3D user positioning method assisted by hybrid reconfigurable intelligent metasurface

Abstract

The invention discloses a hybrid reconfigurable intelligent metasurface-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, an OFDM transmission mode is adopted, and the method relates to the acquisition of receiving signals of the HRIS and the base station, and the positioning of the HRIS and the single-antenna 3D user is realized. A root MUSIC algorithm and a maximum likelihood estimator are adopted to carry out coarse estimation and fine estimation of channel time delay and angle, and finally the positions of the 3D user and the HRIS are determined through a geometrical relationship; the method has the advantages that 3D user positioning can be achieved under the condition that the HRIS position and the state parameters are unknown, the HRIS position and the state parameters are estimated at the same time, and the positioning precision is high.

Description

Technical Field

[0001] The present invention belongs to the field of wireless positioning, and relates to a 3D user positioning technology, and in particular to a 3D user (UE) positioning method assisted by a hybrid reconfigurable intelligent supersurface (HRIS). Background Art

[0002] The latest research evaluation points out that RIS, as an emerging technology, has shown broad application prospects in the field of positioning and sensing. RIS technology intelligently adjusts the propagation of electromagnetic waves in space, assists in building an intelligent and controllable wireless electromagnetic environment, and provides a new paradigm for the development of mobile communications. As a passive technology, RIS adjusts the electromagnetic parameters (such as phase, amplitude, etc.) of the reflected signal by controlling the working state of each component, superimposing them on each other in the wireless space to achieve beamforming, interference suppression and other signal control effects. In the field of positioning and sensing, RIS technology can not only enhance signals, but also be used to assist positioning and perception, provide physical layer secure communications and wireless energy transmission, etc.

[0003] Hybrid Reconfigurable Intelligent Metasurface (HRIS) is a new type of active component-free surface. Different from traditional passive RIS and RIS that combines passive and active receiving antennas, each component of HRIS can be flexibly adjusted to achieve reflection and reception functions at the same time. The development of HRIS technology provides new possibilities for the application of RIS technology, especially in scenarios that require simultaneous processing of signal reflection and reception.

[0004] In most user positioning and synchronization studies, it is usually based on an assumption that the configuration state of the RIS (including position and state parameters) is known in advance. This is because the RIS contains many complex electronic components, which greatly increase the risk of damage during movement and handling. Therefore, in practical applications, it is common practice to pre-arrange the position and state of the RIS. However, this assumption limits the application of RIS technology in dynamic environments, because it is more flexible and challenging to achieve user positioning in the case of unknown RIS position and state parameters. Therefore, studying how to achieve user positioning in the case of unknown RIS position and state parameters is of great significance to 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 intelligent metasurface-assisted 3D user positioning method, which can realize 3D user positioning when the HRIS position and state parameters are unknown, and estimate the HRIS position and state parameters at the same time with high positioning accuracy.

[0006] The technical solution adopted by the present invention to solve the above technical problems is: 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 has 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 wireless communication far-field positioning system adopts OFDM transmission mode, the 3D user transmits a signal, the HRIS receives part of the signal transmitted by the 3D user, the remaining part of the signal is reflected by the HRIS to the base station, and the base station receives the signal transmitted by the 3D user and the signal reflected by the HRIS; the method comprises the following steps:

[0007] Step 1: Obtain the receiving signal of HRIS and the receiving signal of the base station;

[0008] Step 2: The root-finding MUSIC algorithm is used for the received signal of HRIS to obtain a rough estimate of the delay of the channel between the 3D user and HRIS; then the rough estimate of the delay of the channel between the 3D user and HRIS is used to eliminate the delay term in the received signal of HRIS, and then all subcarriers of OFDM are summed to obtain the vector form received signal of HRIS; then, based on the vector form received signal of HRIS, a maximum likelihood optimization problem is constructed to solve the AOA of HRIS when HRIS receives the signal transmitted by the 3D user, and then a rough estimate of the AOA of HRIS is obtained by solving the problem;

[0009] Step 3: According to the rough estimate of the time delay of the channel between the 3D user and the HRIS and the rough estimate of the AOA of the HRIS when the HRIS receives the signal transmitted by the 3D user, a received signal of the HRIS with known angle and time delay is obtained; then, according to the received signal of the HRIS with known angle and time delay, a rough estimate of the channel gain of the channel between the 3D user and the HRIS is obtained;

[0010] Step 4: Use the root-finding MUSIC algorithm on the received signal of the base station to obtain a rough estimate of the delay of the channel between the 3D user and the base station, as well as a rough estimate of the delay of the cascaded channel between the 3D user and the HRIS and the HRIS and the base station; then construct a delay popularity matrix based on the two rough estimates of the delay; then use the delay popularity matrix to eliminate the delay term in the received signal of the base station to obtain the base station's delay-free received signal; then divide the two row vectors of the base station's delay-free received signal into the front and back parts according to the pilot symbols of the front and back halves of all OFDM pilot symbols; then construct a solution to the base station receiving the 3D signal based on the front part of the first row vector of the base station's delay-free received signal. A two-dimensional search problem for the AOA of the base station when the user transmits a signal, and then a rough estimate of the AOA of the base station when the base station receives the signal transmitted by the 3D user is obtained by solving the problem; and according to the rear part of the second row vector of the delay-free received signal of the base station, a two-dimensional search problem for solving the cascade angle is constructed, and then a rough estimate of the cascade angle is obtained by solving the problem, and then a rough estimate of the AOD of the HRIS is obtained when the base station receives the signal reflected by the HRIS; according to the front part of the second row vector of the delay-free received signal of the base station, a two-dimensional search problem for solving the AOA of the base station when the base station receives the signal reflected by the HRIS is constructed, and then a rough estimate of the AOA of the base station when the base station receives the signal reflected by the HRIS is obtained by solving the problem;

[0011] Step 5: According to the rough estimation value of the time delay of the channel between the 3D user and the base station, the rough estimation value of the time delay of the cascaded channel between the 3D user and the HRIS and the HRIS and the base station, the rough estimation value of the AOA of the base station when the base station receives the signal transmitted by the 3D user, the rough estimation value of the cascade angle, and the rough estimation value of the AOA of the base station when the base station receives the signal reflected by the HRIS, a received signal of the base station with known angle and time delay is obtained; then, according to the received signal with known angle and time delay of the base station, a rough estimation value of the channel gain of the channel between the 3D user and the base station, and a rough estimation value of the channel gain of the cascaded channel between the 3D user and the HRIS and the HRIS and the base station are obtained;

[0012] Step 6: Use the maximum likelihood estimator, take the rough estimate values ​​obtained in step 2 and step 3 as the initial value, perform joint optimization, and obtain the corresponding fine estimate value; similarly, use the maximum likelihood estimator, take the rough estimate values ​​obtained in step 4 and step 5 as the initial value, perform joint optimization, and obtain the corresponding fine estimate value;

[0013] Step 7: According to the detailed estimation value obtained in step 6, obtain the angle between the communication link between the base station and the HRIS and the communication link between the HRIS and the 3D user, the angle between the communication link between the 3D user and the base station and the communication link between the HRIS and the base station, and the angle between the communication link between the 3D user and the base station and the communication link between the HRIS and the 3D user; then, according to the three angles and the geometric relationship between the 3D user, the HRIS and the base station, obtain the estimated value of the distance between the 3D user and the base station, and the estimated value of the distance between the HRIS and the base station; then, according to the known position of the base station and the estimated value of the distance between the 3D user and the base station and the estimated value of the distance between the HRIS and the base station, obtain the estimated value of the unknown position of the HRIS and the unknown position of the 3D user.

[0014] In step 1, the HRIS receiving signal Y R Expressed as The base station's received signal Y B Expressed as Among them, ρ UR represents the channel gain of the channel between the 3D user and HRIS, ρ UB represents the channel gain of the channel between the 3D user and the base station, ρ URB represents the channel gain of the cascaded channel between the 3D user and HRIS and the HRIS and the base station, σ represents the reflection coefficient of HRIS, τ UR represents the delay of the channel between the 3D user and HRIS, τ UB represents the delay of the channel between the 3D user and the base station, τ URB represents the delay of the cascaded channel between the 3D user and HRIS and between HRIS and the base station, d(τ UR ) represents τ UR The steering vector, d(τ UB ) represents τ UB The steering vector, d(τ URB ) represents τ URB The steering vector, θ UR represents the AOA of HRIS when HRIS receives the signal transmitted by the 3D user, θ UB represents the AOA of the base station when it receives the signal transmitted by the 3D user, θ RB Indicates the AOA of the base station when the base station receives the signal reflected by HRIS, a R (θ UR ) represents the steering vector at the HRIS when the HRIS receives the signal transmitted by the 3D user, a B (θ UB ) represents the steering vector at the base station when the base station receives the signal transmitted by the 3D user, a B (θ RB) represents the steering vector at the base station when the base station receives the signal reflected by HRIS, c R represents the receiving phase matrix of HRIS, c B represents the receiving phase matrix of the base station, s represents the transmitted signal matrix, ε R represents the additive white Gaussian noise matrix at HRIS, ε B represents the additive white Gaussian noise matrix at the base station, ⊙ is the Hadamard product operator symbol, θ BR Indicates the AOD of HRIS when the base station receives the signal reflected by HRIS, a R (θ BR ) represents the steering vector at the HRIS when the base station receives the signal reflected by the HRIS, and W represents the reflection phase matrix of the 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 For 3D

[0016] The distance between the user and the HRIS, d UB Indicates the distance between the 3D user and the base station, d RB Indicates the distance between HRIS and the base station, p U represents the unknown position of the 3D user, p R Indicates the unknown position of HRIS, p B represents the known location of the base station, c represents the signal propagation speed, Δ R Indicates the clock offset of HRIS, Δ B Indicates the clock offset of the base station; τ UR , τ UB , τ URB τ arb When referring to: e represents the natural base, j represents the imaginary number, Δf represents the subcarrier spacing, and N represents the number of subcarriers that OFDM has;

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

[0018]

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

[0020] [p U -p R ] 1 ,[p U -p R ] 2 ,[p U -p R ] 3 Corresponding to p U -p R The first, second, and third elements of ; is θ UB The azimuth of is θ UB The pitch angle,

[0021]

[0022] [p U -p B ] 1 ,[p U -p B ] 2 ,[p U -p B ] 3 Corresponding to p U -p B The first, second, and third elements of ; is θ RB The azimuth of is θ RB The pitch angle,

[0023]

[0024] [p R -p B ] 1 ,[pR -p B ] 2 ,[p R -p B ] 3 Corresponding to p R -p B The first, second, and third elements of ; is θ BR The azimuth of is θ BR The pitch angle,

[0025]

[0026] [p B -p R ] 1 ,[p B -p R ] 2 ,[p B -p R ] 3 Corresponding to p B -p R The first, second, and third elements of ;

[0027] is the symbol of Crocker inner product, a r (θ UR ), a c (θ UR ) corresponds to the steering vector of the HRIS in the X-axis and Z-axis directions of the local coordinate system constructed by the HRIS when the HRIS receives the signal transmitted by the 3D user, a r (θ UR ) x The elements are

[0028] d represents the spacing between HRIS elements, λ represents the wavelength, and a c (θ UR ) z The elements are m x =1,2,…,M x , m z =1,2,…,M z , M x 、M z It corresponds to the number of HRIS components in the X-axis and Z-axis directions of the local coordinate system constructed by HRIS. The number of HRIS components is M R , M R =Mx M z ;

[0029] a r (θ UB ), a c (θ UB ) corresponds to the steering vector of the base station in the X-axis and Z-axis directions of the global coordinate system constructed by the base station when the base station receives the signal transmitted by the 3D user, a r (θ UB ) x The elements are a c (θ UB ) z The elements are n x =1,2,…,N x , n z =1,2,…,N z , N x 、N z The corresponding number of antennas of the base station in the X-axis and Z-axis directions of the global coordinate system constructed by the base station is N. B , N B =N x N z ; a r (θ RB ), a c (θ RB ) corresponds to the steering vector of the base station in the X-axis and Z-axis directions of the global coordinate system constructed by the base station when the base station receives the signal reflected by the HRIS, a r (θ RB ) x The elements are

[0030] a c (θ RB ) z The elements are [a c (θ RB )] nz , a r (θ BR ), a c (θ BR ) corresponds to the steering vector of the HRIS in the X-axis and Z-axis directions of the local coordinate system constructed by the HRIS when the base station receives the signal reflected by the HRIS, a r (θ BR ) x The elements are

[0031] a c (θ BR ) z The elements are

[0032] c R The dimension is M R ×T f , T f Indicates the number of pilot symbols in OFDM, T f The pilot symbols are the same, c R The tth column vector of R,t , t=1,2,…,T f , c R,t represents the received phase vector of HRIS at the tth pilot symbol, c R,t The i-th element of is [c R,t ] i ,[c R,t ] i ,i=1,...,M R represents the received phase of the ith element of HRIS on the tth pilot symbol, |[c R,t ] i |=1;c B The dimension is N B ×T f , c B The tth column vector of B,t , c B,t represents the base station's received phase vector at the tth pilot symbol, c B,t The i-th element of is [c B,t ] i ,

[0033] [c B,t ] i ,i=1,…,N B represents the receiving phase of the ith antenna of the base station on the tth 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 tth pilot symbol, P represents the average transmission power of 3D users, n=1,2,…,N; ε R , ε BThe dimension is N×T f , ε R and ε B All of them contain variance μ 2 The zero-mean circularly symmetric independent and identically distributed Gaussian element, ε R The element in the nth row and tth column of R,t [n], ε R,t [n] represents the additive white Gaussian noise at the HRIS on the nth subcarrier of the tth pilot symbol, ε B The element in the nth row and tth column of B,t [n], ε B,t [n] represents the additive white Gaussian noise at the base station on the nth subcarrier of the tth 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) corresponds to the steering vector of HRIS in the X-axis and Z-axis directions of the local coordinate system constructed by HRIS, b r (θ) the mth x The elements are b c (θ) the mth z The elements are The dimension of W is M R ×T f , the tth column vector of W is γ t , γ t represents the reflected phase vector of HRIS on the tth pilot symbol, γ t The i-th element of is [γ t ] i , [γ t ] i ,i=1,...,M R represents the reflection phase of the ith element of HRIS on the tth 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 by using the rough estimated value of the delay of the channel between the 3D user and HRIS is expressed as

[0036] in, represents the delay τ of the channel between the 3D user and HRIS UR A rough estimate of Indicates T fdimensional all-1 vector; the vector form of HRIS received signal is represented as

[0037] in, The maximum likelihood optimization problem is described as: The rough estimate of the AOA of the HRIS when it receives the signal transmitted by the 3D user is expressed as in,

[0038] In step 3, the received signal with known angle and delay of HRIS is expressed as

[0039] in, The channel gain ρ of the channel between the 3D user and HRIS UR A rough estimate of in, Indicates Q R The pseudo-inverse.

[0040] In step 4, the delay popularity matrix is ​​expressed as in, represents the delay τ of the channel between the 3D user and the base station UB A rough estimate of represents the delay τ of the cascaded channel between the 3D user and HRIS and between HRIS and the base station URB The rough estimate of the base station's delay-free received signal is expressed as The number of pilot symbols in the first half of OFDM is T 1 , the number of pilot symbols in the second half is T 2 ,and The base station receives the signal without delay The first and second row vectors of and Will Split into two parts and Will It is also divided into two parts, namely and

[0041]

[0042] The two-dimensional search problem of solving the AOA of the base station when the base station receives the signal transmitted by the 3D user is described as: The rough estimate of the AOA of the base station when the base station receives the signal transmitted by the 3D user is expressed as

[0043] in, Indicates c B The front T 1 The submatrix consisting of columns, The two-dimensional search problem for solving the cascade angle is described as:

[0044] A rough estimate of the cascade angle is expressed as The rough 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, Indicates c B After the T 2 The submatrix composed of columns, W 2 Indicates the post-T of W 2 The submatrix consisting of columns, and Corresponding representation The azimuth and elevation angles, and Corresponding representation The azimuth and elevation angles of the base station are described as follows:

[0045] The rough estimate of the AOA of the base station when the base station receives the signal reflected by HRIS is expressed as

[0046] Among them, W 1 Indicates the front T of W 1 The sub-matrix consists of columns.

[0047] In step 5, the received signal of the base station with known angle and delay is expressed as

[0048] Among them, diag(ρ UB ,ρ URB ) means finding the diagonal matrix, The channel gain ρ of the channel between the 3D user and the base station UB A rough estimate of The channel gain ρ of the concatenated channel between the 3D user and HRIS and the HRIS and the base station URB A rough estimate of in, Corresponding representation The first column vector and the second column vector of Corresponding representation The first column vector and the second column vector of

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

[0050]

[0051] in, represents the real part, Indicates taking the imaginary part; then using the maximum likelihood estimator, η R Perform joint optimization, and during the optimization process, η R The rough estimated values ​​of the parameters in are used as the initial values ​​to solve and obtain η R A detailed estimate of Similarly for η B Perform joint optimization, and during the optimization process, η B The rough estimated values ​​of the parameters in are used as the initial values ​​to solve and obtain η B A detailed estimate of in,

[0052] ,

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

[0054] In step 7, the angles between the communication link between the base station and the HRIS and the communication link between the HRIS and the 3D user, the angles between the communication link between the 3D user and the base station and the communication link between the HRIS and the base station, and the angles between the communication link between the 3D user and the base station and the communication link between the HRIS and the 3D user are expressed as ψ 0 , 1 , 2 , ψ 2 =π-ψ 1 -ψ 2 ,

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

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

[0057] In the far field, the method of the present invention utilizes the single radio frequency chain phase design of the base station and the HRIS, receives a signal through the base station, estimates the angle of arrival (AOA) of the base station, the angle of arrival (AOA) and the angle of departure (AOD) of the HRIS, and the channel delay parameters, obtains more accurate parameter estimation through refinement, and then uses the estimated channel parameters to locate the positions of the HRIS and the 3D user through the geometric relationship between the base station, the HRIS, and the 3D user. In the present invention, the position and state parameters of the HRIS can be estimated without knowing the state and position of the HRIS, thereby combining the 3D user positioning and synchronization. It can be seen from the simulation experiment that the root mean square error (RMSE) of the angle and the position are very small, which shows that the accuracy is quite high, and the problem of arranging the RIS position in advance during RIS-assisted positioning is solved.

[0058] In the present invention, in order to avoid complex high-dimensional search problems, a two-dimensional search is used to obtain a rough estimate. Due to the limitations of the two-dimensional search, the rough estimate is globally refined to obtain a more accurate fine estimate. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 A scene diagram for joint synchronous positioning of HRIS and 3D user in the present invention;

[0060] Figure 2 It is a schematic diagram showing the variation of the RMSE of the rough estimation value and the fine estimation value of each time delay obtained by using the method of the present invention in the simulation experiment with the average transmission power of the 3D user;

[0061] Figure 3 is the θ obtained by using the method of the present invention in the simulation experiment UR A schematic diagram showing how the RMSE of the azimuth and elevation angles of the coarse estimate and the fine estimate vary with the average transmit power of the 3D user;

[0062] Figure 4 is the θ obtained by using the method of the present invention in the simulation experiment UB A schematic diagram showing how the RMSE of the azimuth and elevation angles of the coarse estimate and the fine estimate vary with the average transmit power of the 3D user;

[0063] Figure 5 is the θ obtained by using the method of the present invention in the simulation experiment RB A schematic diagram showing how the RMSE of the azimuth and elevation angles of the coarse estimate and the fine estimate vary with the average transmit power of the 3D user;

[0064] Figure 6 is the θ obtained by using the method of the present invention in the simulation experiment BR A schematic diagram showing how the RMSE of the azimuth and elevation angles of the coarse estimate and the fine estimate vary with the average transmit power of the 3D user;

[0065] Figure 7 It is a schematic diagram showing the variation of RMSE of the rough estimation and fine estimation values ​​of the unknown position of HRIS and the unknown position of 3D user obtained by using the method of the present invention in a simulation experiment with the average transmission power of the 3D user. DETAILED DESCRIPTION

[0066] The present invention is further described in detail below with reference to the accompanying drawings.

[0067] The present invention proposes a hybrid reconfigurable intelligent metasurface-assisted 3D user positioning method, which is applied to an uplink wireless communication far-field positioning system, wherein 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 single-antenna 3D user (UE), the base station is a planar array, the base stations are vertically distributed on the ground, the wireless communication far-field positioning system adopts OFDM transmission mode, the 3D user transmits a signal, the HRIS receives part of the signal transmitted by the 3D user, the remaining part of the signal is reflected by the HRIS to the base station, and the base station receives the signal transmitted by the 3D user and the signal reflected by the HRIS; the method comprises the following steps:

[0068] Step 1: Obtain the reception signal of the HRIS and the reception signal of the base station.

[0069] Furthermore, the HRIS receiving signal Y R Expressed as The base station's received signal Y B Expressed as

[0070] Among them, ρ UR represents the channel gain of the channel between the 3D user and HRIS, ρ UB represents the channel gain of the channel between the 3D user and the base station, ρ URB represents the channel gain of the cascaded channel between the 3D user and HRIS and the HRIS and the base station, σ represents the reflection coefficient of HRIS, τ UR represents the delay of the channel between the 3D user and HRIS, τ UB represents the delay of the channel between the 3D user and the base station, τ URB represents the delay of the cascaded channel between the 3D user and HRIS and between HRIS and the base station, d(τ UR ) represents τ UR The steering vector, d(τ UB ) represents τ UB The steering vector, d(τ URB ) represents τ URB The steering vector, θ UR represents the AOA of HRIS when HRIS receives the signal transmitted by the 3D user, θ UR is the channel parameter of the communication link between the 3D user and HRIS, θ UB represents the AOA of the base station when it receives the signal transmitted by the 3D user, θ UB is the channel parameter of the communication link between the 3D user and the base station, θ RB represents the AOA of the base station when the base station receives the signal reflected by HRIS, θ RBis the channel parameter of the communication link between HRIS and the base station, a R (θ UR ) represents the steering vector at the HRIS when the HRIS receives the signal transmitted by the 3D user, a B (θ UB ) represents the steering vector at the base station when the base station receives the signal transmitted by the 3D user, a B (θ RB ) represents the steering vector at the base station when the base station receives the signal reflected by HRIS. The superscript “T” represents the transposition operation of the vector or matrix. R represents the receiving phase matrix of HRIS, c B represents the receiving phase matrix of the base station, s represents the transmitted signal matrix, ε R represents the additive white Gaussian noise matrix at HRIS, ε B represents the additive white Gaussian noise matrix at the base station, ⊙ is the Hadamard product operator symbol,

[0071] θ BR represents the AOD of HRIS when the base station receives the signal reflected by HRIS, θ BR It is also the channel parameter of the communication link between HRIS and the base station, a R (θ BR ) represents the steering vector at the HRIS when the base station receives the signal reflected by the HRIS, and W represents the reflection phase matrix of the HRIS.

[0072] As mentioned 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 the HRIS, d UB Indicates the distance between the 3D user and the base station, d RB Indicates the distance between HRIS and the base station, p U represents the unknown position of the 3D user, p R Indicates the unknown position of HRIS, p B represents the known location of the base station, p U 、p R 、p B They are all 3-dimensional, c represents the signal propagation speed, which is the speed of light, ΔR Indicates the clock offset of HRIS, Δ B Indicates the clock offset of the base station. is the definition symbol, ||·|| is the binary norm operator symbol; τ UR , τ UB , τ URB τ arb When referring to: e represents a natural base, e=2.71…, j is an imaginary number, Δf represents a subcarrier spacing, and N represents the number of subcarriers of OFDM.

[0073] Above, Represents θ UR The azimuth of Represents θ UR The pitch angle,

[0074]

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

[0076] [p U-p B ] 1 ,[p U -p B ] 2 ,[p U -p B ] 3 Corresponding to p U -p B The first, second, and third elements of ; is θ RB The azimuth of is θ RB The pitch angle,

[0077] [p R -p B ] 1 ,[p R -p B ] 2 ,[p R -p B ] 3 Corresponding to p R -p B The first, second, and third elements of ; is θ BR The azimuth of is θ BR The pitch angle,

[0078] [p B -p R ] 1 ,[p B -p R ] 2 ,[p B -p R ] 3 Corresponding to p B -p R The first, second, and third elements of .

[0079] Above, is the symbol of Crocker inner product, a r (θ UR ), a c (θ UR ) corresponds to the steering vector of the HRIS in the X-axis and Z-axis directions of the local coordinate system constructed by the HRIS when the HRIS receives the signal transmitted by the 3D user, a r (θ UR ) x The elements are

[0080] d represents the spacing between the elements of HRIS, λ represents wavelength, a c (θ UR ) z The elements are m x =1,2,…,M x , m z =1,2,…,M z , M x 、M z It corresponds to the number of HRIS components in the X-axis and Z-axis directions of the local coordinate system constructed by HRIS. The number of HRIS components is M R , M R =M x M z ;

[0081] a r (θ UB ), a c (θ UB ) corresponds to the steering vector of the base station in the X-axis and Z-axis directions of the global coordinate system constructed by the base station when the base station receives the signal transmitted by the 3D user, a r (θ UB ) x The elements are a c (θ UB ) z The elements are n x =1,2,…,N x , n z =1,2,…,N z , N x 、N z The corresponding number of antennas of the base station in the X-axis and Z-axis directions of the global coordinate system constructed by the base station is N. B , N B =N x N z ; a r (θ RB ), a c (θ RB ) corresponds to the steering vector of the base station in the X-axis and Z-axis directions of the global coordinate system constructed by the base station when the base station receives the signal reflected by the HRIS, a r (θ RB ) x The elements are

[0082] a c (θ RB ) z The elements are a r (θ BR ), a c (θ BR ) corresponds to the steering vector of the HRIS in the X-axis and Z-axis directions of the local coordinate system constructed by the HRIS when the base station receives the signal reflected by the HRIS, a r (θ BR ) x The elements are

[0083] a c (θ BR ) z The elements are

[0084] Above, c R The dimension is M R ×T f , T f Indicates the number of pilot symbols in OFDM, T f The pilot symbols are the same, c R The tth column vector of R,t , t=1,2,…,T f , c R,t represents the received phase vector of HRIS on the tth pilot symbol, c R,t The i-th element of is [c R,t ] i ,[c R,t ] i ,i=1,...,M R represents the received phase of the ith element of HRIS on the tth pilot symbol, |[c R,t ] i |=1, |·| is the modulus symbol; c B The dimension is N B ×T f , c B The tth column vector of B,t , c B,t represents the received phase vector of the base station on the tth pilot symbol, c B,t The i-th element of is [c B,t ]i ,[c B,t ] i ,i=1,...,N B represents the receiving phase of the ith antenna of the base station on the tth pilot symbol, |[c B,t ] i |=1.

[0085] 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 tth pilot symbol, P represents the average transmission power of 3D users, n=1,2,…,N; ε R , ε B The dimension is N×T f , ε R and ε B All of them contain variance μ 2 The zero-mean circularly symmetric independent and identically distributed Gaussian element, ε R The element in the nth row and tth column of R,t [n], ε R,t [n] represents the additive white Gaussian noise at the HRIS on the nth subcarrier of the tth pilot symbol, ε B The element in the nth row and tth column of B,t [n], ε B,t [n] represents the additive white Gaussian noise at the base station on the nth subcarrier of the tth 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) corresponds to the steering vector of HRIS in the X-axis and Z-axis directions of the local coordinate system constructed by HRIS, b r (θ) the mth x The elements are b c (θ) the mth z The elements are The dimension of W is M R ×T f , the tth column vector of W is γ t , γ t represents the reflected phase vector of HRIS on the t-th pilot symbol, γ t The i-th element of is [γ t ] i , [γ t ]i ,i=1,...,M R represents the reflection phase of the ith element of HRIS on the tth pilot symbol, |[γ t ] i |=1.

[0086] Step 2: The root-finding MUSIC algorithm is used for the received signal of HRIS to obtain a rough estimate of the delay of the channel between the 3D user and HRIS; then the rough estimate of the delay of the channel between the 3D user and HRIS is used to eliminate the delay term in the received signal of HRIS, and then all subcarriers of OFDM are summed to obtain the vector form of the received signal of HRIS; then according to the vector form of the received signal of HRIS, the maximum likelihood optimization problem of solving the AOA of HRIS when HRIS receives the signal transmitted by the 3D user is constructed, and then the rough estimate of the AOA of HRIS when HRIS receives the signal transmitted by the 3D user is obtained by solving it.

[0087] Furthermore, the delay-free received signal of HRIS obtained by eliminating the delay term in the received signal of HRIS by using the rough estimated value of the delay of the channel between the 3D user and HRIS is expressed as in, represents the delay τ of the channel between the 3D user and HRIS UR A rough estimate of Substitution Get Indicates T f dimensional all-1 vector; the vector form of HRIS received signal is represented as in, The maximum likelihood optimization problem is described as: The rough estimate of the AOA of the HRIS when it receives the signal transmitted by the 3D user is expressed as in,

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

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

[0090] in, Substitution Get Substitution Get The channel gain ρ of the channel between the 3D user and HRIS UR A rough estimate of in, Indicates Q R The pseudo-inverse.

[0091] Step 4: Use the root-finding MUSIC algorithm on the received signal of the base station to obtain a rough estimate of the delay of the channel between the 3D user and the base station, as well as a rough estimate of the delay of the cascaded channel between the 3D user and the HRIS and the HRIS and the base station; then construct a delay popularity matrix based on the two rough estimates of the delay; then use the delay popularity matrix to eliminate the delay term in the received signal of the base station to obtain the base station's delay-free received signal; then divide the two row vectors of the base station's delay-free received signal into the front and back parts according to the pilot symbols of the front and back halves of all OFDM pilot symbols; then construct a solution to the base station receiving the 3D signal based on the front part of the first row vector of the base station's delay-free received signal. A two-dimensional search problem for the AOA of the base station when the user transmits a signal is constructed, and then a rough estimate of the AOA of the base station is obtained by solving the problem; and according to the rear part of the second row vector of the base station's delay-free received signal, a two-dimensional search problem for solving the cascade angle is constructed, and then a rough estimate of the cascade angle is obtained by solving the problem, and then a rough estimate of the AOD of the HRIS is obtained when the base station receives the signal reflected by the HRIS; according to the front part of the second row vector of the base station's delay-free received signal, a two-dimensional search problem for solving the AOA of the base station when the base station receives the signal reflected by the HRIS is constructed, and then a rough estimate of the AOA of the base station when the base station receives the signal reflected by the HRIS is obtained by solving the problem.

[0092] Furthermore, the delay popularity matrix is ​​expressed as in, represents the delay τ of the channel between the 3D user and the base station UB A rough estimate of represents the delay τ of the cascaded channel between the 3D user and HRIS and between HRIS and the base station URB A rough estimate of Substitute Get The delay-free received signal of the base station is expressed as in, The number of pilot symbols in the first half of OFDM is T 1 , the number of pilot symbols in the second half is T 2 ,and The base station receives the signal without delay The first and second row vectors of and Will Split into two parts and Will It is also divided into two parts, namely and

[0093]

[0094] The two-dimensional search problem of solving the AOA of the base station when the base station receives the signal transmitted by the 3D user is described as: The rough estimate of the AOA of the base station when the base station receives the signal transmitted by the 3D user is expressed as in, Indicates c B The front T 1 The submatrix consisting of columns, The two-dimensional search problem for solving the cascade angle is described as: A rough estimate of the cascade angle is expressed as The rough 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, Indicates c B After the T 2 The submatrix consisting of columns,

[0095]

[0096] W 2 Indicates the post-T of W 2 The submatrix consisting of columns,

[0097] and Corresponding representation The azimuth and elevation angles, and Corresponding representation The azimuth and elevation angles of the base station are described as follows: The rough estimate of the AOA of the base station when the base station receives the signal reflected by HRIS is expressed as

[0098] in, Substitution Get W 1 Indicates the front T of W 1 The submatrix consisting of columns,

[0099]

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

[0101] Furthermore, the received signal with known angle and delay of the base station is expressed as

[0102] Among them, diag(ρ UB ,ρ URB ) means finding the diagonal matrix, The channel gain ρ of the channel between the 3D user and the base station UB A rough estimate of The channel gain ρ of the concatenated channel between the 3D user and HRIS and the HRIS and the base station URB A rough estimate of

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

[0104] Step 6: Since the use of two-dimensional search will increase the transmission power and the estimation accuracy may tend to saturation, the maximum likelihood (ML) estimator is used, and the coarse estimation values ​​obtained in steps 2 and 3 are used as initial values ​​for joint optimization to obtain the corresponding fine estimation values; similarly, the maximum likelihood (ML) estimator is used, and the coarse estimation values ​​obtained in steps 4 and 5 are used as initial values ​​for joint optimization to obtain the corresponding fine estimation values.

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

[0106]

[0107] in, represents the real part, Represents the imaginary part; then the Nelder-Mead algorithm in the maximum likelihood (ML) estimator is used to calculate η R Perform joint optimization, and during the optimization process, η R The rough estimated values ​​of the parameters in are used as the initial values ​​to solve and obtain η R A detailed estimate of Similarly for η B Perform joint optimization, and during the optimization process, η B The rough estimated values ​​of the parameters in are used as the initial values ​​to solve and obtain η B A detailed estimate of in, |||| F is the F-norm operator symbol.

[0108] Step 7: According to the detailed estimation value obtained in step 6, obtain the angle between the communication link between the base station and the HRIS and the communication link between the HRIS and the 3D user, the angle between the communication link between the 3D user and the base station and the communication link between the HRIS and the base station, and the angle between the communication link between the 3D user and the base station and the communication link between the HRIS and the 3D user; then, according to the three angles and the geometric relationship between the 3D user, the HRIS and the base station, obtain the estimated value of the distance between the 3D user and the base station, and the estimated value of the distance between the HRIS and the base station; then, according to the known position of the base station and the estimated value of the distance between the 3D user and the base station and the estimated value of the distance between the HRIS and the base station, obtain the estimated value of the unknown position of the HRIS and the unknown position of the 3D user.

[0109] Furthermore, the angles between the communication link between the base station and the HRIS and the communication link between the HRIS and the 3D user, the angles between the communication link between the 3D user and the base station and the communication link between the HRIS and the base station, and the angles between the communication link between the 3D user and the base station and the communication link between the HRIS and the 3D user are expressed as ψ 0 , 1 , 2 , ψ 2 =π-ψ 1 -ψ 2, represents the direction vector, Used to refer to Corresponding to θ UR ,θ BR ,θ UB ,θ RB A detailed estimate of Azimuth for The pitch angle is for Corresponding to the fine estimate of θ Azimuth and elevation angles, Corresponding to Azimuth and elevation angles, for The azimuth of for The parameters in for The parameters in Corresponding representation The azimuth and elevation angles of the 3D user and the base station. UB The estimated value of is expressed as The distance d between HRIS and the base station RB The estimated value of is expressed as in, Represents τ UB A detailed estimate of Represents τ URB A detailed estimate of and for Parameters in; the unknown position p of HRIS R The detailed estimate of The unknown position of the 3D user p U The detailed estimate of

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

[0111] In order to further illustrate the feasibility and effectiveness of the method of the present invention, a simulation experiment was carried out on the method of the present invention.

[0112] Consider an outdoor far-field positioning scenario, such as Figure 1 As shown, set the carrier frequency f 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 m, HRIS is located at p R =[-1.3; 2.5; 4.25] T meters, 3D users are located at p U =[1,6,1.75] T The number of Monte Carlo simulations is 1000.

[0114] Figure 2 It is a schematic diagram showing the variation of the RMSE of the rough estimation value and the fine estimation value of each delay obtained by using the method of the present invention in the simulation experiment with the average transmission power of the 3D user. Figure 3 is the θ obtained by using the method of the present invention in the simulation experiment UR Schematic diagram showing the RMSE of the azimuth and elevation angles of the coarse and fine estimates of the 3D user as the average transmit power changes. Figure 4 is the θ obtained by using the method of the present invention in the simulation experiment UB Schematic diagram showing the RMSE of the azimuth and elevation angles of the coarse and fine estimates of the 3D user as the average transmit power changes. Figure 5 is the θ obtained by using the method of the present invention in the simulation experiment RB Schematic diagram showing the RMSE of the azimuth and elevation angles of the coarse and fine estimates of the 3D user as the average transmit power changes. Figure 6 is the θ obtained by using the method of the present invention in the simulation experiment BR Schematic diagram of the RMSE of the azimuth and elevation angles of the coarse estimate and the fine estimate as the average transmit power of the 3D user changes. Figure 7 It is a schematic diagram showing the variation of RMSE of the rough estimation and fine estimation values ​​of the unknown position of HRIS and the unknown position of 3D user obtained by using the method of the present invention in a simulation experiment with the average transmission power of the 3D user.

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

[0116] from Figures 2 to 6It can be seen from the figure that when the average transmission power of 3D users is small, some parameters cannot be estimated because the signal-to-noise ratio is too low. In addition, since the accuracy of the two-dimensional search is limited by the size of the grid, it will tend to saturate as the average transmission power of 3D users increases. However, the refined parameters become more and more accurate as the average transmission power of 3D users increases, and the accuracy is also significantly improved. However, τ UR Because the 3D user is close to the HRIS, the channel gain between the 3D user and the HRIS is one order of magnitude higher than the other channel gains, so τ UR The coarse estimate of is not significantly more accurate than the fine estimate.

[0117] from Figure 7 It can be seen that the greater the average transmission power of the 3D user, the more accurate the estimated position is. Compared with the rough estimate, the positioning effect is significantly improved after the refined parameters.

Claims

1. 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, wherein the wireless communication far-field positioning system has 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 wireless communication far-field positioning system adopts OFDM as a transmission mode, the 3D user transmits a signal, the HRIS receives part of the signal transmitted by the 3D user, the remaining part of the signal is reflected by the HRIS to the base station, and the base station receives the signal transmitted by the 3D user and the signal reflected by the HRIS; the method comprises the following steps: Step 1: Obtain the receiving signal of HRIS and the receiving signal of the base station; Step 2: The root-finding MUSIC algorithm is used for the received signal of HRIS to obtain a rough estimate of the delay of the channel between the 3D user and HRIS; then the rough estimate of the delay of the channel between the 3D user and HRIS is used to eliminate the delay term in the received signal of HRIS, and then all subcarriers of OFDM are summed to obtain the vector form received signal of HRIS; then, based on the vector form received signal of HRIS, a maximum likelihood optimization problem is constructed to solve the AOA of HRIS when HRIS receives the signal transmitted by the 3D user, and then a rough estimate of the AOA of HRIS is obtained by solving the problem; Step 3: According to the rough estimate of the time delay of the channel between the 3D user and the HRIS and the rough estimate of the AOA of the HRIS when the HRIS receives the signal transmitted by the 3D user, a received signal of the HRIS with known angle and time delay is obtained; then, according to the received signal of the HRIS with known angle and time delay, a rough estimate of the channel gain of the channel between the 3D user and the HRIS is obtained; Step 4: Use the root-finding MUSIC algorithm on the received signal of the base station to obtain a rough estimate of the delay of the channel between the 3D user and the base station, as well as a rough estimate of the delay of the cascaded channel between the 3D user and the HRIS and the HRIS and the base station; then construct a delay popularity matrix based on the two rough estimates of the delay; then use the delay popularity matrix to eliminate the delay term in the received signal of the base station to obtain the base station's delay-free received signal; then divide the two row vectors of the base station's delay-free received signal into the front and back parts according to the pilot symbols of the front and back halves of all OFDM pilot symbols; then construct a solution to the base station receiving the 3D signal based on the front part of the first row vector of the base station's delay-free received signal. A two-dimensional search problem for the AOA of the base station when the user transmits a signal, and then a rough estimate of the AOA of the base station when the base station receives the signal transmitted by the 3D user is obtained by solving the problem; and according to the rear part of the second row vector of the delay-free received signal of the base station, a two-dimensional search problem for solving the cascade angle is constructed, and then a rough estimate of the cascade angle is obtained by solving the problem, and then a rough estimate of the AOD of the HRIS is obtained when the base station receives the signal reflected by the HRIS; according to the front part of the second row vector of the delay-free received signal of the base station, a two-dimensional search problem for solving the AOA of the base station when the base station receives the signal reflected by the HRIS is constructed, and then a rough estimate of the AOA of the base station when the base station receives the signal reflected by the HRIS is obtained by solving the problem; Step 5: According to the rough estimation value of the time delay of the channel between the 3D user and the base station, the rough estimation value of the time delay of the cascaded channel between the 3D user and the HRIS and the HRIS and the base station, the rough estimation value of the AOA of the base station when the base station receives the signal transmitted by the 3D user, the rough estimation value of the cascade angle, and the rough estimation value of the AOA of the base station when the base station receives the signal reflected by the HRIS, a received signal of the base station with known angle and time delay is obtained; then, according to the received signal with known angle and time delay of the base station, a rough estimation value of the channel gain of the channel between the 3D user and the base station, and a rough estimation value of the channel gain of the cascaded channel between the 3D user and the HRIS and the HRIS and the base station are obtained; Step 6: Use the maximum likelihood estimator, take the rough estimate values ​​obtained in step 2 and step 3 as the initial value, perform joint optimization, and obtain the corresponding fine estimate value; similarly, use the maximum likelihood estimator, take the rough estimate values ​​obtained in step 4 and step 5 as the initial value, perform joint optimization, and obtain the corresponding fine estimate value; Step 7: According to the detailed estimation value obtained in step 6, obtain the angle between the communication link between the base station and the HRIS and the communication link between the HRIS and the 3D user, the angle between the communication link between the 3D user and the base station and the communication link between the HRIS and the base station, and the angle between the communication link between the 3D user and the base station and the communication link between the HRIS and the 3D user; then, according to the three angles and the geometric relationship between the 3D user, the HRIS and the base station, obtain the estimated value of the distance between the 3D user and the base station, and the estimated value of the distance between the HRIS and the base station; then, according to the known position of the base station and the estimated value of the distance between the 3D user and the base station and the estimated value of the distance between the HRIS and the base station, obtain the estimated value of the unknown position of the HRIS and the unknown position of the 3D user.

2. The hybrid reconfigurable intelligent metasurface-assisted 3D user positioning method according to claim 1, characterized in that In step 1, the HRIS receiving signal Y R Expressed as The base station's received signal Y B Expressed as Among them, ρ UR represents the channel gain of the channel between the 3D user and HRIS, ρ UB represents the channel gain of the channel between the 3D user and the base station, ρ URB represents the channel gain of the cascaded channel between the 3D user and HRIS and the HRIS and the base station, σ represents the reflection coefficient of HRIS, τ UR represents the delay of the channel between the 3D user and HRIS, τ UB represents the delay of the channel between the 3D user and the base station, τ URB represents the delay of the cascaded channel between the 3D user and HRIS and between HRIS and the base station, d(τ UR ) represents τ UR The steering vector, d(τ UB ) represents τ UB The steering vector, d(τ URB ) represents τ URB The steering vector, θ UR represents the AOA of HRIS when HRIS receives the signal transmitted by the 3D user, θ UB represents the AOA of the base station when it receives the signal transmitted by the 3D user, θ RB Indicates the AOA of the base station when the base station receives the signal reflected by HRIS, a R (θ UR ) represents the steering vector at the HRIS when the HRIS receives the signal transmitted by the 3D user, a B (θ UB ) represents the steering vector at the base station when the base station receives the signal transmitted by the 3D user, a B (θ RB ) represents the steering vector at the base station when the base station receives the signal reflected by HRIS, c R represents the receiving phase matrix of HRIS, c B represents the receiving phase matrix of the base station, s represents the transmitted signal matrix, ε R represents the additive white Gaussian noise matrix at HRIS, ε B represents the additive white Gaussian noise matrix at the base station, ⊙ is the Hadamard product operator symbol, θ BR Indicates the AOD of HRIS when the base station receives the signal reflected by HRIS, a R (θ BR ) represents the steering vector at the HRIS when the base station receives the signal reflected by the HRIS, and W represents the reflection phase matrix of the HRIS.

3. The hybrid reconfigurable intelligent metasurface-assisted 3D user positioning method according to claim 2 is 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 the HRIS, d UB Indicates the distance between the 3D user and the base station, d RB Indicates the distance between HRIS and the base station, p U represents the unknown position of the 3D user, p R Indicates the unknown position of HRIS, p B represents the known location of the base station, c represents the signal propagation speed, Δ R Indicates the clock offset of HRIS, Δ B Indicates the clock offset of the base station; τ UR , τ UB , τ URB τ arb When referring to: e represents the natural base, j represents the imaginary number, Δf represents the subcarrier spacing, and N represents the number of subcarriers that OFDM has; Represents θ UR The azimuth of Represents θ UR The pitch angle, R represents a rotation matrix with a dimension of 3×3, R=R γ (z)R β (y)R α (x), R α (x), R β (y), R γ (z) corresponds to the rotation matrix representing the rotation of HRIS around the X-axis, Y-axis, and Z-axis of the local coordinate system constructed by HRIS, α, β, and γ represent the rotation angles of HRIS around the X-axis, Y-axis, and Z-axis of the local coordinate system constructed by HRIS. U -p R ]1,[p U -p R ]2,[p U -p R ]3 corresponds to p U -p R The first, second, and third elements of ; is θ UB The azimuth of is θ UB The 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, second, and third elements of ; is θ RB The azimuth of is θ RB The 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, second, and third elements of ; is θ BR The azimuth of is θ BR The 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, second, and third elements of ; is the symbol of Crocker inner product, a r (θ UR ), a c (θ UR ) corresponds to the steering vector of the HRIS in the X-axis and Z-axis directions of the local coordinate system constructed by the HRIS when the HRIS receives the signal transmitted by the 3D user, a r (θ UR ) x The elements are d represents the spacing between HRIS elements, λ represents the wavelength, and a c (θ UR ) z The elements are m x =1,2,…,M x , m z =1,2,…,M z , M x 、M z It corresponds to the number of HRIS components in the X-axis and Z-axis directions of the local coordinate system constructed by HRIS. The number of HRIS components is M R , M R =M x M z ; a r (θ UB ), a c (θ UB ) corresponds to the steering vector of the base station in the X-axis and Z-axis directions of the global coordinate system constructed by the base station when the base station receives the signal transmitted by the 3D user, a r (θ UB ) x The elements are a c (θ UB ) z The elements are n z =1,2,…,N z , N x 、N z The corresponding number of antennas of the base station in the X-axis and Z-axis directions of the global coordinate system constructed by the base station is N. B , N B =N x N z ; a r (θ RB ), a c (θ RB ) corresponds to the steering vector of the base station in the X-axis and Z-axis directions of the global coordinate system constructed by the base station when the base station receives the signal reflected by the HRIS, a r (θ RB ) x The elements are a c (θ RB ) z The elements are a r (θ BR ), a c (θ BR ) corresponds to the steering vector of the HRIS in the X-axis and Z-axis directions of the local coordinate system constructed by the HRIS when the base station receives the signal reflected by the HRIS, a r (θ BR ) x The elements are a c (θ BR ) z The elements are c R The dimension is M R ×T f , T f Indicates the number of pilot symbols in OFDM, T f The pilot symbols are the same, c R The tth column vector of R,t , t=1,2,…,T f , c R,t represents the received phase vector of HRIS at the tth pilot symbol, c R,t The i-th element of is [c R,t ] i ,[c R,t ] i ,i=1,…,M R represents the received phase of the ith element of HRIS on the tth pilot symbol, |[c R,t ] i |=1;c B The dimension is N B ×T f , c B The tth column vector of B,t , c B,t represents the base station's received phase vector at the tth pilot symbol, c B,t The i-th element of is [c B,t ] i ,[c B,t ] i ,i=1,...,N B represents the receiving phase of the ith antenna of the base station on the tth 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 tth pilot symbol, P represents the average transmission power of 3D users, n=1,2,…,N; ε R , ε B The dimension is N×T f , ε R and ε B All of them contain variance μ 2 The zero-mean circularly symmetric independent and identically distributed Gaussian element, ε R The element in the nth row and tth column of R,t [n], ε R,t [n] represents the additive white Gaussian noise at the HRIS on the nth subcarrier of the tth pilot symbol, ε B The element in the nth row and tth column of B,t [n], ε B,t [n] represents the additive white Gaussian noise at the base station on the nth subcarrier of the tth 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) corresponds to the steering vector of HRIS in the X-axis and Z-axis directions of the local coordinate system constructed by HRIS, b r (θ) the mth x The elements are b c (θ) the mth z The elements are The dimension of W is M R ×T f , the tth column vector of W is γ t , γ t represents the reflected phase vector of HRIS on the tth pilot symbol, γ t The i-th element of is [γ t ] i , [γ t ] i ,i=1,…,M R represents the reflection phase of the ith element of HRIS on the tth pilot symbol, |[γ t ] i |=1.

4. The hybrid reconfigurable intelligent metasurface-assisted 3D user positioning method according to claim 3 is 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 by using the rough estimated value of the delay of the channel between the 3D user and HRIS is expressed as in, represents the delay τ of the channel between the 3D user and HRIS UR A rough estimate of Tf Indicates T f dimensional all-1 vector; the vector form of HRIS received signal is represented as in, The maximum likelihood optimization problem is described as: The rough estimate of the AOA of the HRIS when it receives the signal transmitted by the 3D user is expressed as in, 5. The hybrid reconfigurable intelligent metasurface-assisted 3D user positioning method according to claim 4 is characterized in that In step 3, the received signal with known angle and delay of HRIS is expressed as in, The channel gain ρ of the channel between the 3D user and HRIS UR A rough estimate of in, Indicates Q R The pseudo-inverse.

6. The hybrid reconfigurable intelligent metasurface-assisted 3D user positioning method according to claim 5, characterized in that In step 4, the delay popularity matrix is ​​expressed as in, represents the delay τ of the channel between the 3D user and the base station UB A rough estimate of represents the delay τ of the cascaded channel between the 3D user and HRIS and between HRIS and the base station URB The rough estimate of the base station's delay-free received signal is expressed as The number of pilot symbols in the first half of OFDM is T1, the number of pilot symbols in the second half is T2, and The base station receives the signal without delay The first and second row vectors of and Will Split into two parts and Will It is also divided into two parts, namely and The two-dimensional search problem of solving the AOA of the base station when the base station receives the signal transmitted by the 3D user is described as: The rough estimate of the AOA of the base station when the base station receives the signal transmitted by the 3D user is expressed as in, Indicates c B The submatrix consisting of the first T1 columns of The two-dimensional search problem for solving the cascade angle is described as: A rough estimate of the cascade angle is expressed as The rough 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, Indicates c B W2 represents the submatrix composed of the last T2 columns of W, and Corresponding representation The azimuth and elevation angles, and Corresponding representation The azimuth and elevation angles of the base station are described as follows: The rough estimate of the AOA of the base station when the base station receives the signal reflected by HRIS is expressed as Where W1 represents the submatrix consisting of the first T1 columns of W.

7. The hybrid reconfigurable intelligent metasurface-assisted 3D user positioning method according to claim 6, characterized in that In step 5, the received signal of the base station with known angle and delay is expressed as Among them, diag(ρ UB ,ρ URB ) means finding the diagonal matrix, The channel gain ρ of the channel between the 3D user and the base station UB A rough estimate of The channel gain ρ of the concatenated channel between the 3D user and HRIS and the HRIS and the base station URB A rough estimate of in, Corresponding representation The first column vector and the second column vector of Corresponding representation The first column vector and the second column vector of 8. The hybrid reconfigurable intelligent metasurface-assisted 3D user positioning method according to claim 7, characterized in that The specific process of step 6 is: let n R express Let η B express in, represents the real part, Indicates taking the imaginary part; then using the maximum likelihood estimator, η R Perform joint optimization, and during the optimization process, η R The rough estimated values ​​of the parameters in are used as the initial values ​​to solve and obtain η R A detailed estimate of Similarly for η B Perform joint optimization, and during the optimization process, η B The rough estimated values ​​of the parameters in are used as the initial values ​​to solve and obtain η B A detailed estimate of in, |||| F is the F-norm operator symbol.

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

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