Three-dimensional polar domain channel estimation method for super-large-scale intelligent reflector system

Abstract

The invention discloses a three-dimensional polar domain channel estimation method for a super-large-scale intelligent reflector system, and the method comprises the steps: building an RIS auxiliary communication channel model of UPA-ULA, the RIS being a uniform planar array UPA antenna arrangement, and the base station and the user being a uniform linear array ULA; according to the RIS auxiliary communication channel model, pilot signals received on the subcarriers are obtained; performing polar domain transformation on the received pilot signal to enable the signal to show sparsity in a polar domain; designing a polar domain three-dimensional dictionary containing three near-field polar domain channel variables including a pitch angle, an azimuth angle and a distance based on the pilot signal after polar domain transformation, and sparsely representing channel characteristics; and estimating the channel by using the polar domain three-dimensional dictionary through an orthogonal matching pursuit algorithm, and recovering channel state information. The method provided by the invention can improve the precision and stability of channel estimation in a complex system of RIS auxiliary communication.

Description

Technical Field

[0001] The present invention belongs to the technical field of communication signal processing, relates to a communication system channel estimation technology, and specifically relates to a three-dimensional polar domain channel estimation method for a super-large-scale intelligent reflection surface system. Background Art

[0002] RIS (Reconfigurable Intelligent Surface) assisted communication is a research hotspot in the current wireless communication field, especially in 5G and future 6G communication systems. RIS can change radio waves at the electromagnetic level without complex digital signal processing and active power amplifiers. RIS is an artificial surface structure that can dynamically adjust the propagation direction of electromagnetic waves by electronic control, usually composed of a large number of low-cost passive reflection units. These reflection units can control the incident electromagnetic waves by changing parameters such as phase and amplitude according to the preset control algorithm, thereby changing the propagation direction and scattering characteristics of the beam, and even attenuating or amplifying specific signals. Compared with traditional antenna arrays or repeaters, RIS has the advantages of low power consumption, programmability, and low complexity, which can greatly enhance the performance of communication links.

[0003] Channel estimation is a key technology in wireless communication systems, and plays an important role in improving the performance and reliability of communication systems, optimizing resource allocation, improving energy efficiency, and enhancing physical layer security. By obtaining accurate channel state information, communication systems can dynamically adjust transmission strategies and optimize modulation, coding, beamforming and other operations, thereby improving spectrum efficiency and transmission rate.

[0004] Although RIS-assisted communication has significant advantages in improving system performance, it still faces many shortcomings in channel estimation. First, the high dimensionality and complexity of the RIS system make traditional channel estimation methods computationally intensive and difficult to process in real time. Second, due to hardware defects and environmental changes, traditional methods are difficult to guarantee accuracy and robustness in actual scenarios.

[0005] Through in-depth retrieval and analysis of previous related patents and academic papers, it can be found that most of the research work on channel estimation in the past has focused on two-dimensional variables based on plane models. Although this method has certain research significance in theory, in actual communication systems, there is a large deviation between the plane model and the three-dimensional complexity of the real scene. Therefore, the traditional two-dimensional model is difficult to fully reflect the characteristics of the actual channel environment, especially when considering the three-dimensional distribution of antenna arrays, the diversity of signal propagation paths, and the non-ideal characteristics of different propagation environments, the limitations of this simplified model are particularly prominent. As a result, this method is often difficult to obtain high-precision channel estimates in practical applications, which limits its applicability in real communication systems. Summary of the invention

[0006] Purpose of the invention: In order to overcome the deficiencies in the prior art, a three-dimensional polar domain channel estimation method for a very large-scale intelligent reflection surface system is provided, which can improve the accuracy and stability of channel estimation in complex systems of RIS-assisted communication.

[0007] Technical solution: To achieve the above object, the present invention provides a three-dimensional polar channel estimation method for a very large-scale intelligent reflection surface system, comprising the following steps:

[0008] S1: Establish a RIS-assisted communication channel model of UPA-ULA, where RIS is a uniform planar array UPA antenna arrangement, and both the base station and the user are uniform linear array ULA;

[0009] S2: According to the RIS-assisted communication channel model, the pilot signal received on the subcarrier is obtained;

[0010] S3: performing polar domain transformation on the received pilot signal so that the signal exhibits sparseness in the polar domain;

[0011] S4: Based on the pilot signal after polar domain transformation, a polar domain three-dimensional dictionary containing three near-field polar domain channel variables, namely, elevation angle, azimuth angle and distance, is designed to sparsely represent the channel characteristics;

[0012] S5: The channel is estimated using the polar domain three-dimensional dictionary through the orthogonal matching pursuit (OMP) algorithm to restore the channel state information.

[0013] Furthermore, in step S1, RIS, as an intermediary, can adjust the signal propagation path and enhance the signal quality. The signal transmission between the base station and the user is first reflected by the RIS. The signal propagation process is not only affected by the geometric position of the base station and the user array, but also by the reconfiguration and control of the RIS array.

[0014] The UPA array uses a two-dimensional antenna arrangement, while the ULA array uses a one-dimensional antenna arrangement. Under this layout, factors such as the difference in signal propagation path length, the change in wavefront shape, and its phase difference will affect the propagation characteristics of the signal. When modeling, these factors can be considered and combined with near-field propagation theory to design a near-field channel model that adapts to the RIS configuration to simulate the reflection and redirection effects of RIS on signals under different configurations.

[0015] The establishment of the RIS-assisted communication channel model of UPA-ULA includes:

[0016] The RIS-assisted communication system includes a channel matrix G between the base station and the RIS; a channel matrix H between the RIS and the user; and a RIS phase shift matrix defined as Φ = diag (φ), where represents the phase shift angle;

[0017] The channel matrix G is the far-field channel matrix, and the channel matrix H is the near-field channel matrix, which are modeled by Saleh-Valenzuela and are expressed as

[0018]

[0019] Among them, α and β represent the path loss coefficients respectively; a(·) and b(·) are the corresponding vectors of the array, expressed as

[0020]

[0021]

[0022] in, and θ l denote the azimuth departure angle (AOD) and elevation departure angle (AOD) respectively; since b(·) is the spherical array response on subcarrier m, the vector coordinates are No. The elements and coordinates are The distance between the targets is expressed as

[0023]

[0024] Furthermore, the pilot signal received on the mth subcarrier in step S2 is expressed as

[0025] y m =AGΦH+n m (7)

[0026] Among them, n m represents noise, A represents the overall observation matrix, in which all elements are independent and can be obtained with equal probability from Generated in.

[0027] Furthermore, the polar domain transformation in step S3 converts the signal from the traditional time domain or frequency domain into polar coordinate representation, extracts three variables of pitch angle, azimuth angle and distance, and makes the signal sparse in the polar domain.

[0028] In the near-field channel, the propagation of the signal is not only affected by the distance, but also by the angular changes (elevation and azimuth) of the signal source position. Therefore, the variables of the near-field polar channel mainly include elevation, azimuth and distance. These three variables determine the position of the signal source and the propagation mode.

[0029] The elevation angle and azimuth angle represent the vertical and horizontal components of the signal propagation direction, respectively, and affect the signal's arrival angle, while the distance determines the degree of signal propagation attenuation.

[0030] Furthermore, the design of the polar domain three-dimensional dictionary in step S4 includes the following steps:

[0031] A1: Modeling the near-field propagation characteristics of the RIS array;

[0032] A2: Use Fresnel approximation to optimize the correlation of columns in the dictionary;

[0033] A3: Determine the key distance sampling points by the geometric mean method to minimize the column correlation of the dictionary matrix.

[0034] Furthermore, the step A2 specifically includes:

[0035] First, the spherical array response b(·) must be processed to make its column coherence as small as possible in the polar domain. For this purpose, the expression in equation (5) is simplified using the Fresnel approximation, and the near-field array response is expressed as

[0036]

[0037] On this basis, the spherical array response is defined as:

[0038]

[0039] To ensure satisfactory channel recovery accuracy, the sampling of angles and distances should be designed to minimize the column correlation of the polar domain transformation matrix P. in, and represents any two columns in P; define and The column correlation is expressed as:

[0040]

[0041] For column correlation, the present invention adopts the distance sampling method. Any two vectors sampled, that is The first linear phase term becomes zero and is therefore eliminated; in this case, the column correlation f(θ p ,θ q ,φ p ,· q ,r p ,r q) depends only on the second quadratic phase term, which is affected by the term related to the distance. Due to the inherent complexity of the quadratic phase characteristics, unlike the angle sampling derivation, in order to solve this problem, the cross terms in the quadratic expression can be approximately ignored, and the expression is expressed as

[0042]

[0043] Using the Fresnel function, formula (11) is expressed as

[0044]

[0045] in, In the formula as well as is the Fresnel function.

[0046] The sparse representation of the polar domain three-dimensional dictionary optimizes column correlation through formula (12).

[0047] Furthermore, the step A3 specifically includes:

[0048] Since the G(·) function shows a significant downward trend with slight fluctuations, in order to make the column correlation as small as possible, even if Below the desired threshold η, the threshold β of the column correlation should be calculated first η , so that |G(·)|=η; due to the downward trend of |G(·)|, it is approximately concluded that β≥β η ; Based on the condition β≥β η and Sampling distance r p and r q Must meet

[0049]

[0050] in, Considering the array aperture D y / z =N y / z d, and further express Rη as

[0051] Assume that one of the sampling distances is Where t=1,2,…, then we can deduce

[0052]

[0053] For any given angle and θ, if the distance sampling is

[0054]

[0055] In order to solve the distance rt By two variables and This makes it difficult to obtain a suitable distance during sampling. The geometric mean method is used to express the distance sampling as

[0056]

[0057] in,

[0058] Furthermore, the orthogonal matching pursuit algorithm in step S5 includes the following steps:

[0059] B1: Initialize the received pilot signal, set the residual to the initial signal, initialize the channel estimation vector to all zeros, and create an empty support set to record the dictionary elements selected later;

[0060] B2: Calculate the inner product between the residual and all dictionary elements, select the dictionary element with the largest inner product, regard it as the atom that is most helpful for signal recovery at present, and add the element to the support set;

[0061] B3: Update the channel estimate using the selected dictionary element and calculate the new residual;

[0062] B4: Repeat the above steps until the residual threshold condition is met, combine the dictionary elements in the support set, complete the signal recovery, and obtain the final channel estimation result.

[0063] Through this iterative selection and update, OMP can fully utilize the sparse characteristics of the channel to achieve efficient and accurate channel estimation.

[0064] The method of the present invention can be used for channel estimation in dynamic environments, and can improve communication stability and anti-interference ability in multi-user scenarios. The method is applicable to RIS-assisted communication systems based on UPA-ULA architecture, and can significantly reduce computational complexity while improving channel estimation accuracy and energy efficiency.

[0065] Beneficial effects: Compared with the prior art, the systematic channel modeling and estimation method based on three-dimensional variables provided by the present invention shows significant advantages in RIS-enhanced near-field communication scenarios. By combining the array structure and propagation characteristics of base stations, users and RIS, this method can accurately describe the channel characteristics in near-field propagation, especially when dealing with wavefront effects and distance attenuation. The polar domain transformation is used to show the sparsity of the channel, making the model easier for signal analysis and processing. At the same time, the OMP algorithm selects the most relevant dictionary elements with a step-by-step approximation strategy to achieve efficient and accurate channel estimation, significantly reducing the computational complexity, and also providing theoretical support for optimization design of actual communication systems, which can effectively improve data transmission efficiency, reduce interference and bit error rate, and make full use of the advantages of RIS to achieve stable and efficient communication. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1 is a flow chart of the method of the present invention;

[0067] Figure 2 This is a model diagram of the RIS-assisted communication system in the present invention;

[0068] Figure 3 It is a design flow chart of the polar domain three-dimensional dictionary in the present invention;

[0069] Figure 4 is a flow chart of the OMP near-field channel estimation algorithm of the present invention;

[0070] Figure 5 It is a comparison chart of the algorithm performance in the present invention. DETAILED DESCRIPTION

[0071] The present invention is further explained below in conjunction with the accompanying drawings and specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, various equivalent forms of modifications to the present invention by those skilled in the art all fall within the scope defined by the claims attached to this application.

[0072] like Figure 1 As shown, the present invention provides a three-dimensional polar channel estimation method for a super-large-scale intelligent reflection surface system, comprising the following steps:

[0073] S1: Establish a RIS-assisted communication channel model of UPA-ULA, where RIS is a uniform planar array UPA antenna arrangement, and both the base station and the user are uniform linear array ULA;

[0074] As an intermediary, RIS can adjust the signal propagation path and enhance the signal quality. The signal transmission between the base station and the user is first reflected by the RIS. The signal propagation process is not only affected by the geometric position of the base station and the user array, but also by the reconfiguration and control of the RIS array.

[0075] The UPA array uses a two-dimensional antenna arrangement, while the ULA array uses a one-dimensional antenna arrangement. Under this layout, factors such as the difference in signal propagation path length, the change in wavefront shape, and its phase difference will affect the propagation characteristics of the signal. When modeling, these factors can be considered and combined with near-field propagation theory to design a near-field channel model that adapts to the RIS configuration to simulate the reflection and redirection effects of RIS on signals under different configurations.

[0076] The establishment of the RIS-assisted communication channel model of UPA-ULA includes:

[0077] like Figure 2 As shown, the RIS-assisted communication system includes a channel matrix G between the base station and the RIS; a channel matrix H between the RIS and the user; and a RIS phase shift matrix defined as Φ = diag (φ), where represents the phase shift angle;

[0078] The channel matrix G is the far-field channel matrix, and the channel matrix H is the near-field channel matrix, which are modeled by Saleh-Valenzuela and are expressed as

[0079]

[0080] Among them, α and β represent the path loss coefficients respectively; a(·) and b(·) are the corresponding vectors of the array, expressed as

[0081]

[0082]

[0083] in, and θ l denote the azimuth departure angle (AOD) and elevation departure angle (AOD) respectively; since b(·) is the spherical array response on subcarrier m, Figure 2 In the coordinate system shown, the vector coordinates are No. The elements and coordinates are The distance between the targets is expressed as

[0084]

[0085] S2: According to the RIS-assisted communication channel model, the pilot signal received on the subcarrier is obtained;

[0086] The pilot signal received on the mth subcarrier is expressed as

[0087] y m =AGΦH+n m (7)

[0088] Among them, n m represents noise, A represents the overall observation matrix, in which all elements are independent and can be obtained with equal probability from Generated in.

[0089] S3: performing polar domain transformation on the received pilot signal so that the signal exhibits sparseness in the polar domain;

[0090] Polar domain transform converts the signal from traditional time domain or frequency domain into polar coordinate representation, extracts three variables: pitch angle, azimuth angle and distance, and makes the signal sparse in the polar domain.

[0091] In the near-field channel, the propagation of the signal is not only affected by the distance, but also by the angular changes (elevation and azimuth) of the signal source position. Therefore, the variables of the near-field polar channel mainly include elevation, azimuth and distance. These three variables determine the position of the signal source and the propagation mode.

[0092] The elevation angle and azimuth angle represent the vertical and horizontal components of the signal propagation direction, respectively, and affect the signal's arrival angle, while the distance determines the degree of signal propagation attenuation.

[0093] S4: Based on the pilot signal after polar domain transformation, a polar domain three-dimensional dictionary containing three near-field polar domain channel variables, namely, elevation angle, azimuth angle and distance, is designed to sparsely represent the channel characteristics;

[0094] like Figure 3 As shown, the design of the polar domain three-dimensional dictionary includes the following steps:

[0095] A1: Modeling the near-field propagation characteristics of the RIS array;

[0096] A2: Use Fresnel approximation to optimize the correlation of columns in the dictionary;

[0097] A3: Determine the key distance sampling points by the geometric mean method to minimize the column correlation of the dictionary matrix.

[0098] Step A2 specifically includes:

[0099] First, the spherical array response b(·) must be processed to make its column coherence as small as possible in the polar domain. For this purpose, the expression in equation (5) is simplified using the Fresnel approximation, and the near-field array response is expressed as

[0100]

[0101] On this basis, the spherical array response is defined as:

[0102]

[0103] To ensure satisfactory channel recovery accuracy, the sampling of angles and distances should be designed to minimize the column correlation of the polar domain transformation matrix P. in, and represents any two columns in P; define and The column correlation is expressed as:

[0104]

[0105] For column correlation, the present invention adopts the distance sampling method. Any two vectors sampled, that is The first linear phase term becomes zero and is therefore eliminated; in this case, the column correlation f(θ p ,θ q ,φ p ,φ q ,r p ,r q ) depends only on the second quadratic phase term, which is affected by the term related to the distance. Due to the inherent complexity of the quadratic phase characteristics, unlike the angle sampling derivation, in order to solve this problem, the cross terms in the quadratic expression can be approximately ignored, and the expression is expressed as

[0106]

[0107] Using the Fresnel function, formula (11) is expressed as

[0108]

[0109] in, In the formula as well as is the Fresnel function.

[0110] The sparse representation of the polar domain three-dimensional dictionary optimizes column correlation through formula (12).

[0111] Step A3 specifically includes:

[0112] Since the G(·) function shows a significant downward trend with slight fluctuations, in order to make the column correlation as small as possible, even if Below the desired threshold η, the threshold β of the column correlation should be calculated first η , so that |G(·)|=η; due to the downward trend of \G(·)|, it is approximately concluded that β≥β η ; Based on the condition β≥β n and Sampling distance r p and r q Must meet

[0113]

[0114] in, Considering the array aperture D y / z =N y / z d, further R η Expressed as

[0115] Assume that one of the sampling distances is Where t=1,2,..., then we can deduce

[0116]

[0117] For any given angle and θ, if the distance sampling is

[0118]

[0119] In order to solve the distance r t By two variables and This makes it difficult to obtain a suitable distance during sampling. The present invention uses the geometric mean method to express the distance sampling as

[0120]

[0121] in,

[0122] S5: The channel is estimated using the polar domain three-dimensional dictionary through the orthogonal matching pursuit (OMP) algorithm to restore the channel state information;

[0123] like Figure 4 As shown, the orthogonal matching pursuit algorithm includes the following steps:

[0124] B1: Initialize the received pilot signal, set the residual to the initial signal, and initialize the channel estimation vector to all zeros. At the same time, create an empty support set to record the dictionary elements selected subsequently; the dictionary elements are each column in the generated dictionary matrix;

[0125] B2: Calculate the inner product between the residual and all dictionary elements, select the dictionary element with the largest inner product, regard it as the atom that is most helpful for signal recovery at present, and add the element to the support set;

[0126] B3: Update the channel estimate using the selected dictionary element and calculate the new residual;

[0127] B4: Repeat the above steps until the residual threshold condition is met (iterate to be less than R_eta in the next line of formula (13)), combine the dictionary elements in the support set, complete the signal recovery, and obtain the final channel estimation result.

[0128] Through this iterative selection and update, OMP can fully utilize the sparse characteristics of the channel to achieve efficient and accurate channel estimation.

[0129] In order to verify the effectiveness and effect of the method of the present invention, this embodiment conducts a simulation comparison experiment on the three-dimensional polar channel estimation method provided by the present invention and the existing two-dimensional estimation method, as follows:

[0130] In this embodiment, the normalized mean square error (NMSE) is used as the performance evaluation index. In the simulation, the present invention sets the parameter to β η =1.4.

[0131] Figure 5 The performance of NMSE of different algorithms as the signal-to-noise ratio (SNR) changes under the condition of fixed pilot length is shown. It can be seen from the figure that the NMSE performance of all algorithms improves with the increase of SNR. The OracleLS method represented by the yellow dotted line achieves the lowest NMSE at all SNR values, indicating that it is the upper bound of theoretical performance, and it is the lower bound of theoretical performance with the LS method represented by green. The 3D-P-SOMP method represented by purple is better than the LMS represented by red in both low SNR and high SNR regions. Overall, the 3D-P-SOMP method has the advantage of achieving better NMSE performance at different SNR levels.

Claims

1. A three-dimensional polar channel estimation method for a very large-scale intelligent reflector system, characterized in that: The steps include: S1: Establish a RIS-assisted communication channel model of UPA-ULA, where RIS is a uniform planar array UPA antenna arrangement, and both the base station and the user are uniform linear array ULA; S2: According to the RIS-assisted communication channel model, the pilot signal received on the subcarrier is obtained; S3: performing polar domain transformation on the received pilot signal so that the signal exhibits sparseness in the polar domain; S4: Based on the pilot signal after polar domain transformation, a polar domain three-dimensional dictionary containing three near-field polar domain channel variables, namely, elevation angle, azimuth angle and distance, is designed to sparsely represent the channel characteristics; S5: Through the orthogonal matching pursuit algorithm, the channel is estimated using the polar domain three-dimensional dictionary to restore the channel state information.

2. The three-dimensional polar channel estimation method for a very large-scale intelligent reflection surface system according to claim 1, characterized in that: The establishment of the RIS-assisted communication channel model of the UPA-ULA in step S1 includes: The RIS-assisted communication system includes a channel matrix G between the base station and the RIS; a channel matrix H between the RIS and the user; and a RIS phase shift matrix defined as Φ = diag (φ), where represents the phase shift angle; The channel matrix G is the far-field channel matrix, and the channel matrix H is the near-field channel matrix, which are modeled by Saleh-Valenzuela and are expressed as Among them, α and β represent the path loss coefficients respectively; a(·) and b(·) are the corresponding vectors of the array, expressed as in, and θ l denote the azimuth departure angle and the elevation departure angle respectively; since b(·) is the spherical array response on subcarrier m, the vector coordinates are No. The elements and coordinates are The distance between the targets is expressed as 3. The three-dimensional polar channel estimation method for a very large-scale intelligent reflection surface system according to claim 2, characterized in that: The pilot signal received on the mth subcarrier in step S2 is expressed as y m =AGΦH+n m (7) Where n m represents noise, A represents the overall observation matrix, in which all elements are independent and can be obtained with equal probability from Generated in.

4. The three-dimensional polar channel estimation method for a very large-scale intelligent reflection surface system according to claim 1, characterized in that: In step S3, the polar domain transformation converts the signal from the traditional time domain or frequency domain into polar coordinate representation, extracts three variables of pitch angle, azimuth angle and distance, and makes the signal sparse in the polar domain.

5. The three-dimensional polar channel estimation method for a very large-scale intelligent reflection surface system according to claim 2, characterized in that: The design of the polar domain three-dimensional dictionary in step S4 includes the following steps: A1: Modeling the near-field propagation characteristics of the RIS array; A2: Use Fresnel approximation to optimize the correlation of columns in the dictionary; A3: Determine the key distance sampling points by the geometric mean method to minimize the column correlation of the dictionary matrix.

6. The three-dimensional polar channel estimation method for a very large-scale intelligent reflector system according to claim 5, characterized in that: The step A2 specifically includes: First, the spherical array response b(·) must be processed to make its column coherence as small as possible in the polar domain. For this purpose, the expression in equation (5) is simplified using the Fresnel approximation, and the near-field array response is expressed as On this basis, the spherical array response is defined as: To ensure satisfactory channel recovery accuracy, the sampling of angles and distances should be designed to minimize the column correlation of the polar domain transformation matrix P. in, and represents any two columns in P; define and The column correlation is expressed as: For the same angle θ and Any two vectors sampled, that is The first linear phase term becomes zero and is therefore eliminated; in this case, the column correlation f(θ p ,θ q ,φ p ,φ q ,r p ,r q ) depends only on the second quadratic phase term, which is affected by the term related to the distance. Due to the inherent complexity of the quadratic phase characteristics, unlike the angle sampling derivation, in order to solve this problem, the cross terms in the quadratic expression are approximately ignored, and the expression is expressed as Using the Fresnel function, formula (11) is expressed as in, In the formula as well as is the Fresnel function.

7. The three-dimensional polar channel estimation method for a very large-scale intelligent reflector system according to claim 6, characterized in that: The step A3 specifically includes: Calculate the threshold β for column correlation η , so that |G(·)|=η; due to the downward trend of |G(·)|, it is approximately concluded that β≥β η ; Based on the condition β≥β η and Sampling distance r p and r q Must meet in, Considering the array aperture D y / z =N y / z d, further R η Expressed as Assume that one of the sampling distances is Where t=1,2,..., then we can deduce For any given angle and θ, if the distance sampling is Using the geometric mean method, the distance sampling is expressed as in, 8. The three-dimensional polar channel estimation method for a very large-scale intelligent reflector system according to claim 1, characterized in that: The orthogonal matching pursuit algorithm in step S5 includes the following steps: B1: Initialize the received pilot signal, set the residual to the initial signal, initialize the channel estimation vector to all zeros, and create an empty support set to record the dictionary elements selected later; B2: Calculate the inner product between the residual and all dictionary elements, select the dictionary element with the largest inner product, regard it as the atom that is most helpful for signal recovery at present, and add the element to the support set; B3: Update the channel estimate using the selected dictionary element and calculate the new residual; B4: Repeat the above steps until the residual threshold condition is met, combine the dictionary elements in the support set, complete the signal recovery, and obtain the final channel estimation result.

Images