Reconfigurable intelligent surface assisted siso system user near field positioning method

Abstract

The application belongs to the technical field of wireless positioning and specifically relates to a reconfigurable intelligent surface assisted SISO system user near field positioning method. Regular multivariate decomposition and orthogonal matching pursuit are combined to obtain initial values of TOA and AOD on the RIS, then, a l1-norm regularization method based on sparsity is used to estimate the distance. Then, the maximum likelihood estimation formula is used to refine the initial estimation. Finally, the extended invariance principle is combined with the least square method to recover the position and clock offset. The obtained parameter estimation performance is close to the Cramer-Rao lower bound of the estimation error.

Description

Technical Field

[0001] This invention belongs to the field of wireless positioning technology, specifically relating to a near-field positioning method for users in a reconfigurable smart surface-assisted SISO system. Background Technology

[0002] Due to low hardware costs and reduced power consumption, a large number of passive and reflective components can be integrated into a single RIS panel. RIS panels can be installed to cover the entire roof and walls of a building. However, for very large RIS panels, the typical indoor propagation distance of a few meters is often insufficient to guarantee the validity of far-field conditions and the plane wave assumption. Furthermore, progress in RIS-assisted localization in multipath scenarios has been limited. Summary of the Invention

[0003] Therefore, a reconfigurable smart surface-assisted near-field localization method for SISO systems is required. Initial values ​​for TOA and AOD on the RIS are obtained by combining regular multivariate decomposition and orthogonal matching pursuit. Then, a sparsity-based l1-norm regularization method is used to estimate the distance. The initial estimate is then refined using a maximum likelihood estimation formula. Finally, the position and clock offset are recovered using the extended invariance principle combined with a least squares method. The obtained parameter estimation performance approaches the Cramer-Rao lower bound of the estimation error.

[0004] To achieve the above objectives, the present invention adopts the following technical solution:

[0005] A near-field localization method for users in a reconfigurable smart surface-assisted SISO system.

[0006] The downlink SISO wireless communication three-dimensional near-field positioning system consists of a single-antenna base station, a transmissive RIS, and a single-antenna indoor user. Given the known location of BS, For an unknown user location, the RIS is placed parallel to the xoz plane, with its center point located at... The number of RIS units is N R =N x N z , where N x and N z These correspond to the number of elements along the x-axis and z-axis, respectively. Let represent the known location of the r-th RIS element. Assume there is only one path between the RIS and the base station, but the indoor environment is more complex, with N possible paths. s There are scatterers of unknown number and location, and the position of the s-th scatterer is determined by... Therefore, the unknown geometric parameters include the user's three-dimensional position and the scatterer's three-dimensional position, and the positioning method includes:

[0007] I. Construct a system model for RIS-assisted localization in a multipath environment, including a channel signal model and a signal model;

[0008] II. Define the channel parameter vector and the location vector to be estimated;

[0009] Third, convert the received signal matrix into a third-order tensor;

[0010] IV. Based on the third-order tensor of the received signal, combined with regular multivariate decomposition and orthogonal matching pursuit algorithm, a coarse estimate of the arrival time of the signal and the departure angle of the RIS is obtained.

[0011] 5. Rewrite the received signal matrix using coarse estimates of signal arrival time and RIS departure angle, and estimate the distance using a sparsity-based l1 norm regularization method;

[0012] VI. Estimate the channel gain;

[0013] 8. Construct the maximum likelihood estimate to refine the previously obtained channel parameter estimates;

[0014] 8. Construct a weighted least squares problem to transform the refined channel parameter estimates into position and clock offset estimates.

[0015] A further optimization of this technical solution includes step one:

[0016] S1. Consider a transmission with N subcarriers and T orthogonal frequency division multiplexing pilot symbols, where the frequency of the nth subcarrier is f. n =f c +nΔf-B / 2, where f c Let B be the carrier frequency, Δf be the subcarrier spacing, B = NΔf be the signal bandwidth, λ be the wavelength of the electromagnetic wave, and x be the signal frequency. t [n] represents the transmitted signal at the nth subcarrier and the tth time slot. Where P represents the signal transmission power;

[0017] S2, From the base station to the RIS, there is only a line-of-sight path, while from the RIS to the user, there are N paths. s +1 paths, where N s =0 paths represent line-of-sight paths, and the other paths are non-line-of-sight paths. Then, the channel h of the BS-RIS link can be... BR [n] and the channel h of the RIS-UE link RU [n] are modeled as follows:

[0018]

[0019]

[0020] in, ρ BR τ BR The channel gain and TOA of the BS-RIS path are respectively, ρ RU,s and ρ RU,s These represent the channel gain and signal arrival time of the s-th path from RIS to UE, respectively, where a(p) is a given position p∈{p B ,p s The near-field RIS steering vector of} is defined as

[0021]

[0022] S3, the baseband signal y received from the t-th transmission and the n-th subcarrier. t [n] can be represented as

[0023]

[0024] in, b(p) = a(p)⊙a(pB), where ⊙ represents the Hadamard product. It is the RIS phase offset at the t-th transmission, z t [n] is uncorrelated zero-mean additive complex Gaussian noise with a variance of N0 / 2 for each dimension;

[0025] S4. Based on geometric relationships, the unknown channel parameters can be expressed as:

[0026] τ0=(||p R -p B ||2+||p0-p R ||) / c+Δ,

[0027] τ s =(||p R -p B ||2+||p s -p R ||+||p0-p s ||) / c+Δ,

[0028] φ el,s =arccos([p s -p R ]3 / ||p s -p R ||)

[0029] φ az,s =atan2([p s -p R ]2,[p s -p R ]1)

[0030] d s =||p s -p R ||

[0031] Where τ0 represents the time delay of the line-of-sight path, τ s Let φ represent the delay of the s-th path. el,s φ represents the elevation angle of the s-th path. az,s Let d represent the azimuth angle of the s-th path. s Let represent the distance from the target along the s-th path to the RIS, Δ represent the clock offset, and c represent the speed of light. The known channel parameters of the BS-RIS path can be expressed as:

[0032] θ el =arccos([p B -p R ]3 / ||p B -p R ||)

[0033] α az =atan2([p B -p R ]2,[p B -p R ]1)

[0034] d B =||p B -p R ||

[0035] Where, θ el θ represents the elevation angle of the BS-RIS path. az The azimuth angle of the BS-RIS path is represented by d. B This represents the distance from BS to RIS;

[0036] S5, Define Vectors

[0037]

[0038] Where, N m Let ω be a constant and ω be a variable.

[0039] S6. Then the received signal y can be... t [n] represents an N×T matrix:

[0040]

[0041] in, Z represents Gaussian noise.

[0042] This technical solution is further optimized, and step two includes:

[0043] S7. Define a channel parameter vector based on the received signal:

[0044]

[0045] in, ρ s The real and imaginary parts;

[0046] S8. Further define a position vector:

[0047]

[0048] in,

[0049] This technical solution is further optimized, and step three includes:

[0050] S9. To convert the received signal matrix into a tensor, the near-field steering vector is approximated using the far-field approximation:

[0051]

[0052] in, denoted as Kronecker product, where d is the cell spacing of the RIS;

[0053] S10. After some mathematical simplification, the received signal can be approximately represented as:

[0054]

[0055] in, Indicates the outer product.

[0056]

[0057]

[0058] S11. Design the RIS phase matrix to follow the structure below.

[0059]

[0060] in, And T = T1T2;

[0061] S12, further obtained

[0062]

[0063] S13. Then, the received signal can be represented as a third-order tensor.

[0064]

[0065] in, This is the noise component of the third-order tensor.

[0066] This technical solution is further optimized, and step four includes:

[0067] S14, through estimation and A coarse estimate of the signal arrival time and RIS departure angle can be obtained. The overall method follows the idea of ​​orthogonal matching pursuit, estimating the signal arrival time and RIS departure angle parameters for each path sequentially. In the s-th iteration, regular multivariate decomposition is used to separate the signal components corresponding to the s-th path.

[0068]

[0069] in It is the factor vector along the nth modulus, which can be represented as

[0070]

[0071] in

[0072] S15, will Closed form is represented as

[0073]

[0074] S16. Therefore, rough estimates of TOA and AOD can be obtained by solving the following three one-dimensional search problems respectively.

[0075]

[0076] S17. To remove the correlated components of the signal in the s-th iteration and obtain the updated residual, the projection of the signal is subtracted using the following steps.

[0077]

[0078]

[0079] in, Use the obtained updated residual Reconstructing the tensor Then continue with the next iteration until the signal arrival time and RIS departure angle parameter for all paths are estimated.

[0080] This technical solution is further optimized, and step five includes:

[0081] S18. After obtaining a coarse estimate of the signal arrival time and RIS departure angle, the received signal is rewritten as follows:

[0082]

[0083] in,

[0084]

[0085] S19. Utilizing the sparse characteristics of the received signal in the spatial domain, the distance estimation is transformed into sparse spectral estimation. First, an overcomplete dictionary is constructed. For the s-th path, the following is constructed based on the number of grid samples:

[0086] D s =[d s (d1),…,d s (dm),…,d s (d M )]

[0087] in,

[0088] It is a set of sampled grids containing potential distance values;

[0089] S20, Using an overcomplete dictionary D s For vectorized received signals Perform sparse representation:

[0090]

[0091] Where ζ s Let z represent a sparse vector, where z is a complex Gaussian noise vector;

[0092] S21. Estimate the distance parameters by constructing the following optimization problem.

[0093]

[0094] Where ξ is the regularization coefficient. Solving this optimization problem yields an estimate of ζ, which provides a coarse estimate of the distance.

[0095] This technical solution is further optimized, and step six includes:

[0096] S22. By estimating the distance parameter, the received signal can be expressed as:

[0097]

[0098] in,

[0099] S23. Simplifying the above equation, we can obtain...

[0100]

[0101] S24. Then, the complex channel gain can be estimated as follows:

[0102]

[0103] This technical solution is further optimized, and step seven includes:

[0104] S25. A maximum likelihood estimation method is introduced to jointly refine all channel-related parameters, and the constructed maximum likelihood estimator is:

[0105]

[0106] in, The optimization problem is solved using the Nelder-Mead algorithm, which uses the coarse estimate as the initial value.

[0107] This technical solution is further optimized, and step eight includes:

[0108] S26. Accurate positioning and clock offset estimation are achieved by solving the following weighted least squares problem:

[0109]

[0110] in, The Fisher information matrix of the channel parameters at the estimation point can be obtained from this nonlinear least squares problem using the Nelder-Mead algorithm. The parameters in the equation can be initialized using the following formula.

[0111]

[0112]

[0113] Unlike existing technologies, the above technical solution has the following beneficial effects:

[0114] 1. The effects of multipath propagation were taken into account, and the position of the scatterer was estimated, further improving the positioning and synchronization accuracy.

[0115] 2. Signals from different paths are separated, avoiding parameter pairing.

[0116] 3. By using maximum likelihood estimation, the estimation performance is brought close to the performance limit. Attached Figure Description

[0117] Figure 1 A scenario diagram illustrating RIS-assisted localization and synchronization;

[0118] Figure 2 To obtain the RMSE of the orientation angle as a function of the signal-to-noise ratio using the method of this invention;

[0119] Figure 3 To obtain the RMSE of elevation angle as a function of signal-to-noise ratio using the method of this invention;

[0120] Figure 4 To obtain the RMSE of distance versus signal-to-noise ratio using the method of this invention;

[0121] Figure 5 To obtain the RMSE of the time delay as a function of the signal-to-noise ratio using the method of the present invention;

[0122] Figure 6 The graph showing the change of RMSE of location with signal-to-noise ratio obtained using the method of the present invention;

[0123] Figure 7 The graph shows the variation of RMSE of clock bias with signal-to-noise ratio obtained using the method of this invention. Detailed Implementation

[0124] 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.

[0125] This invention proposes a 3D positioning system that utilizes a single-antenna base station (BS) and a reconfigurable intelligent surface (RIS) for simultaneous localization and synchronization. Initial values ​​for the time of arrival (TOA) and the angle of departure (AOD) of the RIS are obtained by combining canonical polyadic decomposition (CPD) and orthogonal matching pursuit (OMP). Then, a sparsity-based l1-norm regularization method is used to estimate the distance. Maximum likelihood estimation (MLE) is then used to refine the initial estimates. Finally, the extended invariance principle (EXIP) combined with a least squares method is employed to recover the position and clock offset. The obtained parameter estimation performance approaches the Cramer-Rao lower bound of the estimation error.

[0126] See Figure 1 The diagram shows a scenario for RIS-assisted localization and synchronization. Consider a downlink single-input single-output (SISO) wireless communication three-dimensional near-field positioning system, consisting of a single-antenna BS, a transmissive RIS, and a single-antenna indoor user equipment (UE). Given the known location of BS, The UE location is unknown. The RIS is placed parallel to the xoz plane, and its center point is located at... The number of RIS units is N R =N x N z , where N x and N z These correspond to the number of elements along the x-axis and z-axis, respectively. Let represent the known location of the r-th RIS element. Assume there is only one path between RIS and BS, but the indoor environment is complex, with N... s There are scatterers of unknown number and location. The position of the s-th scatterer is determined by... Therefore, the unknown geometric parameters include the three-dimensional position of the UE and the three-dimensional position of the scatterer. The positioning method includes:

[0127] S1. Consider a transmission with N subcarriers and T orthogonal frequency division multiplexing (OFDM) pilot symbols. The frequency of the nth subcarrier is f. n =f c +nΔf-B / 2, where f c Let be the carrier frequency, Δf be the subcarrier spacing, B = NΔf be the signal bandwidth, and λ be the wavelength of the electromagnetic wave. t [n] represents the transmitted signal at the nth subcarrier and the tth time slot. Where P represents the signal transmission power.

[0128] S2, From BS to RIS, there is only a line-of-sight path, while from RIS to UE, there are N paths. s +1 paths, where N s =0 paths represent line-of-sight paths, and the other paths are non-line-of-sight paths. Then, the channel h of the BS-RIS link can be... BR [n] and the channel h of the RIS-UE link RU [n] are modeled as follows:

[0129]

[0130]

[0131] in, ρ BR τ BR The channel gain and TOA of the BS-RIS path are respectively, ρ RU,s and τ RU,s Let a(p) be the channel gain and TOA of the s-th path from RIS to UE, respectively. a(p) is a given position p∈{p B ,p s The near-field RIS steering vector of} is defined as

[0132]

[0133] S3, the baseband signal y received from the t-th transmission and the n-th subcarrier. t [n] can be represented as

[0134]

[0135] in, b(p) = a(p)⊙a(pB), where ⊙ represents the Hadamard product. It is the RIS phase offset at the t-th transmission. t [n] is uncorrelated zero-mean additive complex Gaussian noise with a variance of N0 / 2 for each dimension.

[0136] S4. Based on geometric relationships, the unknown channel parameters can be expressed as:

[0137] τ0=(||p R -p B ||2+||p0-p R ||) / c+Δ,

[0138] τ s =(||p R -p B ||2+||p s -p R ||+||p0-p s ||) / c+Δ,

[0139] φ el,s =arccos([p s -p R ]3 / ||p s -p R ||)

[0140] φ az,s =atan2([p s -p R ]2,[p s -p R ]1)

[0141] d s =||p s -p R ||

[0142] Where τ0 represents the time delay of the line-of-sight path, τ s Let φ represent the delay of the s-th path. el,s φ represents the elevation angle of the s-th path. az,s Let d represent the azimuth angle of the s-th path. s Let represent the distance from the target along the s-th path to the RIS, Δ represent the clock offset, and c represent the speed of light. The known channel parameters of the BS-RIS path can be expressed as:

[0143] θ el =arccos([p B -p R ]3 / ||p B -pR | |)

[0144] θ ax =atan2([p B -p R ]2,[p B -p R ]1)

[0145] d B =||p B -p R ||

[0146] Where, θ el θ represents the elevation angle of the BS-RIS path. az The azimuth angle of the BS-RIS path is represented by d. B This represents the distance from BS to RIS.

[0147] S5, Define Vectors

[0148]

[0149] Where, N m ω is a constant, and ω is a variable.

[0150] S6, Then the received baseband signal y t [n] represents an N×T matrix:

[0151]

[0152] in, Z is the complex Gaussian noise matrix.

[0153] S7. Define a channel parameter vector based on the received signal:

[0154]

[0155] in, ρ s real and imaginary parts

[0156] S8. Further define a position vector:

[0157]

[0158] in,

[0159] S9. To convert the received signal matrix into a tensor, the near-field steering vector is approximated using the far-field approximation:

[0160]

[0161] in, d represents the Kronecker product, where d is the cell spacing of the RIS.

[0162] S10. After some mathematical simplification, the received signal can be approximately represented as:

[0163]

[0164] in, Indicates the outer product.

[0165]

[0166]

[0167] S11. Design the RIS phase matrix to follow the structure below.

[0168]

[0169] in, And T = T1T2.

[0170] S12, further obtained

[0171]

[0172] S13. Then, the received signal can be represented as a third-order tensor.

[0173]

[0174] in, It is a third-order complex Gaussian noise tensor.

[0175] S14, through estimation and Coarse estimates of TOA and AOD can be obtained. The overall method follows the OMP approach, estimating the TOA and AOD parameters for each path sequentially. In the s-th iteration, regular multivariate decomposition is used to separate the signal components corresponding to the s-th path:

[0176]

[0177] in It is the factor vector along the nth modulus, which can be represented as

[0178]

[0179] in

[0180] S15, will Closed form is represented as

[0181]

[0182] S16. Therefore, rough estimates of TOA and AOD can be obtained by solving the following three one-dimensional search problems respectively:

[0183]

[0184] S17. In order to remove the correlation components of the signal in the s-th iteration and obtain the updated residual, the projection of the above signal is subtracted using the following steps.

[0185]

[0186]

[0187] in, Use the obtained updated residual Reconstructing the tensor Then continue with the next iteration until the TOA and AOD parameters for all paths are estimated.

[0188] S18. After obtaining the coarse estimates of TOA and AOD, the received signal is rewritten as follows:

[0189]

[0190] in,

[0191]

[0192] S19. Utilizing the sparsity characteristics of the received signal in the spatial domain, distance estimation is transformed into sparse spectral estimation. First, an overcomplete dictionary is constructed. For the s-th path, the following is constructed based on the number of grid samples:

[0193] D s =[d s (d1),…,d s (d m ),…,d s (d M )]

[0194] in, It is a sampled grid set containing potential distance values.

[0195] S20, Using an overcomplete dictionary D s For vectorized received signals Perform sparse representation:

[0196]

[0197] Where ζ sLet z represent a sparse vector, and z be a complex Gaussian noise vector.

[0198] S21. Estimate the distance parameters by constructing the following optimization problem.

[0199]

[0200] Where ξ is the regularization coefficient. The optimization problem can be solved using existing solvers, and the estimated value of ζ can be used to obtain a coarse estimate of the distance.

[0201] S22. By estimating the distance parameter, the received signal can be expressed as:

[0202]

[0203] in,

[0204] S23. Simplifying the above equation, we can obtain...

[0205]

[0206] S24. Then, the complex channel gain can be estimated as follows:

[0207]

[0208] S25. The far-field approximation has a certain impact on the estimation performance of AOD, and further affects the estimation accuracy of the range parameter. Furthermore, the results of parameter estimation through one-dimensional search are also affected by the grid size. Therefore, a maximum likelihood estimation method is introduced to jointly refine all channel-related parameters. The constructed maximum likelihood estimator is:

[0209]

[0210] in, This optimization problem can be solved using the Nelder-Mead algorithm, which uses the coarse estimate as the initial value.

[0211] S26. Accurate positioning and clock offset estimation are achieved by solving the following weighted least squares problem:

[0212]

[0213] in, The Fisher information matrix of the channel parameters at the estimation point. This nonlinear least squares problem can be solved using the Nelder-Mead algorithm. The parameters in the equation can be initialized using the following equation.

[0214]

[0215]

[0216] Example: Consider an indoor positioning scenario, set f c =2.8GHz, Δf=120kHz, c=3×10 8 m / s, N = 80, T = 256, N x =N z =48. The base station is located at RIS is located in UE located Suppose there exists a scatterer located at The RMSE for azimuth, elevation, distance, latency, and user location and clock offset are as follows: Figure 2-7 As shown. The Monte Carlo simulation was performed 1000 times. Simulation results show that when the signal-to-noise ratio exceeds -15dB, the channel parameter estimation of the UE is close to the performance boundary, and when the signal-to-noise ratio exceeds -10dB, the channel parameter estimation of the scatterer is also close to the performance boundary, verifying the effectiveness of the method.

[0217] 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.

[0218] 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 near-field localization method for users in a reconfigurable smart surface-assisted SISO system, characterized in that, The downlink SISO wireless communication three-dimensional near-field positioning system consists of a single-antenna base station, a transmissive RIS, and a single-antenna indoor user. Given the known location of BS, For unknown user locations, RIS is parallel to Placed on a flat surface, its center point is located at... The number of RIS units is ,in and These correspond to the number of elements along the x-axis and z-axis, respectively. Let represent the known location of the r-th RIS element. Assume there is only one path between the RIS and the base station, but the indoor environment is more complex and has [variable paths]. There are scatterers of unknown number and location, and the position of the s-th scatterer is determined by... Therefore, the unknown geometric parameters include the user's three-dimensional position and the scatterer's three-dimensional position, and the positioning method includes: I. Construct a system model for RIS-assisted localization in a multipath environment, including a channel signal model and a signal model; II. Define the channel parameter vector and the location vector to be estimated; Third, convert the received signal matrix into a third-order tensor; IV. Based on the third-order tensor of the received signal, combined with regular multivariate decomposition and orthogonal matching pursuit algorithm, a coarse estimate of the arrival time of the signal and the departure angle of the RIS is obtained.

5. Rewrite the received signal matrix using coarse estimates of signal arrival time and RIS departure angle, utilizing sparsity-based... The distance is estimated using norm regularization. VI. Estimate the channel gain; 7. Construct the maximum likelihood estimate to refine the previously obtained channel parameter estimates; 8. Construct a weighted least squares problem to transform the refined channel parameter estimates into position and clock offset estimates.

2. The user near-field localization method for a reconfigurable smart surface-assisted SISO system as described in claim 1, characterized in that, Step one includes: S1. Consider a transmission with N subcarriers and T orthogonal frequency division multiplexing pilot symbols, where the frequency of the nth subcarrier is... ,in For carrier frequency, For subcarrier spacing, For signal bandwidth, The wavelength of electromagnetic waves. For the transmitted signal at the nth subcarrier and the tth time slot, ,in Indicates the signal transmission power; S2, From the base station to the RIS, there is only a line-of-sight path, while from the RIS to the user, there is... Paths, among which One path represents the line-of-sight path, and the other paths are non-line-of-sight paths. Then, the channels of the base station-RIS link can be... Channels of the RIS-UE link Modeled as , , in , , These represent the channel gain and signal arrival time of the BS-RIS path, respectively. and Let be the channel gain and signal arrival time of the s-th path from RIS to the user, respectively. It is a given position The near-field RIS steering vector is defined as follows: , S3, the baseband signal received from the t-th transmission and the n-th subcarrier. It can be represented as , in, , , , Represents the Hadamard product. It is the RIS phase offset at the t-th transmission. It is uncorrelated zero-mean additive complex Gaussian noise, with variance in each dimension being... ; S4. Based on geometric relationships, the unknown channel parameters can be expressed as: in, Indicates the time delay of the line-of-sight path. This represents the delay of the s-th path. This represents the elevation angle of the s-th path. This represents the azimuth angle of the s-th path. This represents the distance from the target on the s-th path to RIS. Indicates clock skew. For the speed of light, the known channel parameters of the base station-RIS path can be expressed as: in, Indicates the elevation angle of the base station-RIS path. Indicates the azimuth angle of the base station-RIS path. Indicates the distance from the base station to the RIS; S5, Define Vectors in, It is a constant. As a variable; S6, then the received signal can be... Represented as The matrix: in, , , This is a complex Gaussian noise matrix.

3. The user near-field positioning method for a reconfigurable smart surface-assisted SISO system as described in claim 2, characterized in that, Step two includes: S7. Define a channel parameter vector based on the received signal: in, , , They are respectively The real and imaginary parts; S8. Further define a position vector: in, .

4. The user near-field positioning method for a reconfigurable smart surface-assisted SISO system as described in claim 3, characterized in that, Step three includes: S9. To convert the received signal matrix into a tensor, the near-field steering vector is approximated using the far-field approximation: , in, , , , , Represents the Kronecker product. This refers to the cell spacing of the RIS. S10. After some mathematical simplification, the received signal can be approximately represented as: in, , Indicates the outer product. This represents the elevation angle of the s-th path. This represents the azimuth angle of the s-th path. S11. Design the RIS phase matrix to follow the structure below. in, , and ; S12, further obtained S13. Then, the received signal can be represented as a third-order tensor. in, , , , It is a third-order complex Gaussian noise tensor.

5. The user near-field positioning method for a reconfigurable smart surface-assisted SISO system as described in claim 4, characterized in that, Step four includes: S14, through estimation , and This allows for coarse estimates of the signal arrival time and RIS departure angle. The overall method follows the idea of ​​orthogonal matching pursuit, sequentially estimating the signal arrival time and RIS departure angle parameters for each path. In the s-th iteration, regular multivariate decomposition is used to separate the signal components corresponding to the s-th path. in It is the factor vector along the nth modulus, which can be represented as in ; S15, will Closed form is represented as S16. Therefore, a coarse estimate of the signal arrival time and the RIS departure angle can be obtained by solving the following three one-dimensional search problems respectively. S17. To remove the correlated components of the signal in the s-th iteration and obtain the updated residual, the projection of the signal is subtracted using the following steps. in, Use the obtained updated residual Reconstructing the tensor Then continue with the next iteration until the signal arrival time and RIS departure angle parameters for all paths are estimated.

6. The user near-field positioning method for a reconfigurable smart surface-assisted SISO system as described in claim 5, characterized in that, Step five includes: S18. After obtaining a coarse estimate of the signal arrival time and RIS departure angle, the received signal is rewritten as follows: in, S19. Utilizing the sparse characteristics of the received signal in the spatial domain, the distance estimation is transformed into sparse spectral estimation. First, an overcomplete dictionary is constructed. For the s-th path, the following is constructed based on the number of grid samples: in, , It is a set of sampled grids containing potential distance values; S20. Using an overly complete dictionary For vectorized received signals Perform sparse representation: in Represents a sparse vector. It is a complex Gaussian noise vector; S21. Estimate the distance parameters by constructing the following optimization problem. Where is the regularization coefficient. , Solving this optimization problem yields the following results: The estimated value can be used to obtain a rough estimate of the distance.

7. The user near-field localization method for a reconfigurable smart surface-assisted SISO system as described in claim 6, characterized in that, Step six includes: S22. By estimating the distance parameter, the received signal can be expressed as: in, , , , ; S23. Simplifying the above equation, we can obtain... S24. Then, the complex channel gain can be estimated as follows: .

8. The user near-field localization method for a reconfigurable smart surface-assisted SISO system as described in claim 7, characterized in that, Step seven includes: S25. A maximum likelihood estimation method is introduced to jointly refine all channel-related parameters, and the constructed maximum likelihood estimator is: in, The optimization problem is solved using the Nelder-Mead algorithm, which uses the coarse estimation results as initial values.

9. The user near-field localization method for a reconfigurable smart surface-assisted SISO system as described in claim 8, characterized in that, Step eight includes: S26. Accurate positioning and clock offset estimation are achieved by solving the following weighted least squares problem: in, The Fisher information matrix of the channel parameters at the estimation point can be obtained from this nonlinear least squares problem using the Nelder-Mead algorithm. The parameters in the equation can be initialized using the following formula. The distance from BS to RIS 。

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