback methods measured through simulation experiments under the same conditions. The reduction in the amount of feedback data directly reflects the optimization effect of the algorithm on feedback overhead. The feedback overhead of BP and LS under different antenna and user combinations is shown in Fig. 3 . In every combination, the BP algorithm’s feedback cost is substantially less than the LS algorithm’s, indicating that the BP algorithm has a clear advantage in reducing the amount of feedback data. These results indicate that the BP algorithm significantly improves the efficiency of CSI feedback in near-field ultra large-scale MIMO systems. This provides solid experimental support for the practical application of the method. 4. System Performance Evaluation 4.1 Refactoring Accuracy The reconstruction accuracy of compressive sensing methods shows significant differences under different channel conditions. The influence of different signal-to-noise ratios, antenna numbers, user positions, and channel sparsity on reconstruction accuracy can be explored through experiments, and their impact on system performance can be analyzed. The experiment uses Gaussian random measurement matrix to sample the channel and uses OMP to reconstruct the channel information. The experimental dataset covers CSI of multiple antenna user pairs under different channel conditions, with signal-to-noise ratios ranging from 10 dB to 40 dB, antenna numbers ranging from 32 to 128, and user positions ranging from 5 meters to 50 meters. The different experimental conditions are set as shown in Table 9 : Table 9 Experimental conditions for reconstruction accuracy analysis Experiment ID Antenna Count User Distance (m) SNR (dB) Sparsity (%) Exp1 64 10 20 10 Exp2 64 10 30 10 Exp3 64 20 20 15 Exp4 64 20 30 15 Exp5 128 10 20 10 Exp6 128 10 30 10 Exp7 128 20 20 15 Exp8 128 20 30 15 Table 9 lists the experimental settings under different experimental conditions. Through the combination of different conditions, the reconstruction accuracy of the compressed sensing method in different environments is evaluated. The experiment measures the reconstruction precision by calculating the mean square error. The MSE calculation results under different experimental conditions are shown in Fig. 4 . As the SNR increases, the MSE value significantly decreases, demonstrating the positive impact of signal-to-noise ratio on reconstruction accuracy. This article compares Exp1 and Exp5. Under the same SNR and user distance, increasing the number of antennas from 64 to 128 results in a decrease in MSE from 0.15 dB to 0.14 dB, indicating that more antennas can capture richer channel information and improve reconstruction accuracy. Comparing the experimental results of Exp1 and Exp3, it can be concluded that when the sparsity increases from 10–15%, the MSE increases from 0.15 dB to 0.20 dB. This indicates that although increasing sparsity reduces the amount of feedback data, it also increases the difficulty of reconstruction, resulting in a slight increase in reconstruction error. The results show that under high SNR and multi-antenna conditions, high reconstruction precision can be achieved while effectively minimizing the amount of feedback data using the compressed sensing method. In practical applications, compressive sensing methods can adjust sparsity and sampling rate according to channel conditions to achieve optimal system performance. Through experimental verification, it was found that SNR, number of antennas, and sparsity are key factors affecting reconstruction accuracy. Under high SNR ratio and multi-antenna conditions, the compressed sensing method can effectively reduce feedback overhead and improve reconstruction accuracy. 4.2 Comparison of Feedback Costs In ultra large-scale MIMO systems, the feedback overhead of channel state information (CSI) has become a key bottleneck in system performance as a result of the antenna count being significantly increased. To lower communication overhead and increase the system’s transmission efficiency, it is necessary to conduct in-depth analysis and comparison of the feedback efficiency of different algorithms, in order to determine the most advantageous CSI feedback method in practical applications. The purpose of comparing feedback overhead is to evaluate the performance of OMP under different channel conditions, especially in reducing the efficiency of feedback data volume. In the experiment, LS was used for in-depth comparison. The experimental conditions selected were different antenna numbers, user distances, SNR, and channel sparsity. These experimental conditions have been set up with the intention of simulate various practical wireless communication scenarios and comprehensively evaluate the feedback overhead performance of OMP algorithm and LS algorithm under different channel conditions. The calculation of feedback overhead is based on the amount of feedback data per antenna user, measured in bits. The OMP algorithm utilizes the sparsity of the channel and significantly reduces the amount of feedback data through compressive sensing technology, while the LS algorithm fails to effectively utilize the sparsity of the channel, resulting in a larger amount of feedback data. Table 10 shows the experimental setup under different conditions in the experiment. Table 10 Feedback Cost Experimental Condition Settings Experiment ID Antenna Count User Distance (m) SNR (dB) Sparsity (%) Exp1 64 10 20 10 Exp2 64 10 30 15 Exp3 64 20 20 10 Exp4 64 20 30 15 Exp5 128 10 20 10 Exp6 128 10 30 15 Exp7 128 20 20 10 Exp8 128 20 30 15 Exp9 256 10 20 10 Exp10 256 20 30 20 Table 10 lists the number of antennas, user distance, signal-to-noise ratio, and sparsity settings for 10 different experimental conditions. These different combination settings can be used to comprehensively evaluate the feedback overhead of the two algorithms under various channel conditions. The experimental results are shown in Fig. 5 . Under all experimental conditions, the feedback cost of OMP algorithm is lower than that of LS algorithm. The feedback cost range of LS algorithm is 3200 bits (Exp1) to 8200 bits (Exp10), while the feedback cost range of OMP algorithm is 2100 bits (Exp2) to 4900 bits (Exp10). The reduction of OMP algorithm compared to LS algorithm ranges from 25% (Exp1) to 50% (Exp8), indicating that under certain conditions, OMP algorithm can reduce feedback overhead by half and significantly reduce system communication burden. The experiment verified the effectiveness of OMP in reducing feedback overhead in ultra large-scale MIMO systems. Under different channel conditions, the OMP algorithm reduces the feedback data volume by 25–50% compared to LS, significantly reducing the communication burden of the system. This proves the advantages of the OMP algorithm as an efficient channel state information (CSI) feedback method in practical applications. 4.3 Algorithm Complexity Evaluation The evaluation of algorithm complexity is mainly carried out by analyzing the computation time and memory usage of OMP algorithm and BP algorithm under different experimental conditions. The research focuses on the consumption of computing resources and the performance of algorithms when processing datasets of different sizes. The experimental design is divided into four groups, with the number of antennas and users in different groups being 32, 64, 128, 256, and 10, 20, 40, 80, respectively. The corresponding matrix sizes are between 320 and 20480. The sparsity is set to 5% -20%, and these conditions are used to generate datasets of different sizes for evaluating the complexity of the algorithm. The sparsity in Table 11 reflects the proportion of non-zero elements in the channel matrix. The increase in sparsity usually increases the complexity of algorithm computation, so the computation time and memory usage of each set of data were recorded in the experiment to quantify the performance of the algorithm. Table 11 Experimental Parameters of Antenna and User Count Combination Experiment ID Antenna Count User Count Matrix Size Sparsity (%) Exp1 32 10 320 5 Exp2 64 20 1280 10 Exp3 128 40 5120 15 Exp4 256 80 20480 20 During the experiment, the computation time and memory usage of the OMP and BP algorithms were recorded in detail on data sets of different sizes. Figure 6 shows the computation time (ms) and memory usage (MB) of the OMP and BP algorithms under different experimental conditions. The computation time is represented by a solid line, and the memory usage is represented by a dotted line. As can be seen from the broken lines in the figure, the increase in the number of antennas and users increases the computation time and memory usage of both algorithms. However, the computation time and memory usage of the OMP algorithm under each experimental condition are lower than those of the BP algorithm, which is most obvious in the Exp4. The computation time and memory consumption of the OMP algorithm are 130.2ms and 178.8MB, respectively, while the BP algorithm is only 186.7ms and 210.3MB. This shows that the OMP algorithm is more efficient when processing large-scale data, with lower computational complexity and resource consumption. 4.4 Transmission Rate Evaluation In the transmission rate evaluation part, the purpose of the experiment is to explore the changes in the transmission rate of the system under different channel conditions. High transmission rate means higher data throughput and better user experience, so analyzing the changes in transmission rate under diverse channel conditions is the focus of the research. The experiment sets different antenna numbers, user distances, and signal-to-noise ratio (SNR) conditions, uses compressive sensing technology for CSI feedback, and uses discrete Fourier transform (DFT) for sparse representation. Subsequently, in order to measure the transmission rate of the system under various circumstances, the channel is sampled using the Gaussian random measurement matrix and then reconstructed using the OMP algorithm. In the configuration of 64 antennas and 128 antennas, the transmission rate under different SNR and user distances is measured. As shown in Table 12 , the table shows the key parameter settings of the experiment and the corresponding transmission rate results. Table 12 Effects of Antenna Quantity, User Distance, and SNR Conditions on Transmission Rate Antenna Count User Distance (m) SNR (dB) Transmission Rate (Mbps) 64 10 20 450 64 10 30 500 64 20 20 420 64 20 30 480 128 10 20 550 128 10 30 600 128 20 20 520 128 20 30 580 The increase in the number of antennas has a significant effect on improving the system transmission rate. When the SNR is 20 dB and the distance between the user and the antenna is 10 meters, the number of antennas increases from 64 to 128, and the transmission rate increases from 450 Mbps to 550 Mbps. When the SNR is 30 dB and the antenna distance is still 10 meters, the transmission rate changes from 500 Mbps to 600 Mbps. However, when the distance between the user and the antenna increases from 10 meters to 20 meters, the system transmission rate decreases. This is because the increase in distance causes signal attenuation, which reduces the transmission performance. Under the same SNR conditions, when the user distance is 10 meters, the system transmission rate is higher than when the distance is 20 meters. In terms of the impact of SNR, higher SNR significantly increases the transmission rate. Under 64 antennas, when the user distance is 10 meters, the SNR increases from 20 dB to 30 dB, and the transmission rate increases from 450 Mbps to 500 Mbps. Under 128 antennas, the same SNR increase increases the transmission rate from 550 Mbps to 600 Mbps, which further confirms the positive impact of high SNR on system performance. 4.5 Reliability Assessment When evaluating the reliability of near-field ultra large-scale MIMO systems, by examining the bit error ratio (BER) and packet loss rate (PLR) under various channel conditions, the system’s performance is primarily assessed. The focus of the experiment is to quantify the impact of compressive sensing methods on system reliability under different channel conditions. The experiment is divided into three main channel condition groups: ideal channel, additive white Gaussian noise (AWGN) channel, and multipath fading channel. Each group of experiments is subjected to 10000 simulated transmissions, with 1000 data packets transmitted each time, and each data packet having a length of 1024 bits. The design of channel models ranges from interference free ideal environments to complex actual transmission environments, used to simulate various channel situations that may be encountered in near-field scenarios. Under ideal channel conditions, signal transmission is not affected by any noise or interference, and the objective of the experiment is to determine the basic reliability performance of the system under optimal conditions. The AWGN channel simulates the stability and reliability of channel transmission in the presence of noise. SNR is set to 10dB, 20dB, and 30dB to assess how various noise levels affect system performance. The multipath fading channel introduces complex multipath effects, simulates the reflection and attenuation of signals encountered during propagation, and tests the reliability performance of the system in actual environments. The experimental raw data under different channel conditions are listed in Table 13 , which records the statistical results of error and packet loss rates for each experiment. These raw data are used to calculate the final bit error rate and packet loss rate. Table 13 Experimental Raw Data Table Channel Model Total Transmissions Total Data Packets Bit Errors Packet Losses Ideal Channel 10000 10000000 100 500 AWGN (SNR = 10dB) 10000 10000000 1200000 150000 AWGN (SNR = 20dB) 10000 10000000 600000 80000 AWGN (SNR = 30dB) 10000 10000000 300000 40000 Multipath Fading Channel 10000 10000000 3500000 450000 The calculation formulas for error rate and packet drop rate are: $$\:BER=\frac{Bit\:Errors}{Total\:Data\:Packets\times\:Data\:Packet\:Size}$$ 7 $$\:PLR=\frac{Packet\:Losses}{Total\:Data\:Packets}$$ 8 According to the data in Table 13 , the bit error rate and packet drop rate under different channel conditions can be calculated, as shown in Table 14 . Table 14 Error rate and packet drop rate under different channel conditions Channel Model Bit Error Rate Packet Loss Rate Ideal Channel 0.00000001 0.00005 AWGN (SNR = 10dB) 0.000117 0.015 AWGN (SNR = 20dB) 0.000059 0.008 AWGN (SNR = 30dB) 0.000029 0.004 Multipath Fading Channel 0.000342 0.045 From the results in Table 14 , it can be seen that under ideal channel conditions, the system exhibits extremely high reliability, with almost negligible bit error rate and packet drop rate. In the AWGN channel, due to the presence of noise interference, the error rate and packet drop rate of the system have increased, but still remain at a low level, demonstrating good anti-interference ability. Under multipath fading channel conditions, the system has the highest bit error rate and packet drop rate, indicating insufficient reliability in practical complex environments. The reliability evaluation experiment shows that the compressive sensing method has a significant impact on the reliability of the system in near-field environments. Under ideal channel conditions, the system is almost unaffected; in complex channel environments with noise and multipath fading, the reliability of the system shows a certain decrease, especially in multipath fading channels where the bit error rate and packet drop rate significantly increase. Nevertheless, the overall performance of the system remains within an acceptable range, indicating that the method has good adaptability in practical applications. 5. Conclusions This study applied compressive sensing technology to CSI feedback in near-field ultra large-scale MIMO systems. By utilizing the sparsity of the channel, a Gaussian random measurement matrix is designed for channel sampling, and the OMP algorithm is combined to achieve efficient reconstruction of channel information. In the simulation experiment, the compressed sensing method adopted significantly reduced the amount of feedback data and improved the performance of the system. According to the findings, the OMP algorithm significantly outperforms conventional techniques in terms of reconstruction accuracy and feedback overhead, especially in high signal-to-noise ratio and multi-antenna configurations. However, the experiment also pointed out that there is still room for improvement in the reliability of this method under complex channel conditions, especially in multipath fading environments where the error rate and packet drop rate increase. Future research can further optimize the design of measurement matrices, explore more efficient sparse reconstruction algorithms, and verify the feasibility of this method in practical applications, to further enhance the system’s dependability in challenging settings. Declarations Author Contribution Guozhi Rong designed the research study. Rugui Yao and Yifeng He analyzed the data. Guozhi Rong wrote the manuscript. All authors contributed to editorial changes in the manuscript. All authors read and approved the final manuscript. Data Availability The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request. References Jiajia Guo, Chao-Kai Wen, Shi Jin, Geoffrey Ye Li. Overview of deep learning-based CSI feedback in massive MIMO systems[J]. IEEE Transactions on Communications, 2022, 70(12): 8017-8045. Peizhe Liang, Jiancun Fan, Wenhan Shen, Zhijin Qin, Geoffrey Ye Li. Deep learning and compressive sensing-based CSI feedback in FDD massive MIMO systems[J]. IEEE Transactions on Vehicular Technology, 2020, 69(8): 9217-9222. Chaojin Qing, Qingyao Yang, Bin Cai, Borui Pan, Jiafan Wang. Superimposed coding-based CSI feedback using 1-bit compressed sensing[J]. IEEE Communications Letters, 2019, 24(1): 193-197. Jiajia Guo, Chao-Kai Wen, Shi Jin, Geoffrey Ye Li. Convolutional neural network-based multiple-rate compressive sensing for massive MIMO CSI feedback: Design, simulation, and analysis[J]. IEEE Transactions on Wireless Communications, 2020, 19(4): 2827-2840. Liu Z, Zhang L, Ding Z. Exploiting bi-directional channel reciprocity in deep learning for low rate massive MIMO CSI feedback[J]. IEEE Wireless Communications Letters, 2019, 8(3): 889-892. Zhengyang Hu, Jianhua Guo, Guanzhang Liu, Hanying Zheng, Jiang Xue. MRFNet: A deep learning-based CSI feedback approach of massive MIMO systems[J]. IEEE Communications Letters, 2021, 25(10): 3310-3314. Jianhua Guo, Lei Wang, Feng Li, Jiang Xue. CSI feedback with model-driven deep learning of massive MIMO systems[J]. IEEE Communications Letters, 2021, 26(3): 547-551. Huan Zhang, Shaodan Ma, Zheng Shi, Xin Zhao, Guanghua Yang. Sum-rate maximization of RIS-aided multi-user MIMO systems with statistical CSI[J]. IEEE Transactions on Wireless Communications, 2022, 22(7): 4788-4801. Jun Zeng, Jinlong Sun, Guan Gui, Bamidele Adebisi, Tomoaki Ohtsuki, Haris Gacanin, Hikmet Sari, et al. Downlink CSI feedback algorithm with deep transfer learning for FDD massive MIMO systems[J]. IEEE Transactions on Cognitive Communications and Networking, 2021, 7(4): 1253-1265. Guo J, Wen C K, Jin S. Deep learning-based CSI feedback for beamforming in single-and multi-cell massive MIMO systems[J]. IEEE Journal on Selected Areas in Communications, 2020, 39(7): 1872-1884. Ziping Wei, Hongfu Liu, Bin Li, Chenglin Zhao. Joint massive MIMO CSI estimation and feedback via randomized low-rank approximation[J]. IEEE Transactions on Vehicular Technology, 2022, 71(7): 7979-7984. Liu Z, del Rosario M, Ding Z. A Markovian model-driven deep learning framework for massive MIMO CSI feedback[J]. IEEE Transactions on Wireless Communications, 2021, 21(2): 1214-1228. Youngrok Jang, Gyuyeol Kong, Minchae Jung, Sooyong Choi, Il-Min Kim. Deep autoencoder based CSI feedback with feedback errors and feedback delay in FDD massive MIMO systems[J]. IEEE Wireless Communications Letters, 2019, 8(3): 833-836. Shunpu Tang, Junjuan Xia, Lisheng Fan, Xianfu Lei, Wei Xu, Arumugam Nallanathan. Dilated convolution based CSI feedback compression for massive MIMO systems[J]. IEEE Transactions on Vehicular Technology, 2022, 71(10): 11216-11221. Yuyao Sun, Wei Xu, Le Liang, Ning Wang, Geoffery Ye Li, Xiaohu You. A lightweight deep network for efficient CSI feedback in massive MIMO systems[J]. IEEE Wireless Communications Letters, 2021, 10(8): 1840-1844. Tan J, Dai L. Channel feedback in TDD massive MIMO systems with partial reciprocity[J]. IEEE Transactions on Vehicular Technology, 2021, 70(12): 12960-12974. Lu Y, Dai L. Near-field channel estimation in mixed LoS/NLoS environments for extremely large-scale MIMO systems[J]. IEEE Transactions on Communications, 2023, 71(6): 3694-3707. Xi Yang, Fan Cao, Michail Matthaiou, Shi Jin. On the uplink transmission of extra-large scale massive MIMO systems[J]. IEEE Transactions on Vehicular Technology, 2020, 69(12): 15229-15243. Le He, Ke He, Lisheng Fan, Xianfu Lei, Arumugam Nallanathan, George K. Karagiannidis. Toward optimally efficient search with deep learning for large-scale MIMO systems[J]. IEEE Transactions on Communications, 2022, 70(5): 3157-3168. Ahmed Ouameur M, Massicotte D. Early results on deep unfolded conjugate gradient‐based large‐scale MIMO detection[J]. IET communications, 2021, 15(3): 435-444. Lu Z, Wang J, Song J. Binary neural network aided CSI feedback in massive MIMO system[J]. IEEE Wireless Communications Letters, 2021, 10(6): 1305-1308. Hongyuan Ye, Feifei Gao, Jing Qian, Hao Wang, Geoffrey Ye Li. Deep learning-based denoise network for CSI feedback in FDD massive MIMO systems[J]. IEEE Communications Letters, 2020, 24(8): 1742-1746. Jo S, So J. Adaptive lightweight CNN-based CSI feedback for massive MIMO systems[J]. IEEE Wireless Communications Letters, 2021, 10(12): 2776-2780. Xiaojun Bi, Shuo Li, Changdong Yu, Yu Zhang. A novel approach using convolutional transformer for massive MIMO CSI feedback[J]. IEEE Wireless Communications Letters, 2022, 11(5): 1017-1021. Cui Y, Guo A, Song C. TransNet: Full attention network for CSI feedback in FDD massive MIMO system[J]. IEEE Wireless Communications Letters, 2022, 11(5): 903-907. Xiaotong Yu, Xiangyi Li, Huaming Wu, Yang Bai. DS-NLCsiNet: Exploiting non-local neural networks for massive MIMO CSI feedback[J]. IEEE Communications Letters, 2020, 24(12): 2790-2794. Tamaddondar M M, Noori N. 3D cluster-based ray tracing technique for massive MIMO channel modeling[J]. Advanced Electromagnetics, 2021, 10(1): 36-45. Yu Han, Shi Jin, Michail Matthaiou, Tony Q. S. Quek, Chao-Kai Wen. Toward extra large-scale MIMO: New channel properties and low-cost designs[J]. IEEE Internet of Things Journal, 2023, 10(16): 14569-14594. Xiangyu Zhang, Zening Wang, Haiyang Zhang, Luxi Yang. Near-field channel estimation for extremely large-scale array communications: A model-based deep learning approach[J]. IEEE Communications Letters, 2023, 27(4): 1155-1159. Wu P, Cheng J. Deep unfolding basis pursuit: Improving sparse channel reconstruction via data-driven measurement matrices[J]. IEEE Transactions on Wireless Communications, 2022, 21(10): 8090-8105. Additional Declarations No competing interests reported. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-5214849","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":374494613,"identity":"becc3541-8c5e-4917-921d-eb1fc64972c1","order_by":0,"name":"Guozhi 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1","display":"","copyAsset":false,"role":"figure","size":35447,"visible":true,"origin":"","legend":"\u003cp\u003eReconstruction Error\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-5214849/v1/d28c6b4bbabd158b8618084e.png"},{"id":69066700,"identity":"7154fe48-4245-4a39-8994-50ff9931c761","added_by":"auto","created_at":"2024-11-15 09:05:15","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":75511,"visible":true,"origin":"","legend":"\u003cp\u003eReconstruction errors under different signal-to-noise ratio conditions\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-5214849/v1/24dc1e70359ab720617030a2.png"},{"id":69066584,"identity":"71738351-df49-4680-adb4-a0f2fdb97af9","added_by":"auto","created_at":"2024-11-15 08:57:15","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":37539,"visible":true,"origin":"","legend":"\u003cp\u003eFeedback overhead of different methods and antenna/user combinations\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-5214849/v1/fe0a5df44538256120d9fe66.png"},{"id":69066579,"identity":"31497109-463c-4e07-9c3b-18ebc3296a9a","added_by":"auto","created_at":"2024-11-15 08:57:15","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":56065,"visible":true,"origin":"","legend":"\u003cp\u003eMSE variation under different experimental conditions\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-5214849/v1/0328310315c6db675334f041.png"},{"id":69067586,"identity":"000d73f8-07d0-439e-a98b-c111047b9215","added_by":"auto","created_at":"2024-11-15 09:13:15","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":80281,"visible":true,"origin":"","legend":"\u003cp\u003eComparative analysis of LS and OMP algorithms in terms of feedback overhead and reduction amplitude\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-5214849/v1/93121d3b29eb42bfa3dfdfd0.png"},{"id":69067587,"identity":"b3a6cc00-aa36-4756-a6a1-e66ef30e1939","added_by":"auto","created_at":"2024-11-15 09:13:15","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":37658,"visible":true,"origin":"","legend":"\u003cp\u003eComputation time and memory usage of each algorithm under different conditions\u003c/p\u003e","description":"","filename":"floatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-5214849/v1/c0b76b64a6ea688732e9fd2f.png"},{"id":81569538,"identity":"4efa7640-3284-4fd3-8a02-74ba527dfd3d","added_by":"auto","created_at":"2025-04-28 16:06:07","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1511149,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5214849/v1/21178e64-dc14-4c58-a4f7-aaf063d289e0.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Channel State Feedback in Near Field Ultra Large-scale MIMO Systems Based on Compressed Sensing","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eThe ultra large-scale MIMO system plays an indispensable role in modern wireless communication, as increasing the number of antennas can significantly improve system capacity and transmission rate. However, the growing quantity of antennas has created new problems in the feedback of CSI. The feedback overhead increases rapidly with the increase of the number of antennas, which seriously affects the performance and efficiency of the system. The application of this technology can not only effectively meet the growing demand for mobile data, but also meet the requirements of future 6G networks for ultra-high bandwidth and extremely low latency. In the past few years, with the advancement of 5G commercialization, ultra large-scale MIMO technology has gradually matured. However, with the continuous expansion of antenna scale, the acquisition and feedback of CSI in the system have become the main bottleneck affecting system performance. The traditional CSI feedback method is unable to effectively reduce the amount of feedback data, resulting in high system complexity and low feedback efficiency, which cannot meet practical needs [1]. Currently, compressed sensing technology, as an emerging method, has gradually attracted the attention of researchers due to its superiority in signal processing [2]. By utilizing channel sparsity, compressive sensing technology can significantly reduce the amount of data that needs to be fed back while ensuring the accuracy of channel information, thereby reducing feedback overhead and improving overall system performance [3\u0026ndash;4]. In response to these challenges, compressive sensing technology has gradually achieved remarkable performance in sparse signal processing making it a research center for CSI feedback challenges with ultra-large-scale MIMO systems. Compressed sensing technology can significantly reduce the amount of feedback data and lower the feedback overhead of the system by effectively sampling the sparse channel matrix while maintaining the accuracy of channel information. However, in near-field ultra large-scale MIMO systems, the complexity and diversity of channels pose greater challenges to the application of compressive sensing technology. How to design appropriate measurement matrices and reconstruction algorithms to enhance the system\u0026rsquo;s functionality and reconstruction accuracy of CSI remains an important issue that needs to be addressed.\u003c/p\u003e \u003cp\u003eThe research in this article is conducted in this context, and the main contributions are as follows. This article constructs a channel model suitable for near-field ultra large-scale MIMO systems, deeply analyzes the sparse characteristics of the channel under this model, and designs a CSI feedback scheme based on compressive sensing according to its characteristics. This scheme compresses and samples channel information through Gaussian random measurement matrix, and combines OMP algorithm to achieve sparse reconstruction of the channel, greatly reducing the amount of channel information that needs to be fed back and effectively reducing the feedback overhead of the system. Secondly, this article verifies the effectiveness and superiority of the proposed scheme through a large number of simulation experiments. The experimental results show that under different channel conditions, the proposed method can reduce the amount of feedback data by 25\u0026ndash;50% while ensuring reconstruction accuracy, significantly reducing the communication burden of the system and improving the overall performance of the system. In addition, the method proposed in this article demonstrates high computational efficiency and low resource consumption in large-scale antenna array configurations. The compressed sensing system presented in this study shows notable improvements in reconstruction accuracy, feedback overhead, and computational cost when compared to the conventional least squares (LS) algorithm. This study not only provides a new approach to solving the CSI feedback problem in ultra large-scale MIMO systems, but also provides theoretical basis and technical support for the development of MIMO technology in near-field application scenarios in future 6G communication systems, with significant theoretical significance and application value.\u003c/p\u003e"},{"header":"2. Related Work","content":"\u003cp\u003eIn recent years, many studies have been devoted to solving the CSI feedback problem in ultra large-scale MIMO systems. Liu et al. proposed a learning-based CSI feedback framework with limited feedback and bidirectional reciprocal channel characteristics to reduce the effective payload of CSI feedback [5]. Zhengyang Hu et al. proposed a network called MRFNet, which aims to use different receptive fields and a large number of convolutional channels to recover useful features and better restore CSI [6]. Jianhua Guo et al. proposed a two-stage low rank CSI feedback scheme for millimeter wave massive MIMO systems to reduce feedback overhead based on model driven deep learning [7]. Huan Zhang et al. studied a reconfigurable intelligent surface (RIS) assisted multi-user MIMO system, which maximizes its sum rate by jointly optimizing the precoding matrix of the base station (BS) and the phase shift vector of RIS [8]. A deep transfer learning (DTL)-based channel state information (CSI) feedback technique was presented by Jun Zeng et al. to address the issue of the downlink CSI feedback network\u0026rsquo;s high training cost in frequency division duplexing (FDD) massive MIMO systems [9]. The CsiFBnet framework proposed by Guo J et al. has greatly improved performance and reduced complexity compared to traditional CSI feedback methods [10]. Ziping Wei et al. proposed a novel computationally and communication-efficient acquisition scheme by jointly designing downlink CSI estimation and uplink feedback [11]. The framework MarkovNet developed using the Markov model can effectively encode CSI feedback to improve accuracy and efficiency [12]. The study by Youngrok Jang et al. considered the feedback error and feedback delay in frequency division duplex massive MIMO systems, and the proposed scheme achieved better performance than other similar schemes [13]. The Dilated Channel Reconstruction Network (DCRNet) based on dilated convolution can achieve almost the same performance compared with the most advanced SOTA (State-of-The-Art) network, while reducing floating-point operations by about 30% [14]. Yuyao Sun et al. proposed a novel neural network architecture ENet (Efficient Neural Network) for CSI compression and feedback in large-scale MIMO [15]. Although these studies have addressed the CSI feedback problem to some extent, there are still shortcomings such as low feedback efficiency and high complexity.\u003c/p\u003e \u003cp\u003eMany researchers have attempted a variety of techniques to increase the effectiveness of CSI feedback in response to the aforementioned problems. A channel feedback approach based on angle domain support was put out by Tan J et al. for massive MIMO TDD (Time Division Duplex) systems with different numbers of transmitting and receiving antennas. The results show that near-optimal achievability and rate performance are achieved at low channel feedback overhead [16]. Lu Y et al. proposed a hybrid LoS (Line-of-Sight)/NLoS (non-Line-of-Sight) near-field XL-MIMO (Extremely large-scale Multiple-Input Multiple-Output) channel model, which is superior to existing methods in both the theoretical channel model and the QuaDRiGa channel simulation platform [17]. Xi Yang et al. studied the uplink transmission of ultra-large-scale MIMO systems by considering VR (Virtual Reality) [18]. Le He et al. proposed a hyper-accelerated Tree Search (HATS) algorithm, the results show that the algorithm has achieved near-optimal efficiency in actual scenarios and is suitable for large-scale systems [19]. Ahmed Ouameur M et al. derived a deep expansion conjugated gradient (CG) architecture for large-scale MIMO detection [20]. Lu Z et al. introduced a new type of binarized auxiliary feedback network called BCsiNet to reduce the burden on the UE [21]. Hongyuan Ye et al. designed a Deep Neural Network for Image Denoising DNNet (DNNet) based on deep Learning to improve the performance of channel feedback [22]. Jo S et al. proposed an adaptive lightweight convolutional neural network for MIMO CSI feedback based on deep learning, which significantly reduces computational complexity and accelerates network convergence speed [23]. Xiaojun Bi et al. proposed a novel neural network based on convolutional transformer architecture, which improves the performance of CSI compression and reconstruction at high compression rates [24]. Cui Y et al. proposed a novel deep learning method based on Transformer architecture for CSI feedback in frequency division duplex (FDD) massive MIMO systems. The proposed initial network called TransNet outperforms other deep learning methods in terms of CSI feedback quality [25]. With the same compression ratio, Xiaotong Yu\u0026rsquo;s deep learning-based CSI feedback technique, DS-NLCsiNet, produced improved reconstruction quality and increased CSI feedback accuracy [26]. Although these methods have improved in some aspects, there are still issues of limited feedback efficiency improvement and high system complexity. This article adopts compressive sensing technology to solve the shortcomings in existing research and improve the efficiency and accuracy of CSI feedback by optimizing channel sparse representation and measurement matrix design.\u003c/p\u003e"},{"header":"3. Implementation in Near Field Ultra Large-scale MIMO Systems","content":"\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e3.1 System Model Construction\u003c/h2\u003e \u003cp\u003eThe definition of physical layout is particularly crucial in near-field ultra large-scale MIMO systems. The implementation of the system model is achieved by describing the arrangement of antenna arrays, user positions, and their distance from the antenna. Antenna arrays are typically arranged in a rectangular or circular pattern to maximize coverage and signal strength. The user\u0026rsquo;s location is distributed according to the expected application scenario, and the distance between the user and the antenna is determined through precise measurement.\u003c/p\u003e \u003cp\u003eThe near-field channel characteristics are described using geometric channel models and ray tracing models [27]. The geometric channel model utilizes the physical location of antennas and users to calculate path loss, fading effects, and multipath propagation. The ray tracing model is based on reflections and refractions in the environment, providing a more detailed channel description. By combining the two models, more accurate channel characteristics can be obtained.\u003c/p\u003e \u003cp\u003eDuring the implementation process, establish a coordinate system for the antenna array and user location. Assuming the antenna array in the system is arranged in a rectangular shape, with each antenna position in the array being \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:({x}_{i},{y}_{i},{z}_{i})\\)\u003c/span\u003e\u003c/span\u003e and the user position being \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:({x}_{u},{y}_{u},{z}_{u})\\)\u003c/span\u003e\u003c/span\u003e. Path loss is calculated using the free space path loss formula:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:PL=20{\\text{l}\\text{o}\\text{g}}_{10}\\left(d\\right)+20{\\text{l}\\text{o}\\text{g}}_{10}\\left(f\\right)-147.55$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn the formula, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:d\\)\u003c/span\u003e\u003c/span\u003e is the distance between the antenna and the user, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:f\\)\u003c/span\u003e\u003c/span\u003e is the carrier frequency. The fading effect is described using the Rayleigh fading model, and the multipath propagation is calculated using ray tracing method to reflect the delay of the signal on different paths.\u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e shows the raw data collected from urban environments during the experiment. During the collection, the Rohde\u0026amp;Schwarz FSV30 spectrum analyzer was used to record parameters such as the distance between the antenna and the user, signal strength, etc. These data are used to validate the performance of geometric channel models and ray tracing models.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eExperimental raw data measured\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAntenna ID\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eUser ID\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eDistance (m)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSignal Strength (dB)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eA1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eU1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e10.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-65\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eA2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eU1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e12.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-67\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eA1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eU2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e9.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-64\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eA2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eU2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e11.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-66\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eA1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eU3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e13.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-70\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe data shows that the actual measured signal strength is not significantly different from the signal strength predicted by the geometric channel model and ray tracing model. The comparison data between real measurements and model predictions is displayed in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. The results of the geometric model were obtained through calculations, while the simulation results of the ray tracing model were obtained by combining environmental measurement data with software simulations.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eComparison between Model Prediction and Actual Measurement\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMetric\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eActual Measurement\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGeometric Model\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eRay-Tracing Model\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePath Loss (dB, A1-U1)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-65\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-64.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-65.2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePath Loss (dB, A2-U1)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-67\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-66.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-66.8\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePath Loss (dB, A1-U2)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-64\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-63.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-64.1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePath Loss (dB, A2-U2)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-66\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-65.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-66\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePath Loss (dB, A1-U3)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-69.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-70.1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eComparing the data in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, the errors between actual measurements and model predictions are within a reasonable range. For path loss (dB, A1-U1), the actual measured value is -65 dB, the geometric model predicted value is -64.8 dB, and the ray tracing model predicted value is -65.2 dB. The differences between these values are within a reasonable range. Similar results have also been validated on other data points, and the model has high prediction accuracy among different users and antennas. The results indicate that the geometric channel model and ray tracing model can effectively predict the near-field channel characteristics.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Channel Sparsity Representation\u003c/h2\u003e \u003cp\u003eThe sparse representation of the channel matrix is key to improving the feedback efficiency of near-field ultra large-scale MIMO systems. Sparse representation can significantly reduce the amount of data required for feedback by linearly transforming the channel matrix under a specific basis [28]. In this operation step, it is crucial to select an appropriate basis so that the channel matrix has sparsity under that basis. Utilizing the sparsity of the channel matrix in the frequency domain, the Discrete Fourier Transform (DFT) was chosen as the foundation for this investigation\u0026rsquo;s channel matrix transformation.\u003c/p\u003e \u003cp\u003eLet \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:H\\)\u003c/span\u003e\u003c/span\u003e be the original channel matrix, and obtain the sparse representation matrix \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:S\\)\u003c/span\u003e\u003c/span\u003e through discrete Fourier transform. Its transformation formula is:\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:S=F\\cdot\\:H\\cdot\\:{F}^{H}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eHere, the Fourier transform matrix is represented by \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:F\\)\u003c/span\u003e\u003c/span\u003e, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{F}^{H}\\)\u003c/span\u003e\u003c/span\u003e is its conjugate transpose matrix. The transformed matrix \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:S\\)\u003c/span\u003e\u003c/span\u003e exhibits sparsity on the Fourier basis, with most elements close to zero and only a few non-zero elements.\u003c/p\u003e \u003cp\u003eTo verify the effectiveness of this sparse representation method, simulation experiments were conducted using channel measurements collected from different antenna and user positions in a real wireless communication environment. Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e shows the data collected for simulation experiments.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eExperimental data for validating sparse representation\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAntenna ID\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eUser ID\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eDistance (m)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSignal Strength (dB)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eA3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eU4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e14.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-63\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eA4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eU4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e15.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-65\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eA3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eU5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e13.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-62\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eA4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eU5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e14.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-64\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eA3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eU6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e15.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-68\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTo evaluate sparsity, the number of non-zero elements in the original channel matrix and the sparse matrix after discrete cosine transform were counted, and their proportions were calculated. Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e shows the comparison of non-zero element ratios between the original channel matrix and the sparse matrix.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eComparison of non-zero element ratios between original matrix and sparse matrix\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAntenna ID\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eUser ID\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eNon-zero Elements in Original Matrix (%)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eNon-zero Elements in Sparse Matrix (%)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eA3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eU4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e92\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e8.2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eA4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eU4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e91.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e7.9\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eA3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eU5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e91.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e8.1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eA4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eU5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e92.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e7.8\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eA3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eU6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e90.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e8.4\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eFrom the data in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, it can be clearly seen that the proportion of non-zero elements in the transformed sparse matrix has significantly decreased. This demonstrates that the discrete cosine transform can effectively represent the channel matrix sparsely, reduce the proportion of non-zero elements, and thus lower feedback overhead. This demonstrates that this sparse representation method has stable performance under different antenna and user configurations.\u003c/p\u003e \u003cp\u003eBy using discrete Fourier transform to represent channel sparsity, the feedback overhead in near-field ultra large-scale MIMO systems can be effectively reduced, and the performance of the system can be improved.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e3.3 Design of the Measurement Matrix\u003c/h2\u003e \u003cp\u003eUtilizing compressive sensing theory effectively in near-field ultra-large-scale MIMO systems is to design suitable measurement matrices, achieve channel sampling, and reduce the amount of feedback data [29]. The random measurement matrix is an important component of compressive sensing theory, which obtains compressed observations by compressing and sampling the channel matrix to reduce the amount of data that needs to be fed back.\u003c/p\u003e \u003cp\u003eIn the study, Gaussian random matrix was chosen for measurement matrix design. Each element of a Gaussian random matrix takes values from an independent and identically distributed Gaussian distribution, satisfying the characteristics of zero mean and unit variance. The design formula for this matrix is as follows:\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:{A}_{ij}\\sim\\:\\mathcal{N}\\left(\\text{0,1}\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eAmong them, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{A}_{ij}\\)\u003c/span\u003e\u003c/span\u003e represents the elements in the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:i\\)\u003c/span\u003e\u003c/span\u003eth row and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:j\\)\u003c/span\u003e\u003c/span\u003eth column of the measurement matrix \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:A\\)\u003c/span\u003e\u003c/span\u003e, while \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\mathcal{N}\\left(\\text{0,1}\\right)\\)\u003c/span\u003e\u003c/span\u003e represents a Gaussian distribution with zero mean and one variance. The designed Gaussian random measurement matrix is used to compress and sample the sparse representation of the channel matrix to obtain compressed observations.\u003c/p\u003e \u003cp\u003eOn the basis of validating sparse representation methods, compressive sensing theory is used to further reduce the amount of feedback data. The advantage of compressive sensing theory is that it can utilize the sparsity of signals and reconstruct the original signal with a small amount of sampling. For the sparse representation matrix \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:S\\)\u003c/span\u003e\u003c/span\u003e, it involves compressing and sampling the measurement matrix \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:A\\)\u003c/span\u003e\u003c/span\u003e to obtain the observation vector \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:y\\)\u003c/span\u003e\u003c/span\u003e:\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\:y=A\\cdot\\:S$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn matrix calculation, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:A\\)\u003c/span\u003e\u003c/span\u003e is a randomly generated measurement matrix. The length of observation vector \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:y\\)\u003c/span\u003e\u003c/span\u003e is much smaller than the dimension of the original channel matrix, which greatly reduces the amount of data that needs to be fed back.\u003c/p\u003e \u003cp\u003eIn the experiment, from the observed vectors, the original channel matrix was reconstructed using the OMP technique. The mean square error calculation formula during the reconstruction process is:\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$$\\:MSE=\\frac{1}{N}\\sum\\:_{i=1}^{N}({H}_{i}-\\hat {{H}}_{i}{)}^{2}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn the formula, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{H}_{i}\\)\u003c/span\u003e\u003c/span\u003e is the original channel matrix element, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\hat {{H}}_{i}\\)\u003c/span\u003e\u003c/span\u003e is the reconstructed channel matrix element, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:N\\)\u003c/span\u003e\u003c/span\u003e is the total number of matrix elements. Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e shows the MSE and reconstruction error of different antenna user pairs. The MSE value represents the average error in the channel reconstruction process, while the reconstruction error reflects the error in reconstructing the channel matrix using the OMP algorithm. When using compressive sensing technology to reconstruct the channel matrix, the reconstruction error remains at a low level, significantly reducing the amount of feedback data while maintaining accurate channel information.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe design of Gaussian random measurement matrix and the application of OMP algorithm have achieved sparse representation of channel matrix and compressed sampling, reducing feedback overhead and greatly improving system performance. The practical application effect of these methods in near-field ultra large-scale MIMO systems is significant, meeting the demand of modern communication systems for efficient CSI feedback.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e3.4 Channel Information Reconstruction\u003c/h2\u003e \u003cp\u003eChannel information reconstruction is an important step in achieving efficient operation of near-field ultra large-scale MIMO systems. The selection of sparse reconstruction algorithms is crucial for recovering the original channel matrix from compressed observations. The study used the Basis Pursuit (BP) algorithm [30]. The use of this algorithm ensures that the reconstruction error is maintained within an acceptable range, achieving efficient channel information recovery.\u003c/p\u003e \u003cp\u003eThe BP algorithm solves optimization problems and extracts sparse signals from observation vectors. The objective function of the BP algorithm is as follows:\u003cdiv id=\"Equ6\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ6\" name=\"EquationSource\"\u003e\n$$\\:\\text{m}\\text{i}\\text{n}\\parallel\\:x{\\parallel\\:}_{1}\\text{s}\\text{u}\\text{b}\\text{j}\\text{e}\\text{c}\\text{t}\\:\\text{t}\\text{o}\\:\\:\\:y=A\\cdot\\:x$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e6\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn function calculation, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:x\\)\u003c/span\u003e\u003c/span\u003e is the channel matrix to be reconstructed, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:A\\)\u003c/span\u003e\u003c/span\u003e is the measurement matrix, and the observation vector is \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:y\\)\u003c/span\u003e\u003c/span\u003e. Linear programming techniques are used to solve the optimization problem and obtain sparse signals. In specific operations, the interior point method is used to ensure fast convergence and high accuracy in the reconstruction process.\u003c/p\u003e \u003cp\u003eThrough simulation trials, the BP algorithm\u0026rsquo;s efficacy was confirmed. The experimental data is taken from actual wireless communication environments, covering channel measurements from different antennas and user locations. Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e lists the collected raw data used to evaluate the reconstruction accuracy of sparse reconstruction algorithms.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eRaw data at different frequencies\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAntenna ID\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eUser ID\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eFrequency (GHz)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eAmplitude (dB)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eA1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eU1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-65\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eA2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eU1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-68\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eA1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eU2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-64\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eA2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eU2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-69\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eA1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eU3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-70\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eA2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eU3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-72\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eA1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eU4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-66\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eA2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eU4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-67\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eDuring the experiment, the BP algorithm reconstructs the original channel matrix from the observed vectors and calculates the reconstruction error. Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e shows the reconstructed error data, showcasing the BP algorithm\u0026rsquo;s performance with various antenna and user combinations.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eReconstruction Error Analysis\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAntenna ID\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eUser ID\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eBP Error (dB)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eA1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eU1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.4\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eA2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eU1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eA1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eU2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eA2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eU2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.4\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eA1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eU3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.6\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eA2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eU3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.7\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eA1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eU4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eA2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eU4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.6\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe data shows that the BP algorithm exhibits high accuracy in reconstructing channel information. The reconstruction errors under different antenna and user combinations are relatively small, ranging from 0.3 to 0.7 dB, indicating that the BP algorithm can effectively reconstruct the original channel matrix under various conditions.\u003c/p\u003e \u003cp\u003eHowever, in order to fully illustrate the reconstruction performance of the BP algorithm, experiments were conducted under different SNR conditions. Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e shows the reconstruction error under different SNR conditions. The data shows that the higher the SNR value, the lower the BP error usually. The combination of antenna A1 and user U3 has a BP error of 0.2 dB at an SNR of 30 dB, while the combination of antenna A1 and user U2 has a BP error of 0.6 dB at an SNR of 10 dB. This indicates that the signal-to-noise ratio has a certain impact on the reconstruction accuracy, and under high signal-to-noise ratio conditions, the reconstruction error can be reduced.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eReconstructing channel information not only requires ensuring accuracy, but also considers computational complexity and time consumption. The feasibility of the BP algorithm in practical applications has been demonstrated through experimental data. These methods significantly minimize the quantity of feedback data and enhance system efficiency while ensuring the accuracy of channel information.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e3.5 Simulation and Verification\u003c/h2\u003e \u003cp\u003eIn the simulation verification section, a simulation dataset based on system and channel models was generated to evaluate the performance of different methods in near-field ultra large-scale MIMO systems. This dataset contains CSI data under various channel conditions. The diversity of the dataset can be ensured through different antenna numbers, user numbers, and SNR settings.\u003c/p\u003e \u003cp\u003eIn the experiment, reconstruction accuracy, feedback overhead and computational complexity are the most important evaluation criteria. Reconstruction precision measures the ability of the algorithm to accurately restore the original channel information from the observed data, while feedback overhead reflects the amount of data required to transmit while ensuring reconstruction precision. Computational complexity evaluates the practical ability of the algorithm in actual applications.\u003c/p\u003e \u003cp\u003eSimulation experiments are conducted under various system configurations to comprehensively compare the performance of the compressed sensing method and the traditional CSI feedback method. Table\u0026nbsp;\u003cspan refid=\"Tab7\" class=\"InternalRef\"\u003e7\u003c/span\u003e shows the original data of the simulation dataset.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab7\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 7\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eSimulation Dataset Data\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAntenna ID\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eUser ID\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eFrequency (GHz)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSNR (dB)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eAmplitude (dB)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eA1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eU1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-65\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eA2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eU1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-68\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eA1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eU2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-64\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eA2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eU2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-69\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eA1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eU3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-70\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eA2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eU3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-72\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eA1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eU4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-66\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eA2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eU4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-67\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eDuring the experiment, the BP algorithm and the LS algorithm were utilized to determine the reconstruction error and rebuild the original channel matrix using the observation vector. Table\u0026nbsp;\u003cspan refid=\"Tab8\" class=\"InternalRef\"\u003e8\u003c/span\u003e shows the reconstruction error data, which shows the performance of the two algorithms under different antenna and user combinations.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab8\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 8\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eReconstruction accuracy of different methods\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMethod\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAntenna ID\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eUser ID\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eReconstruction Accuracy (dB)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBP\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eA1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eU1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.4\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBP\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eA2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eU1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBP\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eA1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eU2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBP\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eA2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eU2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.4\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eA1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eU1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.7\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eA2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eU1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.8\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eA1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eU2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.6\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eA2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eU2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.7\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eIt is evident from analyzing the data in Table\u0026nbsp;\u003cspan refid=\"Tab8\" class=\"InternalRef\"\u003e8\u003c/span\u003e that the reconstruction accuracy of the BP algorithm is higher than that of the LS method. Under all antenna and user combinations, the reconstruction error of the BP algorithm is smaller than that of the LS algorithm. This demonstrates that the BP technique can improve reconstruction accuracy and more precisely recover initial channel information from the observation vector.\u003c/p\u003e \u003cp\u003eThe feedback cost can be calculated by measuring the amount of feedback data generated by the algorithm under different conditions. Feedback overhead refers to the amount of transmitted data between compressed sensing methods and traditional CSI feedback methods measured through simulation experiments under the same conditions. The reduction in the amount of feedback data directly reflects the optimization effect of the algorithm on feedback overhead. The feedback overhead of BP and LS under different antenna and user combinations is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. In every combination, the BP algorithm\u0026rsquo;s feedback cost is substantially less than the LS algorithm\u0026rsquo;s, indicating that the BP algorithm has a clear advantage in reducing the amount of feedback data.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThese results indicate that the BP algorithm significantly improves the efficiency of CSI feedback in near-field ultra large-scale MIMO systems. This provides solid experimental support for the practical application of the method.\u003c/p\u003e \u003c/div\u003e"},{"header":"4. System Performance Evaluation","content":"\u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e4.1 Refactoring Accuracy\u003c/h2\u003e \u003cp\u003eThe reconstruction accuracy of compressive sensing methods shows significant differences under different channel conditions. The influence of different signal-to-noise ratios, antenna numbers, user positions, and channel sparsity on reconstruction accuracy can be explored through experiments, and their impact on system performance can be analyzed.\u003c/p\u003e \u003cp\u003eThe experiment uses Gaussian random measurement matrix to sample the channel and uses OMP to reconstruct the channel information. The experimental dataset covers CSI of multiple antenna user pairs under different channel conditions, with signal-to-noise ratios ranging from 10 dB to 40 dB, antenna numbers ranging from 32 to 128, and user positions ranging from 5 meters to 50 meters. The different experimental conditions are set as shown in Table\u0026nbsp;\u003cspan refid=\"Tab9\" class=\"InternalRef\"\u003e9\u003c/span\u003e:\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab9\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 9\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eExperimental conditions for reconstruction accuracy analysis\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eExperiment ID\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAntenna Count\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eUser Distance (m)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSNR (dB)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eSparsity (%)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eExp1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e64\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eExp2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e64\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eExp3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e64\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eExp4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e64\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eExp5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e128\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eExp6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e128\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eExp7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e128\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eExp8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e128\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab9\" class=\"InternalRef\"\u003e9\u003c/span\u003e lists the experimental settings under different experimental conditions. Through the combination of different conditions, the reconstruction accuracy of the compressed sensing method in different environments is evaluated. The experiment measures the reconstruction precision by calculating the mean square error.\u003c/p\u003e \u003cp\u003eThe MSE calculation results under different experimental conditions are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. As the SNR increases, the MSE value significantly decreases, demonstrating the positive impact of signal-to-noise ratio on reconstruction accuracy. This article compares Exp1 and Exp5. Under the same SNR and user distance, increasing the number of antennas from 64 to 128 results in a decrease in MSE from 0.15 dB to 0.14 dB, indicating that more antennas can capture richer channel information and improve reconstruction accuracy. Comparing the experimental results of Exp1 and Exp3, it can be concluded that when the sparsity increases from 10\u0026ndash;15%, the MSE increases from 0.15 dB to 0.20 dB. This indicates that although increasing sparsity reduces the amount of feedback data, it also increases the difficulty of reconstruction, resulting in a slight increase in reconstruction error.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe results show that under high SNR and multi-antenna conditions, high reconstruction precision can be achieved while effectively minimizing the amount of feedback data using the compressed sensing method. In practical applications, compressive sensing methods can adjust sparsity and sampling rate according to channel conditions to achieve optimal system performance. Through experimental verification, it was found that SNR, number of antennas, and sparsity are key factors affecting reconstruction accuracy. Under high SNR ratio and multi-antenna conditions, the compressed sensing method can effectively reduce feedback overhead and improve reconstruction accuracy.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e4.2 Comparison of Feedback Costs\u003c/h2\u003e \u003cp\u003eIn ultra large-scale MIMO systems, the feedback overhead of channel state information (CSI) has become a key bottleneck in system performance as a result of the antenna count being significantly increased. To lower communication overhead and increase the system\u0026rsquo;s transmission efficiency, it is necessary to conduct in-depth analysis and comparison of the feedback efficiency of different algorithms, in order to determine the most advantageous CSI feedback method in practical applications. The purpose of comparing feedback overhead is to evaluate the performance of OMP under different channel conditions, especially in reducing the efficiency of feedback data volume. In the experiment, LS was used for in-depth comparison.\u003c/p\u003e \u003cp\u003eThe experimental conditions selected were different antenna numbers, user distances, SNR, and channel sparsity. These experimental conditions have been set up with the intention of simulate various practical wireless communication scenarios and comprehensively evaluate the feedback overhead performance of OMP algorithm and LS algorithm under different channel conditions.\u003c/p\u003e \u003cp\u003eThe calculation of feedback overhead is based on the amount of feedback data per antenna user, measured in bits. The OMP algorithm utilizes the sparsity of the channel and significantly reduces the amount of feedback data through compressive sensing technology, while the LS algorithm fails to effectively utilize the sparsity of the channel, resulting in a larger amount of feedback data. Table\u0026nbsp;\u003cspan refid=\"Tab10\" class=\"InternalRef\"\u003e10\u003c/span\u003e shows the experimental setup under different conditions in the experiment.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab10\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 10\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eFeedback Cost Experimental Condition Settings\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eExperiment ID\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAntenna Count\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eUser Distance (m)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSNR (dB)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eSparsity (%)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eExp1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e64\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eExp2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e64\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eExp3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e64\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eExp4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e64\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eExp5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e128\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eExp6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e128\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eExp7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e128\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eExp8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e128\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eExp9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e256\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eExp10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e256\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab10\" class=\"InternalRef\"\u003e10\u003c/span\u003e lists the number of antennas, user distance, signal-to-noise ratio, and sparsity settings for 10 different experimental conditions. These different combination settings can be used to comprehensively evaluate the feedback overhead of the two algorithms under various channel conditions.\u003c/p\u003e \u003cp\u003eThe experimental results are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. Under all experimental conditions, the feedback cost of OMP algorithm is lower than that of LS algorithm. The feedback cost range of LS algorithm is 3200 bits (Exp1) to 8200 bits (Exp10), while the feedback cost range of OMP algorithm is 2100 bits (Exp2) to 4900 bits (Exp10). The reduction of OMP algorithm compared to LS algorithm ranges from 25% (Exp1) to 50% (Exp8), indicating that under certain conditions, OMP algorithm can reduce feedback overhead by half and significantly reduce system communication burden.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe experiment verified the effectiveness of OMP in reducing feedback overhead in ultra large-scale MIMO systems. Under different channel conditions, the OMP algorithm reduces the feedback data volume by 25\u0026ndash;50% compared to LS, significantly reducing the communication burden of the system. This proves the advantages of the OMP algorithm as an efficient channel state information (CSI) feedback method in practical applications.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003e4.3 Algorithm Complexity Evaluation\u003c/h2\u003e \u003cp\u003eThe evaluation of algorithm complexity is mainly carried out by analyzing the computation time and memory usage of OMP algorithm and BP algorithm under different experimental conditions. The research focuses on the consumption of computing resources and the performance of algorithms when processing datasets of different sizes.\u003c/p\u003e \u003cp\u003eThe experimental design is divided into four groups, with the number of antennas and users in different groups being 32, 64, 128, 256, and 10, 20, 40, 80, respectively. The corresponding matrix sizes are between 320 and 20480. The sparsity is set to 5% -20%, and these conditions are used to generate datasets of different sizes for evaluating the complexity of the algorithm.\u003c/p\u003e \u003cp\u003eThe sparsity in Table\u0026nbsp;\u003cspan refid=\"Tab11\" class=\"InternalRef\"\u003e11\u003c/span\u003e reflects the proportion of non-zero elements in the channel matrix. The increase in sparsity usually increases the complexity of algorithm computation, so the computation time and memory usage of each set of data were recorded in the experiment to quantify the performance of the algorithm.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab11\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 11\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eExperimental Parameters of Antenna and User Count Combination\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eExperiment ID\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAntenna Count\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eUser Count\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMatrix Size\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eSparsity (%)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eExp1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e32\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e320\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eExp2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e64\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1280\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eExp3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e128\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e5120\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eExp4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e256\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e20480\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eDuring the experiment, the computation time and memory usage of the OMP and BP algorithms were recorded in detail on data sets of different sizes. Figure\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e shows the computation time (ms) and memory usage (MB) of the OMP and BP algorithms under different experimental conditions. The computation time is represented by a solid line, and the memory usage is represented by a dotted line. As can be seen from the broken lines in the figure, the increase in the number of antennas and users increases the computation time and memory usage of both algorithms. However, the computation time and memory usage of the OMP algorithm under each experimental condition are lower than those of the BP algorithm, which is most obvious in the Exp4. The computation time and memory consumption of the OMP algorithm are 130.2ms and 178.8MB, respectively, while the BP algorithm is only 186.7ms and 210.3MB. This shows that the OMP algorithm is more efficient when processing large-scale data, with lower computational complexity and resource consumption.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003e4.4 Transmission Rate Evaluation\u003c/h2\u003e \u003cp\u003eIn the transmission rate evaluation part, the purpose of the experiment is to explore the changes in the transmission rate of the system under different channel conditions. High transmission rate means higher data throughput and better user experience, so analyzing the changes in transmission rate under diverse channel conditions is the focus of the research.\u003c/p\u003e \u003cp\u003eThe experiment sets different antenna numbers, user distances, and signal-to-noise ratio (SNR) conditions, uses compressive sensing technology for CSI feedback, and uses discrete Fourier transform (DFT) for sparse representation. Subsequently, in order to measure the transmission rate of the system under various circumstances, the channel is sampled using the Gaussian random measurement matrix and then reconstructed using the OMP algorithm.\u003c/p\u003e \u003cp\u003eIn the configuration of 64 antennas and 128 antennas, the transmission rate under different SNR and user distances is measured. As shown in Table\u0026nbsp;\u003cspan refid=\"Tab12\" class=\"InternalRef\"\u003e12\u003c/span\u003e, the table shows the key parameter settings of the experiment and the corresponding transmission rate results.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab12\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 12\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eEffects of Antenna Quantity, User Distance, and SNR Conditions on Transmission Rate\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAntenna Count\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eUser Distance (m)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSNR (dB)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eTransmission Rate (Mbps)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e64\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e450\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e64\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e500\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e64\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e420\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e64\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e480\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e128\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e550\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e128\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e600\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e128\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e520\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e128\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e580\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe increase in the number of antennas has a significant effect on improving the system transmission rate. When the SNR is 20 dB and the distance between the user and the antenna is 10 meters, the number of antennas increases from 64 to 128, and the transmission rate increases from 450 Mbps to 550 Mbps. When the SNR is 30 dB and the antenna distance is still 10 meters, the transmission rate changes from 500 Mbps to 600 Mbps. However, when the distance between the user and the antenna increases from 10 meters to 20 meters, the system transmission rate decreases. This is because the increase in distance causes signal attenuation, which reduces the transmission performance. Under the same SNR conditions, when the user distance is 10 meters, the system transmission rate is higher than when the distance is 20 meters.\u003c/p\u003e \u003cp\u003eIn terms of the impact of SNR, higher SNR significantly increases the transmission rate. Under 64 antennas, when the user distance is 10 meters, the SNR increases from 20 dB to 30 dB, and the transmission rate increases from 450 Mbps to 500 Mbps. Under 128 antennas, the same SNR increase increases the transmission rate from 550 Mbps to 600 Mbps, which further confirms the positive impact of high SNR on system performance.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003e4.5 Reliability Assessment\u003c/h2\u003e \u003cp\u003eWhen evaluating the reliability of near-field ultra large-scale MIMO systems, by examining the bit error ratio (BER) and packet loss rate (PLR) under various channel conditions, the system\u0026rsquo;s performance is primarily assessed. The focus of the experiment is to quantify the impact of compressive sensing methods on system reliability under different channel conditions.\u003c/p\u003e \u003cp\u003eThe experiment is divided into three main channel condition groups: ideal channel, additive white Gaussian noise (AWGN) channel, and multipath fading channel. Each group of experiments is subjected to 10000 simulated transmissions, with 1000 data packets transmitted each time, and each data packet having a length of 1024 bits. The design of channel models ranges from interference free ideal environments to complex actual transmission environments, used to simulate various channel situations that may be encountered in near-field scenarios.\u003c/p\u003e \u003cp\u003eUnder ideal channel conditions, signal transmission is not affected by any noise or interference, and the objective of the experiment is to determine the basic reliability performance of the system under optimal conditions. The AWGN channel simulates the stability and reliability of channel transmission in the presence of noise. SNR is set to 10dB, 20dB, and 30dB to assess how various noise levels affect system performance. The multipath fading channel introduces complex multipath effects, simulates the reflection and attenuation of signals encountered during propagation, and tests the reliability performance of the system in actual environments.\u003c/p\u003e \u003cp\u003eThe experimental raw data under different channel conditions are listed in Table\u0026nbsp;\u003cspan refid=\"Tab13\" class=\"InternalRef\"\u003e13\u003c/span\u003e, which records the statistical results of error and packet loss rates for each experiment. These raw data are used to calculate the final bit error rate and packet loss rate.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab13\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 13\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eExperimental Raw Data Table\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eChannel Model\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTotal Transmissions\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTotal Data Packets\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBit Errors\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003ePacket Losses\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eIdeal Channel\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e10000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e10000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e500\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAWGN (SNR\u0026thinsp;=\u0026thinsp;10dB)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e10000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e10000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1200000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e150000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAWGN (SNR\u0026thinsp;=\u0026thinsp;20dB)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e10000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e10000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e600000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e80000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAWGN (SNR\u0026thinsp;=\u0026thinsp;30dB)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e10000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e10000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e300000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e40000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMultipath Fading Channel\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e10000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e10000000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3500000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e450000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe calculation formulas for error rate and packet drop rate are:\u003cdiv id=\"Equ7\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ7\" name=\"EquationSource\"\u003e\n$$\\:BER=\\frac{Bit\\:Errors}{Total\\:Data\\:Packets\\times\\:Data\\:Packet\\:Size}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e7\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ8\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ8\" name=\"EquationSource\"\u003e\n$$\\:PLR=\\frac{Packet\\:Losses}{Total\\:Data\\:Packets}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e8\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eAccording to the data in Table\u0026nbsp;\u003cspan refid=\"Tab13\" class=\"InternalRef\"\u003e13\u003c/span\u003e, the bit error rate and packet drop rate under different channel conditions can be calculated, as shown in Table\u0026nbsp;\u003cspan refid=\"Tab14\" class=\"InternalRef\"\u003e14\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab14\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 14\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eError rate and packet drop rate under different channel conditions\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eChannel Model\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBit Error Rate\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePacket Loss Rate\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eIdeal Channel\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.00000001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.00005\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAWGN (SNR\u0026thinsp;=\u0026thinsp;10dB)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.000117\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.015\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAWGN (SNR\u0026thinsp;=\u0026thinsp;20dB)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.000059\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.008\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAWGN (SNR\u0026thinsp;=\u0026thinsp;30dB)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.000029\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.004\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMultipath Fading Channel\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.000342\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.045\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eFrom the results in Table\u0026nbsp;\u003cspan refid=\"Tab14\" class=\"InternalRef\"\u003e14\u003c/span\u003e, it can be seen that under ideal channel conditions, the system exhibits extremely high reliability, with almost negligible bit error rate and packet drop rate. In the AWGN channel, due to the presence of noise interference, the error rate and packet drop rate of the system have increased, but still remain at a low level, demonstrating good anti-interference ability. Under multipath fading channel conditions, the system has the highest bit error rate and packet drop rate, indicating insufficient reliability in practical complex environments.\u003c/p\u003e \u003cp\u003eThe reliability evaluation experiment shows that the compressive sensing method has a significant impact on the reliability of the system in near-field environments. Under ideal channel conditions, the system is almost unaffected; in complex channel environments with noise and multipath fading, the reliability of the system shows a certain decrease, especially in multipath fading channels where the bit error rate and packet drop rate significantly increase. Nevertheless, the overall performance of the system remains within an acceptable range, indicating that the method has good adaptability in practical applications.\u003c/p\u003e \u003c/div\u003e"},{"header":"5. Conclusions","content":"\u003cp\u003eThis study applied compressive sensing technology to CSI feedback in near-field ultra large-scale MIMO systems. By utilizing the sparsity of the channel, a Gaussian random measurement matrix is designed for channel sampling, and the OMP algorithm is combined to achieve efficient reconstruction of channel information. In the simulation experiment, the compressed sensing method adopted significantly reduced the amount of feedback data and improved the performance of the system. According to the findings, the OMP algorithm significantly outperforms conventional techniques in terms of reconstruction accuracy and feedback overhead, especially in high signal-to-noise ratio and multi-antenna configurations. However, the experiment also pointed out that there is still room for improvement in the reliability of this method under complex channel conditions, especially in multipath fading environments where the error rate and packet drop rate increase. Future research can further optimize the design of measurement matrices, explore more efficient sparse reconstruction algorithms, and verify the feasibility of this method in practical applications, to further enhance the system\u0026rsquo;s dependability in challenging settings.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eGuozhi Rong designed the research study. Rugui Yao and Yifeng He analyzed the data. Guozhi Rong wrote the manuscript. All authors contributed to editorial changes in the manuscript. All authors read and approved the final manuscript.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eThe datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eJiajia Guo, Chao-Kai Wen, Shi Jin, Geoffrey Ye Li. Overview of deep learning-based CSI feedback in massive MIMO systems[J]. IEEE Transactions on Communications, 2022, 70(12): 8017-8045.\u003c/li\u003e\n\u003cli\u003ePeizhe Liang, Jiancun Fan, Wenhan Shen, Zhijin Qin, Geoffrey Ye Li. Deep learning and compressive sensing-based CSI feedback in FDD massive MIMO systems[J]. IEEE Transactions on Vehicular Technology, 2020, 69(8): 9217-9222.\u003c/li\u003e\n\u003cli\u003eChaojin Qing, Qingyao Yang, Bin Cai, Borui Pan, Jiafan Wang. Superimposed coding-based CSI feedback using 1-bit compressed sensing[J]. 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IEEE Transactions on Wireless Communications, 2022, 21(10): 8090-8105.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"discover-computing","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Discover Computing](https://link.springer.com/journal/10791)","snPcode":"10791","submissionUrl":"https://submission.springernature.com/new-submission/10791/3","title":"Discover Computing","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Discover Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Large-scale MIMO Systems, Compressed Sensing, Channel State Information Feedback, Orthogonal Matching Pursuit, Feedback Data Reduction","lastPublishedDoi":"10.21203/rs.3.rs-5214849/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5214849/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe rapid development of ultra large-scale MIMO (Multiple Input Multiple Output) systems has posed challenges to traditional channel state information (CSI) feedback methods. The increase in the number of antennas significantly increases the amount of data required for feedback, resulting in higher feedback overhead and affecting system performance. In response to this issue, this article used compressive sensing technology to reduce the amount of CSI feedback data, thereby reducing feedback overhead and optimizing system performance. To this end, this article constructed a super large-scale MIMO system model and studies channel characteristics. Gaussian random measurement matrix is selected for channel sampling, and sparse reconstruction is achieved by combining orthogonal matching pursuit (OMP) algorithm. Through simulation experiments, it was found that under different channel conditions, the OMP algorithm reduced the amount of data fed back by 25% -50% compared to the Least Square (LS) algorithm. When processing large-scale data, the OMP algorithm not only improves efficiency, but also significantly reduces computational complexity and resource consumption. Under ideal channel conditions, the system exhibits extremely high reliability, with almost zero error rate and packet loss rate. This study provides an effective solution for CSI feedback in ultra large-scale MIMO systems.\u003c/p\u003e","manuscriptTitle":"Channel State Feedback in Near Field Ultra Large-scale MIMO Systems Based on Compressed Sensing","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-11-15 08:57:10","doi":"10.21203/rs.3.rs-5214849/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2024-11-05T17:20:21+00:00","index":"","fulltext":""},{"type":"reviewerAgreed","content":"292607173535538582188926788077419763281","date":"2024-11-01T07:59:50+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"76024878321694859899786479822059509369","date":"2024-10-30T02:01:53+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-10-30T01:21:09+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-10-29T19:56:46+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"239688510155351801710549072322578485112","date":"2024-10-29T16:23:46+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-10-19T14:29:45+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"292860174277318118213771392222605813334","date":"2024-10-19T13:40:44+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"337045729478445167494034651765956511883","date":"2024-10-18T12:01:42+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"90707957021530350212790448377909851045","date":"2024-10-18T01:46:37+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-10-17T16:18:58+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-10-17T15:39:01+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-10-16T06:32:33+00:00","index":"","fulltext":""},{"type":"submitted","content":"Discover Computing","date":"2024-10-07T01:59:54+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"discover-computing","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Discover Computing](https://link.springer.com/journal/10791)","snPcode":"10791","submissionUrl":"https://submission.springernature.com/new-submission/10791/3","title":"Discover Computing","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Discover Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"278384c6-6550-4625-8ff8-2f349fe2d804","owner":[],"postedDate":"November 15th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2025-04-28T15:59:33+00:00","versionOfRecord":{"articleIdentity":"rs-5214849","link":"https://doi.org/10.1007/s10791-025-09542-0","journal":{"identity":"discover-computing","isVorOnly":false,"title":"Discover Computing"},"publishedOn":"2025-04-21 15:57:04","publishedOnDateReadable":"April 21st, 2025"},"versionCreatedAt":"2024-11-15 08:57:10","video":"","vorDoi":"10.1007/s10791-025-09542-0","vorDoiUrl":"https://doi.org/10.1007/s10791-025-09542-0","workflowStages":[]},"version":"v1","identity":"rs-5214849","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5214849","identity":"rs-5214849","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}