Channel estimation method and device, electronic equipment and storage medium

By constructing the pilot symbol matrix at the receiver and filtering out singular values ​​to determine the sparsity parameter, the problem of high computational complexity in channel estimation in the OTFS-MIMO system is solved, achieving high-precision and low-latency channel estimation, which is suitable for high-mobility scenarios.

CN121750408APending Publication Date: 2026-03-27BEIJING UNIV OF POSTS & TELECOMM
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Patent Information

Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-11-28
Publication Date
2026-03-27

AI Technical Summary

Technical Problem

In systems combining OTFS modulation and MIMO technology, the computational complexity of channel estimation is too high, making it difficult to meet real-time processing requirements, especially in high-mobility scenarios.

Method used

By determining the time delay grid parameters and Doppler frequency shift grid parameters of the target domain channel, a receiver pilot symbol matrix is ​​constructed. Singular values ​​are filtered to obtain rank estimates, user sparsity information is determined, and channel sparsity parameters are obtained. Channel estimation is then performed using the receiver pilot symbol matrix and channel sparsity parameters, reducing computational complexity.

Benefits of technology

It improves the accuracy of channel estimation and the reliability of the system, significantly reduces computational complexity, and is suitable for mMIMO-OTFS systems in high mobility and complex channel environments.

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Abstract

The invention provides a channel estimation method and device, electronic equipment and a storage medium, and the method comprises the steps: determining and constructing a time delay grid parameter and a Doppler frequency shift grid parameter of a target domain channel, obtaining a receiving end pilot symbol matrix, then determining a singular value of the receiving end pilot symbol matrix, and carrying out the screening, thereby obtaining a rank estimation value; determining user sparseness information of each user in the target domain channel, and obtaining a channel sparseness parameter based on the rank estimation value and the user sparseness information; estimating based on a pilot symbol matrix of a receiving end, estimating a target domain channel after obtaining a column sampling sub-matrix, and finally obtaining a channel estimation matrix; and obtaining receiving end vector information, and estimating the receiving end vector information through the channel estimation matrix to obtain sending end vector information. According to the method, the accuracy of channel estimation and the reliability of the system are effectively improved, meanwhile, the calculation complexity is remarkably reduced, and the method is particularly suitable for an mMIMO-OTFS system in a high-mobility and complex channel environment.
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Description

TECHNICAL FIELD

[0001] The present disclosure relates to the technical field of wireless communication, and in particular, to a channel estimation method and device, an electronic device, and a storage medium. BACKGROUND

[0002] This section is intended to provide background information to facilitate a better understanding of embodiments of the present disclosure. It is not admitted that any of the information provided in this section is prior art merely because it is included in this section.

[0003] In modern wireless communication, Multiple-Input Multiple-Output (MIMO) technology improves system capacity and reliability through multi-antenna transmission. With the growth of mobile communication demand, massive MIMO technology emerges as the times require and becomes an important part of 5G and future communication. However, in high mobility scenarios such as autonomous driving, unmanned aerial vehicles, and high-speed trains, systems combining Orthogonal Frequency Division Multiplexing (OFDM) modulation and MIMO technology face problems such as inter-carrier interference and inter-symbol interference due to high Doppler effect and time-varying channel characteristics, making it difficult to guarantee high reliability and low latency communication. Orthogonal Time Frequency Space (OTFS) modulation technology exhibits significant advantages due to its Doppler robustness and time-invariance.

[0004] However, in related technologies, the system combining OTFS modulation and MIMO technology faces the problem of excessively high channel estimation calculation complexity, which is difficult to meet real-time processing requirements. SUMMARY

[0005] Therefore, the purpose of the present disclosure is to provide a channel estimation method, device, electronic device, and storage medium, which at least partially solve one of the technical problems in the related art.

[0006] To achieve the above purpose, in a first aspect, an embodiment of the present disclosure provides a channel estimation method applied to a server, the method comprising: determining time delay grid parameters and Doppler frequency shift grid parameters of a target domain channel, constructing a receiving end pilot symbol matrix of the target domain channel based on the time delay grid parameters and the Doppler frequency shift grid parameters; determining singular values of the receiving end pilot symbol matrix, and screening the singular values to obtain a rank estimation value; determining user sparsity information of each user in the target domain channel, and obtaining a channel sparsity parameter based on the rank estimation value and the user sparsity information; estimate based on the received pilot symbol matrix to obtain a column submatrix; estimate based on the received pilot symbol matrix and the channel sparsity parameter to obtain a row submatrix; obtain a channel estimation matrix based on the target domain channel, the column submatrix and the row submatrix; obtain a channel estimation matrix based on the target domain channel, the column submatrix and the row submatrix;

[0007] Based on the same inventive concept, the second aspect of the exemplary embodiments of the present disclosure provides a channel estimation device, comprising: A pilot symbol matrix determination module is configured to determine a delay grid parameter and a Doppler shift grid parameter of a target domain channel, and construct a received pilot symbol matrix of the target domain channel based on the delay grid parameter and the Doppler shift grid parameter. A rank estimation value determination module is configured to determine singular values of the received pilot symbol matrix, and obtain a rank estimation value by screening the singular values. A sparsity parameter determination module is configured to determine user sparsity information of each user in the target domain channel, and obtain a channel sparsity parameter based on the rank estimation value and the user sparsity information. A column submatrix determination module is configured to estimate based on the received pilot symbol matrix to obtain a column submatrix. A row submatrix determination module is configured to estimate based on the received pilot symbol matrix and the channel sparsity parameter to obtain a row submatrix. A channel estimation matrix determination module is configured to obtain a channel estimation matrix based on the target domain channel, the column submatrix and the row submatrix. A transmitter vector determination module is configured to obtain received vector information, and estimate the received vector information by using the channel estimation matrix to obtain transmitter vector information.

[0008] Based on the same inventive concept, the third aspect of the exemplary embodiments of the present disclosure provides an electronic device, comprising a memory, a processor and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the method of the first aspect.

[0009] Based on the same inventive concept, the fourth aspect of the exemplary embodiments of the present disclosure provides a non-transitory computer readable storage medium, which stores computer instructions for causing a computer to execute the method of the first aspect.

[0010] Based on the same inventive concept, the fifth aspect of the exemplary embodiments of the present disclosure provides a computer program product comprising computer program instructions which, when executed on a computer, cause the computer to perform the method according to the first aspect.

[0011] As can be seen from the above, the estimation method, device, electronic equipment and storage medium provided by the embodiments of the present disclosure, the method comprises: determining the delay grid parameter and the Doppler shift grid parameter of the target domain channel, constructing based on the delay grid parameter and the Doppler shift grid parameter to obtain the receive end pilot symbol matrix of the target domain channel; determining the singular value of the receive end pilot symbol matrix, and filtering the singular value to obtain a rank estimation value; determining the user sparsity information of each user in the target domain channel, and obtaining a channel sparsity parameter based on the rank estimation value and the user sparsity information; estimating based on the receive end pilot symbol matrix to obtain a column submatrix; estimating the target domain channel based on the receive end pilot symbol matrix and the channel sparsity parameter to obtain a row submatrix; obtaining a channel estimation matrix based on the target domain channel, the column submatrix and the row submatrix; obtaining receive end vector information, and estimating the transmit end vector information by estimating the receive end vector information through the channel estimation matrix. The present disclosure significantly improves the channel estimation accuracy, and the running time is greatly shortened compared with the traditional scheme, fully meeting the actual needs of high efficiency and low latency. BRIEF DESCRIPTION OF DRAWINGS

[0012] In order to more clearly illustrate the technical solutions in the present disclosure or the related art, the drawings needed to be used in the embodiments or related art description will be briefly introduced. Obviously, the drawings in the following description are only embodiments of the present disclosure, and other drawings can be obtained by those skilled in the art without creative labor.

[0013] Figure 1 An application scenario diagram of the channel estimation method provided by the exemplary embodiments of the present disclosure; Figure 2 A flowchart of the channel estimation method provided by the exemplary embodiments of the present disclosure; Figure 3 An uplink diagram of a high-speed mobile scenario of the channel estimation method provided by the exemplary embodiments of the present disclosure; Figure 4 An equivalent CSI matrix sparse low rank structure diagram of the channel estimation method provided by the exemplary embodiments of the present disclosure; Figure 5An estimation precision-SNR variation comparison diagram of the channel estimation method provided for the exemplary embodiments of the present disclosure; Figure 6 An average calculation time-antenna quantity variation comparison diagram of the channel estimation method provided for the exemplary embodiments of the present disclosure; Figure 7 An BER-SNR variation comparison diagram of the channel estimation method provided for the exemplary embodiments of the present disclosure; Figure 8 A structure diagram of the channel estimation device provided for the exemplary embodiments of the present disclosure; Figure 9 An electronic device hardware structure diagram provided for the exemplary embodiments of the present disclosure. DETAILED DESCRIPTION

[0014] It can be understood that, before using the technical solutions disclosed in the embodiments of the present application, the type, use range, use scenario, etc. of the personal information involved in the present application should be informed to the user and the authorization of the user should be obtained in a proper manner according to relevant laws and regulations.

[0015] For example, in response to receiving the active request of the user, prompt information is sent to the user to explicitly prompt the user that the operation requested to be performed will require obtaining and using the personal information of the user. Thus, the user can voluntarily choose whether to provide the personal information to the electronic device, application program, server or storage medium, etc. software or hardware that performs the operation of the technical solutions of the present application according to the prompt information.

[0016] As an optional but non-limiting implementation manner, in response to receiving the active request of the user, the manner of sending prompt information to the user may, for example, be a pop-up window manner, and the prompt information may be presented in the form of text in the pop-up window. In addition, the pop-up window may also carry a selection control for the user to select "agree" or "disagree" to provide personal information to the electronic device.

[0017] It can be understood that the above notification and user authorization process is only illustrative, and does not limit the implementation manner of the present application, and other manners meeting the relevant laws and regulations can also be applied to the implementation manner of the present application.

[0018] It can be understood that the data (including but not limited to the data itself, the acquisition or use of the data) involved in the present technical solution should comply with the requirements of the relevant laws and regulations and relevant provisions.

[0019] To make the objectives, technical solutions and advantages of the present disclosure clearer, the principles and spirits of the present disclosure will be described below with reference to several exemplary embodiments. It should be understood that the embodiments are only given to enable those skilled in the art to better understand and implement the present disclosure, and do not limit the scope of the present disclosure in any way. On the contrary, the embodiments are provided to make the present disclosure more thorough and complete, and to enable the scope of the present disclosure to be fully conveyed to those skilled in the art.

[0020] In this document, it should be understood that any quantity of elements in the accompanying drawings are used for example, not limitation, and any naming is only used for distinction, not having any limiting meaning.

[0021] It should be noted that, unless otherwise defined, the technical terms or scientific terms used in the embodiments of the present disclosure should be understood as the common meanings understood by those skilled in the art to which the embodiments of the present disclosure belong. The terms "first", "second" and similar terms used in the embodiments of the present disclosure do not represent any order, number or importance, but are only used to distinguish different components. The terms "include" or "contain" and similar terms mean that the elements or objects before the terms encompass the elements or objects listed after the terms and their equivalents, without excluding other elements or objects. The terms "connect" or "connected" and similar terms are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. The terms "upper", "lower", "left", "right" and the like only represent relative positional relationships, and when the absolute positions of the described objects are changed, the relative positional relationships can also be changed accordingly. The article "a" or "an" before an element does not exclude the existence of multiple such elements.

[0022] The principles and spirits of the present disclosure will be described in detail below with reference to several representative embodiments of the present disclosure.

[0023] As described in the background, in the related art, the system combining OFDM modulation and MIMO technology faces the problem of too high channel estimation calculation complexity, which is difficult to meet the real-time processing requirements. Specifically, Multiple-Input Multiple-Output (MIMO) technology is one of the core technologies in modern wireless communication systems, aiming to improve the capacity and reliability of communication systems through joint transmission and reception processing of multiple antennas. With the continuous growth of mobile communication demand and the rapid increase in the number of users, future wireless communication networks have increasing demands for high capacity, low latency and high reliability. To further improve spectrum utilization and expand network capacity, Massive MIMO (mMIMO) technology has emerged as an important part of 5G and subsequent wireless communication systems. Massive Multiple-Input Multiple-Output (Massive Multiple-Input Multiple-Output mMIMO) technology realizes simultaneous data transmission to multiple User Equipment (UE) by deploying a large number of independently controllable antennas at the Base Station (BS).

[0024] The new generation of wireless networks is expected to access various mobile terminals, including autonomous vehicles, drones, Low-Earth-Orbit (LEO) satellites and high-speed trains. The core challenge faced by these new applications is how to achieve high-reliability communication in high-mobility environments. As the main modulation method in 4G / 5G cellular systems and Wi-Fi networks, the system combining Orthogonal Frequency Division Multiplexing (OFDM) modulation and MIMO technology performs well in low-speed or medium-speed mobility environments, with advantages such as anti-multipath fading, improved spectral efficiency, expanded coverage and support for more user access. However, in high-mobility and high-multipath fading environments, due to the fast time-varying and high-Doppler effect of the wireless channel, OFDM modulation will have serious Inter-Carrier Interference (ICI). In order to cope with the time-varying nature of the MIMO channel, various improvements have been proposed, such as using a complex exponential basis expansion model to represent the time-varying channel, or deploying linear equalizers and nonlinear equalizers to effectively eliminate the effects of ICI. However, in some complex high-mobility scenarios, MIMO-OFDM systems still have difficulty in guaranteeing the high reliability and low latency of wireless transmission.

[0025] As a key candidate technology for the next generation of wireless communication systems, Orthogonal Time Frequency Space (OTFS) modulation maps information onto the Delay-Doppler (DD) domain instead of the Time-Frequency (TF) domain relied on by OFDM systems. This shift in modulation paradigm endows OTFS with unique physical layer characteristics: by mapping the time-varying channel in the DD domain to a two-dimensional quasi-static channel matrix, OTFS exhibits significant Doppler robustness and delay invariance. This advantage stems from the decoupling of channel delay and Doppler components in the DD domain, allowing each information symbol to experience approximately constant channel response, effectively suppressing inter-symbol interference (ISI) and ICI in high-speed mobile environments.

[0026] Therefore, the combination of MIMO technology and OTFS provides a new theoretical framework for wireless communication systems, especially in high mobility and complex channel environments. OTFS is designed as a preprocessing step for the transmitter OFDM signal and a post-processing step for the receiver OFDM signal, while MIMO technology uses joint transmission and reception of multiple antennas to improve system capacity and reliability.

[0027] In this system, accurate acquisition of Channel State Information (CSI) is a key step for system deployment and performance optimization. The quality of CSI estimation not only directly affects the accuracy of data detection and the overall performance of the system, but also causes a significant increase in pilot overhead and computational complexity as the antenna scale of the system expands. Traditional channel estimation algorithms, such as Least Square (LS) estimation and Minimum Mean Square Error (MMSE) estimation, can provide relatively accurate CSI estimation in low-speed or moderate mobility scenarios, but their performance is severely affected in high Doppler and high time-varying channel environments. Due to the sparsity of the wireless channel in the DD domain under OTFS modulation, a large number of channel estimation algorithms based on Compress Sensing (CS) or Sparse Bayesian Learning (SBL) have been developed. Although these algorithms can improve estimation accuracy by exploiting the sparsity of the OTFS channel, in mMIMO-OTFS systems, due to the large antenna scale and high computational complexity, these methods face the problem of excessively high computational complexity in practical applications, making it difficult to meet the real-time processing requirements of modern high-speed mobile scenarios.

[0028] To solve the above problems, the present disclosure provides an estimation method, device, electronic equipment and storage medium, the method comprising: determining the time delay grid parameters and the Doppler shift grid parameters of the target domain channel, constructing based on the time delay grid parameters and the Doppler shift grid parameters to obtain the received pilot symbol matrix of the target domain channel; determining the singular value of the received pilot symbol matrix, screening the singular value to obtain the rank estimation value; determining the user sparsity information of each user in the target domain channel, obtaining the channel sparsity parameter based on the rank estimation value and the user sparsity information; estimating based on the received pilot symbol matrix to obtain the column submatrix; estimating the target domain channel based on the received pilot symbol matrix and the channel sparsity parameter to obtain the row submatrix; obtaining the channel estimation matrix based on the target domain channel, the column submatrix and the row submatrix; obtaining the transmitter vector information by estimating the receiver vector information through the channel estimation matrix. The present disclosure improves the accuracy of channel estimation and the reliability of the system, while significantly reducing the computational complexity, and is particularly suitable for mMIMO-OTFS system in high mobility and complex channel environment.

[0029] After introducing the basic principles of the present disclosure, the various non-limiting embodiments of the present disclosure will be specifically introduced below.

[0030] Reference Figure 1 , which is a schematic diagram of an application scenario of the channel estimation method provided by the exemplary embodiments of the present disclosure.

[0031] In this application scenario, it includes a terminal device 101 and a server 102. Wherein, the terminal device 101 and the server 102 can be connected through wired or wireless communication network to realize data interaction.

[0032] The terminal device 101 can be an electronic device close to the user side with data transmission, multimedia input / output function, including but not limited to desktop computer, mobile phone, mobile computer, tablet computer, media player, smart wearable device, personal digital assistant (PDA) or other electronic devices capable of realizing the above functions. The electronic device can include a processor and a display screen with touch input function, the display screen is used to present a graphical user interface, the graphical user interface can display an application interface, the processor is used to process application data, generate a graphical user interface and control the display of the graphical user interface on the display screen.

[0033] The server 102 and the data storage system 103 can each be a standalone physical server, a server cluster composed of multiple physical servers, or a distributed system, and can also be a cloud server providing basic cloud computing services such as cloud service, cloud database, cloud computing, cloud function, cloud storage, network service, cloud communication, middleware service, domain name service, security service, CDN (Content Delivery Network), and big data and artificial intelligence platform.

[0034] In some example embodiments, the channel estimation method can run on the terminal device 101 or the server 102.

[0035] When the channel estimation method runs on the server 102, the server 102 is configured to provide a channel estimation service to a user of the terminal device 101.

[0036] The server 102 determines a delay grid parameter and a Doppler shift grid parameter of a target domain channel, and constructs a received pilot symbol matrix of the target domain channel based on the delay grid parameter and the Doppler shift grid parameter. The server 102 determines a singular value of the received pilot symbol matrix, and filters the singular value to obtain a rank estimation value. The server 102 determines user sparsity information of each user in the target domain channel, and obtains a channel sparsity parameter based on the rank estimation value and the user sparsity information. The server 102 estimates based on the received pilot symbol matrix to obtain a column subsample matrix. The server 102 estimates the target domain channel based on the received pilot symbol matrix and the channel sparsity parameter to obtain a row subsample matrix. The server 102 obtains a channel estimation matrix based on the target domain channel, the column subsample matrix, and the row subsample matrix. The server 102 obtains received end vector information, estimates the received end vector information through the channel estimation matrix to obtain sending end vector information, and then transmits the sending end vector information to the terminal device 101.

[0037] It should be noted that the above application scenarios are only shown for the purpose of facilitating understanding of the spirit and principles of the present disclosure, and the embodiments of the present disclosure are not limited in this respect. On the contrary, the embodiments of the present disclosure can be applied to any applicable scenario.

[0038] Reference Figure 2 The channel estimation method comprises the following steps: Step S210, determine the delay grid parameter and the Doppler shift grid parameter of the target domain channel, and construct based on the delay grid parameter and the Doppler shift grid parameter to obtain the pilot symbol matrix of the receiving end of the target domain channel.

[0039] In this step, the delay grid parameter and the Doppler shift grid parameter of the target domain channel are determined, and the pilot symbol matrix of the receiving end is constructed based on these parameters, which can provide effective data basis and prior structure information for channel estimation of the target domain channel, thereby improving the accuracy and performance of channel estimation.

[0040] In some embodiments, the delay grid parameter includes a delay variable and a delay grid size.

[0041] In specific implementation, the delay variable refers to: In the mMIMO-OTFS system of wireless communication, the delay variable is used to describe the delay experienced by the signal during transmission from the transmitting end to the receiving end. Due to the multipath effect of wireless channels, signals propagate through different paths, and each path corresponds to different delay. The delay variable is used to quantify these delays, which reflects the difference in propagation time of signals on different paths.

[0042] In specific implementation, the delay grid size refers to: In OTFS modulation technology, the delay characteristics of wireless channels are continuous. In order to facilitate digital signal processing and channel modeling, it is necessary to discretize the continuous delay axis. The delay grid size represents the interval of discretization in the delay direction, i.e. the time interval between adjacent delay sampling points. It determines the actual delay value corresponding to each sampling point on the delay axis.

[0043] In some embodiments, the Doppler shift grid parameter includes a Doppler shift and a Doppler grid size.

[0044] In specific implementation, the Doppler shift refers to: The Doppler shift is a phenomenon caused by relative motion (such as moving user equipment, base stations or scatterers) that causes the frequency of the received signal to shift relative to the frequency of the transmitted signal. Specifically, the Doppler shift is an important and complex characteristic in wireless communication systems, which has a significant impact on channel characteristics and signal transmission performance, especially in high mobility environments.

[0045] In specific implementation, the Doppler grid size refers to: The Doppler grid size represents the interval of discretization in the Doppler shift direction, i.e. the frequency interval between adjacent Doppler shift sampling points. It determines the Doppler shift value corresponding to each sampling point on the Doppler shift axis.

[0046] In this exemplary embodiment, the receiver pilot symbol matrix of the target domain channel is constructed based on the time delay grid parameters and the Doppler frequency shift grid parameters, including: Determine the time delay Doppler gain coefficient corresponding to each antenna in the target domain channel. Based on the time delay Doppler gain coefficient, the time delay variable, the time delay grid size, the Doppler frequency shift, and the Doppler grid size, obtain the time delay Doppler domain channel response function. Based on the time delay Doppler gain coefficient, the time delay grid parameter, and the Doppler frequency shift grid parameter, obtain the time delay Doppler domain channel response function. Based on the time delay grid size and the Doppler grid size, a dictionary matrix is ​​obtained; Discretize the time-delay Doppler domain channel response function to obtain the channel state information matrix; The noise matrix of the target domain channel is determined, and the receiver pilot symbol matrix is ​​constructed based on the channel state information matrix, the dictionary matrix, and the noise matrix.

[0047] In specific implementation, the time delay Doppler gain coefficient corresponding to each antenna in the target domain channel refers to: The channel gain value corresponding to each antenna under a specific time delay and Doppler shift is used to characterize the amplitude and phase characteristics of the signal under the corresponding time delay and Doppler shift conditions. Specifically, the... v The receiving antenna and the first u Between the transmitting antennas, corresponding to the first... i The delayed tap and the first j Channel coefficients of a Doppler tap.

[0048] In specific implementation, the time-delay Doppler gain coefficient corresponding to each antenna in the target domain channel (i.e., the DD domain channel) is determined. Based on the time-delay Doppler gain coefficient, the time-delay variable, the time-delay grid size, the Doppler frequency shift, and the Doppler grid size, the time-delay Doppler domain channel response function is obtained. The method for obtaining the time-delay Doppler domain channel response function based on the time-delay Doppler gain coefficient, the time-delay grid parameter, and the Doppler frequency shift grid parameter is as follows: Utilizing the joint sparsity and low-rank properties of the DD domain channel, to handle fractional Doppler frequency shift, a... (This represents the interval of the delay grid in the DD domain channel.) The delay is greater than the maximum delay spread of the channel, that is, the delay corresponding to the longest path the signal travels ( This means that the discrete sampling interval in the delay direction exceeds the maximum delay value of the channel. (Indicates Doppler grid size) Much greater than the upper bound of the maximum Doppler frequency shift of the channel If the Doppler grid size is much larger than the upper bound of the maximum Doppler shift of the channel , it means that the discretization interval in the Doppler shift direction is large enough to cover all possible Doppler shift values in the channel, thus ensuring the completeness and accuracy of the channel model), reconstruct the DD-domain channel based on the sparse grid, and obtain the delay-Doppler domain channel response function , as shown below: ; wherein, is expressed as a channel gain value; is expressed as a delay grid size; is expressed as a Doppler grid size; is expressed as an impulse function in the delay-Doppler domain, used to represent the impulse response of the channel at a specific delay and Doppler shift, wherein : This is an impulse function about delay , representing the impulse response at delay . When , the value of the function is infinite, and zero at other positions; : This is an impulse function about Doppler shift , representing the impulse response at Doppler shift . When , the value of the function is infinite, and zero at other positions.

[0049] In implementation, the way to obtain the dictionary matrix based on the delay grid size and the Doppler grid size is: determine the delay range and the Doppler shift range ; according to the delay grid size and the Doppler grid size , divide the delay range into small intervals, and divide the Doppler shift range into small intervals; for each combination of delay grid and Doppler grid , calculate the corresponding channel response . This usually involves factors such as the impulse response of the channel, Doppler effect, etc.; all the calculated channel responses are taken as column vectors to form a matrix, which is the dictionary matrix.

[0050] In implementation, the way to discretize the delay-Doppler domain channel response function to obtain the channel state information matrix is: The continuous-time DD domain channel impulse response can be expressed as: ; in, For the first Complex gain of the path; and The first The time delay and Doppler shift of the path; Let be the number of valid paths, where let Because the number of scatterers in a wireless channel is limited, only a small number exist. One transmission path, namely .

[0051] Delay axis: Move the delay axis from 0 to... With intervals Discretization yields time-delay grid points. .

[0052] Doppler axis: The Doppler axis is shifted from 0 to... With intervals Discretization yields Doppler grid points. .

[0053] The time delay Doppler response function of the channel Represented at discrete time delays and Doppler grid points as follows: ; in, and They represent the first The index of the path on the time-delay grid and the Doppler grid.

[0054] Through the discretization process described above, a channel state information matrix can be constructed. Each element Indicates the first The time-delay grid point and the first Channel coefficients at each Doppler grid point.

[0055] In specific implementation, the noise matrix of the target domain channel is determined, and the receiver pilot symbol matrix is ​​constructed based on the channel state information matrix, the dictionary matrix, and the noise matrix. In some embodiments, reference Figure 3where the base station (BS) is equipped with a large number of antennas, enabling it to communicate with multiple user equipment (UE) simultaneously and improve signal quality and reliability through techniques such as beamforming; the BS's transmitted signal covers a wide area, including urban buildings, mountainous regions, and railway tracks in different geographical environments, demonstrating the applicability of the mMIMO-OTFS system in complex propagation environments.

[0056] The high-speed train in the lower right corner of the figure represents a high-speed moving UE. In the mMIMO-OTFS system, even if the train moves at high speed, the system can utilize the Doppler robustness of OTFS modulation to ensure that the communication devices of passengers inside the train can obtain stable communication services.

[0057] The truck in the lower left corner of the figure represents a moving UE on land. When the truck is driving on the road, it will experience different channel conditions such as multipath fading and shadowing effects. The mMIMO-OTFS system can provide reliable communication links for the truck through multi-antenna technology and OTFS modulation.

[0058] The drone in the upper part of the figure represents an aerial UE. The drone needs to communicate with the base station during flight, and the mMIMO-OTFS system can adapt to the rapid movement and height changes of the drone to provide high-quality communication services.

[0059] The mountainous region device on the right side of the figure represents a UE in a complex terrain. The mountainous terrain can cause signal blocking and reflection, forming a complex channel environment. The mMIMO-OTFS system can improve the quality of communication in mountainous regions through multi-antenna diversity and the time-delay-doppler decoupling characteristics of OTFS modulation.

[0060] In the figure, the communication links between different types of UEs and the base station face different time delays and Doppler shifts. For example, the high-speed train will produce a large Doppler shift due to its high-speed movement, while the mountainous region device may experience a long time delay due to terrain reflection. Through OTFS modulation, the system can better handle these time-varying channel characteristics, improving the reliability and efficiency of communication. The figure also shows multiple reflection paths (such as buildings, mountains, etc.), which can cause multipath effects. In the mMIMO-OTFS system, the base station can effectively utilize multipath signals through multi-antenna reception and OTFS time-delay-doppler decoupling processing, converting them into useful information to improve system performance.

[0061] In practical wireless channels, due to the limited number of scatterers, the channel typically exhibits sparsity in the delay-Doppler domain. That is, the channel response is zero or close to zero at most locations (zero elements), while only a few locations show significant channel responses (non-zero elements). By identifying the locations and values ​​of these non-zero elements, channel estimation can be performed more efficiently, as only the delay and Doppler shift combinations corresponding to these non-zero elements need to be considered. This helps reduce the complexity of channel estimation while maintaining high estimation accuracy. (See specific references.) Figure 4 In the picture express A complex matrix of rows, where The total number of points in the time-delay-Doppler grid. The matrix represents the number of users. It is composed of stacked channel responses from multiple users. Each row corresponds to the product of the delay-Doppler grid points and the number of users, while each column corresponds to the number of base station receiving antennas. The matrix exhibits significant sparsity (only a few non-zero elements, representing a limited number of multipath components) and low rank (multiple antenna channels share the same delay-Doppler support set, leading to strong correlations between rows and columns). Non-zero elements (such as asterisks or colored blocks) are discretely distributed at grid intersections, while most areas are zero. The multi-antenna sections are aligned using a block structure.

[0062] By stacking The pilot signals received by each antenna can be used to obtain a sparse low-rank channel estimation model based on multiple measurement vectors, and its receiver pilot symbol matrix... for: ; in, Represented as a dictionary matrix; Represented as a channel state information matrix; Represented as a noise matrix, where the noise matrix... Random interference, which is unavoidable at the receiving end, is mathematically represented as the observed signal. With ideal noise-free signal The difference between them.

[0063] Step S220: Determine the singular values ​​of the pilot symbol matrix at the receiving end, and filter the singular values ​​to obtain the rank estimate.

[0064] In this step, the singular values ​​of the pilot symbol matrix at the receiving end are determined and filtered to obtain a rank estimate. Its core function is to reveal the low-rank characteristics of the channel matrix, thereby significantly reducing the estimation complexity. Specifically, by analyzing the pilot symbol matrix... Singular Value Decomposition (SVD) is performed to extract the distribution characteristics of singular values. Then, significantly non-zero singular values ​​are selected based on a pre-defined hard threshold; the number of these significantly non-zero singular values ​​is the rank estimate of the channel matrix. This step not only quantifies the effective degrees of freedom of the channel in the delay-Doppler domain (reflecting multipath sparsity) but also provides crucial prior parameters for subsequent random projection and sparse recovery algorithms (such as SOMP). This ensures that while preserving key channel information, the high-dimensional optimization problem is compressed into a low-dimensional space, achieving a balance between complexity and accuracy.

[0065] In this exemplary embodiment, the singular values ​​are filtered to obtain a rank estimate, including: The singular values ​​are filtered based on a filtering threshold, and if a singular value is greater than the filtering threshold, the singular value is used as the rank estimate.

[0066] In this step of channel estimation, the process of filtering singular values ​​based on a selection threshold aims to determine the effective rank of the channel matrix, i.e., retaining channel paths that significantly contribute to signal transmission. This step first calculates the singular values ​​of the channel matrix, then sets a selection threshold, typically determined based on the statistical properties of the singular values. When a singular value exceeds this threshold, it indicates that the corresponding channel path has a significant impact on signal transmission; therefore, this singular value is retained as part of the rank estimate. In this way, non-zero elements in the channel can be effectively identified and utilized, while paths with minimal impact on signal transmission are ignored, thereby reducing the complexity of channel estimation and improving its accuracy and the performance of the communication system.

[0067] In practice, the singular values ​​are filtered based on a screening threshold. When a singular value exceeds the screening threshold, the singular value is used as the rank estimate, expressed by the following formula: ; in, Represented as a rank estimate; ( This is represented as an indicator function, which takes the value 1 when the condition is met and 0 otherwise; Represented as a matrix No. One singular value; This is represented as the filtering threshold.

[0068] In the exemplary embodiments described above, the method for obtaining the rank estimate was introduced. Below, the method for obtaining the filtering threshold is described in detail: In this exemplary embodiment, the filtering threshold is obtained through the following method: Based on the time delay grid size and the Doppler grid size, the total size of the channel network is obtained; The number of antennas for the target domain channel is determined, and a scaling factor is obtained based on the number of antennas and the total size of the channel network. Based on the aforementioned scaling factor, the adjustment coefficient is obtained; Singular value decomposition is performed on the pilot symbol matrix of the receiving end to obtain the median singular value; The screening threshold is obtained based on the adjustment coefficient and the median singular value.

[0069] In specific implementation, the total size of the channel network is obtained based on the time delay grid size and the Doppler grid size as follows: The total size of the channel network is the total number of delay-Doppler grid points in step S210. .

[0070] In practical implementation, the scaling factor, based on the number of antennas and the total size of the channel network, is obtained using the following formula: ; in, Indicates the scaling factor; This indicates the number of users.

[0071] In practical implementation, the adjustment coefficient is obtained based on the scaling factor using the following formula: ; in, This is represented as an adjustment factor.

[0072] The above formula calculates the adjustment coefficient using a cubic polynomial function. This coefficient is used based on the scaling factor. Adjust the threshold or other relevant parameters to adapt to channel characteristics under different system configurations or operating conditions. This cubic polynomial, derived from experimental data, theoretical analysis, or optimization algorithms, is capable of capturing the scaling factor. With adjustment coefficient The nonlinear relationship between them allows for more precise control of key parameters in channel estimation or other signal processing processes, thereby improving system performance and robustness.

[0073] In practice, singular value decomposition is performed on the receiving pilot symbol matrix to obtain the median separation method: For the pilot symbol matrix at the receiving end Singular value decomposition yields three matrices. ;in It is a unitary matrix. It is a diagonal matrix, and the elements on its diagonal are singular values. Singular values ​​represent the strength or energy of a signal in different directions. In channel estimation, the magnitude of singular values ​​can reflect the significance of different paths in the channel. The median singular value is the value in the middle position after all singular values ​​are arranged in ascending order. If the total number of singular values ​​is odd, the median singular value is the middle value; if it is even, it is the average of the two middle values.

[0074] In practice, the method for obtaining the screening threshold based on the adjustment coefficient and the median singular value is expressed by the following formula: ; in, It is represented as the median singular value.

[0075] Step S230: Determine the user sparsity information for each user in the target domain channel, and obtain the channel sparsity parameter based on the rank estimate and the user sparsity information.

[0076] In practical implementation, the user sparsity information for each user in the target domain channel refers to: In wireless communication, channel sparsity typically refers to the relatively small number of non-zero elements in the channel matrix, meaning that most elements can be considered zero or close to zero. This sparsity is usually determined by the physical characteristics of the channel, such as the number of scatterers, mobility, and multipath propagation. For each user equipment (UE), user sparsity represents the number of significant non-zero elements in that user's channel response. These elements represent paths or scatterers that have a significant impact on signal transmission. Therefore, user sparsity information is represented as the number of non-zero or significant elements in the channel response of a specific UE.

[0077] In specific implementation, the channel sparsity parameters are obtained based on the rank estimate and the user sparsity information in the following way: ; in, Represented as a channel sparsity parameter; This is represented as user sparsity information.

[0078] Step S240: Estimate based on the pilot symbol matrix of the receiving end to obtain the column sampling sub-matrix.

[0079] In this step, the computational complexity of channel estimation is significantly reduced while retaining key channel information. By constructing a column sampling submatrix by randomly or according to a specific strategy selecting some columns from the receiver pilot symbol matrix, the amount of data to be processed is reduced, thereby reducing the dimensionality of matrix operations and the consumption of computational resources.

[0080] In this exemplary embodiment, the column sampling submatrix is ​​obtained through the following method: The pilot symbol matrix at the receiving end is reassembled to obtain a column sampling reassembled matrix; The column sampling submatrix is ​​estimated based on the linear minimum mean square error algorithm.

[0081] In specific implementation, the pilot symbol matrix at the receiving end is reassembled to obtain a column-sampled reassembled matrix in the following way: At the receiving end, for Mb receiving antennas, in order to effectively reduce computational complexity and preserve the integrity of channel information, this paper adopts a uniform random sampling strategy, that is, sampling with probability pk=c / Mb, and randomly selecting qc antennas from the Mb receiving antennas to form a subset of receiving antennas. Based on this, the sampled signal can be reconstructed, and its mathematical expression is as follows: ; in, It is represented as a column sampling reconstruction matrix.

[0082] In specific implementation, the column sampling submatrix is ​​estimated based on the linear minimum mean square error algorithm by means of the column sampling recombination matrix. By applying the LMMSE estimation method, the closed-form solution of Hc can be obtained, and its expression is as follows: ; in, The covariance matrix of Hc is defined as follows: ; Where λ is a noise-related parameter. Describes the MNp-dimensional identity matrix. Represents a matrix The average of all possible values ​​is taken, where It is a column sampling submatrix. yes The conjugate transpose of .

[0083] Step S250: Estimate the target domain channel based on the receiver pilot symbol matrix and the channel sparsity parameter to obtain a row sampling submatrix.

[0084] This step significantly reduces the computational complexity of channel estimation while improving its accuracy. By incorporating sparsity parameters, this step can accurately extract key channel information from the pilot symbol matrix, avoiding direct estimation of the entire high-dimensional channel matrix. This reduces computational resource consumption while maintaining channel estimation accuracy.

[0085] In this exemplary embodiment, the target domain channel is estimated based on the receiver pilot symbol matrix and the channel sparsity parameter to obtain a row sampling sub-matrix, including: The receiving pilot symbol matrix is ​​used as the first residual matrix; Determine the conjugate transpose of the dictionary matrix, and obtain the first relevance index based on the first residual matrix and the conjugate transpose matrix; The first relevance index is stored in a pre-built support set; Based on the correlation index within the support set, the dictionary matrix is ​​filtered to obtain the first measurement matrix corresponding to the support set; Based on the first measurement matrix and the receiver pilot symbol matrix, a first sampling matrix is ​​obtained; The channel sparsity parameter is used as the maximum number of iterations; Determine the current iteration number, and then determine whether the current iteration number has reached the maximum iteration number. In response to the current iteration number reaching the maximum iteration number, the first sampling matrix is ​​used as the row sampling submatrix.

[0086] In specific implementation, the receiving pilot symbol matrix is ​​used as the first residual matrix: Initialize the current iteration number z = 0; support set The support set is used to store the positions of non-zero elements in the identified sparse signal. Initializing it to an empty set means that no positions of any non-zero elements have been identified at the beginning.

[0087] The pilot symbol matrix at the receiving end is used as the first residual matrix to measure the difference between the current channel estimate and the actual received signal.

[0088] In specific implementation, the conjugate transpose of the dictionary matrix is ​​determined, and the first relevance index is obtained based on the first residual matrix and the conjugate transpose matrix as follows: For dictionary matrix The i The conjugate transpose of a column vector is denoted as . The conjugate transpose operation involves taking the complex conjugate of each element and transposing it; then, the conjugate transpose is computed. With the first residual matrix The product of the first residual matrix; this product is actually a vector whose elements reflect the first residual matrix. exist The i Projecting along the column direction. Next, calculate the square of the L2 norm (i.e., the Euclidean norm) of the vector obtained in the previous step, denoted as . The squared L2 norm is a way to measure the length of a vector; it reflects... exist Energy or magnitude in the direction. Finally, iterate through all possible indices. i Finding Largest first relevance index This first relevance index The column vector it points to is related to the current residual matrix. The most relevant dictionary atom can be represented by the following formula: .

[0089] In specific implementation, the first correlation index is stored in a pre-built support set; the dictionary matrix is ​​filtered based on the correlation index within the support set to obtain the first measurement matrix corresponding to the support set; the first sampling matrix is ​​obtained based on the first measurement matrix and the receiver pilot symbol matrix in the following manner: First relevance index Stored in a pre-built support set In the middle, support set Indices used to record the atoms or eigenvectors selected during the iteration process, which are most relevant to the current residual signal, based on the support set. The relevance index stored in the dictionary matrix The corresponding column vectors are selected from the data to form the first measurement matrix. This measurement matrix contains dictionary atoms most relevant to the current residual signal, used for further channel estimation.

[0090] Using the first measurement matrix Construct a system of linear equations ,in, This is the first submatrix; by solving the system of linear equations using the least squares method, we obtain... The goal of least squares is to find an estimated value. , making and The difference between them is minimal. This can be expressed by the formula: ; in, The Frobenius norm is used to measure the "size" or "error" of a matrix. Represented as The estimated value, which represents the current support set. Within the defined subspace, the receiver pilot symbol matrix is ​​best fitted. The channel matrix (i.e., the first channel matrix).

[0091] In specific implementation, the channel sparsity parameter is used as the maximum number of iterations; the current iteration number is determined, and it is judged whether the current iteration number has reached the maximum number of iterations; in response to the current iteration number reaching the maximum number of iterations, the first sampling matrix is ​​used as the row sampling submatrix. Based on the sparsity parameters of the channel To set the maximum number of iterations. Sparsity parameter. This represents the expected number of non-zero elements in the channel matrix, and the first channel matrix is ​​obtained in the above steps. The current iteration number is the current iteration number. If the sparsity parameter at this time So, the maximum number of iterations ,So = Then As a row sampling submatrix.

[0092] In some embodiments, the method further includes constructing a positive interactive projection matrix in response to the current iteration number not reaching the maximum iteration number, and obtaining a second residual matrix based on the positive interactive projection matrix and the receiver pilot symbol matrix. Based on the second residual matrix and the conjugate transpose matrix, the second correlation index is obtained; The second relevance index is stored in a pre-built support set; Based on the correlation index within the support set, the dictionary matrix is ​​filtered to obtain the second measurement matrix corresponding to the support set; based on the second measurement matrix and the receiver pilot symbol matrix, the second sampling matrix is ​​obtained. Determine the current iteration number, and then determine whether the current iteration number has reached the maximum iteration number; In response to the current iteration number reaching the maximum iteration number, the second sampling matrix is ​​used as the row sampling submatrix.

[0093] In specific implementation, in response to the current iteration number not reaching the maximum iteration number, the measurement matrix is ​​constructed to obtain a positive cross-complement projection matrix. Based on the positive cross-complement projection matrix and the receiver pilot symbol matrix, the second residual matrix is ​​obtained in the following manner: If the sparsity parameter is at this time So, the maximum number of iterations Then the current iteration number < For the first measurement matrix Construct, and obtain the positive interactive complement projection matrix. The positive cross complement projection matrix It is used to remove the signal from the first measurement matrix. The captured components. It can be constructed in the following ways: ; in, Represented as the identity matrix, the identity matrix is ​​a special form of square matrix where all elements on its main diagonal are 1, and all elements on the off-diagonal are 0. In matrix multiplication, the identity matrix acts similarly to "1" in number multiplication; that is, multiplying any matrix by the identity matrix does not change its value. yes The conjugate transpose of . yes The inverse matrix.

[0094] Using the positive cross complement projection matrix and receiver pilot symbol matrix The second residual matrix is ​​calculated. It can be expressed by the formula: ; In specific implementation, the second correlation index is obtained based on the second residual matrix and the conjugate transpose matrix; Calculate the conjugate transpose vector With the second residual matrix The product; this product is actually a vector whose elements reflect the second residual matrix. exist The i Projecting along the column direction. Next, calculate the square of the L2 norm (i.e., the Euclidean norm) of the vector obtained in the previous step, denoted as . The squared L2 norm is a way to measure the length of a vector; it reflects... exist Energy or magnitude in the direction. Finally, iterate through all possible indices. i Finding The largest second-most relevant index This second relevance index The column vector it points to is related to the current residual matrix. The most relevant dictionary atom can be represented by the following formula: .

[0095] In specific implementation, the second correlation index is stored in a pre-built support set; the dictionary matrix is ​​filtered based on the correlation index within the support set to obtain the second measurement matrix corresponding to the support set; the second sampling matrix is ​​obtained based on the second measurement matrix and the receiver pilot symbol matrix in the following manner: Second relevance index Stored in a pre-built support set In the middle, support set Indices used to record the atoms or eigenvectors selected during the iteration process, which are most relevant to the current residual signal, based on the support set. The relevance index stored in the dictionary matrix The corresponding column vectors are selected from the data to form the second measurement matrix. This measurement matrix contains dictionary atoms most relevant to the current residual signal, used for further channel estimation.

[0096] Using the second measurement matrix Construct a system of linear equations ,in, This is the first submatrix; by solving the system of linear equations using the least squares method, we obtain... The goal of least squares is to find an estimated value. , making and The difference between them is minimal. This can be expressed by the formula: ; in, The Frobenius norm is used to measure the "size" or "error" of a matrix. Represented as The estimated value, which represents the current support set. Within the defined subspace, the receiver pilot symbol matrix is ​​best fitted. The channel matrix (i.e., the second sampling matrix).

[0097] In specific implementation, the current iteration number is determined, and it is judged whether the current iteration number has reached the maximum iteration number; in response to the current iteration number reaching the maximum iteration number, the second sampling matrix is ​​used as the row sampling submatrix: In the above steps, the second channel matrix is ​​obtained, then the number of iterations at this point is... At this time, the sparsity parameter So, the maximum number of iterations Then As a row sampling submatrix Assuming the sparsity parameter is at this time Then continue the above steps until z = At that time, As the channel estimation matrix.

[0098] Step S260: Obtain the channel estimation matrix based on the target domain channel, the column sampling submatrix, and the row sampling submatrix.

[0099] This step fully utilizes the low-rank and sparsity characteristics of the channel, significantly reducing computational complexity while maintaining high-accuracy channel estimation. This matrix factorization and reconstruction method enables rapid and accurate acquisition of channel state information in high-mobility and complex channel environments.

[0100] In specific implementation, the channel estimation matrix is ​​obtained based on the target domain channel, the column sampling submatrix, and the row sampling submatrix in the following manner: After obtaining the column sampling submatrix and row sampling submatrix, the core matrix is ​​determined using the classic Nyström method, and the high-dimensional CSI matrix is ​​reconstructed.

[0101] The specific goal of CUR decomposition is to sample a submatrix from a given column. Sampling submatrix Under the premise of minimizing the overall reconstruction error by constructing the core matrix Hu, that is: ; in, This can be determined by minimizing the reconstruction error as follows: ; Applying the classic Nyström method, The solution is: ; Therefore, we can obtain an approximate estimate of the equivalent CSI matrix H in the complete DD field: .

[0102] Step S270: Obtain the receiving end vector information. Estimate the receiving end vector information using the channel estimation matrix to obtain the transmitting end vector information.

[0103] In this step, in the mMIMO-OTFS system, the base station (BS) is equipped with a large number of antennas to simultaneously receive signals from multiple user equipment (UEs); the signals received by each antenna are affected by multipath propagation, time delay and Doppler shift, and these signals are digitized to form a received signal vector.

[0104] In the end-to-end mMIMO-OTFS system model, the signal transmission process can be represented by the following matrix equation: ; in, Represented as the information vector at the receiving end; Represented as the information vector from the sending end; Represented as a noise vector; This represents the channel estimation matrix.

[0105] In the exemplary embodiment described above, the receiver pilot symbol matrix is ​​constructed by accurately determining the time delay grid parameters and Doppler frequency shift grid parameters of the target domain channel. Singular value filtering is used to obtain the rank estimate, and user sparsity information is combined to obtain the channel sparsity parameters. This reduces the computational complexity of channel reconstruction while maintaining high accuracy. Based on the constructed sparsity parameters, channel reconstruction is performed on the target domain channel to obtain the channel estimation matrix. This matrix is ​​then used to estimate the receiver vector information, accurately recovering the transmitter vector information. This method solves the problem of excessively high computational complexity in channel estimation during high-reliability communication in mMIMO-OTFS systems under high mobility environments, as mentioned in the background art, significantly improving the system's communication performance and robustness in high-speed mobile scenarios. For specific effects, please refer to... Figure 5 , Figure 6 and Figure 7 Among them, in Figure 5 In the diagram, the horizontal axis represents the signal-to-noise ratio (SNR), measured in dB, ranging from 0 dB to 20 dB; the vertical axis represents the estimation accuracy, typically expressed as a negative logarithm, for example... 10log10 (estimation error), the smaller the value, the higher the estimation accuracy. Different shaped curves represent different channel estimation methods, including circles (RG-BL based on row group sparsity Bayesian learning), asterisks (RG-OMP based on row group sparsity orthogonality), arrows (MFOCUSS for multi-task focus-underdetermined systems), triangles (OMP for orthogonal matching pursuit), squares (SOMP for synchronous orthogonal matching pursuit), and crosses (Proposed method). As SNR increases, the estimation accuracy of all methods improves. The Proposed method (cross) exhibits high estimation accuracy across all SNR values; its curve is at the bottom, indicating the smallest estimation error.

[0106] exist Figure 6In the graph, the horizontal axis represents the number of antennas, ranging from 16 to 64; the vertical axis represents the average computation time in seconds (s). Different shaped curves represent different channel estimation methods, including: circles (RG-BL), asterisks (RG-OMP), arrows (MFOCUSS), triangles (OMP), crosses (Proposed), and squares (SOMP). The average computation time increases for all methods as the number of antennas increases. The Proposed method (cross) exhibits the lowest average computation time across all antenna counts, with its curve at the bottom, indicating the highest computational efficiency.

[0107] exist Figure 7 In the diagram, the horizontal axis represents the signal-to-noise ratio (SNR) in dB, ranging from -15 dB to 5 dB; the vertical axis represents the bit error rate (BER), with smaller values ​​indicating lower BER. Different curve shapes represent different channel estimation methods, including: dashed squares (perfect channel state information, or perfect CSI), circles (RG-BL), asterisks (RG-OMP), arrows (MFOCUSS), triangles (OMP), squares (SOMP), and crosses (Proposed). As SNR increases, the BER decreases for all methods. The Proposed method (cross) exhibits the lowest BER across all SNR values, with its curve at the bottom, indicating the lowest BER.

[0108] It should be noted that the method of this disclosure embodiment can be executed by a single device, such as a computer or server. The method of this embodiment can also be applied to a distributed scenario, where multiple devices cooperate to complete the task. In such a distributed scenario, one of these devices may execute only one or more steps of the method of this disclosure embodiment, and the multiple devices will interact with each other to complete the method described.

[0109] It should be noted that the above description describes some embodiments of this disclosure. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recorded in the claims can be performed in a different order than that shown in the above embodiments and still achieve the desired result. Furthermore, the processes depicted in the drawings do not necessarily require a specific or sequential order to achieve the desired result. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0110] Based on the same inventive concept, corresponding to any of the above-described embodiments, this disclosure also provides a channel estimation device.

[0111] refer to Figure 8The channel estimation device includes: The pilot symbol matrix determination module 810 is configured to determine the time delay grid parameters and Doppler frequency shift grid parameters of the target domain channel, and construct the receiver pilot symbol matrix of the target domain channel based on the time delay grid parameters and the Doppler frequency shift grid parameters. The rank estimation value determination module 820 is configured to determine the singular values ​​of the pilot symbol matrix at the receiving end, filter the singular values, and obtain the rank estimation value. The sparsity parameter determination module 830 is configured to determine the user sparsity information of each user in the target domain channel, and obtain the channel sparsity parameter based on the rank estimate and the user sparsity information. The column sampling submatrix determination module 840 is configured to estimate the column sampling submatrix based on the receiver pilot symbol matrix. The row sampling submatrix determination module 850 is configured to estimate the target domain channel based on the receiver pilot symbol matrix and the channel sparsity parameter to obtain the row sampling submatrix; The channel estimation matrix determination module 860 is configured to obtain a channel estimation matrix based on the target domain channel, the column sampling submatrix, and the row sampling submatrix. The transmitting end vector determination module 870 is configured to acquire the receiving end vector information, estimate the receiving end vector information using the channel estimation matrix, and obtain the transmitting end vector information.

[0112] In this exemplary embodiment, the pilot symbol matrix determination module 810 is specifically configured as follows: The time delay grid parameters and Doppler frequency shift grid parameters of the target domain channel are determined, wherein the time delay grid parameters include: time delay variable and time delay grid size; the Doppler frequency shift grid parameters include: Doppler frequency shift and Doppler grid size; the time delay Doppler gain coefficient corresponding to each antenna in the target domain channel is determined; based on the time delay Doppler gain coefficient, the time delay variable, the time delay grid size, the Doppler frequency shift, and the Doppler grid size, the time delay Doppler domain channel response function is obtained; based on the time delay Doppler gain coefficient, the time delay grid parameters, and the Doppler frequency shift grid parameters, the time delay Doppler domain channel response function is obtained; based on the time delay grid size and the Doppler grid size, a dictionary matrix is ​​obtained; the time delay Doppler domain channel response function is discretized to obtain a channel state information matrix; the noise matrix of the target domain channel is determined, and based on the channel state information matrix, the dictionary matrix, and the noise matrix, the receiver pilot symbol matrix is ​​constructed.

[0113] In this exemplary embodiment, the rank estimation module 820 is specifically configured as follows: The singular values ​​of the receiver pilot symbol matrix are determined, and the singular values ​​are filtered based on a filtering threshold. If a singular value is greater than the filtering threshold, the singular value is used as the rank estimate. The filtering threshold is obtained by: determining the total channel network size based on the delay grid size and the Doppler grid size; determining the number of antennas in the target domain channel; obtaining a scaling factor based on the number of antennas and the total channel network size; obtaining an adjustment coefficient based on the scaling factor; performing singular value decomposition on the receiver pilot symbol matrix to obtain the median singular value; and obtaining the filtering threshold based on the adjustment coefficient and the median singular value.

[0114] In this exemplary embodiment, the sparsity parameter determination module 830 is specifically configured as follows: Determine the user sparsity information for each user in the target domain channel, and obtain the channel sparsity parameter based on the rank estimate and the user sparsity information.

[0115] In this exemplary embodiment, the column sampling submatrix determination module 840 is specifically configured as follows: The pilot symbol matrix at the receiving end is reassembled to obtain a column sampling reassembled matrix; the column sampling reassembled matrix is ​​estimated based on the linear minimum mean square error algorithm to obtain the column sampling submatrix.

[0116] In this exemplary embodiment, the row sampling submatrix determination module 850 is specifically configured as follows: The receiver pilot symbol matrix is ​​used as the first residual matrix; the conjugate transpose of the dictionary matrix is ​​determined, and a first correlation index is obtained based on the first residual matrix and the conjugate transpose matrix; the first correlation index is stored in a pre-constructed support set; the dictionary matrix is ​​filtered based on the correlation index in the support set to obtain the first measurement matrix corresponding to the support set; a first sampling matrix is ​​obtained based on the first measurement matrix and the receiver pilot symbol matrix; the channel sparsity parameter is used as the maximum iteration number; the current iteration number is determined, and it is judged whether the current iteration number has reached the maximum iteration number; in response to the current iteration number reaching the maximum iteration number, the first sampling matrix is ​​used as the row sampling submatrix; in response to the current iteration number not reaching the maximum iteration number, the first sampling matrix is ​​used as the row sampling submatrix; Upon reaching the maximum number of iterations, the measurement matrix is ​​constructed to obtain a positive cross-complement projection matrix. Based on the positive cross-complement projection matrix and the receiver pilot symbol matrix, a second residual matrix is ​​obtained. Based on the second residual matrix and the conjugate transpose matrix, a second correlation index is obtained. The second correlation index is stored in a pre-constructed support set. The dictionary matrix is ​​filtered based on the correlation index in the support set to obtain the second measurement matrix corresponding to the support set. Based on the second measurement matrix and the receiver pilot symbol matrix, a second sampling matrix is ​​obtained. The current iteration number is determined, and it is judged whether the current iteration number has reached the maximum number of iterations. In response to the current iteration number reaching the maximum number of iterations, the second sampling matrix is ​​used as the row sampling submatrix.

[0117] In this exemplary embodiment, the channel estimation matrix determination module 860 is specifically configured as follows: The channel estimation matrix is ​​obtained based on the target domain channel, the column sampling submatrix, and the row sampling submatrix.

[0118] In this exemplary embodiment, the transmitting end vector determination module 870 is specifically configured as follows: The receiving end vector information is obtained, and the transmitting end vector information is obtained by estimating the receiving end vector information using the channel estimation matrix.

[0119] For ease of description, the above apparatus is described in terms of its functions, divided into various modules. Of course, in implementing this disclosure, the functions of each module can be implemented in one or more software and / or hardware.

[0120] The apparatus of the above embodiments is used to implement the corresponding channel estimation method in any of the foregoing embodiments, and has the beneficial effects of the corresponding method embodiments, which will not be repeated here.

[0121] Based on the same inventive concept, corresponding to the methods of any of the above embodiments, this disclosure also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the channel estimation method described in any of the above embodiments.

[0122] Figure 9 This embodiment illustrates a more specific hardware structure of an electronic device, which may include a processor 1010, a memory 1020, an input / output interface 1030, a communication interface 1040, and a bus 1050. The processor 1010, memory 1020, input / output interface 1030, and communication interface 1040 are interconnected internally via the bus 1050.

[0123] The processor 1010 can be implemented using a general-purpose CPU (Central Processing Unit), microprocessor, application-specific integrated circuit (ASIC), or one or more integrated circuits, and is used to execute relevant programs to implement the technical solutions provided in the embodiments of this specification.

[0124] The memory 1020 can be implemented in the form of ROM (Read Only Memory), RAM (Random Access Memory), static storage device, dynamic storage device, etc. The memory 1020 can store the operating system and other applications. When the technical solutions provided in the embodiments of this specification are implemented by software or firmware, the relevant program code is stored in the memory 1020 and is called and executed by the processor 1010.

[0125] The input / output interface 1030 is used to connect input / output modules to realize information input and output. The input / output modules can be configured as components in the device (not shown in the figure) or externally connected to the device to provide corresponding functions. Input devices may include keyboards, mice, touch screens, microphones, various sensors, etc., and output devices may include displays, speakers, vibrators, indicator lights, etc.

[0126] The communication interface 1040 is used to connect a communication module (not shown in the figure) to enable communication between this device and other devices. The communication module can communicate via wired means (such as USB, Ethernet cable, etc.) or wireless means (such as mobile network, WIFI, Bluetooth, etc.).

[0127] Bus 1050 includes a pathway for transmitting information between various components of the device, such as processor 1010, memory 1020, input / output interface 1030, and communication interface 1040.

[0128] It should be noted that although the above-described device only shows the processor 1010, memory 1020, input / output interface 1030, communication interface 1040, and bus 1050, in specific implementations, the device may also include other components necessary for normal operation. Furthermore, those skilled in the art will understand that the above-described device may only include the components necessary for implementing the embodiments of this specification, and not necessarily all the components shown in the figures.

[0129] The electronic devices described above are used to implement the corresponding channel estimation methods in any of the foregoing embodiments and have the beneficial effects of the corresponding method embodiments, which will not be repeated here.

[0130] Based on the same inventive concept, corresponding to the methods of any of the above embodiments, this disclosure also provides a non-transitory computer-readable storage medium storing computer instructions for causing the computer to execute the channel estimation method as described in any of the above embodiments.

[0131] The computer-readable medium of this embodiment includes permanent and non-permanent, removable and non-removable media, and information storage can be implemented by any method or technology. Information can be computer-readable instructions, data structures, program modules, or other data. Examples of computer storage media include, but are not limited to, phase-change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, CD-ROM, digital versatile optical disc (DVD) or other optical storage, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other non-transfer medium that can be used to store information accessible by a computing device.

[0132] The aforementioned non-transitory computer-readable storage media can be any available medium or data storage device that a computer can access, including but not limited to magnetic storage (e.g., floppy disks, hard disks, magnetic tapes, magneto-optical disks (MOs), etc.), optical storage (e.g., CDs, DVDs, BDs, HVDs, etc.), and semiconductor storage (e.g., ROMs, EPROMs, EEPROMs, non-volatile memory (NAND flash), solid-state drives (SSDs)).

[0133] The computer instructions stored in the storage medium of the above embodiments are used to cause the computer to perform the channel estimation method as described in any of the embodiments in the exemplary method section above, and have the beneficial effects of the corresponding method embodiments, which will not be repeated here.

[0134] Based on the same inventive concept, corresponding to the channel estimation method described in any of the above embodiments, this disclosure also provides a computer program product, which includes computer program instructions. In some embodiments, the computer program instructions can be executed by one or more processors of a computer to cause the computer and / or the processors to perform the channel estimation method. Corresponding to the execution entity for each step in each embodiment of the channel estimation method, the processor executing the corresponding step can belong to the corresponding execution entity.

[0135] The computer program products of the above embodiments are used to cause the computer and / or the processor to execute the channel estimation method as described in any of the above embodiments, and have the beneficial effects of the corresponding method embodiments, which will not be repeated here.

[0136] Those skilled in the art will recognize that embodiments of this disclosure can be implemented as a system, method, or computer program product. Therefore, this disclosure can be implemented as entirely hardware, entirely software (including firmware, resident software, microcode, etc.), or a combination of hardware and software, generally referred to herein as a "circuit," "module," or "system." Furthermore, in some embodiments, this disclosure can also be implemented as a computer program product contained in one or more computer-readable media, which includes computer-readable program code.

[0137] Any combination of one or more computer-readable media may be used. A computer-readable medium can be a computer-readable signal medium or a computer-readable storage medium. A computer-readable storage medium can be, for example,, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples (not exhaustive) of a computer-readable storage medium may include: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof. In this document, a computer-readable storage medium can be any tangible medium that contains or stores a program that can be used by or in connection with an instruction execution system, apparatus, or device.

[0138] Computer-readable signal media may include data signals propagated in baseband or as part of a carrier wave, carrying computer-readable program code. Such propagated data signals may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. Computer-readable signal media may also be any computer-readable medium other than computer-readable storage media, capable of sending, propagating, or transmitting programs for use by or in connection with an instruction execution system, apparatus, or device.

[0139] Program code contained on a computer-readable medium may be transmitted using any suitable medium, including but not limited to wireless, wire, optical fiber, RF, etc., or any suitable combination thereof.

[0140] Computer program code for performing the operations of this disclosure can be written in one or more programming languages ​​or a combination thereof, including object-oriented programming languages ​​such as Java, Smalltalk, and C++, and conventional procedural programming languages ​​such as the "C" language or similar programming languages. The program code can be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving remote computers, the remote computer can be connected to the user's computer via any type of network, including a local area network (LAN) or a wide area network (WAN), or it can be connected to an external computer (e.g., via the Internet using an Internet service provider).

[0141] It should be understood that each block of a flowchart and / or block diagram, as well as combinations of blocks in a flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing device to produce a machine that, when executed by a computer or other programmable data processing device, creates means for implementing the functions / operations specified in the blocks of the flowchart and / or block diagram.

[0142] These computer program instructions may also be stored in a computer-readable medium that enables a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable medium produce a product comprising an instruction apparatus that implements the functions / operations specified in the boxes of a flowchart and / or block diagram.

[0143] Computer program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable data processing apparatus, or other device to produce a computer-implemented process, such that the instructions that execute on the computer or other programmable apparatus can provide a process for implementing the functions / operations specified in the boxes of a flowchart and / or block diagram.

[0144] Furthermore, although the operations of the methods of this disclosure are described in a specific order in the accompanying drawings, this does not require or imply that these operations must be performed in that specific order, or that all of the operations shown must be performed to achieve the desired result. Rather, the steps depicted in the flowcharts may be executed in a different order. Additionally or alternatively, certain steps may be omitted, multiple steps may be combined into one step, and / or one step may be broken down into multiple steps.

[0145] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of this application. Each block in a flowchart or block diagram may represent a module, segment, or portion of code, which contains one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in a block diagram or flowchart, and combinations of blocks in a block diagram or flowchart, can be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions.

[0146] It should be noted that although several modules or units for the device used to perform actions have been mentioned in the detailed description above, this division is not mandatory. In fact, according to the embodiments of this application, the features and functions of two or more modules or units described above can be embodied in one module or unit. Conversely, the features and functions of one module or unit described above can be further divided and embodied by multiple modules or units.

[0147] Those skilled in the art should understand that the discussion of any of the above embodiments is merely exemplary and is not intended to imply that the scope of this application (including the claims) is limited to these examples; within the framework of this application, the technical features of the above embodiments or different embodiments can also be combined, the steps can be implemented in any order, and there are many other variations of different aspects of the embodiments of this application as described above, which are not provided in the details for the sake of brevity.

[0148] Additionally, to simplify the description and discussion, and to avoid obscuring the embodiments of this application, the well-known power / ground connections to integrated circuit (IC) chips and other components may or may not be shown in the provided drawings. Furthermore, the apparatus may be shown in block diagram form to avoid obscuring the embodiments of this application, and this also takes into account the fact that the details of the implementation of these block diagram apparatuses are highly dependent on the platform on which the embodiments of this application will be implemented (i.e., these details should be fully understood by those skilled in the art). While specific details (e.g., circuits) have been set forth to describe exemplary embodiments of this application, it will be apparent to those skilled in the art that the embodiments of this application can be implemented without these specific details or with variations thereof. Therefore, these descriptions should be considered illustrative rather than restrictive.

[0149] Although this application has been described in conjunction with specific embodiments thereof, many substitutions, modifications, and variations of these embodiments will be apparent to those skilled in the art from the foregoing description. For example, other memory architectures (e.g., dynamic RAM (DRAM)) may be used with the embodiments discussed.

[0150] The embodiments of this application are intended to cover all such substitutions, modifications, and variations that fall within the broad scope of the appended claims. Therefore, any omissions, modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the embodiments of this application should be included within the protection scope of this application.

[0151] While the spirit and principles of this disclosure have been described with reference to several specific embodiments, it should be understood that this disclosure is not limited to the disclosed specific embodiments, and the division of aspects does not imply that features in these aspects cannot be combined for benefit; such division is merely for convenience of expression. This disclosure is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims. The scope of the appended claims is to be interpreted in the broadest sense, thereby encompassing all such modifications and equivalent structures and functions.

Claims

1. A channel estimation method, characterized in that, include: The time delay grid parameters and Doppler frequency shift grid parameters of the target domain channel are determined, and the receiver pilot symbol matrix of the target domain channel is constructed based on the time delay grid parameters and the Doppler frequency shift grid parameters. Determine the singular values ​​of the pilot symbol matrix at the receiving end, and filter the singular values ​​to obtain the rank estimate; Determine the user sparsity information for each user in the target domain channel, and obtain the channel sparsity parameter based on the rank estimate and the user sparsity information; Based on the received pilot symbol matrix, an estimation is performed to obtain the column sampling submatrix; The target domain channel is estimated based on the receiver pilot symbol matrix and the channel sparsity parameter to obtain the row sampling submatrix; The channel estimation matrix is ​​obtained based on the target domain channel, the column sampling submatrix, and the row sampling submatrix; The receiving end vector information is obtained, and the transmitting end vector information is obtained by estimating the receiving end vector information using the channel estimation matrix.

2. The method according to claim 1, characterized in that, The time delay grid parameters include: time delay variable and time delay grid size; the Doppler frequency shift grid parameters include: Doppler frequency shift and Doppler grid size; The method of constructing the receiver pilot symbol matrix of the target domain channel based on the time delay grid parameters and the Doppler frequency shift grid parameters includes: Determine the time delay Doppler gain coefficient corresponding to each antenna in the target domain channel. Based on the time delay Doppler gain coefficient, the time delay variable, the time delay grid size, the Doppler frequency shift, and the Doppler grid size, obtain the time delay Doppler domain channel response function. Based on the time delay Doppler gain coefficient, the time delay grid parameter, and the Doppler frequency shift grid parameter, obtain the time delay Doppler domain channel response function. Based on the time delay grid size and the Doppler grid size, a dictionary matrix is ​​obtained; Discretize the time-delay Doppler domain channel response function to obtain the channel state information matrix; The noise matrix of the target domain channel is determined, and the receiver pilot symbol matrix is ​​constructed based on the channel state information matrix, the dictionary matrix, and the noise matrix.

3. The method according to claim 2, characterized in that, The process of filtering the singular values ​​to obtain the rank estimate includes: The singular values ​​are filtered based on a filtering threshold, and if a singular value is greater than the filtering threshold, the singular value is used as the rank estimate.

4. The method according to claim 3, characterized in that, The filtering threshold is obtained through the following method: Based on the time delay grid size and the Doppler grid size, the total size of the channel network is obtained; The number of antennas for the target domain channel is determined, and a scaling factor is obtained based on the number of antennas and the total size of the channel network. Based on the aforementioned scaling factor, the adjustment coefficient is obtained; Singular value decomposition is performed on the pilot symbol matrix of the receiving end to obtain the median singular value; The screening threshold is obtained based on the adjustment coefficient and the median singular value.

5. The method according to claim 2, characterized in that, The estimation based on the receiver pilot symbol matrix to obtain the column sampling sub-matrix includes: The pilot symbol matrix at the receiving end is reassembled to obtain a column sampling reassembled matrix; The column sampling submatrix is ​​estimated based on the linear minimum mean square error algorithm.

6. The method according to claim 2, characterized in that, The estimation of the target domain channel based on the receiver pilot symbol matrix and the channel sparsity parameter to obtain a row sampling sub-matrix includes: The receiving pilot symbol matrix is ​​used as the first residual matrix; Determine the conjugate transpose of the dictionary matrix, and obtain the first relevance index based on the first residual matrix and the conjugate transpose matrix; The first relevance index is stored in a pre-built support set; Based on the correlation index within the support set, the dictionary matrix is ​​filtered to obtain the first measurement matrix corresponding to the support set; Based on the first measurement matrix and the receiver pilot symbol matrix, a first sampling matrix is ​​obtained; The channel sparsity parameter is used as the maximum number of iterations; Determine the current iteration number, and then determine whether the current iteration number has reached the maximum iteration number. In response to the current iteration number reaching the maximum iteration number, the first sampling matrix is ​​used as the row sampling submatrix.

7. The method according to claim 6, characterized in that, The method further includes: In response to the fact that the current iteration number has not reached the maximum iteration number, the measurement matrix is ​​constructed to obtain a positive interactive projection matrix, and a second residual matrix is ​​obtained based on the positive interactive projection matrix and the receiver pilot symbol matrix; Based on the second residual matrix and the conjugate transpose matrix, the second correlation index is obtained; The second relevance index is stored in a pre-built support set; Based on the correlation index within the support set, the dictionary matrix is ​​filtered to obtain the second measurement matrix corresponding to the support set; based on the second measurement matrix and the receiver pilot symbol matrix, the second sampling matrix is ​​obtained. Determine the current iteration number, and then determine whether the current iteration number has reached the maximum iteration number; In response to the current iteration number reaching the maximum iteration number, the second sampling matrix is ​​used as the row sampling submatrix.

8. A channel estimation device, characterized in that, include: The pilot symbol matrix determination module is configured to determine the time delay grid parameters and Doppler frequency shift grid parameters of the target domain channel, and construct the receiver pilot symbol matrix of the target domain channel based on the time delay grid parameters and the Doppler frequency shift grid parameters. The rank estimate determination module is configured to determine the singular values ​​of the pilot symbol matrix at the receiving end, filter the singular values, and obtain the rank estimate. The sparsity parameter determination module is configured to determine the user sparsity information of each user in the target domain channel, and obtain the channel sparsity parameter based on the rank estimate and the user sparsity information. The column sampling submatrix determination module is configured to estimate the column sampling submatrix based on the receiver pilot symbol matrix. The row sampling submatrix determination module is configured to estimate the target domain channel based on the receiver pilot symbol matrix and the channel sparsity parameter to obtain the row sampling submatrix; The channel estimation matrix determination module is configured to obtain a channel estimation matrix based on the target domain channel, the column sampling submatrix, and the row sampling submatrix. The transmitter vector determination module is configured to acquire receiver vector information, estimate the receiver vector information using the channel estimation matrix, and obtain transmitter vector information.

9. An electronic device, characterized in that, It includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the program, implements the method as described in any one of claims 1 to 7.

10. A non-transitory computer-readable storage medium, characterized in that, The non-transitory computer-readable storage medium stores computer instructions for causing the computer to perform the method of any one of claims 1 to 7.

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