A DOA estimation method based on spatiotemporal modulation metasurface

Abstract

The present invention discloses a DOA estimation method based on a spatiotemporal modulation metasurface. The method comprises the following steps: first, designing the modulation timing of the metasurface and applying Fourier transform theory to establish a receiving signal model for the spatiotemporal modulation metasurface system; then, illuminating the metasurface with a transmitting horn antenna and placing a receiving horn in the normal direction of the metasurface to obtain sideband signals; then, utilizing the analytical relationship in the signal model and the spatiotemporal modulation matrix, recovering the baseband signal containing azimuth information; and finally, performing rank recovery processing on the covariance matrix of the baseband signal to calculate the incident angle of the incoming signal. The present invention has the advantages of simple hardware structure, low implementation cost, high flexibility and effectiveness, high computational accuracy, strong noise immunity, and the ability to perform multi-source DOA estimation.

Description

Technical Field

[0001] The present invention relates to the field of metasurface technology, and in particular to a DOA estimation method based on spatiotemporal modulation metasurface. Background Art

[0002] DOA estimation is a critical technology in fields such as radio navigation systems, Satellite-on-the-Move (SOTM), and smart antenna systems. Many traditional DOA estimation techniques, such as the MUSIC algorithm, the ESPRIT algorithm, and subspace fitting algorithms, have been widely used. However, these methods are limited by the complex hardware systems of array antennas. Meanwhile, the emergence of electromagnetic metasurfaces has provided new perspectives for traditional engineering applications, attracting the attention of researchers from multiple disciplines.

[0003] Metasurface technology can be used to control electromagnetic properties such as the phase, amplitude, and polarization of electromagnetic waves. By integrating nonlinear active devices such as PIN diodes and varactor diodes into metasurface units, dynamic controllability can be achieved, providing the possibility of achieving spatiotemporal modulation. Existing technologies, such as the time-modulated antenna direction-finding technology proposed by Ni Gang et al. (Ni, Gang, et al. "Direction Finding and Performance Analysis With 1-bit Time Modulated Array." IEEE Transactions on Antennas and Propagation, vol. 69, no. 10, pp. 6881-6893, October 2021), reduce the number of receiving channels but still require a complex hardware system consisting of power splitters and phase shifters. The direction-finding technology based on a time-space modulated metasurface proposed by Dai Junyan et al. (Dai, Jun Yan, et al. "Simultaneous In-situ Direction Finding and Field Manipulation Based on Space-Time-Coding Digital Metasurface." IEEE Transactions on Antennas and Propagation, 2022.) uses the analytical relationship between harmonics for DOA estimation. Although this simplifies the system, it has poor noise immunity and cannot perform multi-source DOA estimation. Therefore, there is an urgent need to study a highly noise-resistant multi-source DOA estimation method with a low-complexity hardware system. Summary of the Invention

[0004] The present invention aims to provide a DOA estimation method which has simple structure, low hardware cost, high flexibility and effectiveness, strong anti-noise performance and can perform multi-source DOA estimation.

[0005] The technical solution to achieve the purpose of the present invention is: a DOA estimation method based on a spatiotemporal modulation metasurface, comprising the following steps:

[0006] Step 1: Design the modulation timing of the metasurface and use Fourier transform theory to establish a receiving signal model of the spatiotemporal modulation metasurface system;

[0007] Step 2: Use the transmitting horn antenna to illuminate the metasurface, and place the receiving horn antenna in the normal direction of the metasurface to obtain the sideband signal;

[0008] Step 3: Using the analytical relationship in the signal model and the spatiotemporal modulation matrix, the baseband signal containing the azimuth information is restored;

[0009] Step 4: After performing rank recovery processing on the covariance matrix of the baseband signal, calculate the incident angle of the incoming signal.

[0010] Compared with the existing technology, the present invention has the following significant advantages: (1) the required hardware system is simpler than that of the traditional array antenna, saving more costs; (2) the method is applicable to a variety of DOA estimation algorithms and has relatively high flexibility and effectiveness; (3) the DOA estimation algorithm is introduced during signal post-processing, which improves the anti-noise performance and can perform multi-source DOA estimation. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Figure 1 The figure is a flow chart of a DOA estimation method based on spatiotemporal modulation metasurface of the present invention.

[0012] Figure 2 Schematic diagram of the structure of the DOA estimation system based on the spatiotemporal modulation metasurface in an embodiment of the present invention.

[0013] Figure 3 Schematic diagram of the unit structure and working state of the spatiotemporal modulation metasurface system in an embodiment of the present invention, where (a) is a schematic diagram of the unit structure, and (b) is a transmission coefficient curve diagram of the diode in the on and off states.

[0014] Figure 4 The circuit and modulation signal designs of the spatiotemporal modulation metasurface for DOA estimation in an embodiment of the present invention are shown, where (a) is a schematic diagram of the metasurface array structure, and (b) is a schematic diagram of the spatiotemporal modulation sequence.

[0015] Figure 5 This is a physical picture of the spatiotemporal modulation metasurface DOA prototype system in an embodiment of the present invention.

[0016] Figure 6 3 is a comparison chart of experimental test results, full-wave simulation results and theoretical values ​​in an embodiment of the present invention.

[0017] Figure 7 Graphs of numerical simulation results in an embodiment of the present invention are shown, where (a) is a graph of the mean square error of DOA estimation for different incident angles when the signal-to-noise ratio is 10 dB, (b) is a graph of the mean square error of DOA estimation for different signal-to-noise ratios when the incident angle is 20°, and (c) is a graph of the DOA estimation results when two coherent signal sources are incident. DETAILED DESCRIPTION

[0018] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0019] Combine Figure 1 The present invention provides a DOA estimation method based on a spatiotemporal modulation metasurface, comprising the following steps:

[0020] A DOA estimation method based on a spatiotemporal modulation metasurface comprises the following steps:

[0021] Step 1: Design the modulation timing of the metasurface and use Fourier transform theory to establish a receiving signal model of the spatiotemporal modulation metasurface system;

[0022] Step 2: Use the transmitting horn antenna to illuminate the metasurface, and place the receiving horn antenna in the normal direction of the metasurface to obtain the sideband signal;

[0023] Step 3: Using the analytical relationship in the signal model and the spatiotemporal modulation matrix, the baseband signal containing the azimuth information is restored;

[0024] Step 4: After performing rank recovery processing on the covariance matrix of the baseband signal, calculate the incident angle of the incoming signal.

[0025] As a specific example, the modulation timing of the metasurface is designed in step 1, and the Fourier transform theory is used to establish a receiving signal model of the spatiotemporal modulation metasurface system, as follows:

[0026] Step 1.1: Combine Figure 2 The DOA estimation system based on the spatiotemporal modulation metasurface simplifies the hardware structure and constructs a signal model through spatiotemporal modulation, reducing the number of receiving channels. Only one far-field receiving horn antenna is needed to receive the required signal. The details are as follows:

[0027] The method disclosed in this invention is not limited to transmissive or reflective metasurface units. Without loss of generality, a transmissive metasurface unit is used as an example. The metasurface DOA estimation system consists of a transmissive electrically adjustable metasurface unit, an FPGA control module, and a receiving horn antenna. The metasurface units are used to form subarrays, thereby forming a metasurface array. The FPGA is used to control the operating state of each subarray. The receiving horn antenna is used to obtain the scattered field spectrum and extract the sideband signal.

[0028] For an electrically tunable metasurface array consisting of N subarrays, the metasurface units are equipped with PIN diodes, allowing the operating state of each subarray to be independently switched using digital coding via an FPGA-based control module. The metasurface subarrays operate in two states: full transmission and full reflection. Spatiotemporal modulation coding is used to manipulate the metasurface's scattering field. Compared to array antennas that utilize a large number of sensors to form a receiving link, the method disclosed in this invention utilizes spatiotemporal modulation of the metasurface to manipulate electromagnetic waves in space, utilizing only a single receiving horn to acquire the scattered field. This reduces the number of receiving channels and saves hardware costs.

[0029] Step 1.2: Take a single narrowband plane wave as an example. When the plane wave is incident at an angle θ i When irradiated on the metasurface, the far-field scattering pattern af(θ,t) in the transmission space can be expressed as:

[0030]

[0031] Among them, θ and t are angle variables and time variables respectively, j represents the imaginary unit, E i (t) represents the incident field in time domain, β is the free space propagation constant, d is the side length of the subarray, τ n (t) is the transmission coefficient of the nth sub-array, which can be expressed as:

[0032]

[0033] Among them, m∈N, represents the mth cycle;

[0034] Step 1.3: According to Fourier transform theory, the transmission coefficient τ n (t) is Fourier expanded and can be decomposed into p are the harmonics of each step, expressed as:

[0035]

[0036] Among them, α n,q The Fourier series representing the qth harmonic of the nth sub-matrix is ​​expanded as:

[0037]

[0038] Step 1.4: Substitute equation (3) into equation (1). Then the frequency domain form of the far-field scattering pattern of the transmission space corresponding to the qth order harmonic is af q The expression of (θ) is:

[0039]

[0040] Among them, E iRepresents the frequency domain form of the incident field and is a constant;

[0041] Step 1.5: Place the receiving horn antenna directly behind the metasurface, that is, at θ = 0°. The qth-order harmonic component received at this time, that is, the signal model is:

[0042]

[0043] As a specific example, in step 2, the transmitting horn antenna is used to illuminate the metasurface, and the receiving horn antenna is placed in the normal direction of the metasurface to obtain the sideband signal, as follows:

[0044] In step 2.1, both the transmitting and receiving horn antennas are standard horn antennas, located on either side of the metasurface, and both meet far-field conditions. Connect the transmitting horn antennas to a signal generator, emitting a single-frequency sine wave that illuminates the metasurface at a specific angle, simulating a plane wave arriving at infinity.

[0045] Step 2.2: After the plane wave is modulated by the metasurface, the resulting transmission field is acquired by the receiving horn antenna. The receiving horn antenna is located in the normal direction of the metasurface and its relative position to the metasurface remains unchanged to ensure that the wave path from each subarray to the receiving horn antenna remains unchanged.

[0046] Step 2.3: Use the receiving horn antenna to connect to the spectrum analyzer, observe the spectrum of the transmitted field, read the spectrum data with a computer, extract the -Q to +Q order 2Q+1 order harmonic components, store them in the matrix Y, and complete the extraction of the sideband signal.

[0047] The matrix Y has the following form:

[0048]

[0049] As a specific example, step 3 utilizes the analytical relationship in the signal model and the spatiotemporal modulation matrix to restore the baseband signal containing the azimuth information, as follows:

[0050] Step 3.1: Using the 2Q+1 order harmonic components extracted in step 2, rewrite equation (6) into a matrix form:

[0051]

[0052] Step 3.2: Simplify formula (8) as follows:

[0053] AX=Y (9)

[0054] Among them, matrix A and matrix X are:

[0055]

[0056] In formula (10), the matrix A is composed of the Fourier series of the time-varying transmission coefficients of each sub-array of the metasurface, which is called the spatiotemporal modulation matrix and is determined by the coding timing of the spatiotemporal modulation metasurface. The matrix X represents the baseband signal, that is, the original unmodulated signal emitted by the source. The phase difference between the matrix elements comes from the plane wave with an incident angle θ. i Spatial phase difference between metasurface subarrays at oblique incidence.

[0057] Step 3.3: When the column rank of matrix A is full, there exists a generalized inverse matrix A -1 , the baseband signal X is obtained through analytical relationship:

[0058] X=A -1 Y (11)

[0059] As a specific example, after performing rank recovery processing on the covariance matrix of the baseband signal in step 4, the incident angle of the incoming signal is calculated as follows:

[0060] Step 4.1: Compared to using purely analytical methods to calculate the angle of incidence, the method disclosed in this invention introduces a DOA estimation algorithm during data post-processing, which improves noise immunity and has the ability to estimate DOA from multiple sources. Before using the spatial spectrum estimation algorithm to solve the angle of incidence, the baseband signal needs to be preprocessed. First, the covariance matrix R of the baseband signal is obtained:

[0061] R=E[XX H ] (12)

[0062] In the above formula, the matrix X H is the conjugate transpose of matrix X, and E represents the mathematical expectation.

[0063] In step 4.2, the above method for recovering the baseband signal still applies when multiple sources are incident. However, in complex electromagnetic environments, the signals incident on the metasurface contain coherent signals. These coherent signals include co-channel interference and multipath propagation caused by background reflections. In a multi-source incident scenario, if the electromagnetic metasurface simultaneously receives coherent signals from different directions, the baseband signal covariance matrix will be rank-deficient, causing the eigenvectors of the signal subspace to diverge into the noise subspace. This will prevent the spatial spectrum estimation algorithm from correctly solving the incident angle problem. Therefore, it is necessary to perform decorrelation preprocessing on the signal covariance matrix to restore the rank to that equivalent to the number of sources.

[0064] Let matrix I R is the N×N inverse identity matrix, that is

[0065]

[0066] Utilize I R The baseband signal covariance matrix is ​​modified, that is

[0067] R X =R+I R R * I R (14)

[0068] Among them, the matrix R * is the conjugate of the matrix R.

[0069] Step 4.3: Since R is a Hermite matrix, after modifying it using the Toeplitz property, we get the estimated value matrix R of the signal covariance matrix. X , then obviously R X is the Hermite Toeplitz matrix, that is, R X is an unbiased estimate of R. X The noise subspace is decomposed and the eigenvector is substituted into the MUSIC algorithm to calculate the incident angle of the incoming signal.

[0070] As a specific example, the present invention is not limited to the MUSIC algorithm. After obtaining the baseband signal, other DOA estimation algorithms can also be used to accurately calculate the incident angle. Therefore, algorithms with different advantages can be selected according to the application scenario, which has a certain degree of flexibility.

[0071] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0072] Example

[0073] Combine Figure 1 In this embodiment, a DOA estimation method based on a spatiotemporal modulation metasurface includes the following steps:

[0074] Step 1: Design the modulation timing of the metasurface and use Fourier transform theory to establish a receiving signal model for the spatiotemporal modulation metasurface system. The details are as follows:

[0075] Step 1.1: Combine Figure 2 The DOA estimation system based on the spatiotemporal modulation metasurface simplifies the hardware structure and constructs a signal model through spatiotemporal modulation, reducing the number of receiving channels. Only one far-field receiving horn antenna is needed to receive the required signal. The details are as follows:

[0076] The method disclosed in this invention is not limited to transmissive or reflective metasurface units. Without loss of generality, a transmissive metasurface unit is used as an example. The metasurface DOA estimation system consists of a transmissive electrically adjustable metasurface unit, an FPGA control module, and a receiving horn antenna. The metasurface units are used to form subarrays, thereby forming a metasurface array. The FPGA is used to control the operating state of each subarray. The receiving horn antenna is used to obtain the scattered field spectrum and extract the sideband signal.

[0077] For an electrically tunable metasurface array consisting of N subarrays, the metasurface units are equipped with PIN diodes, allowing the operating state of each subarray to be independently switched using digital coding via an FPGA-based control module. The metasurface subarrays operate in two states: full transmission and full reflection. Spatiotemporal modulation coding is used to manipulate the metasurface's scattering field. Compared to array antennas that utilize a large number of sensors to form a receiving link, the method disclosed in this invention utilizes spatiotemporal modulation of the metasurface to manipulate electromagnetic waves in space, utilizing only a single receiving horn to acquire the scattered field. This reduces the number of receiving channels and saves hardware costs.

[0078] Step 1.2: Take a single narrowband plane wave as an example. When the plane wave is incident at an angle θ i When irradiated on the metasurface, the far-field scattering pattern af(θ,t) in the transmission space can be expressed as:

[0079]

[0080] Among them, θ and t are angle variables and time variables respectively, j represents the imaginary unit, E i (t) represents the incident field in time domain, β is the free space propagation constant, d is the side length of the subarray, τ n (t) is the transmission coefficient of the nth sub-array, which can be expressed as:

[0081]

[0082] Among them, m∈N represents the mth cycle.

[0083] Combine Figure 3 , gives the electrically adjustable metasurface unit structure used in this embodiment, and the unit transmission coefficient in two working states. Specifically, the metasurface unit used in this embodiment consists of a metal patch on the surface, a PIN diode, and a dielectric substrate. The size of the metal patch has been Figure 3 As shown in (a), the PIN diode model is SMP 1320-040LF, and the dielectric substrate is 0.2mm thick Rogers RO4003C high-frequency board. In addition, Figure 3 (b) shows the transmission coefficient of the metasurface unit when the diode is on and off. It can be seen from the figure that the transmission coefficient does not switch between the ideal 0 and 1, which will introduce errors in the angle measurement results, but it can still be used to verify the correctness of this method.

[0084] Combine Figure 4 , a schematic diagram of the array structure and modulation timing of the spatiotemporal modulation metasurface used in this embodiment is given. Figure 4(a) shows the circuit layout of the metasurface, including the design of the unit arrangement and the design of the feed network. There are a total of 24×32 electrically adjustable units, with 96 units in 3 columns as a subarray. The modulation timing is set for each subarray, as shown in the following figure: Figure 4 As shown in (b), time-space modulation is realized, where "1" represents the diode conduction state and "0" represents the diode cutoff state.

[0085] Step 1.3: According to Fourier transform theory, the transmission coefficient τ n (t) is Fourier expanded and can be decomposed into p are the harmonics of each step, expressed as:

[0086]

[0087] Among them, α n,q The Fourier series representing the qth harmonic of the nth sub-matrix is ​​expanded as:

[0088]

[0089] Step 1.4: Substitute equation (3) into equation (1). Then the frequency domain form of the far-field scattering pattern of the transmission space corresponding to the qth order harmonic is af q The expression of (θ) is:

[0090]

[0091] Among them, E i Represents the frequency domain form of the incident field and is a constant.

[0092] Step 1.5: Place the receiving horn antenna directly behind the metasurface, that is, at θ = 0°. The qth-order harmonic component received at this time, that is, the signal model is:

[0093]

[0094] Step 2: Use the transmitting horn antenna to illuminate the metasurface, and place the receiving horn antenna in the normal direction of the metasurface to obtain the sideband signal, as follows:

[0095] Combine Figure 5 , a physical diagram of the metasurface DOA prototype system is given. The FPGA control module sends digital control signals to the electrically adjustable metasurface, and periodically changes the working state of each sub-array according to the designed modulation timing.

[0096] In step 2.1, standard horn antennas are used for both the transmitting and receiving horn antennas, located on either side of the metasurface. Both antennas must meet far-field conditions. Connect a signal generator to the transmitting horn antennas and emit a single-frequency sine wave, illuminating the metasurface at a specific angle to simulate a plane wave arriving from infinite distance.

[0097] Step 2.2: After the plane wave is modulated by the metasurface, the generated transmission field is acquired by the receiving horn antenna. The receiving horn antenna is located in the normal direction of the metasurface and its relative position to the metasurface remains unchanged to ensure that the wave path from each subarray to the receiving horn antenna remains unchanged.

[0098] To validate the proposed method, a prototype experiment was conducted in a microwave anechoic chamber. The metasurface prototype system was placed at the center of rotation of a turntable, and the receiving horn antenna was attached to the turntable's telescopic arm. During the turntable's rotation, the relative position of the receiving horn antenna and the metasurface remained constant. The transmitting horn antenna was independent of the turntable, placed in the far field, and remained stationary during the experiment.

[0099] Step 2.3: Use the receiving horn antenna to connect to the spectrum analyzer, observe the spectrum of the transmitted field, read the spectrum data with a computer, extract the -Q to +Q order 2Q+1 order harmonic components, store them in the matrix Y, and complete the extraction of the sideband signal.

[0100] The matrix Y has the following form:

[0101]

[0102] Step 3: Use the analytical relationship in the signal model and the spatiotemporal modulation matrix to recover the baseband signal containing the azimuth information, as follows:

[0103] Step 3.1: Using the 2Q+1 order harmonic components extracted in step 2, rewrite equation (6) into a matrix form:

[0104]

[0105] Step 3.2: Simplify formula (8) as follows:

[0106] AX=Y (9)

[0107] Among them, matrix A and matrix X are:

[0108]

[0109] In formula (10), the matrix A is composed of the Fourier series of the time-varying transmission coefficients of each sub-array of the metasurface, which is called the spatiotemporal modulation matrix and is determined by the coding timing of the spatiotemporal modulation metasurface. The matrix X represents the baseband signal, that is, the original unmodulated signal emitted by the source. The phase difference between the matrix elements comes from the plane wave with an incident angle θ. i Spatial phase difference between metasurface subarrays at oblique incidence.

[0110] Step 3.3: When the column rank of matrix A is full, there exists a generalized inverse matrix A -1 , the baseband signal X is obtained through analytical relationship:

[0111] X=A -1 Y (11)

[0112] Step 4: After performing rank recovery on the covariance matrix of the baseband signal, calculate the incident angle of the incoming signal, as follows:

[0113] Step 4.1: Compared to using purely analytical methods to calculate the angle of incidence, the method disclosed in this invention introduces a DOA estimation algorithm during data post-processing, which improves noise immunity and has the ability to estimate DOA from multiple sources. Before using the spatial spectrum estimation algorithm to solve the angle of incidence, the baseband signal needs to be preprocessed. First, the covariance matrix R of the baseband signal is obtained:

[0114] R=E[XX H ] (12)

[0115] In the above formula, the matrix X H is the conjugate transpose of matrix X, and E represents the mathematical expectation.

[0116] In step 4.2, the above method for recovering the baseband signal still applies when multiple sources are incident. However, in complex electromagnetic environments, the signals incident on the metasurface contain coherent signals. These coherent signals include co-channel interference and multipath propagation caused by background reflections. In a multi-source incident scenario, if the electromagnetic metasurface simultaneously receives coherent signals from different directions, the baseband signal covariance matrix will be rank-deficient, causing the eigenvectors of the signal subspace to diverge into the noise subspace. This will prevent the spatial spectrum estimation algorithm from correctly solving the incident angle problem. Therefore, it is necessary to perform decorrelation preprocessing on the signal covariance matrix to restore the rank to that equivalent to the number of sources.

[0117] Let matrix I R is the N×N inverse identity matrix, that is

[0118]

[0119] Utilize I R The baseband signal covariance matrix is ​​modified, that is

[0120] R X =R+I R R * I R (14)

[0121] Among them, the matrix R * is the conjugate of the matrix R.

[0122] Step 4.3: Since R is a Hermite matrix, after modifying it using the Toeplitz property, we get the estimated value matrix R of the signal covariance matrix. X , then obviously R X is the Hermite Toeplitz matrix, that is, R X is an unbiased estimate of R. X The noise subspace is decomposed and the eigenvector is substituted into the MUSIC algorithm to calculate the incident angle of the incoming signal.

[0123] Furthermore, this method is not limited to the MUSIC algorithm. After obtaining the baseband signal, other DOA estimation algorithms can also be used to accurately calculate the incident angle. Therefore, algorithms with different advantages can be selected according to the application scenario, which has a certain degree of flexibility.

[0124] Combine Figure 6 , gives the comparison of the experimental test results, full-wave simulation results and theoretical values ​​in this embodiment. In the experiment and simulation process, the center frequency is set to 9GHz, the modulation frequency is 1MHz, the sampling frequency is 1GHz, and the MUSIC algorithm is used in post-processing. Figure 6 As can be seen in the figure, the experimental test results are highly consistent with the full-wave simulation results, and both can accurately estimate DOA, proving the feasibility of the method. It is worth noting that in this embodiment, when the incident angle is greater than 50°, the DOA estimation accuracy decreases. This is due to the non-ideal transmission response of the metasurface unit used in this embodiment and is not an inherent defect of this method.

[0125] Combine Figure 7 , the results of numerical simulation are given, that is, the ideal transmission response is used instead of the actual transmission response of the metasurface unit for simulation to verify the correctness of this method. The remaining parameter settings are the same as those of the full-wave simulation. Figure 7 (a) shows the mean square error of DOA estimation at different incident angles when the signal-to-noise ratio is 10 dB in 1000 Monte Carlo experiments; Figure 7 (b) shows the mean square error of DOA estimation under different signal-to-noise ratios when the incident angle is 20° in 1000 Monte Carlo experiments; Figure 7Figure (c) shows the DOA estimation results for dual-coherent sources with a signal-to-noise ratio of 10 dB and incident angles of 10° and 20°, respectively. The numerical simulation results show that this method has excellent noise immunity and can accurately estimate the DOA of multiple sources.

Claims

1. A DOA estimation method based on spatiotemporal modulation metasurface, characterized in that: The following steps are involved: Step 1: Design the modulation timing of the metasurface and use Fourier transform theory to establish a receiving signal model of the spatiotemporal modulation metasurface system; Step 2: Use the transmitting horn antenna to illuminate the metasurface, and place the receiving horn antenna in the normal direction of the metasurface to obtain the sideband signal; Step 3: Using the analytical relationship in the signal model and the spatiotemporal modulation matrix, the baseband signal containing the azimuth information is restored; Step 4: After performing rank recovery processing on the covariance matrix of the baseband signal, the incident angle of the incoming signal is calculated; Step 1 is as follows: Step 1.

1. Establish a metasurface DOA estimation system, including a transmissive electrically adjustable metasurface unit, an FPGA control module, and a receiving horn antenna; the transmissive electrically adjustable metasurface unit is used to form a subarray, and then a metasurface array; the FPGA control module is used to control the working state of each subarray; the receiving horn antenna is used to obtain the scattered field spectrum and extract the sideband signal; For an electrically tunable metasurface array consisting of N subarrays, the metasurface units are equipped with PIN photodiodes, allowing the operating state of each subarray to be independently switched in the form of digital coding through the FPGA control module. The metasurface subarrays have two operating states: full transmission and full reflection. The scattering field of the metasurface is manipulated through spatiotemporal modulation coding. The spatiotemporal modulation metasurface is used to manipulate electromagnetic waves in space, and the scattered field is obtained using a single receiving horn antenna. Step 1.2: For a single narrowband plane wave, when the plane wave is incident at an angle θ i When irradiated on the metasurface, the far-field scattering pattern af(θ,t) in the transmission space is expressed as: Among them, θ and t are angle variables and time variables respectively, j represents the imaginary unit, E i (t) represents the incident field in the time domain, β is the free space propagation constant, and d is the side length of the subarray; τ n (t) is the transmission coefficient of the nth sub-array, expressed as: Where m is a positive integer, indicating the mth cycle; Step 1.3: According to Fourier transform theory, the transmission coefficient τ n (t) is Fourier expanded and decomposed into the modulation frequency f p are the harmonics of each step, expressed as: Among them, α n,q The Fourier series representing the qth harmonic of the nth sub-matrix is ​​expanded as: Step 1.4: Substitute equation (3) into equation (1). Then the frequency domain form of the far-field scattering pattern of the transmission space corresponding to the qth order harmonic is af q The expression of (θ) is: Among them, E i Represents the frequency domain form of the incident field and is a constant; Step 1.5: Place the receiving horn antenna directly behind the metasurface, that is, at θ = 0°. The qth-order harmonic component received at this time, that is, the signal model is: Step 2 is as follows: Step 2.1: Both the transmitting horn antenna and the receiving horn antenna are standard horn antennas, located on either side of the metasurface, and both meet far-field conditions. Connect the transmitting horn antenna with a signal generator to emit a single-frequency sine wave, illuminating the metasurface at a set angle to simulate a plane wave arriving at infinity. Step 2.2: After the plane wave is modulated by the metasurface, the resulting transmission field is acquired by the receiving horn antenna. The receiving horn antenna is located in the normal direction of the metasurface and its relative position to the metasurface remains unchanged to ensure that the wave path from each subarray to the receiving horn antenna remains unchanged. Step 2.3: Connect the receiving horn antenna to a spectrum analyzer to observe the spectrum of the transmitted field. Use a computer to read the spectrum data, extract the -Q to +Q order harmonic components (2Q+1), and store them in matrix Y to complete the extraction of the sideband signal. The matrix Y described in step 2.3 is of the following form: Step 3 is as follows: Step 3.1: Using the 2Q+1 order harmonic components extracted in step 2, rewrite equation (6) into a matrix form: Step 3.2: Simplify formula (8) as follows: AX=Y (9) Among them, matrix A and matrix X are: In formula (10), the matrix A is composed of the Fourier series of the time-varying transmission coefficients of each sub-array of the metasurface, which is called the spatiotemporal modulation matrix and is determined by the coding timing of the spatiotemporal modulation metasurface. The matrix X represents the baseband signal, that is, the original unmodulated signal emitted by the source. The phase difference between the matrix elements comes from the plane wave with an incident angle θ. i The spatial phase difference between metasurface sub-arrays at oblique incidence; Step 3.3: When the column rank of matrix A is full, there exists a generalized inverse matrix A -1 , the baseband signal X is obtained through analytical relationship: X=A -1 And (11)。 2. The DOA estimation method based on the spatiotemporal modulation metasurface according to claim 1, characterized in that: After performing rank recovery on the covariance matrix of the baseband signal in step 4, the incident angle of the incoming signal is calculated as follows: Step 4.1, obtain the covariance matrix R of the baseband signal: R=E[XX H ] (12) In the above formula, X represents the baseband signal, and the matrix X H is the conjugate transpose of matrix X, and E represents the mathematical expectation; Step 4.2: In the case of multiple signal sources, there are coherent signals in the signals incident on the metasurface. The coherent signal sources include co-frequency interference and multipath propagation signals caused by background reflections. If the electromagnetic metasurface receives coherent signals from different directions at the same time, it will lead to rank deficiency of the baseband signal covariance matrix, causing the eigenvectors of the signal subspace to diverge into the noise subspace, resulting in the spatial spectrum estimation algorithm being unable to correctly solve the problem of incident angle. Therefore, it is necessary to perform decorrelation preprocessing on the signal covariance matrix to restore the rank to the same as the number of signal sources. Let matrix I R is the N×N inverse identity matrix, that is Utilize I R Correct the baseband signal covariance matrix to obtain the estimated value matrix R of the baseband signal covariance matrix X ,Right now R X =R+I R R * I R (14) Among them, the matrix R * is the conjugate of the matrix R; Step 4.3: Since R is a Hermite matrix, after modifying it using the Toeplitz property, we get the estimated value matrix R of the signal covariance matrix. X , then R X is the Hermite Toeplitz matrix, that is, R X is an unbiased estimate of R; R X The noise subspace is decomposed and the eigenvector is substituted into the MUSIC algorithm to calculate the incident angle of the incoming signal.

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