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

Abstract

The invention provides an RIS system multipath channel parameter estimation method based on structured tensor decomposition, and the method comprises the steps: firstly constructing a multipath signal tensor: designing a pilot frequency sequence, an RIS reflection coefficient matrix and a base station receiving merging matrix, collecting baseband receiving signals of each subcarrier and time slot, reconstructing a five-order signal tensor, and carrying out the reconstruction of the five-order signal tensor; the expression contains a Vandermonde matrix as a modal 1 factor matrix A1; then Vandermonde structured tensor decomposition is carried out, a Vandermonde structure multiplexing receiving signal of the matrix A1 is used, a fifth-order signal tensor is widened to a sixth-order signal tensor, the factor matrix A1 is recovered by using an ESPRIT algorithm, and then other factor matrixes are recovered, so that the fifth-order signal tensor is recovered; and finally, estimating multipath channel parameters by using the recovered five-order signal tensor. According to the invention, RIS system multipath channel parameter estimation in a full multipath environment can be realized.

Description

Technical Field

[0001] The invention belongs to the field 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 Surface (RIS) is a key enabling technology for the next generation of wireless systems and has received widespread attention in academia and industry. Typically, RIS is a two-dimensional surface composed of many reflective units, each of which can intelligently adjust the outgoing phase of the incident signal. By optimizing the RIS beamforming coefficients, wireless communication signals can be efficiently enhanced through RIS. In addition, RIS can be used as an anchor point in the positioning system and can provide high angular resolution to enhance positioning performance.

[0003] In the field of wireless communications, channel state information (CSI) is the basis for optimal beamforming design. In addition, in the field of navigation and positioning, the basis of position perception is to obtain observations, that is, channel parameters. Therefore, in order to optimize the communication and perception performance of RIS-assisted wireless systems, it is necessary to study the problem of high-precision channel parameter estimation of RIS-assisted wireless systems.

[0004] In the paper "An ESPRIT-Based Supervised Channel Estimation Method Using Tensor TrainDecomposition for mmWave 3-D MIMO-OFDM Systems" on pages 555–570 of the IEEE TRANSACTIONS ON SIGNAL PROCESSING journal, volume 71, 2023, it is mentioned that in recent years, the channel parameter estimation method of RIS system based on tensor theory has emerged, with the advantages of excellent estimation accuracy, strong decoupling capability, and high modeling adaptability. Among them, the channel parameter estimation method based on structured tensor decomposition is superior, which utilizes the special structure of the factor matrix, which can greatly save 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 a 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 all exist and are multipath channels, if Figure 1 As shown, the generalized channel parameter estimation problem needs to be studied.

[0006] In summary, the problem of multipath channel parameter estimation for RIS systems based on structured tensor decomposition in a full multipath environment is of great research significance, which is an unsolved 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 receiving merging matrix, collect the baseband receiving signals of each subcarrier and time slot, and reconstruct them into a 5th-order signal tensor; wherein the RIS reflection coefficient matrix and the base station receiving merging matrix are composed of the Kronecker product of the Vandermonde matrix; the expression of the 5th-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 the factor matrix A1 to multiplex the received signal, and equivalently split the factor matrix A1 in the form of the Vandermonde matrix in the 5th-order signal tensor into two sub-matrices, thereby expanding the 5th-order signal tensor to a 6th-order signal tensor; utilize the ESPRIT algorithm to restore the factor matrix A1, that is, equivalently obtain two factor matrix estimates in the 6th-order signal tensor, and 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, step 3 further comprises: recovering the multipath channel parameter, 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;

[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 restored 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: the pilot sequence, the RIS reflection coefficient matrix and the base station receiving merging matrix are designed as follows:

[0017] Step 1a, modeling 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 multipath channel of the cascaded link between user-RIS-base station is represented by It means, k=1,…,K, g=1,…,G;

[0018] Define a function vector a related to parameters M and ω (M) (ω)=[1,e jω ,...,e j(M-1)ω ] T ; then the channel and They are 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 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; 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 of 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-base station is represented by express;

[0030] The baseband received signals of each subcarrier and time slot are vertically stacked to obtain vector y, and then vector y is reconstructed into a 5th-order signal tensor with a dimension size of K×G1×G2×N1×N2 The rank of the signal tensor is T = D + PQ, 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 a 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 recorded as the new mode 1 and mode 6, where K1+K2-1=K, and the mode 2 to mode 5 of the 5th-order signal tensor remain unchanged, so as to obtain 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 restoring 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, Σ are two unitary matrices and a diagonal matrix obtained by singular value decomposition; then calculate Among them J ↑ and J ↓ are 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 denoted 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 estimates of the factor matrices B1 and B6;

[0044] Step 2c, let Represents a 6th-order signal tensor The column r of the modal n factor matrix is ​​estimated, and let and The matrices are and The columns of 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 left singular vectors and right singular vectors, respectively, where unvec(·) and I are matrix operators and unit matrices, respectively; Composition B3 estimate, each Construct the B4 estimate, thus 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, thus 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 diagonal elements being 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, step 3 further comprises: estimating the multipath channel parameters, i.e., the angular frequencies, of the factor matrices of modes 2-5 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 5th-order signal tensor, and r is the rank number of the tensor; function For every 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 space size is fixed in each round of iteration; in the search space described in formula (II), find the angular frequency that makes the objective function of formula (I) maximum as the output of this round of iteration; then narrow the search interval for the next round of iteration, that is, let

[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] The present invention is oriented to the full multipath environment and proposes a structured tensor decomposition RIS system multipath channel parameter estimation method, which can accurately output the path gain, angle, delay and other parameters of the direct link and the cascade link. Compared with the existing methods, this method is aimed at a generalized channel model, that is, the three links of user-base station, user-RIS and RIS-base station all exist and are multipath channels, so this method is more universal.

[0061] In addition, this method has low computational complexity, so it can be well applied to practical engineering implementation. The low computational complexity is reflected in the following two points: first, compared with the traditional iterative tensor decomposition method based on alternating optimization, this method adopts a structured tensor decomposition strategy, which only requires simple algebraic operations and can greatly reduce the computational complexity of tensor decomposition; second, this method avoids the traditional exhaustive parameter estimation method and innovatively adopts a two-stage iterative search method, which greatly reduces the search computational complexity. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 It is a schematic diagram of RIS-assisted wireless system in multipath environment;

[0063] Figure 2 is a 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] The 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 constitutes a user-RIS-base station cascade link. The three links of user-base station, user-RIS and RIS-base station are all located in a multipath environment, that is, there are several scatterers. Consider an orthogonal frequency-division multiplexing (OFDM) system with a total of 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 They 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 associated with 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 angle / 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 angle of RIS, and are the arrival azimuth and elevation angle of the direct path at the base station, and are the arrival azimuth and elevation angle 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 RF links of the base station, and 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 following text uses a noise-free signal In the actual noisy system, it is necessary to use y in the substitution 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 the signal tensor: specially design the pilot sequence, RIS reflection coefficient matrix and base station receiving merging matrix, collect the baseband receiving 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 to augment the original signal tensor, the 5th-order signal tensor is augmented to a 6th-order signal tensor; use ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques) to restore one of the factor matrices, and on this basis, obtain the other factor matrices.

[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, the factor matrix A1 is equivalently split into two sub-matrices by multiplexing the received signal, which serves as the factor matrix of the 6th-order signal tensor. Then in this step, the factor matrix A1 can be restored using the ESPRIT algorithm, that is, two factor matrix estimates in the 6th-order signal tensor can be equivalently obtained, and then the factor matrix estimates of other modes in the 6th-order signal tensor are obtained using these two factor matrix estimates. 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 restored.

[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 a correlation strategy is used for iterative update to complete a precise 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 matrix of all 1s (the 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, that is, 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, according to 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 recorded as the new mode 1 and mode 6, where K1+K2-1=K, and the mode 2 to mode 5 of the 5th-order signal tensor remain unchanged, so as to obtain the 6th-order augmented signal tensor; that is,

[0100]

[0101] Among them, 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 the matrix A1 respectively.

[0104] Step 2.2, based on the Vandermonde structure, use ESPRIT to recover one of the factor matrices A1.

[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, Σ are two unitary matrices and a diagonal matrix obtained by singular value decomposition. It can be obtained 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 inverse operator, J ↑ and J ↓ For 2 selection matrices, the expression is:

[0108]

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

[0110] 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 of the modal n factor matrix is ​​estimated, and let and The matrices are 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 (the dimension is written in the subscript). Composition B3 estimate, each Construct the B4 estimate, thus 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, thus completing the estimation of factor matrices B4 and B5.

[0119] Furthermore, estimating 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 mode 2-5 (equivalent to the multipath channel parameters) is:

[0121]

[0122] Among them, F n is a diagonal matrix with diagonal elements being 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 of 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, iteratively update using 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, which is most similar to the corresponding column of the restored 5th-order signal tensor under the cosine distance criterion.

[0124] The optimization problem is:

[0125]

[0126] Among them, the function For every n∈{2,3,4,5}, It can be proved that in b n,r When the estimation error follows a complex Gaussian distribution, the estimator in 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 equation (11) as the output of this round of iteration.

[0129] Then the search interval is reduced for the next iteration, that is,

[0130]

[0131] The reduction factor 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 protection scope of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope 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 receiving merging matrix, collect the baseband receiving signals of each subcarrier and time slot, and reconstruct them into a 5th-order signal tensor; wherein the RIS reflection coefficient matrix and the base station receiving merging matrix are composed of the Kronecker product of the Vandermonde matrix; the expression of the 5th-order signal tensor contains the Vandermonde matrix as the mode 1 factor matrix A1; Step 2, structured tensor decomposition: utilize the Vandermonde structure of the factor matrix A1 to multiplex the received signal, and equivalently split the factor matrix A1 in the form of the Vandermonde matrix in the 5th-order signal tensor into two sub-matrices, thereby expanding the 5th-order signal tensor to a 6th-order signal tensor; utilize the ESPRIT algorithm to restore the factor matrix A1, that is, equivalently obtain two factor matrix estimates in the 6th-order signal tensor, and 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, characterized in that The step 3 further comprises: recovering the multipath channel parameter, 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 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 restored 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, characterized in that In step 1, the multipath signal tensor is constructed: the pilot sequence, RIS reflection coefficient matrix and base station receiving merging matrix are designed as: Step 1a, modeling 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 multipath channel of the cascaded link between user-RIS-base station is represented by It means, k=1,...,K, g=1,...,G; Define a function vector related to parameters M and ω Channel and They are 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 of 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, characterized in that 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-base station is represented by express; The baseband received signals of each subcarrier and time slot are vertically stacked to obtain vector y, and then vector y is reconstructed into a 5th-order signal tensor with a dimension size of K×G1×G2×N1×N2 The rank of the signal tensor is T = D + PQ, 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, characterized in that In step 2, the process of expanding the 5th-order signal tensor to the 6th-order signal tensor is: 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 recorded as the new mode 1 and mode 6, where K1+K2-1=K, and the mode 2 to mode 5 of the 5th-order signal tensor remain unchanged, so as to obtain 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, characterized in that 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, Σ are two unitary matrices and a diagonal matrix obtained by singular value decomposition; then calculate Among them J ↑ and J ↓ are 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 denoted 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 estimates of the factor matrices B1 and B6; Step 2c, let Represents a 6th-order signal tensor The column r of the modal n factor matrix is ​​estimated, and let and The matrices are and The columns of 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 left singular vectors and right singular vectors, respectively, where unvec(·) and I are matrix operators and unit matrices, respectively; Composition B3 estimate, each Construct the B4 estimate, thus 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, thus completing the estimation of factor matrices B4 and B5.

7. The method according to claim 3, characterized in that 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 diagonal elements being 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, characterized in that The step 3 further comprises: estimating the multipath channel parameters, i.e., the angular frequencies, of the factor matrix of modes 2-5 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 5th-order signal tensor, and r is the rank number of the tensor; function For every 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 space size is fixed in each round of iteration; in the search space described in formula (II), find the angular frequency that makes the objective function of formula (I) maximum as the output of this round of iteration; then narrow the search interval for the next round of iteration, that is, let 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.

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