An angle prior assisted intelligent metasurface phase coding design method for two-dimensional direction of arrival estimation

Abstract

The application discloses a kind of angle priori auxiliary intelligent metasurface phase encoding design methods for two-dimensional DOA estimation.Methods include: constructing the system model of intelligent metasurface single receiving channel two-dimensional DOA estimation, deducing the explicit relationship between the CRB of two-dimensional DOA estimation parameter and phase encoding matrix;Utilize the priori range information of target two-dimensional angle, construct the phase encoding matrix optimization problem with unit module constraint with the goal of minimizing average CRB;Efficiently solve the non-convex problem using Riemannian manifold optimization algorithm, obtain the optimal phase encoding matrix.The present application directly correlates the encoding design with the lower bound of theoretical performance, focuses the beam energy on the target priori angle region by optimizing the encoding, significantly improves the two-dimensional DOA estimation accuracy of azimuth and elevation within the angle priori range, reduces the required measurement overhead, and shows good robustness under one-bit phase encoding.

Description

Technical Field

[0001] This invention belongs to the field of array signal processing and wireless communication technology, specifically an angle prior-aided intelligent metasurface phase coding design method for two-dimensional direction of arrival estimation. Background Technology

[0002] Direction of arrival (DOA) estimation is a key technology in array signal processing, playing a crucial role in radar, sonar, and wireless communication. Traditional DOA estimation relies on multi-antenna array structures to spatially sample incident electromagnetic waves to obtain directional information, and its performance is limited by the array's physical aperture and the number of array elements. Although advanced signal processing algorithms such as Multiple Signal Classification (MUSIC) and Rotation Invariant (ESPRIT) algorithms have been proposed to some extent to overcome the Rayleigh limit and improve estimation performance, they have not fundamentally eliminated the dependence of traditional architectures on a large number of array elements. Furthermore, each array element still requires a separate, costly, and high-power RF link, limiting its application in low-cost, miniaturized, and low-power scenarios.

[0003] Smart metasurfaces, as low-cost, programmable artificial electromagnetic surfaces, can modulate the amplitude, phase, or polarization response to incident electromagnetic waves by changing the bias state of adjustable elements through external control signals, providing a new approach to reducing the complexity of direction-of-arrival (DOA) estimation systems. By combining smart metasurfaces with a single receiving channel, DOA estimation can be achieved with significantly simplified hardware. However, the performance of existing smart metasurface-assisted DOA estimation methods is limited by the reconfigurable coding matrix, and coding optimization methods often aim to improve the cross-correlation of the sensing matrix. Their optimization criteria lack a direct and explicit mathematical connection with the core performance indicators of DOA estimation—estimation accuracy and its theoretical lower bound, the Cramer-Rao bound (CRB). This results in the underutilization of the performance improvement potential of coding design. Furthermore, although some studies have attempted phase design based on minimizing the Cramer-Rao bound, this usually requires prior knowledge of the target's angle, which is difficult to obtain in practice, limiting the practicality of the methods. Summary of the Invention

[0004] To address the shortcomings of existing technologies, the purpose of this invention is to provide an angle-prior-assisted intelligent metasurface phase coding design method for two-dimensional direction-of-arrival estimation.

[0005] The technical solution to achieve the purpose of this invention is: an angle prior-aided intelligent metasurface phase coding design method for two-dimensional direction-of-arrival estimation, comprising:

[0006] Step 1: Construct a two-dimensional direction-of-arrival estimation system model for a single receiving channel on an intelligent metasurface;

[0007] Step 2: Based on the system model, derive the mathematical expression between the Cramer-Rao bound and the phase coding matrix of the two-dimensional direction-of-arrival estimation parameters;

[0008] Step 3: Using the prior range information of the target azimuth and elevation angles, construct an optimization problem with minimizing the average Cramer-Rao bound within the prior range as the optimization objective and the unit modulus of the phase encoding matrix elements as the constraint.

[0009] Step 4: Solve the optimization problem using the Riemannian manifold optimization algorithm to obtain the optimal phase encoding matrix;

[0010] Compared with the prior art, the significant features of this invention are:

[0011] (1) The design of the phase coding matrix of the intelligent metasurface is directly and explicitly linked to the Cramer-Rao bound, the theoretical performance lower bound of the direction of arrival estimation. By minimizing the Cramer-Rao bound, the coding is optimized, which in principle ensures that the optimized coding can maximize the potential of the estimation accuracy.

[0012] (2) The rough prior range information of the target angle is modeled into the optimization framework so that the optimized intelligent metasurface beam pattern can focus energy on the region where the target may appear, thereby significantly improving the estimation performance in that region.

[0013] (3) For non-convex optimization problems with unit modulus constraints, an optimization algorithm based on Riemannian manifold is proposed, which naturally integrates the constraints into the iterative process to achieve efficient and stable convergence.

[0014] (4) The method of the present invention can still maintain significant performance advantages and has good robustness under one-bit phase encoding.

[0015] The objects and other advantages of the present invention can be realized and obtained by means of the structures particularly pointed out in the written description, claims and drawings. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of the intelligent metasurface single-receiver channel two-dimensional direction of arrival estimation system model provided in an embodiment of the present invention.

[0017] Figure 2 This is a graph showing the convergence process of the objective function in an embodiment of the present invention as a function of the number of iterations.

[0018] Figure 3 This is a comparison diagram of the beam directions of embodiments of the present invention with random coding and Hadamard coding methods.

[0019] Figure 4 This is a comparison chart of the root mean square error and Cramer-Rao boundary of the estimation of the embodiments of the present invention and the comparison method under different signal-to-noise ratios.

[0020] Figure 5 This is a comparison chart of the root mean square error of the estimation and the Cramer-Rao boundary under different azimuth angles of the embodiments and comparison methods of the present invention.

[0021] Figure 6 This is a comparison chart of the root mean square error and Cramer-Rao boundary estimated by the embodiments and comparison methods of the present invention under different numbers of measurements.

[0022] Figure 7 This is a comparison diagram of the beam direction under one-bit phase coding of the embodiments of the present invention and the comparison method. Detailed Implementation

[0023] It is readily understood that, based on the technical solution of this invention, various embodiments of the invention can be conceived by those skilled in the art without altering the essential spirit of the invention. Therefore, the following detailed embodiments and accompanying drawings are merely illustrative examples of the technical solution of this invention and should not be considered as the entirety of the invention or as limitations or restrictions on the technical solution of this invention. Rather, these embodiments are provided to enable those skilled in the art to gain a more thorough understanding of the invention. Preferred embodiments of the invention are described below in conjunction with the accompanying drawings, which form part of this application and, together with the embodiments of the invention, serve to illustrate the innovative concept of the invention.

[0024] An angle-prior-assisted intelligent metasurface phase coding design method for two-dimensional direction-of-arrival estimation, the specific steps of which are as follows:

[0025] Step 1: Construct a two-dimensional direction-of-arrival estimation system model for a single-receiver channel on an intelligent metasurface, specifically as follows:

[0026] consider A far-field source is incident on a... On a uniform array composed of transmissive intelligent metasurface units It is the number of row cells arranged horizontally in the metasurface array. This is the number of column units arranged vertically in the metasurface array. shaft and The intervals along the axial direction are respectively and , No. The center coordinates of a metasurface unit can be expressed as: , .

[0027] No. During the second measurement, , No. The signal received by each metasurface unit is

[0028]

[0029] in For the first During the second measurement The complex envelope of a source, Assuming the signal remains constant within a certain measurement interval, that is... , It's the wavelength. and They are the first The azimuth and elevation angles of the source, It is the first During the second measurement Noise term of each metasurface unit, It is the noise power of the metasurface unit.

[0030] The transmissive metasurface performs phase encoding on the received signal, and the encoded signal is represented as follows:

[0031]

[0032] in Indicates the first In the second measurement Phase encoding value of each metasurface unit.

[0033] The transmitted signals from all metasurface units propagate through free space to the same receiving channel, which is the first receiving channel. The received signal of this measurement is represented as

[0034]

[0035] in For the first The distance from each metasurface unit to the receiving channel, For the receiving channel relative to the center of the metasurface array Axis offset, It is the first Thermal noise at the receiver during the second measurement It is the receiver noise power.

[0036] Vectorize (3), the first... The received signal of this measurement is represented as

[0037]

[0038] in For the first Phase encoding vector of the second measurement Defined as the propagation phase delay matrix and , It is the signal source vector. Indicates the first The noise vector of the metasurface array measured in the second measurement. It is an array steering matrix. It is the first The array steering vector corresponding to each signal source, where

[0039]

[0040]

[0041]

[0042] In the formula, It is the first A signal source in Sub-guidance vector of direction, It is the first The signal source is The sub-guiding vector of the direction.

[0043] All The next measurement is stacked as The overall model for estimating the direction of arrival (DOA) of a single receiver channel assisted by a smart metasurface array is as follows:

[0044]

[0045] in Defined as a phase encoding matrix, , Represents the diagonal matrix of the construct block. , express The identity matrix, , .

[0046] Step 2: Based on the system model, derive the mathematical expression between the Cramer-Rao bound and the phase encoding matrix of the two-dimensional direction-of-arrival estimation parameters, specifically as follows:

[0047] Consider the case of a single signal source. Based on the signal model given in (8), the received signal is represented as...

[0048]

[0049] Define parameter vector .because , And since the two are independent of each other, the received signal satisfies For this complex Gaussian distribution, the general elements of its FIM matrix are:

[0050]

[0051] in The mean, Let be the covariance matrix.

[0052] because With unknown parameters Irrelevant, therefore the FIM matrix simplifies to

[0053]

[0054] in , , .

[0055] Assuming the total noise of the received signal model is dominated by metasurface noise, i.e. At the same time, due to ,but Simplified to

[0056]

[0057] The Cramérob boundary matrix is ​​represented as , the Cramer-Rao boundary matrix The relevant angle parameters in the upper left corner are the azimuth angles. and pitch angle of The submatrix, denoted as . Matrix Rewritten in the following block format:

[0058]

[0059] in

[0060]

[0061] Based on the formula for inverting a block matrix:

[0062]

[0063] in We can obtain:

[0064]

[0065] Define a scalar function:

[0066]

[0067] in, This represents the trace operation on a matrix. The mathematical expression between the CRB of the two-dimensional DOA estimation parameters and the phase encoding matrix is: .

[0068] Step 3: Utilizing the prior range information of the target azimuth and elevation angles, construct an optimization problem with the objective of minimizing the average Cramer-Rao bound within the prior range and the unit modulus of the phase encoding matrix elements as the constraint. Specifically:

[0069] Through optimization Minimizing the Cramer-Rao bound is equivalent to solving the following problem:

[0070]

[0071] Let the prior ranges of azimuth and elevation be denoted as follows: and Perform uniform sampling on it:

[0072]

[0073]

[0074] The optimization problem is reformulated as optimization under unity modulus constraints. To minimize the average Cramer-Rao bound within the a priori direction of arrival, i.e.

[0075]

[0076] in, This corresponds to the unknown angle parameter in (19). and Replace with specific and .

[0077] Step 4: Solve the optimization problem using the Riemannian manifold optimization algorithm to obtain the optimal phase encoding matrix, specifically as follows:

[0078] Step 4.1: Represent the feasible set of the phase encoding matrix as a Riemannian manifold.

[0079] Phase encoding matrix The feasible set is represented as a Riemannian manifold, i.e.

[0080]

[0081] In the formula, Representing a dimension as A complex matrix.

[0082] Step 4.2: Derive the conjugate Euclidean gradient of the objective function

[0083] Before performing Riemannian manifold optimization, it is necessary to derive the objective function. conjugate Euclidean gradient The derivation process first requires a solution. To simplify the symbolic representation, the following auxiliary matrix is ​​introduced:

[0084]

[0085] Based on the definition of the auxiliary matrix, it can be deduced that...

[0086]

[0087] In the formula, and These represent the trace and differentiation operations on a matrix, respectively.

[0088] because

[0089]

[0090]

[0091] in , Representing the matrix and Taking the complex conjugate operation, then It can be further transformed into:

[0092]

[0093] For a scalar function, its differential can be expressed by its conjugate Euclidean gradient as follows:

[0094]

[0095] Therefore, in order to extract , need to Organized into Format:

[0096]

[0097] in, , , , , .

[0098] By matching The coefficient can be obtained. The expression is

[0099]

[0100] Therefore, the conjugate Euclidean gradient of the objective function It can be represented as:

[0101]

[0102] Step 4.3: Calculate the Riemann gradient of the objective function.

[0103] The Riemann gradient is the conjugate Euclidean gradient. The projection onto the tangent space, where the tangent space is composed of... All tangent vectors at a given point span the length of the vector. Projecting onto this tangent space yields the Riemann gradient:

[0104]

[0105] in, This indicates the operation of taking the real part. Represents a matrix Take the complex conjugate operation, For Hadama accumulation.

[0106] Step 4.4: Determine the search direction and step size

[0107] set up Phase encoding matrix No. The iteration matrix for this iteration takes the negative direction of the Riemann gradient as the descent search direction for the objective function in this iteration, i.e. descent search direction along the objective function Perform a line search to obtain matrix-type iteration points on the manifold. ,in The search step size for the Armijo backtracking line is determined by starting from the initial step size. proportionally Gradually narrow down the found satisfaction The step size.

[0108] Step 4.5: Perform a retraction mapping to update the phase encoding matrix.

[0109] The points obtained in step 4.4 It may not be on a manifold Above. Therefore, a shrinkage operator is employed. Map this point back to the manifold This ensures that the value taken in the next iteration remains on the manifold. Above. Therefore, the first... The update formula for the next iteration is:

[0110]

[0111] In the formula, This indicates taking the nth element in the matrix. line, number Column elements, , Determine if the current phase encoding matrix satisfies... ,in The convergence threshold is [value]. If [condition] is satisfied, the resulting phase encoding matrix is ​​[value]. That is, the optimal phase encoding matrix. Otherwise, return to step 4.2.

[0112] Example 1

[0113] This invention is verified using computer simulation, and all steps and conclusions have been verified to be correct using MATLAB.

[0114] The simulation parameters are configured as follows: element spacing , the number of UPA array elements , Number of measurements The true azimuth angle of the signal source is The pitch angle is Signal-to-noise ratio at metasurface array Signal-to-noise ratio at the receiver All Set a narrow prior angle range: azimuth. Pitch angle Wide prior angle range: azimuth Pitch angle In the simulation, the performance of the proposed CRB-MO method is compared with that of the random coding method and the Hadamard coding method in both narrow and wide prior angle ranges, using these as benchmarks.

[0115] A single far-field source incident on a by On a uniform array composed of transmissive intelligent metasurface units, as shown in the attached diagram of the instruction manual. Figure 1 As shown. The overall model for intelligent metasurface array-assisted single-receiver channel direction-of-arrival estimation is as follows:

[0116]

[0117] in, It is a phase encoding matrix. , Indicates the first In the second measurement Phase encoding values ​​of each metasurface unit; It is the propagation phase delay matrix. ,

[0118] For the first The distance from each metasurface unit to the receiving channel, and The arrays are respectively in shaft and Spacing in the axial direction, For the receiving channel relative to the center of the metasurface array Axis offset; It is the complex envelope of the single source; , , , Indicates the first The noise vector of the metasurface array in the second measurement. It is the first During the second measurement Noise term of each metasurface unit; , It is the first Thermal noise at the receiver during the measurement. It is the array steering vector, where

[0119]

[0120]

[0121] Based on the above system model, the objective function of the phase coding design based on minimizing the Cramer-Rao bound is expressed as follows:

[0122]

[0123] in and , , , , , The prior ranges for azimuth and elevation angles are denoted as follows: and , and They are respectively represented as

[0124]

[0125]

[0126] The gradient descent algorithm is extended to Riemannian manifolds to solve the objective function minimization problem. In the... In the next iteration The update can be represented as

[0127]

[0128] in, This indicates the search direction along the negative Riemann gradient. , , , , , , , This is the step size obtained using the Armijo backtracking strategy.

[0129] make An initial phase matrix is ​​randomly generated as the convergence threshold. And continue to iterate until the conditions are met. hour,

[0130] Obtain the optimal phase coding design matrix .

[0131] Based on the above simulation conditions, the simulation graphics are shown in the attached figures in the instruction manual.

[0132] Simulation 1: Simulate the convergence process of the objective function. Figure 2 (a) and Figure 2 (b) shows the changes in the objective function values ​​with the number of iterations for narrow and wide prior angle ranges, respectively. The objective function value is the upper left corner of the Cramer-Rao bounding matrix related to the azimuth and elevation angle estimations. The trace of the submatrix. Within the prior angle range, both azimuth and elevation angles are... The sampling step size is shown in the figure. As can be seen from the figure, within a narrow prior angle range, the objective function value decreases rapidly with the number of iterations and tends to stabilize after approximately the 12th iteration. This indicates that the CRB-MO method can converge quickly and efficiently approach the optimal solution with relatively accurate prior information. Within a wide prior angle range, the algorithm requires more iterations and converges relatively more slowly, but it still ultimately achieves stable optimization.

[0133] Simulation 2: The beam pattern of the array is further presented. The beam pattern describes the spatial power response of the antenna array and is defined as follows: Its shape directly reflects the array's ability to enhance or suppress signals in a specific angular region. The fixed pitch angle is... The array gain varies with the azimuth angle. The relationship of change is as follows Figure 3 As shown. By Figure 3 It is evident that both the random coding method and the Hadamard coding method exhibit a relatively flat power distribution across the entire angular domain, with the random coding method exhibiting greater fluctuations. The CRB-MO method utilizes prior angular information, concentrating the power of the generated beam within a specific direction-of-arrival (DOA) range. Furthermore, thanks to more specific prior angular information, a narrower prior angular range results in a more concentrated power distribution than a wider prior angular range. The CRB-MO method focuses radiated energy on the angular region where the target is likely to appear through coding optimization, explaining why it demonstrates superior performance in DOA estimation.

[0134] Simulation 3: Figure 4 The study demonstrates the Cramer-Rao bound and RMSE of the azimuth angle with signal-to-noise ratio (SNR) for both the baseline coding method and the CRB-MO method across narrow and wide prior angle ranges. The SNR range is shown in the figure. The step size was 5 dB. As shown in the figure, with increasing signal-to-noise ratio (SNR), the Cramer-Rao bound and RMSE of both baseline coding methods and the CRB-MO method gradually decreased. In the low SNR range, the RMSE of all three methods was dominated by noise and had a certain distance from the Cramer-Rao bound, but the CRB-MO method still maintained a significant advantage over the two baseline coding methods. Furthermore, the CRB-MO method converged faster; when SNR > -10 dB, the RMSE curves of the CRB-MO method for different prior angle ranges began to approach the Cramer-Rao bound.

[0135] Simulation 4: Figure 5 This study demonstrates the Cramer-Rao bound and RMSE trends of the azimuth angle with respect to the source azimuth angle for both the baseline coding method and the CRB-MO method in narrow and wide prior angle ranges. The test range for the azimuth angle is as follows: ,by The step size. (And) Figure 3 Corresponding to the beam diagrams, the baseline coding method exhibits an approximately uniform power distribution across the entire angular domain. Therefore, its Cramer-Rao bound and RMSE curves are almost identical across the entire test angle range. However, due to power dispersion, the Cramer-Rao bound and RMSE curves of both baseline coding methods are generally higher than those of the CRB-MO method. The Cramer-Rao bound and RMSE curves of the CRB-MO method are approximately symmetrically distributed. Because of its more concentrated power within the prior angle range, the CRB-MO methods in different prior angle ranges have lower Cramer-Rao bounds and RMSEs within their respective prior angle ranges. However, outside the prior angle range, the Cramer-Rao bound and RMSE of the CRB-MO method both increase significantly, exceeding those of the baseline coding method.

[0136] Simulation 5: Figure 6 The study demonstrates the trends of the Cramer-Rao boundary and RMSE of azimuth angles with the number of measurements for both the baseline coding method and the CRB-MO method in narrow and wide prior angle ranges. The number of measurements is set to... As shown in the figure, with the increase in the number of measurements, the Cramer-Rao bound and RMSE of both the baseline encoding method and the CRB-MO method gradually decrease and eventually plateau. At the same number of measurements, the Cramer-Rao bound and RMSE of the CRB-MO method are consistently much lower than those of the baseline encoding method. Furthermore, more accurate angle prior information can significantly reduce the number of measurements required to achieve the same estimation accuracy, which is beneficial for reducing training overhead.

[0137] Simulation 6: For reconfigurable smart metasurfaces, some can only realize 0 and 2. Two discrete phases. The CRB-MO method does not incorporate this constraint when designing the phase encoding matrix; therefore, it is necessary to examine the algorithm's effectiveness under hardware constraints involving phase quantization. The beam pattern after one-bit phase encoding is shown below. Figure 7 As shown, compared to Figure 3 The beam pattern exhibits greater fluctuations after one-bit phase encoding. However, it is noteworthy that the quantization operation did not alter the relative power distribution characteristics of the baseline method and the CRB-MO method under different prior angle ranges. Furthermore, simulation verification shows that the direction-of-arrival estimation performance obtained using the one-bit phase-encoded matrix is ​​consistent with that of the unquantized method. The CRB-MO method remains effective and outperforms both baseline encoding methods, demonstrating the proposed algorithm's robustness.

[0138] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto.

[0139] Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this invention should be included within the protection scope of this invention.

[0140] It should be understood that, in order to simplify the present invention and help those skilled in the art understand its various aspects, in the above description of exemplary embodiments of the present invention, various features of the present invention are sometimes described in a single embodiment or with reference to a single figure. However, the present invention should not be construed as including all features in the exemplary embodiments as essential technical features of the claims of this patent.

Claims

1. A method for designing phase encoding of an angle prior-aided intelligent metasurface for two-dimensional DOA estimation, characterized in that, Includes the following steps: Step 1: Construct a two-dimensional DOA estimation system model for a single receiver channel on an intelligent metasurface; Step 2: Based on the intelligent metasurface single-receiver channel two-dimensional DOA estimation system model, derive the mathematical expression between the CRB of the two-dimensional DOA estimation parameters and the phase coding matrix; Step 3: Using the prior range information of the target azimuth and elevation angles, construct an optimization problem with minimizing the average CRB within the prior range as the optimization objective and the unit modulus of the phase encoding matrix elements as the constraint. Step 4: Solve the optimization problem using the Riemannian manifold optimization algorithm to obtain the optimal phase encoding matrix. The specific method is as follows: Step 7.1: Represent the feasible set of the phase encoding matrix as a Riemannian manifold, specifically as follows: ； In the formula, Representing a dimension as Complex matrices; Step 7.2: Determine the conjugate Euclidean gradient of the objective function ,in Azimuth sampling point and pitch angle sampling points After discretization, the conjugate gradient of the function is obtained; Step 7.3: Find the conjugate Euclidean gradient of the objective function. The Riemann gradient is calculated by projecting the gradient onto the tangent space of the Riemann manifold. ; Step 7.4: Take the negative direction of the Riemann gradient as the descent search direction of the objective function in this iteration, i.e. descent search direction along the objective function Perform a line search to obtain matrix-type iteration points on the manifold. ,in The search step size for the Almiho backtracking line; Step 7.5: Employ the shrinkage operator The above matrix-type iteration points Mapping back manifold , obtained the Phase encoding matrix of the next iteration: ； In the formula, This indicates taking the nth element in the matrix. line, number Column elements, , ; Step 7.6: Determine whether the current phase encoding matrix satisfies the following conditions. ,in The convergence threshold is [value]. If [condition] is satisfied, the resulting phase encoding matrix is ​​[value]. That is, the optimal phase encoding matrix. Otherwise, return to step 7.

2.

2. The angle prior-aided intelligent metasurface phase coding design method for two-dimensional DOA estimation according to claim 1, characterized in that, The specific model of the intelligent metasurface single-receiver channel two-dimensional DOA estimation system is as follows: ； in, It is a phase encoding matrix. For the first Phase encoding vector of the second measurement , This is the total number of measurements; It is the propagation phase delay matrix. It is the signal source vector. , Represents the diagonal matrix of the construct block. , express The identity matrix, This represents the noise matrix of the metasurface array. This represents the thermal noise matrix at the receiver. This represents the array steering matrix.

3. The angle prior-aided intelligent metasurface phase coding design method for two-dimensional DOA estimation according to claim 2, characterized in that, The propagation phase delay matrix is ​​as follows: ； in, , It's the wavelength. For the first The distance from each metasurface unit to the receiving channel, and The arrays are respectively in shaft and Spacing in the axial direction, For the receiving channel relative to the center of the metasurface array Axis offset, It is the number of row cells arranged horizontally in the metasurface array. It is the number of column units arranged in the vertical direction of the metasurface array.

4. The angle prior-aided intelligent metasurface phase coding design method for two-dimensional DOA estimation according to claim 2, characterized in that, The array steering matrix is ​​as follows: ； In the formula, It is the first The array steering vector corresponding to each signal source is expressed as: ； ； ； In the formula, It is the first A signal source in Sub-guidance vector of direction, It is the first The signal source is Sub-guidance vector of direction, It is the first The azimuth angle of each signal source. It is the first The elevation angle of a signal source, It is the number of row cells arranged horizontally in the metasurface array. It is the number of column units arranged in the vertical direction of the metasurface array. and The arrays are respectively in shaft and Spacing in the axial direction.

5. The angle prior-aided intelligent metasurface phase coding design method for two-dimensional DOA estimation according to claim 2, characterized in that, The mathematical expression for the relationship between the CRB and the phase encoding matrix of the two-dimensional DOA estimation parameters is as follows: ； in, This represents the 2×2 submatrix at the top left corner of the Cramérob boundary matrix. Taking traces, Estimate the azimuth parameter for DOA. To estimate the pitch angle parameter for DOA, It is a single-source complex amplitude signal. , , , , , It is the array steering vector corresponding to a single signal source. It is the number of row cells arranged horizontally in the metasurface array. It is the number of column units arranged in the vertical direction of the metasurface array. It is the noise power of the metasurface unit.

6. The angle prior-aided intelligent metasurface phase coding design method for two-dimensional DOA estimation according to claim 5, characterized in that, Using prior information about the target azimuth and elevation angles, the optimization problem constructed with minimizing the average CRB within the prior range as the optimization objective and the unit modulus of the phase encoding matrix elements as the constraint is as follows: ； in Let be the objective function. , , The number of azimuth angle samples. This represents the prior range of the azimuth angle. , The number of pitch angle samples. For the prior range of the pitch angle, It is a phase encoding matrix The Line 1 Column elements, , It is the number of row cells arranged horizontally in the metasurface array. It is the number of column units arranged in the vertical direction of the metasurface array. This represents the total number of measurements.

7. The angle prior-aided intelligent metasurface phase coding design method for two-dimensional DOA estimation according to claim 1, characterized in that, Determine the azimuth sampling point and pitch angle sampling points Discretize the function and then use the conjugate gradient. The specific method is as follows: Introduce the following auxiliary matrix: ； Determined based on the definition of the auxiliary matrix ； In the formula, and These represent the trace and differentiation operations on a matrix, respectively. because ； ； in, , Representing the matrix and Take the conjugate operation; but Further transformed into: ； The differential of the scalar function can be expressed using the conjugate Euclidean gradient as follows: ； Will Organized into Format: ； in, , , , , ; By matching The coefficient is obtained. The expression is: 。 8. The angle prior-aided intelligent metasurface phase coding design method for two-dimensional DOA estimation according to claim 1, characterized in that, The Riemann gradient is specifically: ； In the formula, This indicates the operation of taking the real part. Represents a matrix Take the complex conjugate operation, For Hadama accumulation.

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