A multipath channel parameter estimation method for RIS system based on structured tensor decomposition

Abstract

The present disclosure provides a method for estimating multipath channel parameters in a RIS system using structured tensor decomposition. The method first constructs a multipath signal tensor by designing a pilot sequence, a RIS reflection coefficient matrix, and a base station receive combining matrix. The baseband received signals for each subcarrier and time slot are collected and reconstructed into a fifth-order signal tensor whose expression contains a Vandermonde matrix as a mode 1 factor matrix A1. Vandermonde structured tensor decomposition is then performed: the Vandermonde structure of matrix A1 is used to multiplex the received signals, augmenting the fifth-order signal tensor into a sixth-order signal tensor. The factor matrix A1 is recovered using the ESPRIT algorithm, and then other factor matrices are recovered to recover the fifth-order signal tensor. Finally, the recovered fifth-order signal tensor is used to estimate the multipath channel parameters. The present invention enables multipath channel parameter estimation for a RIS system in a full multipath environment.

Description

Technical Field

[0001] The invention belongs to the fields of navigation positioning and wireless communication, and in particular relates to a multipath channel parameter estimation method of a RIS system based on structured tensor decomposition. Background Art

[0002] Reconfigurable Intelligent Surfaces (RIS) are a key enabling technology for next-generation wireless systems and have garnered widespread attention in both academia and industry. Typically, a RIS is a two-dimensional surface composed of numerous reflective elements, each of which intelligently adjusts the outgoing phase of an incident signal. By optimizing the RIS beamforming coefficients, wireless communication signals can be efficiently enhanced through the RIS. Furthermore, RIS can serve as anchor points in positioning systems and provide high angular resolution to enhance positioning performance.

[0003] In wireless communications, channel state information (CSI) is the foundation for optimal beamforming design. Furthermore, in navigation and positioning, location awareness relies on obtaining observations, or channel parameters. Therefore, to optimize the communication and perception performance of RIS-assisted wireless systems, research is needed on high-precision channel parameter estimation.

[0004] The paper "An ESPRIT-Based Supervised Channel Estimation Method Using Tensor Train Decomposition for mmWave 3-D MIMO-OFDM Systems," published in the 2023 IEEE Transactions on Signal Processing, Volume 71, pages 555–570, mentions that in recent years, channel parameter estimation methods for RIS systems based on tensor theory have emerged, offering advantages such as excellent estimation accuracy, strong decoupling capabilities, and high modeling adaptability. Among them, channel parameter estimation methods based on structured tensor decomposition are particularly advantageous, leveraging the unique structure of factor matrices to significantly reduce computational overhead while ensuring accuracy.

[0005] However, existing related studies have made the following two assumptions on the system model, thus simplifying the channel model. First, most studies assume that all paths of the user-base station direct link are blocked, and therefore assume that the user-base station direct link does not exist. Second, some studies assume that among the three links of user-base station, user-RIS and RIS-base station, one or more links are in the line-of-sight (LOS) environment. Therefore, in a full multipath environment, that is, when the three links of user-base station, user-RIS and RIS-base station exist and are multipath channels, if Figure 1 As shown, the generalized channel parameter estimation problem remains to be studied.

[0006] In summary, the problem of multipath channel parameter estimation of RIS system based on structured tensor decomposition in full multipath environment has important research significance, which is an unresolved problem at present. Summary of the Invention

[0007] In view of this, the present invention provides a method for estimating multipath channel parameters of a RIS system based on structured tensor decomposition, which can realize multipath channel parameter estimation of a RIS system in a full multipath environment.

[0008] In order to solve the above technical problems, the present invention is implemented as follows.

[0009] A method for estimating multipath channel parameters of a RIS system based on structured tensor decomposition, comprising:

[0010] Step 1: Construct a multipath signal tensor: Design a pilot sequence, a RIS reflection coefficient matrix, and a base station receive combining matrix. Collect the baseband receive signals for each subcarrier and time slot and reconstruct them into a fifth-order signal tensor. The RIS reflection coefficient matrix and the base station receive combining matrix are constructed by the Kronecker product of the Vandermonde matrix. The expression of the fifth-order signal tensor contains the Vandermonde matrix as the mode 1 factor matrix A1.

[0011] Step 2: Structured tensor decomposition: Utilize the Vandermonde structure of factor matrix A1 to multiplex the received signal and effectively split the Vandermonde matrix factor matrix A1 in the 5th-order signal tensor into two sub-matrices, thereby expanding the 5th-order signal tensor into a 6th-order signal tensor. Use the ESPRIT algorithm to restore the factor matrix A1, that is, to equivalently obtain two factor matrix estimates in the 6th-order signal tensor. Use these two factor matrix estimates to obtain factor matrix estimates of other modes in the 6th-order signal tensor, thereby restoring the 5th-order signal tensor.

[0012] Step 3: Estimate the multipath channel parameters using the fifth-order signal tensor recovered in step 2.

[0013] Preferably, the step 3 further comprises: converting the recovered multipath channel parameter, ie, the angular frequency As a rough estimation result, the optimization target is constructed using the correlation calculation strategy, and the fine estimation is completed through iteration;

[0014] The correlation calculation strategy is to find an angular frequency value and construct an estimate of the corresponding column of the factor matrix based on the angular frequency value, which is most similar to the corresponding column of the recovered 5th-order signal tensor under the cosine distance criterion;

[0015] In each round of iteration, the search interval of the search space is gradually reduced; after reaching the upper limit of the number of iterations, the angular frequency estimation of each mode is output to complete the precise estimation of the multipath channel parameters.

[0016] Preferably, in step 1, the multipath signal tensor is constructed by designing the pilot sequence, the RIS reflection coefficient matrix and the base station receiving combining matrix as follows:

[0017] Step 1a: Model the RIS system in a multipath environment: there are G time slots, each of which has K subcarriers for pilot transmission; the user is a single-antenna device, and the base station and the RIS system are equipped with uniform planar array antennas with array sizes of and M y ×M z ; The channel of the direct link between the user and the base station is represented by the symbol The multipath channel of the cascade link between user-RIS-base station is represented by the symbol Indicates that k=1,…,K,g=1,…,G;

[0018] Define the function vector a related to the parameters M and ω (M) (ω)=[1,e jω ,...,e j(M-1)ω ] T ; then the channel and Modeled as:

[0019]

[0020] where D, P, and Q are the multipath numbers of the user-base station, user-RIS, and RIS-base station links, respectively, = 1,...,D, p = 1,...,P, q = 1,...,Q, and are the path gains of the direct link and the cascade link respectively, j is the imaginary unit, is the angular frequency associated with the direct link delay, is the angular frequency related to the cascade link delay, and is the angular frequency related to the angle of arrival of the direct link at the base station, and is the angular frequency related to the angle of arrival of the cascaded link at the base station, is the Kronecker product operator; Gain for the RIS system;

[0021]

[0022] Among them, γ (g) is the reflection coefficient vector of the RIS system, and are parameters related to the RIS arrival and departure angles;

[0023] Step 1b: Based on the modeling in step 1a, the designed pilot sequence, RIS reflection coefficient matrix, and base station receiving combining matrix are:

[0024]

[0025] Among them, x (k) =[x (k,1) ,...,x (k,G) ] T is the pilot vector, k=1,...,K, x=diag(x (k) ), diag(·) is a diagonal matrix operator, G1 and G2 satisfy G=G1G2, 1 is an all-one matrix, and the subscript 1 indicates the dimension; Φ is the RIS reflection coefficient matrix, T2 and T3 are two Vandermonde matrices used to construct Φ; T2 and T3 are two Vandermonde matrices used to construct the base station receive combining matrix R.

[0026] Preferably, in step 1, the baseband received signals of each subcarrier and time slot are collected and reconstructed into a 5th-order signal tensor:

[0027] The baseband received signal at the base station is represented by collecting the baseband received signals of each subcarrier and time slot:

[0028]

[0029] in, is the baseband received signal of the kth subcarrier and the gth time slot; k=1,...,K,g=1,...,G, there are G time slots in total, and K subcarriers in each time slot are used for pilot transmission; R is the base station receiving combining matrix, x (k,g) is the transmission symbol of the kth subcarrier and the gth time slot, w (k,g) is the receiving noise; the channel of the direct link between the user and the base station is represented by The channel of the cascade link between user, RIS and base station is represented by express;

[0030] The baseband received signals of each subcarrier and time slot are vertically stacked to obtain vector y, which is then reconstructed into a 5th-order signal tensor with a dimension of K×G1×G2×N1×N2. The rank of the signal tensor is T=D+PQ, where N1N2 is the number of base station radio frequency links; It can be written in the form of a CP tensor:

[0031]

[0032] in,

[0033]

[0034] Where A1 is a Vandermonde matrix.

[0035] Preferably, in step 2, the process of expanding the 5th-order signal tensor to the 6th-order signal tensor is:

[0036] According to the Vandermonde structure, based on the spatial domain smoothing augmentation of the 5th-order signal tensor, the factor matrix with mode 1 in the 5th-order signal tensor is expanded from the original K×T dimensional matrix to two factor matrices of K1×T and K2×T dimensions, which are respectively denoted as the new mode 1 and mode 6, where K1+K2-1=K. The modes 2 to 5 of the 5th-order signal tensor remain unchanged, thus obtaining the 6th-order augmented signal tensor.

[0037] Augmented tensor Expressed as a CP tensor:

[0038]

[0039] Among them, B1 and B6 are sub-matrices composed of the first K1 rows and the first K2 rows of the factor matrix A1 in the 5th-order signal tensor, respectively.

[0040] Preferably, in step 2, the process of recovering the 5th-order signal tensor is:

[0041] Step 2a, based on the Vandermonde structure, use the ESPRIT algorithm to recover the factor matrix A1 corresponding to mode 1 of the 5th-order signal tensor:

[0042] First, the 6th order signal tensor Expand and reconstruct the matrix according to mode 3 And perform singular value decomposition on it, we get Among them, U, V, and Σ are two unitary matrices and a diagonal matrix obtained by singular value decomposition respectively; then calculate Among them J ↑ and J ↓ For 2 selection matrices, is the inverse operator; then calculate the eigenvalue decomposition of the matrix Ψ to obtain the eigenvalue and eigenvector matrix At this time, the tensor The angular frequency estimate corresponding to mode 1 is recorded as It can be obtained from the eigenvalue of the matrix Ψ, using the obtained Construct factor matrix A1;

[0043] Step 2b: Extract the first K1 rows and the first K2 rows from the recovered factor matrix A1 to form the estimates of the factor matrices B1 and B6;

[0044] Step 2c, let Represents a 6th-order signal tensor The column r estimates of the modal n factor matrix, and let and The matrices and Column r, n=1,...,6,r=1,...,T,b 1,r Estimate column r of factor matrix B1; calculate The singular value decomposition of and are the left singular vector and the right singular vector respectively, where unvec(·) and I are the matrix operator and the identity matrix respectively; Composition B3 estimate, each Construct the B4 estimate, thereby completing the estimation of factor matrices B3 and B4;

[0045] Step 2d, let b 6,r Estimate column r of factor matrix B6; calculate The singular value decomposition of and are the left singular vector and the right singular vector respectively; Composition B4 estimate, each Construct the B5 estimate, thereby completing the estimation of factor matrices B4 and B5.

[0046] Preferably, in step 3, the multipath channel parameters are estimated using the fifth-order signal tensor recovered in step 2 as follows:

[0047]

[0048] in, is the angular velocity, is the estimated multipath channel parameter; Q n is the projection matrix, F n is a diagonal matrix with Vandermonde matrices T n The generating factor, is the inverse operator; b n,rEstimate column r of the factor matrix of mode n in the 6th-order signal tensor obtained in step 2.

[0049] Preferably, the step 3 further comprises: estimating the multipath channel parameters of the factor matrix of modes 2-5, i.e., the angular frequency As a rough estimation result, the optimization target is constructed using the correlation calculation strategy, and the fine estimation is completed through iteration;

[0050] The correlation calculation strategy is:

[0051]

[0052] in, is the rough estimation result, n is the modal number of the factor matrix, R is the rank of the 5-order signal tensor, and r is the rank number of the tensor; function For each n∈{2,3,4,5}, b n,r is the column r estimate of the factor matrix of mode n in the 6th-order signal tensor;

[0053] In each iteration, the search space is constructed as:

[0054]

[0055] in, is the search interval of the i-th iteration, is the angular frequency estimate of the i-1th iteration, The size of the space is fixed in each round of iteration; in the search space described by formula (II), the angular frequency that makes the objective function of formula (I) maximum is found as the output of this round of iteration; then the search interval is narrowed for use in the next round of iteration, that is,

[0056]

[0057] Among them, the reduction coefficient 0<ζ n <1;

[0058] After reaching the upper limit of the number of iterations, the angular frequency estimation of each mode is output to complete the precise estimation of the multipath channel parameters.

[0059] Beneficial effects:

[0060] This paper proposes a multipath channel parameter estimation method for RIS systems based on structured tensor decomposition, targeting full multipath environments. This method accurately outputs parameters such as path gain, angle, and delay for both direct and cascaded links. Compared to existing methods, this method targets a generalized channel model where all three links—user-base station, user-RIS, and RIS-base station—exist in multipath channels, making it more universally applicable.

[0061] Furthermore, this method has low computational complexity, making it well-suited for practical engineering implementation. This low computational complexity is reflected in two key aspects: First, compared to traditional iterative tensor decomposition methods based on alternating optimization, this method employs a structured tensor decomposition strategy that requires only simple algebraic operations, significantly reducing the computational complexity of tensor decomposition. Second, this method avoids traditional exhaustive parameter estimation methods and instead employs an innovative two-stage iterative search approach, significantly reducing the computational complexity of the search. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 Schematic diagram of RIS-assisted wireless system in multipath environment;

[0063] Figure 2 Flow chart of the method of the present invention;

[0064] Figure 3 This is a flow chart of channel parameter estimation in step 3 in a preferred embodiment of the present invention. DETAILED DESCRIPTION

[0065] The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0066] This method is based on RIS-assisted wireless system in multipath environment, such as Figure 1 As shown. The user establishes an uplink connection with the base station, where the RIS forms a user-RIS-base station cascade link. The three links of user-base station, user-RIS and RIS-base station are all in a multipath environment, that is, there are several scatterers. Considering the Orthogonal Frequency-Division Multiplexing (OFDM) system, there are G time slots, and each time slot has K subcarriers for pilot transmission. Assume that the user is a single-antenna device, and the base station and RIS are equipped with uniform planar array (UPA) antennas, and their array sizes are respectively and M y ×M z The multipath channels of the direct user-base station link and the cascaded user-RIS-base station link are denoted by and Indicates that k=1,...,K,g=1,...,G.

[0067] Define a related to parameters M and ω (M) (ω)=[1,e ω ,...,e (M-1)ω ] T Then the channel and Can be modeled as:

[0068]

[0069] where D, P, and Q are the multipath numbers of the user-base station, user-RIS, and RIS-base station links, respectively. l=1,...,D,p=1,...,P,q=1,...,Q, and are the path gains of the direct user-base station link (hereinafter referred to as the “direct link”) and the cascaded user-RIS-base station link (hereinafter referred to as the “cascaded link”), respectively. j is an imaginary unit. is the angular frequency associated with the direct link delay, is the angular frequency related to the cascade link delay, and is the angular frequency related to the angle of arrival of the direct link at the base station, and is the angular frequency related to the angle of arrival of the cascaded link at the base station, is the Kronecker product operator, RIS gain The expression is:

[0070]

[0071] Among them, γ (g) is the RIS reflection coefficient vector, and is a parameter related to the RIS arrival / departure angle.

[0072] The expressions of the above angular frequencies are:

[0073]

[0074] Among them, Δ f is the subcarrier frequency spacing, and are the delays of the direct link and the cascade link respectively, λ is the wavelength, d R and d B are the cell spacings of RIS and base station, and are the arrival azimuth and elevation angle of RIS, and are the departure azimuth and elevation angles of RIS, and are the arrival azimuth and elevation angles of the direct path at the base station, and are the arrival azimuth and elevation angles of the cascade path at the base station, respectively.

[0075] From equations (1)-(3), it can be seen that in order to estimate the multipath channel parameters of the direct link and the cascade link, the parameters to be obtained are the angular frequencies.

[0076] Furthermore, the baseband received signal at the base station can be expressed as:

[0077]

[0078] in, The matrix R of dimension is the receiving combining matrix at the base station, N1N2 is the number of base station radio frequency links, x (k,g) is the emission symbol, w (k,g) To receive noise. In order to more intuitively reveal the principle of the proposed method, the noise-free signal is used in the following text. In actual noisy systems, it is necessary to use y in the replacement algorithm (k,g) .

[0079] Based on the above modeling, the RIS system multipath channel parameter estimation method based on structured tensor decomposition proposed in the present invention specifically includes the following steps: Figure 2 As shown:

[0080] Step 1: Construct a signal tensor: specially design the pilot sequence, RIS reflection coefficient matrix, and base station receive combining matrix, collect the baseband receive signals of each subcarrier and time slot, and reconstruct them into a 5th-order signal tensor.

[0081] Step 2: Perform structured tensor decomposition based on the Vandermonde matrix: Based on spatial domain smoothing and augmenting the original signal tensor, the 5th-order signal tensor is augmented to a 6th-order signal tensor; ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques) is used to restore one of the factor matrices, and on this basis, the other factor matrices are obtained.

[0082] In step 1, a special construction is used to make the 5th-order signal tensor contain the Vandermonde matrix, that is, the factor matrix A1 of mode 1. During augmentation, by multiplexing the received signal, the factor matrix A1 is equivalently split into two sub-matrices, which serve as the factor matrix of the 6th-order signal tensor. Then, in this step, the ESPRIT algorithm can be used to recover the factor matrix A1, that is, two factor matrix estimates in the 6th-order signal tensor can be equivalently obtained, and then these two factor matrix estimates are used to obtain the factor matrix estimates of other modes in the 6th-order signal tensor. Since the "factor matrices of other modes" in the 5th-order signal tensor and the 6th-order signal tensor are the same, the 5th-order signal tensor is recovered.

[0083] Step 3: Estimate the multipath channel parameters using the fifth-order signal tensor recovered in step 2.

[0084] Preferably, in this step, an algebraic solution is first constructed based on ESPRIT to perform a rough estimate, and then an iterative update is performed using a correlation strategy to complete a fine estimate.

[0085] The following is a detailed description of each of the above steps.

[0086] In step 1, the signal tensor is constructed, which includes the following steps:

[0087] Step 1.1, specially design the pilot sequence, RIS reflection coefficient matrix and base station receiving combining matrix. Specifically, let:

[0088] Among them, x (k) =[x (k,1) ,...,x (k,G) ] T is the pilot vector, G1 and G2 satisfy G = G1G2, 1 is a full 1 matrix (dimension is recorded in the subscript); Φ = [γ (1) ,...,γ (G) ] T is the RIS reflection coefficient matrix, T2 and T3 are two Vandermonde matrices, and diag(·) is the diagonal matrix operator; T2 and T3 are also two Vandermonde matrices.

[0089] Step 1.2: vertically stack the baseband received signal vectors of each subcarrier and time slot, i.e. let y = [y (1,1) ,...,y (K ,G) ] T The expression of the vector y is:

[0090]

[0091] Substituting into equation (5), vector y can be further expressed as:

[0092]

[0093] Then reconstruct the vector y into a tensor of dimension K×G1×G2×N1×N2 The rank of this tensor is T = D + PQ. It can be written in the form of a CP (Canonical Polyadic) tensor:

[0094]

[0095] in,

[0096]

[0097] It can be observed that A1 is a Vandermonde matrix.

[0098] In step 2, structured tensor decomposition is performed based on the Vandermonde factor matrix, which specifically includes the following steps.

[0099] Step 2.1: Based on the Vandermonde factor matrix, the original signal tensor is augmented based on spatial domain smoothing. Specifically, the factor matrix with mode 1 in the 5th-order signal tensor is expanded from the original K×T-dimensional matrix to two factor matrices with dimensions of K1×T and K2×T, which are respectively denoted as the new mode 1 and mode 6, where K1+K2-1=K. The modes 2 to 5 of the 5th-order signal tensor remain unchanged, so as to obtain the 6th-order augmented signal tensor; that is,

[0100]

[0101] Where k1=1,...,K1,k2=1,...,K2. Augmented tensor It can be further expressed in the form of a CP tensor:

[0102]

[0103] Among them, B1 and B6 are sub-matrices consisting of the first K1 rows and the first K2 rows of matrix A1 respectively.

[0104] In step 2.2, one of the factor matrices A1 is recovered using ESPRIT according to the Vandermonde structure.

[0105] First, the tensor Expand and reconstruct the matrix according to mode 3 It can be expressed as:

[0106]

[0107] Where ⊙ represents the Khatri-Rao product operator. Perform singular value decomposition and get Among them, U, V, and Σ are two unitary matrices and a diagonal matrix obtained by singular value decomposition. It can be seen here that U and B1⊙B2⊙B3 have the same column space, so B1⊙B2⊙B3=UD, where D is a non-singular basis transformation matrix. Then calculate in is the violation operator, J ↑ and J ↓ For 2 selection matrices, the expression is:

[0108]

[0109] Then calculate the eigenvalue decomposition of the matrix Ψ and get the eigenvalue and eigenvector matrix At this time, the tensor The angular frequency estimate corresponding to mode 1 is recorded as can be obtained from the eigenvalues ​​of the matrix Ψ. Equivalently, the tensor The factor matrix A1 corresponding to mode 1.

[0110] In step 2.3, from the recovered factor matrix A1, extract the first K1 rows and the first K2 rows to form the estimates of the factor matrices B1 and B6.

[0111] Step 2.4, obtain other factor matrices:

[0112] make Representing a tensor The column r estimates of the modal n factor matrix, and let and The matrices and Column r, n=1,...,6,r=1,...,T.

[0113] Because there is

[0114]

[0115] calculate The singular value decomposition of and are the left and right singular vectors, respectively. Where unvec(·) and I are the matrix operator and the identity matrix (dimensions are written in subscripts). Composition B3 estimate, each Construct the B4 estimate, thereby completing the estimation of factor matrices B3 and B4.

[0116] Similarly, there are

[0117]

[0118] calculate The singular value decomposition of and are the left and right singular vectors, respectively. each Composition B4 estimate, each Construct the B5 estimate, thereby completing the estimation of factor matrices B4 and B5.

[0119] Furthermore, estimating the multipath channel parameters in step 3 specifically includes the following steps.

[0120] Step 3.1, construct an algebraic solution based on ESPRIT to make a rough estimate. Specifically, the tensor The rough estimate of the angular frequency of modes 2-5 (equivalent to the multipath channel parameters) is expressed as:

[0121]

[0122] Among them, F n is a diagonal matrix with Vandermonde matrices T n The generation factor, Q n is a projection matrix, Q n The construction method is: first, the matrix The first column of vectors and matrices and The product of the last column vectors, these two vectors are arranged horizontally to form a new matrix, Q n That is the orthogonal projection matrix of the matrix column space.

[0123] Step 3.2: Iterate and update the correlation calculation strategy to complete the precise estimation. The correlation calculation strategy is to find an angular frequency value and construct an estimate of the corresponding column of the factor matrix based on it. This estimate is most similar to the corresponding column of the recovered 5th-order signal tensor under the cosine distance criterion.

[0124] The optimization problem is:

[0125]

[0126] Among them, the function For each n∈{2,3,4,5}, It can be proved that in b n,r When the estimation error obeys the complex Gaussian distribution, the estimator of formula (11) is equivalent to the maximum likelihood (ML) estimator. For each n and r, different from the traditional one-dimensional exhaustive search solution strategy, the present invention converts the output of step 3.1 into As the initial value, and iteratively update Specifically, in each iteration, the search space is constructed as:

[0127]

[0128] in, is the search interval of the i-th iteration, is the angular frequency estimate of the i-1th iteration, The size of the space is fixed in each iteration. In the above search space, find an angular frequency that maximizes the objective function in formula (11) as the output of this round of iteration.

[0129] Then the search interval is narrowed for the next iteration, i.e.

[0130]

[0131] The reduction coefficient is 0<ζ n <1. After reaching the upper limit of the number of iterations, the angular frequency estimation of each mode is output to complete the precise estimation of the multipath channel parameters.

[0132] In summary, the above are only preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for estimating multipath channel parameters of a RIS system based on structured tensor decomposition, characterized in that: include: Step 1: Construct a multipath signal tensor: Design a pilot sequence, a RIS reflection coefficient matrix, and a base station receive combining matrix. Collect the baseband receive signals for each subcarrier and time slot and reconstruct them into a fifth-order signal tensor. The RIS reflection coefficient matrix and the base station receive combining matrix are constructed by the Kronecker product of the Vandermonde matrix. The expression of the fifth-order signal tensor contains the Vandermonde matrix as the mode 1 factor matrix A1. Step 2: Structured tensor decomposition: Utilize the Vandermonde structure of factor matrix A1 to multiplex the received signal and effectively split the Vandermonde matrix factor matrix A1 in the 5th-order signal tensor into two sub-matrices, thereby expanding the 5th-order signal tensor into a 6th-order signal tensor. Use the ESPRIT algorithm to restore the factor matrix A1, that is, to equivalently obtain two factor matrix estimates in the 6th-order signal tensor. Use these two factor matrix estimates to obtain factor matrix estimates of other modes in the 6th-order signal tensor, thereby restoring the 5th-order signal tensor. Step 3: Estimate the multipath channel parameters using the fifth-order signal tensor recovered in step 2.

2. The method according to claim 1, wherein The step 3 further comprises: As a rough estimation result, the optimization target is constructed using the correlation calculation strategy, and the fine estimation is completed through iteration; The correlation calculation strategy is to find an angular frequency value and construct an estimate of the corresponding column of the factor matrix based on the angular frequency value, which is most similar to the corresponding column of the recovered 5th-order signal tensor under the cosine distance criterion; In each round of iteration, the search interval of the search space is gradually reduced; after reaching the upper limit of the number of iterations, the angular frequency estimation of each mode is output to complete the precise estimation of the multipath channel parameters.

3. The method according to claim 1, wherein In step 1, the multipath signal tensor is constructed by designing the pilot sequence, RIS reflection coefficient matrix and base station receiving combining matrix as follows: Step 1a: Model the RIS system in a multipath environment: there are G time slots, each of which has K subcarriers for pilot transmission; the user is a single-antenna device, and the base station and the RIS system are equipped with uniform planar array antennas with array sizes of and M y ×M z ; The channel of the direct link between the user and the base station is represented by the symbol The multipath channel of the cascade link between user-RIS-base station is represented by the symbol Indicates that k=1,...,K,g=1,...,G; Define a function vector related to parameters M and ω Channel and Modeled as: Where D, P, and Q are the multipath numbers of the user-base station, user-RIS, and RIS-base station links, respectively. l=1,...,D,p=1,...,P,q=1,...,Q, and are the path gains of the direct link and the cascade link respectively, is the imaginary unit, is the angular frequency associated with the direct link delay, is the angular frequency related to the cascade link delay, and is the angular frequency related to the angle of arrival of the direct link at the base station, and is the angular frequency related to the angle of arrival of the cascaded link at the base station, is the Kronecker product operator; Gain for the RIS system; Among them, γ (g) is the reflection coefficient vector of the RIS system, and are parameters related to the RIS arrival and departure angles; Step 1b: Based on the modeling in step 1a, the designed pilot sequence, RIS reflection coefficient matrix, and base station receiving combining matrix are: Among them, x (k) =[x (k,1) ,...,x (k,G) ] T is the pilot vector, k=1,...,K, x=diag(x (k) ), diag(·) is a diagonal matrix operator, G1 and G2 satisfy G=G1G2, 1 is an all-one matrix, and the subscript 1 indicates the dimension; Φ is the RIS reflection coefficient matrix, T2 and T3 are two Vandermonde matrices used to construct Φ; T2 and T3 are two Vandermonde matrices used to construct the base station receive combining matrix R.

4. The method according to claim 3, wherein In step 1, the baseband received signals of each subcarrier and time slot are collected and reconstructed into a 5th-order signal tensor: The baseband received signal at the base station is represented by collecting the baseband received signals of each subcarrier and time slot: in, ) is the baseband received signal of the kth subcarrier and the gth time slot; k=1,...,K,g=1,...,G, there are G time slots in total, and K subcarriers in each time slot are used for pilot transmission; R is the base station receiving combining matrix, x (k,g) is the transmission symbol of the kth subcarrier and the gth time slot, w (k,g) is the receiving noise; the channel of the direct link between the user and the base station is represented by The channel of the cascade link between user, RIS and base station is represented by express; The baseband received signals of each subcarrier and time slot are vertically stacked to obtain vector y, which is then reconstructed into a 5th-order signal tensor with a dimension of K×G1×G2×N1×N2. The rank of the signal tensor is T=D+PQ, where N1N2 is the number of base station radio frequency links; It can be written in the form of a CP tensor: in, Where A1 is a Vandermonde matrix.

5. The method according to claim 3, wherein In step 2, the process of expanding the 5th-order signal tensor to the 6th-order signal tensor is as follows: According to the Vandermonde structure, based on the spatial domain smoothing augmentation of the 5th-order signal tensor, the factor matrix with mode 1 in the 5th-order signal tensor is expanded from the original K×T dimensional matrix to two factor matrices of K1×T and K2×T dimensions, which are respectively denoted as the new mode 1 and mode 6, where K1+K2-1=K. The modes 2 to 5 of the 5th-order signal tensor remain unchanged, thus obtaining the 6th-order augmented signal tensor. Augmented tensor Expressed as a CP tensor: Among them, B1 and B6 are sub-matrices composed of the first K1 rows and the first K2 rows of the factor matrix A1 in the 5th-order signal tensor, respectively.

6. The method according to claim 5, wherein In step 2, the process of recovering the 5th-order signal tensor is: Step 2a, based on the Vandermonde structure, use the ESPRIT algorithm to recover the factor matrix A1 corresponding to mode 1 of the 5th-order signal tensor: First, the 6th order signal tensor Expand and reconstruct the matrix according to mode 3 And perform singular value decomposition on it, we get Among them, U, V, and Σ are two unitary matrices and a diagonal matrix obtained by singular value decomposition respectively; then calculate Among them J ↑ and J ↓ For 2 selection matrices, is the inverse operator; then calculate the eigenvalue decomposition of the matrix Ψ to obtain the eigenvalue and eigenvector matrix At this time, the tensor The angular frequency estimate corresponding to mode 1 is recorded as It can be obtained from the eigenvalue of the matrix Ψ, using the obtained Construct factor matrix A1; Step 2b: Extract the first K1 rows and the first K2 rows from the recovered factor matrix A1 to form the estimates of the factor matrices B1 and B6; Step 2c, let Represents a 6th-order signal tensor The column r estimates of the modal n factor matrix, and let and The matrices and Column r, n=1,…,6,r=1,…,T,b 1,r Estimate column r of factor matrix B1; calculate The singular value decomposition of and are the left singular vector and the right singular vector respectively, where unvec(·) and I are the matrix operator and the identity matrix respectively; Composition B3 estimate, each Construct the B4 estimate, thereby completing the estimation of factor matrices B3 and B4; Step 2d, let b 6,r Estimate column r of factor matrix B6; calculate The singular value decomposition of and are the left singular vector and the right singular vector respectively; Composition B4 estimate, each Construct the B5 estimate, thereby completing the estimation of factor matrices B4 and B5.

7. The method according to claim 3, wherein In step 3, the multipath channel parameters are estimated using the fifth-order signal tensor recovered in step 2: in, is the angular velocity, is the estimated multipath channel parameter; Q n is the projection matrix, F n is a diagonal matrix with Vandermonde matrices T n The generating factor, is the inverse operator; b n,r Estimate column r of the factor matrix of mode n in the 6th-order signal tensor obtained in step 2.

8. The method according to claim 3, wherein The step 3 further comprises: estimating the multipath channel parameters of the factor matrix of modes 2-5, i.e., the angular frequency As a rough estimation result, the optimization target is constructed using the correlation calculation strategy, and the fine estimation is completed through iteration; The correlation calculation strategy is: in, is the rough estimation result, n is the modal number of the factor matrix, R is the rank of the 5-order signal tensor, and r is the rank number of the tensor; function For each n∈{2,3,4,5}, b n,r is the column r estimate of the factor matrix of mode n in the 6th-order signal tensor; In each iteration, the search space is constructed as: in, is the search interval of the i-th iteration, is the angular frequency estimate of the i-1th iteration, The size of the space is fixed in each round of iteration; in the search space described by formula (II), the angular frequency that makes the objective function of formula (I) maximum is found as the output of this round of iteration; then the search interval is narrowed for use in the next round of iteration, that is, Among them, the reduction coefficient 0<ζ n <1; After reaching the upper limit of the number of iterations, the angular frequency estimation of each mode is output to complete the precise estimation of the multipath channel parameters.

Images