Hybrid reconfigurable intelligent surface assisted 3d user positioning method

Abstract

The application discloses a mixed reconfigurable intelligent surface assisted 3D user positioning method, which is suitable for an uplink wireless communication far-field positioning system, the system comprises a multi-antenna base station, a single radio frequency chain HRIS and a single-antenna 3D user, and adopts an OFDM transmission mode, the method relates to obtaining the receiving signals of the HRIS and the base station, performing coarse estimation and fine estimation of channel time delay and angle by using a root MUSIC algorithm and a maximum likelihood estimator, and finally determining the positions of the 3D user and the HRIS through geometric relations; the method has the advantages that the 3D user can be positioned under the condition that the HRIS position and state parameters are unknown, the HRIS position and state parameters can be estimated at the same time, and the positioning precision is high.

Description

Technical Field

[0001] This invention belongs to the field of wireless positioning and relates to a 3D user positioning technology, and more particularly to a 3D user (UE) positioning method assisted by a Hybrid Reconfigurable Intelligent Surface (HRIS). Background Technology

[0002] Recent research assessments indicate that RIS, as an emerging technology, has shown broad application prospects in the fields of positioning and sensing. RIS technology intelligently regulates the propagation of electromagnetic waves in space, assisting in the construction of an intelligent and controllable wireless electromagnetic environment, providing a new paradigm for the development of mobile communications. As a passive technology, RIS adjusts the electromagnetic parameters (such as phase and amplitude) of reflected signals by controlling the operating state of each component, superimposing them in the wireless space to achieve various signal control effects such as beamforming and interference suppression. In the fields of positioning and sensing, RIS technology can not only enhance signals but also be used to assist in positioning and sensing, providing physical layer secure communication and wireless power transmission.

[0003] Hybrid Reconfigurable Smart Metasurfaces (HRIS) are a novel type of active componentless surface. Unlike traditional passive RIS and RIS that combine passive and active receiving antennas, each element of an HRIS can be flexibly adjusted to simultaneously achieve reflection and reception functions. The development of HRIS technology has provided new possibilities for the application of RIS technology, especially in scenarios that require simultaneous handling of signal reflection and reception.

[0004] In most user localization and synchronization studies, a common assumption is that the configuration state of the RIS (including its location and status parameters) is known in advance. This is because RIS contains many complex electronic components, which significantly increase the risk of damage during movement and handling. Therefore, in practical applications, pre-arranging the location and status of the RIS is a common practice. However, this assumption limits the application of RIS technology in dynamic environments, as achieving user localization without knowing the RIS's location and status parameters is more flexible and challenging. Therefore, researching how to achieve user localization without knowing the RIS's location and status parameters is of great significance for improving the practicality and flexibility of RIS technology. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a hybrid reconfigurable smart metasurface-assisted 3D user positioning method, which can realize 3D user positioning without knowing the HRIS position and state parameters, while estimating the HRIS position and state parameters, and with high positioning accuracy.

[0006] The technical solution adopted by this invention to solve the above-mentioned technical problems is as follows: a hybrid reconfigurable intelligent metasurface-assisted 3D user positioning method, characterized in that the method is applied to an uplink wireless communication far-field positioning system, the wireless communication far-field positioning system having a base station with multiple antennas and equipped with a single radio frequency chain, an HRIS equipped with a single radio frequency chain, and a 3D user with a single antenna. The base station is a planar array, the transmission mode of the wireless communication far-field positioning system adopts OFDM, the 3D user transmits signals, the HRIS receives part of the signals transmitted by the 3D user, and the remaining part of the signals is reflected by the HRIS back to the base station, the base station receives the signals transmitted by the 3D user and the signals reflected by the HRIS; the method includes the following steps:

[0007] Step 1: Obtain the received signal from HRIS and the received signal from the base station;

[0008] Step 2: Apply the root-finding MUSIC algorithm to the received signal of HRIS to obtain a coarse estimate of the channel delay between the 3D user and HRIS; then use the coarse estimate of the channel delay between the 3D user and HRIS to eliminate the delay term in the received signal of HRIS; then sum over all subcarriers of OFDM to obtain the vector form of the received signal of HRIS; next, based on the vector form of the received signal of HRIS, construct a maximum likelihood optimization problem to solve the AOA of HRIS when HRIS receives the signal transmitted by the 3D user, and then solve it to obtain a coarse estimate of the AOA of HRIS when HRIS receives the signal transmitted by the 3D user.

[0009] Step 3: Based on the coarse estimate of the channel delay between the 3D user and HRIS and the coarse estimate of the AOA of HRIS when HRIS receives the signal transmitted by the 3D user, obtain the received signal with known angle and time delay of HRIS; then, based on the received signal with known angle and time delay of HRIS, obtain the coarse estimate of the channel gain between the 3D user and HRIS.

[0010] Step 4: Apply the root-finding MUSIC algorithm to the received signal from the base station to obtain coarse estimates of the channel delay between the 3D user and the base station, as well as coarse estimates of the cascaded channel delays between the 3D user and HRIS, and between HRIS and the base station. Then, construct a delay propagation matrix based on the two coarse delay estimates. Next, use the delay propagation matrix to eliminate the delay term in the received signal from the base station, obtaining the delay-free received signal from the base station. Then, according to the pilot symbols of the first and second halves of all OFDM pilot symbols, divide the two row vectors of the delay-free received signal from the base station into two parts respectively. Finally, based on the first part of the first row vector of the delay-free received signal from the base station, construct a solution for the delay term received by the base station from the 3D user. This involves a two-dimensional search problem for the base station's AOA when the user transmits a signal, followed by a coarse estimate of the base station's AOA when the base station receives a signal transmitted by the 3D user. Then, based on the latter part of the second row vector of the base station's delay-free received signal, a two-dimensional search problem for the cascading angle is constructed, and a coarse estimate of the cascading angle is obtained. This leads to a coarse estimate of the HRIS's AOD when the base station receives a signal reflected from the HRIS. Finally, based on the first part of the second row vector of the base station's delay-free received signal, a two-dimensional search problem for the base station's AOA when the base station receives a signal reflected from the HRIS is constructed, and a coarse estimate of the base station's AOA when the base station receives a signal reflected from the HRIS is obtained.

[0011] Step 5: Based on the coarse estimates of the channel delay between the 3D user and the base station, the coarse estimates of the cascaded channel delay between the 3D user and HRIS and between HRIS and the base station, the coarse estimates of the base station's AOA when the base station receives the signal transmitted by the 3D user, the coarse estimates of the cascaded angle, and the coarse estimates of the base station's AOA when the base station receives the signal reflected by HRIS, obtain the received signal with known angle and time delay of the base station; then, based on the received signal with known angle and time delay of the base station, obtain the coarse estimates of the channel gain between the 3D user and the base station, as well as the coarse estimates of the channel gain of the cascaded channel between the 3D user and HRIS and between HRIS and the base station.

[0012] Step 6: Using the maximum likelihood estimator, the coarse estimates obtained in Step 2 and Step 3 are used as initial values ​​for joint optimization to obtain the corresponding fine estimates; similarly, the maximum likelihood estimator is used, the coarse estimates obtained in Step 4 and Step 5 are used as initial values ​​for joint optimization to obtain the corresponding fine estimates.

[0013] Step 7: Based on the detailed estimates obtained in Step 6, obtain the angles between the communication links between the base station and HRIS, and between HRIS and the 3D user; the angles between the communication links between the 3D user and the base station, and between HRIS and the base station; and the angles between the communication links between the 3D user and the base station, and between HRIS and the 3D user; then, based on the three angles and the geometric relationships between the 3D user, HRIS, and base station, obtain the estimated distances between the 3D user and the base station, and between HRIS and the base station; finally, based on the known location of the base station, the estimated distances between the 3D user and the base station, and between HRIS and the base station, obtain the estimated unknown locations of HRIS and the 3D user.

[0014] In step 1, the received signal Y of HRIS is... R Represented as The base station received the signal Y B Represented as Where, ρ UR ρ represents the channel gain of the channel between the 3D user and the HRIS. UB ρ represents the channel gain of the channel between the 3D user and the base station. URB The channel gain represents the cascaded channel between the 3D user and HRIS, and between HRIS and the base station; σ represents the reflection coefficient of HRIS; τ UR τ represents the channel delay between the 3D user and HRIS. UB τ represents the channel delay between the 3D user and the base station. URB d(τ) represents the time delay of the cascaded channels between the 3D user and HRIS, and between HRIS and the base station. UR ) represents τ UR The guiding vector, d(τ) UB ) represents τ UB The guiding vector, d(τ) URB ) represents τ URB The guiding vector, θ UR This indicates the AOA (Area of ​​Interest) of HRIS when it receives a signal transmitted by a 3D user, θ. UB θ represents the base station's AOA when it receives a signal transmitted by a 3D user. RB This indicates the base station's AOA (Area of ​​Interest) when it receives the signal reflected from HRIS. R (θ UR ) represents the steering vector at HRIS when HRIS receives the signal transmitted by the 3D user, a B (θ UB ) represents the steering vector at the base station when it receives a signal transmitted by a 3D user. B (θ RB) represents the steering vector at the base station when the base station receives the signal reflected from HRIS, c R c represents the HRIS receive phase matrix. B Let s represent the received phase matrix of the base station, s represent the transmitted signal matrix, and ε represent the received phase matrix of the base station. R Let ε represent the additive white Gaussian noise matrix at HRIS. B This represents the additive white Gaussian noise matrix at the base station, and ⊙ is the Hadamard product operator. θ BR This indicates the AOD of HRIS when the base station receives the signal reflected by HRIS, a R (θ BR ) represents the steering vector at HRIS when the base station receives the signal reflected by HRIS, and W represents the reflection phase matrix of HRIS.

[0015] τ UR =(d UR ) / c+Δ R , τ UB =(d UB ) / c+Δ B , τ URB =(d UR +d RB ) / c+Δ B d UR 3D is used to represent

[0016] The distance between the household and HRIS d UB Indicates the distance between the 3D user and the base station. d RB This indicates the distance between the HRIS and the base station. p U p represents the unknown location of the 3D user. R p represents the unknown location of HRIS. B Let c represent the known location of the base station, Δ represent the signal propagation speed, and Δ represent the signal propagation speed. R Indicates the clock skew present in HRIS, Δ B This indicates the clock offset present at the base station; τ UR τ UB τ URB All use τ arb When referring to someone, there are: e represents the natural base, j represents the imaginary number, Δf represents the subcarrier spacing, and N represents the number of subcarriers in OFDM.

[0017] Represents θ UR azimuth angle, Represents θ UR pitch angle,

[0018]

[0019] R represents a rotation matrix of dimension 3×3, R = R γ (z)R β (y)R α (x), R α (x), R β (y), R γ (z) represents the rotation matrix of HRIS around the X, Y, and Z axes of the local coordinate system constructed with HRIS. α, β, and γ represent the rotation angles of HRIS around the X, Y, and Z axes of the local coordinate system constructed using HRIS.

[0020] [p U -p R ]1,[p U -p R ]2,[p U -p R ]3 corresponds to p U -p R The first element, the second element, and the third element; For θ UB azimuth angle, For θ UB pitch angle,

[0021]

[0022] [p U -p B ]1,[p U -p B ]2,[p U -p B ]3 corresponds to p U -p B The first element, the second element, and the third element; For θ RB azimuth angle, For θ RB pitch angle,

[0023]

[0024] [p R -p B ]1,[p R -p B ]2,[p R -p B ]3 corresponds to p R -pB The first element, the second element, and the third element; For θ BR azimuth angle, For θ BR pitch angle,

[0025]

[0026] [p B -p R ]1,[p B -p R ]2,[p B -p R ]3 corresponds to p B -p R The first element, the second element, and the third element;

[0027] Let a be the symbol for the Krock inner product. r (θ UR ), a c (θ UR The corresponding vector represents the guide vector of HRIS in the X and Z axes of the local coordinate system constructed by HRIS when HRIS receives the signal transmitted by the 3D user. r (θ UR The mth x The elements are

[0028] d represents the spacing between HRIS components, λ represents the wavelength, and a c (θ UR The mth z The elements are m x =1,2,…,M x m z =1,2,…,M z M x M z The corresponding numbers represent the number of HRIS components along the X and Z axes in the local coordinate system constructed using HRIS. The total number of HRIS components is M. R M R =M x M z ;

[0029] a r (θ UB ), a c (θ UBThe corresponding vector represents the guidance vector of the base station in the X and Z axes of the global coordinate system constructed with the base station when the base station receives the signal transmitted by the 3D user. r (θ UB The nth x The elements are a c (θ UB The nth z The elements are n x =1,2,…,N x n z =1,2,…,N z N x N z The corresponding numbers represent the number of antennas of the base station along the X and Z axes in the global coordinate system constructed with the base station. The number of antennas of the base station is N. B N B =N x N z ; a r (θ RB ), a c (θ RB The corresponding vector represents the guidance vector of the base station in the X and Z axes of the global coordinate system constructed with the base station when the base station receives the signal reflected by HRIS. r (θ RB The nth x The elements are

[0030] a c (θ RB The nth z The elements are [a] c (θ RB )] nz , a r (θ BR ), a c (θ BR The corresponding vector represents the steering vector of HRIS in the X and Z axes of the local coordinate system constructed with HRIS when the base station receives the signal reflected by HRIS. r (θ BR The mth x The elements are

[0031] a c (θ BR The mth z The elements are

[0032] c R The dimension is M R ×T f T f T represents the number of pilot symbols in OFDM. f All pilot symbols are the same, c R The t-th column vector is c R,t t=1,2,…,T f c R,t c represents the HRIS receive phase vector on the t-th pilot symbol. R,t The i-th element is [c R,t ] i , [c R,t ] i i = 1, ..., M R This represents the receive phase of the i-th element of HRIS on the t-th pilot symbol, |[c R,t ] i |=1;c B The dimension is N B ×T f c B The t-th column vector is c B,t c B,t c represents the received phase vector of the base station on the t-th pilot symbol. B,t The i-th element is [c B,t ] i ,

[0033] [c B,t ] i i = 1, ..., N B This represents the received phase of the i-th antenna of the base station on the t-th pilot symbol, |[c B,t ] i |=1;

[0034] The dimension of s is N×T f The element in the nth row and tth column of s is s t [n], s t [n] represents the signal transmitted on the nth subcarrier of the t-th pilot symbol. P represents the average transmit power of the 3D user, n = 1, 2, ..., N; ε R ε B The dimension is N×T f , ε R and ε B All contain variance of μ 2 Zero-mean circularly symmetric independent and identically distributed Gaussian elements, ε R The element in the nth row and tth column is ε R,t[n],ε R,t [n] represents the additive white Gaussian noise at the HRIS on the nth subcarrier of the t-th pilot symbol, ε B The element in the nth row and tth column is ε B,t [n],ε B,t [n] represents the additive white Gaussian noise at the base station on the nth subcarrier of the t-th pilot symbol, ε R,t [n]、ε B,t The variance of [n] is μ 2 ; θ represents the cascade angle, b r (θ), b c (θ) represents the guide vector of HRIS in the X and Z axes of the local coordinate system constructed with HRIS, b r (θ) mth x The elements are b c (θ) mth z The elements are The dimension of W is M R ×T f The t-th column vector of W is γ t γ t γ represents the reflection phase vector of HRIS on the t-th pilot symbol. t The i-th element is [γ t ] i , [γ t ] i i = 1, ..., M R Represents the reflection phase of the i-th element of HRIS on the t-th pilot symbol, |[γ t ] i |=1.

[0035] In step 2, the delay-free received signal of HRIS, obtained by eliminating the delay term in the received signal of HRIS using a coarse estimate of the channel delay between the 3D user and HRIS, is represented as follows:

[0036] in, The time delay τ between the 3D user and the HRIS channel represents the time delay of the channel. UR The rough estimate, T represents f A vector of all 1s; representing the vector form of the received signal from HRIS as...

[0037] in, The maximum likelihood optimization problem can be described as follows: The coarse estimate of the AOA of HRIS when it receives signals transmitted by 3D users is expressed as: in,

[0038] In step 3, the received signal with known HRIS angle and time delay is represented as...

[0039] in, Channel gain ρ of the channel between the 3D user and HRIS UR The rough estimate is expressed as in, Q represents R The false rebellion.

[0040] In step 4, the delay manifold matrix is ​​represented as follows: in, The time delay τ between the 3D user and the base station represents the channel delay. UB The rough estimate, The time delay τ represents the concatenated channel between the 3D user and HRIS, and between HRIS and the base station. URB A rough estimate; the base station's delay-free received signal is expressed as... The number of pilot symbols in the first half of the OFDM is T1, and the number of pilot symbols in the second half is T2. The base station receives the signal with zero delay. The first and second row vectors are represented as follows: and Will Split into two parts and Will It is also divided into two parts, namely and

[0041]

[0042] The two-dimensional search problem for the AOA of a base station when it receives signals transmitted by a 3D user is described as follows: The coarse estimate of the base station's AOA when it receives signals transmitted by a 3D user is expressed as:

[0043] in, c B The submatrix formed by the first T1 columns, The two-dimensional search problem for solving cascade angles is described as follows:

[0044] The coarse estimate of the cascade angle is expressed as: The coarse estimate of the AOD of HRIS when the base station receives the signal reflected by HRIS is expressed as: azimuth for The pitch angle is for in, c B The submatrix formed by the last T2 columns of W, where W2 represents the submatrix formed by the last T2 columns of W. and Corresponding representation azimuth and elevation angles and Corresponding representation The azimuth and elevation angles; the two-dimensional search problem for the base station's AOA when the base station receives the signal reflected from HRIS is described as follows:

[0045] The coarse estimate of the base station's AOA when the base station receives the signal reflected from HRIS is expressed as:

[0046] Where W1 represents the submatrix formed by the first T1 columns of W.

[0047] In step 5, the received signal with known base station angle and time delay is represented as...

[0048] Where, diag(ρ UB ,ρ URB ) represents finding the diagonal matrix. The channel gain ρ of the channel between the 3D user and the base station UB The rough estimate is expressed as Channel gain ρ of the cascaded channels between 3D users and HRIS, and between HRIS and base station URB The rough estimate is expressed as in, Corresponding representation The first column vector, the second column vector, Corresponding representation The first column vector, the second column vector,

[0049] The specific process of step 6 is as follows: Let η R express Let η B express

[0050]

[0051] in, Indicates taking the real part, This indicates taking the imaginary part; then using the maximum likelihood estimator, for η... R Joint optimization is performed, and η is used in the optimization process. R The rough estimates of each parameter are used as initial values ​​to solve for η. R Detailed estimate Similarly for η B Joint optimization is performed, and η is used in the optimization process. B The rough estimates of each parameter are used as initial values ​​to solve for η. B Detailed estimate in,

[0052]

[0053] || || F This is the F-norm operator.

[0054] In step 7, the angles between the communication links between the base station and HRIS and between HRIS and 3D users, the angles between the communication links between the 3D user and the base station and between HRIS and the base station, and the angles between the communication links between the 3D user and the base station and between HRIS and the 3D user are represented as ψ0, ψ1, and ψ2, respectively. ψ2=π-ψ1-ψ2,

[0055] Represents the direction vector. Used to refer to Corresponding to θ UR θ BR θ UB θ RB Detailed estimates, azimuth for The pitch angle is for The corresponding fine estimate of θ azimuth and elevation angles Corresponding to azimuth and elevation angles for azimuth angle, Corresponding representation The azimuth and elevation angles; the distance d between the 3D user and the base station. UBThe estimated value is expressed as The distance d between HRIS and base station RB The estimated value is expressed as in, Represents τ UB Detailed estimates, Represents τ URB Detailed estimates; the unknown location p of HRIS R The detailed estimate is expressed as The unknown location of the 3D user p U The detailed estimate is expressed as

[0056] Compared with the prior art, the advantages of the present invention are as follows:

[0057] In far-field scenarios, this invention utilizes a single-RF chain phase design for the base station and HRIS. By receiving signals from the base station, it estimates the angle of arrival (AOA) of the base station, the angle of arrival (AOA) and departure (AOD) of the HRIS, and channel delay parameters. Through refinement, more accurate parameter estimates are obtained. Then, using the estimated channel parameters and the geometric relationships between the base station, HRIS, and 3D users, the positions of the HRIS and 3D users are located. In this invention, the state and position of the HRIS can be combined with 3D user positioning and synchronization without knowing the HRIS's status and position, estimating the HRIS's position and state parameters. Simulation experiments show that the root mean square error (RMSE) of the angle and position is very small, indicating high accuracy. This solves the problem of pre-arranging the RIS's position in RIS-assisted positioning.

[0058] In this invention, in order to avoid complex high-dimensional search problems, a two-dimensional search is used to obtain a coarse estimate. However, due to the limitations of the two-dimensional search, the coarse estimate is further refined globally to obtain a more accurate fine estimate. Attached Figure Description

[0059] Figure 1 This is a scene diagram illustrating the joint synchronous positioning of HRIS and 3D users in this invention.

[0060] Figure 2 This is a schematic diagram showing the variation of the RMSE of the coarse and fine estimates of various time delays obtained using the method of this invention in a simulation experiment as a function of the average transmit power of the 3D user.

[0061] Figure 3 θ obtained using the method of this invention in simulation experiments UR A schematic diagram showing the variation of the RMSE of the coarse and fine estimates of azimuth and elevation angles with the average transmit power of the 3D user;

[0062] Figure 4 θ obtained using the method of this invention in simulation experiments UB A schematic diagram showing the variation of the RMSE of the coarse and fine estimates of azimuth and elevation angles with the average transmit power of the 3D user;

[0063] Figure 5 θ obtained using the method of this invention in simulation experiments RB A schematic diagram showing the variation of the RMSE of the coarse and fine estimates of azimuth and elevation angles with the average transmit power of the 3D user;

[0064] Figure 6 θ obtained using the method of this invention in simulation experiments BR A schematic diagram showing the variation of the RMSE of the coarse and fine estimates of azimuth and elevation angles with the average transmit power of the 3D user;

[0065] Figure 7 This is a schematic diagram showing the variation of the RMSE of the coarse and fine estimates of the unknown location of HRIS and the unknown location of 3D users obtained using the method of this invention in a simulation experiment, as a function of the average transmit power of the 3D user. Detailed Implementation

[0066] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0067] This invention proposes a hybrid reconfigurable smart metasurface-assisted 3D user positioning method. This method is applied to an uplink wireless communication far-field positioning system. The wireless communication far-field positioning system has a base station (BS) with multiple antennas and equipped with a single radio frequency chain (RX-RF), an HRIS equipped with a single radio frequency chain (RX-RF), and a 3D user (UE) with a single antenna. The base station is a planar array, vertically distributed on the ground. The transmission mode of the wireless communication far-field positioning system is OFDM. The 3D user transmits signals, the HRIS receives a portion of the transmitted signals, and the remaining signals are reflected back to the base station by the HRIS. The base station receives both the transmitted signals from the 3D user and the reflected signals from the HRIS. The method includes the following steps:

[0068] Step 1: Obtain the received signal from HRIS and the received signal from the base station.

[0069] Furthermore, the received signal Y from HRIS R Represented as The base station received the signal Y B Represented as

[0070] Where, ρ UR ρ represents the channel gain of the channel between the 3D user and the HRIS.UB ρ represents the channel gain of the channel between the 3D user and the base station. URB The channel gain represents the cascaded channel between the 3D user and HRIS, and between HRIS and the base station; σ represents the reflection coefficient of HRIS; τ UR τ represents the channel delay between the 3D user and HRIS. UB τ represents the channel delay between the 3D user and the base station. URB d(τ) represents the time delay of the cascaded channels between the 3D user and HRIS, and between HRIS and the base station. UR ) represents τ UR The guiding vector, d(τ) UB ) represents τ UB The guiding vector, d(τ) URB ) represents τ URB The guiding vector, θ UR This indicates the AOA (Area of ​​Interest) of HRIS when it receives a signal transmitted by a 3D user, θ. UR θ represents the channel parameters of the communication link between the 3D user and HRIS. UB θ represents the base station's AOA when it receives a signal transmitted by a 3D user. UB θ represents the channel parameters of the communication link between the 3D user and the base station. RB θ represents the base station's AOA when it receives the signal reflected from HRIS. RB Here are the channel parameters for the communication link between HRIS and the base station, a R (θ UR ) represents the steering vector at HRIS when HRIS receives the signal transmitted by the 3D user, a B (θ UB ) represents the steering vector at the base station when it receives a signal transmitted by a 3D user. B (θ RB This represents the steering vector at the base station when it receives the signal reflected from HRIS. The superscript "T" indicates the transpose of the vector or matrix. R c represents the HRIS receive phase matrix. B Let s represent the received phase matrix of the base station, s represent the transmitted signal matrix, and ε represent the received phase matrix of the base station. R Let ε represent the additive white Gaussian noise matrix at HRIS. B This represents the additive white Gaussian noise matrix at the base station, and ⊙ is the Hadamard product operator.

[0071] θ BR This represents the AOD of HRIS when the base station receives the signal reflected by HRIS, θ. BR Also, it refers to the channel parameters of the communication link between HRIS and the base station, a R (θBR ) represents the steering vector at HRIS when the base station receives the signal reflected by HRIS, and W represents the reflection phase matrix of HRIS.

[0072] The above, τ UR =(d UR ) / c+Δ R , τ UB =(d UB ) / c+Δ B , τ URB =(d UR +d RB ) / c+Δ B d UR Indicates the distance between the 3D user and HRIS. d UB Indicates the distance between the 3D user and the base station. d RB This indicates the distance between the HRIS and the base station. p U p represents the unknown location of the 3D user. R p represents the unknown location of HRIS. B p represents the known location of the base station. U p R p B Both are 3D, where c represents the signal propagation speed, which is the speed of light, and Δ R Indicates the clock skew present in HRIS, Δ B This indicates a clock offset present in the base station. To define the symbol, ||·|| is the 2-norm operator; τ UR τ UB τ URB All use τ arb When referring to someone, there are: e represents the natural base, e = 2.71…, j is an imaginary number, Δf represents the subcarrier spacing, and N represents the number of subcarriers in OFDM.

[0073] The above, Represents θ UR azimuth angle, Represents θ UR pitch angle,

[0074]

[0075] R represents a 3×3 rotation matrix that belongs to the special orthogonal group So. (3) That is, an orthogonal matrix with a unit determinant, R = R γ (z)R β (y)Rα (x), R α (x), R β (y), R γ (z) represents the rotation matrix of HRIS around the X, Y, and Z axes of the local coordinate system constructed with HRIS. α, β, and γ represent the rotation angles of HRIS around the X, Y, and Z axes of the local coordinate system constructed using HRIS. These three rotation angles (HRIS state parameters) are unknown. [p] U -p R ]1,[p U -p R ]2,[p U -p R ]3 corresponds to p U -p R The first element, the second element, and the third element; For θ UB azimuth angle, For θ UB pitch angle,

[0076] [p U -p B ]1,[p U -p B ]2,[p U -p B ]3 corresponds to p U -p B The first element, the second element, and the third element; For θ RB azimuth angle, For θ RB pitch angle,

[0077] [p R -p B ]1,[p R -p B ]2,[p R -p B ]3 corresponds to p R -p B The first element, the second element, and the third element; For θ BR azimuth angle, For θ BR pitch angle,

[0078] [p B -p R ]1,[p B -p R ]2,[p B -p R ]3 corresponds to p B -p R The first element, the second element, and the third element.

[0079] The above, Let a be the symbol for the Krock inner product. r (θ UR ), a c (θ UR The corresponding vector represents the guide vector of HRIS in the X and Z axes of the local coordinate system constructed by HRIS when HRIS receives the signal transmitted by the 3D user. r (θ UR The mth x The elements are

[0080] d represents the spacing between HRIS components. λ represents wavelength, a c (θ UR The mth z The elements are m x =1,2,…,M x m z =1,2,…,M z M x M z The corresponding numbers represent the number of HRIS components along the X and Z axes in the local coordinate system constructed using HRIS. The total number of HRIS components is M. R M R =M x M z ;

[0081] a r (θ UB ), a c (θ UB The corresponding vector represents the guidance vector of the base station in the X and Z axes of the global coordinate system constructed with the base station when the base station receives the signal transmitted by the 3D user. r (θ UB The nth x The elements are a c (θ UB The nth z The elements are nx =1,2,…,N x n z =1,2,…,N z N x N z The corresponding numbers represent the number of antennas of the base station along the X and Z axes in the global coordinate system constructed with the base station. The number of antennas of the base station is N. B N B =N x N z ; a r (θ RB ), a c (θ RB The corresponding vector represents the guidance vector of the base station in the X and Z axes of the global coordinate system constructed with the base station when the base station receives the signal reflected by HRIS. r (θ RB The nth x The elements are

[0082] a c (θ RB The nth z The elements are a r (θ BR ), a c (θ BR The corresponding vector represents the steering vector of HRIS in the X and Z axes of the local coordinate system constructed with HRIS when the base station receives the signal reflected by HRIS. r (θ BR The mth x The elements are

[0083] a c (θ BR The mth z The elements are

[0084] The above, c R The dimension is M R ×T f T f T represents the number of pilot symbols in OFDM. f All pilot symbols are the same, c R The t-th column vector is c R,t t=1,2,…,T f c R,tThis represents the HRIS receive phase vector on the t-th pilot symbol. c R,t The i-th element is [c R,t ] i , [c R,t ] i i = 1, ..., M R This represents the receive phase of the i-th element of HRIS on the t-th pilot symbol, |[c R,t ] i |=1, |·| is the modulo operator; c B The dimension is N B ×T f c B The t-th column vector is c B,t c B,t This represents the received phase vector of the base station on the t-th pilot symbol. c B,t The i-th element is [c B,t ] i , [c B,t ] i i = 1, ..., N B This represents the received phase of the i-th antenna of the base station on the t-th pilot symbol, |[c B,t ] i |=1.

[0085] As mentioned above, the dimension of s is N×T. f The element in the nth row and tth column of s is s t [n], s t [n] represents the signal transmitted on the nth subcarrier of the t-th pilot symbol. P represents the average transmit power of the 3D user, n = 1, 2, ..., N; ε R ε B The dimension is N×T f , ε R and ε B All contain variance of μ 2 Zero-mean circularly symmetric independent and identically distributed Gaussian elements, ε R The element in the nth row and tth column is ε R,t [n],ε R,t [n] represents the additive white Gaussian noise at the HRIS on the nth subcarrier of the t-th pilot symbol, ε B The element in the nth row and tth column is ε B,t [n],ε B,t [n] represents the additive white Gaussian noise at the base station on the nth subcarrier of the t-th pilot symbol, ε R,t [n]、ε B,t The variance of [n] is μ2 ; θ represents the cascade angle, b r (θ), b c (θ) represents the guide vector of HRIS in the X and Z axes of the local coordinate system constructed with HRIS, b r (θ) mth x The elements are b c (θ) mth z The elements are The dimension of W is M R ×T f The t-th column vector of W is γ t γ t This represents the reflection phase vector of HRIS on the t-th pilot symbol. γ t The i-th element is [γ t ] i , [γ t ] i i = 1, ..., M R Represents the reflection phase of the i-th element of HRIS on the t-th pilot symbol, |[γ t ] i |=1.

[0086] Step 2: Apply the root-finding MUSIC algorithm to the received signal of HRIS to obtain a coarse estimate of the channel delay between the 3D user and HRIS; then use the coarse estimate of the channel delay between the 3D user and HRIS to eliminate the delay term in the received signal of HRIS, and then sum over all subcarriers of OFDM to obtain the vector form of the received signal of HRIS; next, based on the vector form of the received signal of HRIS, construct a maximum likelihood optimization problem to solve the AOA of HRIS when HRIS receives the signal transmitted by the 3D user, and then solve it to obtain a coarse estimate of the AOA of HRIS when HRIS receives the signal transmitted by the 3D user.

[0087] Furthermore, the delay-free received signal of HRIS, obtained by eliminating the delay term in the received signal of HRIS using a coarse estimate of the channel delay between the 3D user and HRIS, is expressed as follows: in, The time delay τ between the 3D user and the HRIS channel represents the time delay of the channel. UR The rough estimate, Substitution From T represents f A vector of all 1s; representing the vector form of the received signal from HRIS as... in, The maximum likelihood optimization problem can be described as follows: The coarse estimate of the AOA of HRIS when it receives signals transmitted by 3D users is expressed as: in,

[0088] Step 3: Based on the coarse estimate of the channel delay between the 3D user and HRIS and the coarse estimate of HRIS's AOA when HRIS receives the signal transmitted by the 3D user, obtain the received signal with known angle and time delay of HRIS; then, based on the received signal with known angle and time delay of HRIS, obtain the coarse estimate of the channel gain between the 3D user and HRIS.

[0089] Furthermore, the received signal with known angle and time delay of HRIS is expressed as:

[0090] in, Substitution From Substitution From Channel gain ρ of the channel between the 3D user and HRIS UR The rough estimate is expressed as in, Q represents R The false rebellion.

[0091] Step 4: Apply the root-finding MUSIC algorithm to the received signal from the base station to obtain coarse estimates of the channel delay between the 3D user and the base station, as well as coarse estimates of the cascaded channel delays between the 3D user and HRIS, and between HRIS and the base station. Then, construct a delay propagation matrix based on the two coarse delay estimates. Next, use the delay propagation matrix to eliminate the delay term in the received signal from the base station, obtaining the delay-free received signal from the base station. Then, according to the pilot symbols of the first and second halves of all OFDM pilot symbols, divide the two row vectors of the delay-free received signal from the base station into two parts respectively. Finally, based on the first part of the first row vector of the delay-free received signal from the base station, construct a solution for the delay term received by the base station from the 3D user. The problem involves a two-dimensional search for the base station's AOA when the user transmits a signal, followed by a coarse estimate of the base station's AOA when the base station receives a signal transmitted by the 3D user. Then, based on the latter part of the second row vector of the base station's delay-free received signal, a two-dimensional search for the cascading angle is constructed, and a coarse estimate of the cascading angle is obtained. This leads to a coarse estimate of the HRIS's AOD when the base station receives a signal reflected from the HRIS. Finally, based on the first part of the second row vector of the base station's delay-free received signal, a two-dimensional search for the base station's AOA when the base station receives a signal reflected from the HRIS is constructed, and a coarse estimate of the base station's AOA when the base station receives a signal reflected from the HRIS is obtained.

[0092] Furthermore, the delay-based manifold matrix is ​​represented as... in, The time delay τ between the 3D user and the base station represents the channel delay. UB The rough estimate, The time delay τ represents the concatenated channel between the 3D user and HRIS, and between HRIS and the base station. URB The rough estimate, Substitute them separately From The base station's delay-free received signal is represented as in, The number of pilot symbols in the first half of the OFDM is T1, and the number of pilot symbols in the second half is T2. The base station receives the signal with zero delay. The first and second row vectors are represented as follows: and Will Split into two parts and Will It is also divided into two parts, namely and

[0093]

[0094] The two-dimensional search problem for the AOA of a base station when it receives signals transmitted by a 3D user is described as follows: The coarse estimate of the base station's AOA when it receives signals transmitted by a 3D user is expressed as: in, c B The submatrix formed by the first T1 columns, The two-dimensional search problem for solving cascade angles is described as follows: The coarse estimate of the cascade angle is expressed as: The coarse estimate of the AOD of HRIS when the base station receives the signal reflected by HRIS is expressed as: azimuth for The pitch angle is for in, c B The submatrix formed by the last T2 columns,

[0095]

[0096] W2 represents the submatrix formed by the last T2 columns of W.

[0097] and Corresponding representation azimuth and elevation angles and Corresponding representation The azimuth and elevation angles; the two-dimensional search problem for the base station's AOA when the base station receives the signal reflected from HRIS is described as follows: The coarse estimate of the base station's AOA when the base station receives the signal reflected from HRIS is expressed as:

[0098] in, Substitution From W1 represents the submatrix formed by the first T1 columns of W.

[0099]

[0100] Step 5: Based on the coarse estimates of the channel delay between the 3D user and the base station, the coarse estimates of the cascaded channel delay between the 3D user and HRIS and between HRIS and the base station, the coarse estimates of the base station's AOA when the base station receives the signal transmitted by the 3D user, the coarse estimates of the cascade angle, and the coarse estimates of the base station's AOA when the base station receives the signal reflected by HRIS, obtain the received signal with known angle and time delay of the base station; then, based on the received signal with known angle and time delay of the base station, obtain the coarse estimates of the channel gain between the 3D user and the base station, as well as the coarse estimates of the channel gain of the cascaded channel between the 3D user and HRIS and between HRIS and the base station.

[0101] Furthermore, the received signal with known base station angle and time delay is represented as...

[0102] Where, diag(ρ UB ,ρ URB ) represents finding the diagonal matrix. The channel gain ρ of the channel between the 3D user and the base station UB The rough estimate is expressed as Channel gain ρ of the cascaded channels between 3D users and HRIS, and between HRIS and base station URB The rough estimate is expressed as

[0103] in, Corresponding representation The first column vector, the second column vector, Corresponding representation The first column vector, the second column vector,

[0104] Step 6: Since using a two-dimensional search will increase the transmission power and the estimation accuracy may tend to saturate, the maximum likelihood (ML) estimator is used to take the coarse estimates obtained in Step 2 and Step 3 as initial values ​​and perform joint optimization to obtain the corresponding fine estimates. Similarly, the maximum likelihood (ML) estimator is used to take the coarse estimates obtained in Step 4 and Step 5 as initial values ​​and perform joint optimization to obtain the corresponding fine estimates.

[0105] In this embodiment, the specific process of step 6 is as follows: Let η R express Let η B express

[0106]

[0107] in, Indicates taking the real part, This indicates taking the imaginary part; then using the Nelder-Mead algorithm in the maximum likelihood (ML) estimator, for η... R Joint optimization is performed, and η is used in the optimization process. R The rough estimates of each parameter are used as initial values ​​to solve for η. R Detailed estimate Similarly for η B Joint optimization is performed, and η is used in the optimization process. B The rough estimates of each parameter are used as initial values ​​to solve for η. B Detailed estimate in, |||| F This is the F-norm operator.

[0108] Step 7: Based on the detailed estimates obtained in Step 6, obtain the angles between the communication links between the base station and HRIS, and between HRIS and the 3D user; the angles between the communication links between the 3D user and the base station, and between HRIS and the base station; and the angles between the communication links between the 3D user and the base station, and between HRIS and the 3D user; then, based on the three angles and the geometric relationships between the 3D user, HRIS, and base station, obtain the estimated distances between the 3D user and the base station, and between HRIS and the base station; finally, based on the known location of the base station, the estimated distances between the 3D user and the base station, and between HRIS and the base station, obtain the estimated unknown locations of HRIS and the 3D user.

[0109] Furthermore, the angles between the communication links between the base station and HRIS and between HRIS and 3D users, the angles between the communication links between the 3D user and the base station and between HRIS and the base station, and the angles between the communication links between the 3D user and the base station and between HRIS and the 3D user are respectively represented as ψ0, ψ1, and ψ2. ψ2=π-ψ1-ψ2, Represents the direction vector. Used to refer to Corresponding to θ UR θ BR θ UB θ RB Detailed estimates, azimuth for The pitch angle is for The corresponding fine estimate of θ azimuth and elevation angles Corresponding to azimuth and elevation angles for azimuth angle, for The parameters in for The parameters in Corresponding representation The azimuth and elevation angles; the distance d between the 3D user and the base station. UB The estimated value is expressed as The distance d between HRIS and base station RB The estimated value is expressed as in, Represents τ UB Detailed estimates, Represents τURB Detailed estimates, and for The parameters in; the unknown location p of HRIS R The detailed estimate is expressed as The unknown location of the 3D user p U The detailed estimate is expressed as

[0110] In the above, the coordinate axes of the global coordinate system constructed with the base station and the local coordinate system constructed with HRIS are aligned, and the two maintain consistency.

[0111] To further illustrate the feasibility and effectiveness of the method of the present invention, simulation experiments were conducted on the method of the present invention.

[0112] Consider an outdoor far-field positioning scenario, such as Figure 1 As shown, the carrier frequency f is set. c =2.8GHz, Δf=120kHz, c=3×10 8 m / s, N = 200, T f =400, σ=0.8, M x =M z =15,

[0113] N x =N z =5, the base station is located at p B =[0,0,0] T Meters, HRIS is located in p R = [-1.3; 2.5; 4.25] T Meters, 3D users are located in p U =[1,6,1.75] T Meters. Monte Carlo count: 1000.

[0114] Figure 2 This diagram illustrates the variation of the RMSE of the coarse and fine estimates of various time delays obtained using the method of this invention in a simulation experiment as a function of the average transmit power of the 3D user. Figure 3 θ obtained using the method of this invention in simulation experiments UR A schematic diagram showing the variation of the RMSE of the coarse and fine estimates of azimuth and elevation angles with the average transmit power of the 3D user. Figure 4 θ obtained using the method of this invention in simulation experiments UB A schematic diagram showing the variation of the RMSE of the coarse and fine estimates of azimuth and elevation angles with the average transmit power of the 3D user. Figure 5 θ obtained using the method of this invention in simulation experiments RBA schematic diagram showing the variation of the RMSE of the coarse and fine estimates of azimuth and elevation angles with the average transmit power of the 3D user. Figure 6 θ obtained using the method of this invention in simulation experiments BR A schematic diagram showing how the RMSE of the coarse and fine estimates of the azimuth and elevation angles varies with the average transmit power of the 3D user. Figure 7 This is a schematic diagram showing the variation of the RMSE of the coarse and fine estimates of the unknown location of HRIS and the unknown location of 3D users obtained using the method of this invention in a simulation experiment, as a function of the average transmit power of the 3D user.

[0115] Figures 2 to 7 middle These are all rough estimates. All are detailed estimates.

[0116] from Figures 2 to 6 As can be seen, when the average transmit power of 3D users is low, some parameters cannot be estimated due to the low signal-to-noise ratio. Furthermore, the accuracy of the 2D search is limited by the grid size, and tends to saturate as the average transmit power of 3D users increases. However, the refined parameters become increasingly accurate with the increase of the average transmit power of 3D users, and the accuracy also improves significantly. However, τ... UR Because the 3D user is relatively close to the HRIS location, the channel gain of the channel between the 3D user and the HRIS is an order of magnitude higher than that of other channels, therefore τ UR The accuracy of the coarse estimate is not significantly improved compared to the fine estimate.

[0117] from Figure 7 As can be seen, the higher the average transmission power of 3D users, the more accurate the estimated location. The refined parameters compared with the rough estimate show a significant improvement in positioning performance.

Claims

1. A hybrid reconfigurable intelligent metasurface-assisted 3D user positioning method, characterized in that... This method is applied to an uplink wireless communication far-field positioning system. The system includes a base station with multiple antennas and a single radio frequency chain, an HRIS (High-Resolution Indicator) equipped with a single radio frequency chain, and a 3D user with a single antenna. The 3D position of the base station is known, while the 3D positions of the HRIS and the 3D user are unknown. The base station is an area array. The transmission mode of the wireless communication far-field positioning system is OFDM. The 3D user transmits signals, the HRIS receives a portion of the transmitted signals, and the remaining signals are reflected back to the base station. The base station receives both the transmitted signals from the 3D user and the reflected signals from the HRIS. The method includes the following steps: Step 1: Obtain the received signal from HRIS and the received signal from the base station; In step 1, the received signal Y of HRIS R Represented as The base station received the signal Y B Represented as Where, ρ UR ρ represents the channel gain of the channel between the 3D user and the HRIS. UB ρ represents the channel gain of the channel between the 3D user and the base station. URB The channel gain represents the cascaded channel between the 3D user and HRIS, and between HRIS and the base station; σ represents the reflection coefficient of HRIS; τ UR τ represents the channel delay between the 3D user and HRIS. UB τ represents the channel delay between the 3D user and the base station. URB d(τ) represents the time delay of the cascaded channels between the 3D user and HRIS, and between HRIS and the base station. UR ) represents τ UR The guiding vector, d(τ) UB ) represents τ UB The guiding vector, d(τ) URB ) represents τ URB The guiding vector, θ UR This indicates the AOA (Area of ​​Interest) of HRIS when it receives a signal transmitted by a 3D user, θ. UB θ represents the base station's AOA when it receives a signal transmitted by a 3D user. RB This indicates the base station's AOA (Area of ​​Interest) when it receives the signal reflected from HRIS. R (θ UR ) represents the steering vector at HRIS when HRIS receives the signal transmitted by the 3D user, a B (θ UB ) represents the steering vector at the base station when it receives a signal transmitted by a 3D user. B (θ RB ) represents the steering vector at the base station when the base station receives the signal reflected from HRIS, c R c represents the HRIS receive phase matrix. B Let s represent the received phase matrix of the base station, s represent the transmitted signal matrix, and ε represent the received phase matrix of the base station. R Let ε represent the additive white Gaussian noise matrix at HRIS. B This represents the additive white Gaussian noise matrix at the base station, and ⊙ is the Hadamard product operator. θ BR This indicates the AOD of HRIS when the base station receives the signal reflected by HRIS, a R (θ BR ) represents the steering vector at HRIS when the base station receives the signal reflected by HRIS, and W represents the reflection phase matrix of HRIS; Step 2: Apply the root-finding MUSIC algorithm to the received signal of HRIS to obtain a coarse estimate of the channel delay between the 3D user and HRIS; then use the coarse estimate of the channel delay between the 3D user and HRIS to eliminate the delay term in the received signal of HRIS; then sum over all subcarriers of OFDM to obtain the vector form of the received signal of HRIS; next, based on the vector form of the received signal of HRIS, construct a maximum likelihood optimization problem to solve the AOA of HRIS when HRIS receives the signal transmitted by the 3D user, and then solve it to obtain a coarse estimate of the AOA of HRIS when HRIS receives the signal transmitted by the 3D user. Step 3: Based on the coarse estimate of the channel delay between the 3D user and HRIS and the coarse estimate of the AOA of HRIS when HRIS receives the signal transmitted by the 3D user, obtain the received signal with known angle and time delay of HRIS; then, based on the received signal with known angle and time delay of HRIS, obtain the coarse estimate of the channel gain between the 3D user and HRIS. Step 4: Apply the root-finding MUSIC algorithm to the received signal from the base station to obtain coarse estimates of the channel delay between the 3D user and the base station, as well as coarse estimates of the cascaded channel delays between the 3D user and HRIS, and between HRIS and the base station. Then, construct a delay propagation matrix based on the two coarse delay estimates. Next, use the delay propagation matrix to eliminate the delay term in the received signal from the base station, obtaining the delay-free received signal from the base station. Then, according to the pilot symbols of the first and second halves of all OFDM pilot symbols, divide the two row vectors of the delay-free received signal from the base station into two parts respectively. Finally, based on the first part of the first row vector of the delay-free received signal from the base station, construct a solution for the delay term received by the base station from the 3D user. This involves a two-dimensional search problem for the base station's AOA when the user transmits a signal, followed by a coarse estimate of the base station's AOA when the base station receives a signal transmitted by the 3D user. Then, based on the latter part of the second row vector of the base station's delay-free received signal, a two-dimensional search problem for the cascading angle is constructed, and a coarse estimate of the cascading angle is obtained. This leads to a coarse estimate of the HRIS's AOD when the base station receives a signal reflected from the HRIS. Finally, based on the first part of the second row vector of the base station's delay-free received signal, a two-dimensional search problem for the base station's AOA when the base station receives a signal reflected from the HRIS is constructed, and a coarse estimate of the base station's AOA when the base station receives a signal reflected from the HRIS is obtained. Step 5: Based on the coarse estimates of the channel delay between the 3D user and the base station, the coarse estimates of the cascaded channel delay between the 3D user and HRIS and between HRIS and the base station, the coarse estimates of the base station's AOA when the base station receives the signal transmitted by the 3D user, the coarse estimates of the cascaded angle, and the coarse estimates of the base station's AOA when the base station receives the signal reflected by HRIS, obtain the received signal with known angle and time delay of the base station; then, based on the received signal with known angle and time delay of the base station, obtain the coarse estimates of the channel gain between the 3D user and the base station, as well as the coarse estimates of the channel gain of the cascaded channel between the 3D user and HRIS and between HRIS and the base station. Step 6: Using the maximum likelihood estimator, the coarse estimates obtained in Step 2 and Step 3 are used as initial values ​​for joint optimization to obtain the corresponding fine estimates; similarly, the maximum likelihood estimator is used, the coarse estimates obtained in Step 4 and Step 5 are used as initial values ​​for joint optimization to obtain the corresponding fine estimates. Step 7: Based on the detailed estimates obtained in Step 6, obtain the angles between the communication links between the base station and HRIS, and between HRIS and the 3D user; the angles between the communication links between the 3D user and the base station, and between HRIS and the base station; and the angles between the communication links between the 3D user and the base station, and between HRIS and the 3D user; then, based on the three angles and the geometric relationships between the 3D user, HRIS, and base station, obtain the estimated distances between the 3D user and the base station, and between HRIS and the base station; finally, based on the known location of the base station, the estimated distances between the 3D user and the base station, and between HRIS and the base station, obtain the estimated unknown locations of HRIS and the 3D user.

2. The hybrid reconfigurable intelligent metasurface-assisted 3D user positioning method according to claim 1, characterized in that... τ UR =(d UR ) / c+Δ R , τ UB =(d UB ) / c+Δ B , τ URB =(d UR +d RB ) / c+Δ B d UR Indicates the distance between the 3D user and HRIS. d UB Indicates the distance between the 3D user and the base station. d RB This indicates the distance between the HRIS and the base station. p U p represents the unknown location of the 3D user. R p represents the unknown location of HRIS. B Let c represent the known location of the base station, Δ represent the signal propagation speed, and Δ represent the signal propagation speed. R Indicates the clock skew present in HRIS, Δ B This indicates the clock offset present at the base station; τ UR τ UB τ URB All use τ arb When referring to someone, there are: e represents the natural base, j represents the imaginary number, Δf represents the subcarrier spacing, and N represents the number of subcarriers in OFDM. Represents θ UR azimuth angle, Represents θ UR pitch angle, R represents a rotation matrix of dimension 3×3, R = R γ (z)R β (y)R α (x), R α (x), R β (y), R γ (z) represents the rotation matrix of HRIS around the X, Y, and Z axes of the local coordinate system constructed with HRIS. α, β, and γ represent the rotation angles of HRIS around the X, Y, and Z axes of a local coordinate system constructed using HRIS, respectively. U -p R ]1,[p U -p R ]2,[p U -p R ]3 corresponds to p U -p R The first element, the second element, and the third element; For θ UB azimuth angle, For θ UB pitch angle, [p U -p B ]1,[p U -p B ]2,[p U -p B ]3 corresponds to p U -p B The first element, the second element, and the third element; For θ RB azimuth angle, For θ RB pitch angle, [p R -p B ]1,[p R -p B ]2,[p R -p B ]3 corresponds to p R -p B The first element, the second element, and the third element; For θ BR azimuth angle, For θ BR pitch angle, [p B -p R ]1,[p B -p R ]2,[p B -p R ]3 corresponds to p B -p R The first element, the second element, and the third element; Let a be the symbol for the Krock inner product. r (θ UR ), a c (θ UR The corresponding vector represents the guide vector of HRIS in the X and Z axes of the local coordinate system constructed by HRIS when HRIS receives the signal transmitted by the 3D user. r (θ UR The mth x The elements are d represents the spacing between HRIS components, λ represents the wavelength, and a c (θ UR The mth z The elements are m x =1,2,…,M x m z =1,2,…,M z M x M z The corresponding numbers represent the number of HRIS components along the X and Z axes in the local coordinate system constructed using HRIS. The total number of HRIS components is M. R M R =M x M z ; a r (θ UB ), a c (θ UB The corresponding vector represents the guidance vector of the base station in the X and Z axes of the global coordinate system constructed with the base station when the base station receives the signal transmitted by the 3D user. r (θ UB The nth x The elements are a c (θ UB The nth z The elements are n x =1,2,…,N x n z =1,2,…,N z N x N z The corresponding numbers represent the number of antennas of the base station along the X and Z axes in the global coordinate system constructed with the base station. The number of antennas of the base station is N. B N B =N x N z ; a r (θ RB ), a c (θ RB The corresponding vector represents the guidance vector of the base station in the X and Z axes of the global coordinate system constructed with the base station when the base station receives the signal reflected by HRIS. r (θ RB The nth x The elements are a c (θ RB The nth z The elements are a r (θ BR ), a c (θ BR The corresponding vector represents the steering vector of HRIS in the X and Z axes of the local coordinate system constructed with HRIS when the base station receives the signal reflected by HRIS. r (θ BR The mth x The elements are a c (θ BR The mth z The elements are c R The dimension is M R ×T f T f T represents the number of pilot symbols in OFDM. f All pilot symbols are identical, c R The t-th column vector is c R,t t=1,2,…,T f c R,t c represents the HRIS receive phase vector on the t-th pilot symbol. R,t The i-th element is [c R,t ] i , [c R,t ] i i = 1, ..., M R This represents the receive phase of the i-th element of HRIS on the t-th pilot symbol, |[c R,t ] i |=1;c B The dimension is N B ×T f c B The t-th column vector is c B,t c B,t c represents the received phase vector of the base station on the t-th pilot symbol. B,t The i-th element is [c B,t ] i , [c B,t ] i i = 1, ..., N B This represents the received phase of the i-th antenna of the base station on the t-th pilot symbol, |[c B,t ] i |=1; The dimension of s is N×T f The element in the nth row and tth column of s is s t [n], s t [n] represents the signal transmitted on the nth subcarrier of the t-th pilot symbol. P represents the average transmit power of the 3D user, n = 1, 2, ..., N; ε R ε B The dimension is N×T f , ε R and ε B All contain variance of μ 2 Zero-mean circularly symmetric independent and identically distributed Gaussian elements, ε R The element in the nth row and tth column is ε R,t [n],ε R,t [n] represents the additive white Gaussian noise at the HRIS on the nth subcarrier of the t-th pilot symbol, ε B The element in the nth row and tth column is ε B,t [n],ε B,t [n] represents the additive white Gaussian noise at the base station on the nth subcarrier of the t-th pilot symbol, ε R,t [n]、ε B,t The variance of [n] is μ 2 ; θ represents the cascade angle, b r (θ), b c (θ) represents the guide vector of HRIS in the X and Z axes of the local coordinate system constructed with HRIS, b r (θ) mth x The elements are b c (θ) mth z The elements are The dimension of W is M R ×T f The t-th column vector of W is γ t γ t γ represents the reflection phase vector of HRIS on the t-th pilot symbol. t The i-th element is [γ t ] i , [γ t ] i i = 1, ..., M R Represents the reflection phase of the i-th element of HRIS on the t-th pilot symbol, |[γ t ] i |=1.

3. The hybrid reconfigurable intelligent metasurface-assisted 3D user positioning method according to claim 2, characterized in that... In step 2, the delay-free received signal of HRIS, obtained by eliminating the delay term in the received signal of HRIS using a coarse estimate of the channel delay between the 3D user and HRIS, is represented as follows: in, The time delay τ between the 3D user and the HRIS channel represents the time delay of the channel. UR The rough estimate, T represents f A vector of all 1s; representing the vector form of the received signal from HRIS as... in, The maximum likelihood optimization problem can be described as follows: The coarse estimate of the AOA of HRIS when it receives signals transmitted by 3D users is expressed as: in, 4. The hybrid reconfigurable intelligent metasurface-assisted 3D user positioning method according to claim 3, characterized in that... In step 3, the received signal with known HRIS angle and time delay is represented as... in, Channel gain ρ of the channel between the 3D user and HRIS UR The rough estimate is expressed as in, Q represents R The false rebellion.

5. The hybrid reconfigurable intelligent metasurface-assisted 3D user positioning method according to claim 4, characterized in that... In step 4, the delay manifold matrix is ​​represented as follows: in, The time delay τ between the 3D user and the base station represents the channel delay. UB The rough estimate, The time delay τ represents the concatenated channel between the 3D user and HRIS, and between HRIS and the base station. URB A rough estimate; the base station's delay-free received signal is expressed as... The number of pilot symbols in the first half of the OFDM is T1, and the number of pilot symbols in the second half is T2. The base station receives the signal with zero delay. The first and second row vectors are represented as follows: and Will Split into two parts and Will It is also divided into two parts, namely and The two-dimensional search problem for the AOA of a base station when it receives signals transmitted by a 3D user is described as follows: The coarse estimate of the base station's AOA when it receives signals transmitted by a 3D user is expressed as: in, c B The submatrix formed by the first T1 columns, The two-dimensional search problem for solving cascade angles is described as follows: The coarse estimate of the cascade angle is expressed as: The coarse estimate of the AOD of HRIS when the base station receives the signal reflected by HRIS is expressed as: azimuth for The pitch angle is for in, c B The submatrix formed by the last T2 columns of W, where W2 represents the submatrix formed by the last T2 columns of W. and Corresponding representation azimuth and elevation angles and Corresponding representation The azimuth and elevation angles; the two-dimensional search problem for the base station's AOA when the base station receives the signal reflected from HRIS is described as follows: The coarse estimate of the base station's AOA when the base station receives the signal reflected from HRIS is expressed as: Where W1 represents the submatrix formed by the first T1 columns of W.

6. The hybrid reconfigurable intelligent metasurface-assisted 3D user positioning method according to claim 5, characterized in that... In step 5, the received signal with known base station angle and time delay is represented as... Where, diag(ρ UB ,ρ URB ) represents finding the diagonal matrix. The channel gain ρ of the channel between the 3D user and the base station UB The rough estimate is expressed as Channel gain ρ of the cascaded channels between 3D users and HRIS, and between HRIS and base station URB The rough estimate is expressed as in, Corresponding representation The first column vector, the second column vector, Corresponding representation The first column vector, the second column vector, 7. The hybrid reconfigurable intelligent metasurface-assisted 3D user positioning method according to claim 6, characterized in that... The specific process of step 6 is as follows: Let η R express Let η B express in, Indicates taking the real part, This indicates taking the imaginary part; then using the maximum likelihood estimator, for η... R Joint optimization is performed, and η is used in the optimization process. R The rough estimates of each parameter are used as initial values ​​to solve for η. R Detailed estimate Similarly for η B Joint optimization is performed, and η is used in the optimization process. B The rough estimates of each parameter are used as initial values ​​to solve for η. B Detailed estimate in, || || F This is the F-norm operator.

8. The hybrid reconfigurable intelligent metasurface-assisted 3D user positioning method according to claim 7, characterized in that... In step 7, the angles between the communication links between the base station and HRIS and between HRIS and 3D users, the angles between the communication links between the 3D user and the base station and between HRIS and the base station, and the angles between the communication links between the 3D user and the base station and between HRIS and the 3D user are represented as ψ0, ψ1, and ψ2, respectively. ψ2=π-ψ1-ψ2, Represents the direction vector. Used to refer to Corresponding to θ UR θ BR θ UB θ RB Detailed estimates, azimuth for The pitch angle is for The corresponding fine estimate of θ azimuth and elevation angles Corresponding to azimuth and elevation angles for azimuth angle, Corresponding representation The azimuth and elevation angles; the distance d between the 3D user and the base station. UB The estimated value is expressed as The distance d between HRIS and base station RB The estimated value is expressed as in, Represents τ UB Detailed estimates, Represents τ URB Detailed estimates; the unknown location p of HRIS R The detailed estimate is expressed as The unknown location of the 3D user p U The detailed estimate is expressed as

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