Smart reflector assisted cascaded planar array channel nested tensor decomposition estimation method

Abstract

The application discloses a kind of intelligent reflecting surface auxiliary cascading surface array channel nested tensor decomposition estimation methods, first constructs cascading channel model, initialization each end guiding matrix and channel matrix in turn;Zero intelligent reflecting surface phase shift is first placed, respectively constructs the tensor model of transceiver end parallel factor decomposition, combined with three linear alternating least square method and least square method, completes two-dimensional angle estimation of transceiver end;Again control phase shift, through two linear alternating least square method, Khatri-Rao decomposition, complete intelligent reflecting surface two-way angle estimation, finally rely on Kronecker product and Khatri-Rao product model solves beam gain.The application relies on nested parallel factor decomposition, realizes four angles automatic pairing, adapts single, multi-beam scene, reduces high-dimensional calculation amount, suppresses off-grid energy leakage, without signal autocorrelation matrix and complex angle pairing, adapts super large scale surface array, improves channel estimation applicability, supports sensing integration system design.

Description

Technical Field

[0001] This invention relates to the fields of 5G (fifth-generation mobile communication) and 6G (sixth-generation mobile communication), and in particular to a method for estimating channel nested tensor decomposition of intelligent reflector-assisted cascaded arrays. Background Technology

[0002] Reconfigurable Intelligent Surfaces (RIS) are a novel type of metamaterial with an artificial planar structure integrating electronic circuitry, allowing for the programmable manipulation of incident electromagnetic waves. RIS typically consists of a large number of passive reflective elements, each capable of altering the phase of the input signal without requiring a dedicated power amplifier. It can replace active relay systems needed in traditional amplification and relaying. Its low cost and low power consumption have garnered significant attention in 5G and 6G systems.

[0003] In the channel estimation problem of RIS-assisted large-scale and very large-scale multiple-input multiple-output (MIMO) transmission systems, scholars have provided numerous solutions. For example, for RIS-assisted multi-user multiple-input single-output communication systems, parallel factorization models are used to estimate the channels between the base station and the RIS, as well as between the RIS and the users. This decomposition model has also been applied to RIS-assisted MIMO communication systems. The decomposed model generally uses the bilinear alternating least squares method and its improved algorithms to alternately estimate the two channel segments. RIS-assisted cascaded sparse channel acquisition methods based on compressed sensing (CS) have also been extensively studied. For instance, by utilizing the sparsity of slowly varying channels and channels in the angular domain, message passing algorithms are used to transform the cascaded channel estimation problem into a sparse matrix decomposition problem. Alternatively, the cascaded channel matrix can be transformed into a sparse matrix recovery problem and solved using CS-based methods. Furthermore, a two-stage iterative reweighting method is used for sequential estimation. In acquiring angular domain information, a two-stage atomic norm minimization method is used to estimate the arrival angle and departure angle. In acquiring cascaded channel state information, to reduce pilot overhead, a three-phase pilot channel estimation framework can be used. This framework can accurately estimate a large number of channel coefficients with a small number of pilots, requiring accurate adjustment of the RIS phase shift during the estimation process. Furthermore, pilot overhead can be reduced by estimating the RIS reflection coefficients and maximizing the reflection coefficient vector. A two-stage orthogonal matched pursuit algorithm can also be used to estimate the cascaded channel with a smaller training load. For the channel estimation problem of RIS-assisted wireless communication systems in time-varying scenarios, the cascaded channel can be modeled as a state-space model using the Kronecker product and Khatri-Rao product, and a Kalman filter can be used to track the channel. However, due to the high dimensionality of the cascaded channel matrix, this undecomposed estimation method can only handle small-scale MIMO cascaded channels. Other researchers have studied RIS-assisted orthogonal frequency division multiplexing systems, using enhanced extreme learning machines (ELM) to ensure accurate channel estimation, and deep learning methods to acquire channel state information.

[0004] However, these conventional methods still face drawbacks in estimating such channels, such as high computational cost due to high dimensionality and unknown sparsity due to off-cell energy leakage. Summary of the Invention

[0005] The purpose of this invention is to propose a nested tensor decomposition estimation method for intelligent reflector-assisted cascaded array channels. This method obtains the angular parameter information contained in the intelligent reflector-assisted cascaded array channel model, overcoming the shortcomings of conventional methods in estimating such channels, such as high computational complexity due to high dimensionality and unknown sparsity due to out-of-dimension energy leakage. Utilizing the unique received signal structure characteristics of array channels, the cascaded channel model is transformed into a parallel factor decomposition tensor model under the array channel, estimating the two-dimensional angle of arrival (Angle of Arrival) at the receiver and the two-dimensional departure (Angle of Departure) at the transmitter. Then, using the parallel factor decomposition tensor model of the cascaded channel, the channel between the receiver and the RIS is estimated. When the information is roughly known, the MIMO cascaded channel is estimated using the bilinear alternating least squares method. Then, the Khratri-Rao decomposition is used to obtain the two-dimensional angle of arrival of the incoming wave at the RIS end and the two-dimensional departure angle of the outgoing wave at the RIS end, which are implicit in the two channels. The channel gain is obtained through the vectorization model of the cascaded channel.

[0006] The objective of this invention can be achieved through the following technical solutions: A method for estimating channel nested tensor decomposition of a smart reflector-assisted cascaded array, comprising the following steps: S1. Establish the channel model between the communication receiver and the intelligent reflector and the channel model between the transmitter and the intelligent reflector; S2. Before estimating the channel using the observations on the pilot symbols at the communication receiver, initialize the estimated values ​​corresponding to the channel matrix and the pilot matrix respectively. S3. After initialization, adjust the phase shift of the intelligent reflector element to zero, and use the transmission model of the intelligent reflector-assisted cascaded array channel to transform the transmission model into the parallel factorization tensor model of the receiver. S4. Calculate the estimated values ​​of the steering matrix in the x and y directions of the incoming wave at the receiver using the trilinear alternating least squares method, and obtain the estimated values ​​of the elevation angle and azimuth angle of the incoming wave at the receiver. S5. Transform the transmission model into a parallel factorization tensor model at the transmitting end. S6. Calculate the estimated values ​​of the guide matrix in the x and y directions of the transmitter using the trilinear alternating least squares method, and obtain the estimated values ​​of the transmitter elevation angle and the transmitter azimuth angle. S7. Adjust the phase shift of the smart reflector element on each pilot symbol, and estimate the channel matrix between the communication receiver and the smart reflector and the channel matrix between the transmitter and the smart reflector. S8. Based on the channel matrix between the receiver and the smart reflector, obtain the estimated value of the smart reflector deflection steering matrix, and then obtain the estimated value of the smart reflector deflection elevation angle and the estimated value of the smart reflector deflection azimuth angle. S9. Based on the channel matrix between the transmitter and the smart reflector, obtain the estimated value of the smart reflector waveguide matrix, and then obtain the estimated value of the smart reflector wave elevation angle and the smart reflector wave azimuth angle. S10. Estimate the beam gain product based on the receiver's arrival elevation angle estimate, receiver's arrival azimuth angle estimate, transmitter's departure elevation angle estimate, transmitter's departure azimuth angle estimate, smart transmitter's departure elevation angle estimate, smart reflector's departure azimuth angle estimate, smart reflector's arrival elevation angle estimate, and smart reflector's arrival azimuth angle estimate.

[0007] Furthermore, the channel model between the communication receiver and the smart reflector is as follows: in, For the communication receiver Root surface array antenna and The combination of individual intelligent reflective surface elements 3D complex channel matrix; For the incoming wave in the x direction at the receiving end 3D guided matrix, The number of incoming waves between the communication receiver and the smart reflector. For the incoming wave in the y direction at the receiving end 3D guiding matrix; This represents a stacked matrix formed by successively diagonalizing the rows of the matrix. For intelligent reflective surfaces, the x-direction wave is removed. 3D guided matrix, For intelligent reflective surfaces to remove waves in the y-direction 3D guiding matrix; for The diagonal gain matrix of the beam between the 3D communication receiver and the smart reflector; Indicates conjugate transpose; The channel model between the transmitter and the smart reflector is as follows: For the communication sending end Root surface array antenna and The combination of individual intelligent reflective surface elements 3D complex channel matrix; For the intelligent reflector, the wave direction in the x direction 3D guided matrix, The number of incoming waves between the communication transmitter and the smart reflector. For the intelligent reflector, the wave direction in the y-direction 3D guiding matrix; For the transmitter, de-wave in the x direction 3D guided matrix, For the transmitter, de-electrode in the y-direction 3D guiding matrix; for Gain diagonal matrix of the beam between the 3D communication transmitter and the smart reflector and These represent the number of antennas in the x and y directions of the receiver's array antenna, respectively. The total number of array antennas in the receiver is... , and Let x and y represent the number of reflective elements in the smart reflective surface in the x and y directions, respectively. The total number of elements in the smart reflective surface is: , and Let x and y represent the number of transmitting antennas at the transmitting end in the x and y directions, respectively. The total number of antennas at the transmitting end is: .

[0008] Furthermore, the specific steps for initializing the estimated values ​​corresponding to the channel matrix and steering matrix are as follows: Initialize one end of the cascaded channel Complex channel matrix The estimated value or Complex channel matrix The estimated value ;initialization 3D guiding matrix The estimated value ,initialization 3D guiding matrix The estimated value ,initialization 3D guiding matrix The estimated value ,initialization 3D guiding matrix The estimated value ;initialization 3D guiding matrix The estimated value ,initialization 3D guiding matrix The estimated value ,initialization 3D guiding matrix The estimated value ,initialization 3D guiding matrix The estimated value .

[0009] Furthermore, the specific steps for calculating the estimated values ​​of the steering matrix in the x and y directions of the incoming wave at the receiver using the trilinear alternating least squares method, and obtaining the estimated values ​​of the elevation angle and azimuth angle of the incoming wave at the receiver, are as follows: 1) Set the threshold value for iteration error Set the old value of the fitting error of the parallel factorization tensor mode 1 matrix at the receiving end. ; 2) Setting parameters early Based on the estimated initial value And calculate the new value of the fitting error from the tensor mode 1 matrix of the receiver parallel factor decomposition. , Denotes the Frobenius norm; 3) Determine if the condition is met. , Let represent the absolute value; if the condition is met, let Then, the three factor matrices are updated alternately, and the new value of the fitting error of the parallel factorization tensor pattern 1 matrix at the receiving end is calculated again. Return to step 3). If the condition is not met, the iteration ends and the estimated value of the steering matrix is ​​output. and Then, the estimated values ​​of the incoming wave elevation angle and the estimated value of the incoming wave azimuth angle are determined.

[0010] Furthermore, the method for calculating the estimated values ​​of the steering matrix in the x and y directions of the transmitting end using the trilinear alternating least squares method is the same as the method for calculating the estimated values ​​of the steering matrix in the x and y directions of the receiving end using the trilinear alternating least squares method.

[0011] Furthermore, S7 specifically refers to: By adjusting the phase shift of the intelligent reflector element on each pilot symbol, the transmission model and complex channel matrix are obtained. , and Constructing parallel factorization tensors , The number of pilot symbols used. For intelligent reflective surfaces Phase shift vector on each pilot symbol The phase shift matrix formed by the tensor Mapping relationship of the pattern 1 matrix , This is the noise matrix under mode 1 matrix, with the symbol... Represents the Khatri-Rao product, symbol Then, based on the mapping relationship of the pattern 2 matrix... , For the noise matrix under mode 2, the estimated value is updated using the bilinear alternating least squares method. and The process continues until the iteration error threshold is met, at which point the channel matrix between the communication receiver and the smart reflector is obtained. Channel matrix between the transmitter and the smart reflector .

[0012] Furthermore, the specific steps of S8 are as follows: Channel matrix between the communication receiver and the smart reflector and receiver steering matrix estimate and The Khratri-Rao product of the estimated waveguide matrix of the intelligent reflector is obtained by using the least squares estimation method. Then, Khratri-Rao decomposition is performed on the Khratri-Rao product to obtain the estimated value of the wave steering matrix of the intelligent reflector. and Then, the estimated values ​​of the elevation angle and azimuth angle of the intelligent reflector are obtained.

[0013] Furthermore, the method for S9 is the same as that for S8.

[0014] Compared with the prior art, the present invention has the following beneficial effects: 1. The tensor form in the channel model of a smart reflector-assisted cascaded array antenna was explored. A characteristic of the array antenna is that the path differences of its subarray elements in the xy plane (or xz, yz plane) are respectively the steering matrix. Multiply (or Multiply , Multiply This is suitable for using parallel factorization techniques, thereby transforming the transmission model of large-scale arrays into tensor form.

[0015] 2. Two-dimensional angle estimation of the incoming wave direction at the receiver is insensitive to the form of the pilot matrix under the parallel factor decomposition technique, but the uniqueness condition of the parallel factor decomposition must be met. In two-dimensional angle estimation, the number of pilot slots should not be less than the number of beams, and the number of pilot slots can be selected as the number of slots contained in one pilot symbol.

[0016] 3. The tensor model of the transmitted signal for two-dimensional angle estimation of the wave direction at the transmitting end is the tensor model after transposing the receiving model.

[0017] 4. The two-dimensional angle estimation of the outgoing and incoming directions of the intelligent reflector depends on the estimation accuracy of the two cascaded channels. When using the bilinear alternating least squares method for estimation, it is easy to get stuck in the swamp effect and fall into the local optimum. Therefore, the characteristics of intelligent reflector deployment should be utilized to obtain a rough estimate of one channel and use it as the initial value for the bilinear alternating least squares estimation, thereby obtaining a more accurate estimate of the two channel segments.

[0018] 5. Scale ambiguity is inherent in parallel factor decomposition. Beam gain is contained in the factor matrix of parallel factor decomposition. The angle estimates of the outgoing and incoming directions of the smart reflector can be obtained by Khatri-Rao decomposition. Although the magnitude of the gain values ​​of multiple beams in a channel and the distribution of beam gain on two channels will affect the signal-to-noise ratio at the receiver, they will have little impact on the angle estimation. 6. Using the estimated value of the beam steering matrix with the two-dimensional angle with the angle estimation error will affect the estimation of the beam gain matrix, resulting in a large normalized mean square error of the cascaded channel constructed by the estimated steering matrix and beam gain. This can be attributed to energy leakage caused by the off-grid effect, etc. However, this acquisition technique contains all the detailed features of the angle parameters. Attached Figure Description

[0019] Figure 1 This is a flowchart of the present invention; Figure 2 This is a schematic diagram illustrating an application scenario of the present invention; Figure 3 This is a two-dimensional angle diagram of the present invention; Figure 4 Scatter plots of four pairs of two-dimensional angle estimates at signal-to-noise ratios of -5, 0, 5, 10, 15, 20, 25, and 30 dB when both channels have a beam. Figure 5 The root mean square error (RMSE8) curves for eight estimated angles when both channels have one beam. Figure 6 When both channels have one beam, four pairs of root mean square error (RMSE4) curves for estimated angles are shown. The root mean square error curves for incoming and outgoing waves at the receiver and the transmitter, estimated using the Unitary-ESPRIT method, are also shown. Figure 7 The total root mean square error (RMSE) curves for all angles when both channels have one beam, and the normalized mean square error (NMSE1 and NMSE2) curves for the cascaded channels obtained by using the bilinear alternating least squares method and by using the estimated steering matrix and beam gain. Figure 8 For both channels having one beam, the four pairs of angles are successfully estimated (RMSE4 ≤ 0.5). Cumulative probability curve; Figure 9 The diagram shows that both channels have one beam. (All are square arrays), and the root mean square error (RMSE) curves are obtained when the total number of arrays is [36, 64, 100, 144, 196, 256].

[0020] Figure 10 The diagram shows that both channels have one beam. (All are square arrays), with a total number of arrays of [36, 64, 100, 144, 196, 256], the obtained success estimate (root mean square error RMSE ≤ 0.5) Cumulative probability curve.

[0021] Figure 11 Scatter plots of four pairs of two-dimensional angle estimates at signal-to-noise ratios of -5, 0, 5, 10, 15, 20, 25 and 30 dB when both channels have two beams. Figure 12 The root mean square error (RMSE8) curves for eight estimated angles when both channels have two beams. Figure 13 When both channels have two beams, four pairs of root mean square error (RMSE4) curves for the estimated angles are shown. The root mean square error curves for the incoming wave at the receiver and the outgoing wave at the transmitter, estimated using the Unitary-ESPRIT method, are also shown. Figure 14 The total root mean square error (RMSE) curves for all angles when both channels have two beams, and the normalized mean square error (NMSE1 and NMSE2) curves for the cascaded channels obtained by using the bilinear alternating least squares method and by estimating the steering matrix and beam gain. Figure 15 For two channels each with two beams, the four pairs of angles are successfully estimated (RMSE4 ≤ 0.5). Cumulative probability curve; Figure 16 The diagram shows that both channels have two beams. (All are square arrays), and the RMSE curves obtained when the total number of arrays is [36, 64, 100, 144, 196, 256].

[0022] Figure 17 The diagram shows that both channels have two beams. (All are square arrays), with a total number of arrays of [36, 64, 100, 144, 196, 256], the obtained success estimate (root mean square error RMSE ≤ 0.5) Cumulative probability curve.

[0023] Figure 18 Scatter plots of four pairs of two-dimensional angle estimates when both channels have three beams and the signal-to-noise ratios are -5, 0, 5, 10, 15, 20, 25 and 30 dB. Figure 19 The root mean square error (RMSE8) curves for eight estimated angles when both channels have three beams. Figure 20 The four pairs of root mean square error (RMSE4) curves for the estimated angles are shown when both channels have three beams. The root mean square error curves for the incoming wave at the receiver and the outgoing wave at the transmitter, estimated using the Unitary-ESPRIT method, are also shown. Figure 21 The total root mean square error (RMSE) curves for all angles when both channels have three beams, and the normalized mean square error (NMSE1 and NMSE2) curves for the cascaded channels obtained by using the bilinear alternating least squares method and by using the estimated steering matrix and beam gain. Figure 22 For two channels with three beams each, successful estimation of four pairs of angles (RMSE ≤ 0.5) is achieved. Cumulative probability curve; Figure 23 The diagram shows that both channels have three beams. (All are square arrays), and the RMSE curves obtained when the total number of arrays is [36, 64, 100, 144, 196, 256].

[0024] Figure 24 The diagram shows that both channels have three beams. (All are square arrays), with a total number of arrays of [36, 64, 100, 144, 196, 256], the obtained success estimate (root mean square error RMSE ≤ 0.5) Cumulative probability curve.

[0025] Figure 25 In the two channels Includes a single beam ( ,and Includes two beams ( Scatter plots of four pairs of two-dimensional angle estimates at signal-to-noise ratios of -5, 0, 5, 10, 15, 20, 25, and 30 dB. Detailed Implementation

[0026] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0027] Definitions: Intelligent Reflective Surface – RIS; Multiple inputs, multiple outputs—MIMO.

[0028] This invention proposes a method for channel nesting tensor decomposition estimation using intelligent reflector-assisted cascaded arrays. The flowchart of the method is as follows: Figure 1 As shown. Application scenarios of this invention include, for example... Figure 2 In the scenario shown, the two-dimensional arrival angle (including elevation and azimuth) and the two-dimensional departure angle (including elevation and azimuth) referred to in this invention are as follows: Figure 3 As shown.

[0029] The intelligent transmitter-assisted cascaded array channel model of this invention refers to an array channel model in the millimeter-wave or terahertz bands, where the intelligent transmitter is generally a planar array. The angular domain parameters of the two channel segments are related to the number of paths, the departure angle and arrival angle of the path beams, and the corresponding steering vectors, and can be expressed as follows: (1) (2) In equations (1) and (2), and Indicates the number of beams in the two channels. and Indicates beam gain. and as well as and These represent the signal incident (superscript) ) and launch (superscript) ) azimuth and elevation angles.

[0030] When the angle parameter ( , ), ( , and the corresponding beam gain and Even the number of beams and Given the information, the channel of the intelligent transmitter surface-assisted cascaded array can be determined.

[0031] This invention, in a cascaded transmission system composed of massive MIMO and massive RIS, obtains the cascaded channel by acquiring the product values ​​of four pairs of angles and beam gain in the angle domain. The main idea of ​​this invention is to utilize the parallel factorization technique of massive MIMO arrays. In the first stage, the steering matrices of the receiver and transmitter are estimated using trilinear alternating least squares, and the elevation and azimuth angles of the incoming wave at the receiver and the outgoing wave at the transmitter are estimated using least squares. In the second stage, a nested tensor model of parallel factorization consisting of two channels and a smart reflector is used. The steering matrices of the incoming and outgoing waves of the smart reflector are obtained using bilinear least squares, and the elevation and azimuth angles are estimated using least squares. The beam gain is obtained through a vector model of the Kronecker product and Khatri-Rao product of the two channels.

[0032] The method of the present invention includes the following steps: Step 1: Establish a channel model for the intelligent reflector-assisted cascaded array. The channel between the communication receiver and the intelligent reflector is... (3) in, For the communication receiver Root surface array antenna and The combination of individual intelligent reflective surface elements 3D complex channel matrix; For the incoming wave in the x direction at the receiving end 3D guided matrix, The number of incoming waves between the communication receiver and the smart reflector. For the incoming wave in the y direction at the receiving end 3D guiding matrix; For intelligent reflective surfaces, the x-direction wave is removed. 3D guided matrix, For intelligent reflective surfaces to remove waves in the y-direction 3D guiding matrix; for The diagonal gain matrix of the beam between the 3D communication receiver and the smart reflector; Indicates conjugate transpose; The steering matrix and gain matrix are further expressed as Antenna spacing, For wavelength, ; and These are the azimuth and elevation angles of the incoming wave at the receiving end (collectively referred to as DOA1). and These are the azimuth and elevation angles of the intelligent reflector for wave removal (collectively referred to as DOD1). The channel between the transmitter and the smart reflector is (4) in, For the communication sending end Root surface array antenna and The combination of individual intelligent reflective surface elements 3D complex channel matrix; For the intelligent reflector, the wave direction in the x direction 3D guided matrix, The number of incoming waves between the communication transmitter and the smart reflector. For the intelligent reflector, the wave direction in the y-direction 3D guiding matrix; For the transmitter, de-wave in the x direction 3D guided matrix, For the transmitter, de-electrode in the y-direction 3D guiding matrix; for Gain diagonal matrix of the beam between the 3D communication transmitter and the smart reflector; The steering matrix and gain matrix are further expressed as Antenna spacing, For wavelength, , and These are the azimuth and elevation angles of the incoming wave from the intelligent transmitting surface (collectively referred to as DOA2). and The azimuth and elevation angles of the transmitting end (collectively referred to as DOD2) are respectively. The orientation matrix given in this step lies in the xy plane. If it lies in the xz or yz plane, then it is determined according to the spatial order. Individual element and reference element Path difference between Change to the corresponding array steering matrix, The pitch angle, It is the azimuth angle; Step 2: Before estimating the channel using observations on pilot symbols at the communication receiver, initialize one end of the cascaded channel. Complex channel matrix The estimated value Complex channel matrix The estimated value ;initialization 3D guiding matrix The estimated value ,initialization 3D guiding matrix The estimated value ,initialization 3D guiding matrix The estimated value ,initialization 3D guiding matrix The estimated value ;initialization 3D guiding matrix The estimated value ,initialization 3D guiding matrix The estimated value ,initialization 3D guiding matrix The estimated value ,initialization 3D guiding matrix The estimated value ; Step 3: In the first stage of channel estimation, adjust the phase shift of the smart reflector element to zero, and use the smart reflector-assisted cascaded array channel transmission model. (5) in, For the received signal matrix, For pilot signals, The number of pilot symbols used. To receive noise; (Note: The last part is a Chinese character and doesn't translate directly.) (6) Transmission Model (7) Transformed from , and The parallel factorization tensor model is constructed. The pilot symbol in step S3 Alternatively, it can be designed as an orthogonal pilot matrix. The orthogonal pilot matrix can be either a Fourier transform matrix or an identity matrix. The Fourier transform matrix is... ; Communication sending end root transmitting antenna The former The line is used as a pilot symbol; Step 4: Obtain the guiding matrix using the trilinear alternating least squares method. and The estimated value and The method is as follows: ① Set a threshold value for the iteration error. Set the old value of the fitting error of the parallel factorization tensor pattern 1 matrix to a decimal. ; ②Settings Estimate initial value The estimated initial value set in step S2 and ,calculate Calculate the new value of the fitting error of the parallel factorization tensor pattern 1 matrix. ③ Determine whether If the conditions are met, let Then, the three factor matrices are updated alternately, i.e. Depend on The calculation formula (8) Indicates will Update the diagonal matrix of the j-th row vector diagonalization The estimated value is (9) This indicates the Moore-Penrose pseudo-inverse; Depend on The calculation formula (10) renew The estimated value is (11) Depend on The calculation formula (12) renew The estimated value is (13) Then calculate from the current estimate. Calculate the new value of the fitting error of the parallel factorization tensor pattern 1 matrix. Return to step ③, iterate and update the three factor matrices until the condition is no longer met, then the iteration ends and outputs the result. ; Calculate separately and The phase angle of each column of complex elements, and supplemented by 2. Construct a matrix to ensure the phase angles of each column are continuous. calculate , The estimated pitch angle is azimuth angle is ; Step 5: Calculation ,remember (14) The conjugate transpose of the transmission model (15) Transform it into a parallel factorization tensor model; Step 6: Obtain the guiding matrix using the trilinear alternating least squares method. and The estimated value and The procedure is as follows: ① Set a threshold value for the iteration error. Set the old value of the fitting error of the parallel factorization tensor pattern 1 matrix to a decimal. , ②Settings Estimate initial value The estimated initial value set in step S2 and ,calculate Calculate the new value of the fitting error of the parallel factorization tensor pattern 1 matrix. , ③Judgment If the conditions are met, let Then, the three factor matrices are updated alternately, i.e. Depend on The calculation formula (16) renew The estimated value is (17) Depend on The calculation formula (18) renew The estimated value is (19) Depend on The calculation formula (20) renew The estimated value is (twenty one) Then calculate Calculate the new value of the fitting error of the parallel factorization tensor pattern 1 matrix. Return to step ③, iterate and update the three matrices until the condition is no longer met, then the iteration ends and outputs the result. ; Calculate separately and The phase angle of each column of complex elements, and supplemented by 2. By making the phase angles of each column continuous, we obtain... , The estimated pitch angle is azimuth angle is ; Step 7: In the second stage of channel estimation, adjust the phase shift of the smart reflector element on each pilot symbol. At this point, the transmission model is... (twenty two) in, For the received signal matrix, The number of pilot symbols used. For intelligent reflective surfaces Phase shift vector on each pilot symbol The phase shift matrix formed, To receive noise; by , and Constructing parallel factorization tensors , by tensor Mapping relationship of the pattern 1 matrix , This is the noise matrix under mode 1 matrix, with the symbol... Represents the Khatri-Rao product, symbol Then, based on the mapping relationship of the pattern 2 matrix... , For the noise matrix under mode 2, the estimated value is updated using the bilinear alternating least squares method. and Continue until the iteration error threshold is met; The aforementioned intelligent reflective surface Phase shift vector of each element Each element is a complex value, containing amplitude and argument. When using a passive intelligent reflector without amplification, the amplitude of each element is typically 1, and the argument is... The phase shift matrix is ​​composed of discrete subsets with a small number of quantization bits; The steps of the bilinear alternating least squares method are as follows: ① Set the threshold value for the iteration error. Set the old value of the fitting error of the parallel factorization tensor pattern 1 matrix to a decimal. ; ② Calculate the new value of the fitting error of the parallel factorization tensor pattern 1 matrix. ③ Determine whether If the conditions are met, let From the current ,renew From the current and ,renew Return to step ②; if condition ③ is not met, the iteration ends and outputs the result. and , and then get .

[0033] Step 8: From the estimated value and Obtain the estimated value of the guidance matrix Then through the estimated value estimate Then to Khratri-Rao decomposition yielded and According to (twenty three) When the estimated value is obtained Afterwards, from Starting from the first column up to the... Columns, each Transform into matrices sequentially dimensional matrix ,right Perform singular value decomposition (twenty four) Its best rank Approximating the largest eigenvalue The corresponding left eigenvector and right eigenvectors ,get , (25) Based on the estimated value and Calculate using the least squares method respectively and The phase angle of each column of complex elements, and supplemented by 2. By making the phase angles of each column continuous, we obtain... , The estimated pitch angle is azimuth angle is ; Step 9: From the estimated value and Construct the guiding matrix Then from the estimated value estimate Then to Khratri-Rao decomposition yielded and According to (26) When the estimated value is obtained Afterwards, from Starting from the first column up to the... Each of them Transform into matrices sequentially dimensional matrix ,right Perform singular value decomposition, i.e. (27) Its best rank Approximating the largest eigenvalue The corresponding left eigenvector and right eigenvectors ,get , (28) Based on the estimated value and Calculate using the least squares method respectively and The phase angle of each column of complex elements, and supplemented by 2. By making the phase angles of each column continuous, we obtain... , The estimated pitch angle is azimuth angle is ; Step 10: Based on the guidance matrix model, construct the estimated values ​​of eight guidance matrices using the estimated values ​​of four pairs of two-dimensional angles. , , , , , , and Then substitute it into the vectorized model of the cascaded channel. , To denote the complex conjugate operation, denoted as... For beam gain ), its estimated value is ) (29) Then transform the beam gain matrix into A dimensional matrix whose diagonal elements are estimates of the product of the gains of the two beam segments.

[0034] Cascaded Channels The normalized mean square error (NMSE) is defined as follows: (30) in, It is the first Estimates from the Monte Carlo experiment.

[0035] Let NMSE1 be the NMSE of the cascaded channel obtained by the bilinear least squares method; let NMSE2 be the NMSE of the cascaded channel obtained by the estimated steering matrix and beam gain.

[0036] Define the total root mean square error (RMSE) of angle estimation as: (31) Among them, The maximum number of beams in the two channel segments (i.e. ), This represents the square root operation. It is the first The estimated azimuth vector value of the Monte Carlo experiment. It is the first The pitch angle vector estimates from the Monte Carlo experiment, with superscripts A1, B1, A2, and B2 representing the four pairs of angles respectively.

[0037] When the The RMSE of the Monte Carlo experiment was less than 0.5 degrees, meaning that... (32) If so, the angle estimation is successful.

[0038] The root mean square error of the eight angle vectors is defined as (33) in, The number of beams in this channel segment (i.e. or ), For the first The estimated value of a certain angle vector in the Monte Carlo experiment. This is the true value of the angle vector.

[0039] The root mean square error of four pairs of angle vectors is defined as follows: (34) in The number of beams in this channel segment (i.e. or ).

[0040] When the The RMSE4 in the Monte Carlo experiment was less than 0.5 degrees, meaning that... (35) At that point, the angle estimation is considered successful.

[0041] The following uses unit diagonal pilot symbols, with one pilot symbol used in the first stage and [a different symbol used in the second stage]. There are pilot symbols and RIS has The method of the present invention will be described when channel estimation is performed using an independent phase shift vector.

[0042] When implementing the intelligent reflector-assisted cascaded array channel nesting tensor decomposition estimation method of the present invention at the communication receiver, when it is known , The specific implementation steps are as follows.

[0043] Step 1: Establish a channel model for the cascaded intelligent reflector-assisted array. At this point, , , , , , , , , , ; Step 2: Initialization For a rough estimate (the true value superimposed with Gaussian white noise determined by the signal-to-noise ratio), initialize... , , , , and They are respectively A complex Gaussian random vector with mean 0 and variance 1; Step 3: Transform the transmission model into a parallel factorization tensor model of the receiving array. This means that the subarray in the x-direction is offset along the y-axis by the corresponding path difference; Step 4: Estimate the waveguide matrix at the receiver using the trilinear alternating least squares method, and set a threshold value for the iteration error. Iterative updates , and The estimated values; respectively by and Obtain the phase angle of each column of complex elements and supplement by 2. To ensure phase continuity, estimate the pitch angle using the least squares method. and azimuth ; Step 5: Calculation To eliminate the filtering effect of pilot symbols on the transmitter, the transmission model is transposed and transformed into a parallel factorization tensor model of the transmitter's area array. ; Step 6: Estimate the waveguide matrix at the transmitter using the trilinear alternating least squares method, and set a threshold value for the iteration error. Iterative updates , and The estimated values; respectively by Obtain the phase angle of each column of complex elements and supplement by 2. To ensure phase continuity, estimate the pitch angle using the least squares method. and azimuth ; Step 7: Adjust the phase shift vector of the smart reflector on each pilot symbol. Constructing a phase shift matrix (Designed as a Fourier transform matrix), at this point, the transmission model is... , and Parallel factorization tensor model Update the estimated value using bilinear alternating least squares method. and Until the iteration error threshold is met ; Step 8: Use pseudo-inverse operations and estimated values The estimated value of the steering matrix for wave removal from the intelligent transmitter surface is obtained. Then use the rank-1 approximation pair Khratri-Rao decomposition yielded and Then by and Estimating the pitch angle of the smart reflector using the least squares method and azimuth ; Step 9: Use pseudo-inverse operations and estimated values The estimated value of the steering matrix of the incoming wave from the intelligent transmitting surface is obtained. Then use the rank-1 approximation pair Khratri-Rao decomposition yielded and Then by and Estimating the wave elevation angle of a smart reflector using the least squares method and azimuth ; Step 10: Construct a steering matrix from the estimated four pairs of angles, and estimate the beam gain product using the vectorized form of the Kronecker product and Khatri-Rao product of the cascaded channels.

[0044] Set the angle parameters as follows: , , Set the beam gains as follows: In this scenario, as shown in the attached document Figure 4 Appendix Figure 5 Appendix Figure 6 Appendix Figure 7 Appendix Figure 8 The figures show scatter plots of the angle estimates obtained by the method of this invention at signal-to-noise ratios (SNR) of [-5, 0, 5, 10, 15, 20, 25, 30] dB, root mean square errors (RMSE8) for eight angles, root mean square errors (RMSE4), NMSE1, NMSE2, and RMSE for four pairs of angles, and curves showing the success probability of estimation as a function of SNR. The figures also show the RMSE4 curves for the received signal and the transmitted signal obtained using the Unitary-ESPRIT method, and the success estimation (RMSE4 ≤ 0.5). The cumulative probability curve shows that the method of this invention has a smaller root mean square error and a higher probability of successful estimation at low signal-to-noise ratios.

[0045] Appendix Figure 9 and attached Figure 10 The figures shown are respectively (All are square arrays), with the total number of arrays being [36, 64, 100, 144, 196, 256], the obtained RMSE curves and estimation success (RMSE ≤ 0.5) are as follows. The cumulative probability curve shows that the nested tensor technique used in this invention can estimate the channel parameters of large-scale and ultra-large-scale arrays.

[0046] When known , The specific implementation steps are as follows: Step 1: Establish a channel model for the cascaded smart reflector-assisted array antennas. At this point, , , , , , , , , , ; Step 2: Initialization For a rough estimate (the true value superimposed with Gaussian white noise determined by the signal-to-noise ratio), initialize... , , , for Deviation from true value The steering matrix of the area array formed by the angle estimates of Gaussian white noise; Steps three through ten are the same as in the above embodiment.

[0047] Set the angle parameters as follows: In this scenario, as shown in the attached document Figure 11 Appendix Figure 12 Appendix Figure 13 Appendix Figure 14 Appendix Figure 15 The figures show scatter plots of the angle estimates obtained by the method of this invention at SNR values ​​of [-5, 0, 5, 10, 15, 20, 25, 30] dB, root mean square error (RMSE8) for eight angles, root mean square error (RMSE4), NMSE1, NMSE2, and RMSE for four pairs of angles, and curves showing the success probability of estimation as a function of SNR. The figures also show the RMSE4 curves for the received signal and the transmitted signal obtained using the Unitary-ESPRIT method, and the success estimation (RMSE4 ≤ 0.5). The cumulative probability curve shows that the method of this invention has a smaller root mean square error and a higher probability of successful estimation at low signal-to-noise ratios.

[0048] Appendix Figure 16 and attached Figure 17 The diagram shows that both channels have two beams. (All are square arrays), with the total number of arrays being [36, 64, 100, 144, 196, 256], the obtained RMSE curves and estimation success (RMSE4 ≤ 0.5) are as follows. The cumulative probability curve shows that the nested tensor technique used in this invention can estimate the channel parameters of large-scale and ultra-large-scale arrays.

[0049] when The specific implementation steps are as follows.

[0050] Step 1: Establish a channel model for the cascaded smart reflector-assisted array antennas. At this point, , , , , , ,, , , , ; Step 2: Initialization For a rough estimate (the real channel plus a complex Gaussian random vector with a mean of 0 and a variance of 1), initialize... , , , for Deviation from true value The steering matrix of the area array formed by the angle estimates of Gaussian white noise; Steps three through ten are the same as in the above embodiment.

[0051] Set the angle vectors as follows: , These are three-dimensional unit diagonal matrices.

[0052] In this scenario, as shown in the attached document Figure 18 Appendix Figure 19 Appendix Figure 20 Appendix Figure 21 Appendix Figure 22The figures show scatter plots of the angle estimates obtained by the method of this invention at SNR values ​​of [-5, 0, 5, 10, 15, 20, 25, 30] dB, root mean square error (RMSE8) for eight angles, root mean square error (RMSE4), NMSE1, NMSE2, and RMSE for four pairs of angles, and curves showing the success probability of estimation as a function of SNR. The figures also show the RMSE4 curves for the received signal and the transmitted signal obtained using the Unitary-ESPRIT method, and the success estimation (RMSE4 ≤ 0.5). The cumulative probability curve shows that the method of this invention has a smaller root mean square error and a higher probability of successful estimation at low signal-to-noise ratios.

[0053] Appendix Figure 23 and attached Figure 24 The two channels shown each have three beams. (All are square arrays), with the total number of arrays being [36, 64, 100, 144, 196, 256], the RMSE curves and estimation success probability curves are obtained. It can be seen that the nested tensor technique used in this invention can estimate the channel parameters of large-scale and ultra-large-scale area arrays.

[0054] when At that time, because the ranks of the two channels are unequal, the number of parallel factors degenerates to In such scenarios, only the two-dimensional angle value of the side with the smaller rank can be estimated. For example... The specific implementation steps are as follows: Step 1: Establish a channel model for the cascaded smart reflector-assisted array antennas. At this point, , , , , , , , , , ; Step 2: Initialization For a rough estimate (the true value superimposed with Gaussian white noise determined by the signal-to-noise ratio), initialize... , , , To the deviation of the true value The steering matrix of the area array formed by the angle estimates of Gaussian white noise; Steps three through ten are the same as in the above embodiment.

[0055] Set the angle parameter to .

[0056] In this scenario, as shown in the attached document Figure 25 The diagram shows a scatter plot of the angle estimates obtained by the method of this invention when the SNR is [-5, 0, 5, 10, 15, 20, 25, 30] dB. It can be seen that only the two-dimensional angle between the receiver and the smart reflector is estimated relatively accurately, while the two-dimensional angle between the transmitter and the smart transmitter shows a large error and cannot be estimated. This is because the condition for the parallel factor decomposition of the two channel segments is not met; in this case, the number of parallel factors is only one. The above description is merely a specific embodiment of this invention, but the scope of protection of this invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in this invention, and these modifications or substitutions should all be covered within the scope of protection of this invention. Therefore, the scope of protection of this invention should be determined by the scope of the claims.

[0057] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

Claims

1. A method for estimating channel nested tensor decomposition of a smart reflector-assisted cascaded array, characterized in that, The method includes the following steps: S1. Establish the channel model between the communication receiver and the intelligent reflector and the channel model between the transmitter and the intelligent reflector; S2. Before estimating the channel using the observations on the pilot symbols at the communication receiver, initialize the estimated values ​​corresponding to the channel matrix and the pilot matrix respectively. S3. After initialization, adjust the phase shift of the intelligent reflector element to zero, and use the transmission model of the intelligent reflector-assisted cascaded array channel to transform the transmission model into the parallel factorization tensor model of the receiver. S4. Calculate the estimated values ​​of the steering matrix in the x and y directions of the incoming wave at the receiver using the trilinear alternating least squares method, and obtain the estimated values ​​of the elevation angle and azimuth angle of the incoming wave at the receiver. S5. Transform the transmission model into a parallel factorization tensor model at the transmitting end. S6. Calculate the estimated values ​​of the guide matrix in the x and y directions of the transmitter using the trilinear alternating least squares method, and obtain the estimated values ​​of the transmitter elevation angle and the transmitter azimuth angle. S7. Adjust the phase shift of the smart reflector element on each pilot symbol, and estimate the channel matrix between the communication receiver and the smart reflector and the channel matrix between the transmitter and the smart reflector. S8. Based on the channel matrix between the receiver and the smart reflector, obtain the estimated value of the smart reflector deflection steering matrix, and then obtain the estimated value of the smart reflector deflection elevation angle and the estimated value of the smart reflector deflection azimuth angle. S9. Based on the channel matrix between the transmitter and the smart reflector, obtain the estimated value of the smart reflector waveguide matrix, and then obtain the estimated value of the smart reflector wave elevation angle and the smart reflector wave azimuth angle. S10. Estimate the beam gain product based on the receiver's arrival elevation angle estimate, receiver's arrival azimuth angle estimate, transmitter's departure elevation angle estimate, transmitter's departure azimuth angle estimate, smart transmitter's departure elevation angle estimate, smart reflector's departure azimuth angle estimate, smart reflector's arrival elevation angle estimate, and smart reflector's arrival azimuth angle estimate.

2. The intelligent reflector-assisted cascaded array channel nested tensor decomposition estimation method according to claim 1, characterized in that, The channel model between the communication receiver and the smart reflector is as follows: in, For the communication receiver Root surface array antenna and The combination of individual intelligent reflective surface elements 3D complex channel matrix; For the incoming wave in the x direction at the receiving end 3D guided matrix, The number of incoming waves between the communication receiver and the smart reflector. For the incoming wave in the y direction at the receiving end 3D guiding matrix; This represents a stacked matrix formed by successively diagonalizing the rows of the matrix. For intelligent reflective surfaces, the x-direction wave is removed. 3D guided matrix, For intelligent reflective surfaces to remove waves in the y-direction 3D guiding matrix; for The diagonal gain matrix of the beam between the 3D communication receiver and the smart reflector; Indicates conjugate transpose; The channel model between the transmitter and the smart reflector is as follows: For the communication sending end Root surface array antenna and The combination of individual intelligent reflective surface elements 3D complex channel matrix; For the intelligent reflector, the wave direction in the x direction 3D guided matrix, The number of incoming waves between the communication transmitter and the smart reflector. For the intelligent reflector, the wave direction in the y-direction 3D guiding matrix; For the transmitter, de-wave in the x direction 3D guided matrix, For the transmitter, de-electrode in the y-direction 3D guiding matrix; for Gain diagonal matrix of the beam between the 3D communication transmitter and the smart reflector and These represent the number of antennas in the x and y directions of the receiver's array antenna, respectively. The total number of array antennas in the receiver is... , and Let x and y represent the number of reflective elements in the smart reflective surface in the x and y directions, respectively. The total number of elements in the smart reflective surface is: , and Let x and y represent the number of transmitting antennas at the transmitting end in the x and y directions, respectively. The total number of antennas at the transmitting end is: .

3. The intelligent reflector-assisted cascaded array channel nested tensor decomposition estimation method according to claim 2, characterized in that, The specific steps for initializing the estimated values ​​of the channel matrix and steering matrix are as follows: Initialize one end of the cascaded channel Complex channel matrix The estimated value or Complex channel matrix The estimated value ;initialization 3D guiding matrix The estimated value ,initialization 3D guiding matrix The estimated value ,initialization 3D guiding matrix The estimated value ,initialization 3D guiding matrix The estimated value ;initialization 3D guiding matrix The estimated value ,initialization 3D guiding matrix The estimated value ,initialization 3D guiding matrix The estimated value ,initialization 3D guiding matrix The estimated value .

4. The intelligent reflector-assisted cascaded array channel nested tensor decomposition estimation method according to claim 3, characterized in that, The specific steps for calculating the estimated values ​​of the steering matrix in the x and y directions of the incoming wave at the receiver using the trilinear alternating least squares method, and obtaining the estimated values ​​of the elevation angle and azimuth angle of the incoming wave at the receiver, are as follows: 1) Set the threshold value for iteration error Set the old value of the fitting error of the parallel factorization tensor mode 1 matrix at the receiving end. ; 2) Setting parameters early Based on the estimated initial value And calculate the new value of the fitting error from the tensor mode 1 matrix of the receiver parallel factorization. , Denotes the Frobenius norm; 3) Determine if the condition is met. , Let represent the absolute value; if the condition is met, let Then, the three factor matrices are updated alternately, and the new value of the fitting error of the parallel factorization tensor pattern 1 matrix at the receiving end is calculated again. Return to step 3). If the condition is not met, the iteration ends and the estimated value of the steering matrix is ​​output. and Then, the estimated values ​​of the incoming wave elevation angle and the incoming wave azimuth angle at the receiving end are determined.

5. The intelligent reflector-assisted cascaded array channel nested tensor decomposition estimation method according to claim 4, characterized in that, The method for calculating the estimated values ​​of the steering matrix in the x and y directions of the transmitter using the trilinear alternating least squares method is the same as the method for calculating the estimated values ​​of the steering matrix in the x and y directions of the receiver using the trilinear alternating least squares method.

6. The intelligent reflector-assisted cascaded array channel nested tensor decomposition estimation method according to claim 5, characterized in that, S7 specifically refers to: Adjusting the phase shift of the intelligent reflector element on each pilot symbol yields the transmission model and complex channel matrix. , and Constructing parallel factorization tensors , The number of pilot symbols used. For intelligent reflective surfaces in Phase shift vector on each pilot symbol The phase shift matrix formed by the tensor Mapping relationship of the pattern 1 matrix , This is the noise matrix under mode 1 matrix, with the symbol... Represents the Khatri-Rao product, symbol Then, based on the mapping relationship of the pattern 2 matrix... , For the noise matrix under mode 2, the estimated value is updated using the bilinear alternating least squares method. and The process continues until the iteration error threshold is met, at which point the channel matrix between the communication receiver and the smart reflector is obtained. Channel matrix between the transmitter and the smart reflector .

7. The intelligent reflector-assisted cascaded array channel nested tensor decomposition estimation method according to claim 6, characterized in that, The specific steps for S8 are as follows: Channel matrix between the communication receiver and the smart reflector and receiver steering matrix estimate and The Khratri-Rao product of the estimated waveguide matrix of the intelligent reflector is obtained by using the least squares estimation method. Then, Khratri-Rao decomposition is performed on the Khratri-Rao product to obtain the estimated value of the wave steering matrix of the intelligent reflector. and Then, the estimated values ​​of the elevation angle and azimuth angle of the intelligent reflector are obtained.

8. The intelligent reflector-assisted cascaded array channel nested tensor decomposition estimation method according to claim 7, characterized in that, The method for S9 is the same as that for S8.

9. A smart reflector-assisted cascaded array channel nested tensor decomposition estimation device, comprising a memory, a processor, and a program stored in the memory, characterized in that, When the processor executes the program, it implements the method as described in any one of claims 1-8.

10. A storage medium having a program stored thereon, characterized in that, When the program is executed, it implements the method as described in any one of claims 1-8.

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