Non-line-of-sight near-field source parameter estimation and correction method based on decoupling atom norm

Abstract

The invention belongs to the technical field of near-field RIS target positioning, and particularly relates to a non-line-of-sight near-field source parameter estimation and correction method based on decoupling atom norms. According to the method, through cross-correlation operation and pseudo-snapshot processing, angle information and distance information are decoupled while the array aperture is expanded. In addition, the single-snapshot decoupling atom norm algorithm based on the virtual aperture is provided while the advantage of super-resolution performance of the atom norm under the single snapshot is reserved. And through a decoupling atom norm method, the pitch angle and the azimuth angle on the RIS are further decoupled, and the algorithm complexity is reduced. And finally, designing a total least square parameter compensation algorithm based on an accurate model so as to reduce system errors caused by Fresnel approximation.

Description

Technical Field

[0001] This invention belongs to the field of near-field RIS target localization technology, and more specifically, relates to a non-line-of-sight near-field source parameter estimation and correction method based on decoupled atomic norm. Background Technology

[0002] In recent years, groundbreaking advancements in wireless network capabilities have made wireless positioning technology a hot research topic. The next-generation 6G network will leverage the high-frequency and ultra-wide bandwidth characteristics of millimeter waves to achieve ultra-high-precision, super-resolution positioning. However, non-line-of-sight transmission caused by obstacles leads to a significant performance degradation of traditional subspace-based direction-of-arrival (DOA) estimation algorithms, such as rotation-invariant signal parameter estimation and the MUSIC algorithm.

[0003] Reconfigurable Smart Surfaces (RIS), with their low cost and flexible spatial configuration capabilities, are considered an effective solution for enhancing non-line-of-sight transmission. Specifically, the integration of sparse methods and RIS techniques has been extensively studied. Wang et al. proposed a RIS channel estimation method based on compressed sensing. To suppress the impact of off-network errors, You et al. proposed a discrete-continuous optimization orthogonal matched pursuit method. Wu et al. proposed an individual channel estimation method based on atomic norm minimization. To reduce complexity, Tian et al. proposed a two-dimensional angle estimation method based on the Decoupled Atomic Norm (DANM). Zheng et al. further proposed a decoupled atomic norm method using alternating multiplier method to further reduce complexity.

[0004] However, most sparse methods assume that the user is in the far field. The Rayleigh distance, the boundary between the far and near fields, expands as the RIS array elements increase, and communication between the user and the RIS will occur in the near field region. Therefore, the classic far-field plane wave propagation model becomes inapplicable. This shift renders the RIS target localization method, which was previously based on the far-field assumption, no longer applicable. Summary of the Invention

[0005] To address the aforementioned issues, this invention proposes a non-line-of-sight near-field source parameter estimation and correction method based on decoupled atomic norms. This method utilizes the spatiotemporal information of the signal, employing cross-correlation operations and pseudo-snapshot processing to eliminate the influence of the near-field range term while maintaining the virtual aperture of the extended RIS. Furthermore, the decoupled atomic norm is used to calculate the covariance matrices with respect to the X and Z axes, respectively, to estimate the target angle. The distance is then estimated using a one-dimensional spectral peak search based on the return-band angle. Finally, overall least squares are used to reduce the systematic error caused by the Fresnel approximation, thereby improving accuracy.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A non-line-of-sight near-field source parameter estimation and correction method based on decoupled atomic norms includes the following steps:

[0008] Step 1: System Modeling and Signal Reception. A near-field single-input multiple-output (SIMO) positioning system model assisted by a RIS (Reference-Instrument-Assisted System) is constructed. The base station is equipped with a uniform array, and the RIS adopts a uniform array (UPA) structure. Through sub-time slot configuration, the full rank of the received signal matrix is ​​ensured, and the array received signal containing near-field range and angle information is obtained. The reflected signal from the RIS array is then obtained through pseudo-inverse operations.

[0009] Step 2: Near-field distance term elimination and virtual aperture expansion. Cross-correlation is performed on the RIS array reflection signal to eliminate the influence of quadratic and cross terms in the near-field model. Through pseudo-snapshot processing and vectorization operations, the virtual array aperture of the RIS is expanded to construct virtual reflection data suitable for single-snapshot processing.

[0010] Step 3: Based on the virtual reflection data of a single snapshot, construct a decoupled atomic norm model about the X-axis and Z-axis, and solve the corresponding covariance matrix with Toeplitz structure respectively; extract angle information through the MUSIC algorithm, and use the angle matching algorithm to realize the automatic pairing of azimuth and elevation angles.

[0011] Step 4: Distance parameter estimation and error correction. Substitute the estimated target angle back into the near-field signal model and estimate the target distance through one-dimensional spectral peak search. To address the systematic error introduced by the Fresnel approximation, use the overall least squares method to jointly correct the angle and distance parameters, thereby improving the accuracy of parameter estimation.

[0012] A further optimization of this technical solution includes step one:

[0013] Considering RIS-assisted near-field positioning under a single-input multiple-output transmission model, the base station is equipped with a uniform array of N antenna elements. When there is an obstacle blocking the direct path between the base station and the user equipment, the base station can receive the signal from the user equipment through the signal reflected from the RIS. There are K narrowband signal sources in space. For the RIS located in the xoz plane, there are M array elements arranged in a uniform array structure, where M = (2m x +1)×(2n z +1), m x n is the number of elements along the positive x-axis. z It is the number of elements along the positive z-axis, and for time slot t, the reflected signal y of the array element at (m,n) of the RIS. m,n (t) is:

[0014]

[0015] Where m is the array index of the RIS array along the x-axis, and n is the array index of the RIS array along the z-axis. θ k r k Let s represent the azimuth, elevation, and range of the Kth target, respectively. k (t) represents the near-field source signal and the steering vector. λ is the wavelength of the near-field source signal, where the path difference of the k-th signal relative to the array element located at (m,n) is... for:

[0016]

[0017] in This represents the distance from the k-th signal to the element at (0,0), and the distance of the k-th signal relative to the element at (m,n).

[0018]

[0019] Record the path difference According to the Fresnel approximation, we have:

[0020]

[0021] in Array element spacing λ represents the signal wavelength. After Fresnel approximation, the steering vector of (1) The reflected signal Y(t) of the RIS array is:

[0022]

[0023] Suppose the phase matrix on the RIS in the t-th time slot is represented as W = diag(w), where Where ψ m,n Given random numbers between 0 and 2π, assuming W is the same in each time slot, the spatial response matrix at the base station is... Let θ be the pitch angle of BS relative to RIS. bs Let y be the azimuth angle of BS relative to RIS, then the received signal y of the base station in the t-th time slot. BS (t) is represented as:

[0024]

[0025] Where ζ(t) represents the array element (m,n) with a mean of zero and a variance of . Gaussian white noise, vec(·) denotes the vectorization operation on the matrix;

[0026] Since the locations of the base station and RIS are known, it is assumed that... It is completely known that if N≥M, then Existence, in which This indicates a pseudo-inverse operation on the matrix; however, when N < M, therefore It is not a full-rank matrix. Each time slot is divided into L sub-time slots. In each time slot, RIS uses L different configurations. Then (6) can rewrite the base station received signals of the L sub-time slots in the t-th time slot with different configurations. for:

[0027]

[0028] in I L Represented as an identity matrix of dimension L, Among them W L This represents the phase matrix of the RIS in the Lth sub-slot. Indicates the Kronecker product, [·] T This indicates that the matrix is ​​transposed, and as long as L is large enough, it can be guaranteed that... If it is a column full-rank matrix, then (7) can rewrite the base station received signal after the pseudo-inverse operation at the BS end in the t-th time slot. for:

[0029]

[0030] A further optimization of this technical solution includes step two:

[0031] First, the guide vector needs to be eliminated. The effects of the quadratic and cross terms with respect to r in the time delay τ, on... By performing cross-correlation calculations on the data, the virtual far-field reflection signal at (m,n) of the RIS array can be obtained.

[0032] Among them l m,n Denotes the (m,n) array elements of RIS, l -m,-n Represents the (-m, -n) array elements of RIS, u = (2m x +1)(n+n z )+(m+m x +1), v=(2m x +1)(-n+n z )+(-m+m x +1), s(τ)=[E{s1(t+τ)(s1(t)) *},E{s2(t+τ)(s2(t))*},…,E{s K (t+τ)(s K (t)) *}] T , [·] u This indicates that the u-th element of the vector is extracted (·). * For the conjugate operation, E{·} represents the expectation;

[0033] For the virtual far-field reflected signal at (m,n) of the RIS array By iterating through all array elements on the X and Z axes respectively and arranging them into a matrix, we can obtain the virtual far-field reflection signal matrix H(τ) of the RIS array:

[0034]

[0035] Where A x =[a x (-m x ),a x (-m x +1),…,a x (m x )] T A z =[a z (-n z ),a z (-n z +1),…,a z (n z )] T ;

[0036] Vectorizing the virtual far-field reflection signal matrix H(τ) of the RIS array yields h(τ):

[0037]

[0038] in

[0039] By performing pseudo-snapshot processing on h(τ) and merging the L pseudo-snapshot data, the virtual far-field reflection signal after pseudo-snapshot sampling can be obtained.

[0040]

[0041] To expand the virtual array of RIS, the above By performing covariance and vectorization, the single-shot virtual far-field reflection signal after expanding the array aperture can be obtained.

[0042]

[0043] in q k =E{[s(τ)] k ([s(τ)] k ) H}, q=[q1,q2,…,q K ] T q K Let be the signal power of the Kth target, (·) H ∠ represents the conjugate transpose operation, and ⊙ represents the Khatri-Rao product.

[0044] This technical solution is further optimized, and in step three, according to the above... Constructing a two-dimensional atomic norm for a single snapshot is challenging due to the high complexity of parameter calculation caused by the influence of the number of RIS array elements on the dimensionality of the two-dimensional Toeplitz matrix. A decoupled atomic norm based on virtual aperture is proposed, which decomposes the two-dimensional Toeplitz matrix into two one-dimensional Toeplitz matrices. The corresponding pitch and azimuth angles are then calculated using the music algorithm, and an angle matching algorithm is used to address the pitch and azimuth mismatch caused by decoupling. Finally, the range of near-field targets is calculated using the estimated angle information.

[0045] A further optimization of this technical solution includes step three:

[0046] Since the array elements of RIS are extended, the virtual received data z is a single snapshot. In order to perform RIS-assisted meshless 2D-DOA estimation of the single-input multiple-output model in the near field, the atomic norm under the single snapshot is used to solve the parameters.

[0047] Let the set of atoms of the atomic norm be represented as in and These are the virtual matrix element dimensions and atomic sets for the x and z axes after RIS expansion. The atomic norm of z is defined as

[0048] The minimum atomic norm of RIS can be written as:

[0049]

[0050] in It is a two-level Toeplitz matrix, u1 is T x,z The first element of the first column and first row of (u) x is a constant, and ||·||2 represents the l2 norm;

[0051] Due to the aforementioned optimization problems, and The growth and complexity have increased dramatically, so we decouple the array element information on the X and Z axes of the RIS array elements into two separate dimensions.

[0052] The definition of the decoupled atom set of RIS is... Atom set The atomic norm of z is defined as

[0053] but

[0054]

[0055] Where tr(·) represents the trace operation;

[0056] For the above T x (u) and T z (u) Perform the MUSIC algorithm separately to obtain... and in Because the above method yields... and It will not automatically pair; it will find the correct one. An angle matching algorithm is proposed:

[0057]

[0058] In found After that, we can obtain Thus, the corresponding pitch angle can be found. For distance estimation, the above estimates will be used. Substitution Then perform the MUSIC algorithm to obtain...

[0059] In a further optimization of this technical solution, step four involves designing a total least squares parameter compensation method based on an accurate model. This method calculates the approximate path delay from the previously estimated angle and distance parameters, then substitutes it into the path delay under the accurate model, traverses all RIS array elements to construct an overdetermined system of equations, and finally uses total least squares to solve the system of equations to obtain the three-dimensional parameters of the near-field target after parameter compensation.

[0060] A further optimization of this technical solution includes step four:

[0061] The estimated under the approximate model By reverting to (4), the path difference under the approximate model can be obtained. Will Substitute We can obtain:

[0062]

[0063] In equation (17) and Treating them as unknown variables, we can obtain the overdetermined system matrix P of the following M equations. ，

[0064]

[0065] set up Let f be the right singularity corresponding to the smallest singular value of matrix P in equation (18). Then f is the corresponding solution. Through f, we can obtain

[0066] Unlike existing technologies, the above technical solution has the following beneficial effects:

[0067] By employing cross-correlation and pseudo-snapshot processing, near-field range term interference is effectively eliminated while expanding the virtual aperture, making it suitable for near-field positioning scenarios under large-scale RIS arrays. A decoupled atomic norm method is used to decompose the high-dimensional optimization problem into two low-dimensional sub-problems, significantly reducing computational complexity while maintaining the global optimality of parameter estimation. A global least squares correction mechanism is introduced to effectively suppress systematic errors caused by Fresnel approximation, especially under high signal-to-noise ratio conditions, significantly improving the estimation accuracy of azimuth and elevation angles. This method is applicable to non-line-of-sight propagation environments, expanding the application scope of RIS in near-field positioning and providing effective technical support for high-precision positioning in the 6G high-frequency band. Attached Figure Description

[0068] Figure 1 This is a near-field target localization model based on RIS assistance;

[0069] Figure 2 A three-dimensional scatter plot of the near-field source;

[0070] Figure 3 For RMSE as it changes with SNR;

[0071] Figure 4 The RMSE varies with the number of snapshots. Detailed Implementation

[0072] To explain in detail the technical content, structural features, objectives, and effects of the technical solution, the following description is provided in conjunction with specific embodiments and accompanying drawings.

[0073] This invention proposes a non-line-of-sight near-field source parameter estimation and correction method based on decoupled atomic norm, comprising the following steps:

[0074] Step 1: System Modeling and Signal Reception. A near-field single-input multiple-output (SIMO) positioning system model assisted by a RIS (Reference-Instrument-Assisted System) is constructed. The base station is equipped with a uniform array, and the RIS adopts a uniform array (UPA) structure. Through sub-time slot configuration, the full rank of the received signal matrix is ​​ensured, and the array received signal containing near-field range and angle information is obtained. The reflected signal from the RIS array is then obtained through pseudo-inverse operations.

[0075] An array received signal model incorporating near-field range and angle information is established. By designing a multi-slot and sub-slot RIS phase configuration, a full-rank array received signal matrix is ​​constructed and obtained. Through pseudo-inverse operation, the reflected signal from the near-field target to the RIS is obtained from the received data at the base station (BS).

[0076] Consider RIS-assisted near-field positioning under the SIMO transmission model. The BS is equipped with a uniform array of N antenna elements. When an obstacle obstructs the direct path between the BS and the user equipment, the BS can receive signals from the UE via signals reflected from the RIS. (See also...) Figure 1 The image shows a near-field target localization model based on RIS assistance. Figure 1 As can be seen, there are K narrowband signal sources in space. For a RIS located in the xoz plane, M array elements are arranged in a uniform area array structure, where M = (2m... x +1)×(2n z +1), m x n is the number of elements along the positive x-axis. z This represents the number of elements along the positive z-axis. For time slot t, the reflected signal y from the array element at (m,n) of the RIS is... m,n (t) is:

[0077]

[0078] Where m is the array index of the RIS array along the x-axis, and n is the array index of the RIS array along the z-axis. θ k r k Let be the azimuth, elevation, and range of the Kth target, respectively. k (t) represents the near-field source signal. λ is the wavelength of the near-field source signal, where the path difference of the k-th signal relative to the array element located at (m,n) is... for:

[0079]

[0080] in This represents the distance from the k-th signal to the array element at (0,0). It also represents the distance of the k-th signal relative to the array element at (m,n).

[0081]

[0082] Record the path difference According to the Fresnel approximation, we have:

[0083]

[0084] in Array element spacing λ represents the signal wavelength. After the Fresnel approximation, the steering vector of (1) The reflected signal Y(t) of the RIS array is:

[0085]

[0086] Suppose the phase matrix on the RIS in the t-th time slot is represented as W = diag(w), where Where ψ m,n The values ​​are random numbers between 0 and 2π. For simplicity, it is assumed that W is the same in each time slot. The spatial response matrix on BS is... Let θ be the pitch angle of BS relative to RIS. bs Let y be the azimuth angle of BS relative to RIS, then the received signal y of BS in the t-th time slot. BS (t) is represented as:

[0087]

[0088] Where ζ(t) represents the array element (m,n) with a mean of zero and a variance of . Gaussian white noise, vec(·) denotes the vectorization operation on the matrix.

[0089] Since the locations of BS and RIS are known, it is assumed that... It is completely known. If N≥M, then It exists. Among them... This indicates a pseudo-inverse operation on the matrix. However, this is only possible when N < M. Therefore... It is not a full-rank matrix. To solve the above problem, each time slot is divided into L sub-time slots. In each time slot, RIS adopts L different configurations. Then (6) can rewrite the L sub-time slots in the t-th time slot with different base station received signals. for:

[0090]

[0091] in I L Represented as an identity matrix of dimension L, Among them W L Let represent the phase matrix of RIS in the Lth sub-slot. Indicates the Kronecker product, [·] T This indicates a transpose operation on the matrix. As long as L is large enough, it can be guaranteed... Let be a column full-rank matrix. Then (7) can rewrite the base station received signal after the pseudo-inverse operation at the BS end in the t-th time slot. for:

[0092]

[0093] Step 2: Near-field distance term elimination and virtual aperture expansion. Cross-correlation is performed on the RIS array reflection signal to eliminate the influence of quadratic and cross terms in the near-field model. Through pseudo-snapshot processing and vectorization operations, the virtual array aperture of the RIS is expanded to construct virtual reflection data suitable for single-snapshot processing.

[0094] To efficiently estimate the angle of near-field targets, cross-correlation is performed on the received signals to eliminate interference from the quadratic range term and cross-term in the near-field model, thereby decoupling the angle and range information. Furthermore, pseudo-snapshot processing and vectorization operations are used to expand the RIS array elements without increasing the number of physical elements, thus improving subsequent near-field target parameter estimation.

[0095] First, the guide vector needs to be eliminated. The influence of the quadratic and cross terms with respect to r in the equation. Under time delay τ, for... By performing cross-correlation calculations on the data, the virtual far-field reflection signal at (m,n) of the RIS array can be obtained.

[0096] Among them l m,n Denotes the (m,n) array elements of RIS, l -m,-n Represents the (-m, -n) array elements of RIS, u = (2m x +1)(n+n z )+(m+m x +1), v=(2m x +1)(-n+n z )+(-m+m x +1), s(τ)=[E{s1(t+τ)(s1(t)) *},E{s2(t+τ)(s2(t)) *},…,E{s K (t+τ)(s K (t)) *}]T , [·] u This indicates that the u-th element of the vector is extracted (·). * Let E{·} denote the conjugate operation, and E{·} denote the expectation.

[0097] For the virtual far-field reflected signal at (m,n) of the RIS array By iterating through all array elements on the X and Z axes respectively and arranging them into a matrix, we can obtain the virtual far-field reflection signal matrix H(τ) of the RIS array:

[0098]

[0099] Where A x =[a x (-m x ),a x (-m x +1),…,a x (m x )] T A z =[a z (-n z ),a z (-n z +1),…,a z (n z )] T .

[0100] Vectorizing the virtual far-field reflection signal matrix H(τ) of the RIS array yields h(τ):

[0101]

[0102] in

[0103] By performing pseudo-snapshot processing on h(τ) and merging the L pseudo-snapshot data, the virtual far-field reflection signal after pseudo-snapshot sampling can be obtained.

[0104]

[0105] To expand the virtual array of RIS, the above By performing covariance and vectorization, the single-shot virtual far-field reflection signal after expanding the array aperture can be obtained.

[0106]

[0107] in q k =E{[s(τ)] k ([s(τ)]k ) H}, q=[q1,q2,…,q K ] T q K Let be the signal power of the Kth target, (·) H ∠ represents the conjugate transpose operation, and ⊙ represents the Khatri-Rao product.

[0108] Step 3: Based on the virtual reflection data of a single snapshot, construct a decoupled atomic norm model about the X-axis and Z-axis, and solve the corresponding covariance matrix with Toeplitz structure respectively; extract angle information through the MUSIC algorithm, and use the angle matching algorithm to realize the automatic pairing of azimuth and elevation angles.

[0109] Based on the above A two-dimensional atomic norm for a single snapshot is constructed. Since the dimension of the two-dimensional Toeplitz matrix is ​​affected by the number of elements in the RIS matrix, the parameter calculation is complex. A decoupled atomic norm based on a virtual aperture is proposed, decomposing the two-dimensional Toeplitz matrix into two one-dimensional Toeplitz matrices, and then using the music algorithm to solve for the corresponding elevation and azimuth angles. An angle matching algorithm is used to solve the elevation and azimuth mismatch problem caused by decoupling. Finally, the range of near-field targets is calculated using the estimated angle information.

[0110] Due to the extended RIS array elements, the virtual received data z is a single snapshot. To perform RIS-assisted meshless 2D-DOA estimation of the SIMO model in the near field, this embodiment uses the atomic norm under a single snapshot to solve for the parameters.

[0111] Let the set of atoms of the atomic norm be represented as in and These are the virtual matrix element dimensions of the x-axis and z-axis after RIS expansion, respectively. Atom set The atomic norm of z is defined as

[0112] The minimum atomic norm of RIS can be written as:

[0113]

[0114] in It is a two-level Toeplitz matrix, u1 is T x,z The first element of the first column and first row of (u) x is a constant, and ||·||2 represents the l2 norm.

[0115] Due to the aforementioned optimization problems, and The growth leads to a significant increase in complexity. To reduce complexity, we decouple the element information of the RIS array elements about the X and Z axes into two separate dimensions, while maintaining optimal performance by jointly utilizing all information from both dimensions.

[0116] The definition of the decoupled atom set of RIS is... Atom set The atomic norm of z is defined as ,but

[0117]

[0118] Where tr(·) represents the trace operation.

[0119] For the above T x (u) and T z (u) Perform the MUSIC algorithm separately to obtain... and in Because the above method yields... and It will not automatically pair; it will find the correct one. This embodiment proposes an angle matching algorithm:

[0120]

[0121] In found After that, we can obtain Thus, the corresponding pitch angle can be found. For distance estimation, the above estimates can be used... Substitution Then perform the MUSIC algorithm to obtain...

[0122] Step 4: Distance parameter estimation and error correction. Substitute the estimated target angle back into the near-field signal model and estimate the target distance through one-dimensional spectral peak search. To address the systematic error introduced by the Fresnel approximation, use the overall least squares method to jointly correct the angle and distance parameters, thereby improving the accuracy of parameter estimation.

[0123] A total least squares parameter compensation method based on an accurate model was designed. The approximate path delay was calculated from the originally estimated angle and distance parameters, and then substituted into the path delay under the accurate model. An overdetermined system of equations was constructed by traversing all RIS array elements, and then the total least squares method was used to solve the system of equations to obtain the three-dimensional parameters of the near-field target after parameter compensation.

[0124] To reduce algorithm complexity and ensure the steering vector conforms to the Vandermonde structure, the original exact model was approximated using Fresnel approximation. However, this introduced unavoidable estimation bias. To reduce the systematic error under the Fresnel approximation, a method using Total Least Squares (TLS) is proposed to minimize the parameter estimation bias. The estimated parameters under the approximation model... By reverting to (4), the path difference under the approximate model can be obtained. Will Substitute We can obtain:

[0125]

[0126] In equation (17) and Treating them as unknown variables, we can obtain the overdetermined system matrix P of the following M equations.

[0127]

[0128] set up Let f be the right singularity corresponding to the smallest singular value of matrix P in equation (18). Then f is the corresponding solution. Through f, we can obtain...

[0129] Algorithm Simulation

[0130] To verify the effectiveness of the proposed algorithm in this embodiment, two sets of experiments will be conducted to simulate and verify its performance. Experiment 1 examines the root mean square error (RMSE) of the proposed algorithm under different signal-to-noise ratios (SNR), and Experiment 2 examines the RMSE under different snapshots.

[0131] During the simulation, the element spacing d = λ / 4, and the total number of snapshots is T. The definition of SNR is as follows:

[0132]

[0133] definition The root mean square error of the Monte Carlo experiment is in, For the first The estimated value of the k-th source parameter in the Monte Carlo experiment, η k This corresponds to the theoretical value. and η k Both can represent the azimuth angle θ k ,angle of depression and distance r k .

[0134] Experiment 1: Near-field target estimation performance of the proposed algorithm

[0135] In this experiment, it is assumed that there are 5 narrowband near-field signal sources incident on the scene. Figure 1 On the array shown, the signal-to-noise ratio was set to 20dB, and the number of snapshots was set to 1000, including 250 pseudo-snapshots. Experimental results are as follows... Figure 2 As shown in the figure, the two-dimensional angle and distance parameters of the five sources can be roughly estimated and correctly matched. Therefore, the proposed method is effective in estimating near-field sources. However, due to the existence of systematic errors, each estimated point deviates somewhat from the true value.

[0136] Experiment 2: Changes in RMSE with SNR

[0137] In this experiment, it is assumed that there are two narrowband near-field sources in space: (48.4223°, 138.5400°, 0.5181m) and (124.8461°, 140.6148°, 0.5847m), incident on a scene such that... Figure 1 On the RIS shown, where m x =m z =8. Signal-to-noise ratio is set to -10dB to 30dB, and the number of snapshots is set to 800, including 200 pseudo-snapshots. Figure 3 (a) in the text represents the near-field target. The RMSE plots with SNR are shown in (b) and (c). (b) shows the RMSE plot of θ with SNR for a near-field target, and (c) shows the RMSE plot of r with SNR for a near-field target. Figure 3 It can be seen that DANM+TLS outperforms DANM in terms of angle RMSE across the entire SNR range. Furthermore, as the signal-to-noise ratio increases, the dominant error gradually shifts from noise error to Fresnel approximation error, thus widening the RMSE difference between the two. For distance RMSE, the overall improvement of DANM+TLS is less significant.

[0138] Experiment 3: Changes in RMSE with the number of snapshots

[0139] In this experiment, the number of RIS array elements and target position parameters were the same as in Experiment 1. The signal-to-noise ratio was set to 5dB, and the number of snapshots ranged from 100 to 1200, with pseudo-snapshots accounting for one-quarter of the total number of snapshots. Figure 4 (a) in the text represents the near-field target. The RMSE plots for the near-field target are shown in (b) and (c) respectively. (b) represents the RMSE plot of θ as a function of the number of shots for the near-field target, while (c) represents the RMSE plot of r as a function of the number of shots for the near-field target. Figure 4 It can be seen that as the number of fast points increases, the RMSE of the DANM+TLS angle is better than that of the DANM, and the RMSE of the distances of the two are roughly equal.

[0140] This invention proposes a non-line-of-sight near-field source parameter estimation and correction method based on decoupled atomic norms. While reducing algorithm complexity, the systematic error of the Fresnel approximation is compensated for by the TLS algorithm. Under high signal-to-noise ratio conditions, the accuracy of azimuth and elevation angles is significantly improved, but the range improvement is not significant. Simulations verify the feasibility of the algorithm.

[0141] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or terminal device that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or terminal device. Unless otherwise specified, an element defined by the phrase "comprising..." or "including..." does not exclude the presence of additional elements in the process, method, article, or terminal device that includes said element. Additionally, in this document, "greater than," "less than," "exceeding," etc., are understood to exclude the stated number; "above," "below," "within," etc., are understood to include the stated number.

[0142] Although the above embodiments have been described, those skilled in the art, once they understand the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the above descriptions are merely embodiments of the present invention and do not limit the scope of patent protection of the present invention. Any equivalent structural or procedural transformations made using the content of the present invention's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the scope of patent protection of the present invention.

Claims

1. A non-line-of-sight near-field source parameter estimation and correction method based on decoupled atomic norm, characterized in that: Includes the following steps, Step 1: System modeling and signal reception. Construct a near-field single-input multiple-output (RIS) assisted positioning system model, in which the base station is equipped with a uniform array and the RIS adopts a uniform array structure. Through sub-time slot configuration, ensure that the columns of the received signal matrix are full rank, obtain the array received signal containing near-field range and angle information, and obtain the RIS array reflected signal through pseudo-inverse operation. Step 2: Near-field range term elimination and virtual aperture expansion. Cross-correlation is performed on the RIS array reflection signal to eliminate the influence of quadratic and cross terms in the near-field range term. Through pseudo-snapshot processing and vectorization operations, the virtual array aperture of the RIS is expanded to construct virtual reflection data suitable for single-snapshot processing. Step 3: Based on the virtual reflection data of a single snapshot, construct a decoupled atomic norm model about the X-axis and Z-axis, and solve the corresponding covariance matrix with Toeplitz structure respectively; extract angle information through the MUSIC algorithm, and use the angle matching algorithm to realize the automatic pairing of azimuth and elevation angles; Step 4: Range parameter estimation and error correction. Substitute the estimated azimuth and elevation angles back into the steering vector and estimate the target distance using a one-dimensional spectral peak search. To address the systematic errors introduced by the Fresnel approximation, use the overall least squares method to jointly correct the angle and near-field range parameters, thereby improving the accuracy of parameter estimation.

2. The non-line-of-sight near-field source parameter estimation and correction method based on decoupled atomic norm as described in claim 1, characterized in that, Step one includes: Considering RIS-assisted near-field positioning under a single-input multiple-output transmission model, the base station is equipped with a uniform array of N antenna elements. When there is an obstacle blocking the direct path between the base station and the user equipment, the base station can receive the signal from the user equipment through the signal reflected from the RIS. There are K narrowband signal sources in space. For the RIS located in the xoz plane, there are M array elements arranged in a uniform array structure, where M = (2m x +1)×(2n z +1), m x n is the number of elements along the positive x-axis. z It is the number of elements along the positive z-axis, and for time slot t, the reflected signal y of the array element at (m,n) of the RIS. m,n (t) is: Where m is the array index of the RIS array along the x-axis, and n is the array index of the RIS array along the z-axis. θ k r k Let s represent the azimuth, elevation, and range of the Kth target, respectively. k (t) represents the near-field source signal and the steering vector. λ is the wavelength of the near-field source signal, where the path difference of the k-th signal relative to the array element located at (m,n) is... for: in This represents the distance from the k-th signal to the element at (0,0), and the distance of the k-th signal relative to the element at (m,n). : Record the path difference According to the Fresnel approximation, we have: in Array element spacing λ represents the signal wavelength. After Fresnel approximation, the steering vector of (1) The reflected signal Y(t) of the RIS array is: Suppose the phase matrix on the RIS in the t-th time slot is represented as W = diag(w), where Where ψ m,n Given random numbers between 0 and 2π, assuming W is the same in each time slot, the spatial response matrix at the base station is... Let θ be the elevation angle of the base station relative to the RIS. bs Let be the azimuth angle of the base station relative to the RIS, then the received signal y of the base station in the t-th time slot is... BS (t) is represented as: Where ζ(t) represents the array element (m,n) with a mean of zero and a variance of . Gaussian white noise, vec(·) denotes the vectorization operation on the matrix; Since the locations of the base station and RIS are known, it is assumed that... It is completely known that if N≥M, then Existence, in which This indicates a pseudo-inverse operation on the matrix; however, when N < M, therefore It is not a full-rank matrix. Each time slot is divided into L sub-time slots. In each time slot, RIS uses L different configurations. Then (6) can rewrite the base station received signals of the L sub-time slots in the t-th time slot with different configurations. for: in I L Represented as an identity matrix of dimension L, Among them W L This represents the phase matrix of the RIS in the Lth sub-slot. Indicates the Kronecker product, [·] T This indicates that the matrix is ​​transposed, and as long as L is large enough, it guarantees that... If it is a full-rank column matrix, then (7) rewrite the base station received signal after the pseudo-inverse operation at the BS end in the t-th time slot. for:

3. The non-line-of-sight near-field source parameter estimation and correction method based on decoupled atomic norm as described in claim 2, characterized in that, Step two includes: First, the guide vector needs to be eliminated. The effects of the quadratic and cross terms with respect to r in the time delay τ, on... By performing cross-correlation calculations on the data, the virtual far-field reflection signal at (m,n) of the RIS array can be obtained. : Among them l m,n Denotes the (m,n) array elements of RIS, l -m,-n Represents the (-m, -n) array elements of RIS, u = (2m x +1)(n+n z )+(m+m x +1), v=(2m x +1)(-n+n z )+(-m+m x +1), s(τ)=[E{s1(t+τ)(s1(t)) * },E{s2(t+τ)(s2(t)) * },…,E{s K (t+τ)(s K (t)) * }] T , [·] u This indicates that the u-th element of the vector is extracted (·). * For the conjugate operation, E{·} represents the expectation; For the virtual far-field reflected signal at (m,n) of the RIS array By iterating through all array elements on the X and Z axes respectively and arranging them into a matrix, we can obtain the virtual far-field reflection signal matrix H(τ) of the RIS array: where A x = [a x (-m x ), a x (-m x + 1), …, a x (m x )] T , A z = [a z (-n z ), a z (-n z + 1), …, a z (n z )] T ; Vectorizing the virtual far-field reflection signal matrix H(τ) of the RIS array yields h(τ): in By performing pseudo-snapshot processing on h(τ) and merging the L pseudo-snapshot data, the virtual far-field reflection signal after pseudo-snapshot sampling can be obtained. : To expand the virtual array of RIS, the above By performing covariance and vectorization, the single-shot virtual far-field reflection signal after expanding the array aperture can be obtained. : in q = [q1, q2, ..., q K ] T q K Let be the signal power of the Kth target, (·) H ∠ represents the conjugate transpose operation, and ⊙ represents the Khatri-Rao product.

4. The non-line-of-sight near-field source parameter estimation and correction method based on decoupled atomic norm as described in claim 3, characterized in that, In step three, according to the above... Constructing a two-dimensional atomic norm for a single snapshot is challenging due to the high complexity of parameter calculation caused by the influence of the number of RIS array elements on the dimensionality of the two-dimensional Toeplitz matrix. A decoupled atomic norm based on virtual aperture is proposed, which decomposes the two-dimensional Toeplitz matrix into two one-dimensional Toeplitz matrices. The corresponding pitch and azimuth angles are then calculated using the music algorithm, and an angle matching algorithm is used to address the pitch and azimuth mismatch caused by decoupling. Finally, the range of near-field targets is calculated using the estimated angle information.

5. The non-line-of-sight near-field source parameter estimation and correction method based on decoupled atomic norm as described in claim 3, characterized in that, Step three includes: Since the array elements of RIS are extended, the virtual received data z is a single snapshot. In order to perform RIS-assisted meshless 2D-DOA estimation of the single-input multiple-output model in the near field, the atomic norm under the single snapshot is used to solve the parameters. Let the set of atoms of the atomic norm be represented as in and These are the virtual matrix element dimensions and atomic sets for the x and z axes after RIS expansion. The atomic norm of z is defined as The minimum atomic norm of RIS is written as: in It is a two-level Toeplitz matrix, u1 is T x,z The first element of the first column and first row of (u) x is a constant, and ||·||2 represents the l2 norm; Due to the aforementioned optimization problems, and The growth and complexity have increased dramatically, so we decouple the array element information on the X and Z axes of the RIS array elements into two separate dimensions. The definition of the decoupled atom set of RIS is... Atom set The atomic norm of z is defined as but Where tr(·) represents the trace operation; For the above T x (u) and T z (u) Perform the MUSIC algorithm separately to obtain... and in Because the above method yields... and It will not automatically pair; it will find the correct one. An angle matching algorithm is proposed: In found After that, we can obtain Thus, the corresponding pitch angle can be found. For distance estimation, the above estimates will be used. Substitution Then perform the MUSIC algorithm to obtain...

6. The non-line-of-sight near-field source parameter estimation and correction method based on decoupled atomic norm as described in claim 1, characterized in that, In step four, a total least squares parameter compensation method based on the accurate model is designed. The estimated angle and distance parameters are used to calculate the approximate path delay, which is then substituted into the path delay under the accurate model. The overdetermined system of equations is constructed by traversing all RIS array elements, and the system of equations is solved by total least squares to obtain the three-dimensional parameters of the near-field target after parameter compensation.

7. The non-line-of-sight near-field source parameter estimation and correction method based on decoupled atomic norm as described in claim 5, characterized in that, Step four includes: The estimated under the approximate model By reverting to (4), the path difference under the approximate model can be obtained. Will Substitute We can obtain: In equation (17) and Treating these as unknown variables, we obtain the overdetermined system matrix P of the following M equations. ， set up If f is the right singular corresponding to the smallest singular value of matrix P in equation (18), then f is the corresponding solution. Through f, we obtain...

Images