A near-field positioning method based on dynamic metamaterial antenna

Abstract

The present application relates to the field of near-field positioning, in particular to a kind of near-field positioning method based on dynamic metamaterial antenna, comprising the following steps: step 1, based on DMA receiving signal;Step 2, based on the MLE positioning algorithm of near-field hypothesis, and establish problem;Step 3: the influence of DMA coefficient on estimation process is discussed, then the design significance is explained;Step 4: by introducing DMA precoding theory, the optimization scheme of matrix Q is obtained;Step 5: an iterative optimization scheme is proposed to approximate the optimal solution;The present application uses a kind of direct estimation method based on incident wavefront curvature to obtain source position estimation, and the influence of DMA coefficient on estimation accuracy is evaluated, and a suboptimal iterative optimization algorithm is proposed without any prior knowledge.Simulation results show that, in the case of high signal-to-noise ratio, the algorithm can quickly approximate the optimal solution.

Description

Technical Field

[0001] This invention relates to the field of near-field positioning, and more specifically, to a near-field positioning method based on a dynamic metamaterial antenna. Background Technology

[0002] Radio positioning applications are expected to see significant enhancement and widespread adoption in sixth-generation (6G) cellular networks. The deployment of large antenna arrays and high-frequency communication will facilitate accurate radio frequency positioning and reduce reliance on reliable positioning via global navigation satellite systems. However, the combination of large antennas and high frequencies means that radio frequency signals may radiate in the near-field region, which means that the traditional far-field-based plane wave assumption no longer holds. Furthermore, implementing arrays with a large number of components using traditional all-digital designs is extremely costly.

[0003] On the other hand, operations in the radiated near field can also enhance positioning capabilities by introducing new degrees of freedom not present in the traditional far field. These are encapsulated in the spherical waves of the received signal, thus enhancing wireless positioning through holographic positioning. Typically, source positioning is based on a two-step positioning algorithm, involving joint estimation of angle of arrival and time of arrival. Such a process requires precise synchronization or the participation of multiple access points, often resulting in suboptimal performance. In the radiated near field, positioning can be achieved by estimating the curvature of arrival (COA), an algorithm that takes advantage of the fact that the received signal is a spherical wave rather than a plane wave. While COA-based positioning is widely used in acoustics or microwave fields, it has only recently been introduced into intelligent radio communications. For example, the Cramér-Rao bound (CRB) for near-field positioning is discussed. A large reconfigurable smart surface (RIS)-assisted positioning scenario is considered, a unified framework is established, and a direct positioning algorithm is used to estimate the performance boundary. A dynamic tracking scheme is discussed, considering several practical tracking and positioning schemes based on array antenna phase difference estimation and the posterior CRB.

[0004] The aforementioned wireless positioning methods all sampled fully connected structures based on all-digital antennas. However, 6G MIMO receivers typically reduce the radio frequency (RF) chain, and antenna structures with reduced RF chains are usually implemented using dedicated analog circuitry, including complex gain filters, vector modulators, phase-shifting networks, and switch-based operations. Summary of the Invention

[0005] The purpose of this invention is to propose a location estimation processing architecture using DMAs, and to design an ad-hoc direct localization method based on COA to obtain the location estimate of the source in this receiving mode. Specifically, unlike all-digital antennas, a DMA antenna is considered to preprocess the received signal to reduce its dimensionality, and how this affects the final MLE estimation result is explained. The process is then described in a manner very similar to precoding in DMA beamforming, which makes it possible to compute the optimal DMA coefficients for localization to improve the quality of the received signal. Furthermore, considering that the optimal method requires prior knowledge of the source location, which is an unknown estimate, an iterative optimization algorithm is proposed to design the DMA coefficients. The joint localization and coefficient design method proposed in this invention is based on internal iterations within the receiver, avoiding frequent remote interactions. Performance comparisons with random and optimal coefficient schemes in simulations verify that, by setting an appropriate number of iterations, the proposed method can approach the optimal solution.

[0006] The specific technical solution adopted in this invention is as follows:

[0007] A near-field localization method based on a dynamic metamaterial antenna includes the following steps:

[0008] Step 1: Receive signals based on DMA;

[0009] Step 2: Develop the MLE localization algorithm based on the near-field assumption and establish the problem;

[0010] Step 3: The impact of the DMA coefficient on the estimation process was discussed, and then the design significance was explained;

[0011] Step 4: By introducing DMA precoding theory, an optimized scheme for matrix Q was obtained;

[0012] Step 5: An iterative optimization scheme is proposed to approximate the optimal solution.

[0013] In this invention, step 1, the process of receiving signals based on DMA, considers a single-user positioning scenario where the base station receives pilot signals from the user and estimates the source location. The base station is a large DMA array containing N receiving antennas. The DMA array contains N... d Row microstrips, each row microstrip contains N e One metamaterial receiving element, i.e., N = N d N e Each row of microstrip has only one RF chain output. The process of signal reception in the i-th row of microstrip is illustrated, where the pilot signal is received as a spherical wave because the user is located within the Fresnel region of the DMA array. An ideal model neglecting synchronization errors is considered; therefore, the signal received by the l-th antenna of the i-th row of microstrip at time t can be expressed as:

[0014]

[0015] Where r i,l (t) represents the received signal, i∈{1,2,…,N} d}, l∈{1,2,…,N e}, a i,l f is the amplitude. p It is the pilot frequency, ω i,l (t) is additive white noise with variance σ, v i,l Represents the signal phase, with Where d i,l t represents the distance between the antenna and the source, and c represents the electromagnetic velocity. For convenience, the time index t will be omitted in the remainder of this invention.

[0016] Define vector and These represent the antenna signal vector and noise vector, respectively. Since each microstrip has only one output, the actual array receive vector is an N vector. d A dimensional vector is represented as:

[0017] y=QH(r+ω), (2)

[0018] in H represents the output vector of all microstrips, and is an N-dimensional diagonal matrix with diagonal elements of 1. h i,l The effect of signal propagation is encapsulated within a microstrip. The response is considered to be frequency-flat, and the frequency response of the metamaterial element conforms to the Lorentz-constrained phase model, i.e.,

[0019]

[0020] Where α i It is the waveguide attenuation coefficient, β i It is the wave number, ρ i,l This indicates the position of the corresponding antenna. (Matrix) The configurable weights of the DMA have structural constraints:

[0021]

[0022] Where q i, l The adjustable response of the corresponding antenna, which also conforms to the Lorentz-constrained phase model, is as follows:

[0023]

[0024] Therefore, by expressing y in scalar form, the general model of the received signal can be rewritten as:

[0025]

[0026] Where y i Let represent the i-th element of y, i.e., the output of the i-th row of microstrip lines. Therefore, the DMA output can be considered as the weighted sum of all received signals in the corresponding row of microstrip lines.

[0027] In this invention, step 2 involves an MLE localization algorithm based on the near-field assumption, and the following problem is established:

[0028] According to the definition of the received signal in formula (2), the phase of the received signal is determined by the corresponding propagation distance, and the phase difference between different antennas is related to the curvature of the spherical wave of the received signal. Therefore, the signal source can be located by processing the received phase. The location of the seismic source can be represented in spherical coordinates, that is, the distance, azimuth, and elevation angle from the seismic source to the base station.

[0029] Set a reference point for the receiving array (usually one of the array's antennas). Define the distance from the source to the reference point, elevation angle, and azimuth angle as follows: As a location marker of the source, and at the same time define This serves as the position marker for the l-th antenna in the i-th row of the microstrip. Based on the triangular relationship between the reference point, the antenna, and the source, we have:

[0030]

[0031]

[0032] From (7) and (8), the correspondence between phase and source location is obtained; however, this is a highly nonlinear expression. Therefore, a possible solution for estimating the source location is through the MLE algorithm, which maximizes the following function:

[0033]

[0034] in The log-likelihood function of the received signal vector is given as follows:

[0035]

[0036]

[0037] Where M is the number of samples used for estimation. It is a guide vector, element in Given by (7) and (8).

[0038] Therefore, for (9), the position estimate is found by constructing a steering vector that maximizes (10). The difference between this invention and previous studies is that the received vector is preprocessed by DMA instead of being directly received by the antenna; therefore, this preprocessing process can be designed to improve the performance of the positioning algorithm.

[0039] The performance of localization algorithms is typically measured by the CRB, which represents the lower bound of the variance of the estimation result and is inversely proportional to the Fisher information matrix (FIM) of the estimated vector. While minimizing the error boundary can yield the best estimate, this is difficult because it involves minimizing the inverse of the FIM.

[0040] Another criterion is to consider maximizing the sum of the signal-to-noise ratios (SNR) of each receiving antenna. Although it is known from (2) that the DMA coefficients affect both the signal and noise vectors, relaxing this problem to consider only the signal gain means considering the following optimization problem to maximize the signal power:

[0041]

[0042] While this relaxation might make the results unreliable at low signal-to-noise ratios, the optimization problem in the above formula is similar to the precoding process discussed in past DMA beamforming studies, so a similar approach can be used to design the DMA coefficients. It also explains, from another perspective, the importance of designing Q for position estimation.

[0043] In this invention, step 3 discusses the impact of DMA coefficients on the estimation process and then explains the design significance. Before introducing the design scheme of DMA coefficients, the impact of DMA coefficients on the MLE process is explained first: DMA coefficients are determined by matrices H and Q, where H represents the fixed attenuation determined by the array structure. Therefore, they will be ignored in the subsequent analysis, and only the adjustable response determined by Q will be considered.

[0044] On the other hand, formula (10) can be rewritten as:

[0045]

[0046] in Let y(t) be the defense matrix. Introducing (2) into (13) and considering (11) simultaneously, we get:

[0047]

[0048] in It is the defense matrix of r(t), an N-dimensional vector.

[0049] Through (14), Q can be regarded as a compression matrix, and the DMA-based MLE process can also be regarded as obtaining position information from the compressed data. Therefore, the design of Q can also be interpreted as reducing the impact of compression on the MLE estimation process, that is, increasing the amount of information in the received signal as discussed in the previous section.

[0050] In this invention, step 4 introduces DMA precoding theory to obtain an optimized scheme for matrix Q; the optimization problem (12) is not easy to solve because each element of matrix Q corresponds to the response q. i,l The Lorentz constraint form in (5) should be used, therefore q i,l The phase and amplitude are coupled. To address this issue, the Lorentz constraint can be relaxed to a phase-weighted constraint with constant amplitude and arbitrary phase:

[0051]

[0052] The feasible set F is a circle of unit radius centered at the origin. First, solve the problem after Q is replaced by F (12), and then use the solution of F to adjust the Lorentz constraint weights by projection.

[0053] Since this invention considers a single-user scenario, problem (12) can be easily evaluated after relaxing the constraints. In fact, the receiving process is similar to the precoding process in DMA beamforming, only in the opposite direction. Therefore, by borrowing from relevant research, the optimal response coefficients can be directly obtained by following the lemma:

[0054] Theorem 1: Let Q * For the optimal solution of (12) under F constraint, Q under structural constraint (5) * Non-zero elements are in

[0055] Proof: Replacing Q with F and rewriting (12) in scalar form to remove structural constraint (5), we have:

[0056]

[0057] In other words, (16) decomposes (12) into N d The sub-problem is to replace r in (1) with a sub-problem. i,l and h in (3) i,l Substituting each subproblem, we have the expression for the i-th subproblem:

[0058]

[0059] in It is the pilot signal sent by the source. Therefore, according to the triangle inequality, the solution to (17) is:

[0060]

[0061] Q.E.D.

[0062] As can be seen, the optimized phase response It consists of two parts: the first part is the phase of each received antenna signal, which means that the optimal coefficient should match the antenna phase profile, and in beamforming, this is interpreted as achieving beam focusing; the other part compensates for the transmission delay in the microstrip given by (3), so that the signals are transmitted synchronously.

[0063] q i,l It does not satisfy the Lorentz form, therefore it is projected onto (5), by The final weights are given. Although this is only an approximation of (12), it retains the properties mentioned in (18) with the addition of a constant phase shift. Numerical results also verify the validity of this result.

[0064] In this invention, step 5 proposes an iterative optimization scheme to approximate the optimal solution.

[0065] Unfortunately, the optimal result in Theorem 1 depends on the source location, which is an unknown quantity to be estimated. To address this, an iterative optimization algorithm is proposed to simultaneously estimate the source location and optimize the DMA coefficients.

[0066] Experiments showed that the algorithm converges with only one iteration under high signal-to-noise ratio conditions, but requires multiple iterations under low signal-to-noise ratio conditions. Therefore, the number of iterations for the algorithm was set.

[0067] It is noted that a similar design approach was used in the design of the RIS coefficients to maximize the sum of SNR at the base station. However, in contrast, the study considered a combination with DMA beam focusing theory, where the design work only occurs on the base station antenna, thus avoiding frequent remote interactions and being easier to implement.

[0068] Compared with existing technologies, this invention has the following advantages: The proposed application of a dynamic metasurface antenna array in near-field positioning within sixth-generation cellular communication utilizes a direct estimation method based on the incident wavefront curvature to obtain source location estimation. The impact of the DMA coefficient on estimation accuracy is evaluated, and a suboptimal iterative optimization algorithm requiring no prior knowledge is proposed. Simulation results show that, under high signal-to-noise ratio conditions, this algorithm can quickly approximate the optimal solution. Attached Figure Description

[0069] Figure 1 This is the iterative optimization algorithm of the present invention.

[0070] Figure 2 This refers to the distortion contrast of various contrast schemes under different signal-to-noise ratios according to the present invention.

[0071] Figure 3 The distortion of the iterative algorithm under different iteration numbers of this invention. Detailed Implementation

[0072] To facilitate understanding and implementation of the present invention by those skilled in the art, the present invention will be further described in detail below with reference to embodiments. It should be understood that the embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0073] Example:

[0074] A near-field localization method based on a dynamic metamaterial antenna aims to obtain source location estimation using a direct estimation method based on the incident wavefront arrival curvature, and evaluates the impact of the DMA coefficient on the estimation accuracy. A suboptimal iterative optimization algorithm that does not require any prior knowledge is proposed.

[0075] The steps of the method are as follows:

[0076] Step 1: The process of receiving signals based on DMA;

[0077] Step 2: Develop the MLE localization algorithm based on the near-field assumption and establish the problem;

[0078] Step 3: The impact of the DMA coefficient on the estimation process was discussed, and then the design significance was explained;

[0079] Step 4: By introducing DMA precoding theory, an optimized scheme for matrix Q was obtained;

[0080] Step 5: An iterative optimization scheme is proposed to approximate the optimal solution.

[0081] In this invention, step 1 involves the process of receiving signals based on DMA:

[0082] The base station receives pilot signals from users and estimates the source location. The base station is defined as a large DMA array containing N receiving antennas. The DMA array structure is as follows: Figure 1 As shown, the array contains N d Row microstrips, each row microstrip contains N e One metamaterial receiving element, i.e., N = N d N eEach row of microstrip has only one RF chain output. The process of signal reception in the i-th row of microstrip is illustrated, where the pilot signal is received as a spherical wave because the user is located within the Fresnel region of the DMA array. An ideal model neglecting synchronization errors is considered; therefore, the signal received by the l-th antenna of the i-th row of microstrip at time t can be expressed as:

[0083]

[0084] Where r i,l (t) represents the received signal, i∈{1,2,…,N} d}, l∈{1,2,…,N e}, a i,l f is the amplitude. p It is the pilot frequency, ω i,l (t) is additive white noise with variance σ, v i,l Represents the signal phase, with Where d i,l t represents the distance between the antenna and the source, and c represents the electromagnetic velocity. For convenience, the time index t will be omitted in the remainder of this invention.

[0085] Define vector and These represent the antenna signal vector and noise vector, respectively. Since each microstrip has only one output, the actual array receive vector is an N vector. d A dimensional vector is represented as:

[0086] y=QH(r+ω), (2)

[0087] in H represents the output vector of all microstrips, and is an N-dimensional diagonal matrix with diagonal elements of 1. h i,l The effect of signal propagation is encapsulated within a microstrip. The response is considered to be frequency-flat, and the frequency response of the metamaterial element conforms to the Lorentz-constrained phase model, i.e.,

[0088]

[0089] Where α i It is the waveguide attenuation coefficient, β i It is the wave number, ρ i,l This indicates the position of the corresponding antenna. (Matrix) The configurable weights of the DMA have structural constraints:

[0090]

[0091] Where q i,l The adjustable response of the corresponding antenna, which also conforms to the Lorentz-constrained phase model, is as follows:

[0092]

[0093] Therefore, by expressing y in scalar form, the general model of the received signal can be rewritten as:

[0094]

[0095] Where y i This represents the i-th element of y, i.e., the output of the i-th row of microstrip lines.

[0096] Therefore, the DMA output can be viewed as the result of a weighted sum of all received signals in the corresponding row microstrip.

[0097] In step 2, the MLE localization algorithm based on the near-field assumption is used, and the problem is established:

[0098] According to the definition of received signal in (2), the phase of the received signal is determined by the corresponding propagation distance, and the phase difference between different antennas is related to the curvature of the spherical wave of the received signal. Therefore, the source can be located by processing the received phase. The location of the seismic source can be represented in spherical coordinates, i.e., the distance, azimuth, and elevation angle from the source to the base station.

[0099] Set a reference point for the receiving array (usually one of the array's antennas). Define the distance from the source to the reference point, elevation angle, and azimuth angle as follows: As a location marker of the source, and at the same time define This serves as the position marker for the l-th antenna in the i-th row of the microstrip. All relative positional relationships are as follows: Figure 3 As shown, based on the triangular relationship between the reference point, antenna, and source, we have:

[0100]

[0101]

[0102] From (7) and (8), the correspondence between phase and source location is obtained; however, this is a highly nonlinear expression. Therefore, a possible solution for estimating the source location is through the MLE algorithm, which maximizes the following function:

[0103]

[0104] in The log-likelihood function of the received signal vector is given as follows:

[0105]

[0106]

[0107] Where M is the number of samples used for estimation. It is a guide vector, element in Given by (7) and (8).

[0108] Therefore, for (9), the position estimate is found by constructing a steering vector that maximizes (10). The difference between this invention and previous studies is that the received vector is preprocessed by DMA instead of being directly received by the antenna; therefore, this preprocessing process can be designed to improve the performance of the positioning algorithm.

[0109] The performance of localization algorithms is typically measured by the CRB, which represents the lower bound of the variance of the estimation result and is inversely proportional to the Fisher information matrix (FIM) of the estimated vector. While minimizing the error boundary can yield the best estimate, this is difficult because it involves minimizing the inverse of the FIM.

[0110] Another criterion is to consider maximizing the sum of the signal-to-noise ratios (SNR) of each receiving antenna. Although it is known from (2) that the DMA coefficients affect both the signal and noise vectors, relaxing this problem to consider only the signal gain means considering the following optimization problem to maximize the signal power:

[0111]

[0112] While this relaxation might make the results unreliable at low signal-to-noise ratios, the optimization problem in the above formula is similar to the precoding process discussed in past DMA beamforming studies, so a similar approach can be used to design the DMA coefficients. It also explains, from another perspective, the importance of designing Q for position estimation.

[0113] In step 3, the impact of the DMA coefficient on the estimation process is discussed, and then the design significance is explained;

[0114] Before introducing the design scheme of the DMA coefficients, we will first explain the impact of the DMA coefficients on the MLE process. The DMA coefficients are determined by matrices H and Q, where H represents the fixed attenuation determined by the array structure. Therefore, they will be ignored in the following analysis, and only the adjustable response determined by Q will be considered.

[0115] On the other hand, formula (10) can be rewritten as:

[0116]

[0117] in Let y(t) be the defense matrix. Introducing (2) into (13) and considering (11) simultaneously, we get:

[0118]

[0119] in It is the defense matrix of r(t), an N-dimensional vector.

[0120] Through (14), Q can be regarded as a compression matrix, and the DMA-based MLE process can also be regarded as obtaining position information from the compressed data. Therefore, the design of Q can also be interpreted as reducing the impact of compression on the MLE estimation process, that is, increasing the amount of information in the received signal as discussed in the previous section.

[0121] In step 4, by introducing DMA precoding theory, an optimized scheme for matrix Q was obtained;

[0122] Optimization problem (12) is not easy to solve because each element of matrix Q corresponds to a response q. i,l The Lorentz constraint form in (5) should be used, therefore qi , The phase and amplitude of l are coupled. To address this issue, the Lorentz constraint can be relaxed to a phase-weighted constraint with constant amplitude and arbitrary phase:

[0123]

[0124] The feasible set F is a circle of unit radius centered at the origin. First, solve the problem after Q is replaced by F (12), and then use the solution of F to adjust the Lorentz constraint weights by projection.

[0125] Since this invention considers a single-user scenario, problem (12) can be easily evaluated after relaxing the constraints. In fact, the receiving process is similar to the precoding process in DMA beamforming, only in the opposite direction.

[0126] As can be seen, the optimized phase response It consists of two parts: the first part is the phase of each received antenna signal, which means that the optimal coefficient should match the antenna phase profile, and in beamforming, this is interpreted as achieving beam focusing; the other part compensates for the transmission delay in the microstrip given by (3), so that the signals are transmitted synchronously.

[0127] q i,l It does not satisfy the Lorentz form, therefore it is projected onto (5), by The final weights are given. Although this is only an approximation of (12), it retains the properties mentioned in (18) with the addition of a constant phase shift. Numerical results also verify the validity of this result.

[0128] Step 5 proposes an iterative optimization scheme to approximate the optimal solution.

[0129] Unfortunately, the optimal result in Lemma.1 depends on the source location, which is an unknown quantity to be estimated. To address this, an iterative optimization algorithm is proposed to simultaneously estimate the source location and optimize the DMA coefficients, as shown in Algorithm 1.

[0130] Based on the above example, perform data simulation:

[0131] The positioning performance under various DMA coefficient settings was evaluated for different signal-to-noise ratios. The geometry of the receiving DMA was set to a plane, and the elevation angle between the source and reference antennas was set to θ0 = 0°. Therefore, the source position can be expressed as... Specifically, the DMA array is configured as a uniformly spaced 18×18cm square array, with the first antenna element located at the origin of the spatial coordinate system as the antenna reference point. The array plane is set to the XoZ plane, and the carrier frequency is set to f. p =28GHz.

[0132] Furthermore, the source is located in the Fresnel region of the array, meaning the array aperture D and distance d0 should satisfy:

[0133]

[0134] Then, the DMA coefficient matrix Q is set to random coefficients, optimal coefficients, and coefficients obtained by the proposed iterative algorithm, respectively, and the performance of these schemes is compared under different signal-to-noise ratio (SNR) conditions. The SNR is defined as...

[0135] The root mean square error (RMSE) is used as a measure of the quality of the difference between the estimated and actual positions, and it is calculated as follows:

[0136]

[0137] Where N me N represents the number of Monte Carlo experiments. me =500, It is the mean square error (i.e., distortion) of the positioning, while These are the distance and azimuth estimated by the m-th Monte Carlo method.

[0138] With the signal-to-noise ratio (SNR) fixed at -10dB, the positioning error of the alternating algorithm gradually decreases with increasing iterations, eventually approaching the optimal coefficient scheme. This demonstrates that the performance of the iterative algorithm cannot exceed that of the optimal coefficient scheme. However, experiments also revealed that when the SNR is too low, the alternating algorithm fails to converge, instead fluctuating after the distortion drops to a certain value. This may pose a challenge to setting the convergence threshold in practical applications. Similar issues arise with other fixed SNR values, with the fluctuation range depending on the accuracy of the best estimate. Therefore, more iterations are not necessarily better. Even under low SNR (-10dB) conditions, only 2 to 3 iterations are sufficient, making the algorithm's complexity manageable.

[0139] The above description is merely an embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principle of the present invention should be included within the scope of the claims of the present invention.

Claims

1. A near-field positioning method based on a dynamic metamaterial antenna, characterized in that, Includes the following steps: Step 1: DMA-based signal reception: The base station receives pilot signals from users and estimates the source location. The base station is set as a large DMA array containing N receiving antennas and N... d Row microstrips, each row microstrip contains N e One metamaterial receiving element, i.e., N = N d N e Each microstrip has only one RF chain output; the antenna signal vector r and noise vector ω are defined, and the actual array receive vector is expressed as: ； in H represents the output vector of all microstrips, which is an N-dimensional diagonal matrix, and Q is the configuration weight matrix of the DMA. Matrix Q has structural constraints: the non-zero elements of Q This indicates the adjustable response of the corresponding antenna, and Conforms to the Lorentz-constrained phase model; i∈{1,2,…,N d }, l∈{1,2,…,N e }; Step 2: Determine the source location using the MLE localization algorithm based on the near-field assumption: Set a reference point for the receiving array, and establish the distance between the corresponding antenna and the source based on the triangular relationship between the reference point, the antenna, and the source. With source location parameters The relationship between phase and source position was obtained by using the formula; the source position was estimated by maximizing the log-likelihood function using the MLE algorithm; where The log-likelihood function of the received signal vector is given as follows: Where M is the number of samples for estimation, s∈N d It is a guide vector; Step 3: Analyze the impact of matrix Q on the estimation process and its design significance: Rewrite formula (10) as follows: in Let y(t) be the covariance matrix. Introducing formula (2) into formula (13) while considering formula (11), we get: in It is the cosquare matrix of r(t), where r(t) is the received signal, an N-dimensional vector. ,in, f is the amplitude. p Where c is the pilot frequency and c is the electromagnetic velocity; Using formula (14), Q is regarded as a compression matrix. The design of matrix Q is interpreted as reducing the impact of compression on the MLE estimation process. Step 4: Optimize matrix Q by introducing DMA precoding theory: The optimization problem of matrix Q is established as follows: With the Lorentz constraints relaxed to phase-weighted constraints only, the optimization problem is decomposed into N d For this subproblem, according to the triangle inequality, the solution for the optimal phase response is: ； Then, projecting the optimal phase response back onto the Lorentz constraints, we obtain: ； in, It is the wave number. Indicates the position of the corresponding antenna; Step 5: Approximate the optimal localization solution through iterative optimization: Since the optimal Q in Step 4 depends on the unknown source location, an iterative optimization scheme that does not require prior knowledge of the source location is adopted. The source location estimation and DMA weight matrix Q update are performed alternately to iteratively approximate the optimal localization solution.

2. The near-field positioning method based on a dynamic metamaterial antenna according to claim 1, characterized in that, In step 1, the signal received by the l-th antenna of the i-th row microstrip at time t is represented as: in Represents the received signal, i∈{1,2,…,N} d }, l∈{1,2,…,N e }, f is the amplitude. p It is the pilot frequency. It is additive white noise with variance σ. Represents the signal phase, with in is the distance between the antenna and the source, and c is the electromagnetic velocity.

3. The near-field positioning method based on a dynamic metamaterial antenna according to claim 2, characterized in that, In step 1, Define antenna signal vector and noise vector Since each microstrip has only one output, the actual array receive vector is an N-dimensional vector. d dimensional vector; The diagonal elements of H are The effect of signal propagation is encapsulated within a microstrip; the response is considered to be frequency-flat, and the frequency response of the metamaterial element conforms to the Lorentz-constrained phase model, i.e., Where α i It is the waveguide attenuation coefficient, β i It is the wave number. The matrix represents the position of the corresponding antenna. It has structural constraints: in The adjustable response of the corresponding antenna, which also conforms to the Lorentz-constrained phase model, is as follows: Therefore, by expressing y in scalar form, the general model of the received signal is rewritten as: Where y i Let represent the i-th element of y, i.e., the output of the i-th row of microstrip lines. Therefore, the DMA output is considered as the result of a weighted sum of all received signals in the corresponding row of microstrip lines.

4. The near-field positioning method based on a dynamic metamaterial antenna according to claim 3, characterized in that, In step 2, the signal source is located by processing the received phase: The distance from the source to the reference point, the elevation angle, and the azimuth angle are defined as follows: As a location marker of the source, and at the same time define As the position marker for the l-th antenna in the i-th row of microstrip, based on the triangular relationship between the reference point, antenna, and source, we have: From formulas (7) and (8), the correspondence between phase and source position is obtained. Using the MLE algorithm, the following function is maximized: The elements of s , It is given by formulas (7) and (8).

5. The near-field positioning method based on a dynamic metamaterial antenna according to claim 3, characterized in that, In step 4, the response corresponding to each element of matrix Q Using the Lorentz constraint form in formula (5), therefore The phase and amplitude are coupled, so the Lorentz constraint is relaxed to a phase-weighted constraint with constant amplitude and arbitrary phase: 。

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