Sparse signal modeling method and device for electromagnetic metasurface

Abstract

The invention discloses an electromagnetic metasurface sparse signal modeling method and device. The method comprises the steps that S1, sparse electromagnetic signals of an electromagnetic metasurface are acquired; s2, solving through signal sparse prior knowledge under the constraint of an electromagnetic constitutive equation to obtain a sparse signal distribution function; s3, according to the sparse signal distribution function, obtaining the coordinate system representation of the sparse signal in the Riemannian manifold space; and S4, according to the coordinate system representation of the sparse signal in the Riemannian manifold space, establishing a signal electromagnetic field manifold embedding model of the sparse signal mapped in the Riemannian space based on the electromagnetic metasurface. By the adoption of the technical scheme, the problems of an existing electromagnetic metasurface sparse signal modeling method in the aspects of algorithm efficiency, model adaptability and hardware collaboration are solved.

Description

Technical Field

[0001] The present invention belongs to the technical field of sparse signal processing, and in particular relates to a method and device for modeling sparse signals on an electromagnetic metasurface. Background Art

[0002] As an artificial electromagnetic structure, electromagnetic metasurfaces control the phase, amplitude, and polarization characteristics of electromagnetic waves through subwavelength-scale unit arrays. In recent years, they have demonstrated significant advantages in wireless communications, radar detection, imaging systems, and other fields. However, as application scenarios expand toward high-frequency bands, large bandwidths, and the joint control of multi-dimensional parameters, the contradiction between the surge in signal dimensions and limited hardware resources faced by metasurface systems has become increasingly prominent. Sparse signal processing methods, as a key technology to reduce the complexity of signal sampling and processing, have been introduced into the field of metasurfaces to solve the problem of high-dimensional electromagnetic signal reconstruction and modeling.

[0003] Existing technical solutions mainly focus on three directions: compressed sensing framework, physical model-driven optimization, and hardware collaborative design. However, there are still technical bottlenecks in algorithm efficiency, reconstruction accuracy, and engineering adaptability. The details are as follows:

[0004] 1) Traditional sparse reconstruction methods based on compressed sensing: Based on the theoretical framework of compressed sensing, the spatial sparsity of metasurface units is exploited to construct the measurement matrix, and signal modeling and reconstruction are achieved through a small number of random measurements. This method has the following limitations: ① The electromagnetic coupling effect between metasurface units leads to non-idealization of the measurement matrix, which destroys the restricted isometry condition of compressed sensing and causes cumulative modeling errors; ② Noise sensitivity is prominent, especially in low signal-to-noise ratio scenarios, where sparse basis mismatch leads to a sharp decline in performance.

[0005] 2) Physical model-driven sparse modeling methods: To address the lack of generalization of traditional data modeling methods, signal modeling is achieved by combining the electromagnetic physical properties of metasurfaces. A structured dictionary matrix is constructed using prior knowledge of the unit phase response, and the sparse coefficients and metasurface configuration parameters are jointly optimized using a convex optimization algorithm. While this method improves the stability of signal modeling, it has the following limitations: ① The nonlinear frequency response characteristics of the metasurface units lead to modeling errors in the dictionary matrix, making it difficult to ensure the completeness of the sparse representation, especially in wideband scenarios; ② The trade-off between optimization model complexity and hardware feasibility is difficult.

[0006] 3) Sparse modeling methods under hardware constraints: To adapt to the programmable nature of metasurfaces, existing technologies have explored hardware-algorithm co-design paths. For example, FPGA-based sparse signal modeling architectures dynamically activate some metasurface units to generate sparse measurement patterns and use distributed processing units to parallelly calculate sparse coefficients. This approach has the following limitations: ① The contradiction between the metasurface control speed and the number of algorithm iterations: high-speed switching can easily introduce timing jitter errors; ② The coupling between hardware resource allocation strategies and electromagnetic performance indicators is not fully modeled, resulting in low energy efficiency.

[0007] In summary, existing sparse signal modeling methods for electromagnetic metasurfaces have significant deficiencies in algorithmic efficiency, model adaptability, and hardware coordination. These shortcomings severely restrict the engineering application of electromagnetic metasurface signal modeling in high-dynamic scenarios. There is an urgent need to develop new sparse signal modeling theories and methods to overcome existing technical bottlenecks. Summary of the Invention

[0008] The technical problem to be solved by the present invention is to provide a method and device for sparse signal modeling of an electromagnetic metasurface.

[0009] To achieve the above object, the present invention adopts the following technical solutions:

[0010] A method for modeling sparse signals on an electromagnetic metasurface, comprising:

[0011] Step S1, obtaining a sparse electromagnetic signal of an electromagnetic metasurface;

[0012] Step S2, solving the signal sparse priori knowledge under the constraints of the electromagnetic constitutive equation to obtain a sparse signal distribution function;

[0013] Step S3: obtaining a coordinate system representation of the sparse signal in the Riemannian manifold space according to the sparse signal distribution function;

[0014] Step S4: According to the coordinate system representation of the sparse signal in the Riemannian manifold space, a signal electromagnetic field manifold embedding model of the sparse signal after the sparse signal is mapped in the Riemannian space based on the electromagnetic metasurface is obtained.

[0015] Preferably, in step S1, a sparse electromagnetic signal of the electromagnetic metasurface is acquired based on a dynamic modulation method.

[0016] Preferably, the sparse signal distribution function is:

[0017]

[0018] Where K is the component order of the multi-scale Gaussian mixture model; Represents the mixing weight coefficient of the i-th component and satisfies represents the distribution function of the i-th component; μ i represents the mean of the i-th component; represents the variance of the i-th component.

[0019] As a preference, the electromagnetic field manifold embedding model of the signal after the sparse signal based on the electromagnetic metasurface is mapped in the Riemann space is expressed as:

[0020]

[0021] in,

[0022] The present invention also provides an electromagnetic metasurface sparse signal modeling device, comprising:

[0023] A first processing module is used to obtain a sparse electromagnetic signal of the electromagnetic metasurface;

[0024] The second processing module is used to solve the signal sparse prior knowledge under the constraints of the electromagnetic constitutive equation to obtain the sparse signal distribution function;

[0025] The third processing module is used to obtain a coordinate system representation of the sparse signal in the Riemannian manifold space according to the sparse signal distribution function;

[0026] The fourth processing module is used to obtain a signal electromagnetic field manifold embedding model after the sparse signal is mapped in the Riemannian space based on the electromagnetic metasurface according to the coordinate system representation of the sparse signal in the Riemannian manifold space.

[0027] Preferably, the first processing module acquires the sparse electromagnetic signal of the electromagnetic metasurface based on a dynamic modulation method.

[0028] Preferably, the sparse signal distribution function is:

[0029]

[0030] Where K is the component order of the multi-scale Gaussian mixture model; Represents the mixing weight coefficient of the i-th component and satisfies represents the distribution function of the i-th component; μ i represents the mean of the i-th component; represents the variance of the i-th component.

[0031] As a preference, the electromagnetic field manifold embedding model of the signal after the sparse signal based on the electromagnetic metasurface is mapped in the Riemann space is expressed as:

[0032]

[0033] in,

[0034] The present invention couples the physical laws of the spatial electromagnetic field with the signal sparsity prior of the signal to model, and proposes to establish a sparse signal representation model under the constraints of Maxwell's equations. Through the sparse signal distribution function approximation solution method that includes the propagation characteristics of electromagnetic waves, the Riemannian geometry manifold space is embedded in the signal space to describe the signal statistical moment characteristics. At the same time, the vector wave equation constraint term is introduced to characterize the curl characteristics of the electromagnetic field, completing the construction of the electromagnetic field manifold embedded sparse signal model based on differential geometry. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are merely embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying any creative work.

[0036] Figure 1 This is a flow chart of the electromagnetic metasurface sparse signal modeling method according to an embodiment of the present invention. DETAILED DESCRIPTION

[0037] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0038] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0039] Example 1:

[0040] like Figure 1 As shown, an embodiment of the present invention provides a method for modeling sparse signals of an electromagnetic metasurface, comprising:

[0041] Step S1: Acquire the sparse electromagnetic signal of the metasurface

[0042] Based on the dynamic and adjustable acquisition of sparse electromagnetic signals from the metasurface, the compressed sensing measurement matrix is solved through the metasurface physical layer, specifically including:

[0043] 1) Dynamically Adjustable Metasurface Structure Design: The electromagnetic metasurface array consists of M×N independently tunable subwavelength elements, each of which achieves dynamic phase modulation from 0 to 2π using a PIN diode or varactor diode. A field-programmable gate array (FPGA)-based control module drives the electromagnetic metasurface array elements to generate a pseudo-random phase distribution sequence {Φ_k}, where k = 1, 2, ..., K. The metasurface reflection / transmission receivers receive the composite and sparse signals and transmit the received data to a signal processing unit for preprocessing.

[0044] Among them, the dynamic modulation of the metasurface generates high-order harmonic components when the metasurface units switch the resonant state in the time domain according to a nonlinear coding sequence. Its spatial distribution is strongly coupled with the phase gradient morphology. By establishing a mapping model between harmonic components and phase gradient distribution parameters and designing a feedback algorithm based on gradient descent, the coding sequence parameters can be optimized in real time, so that the target harmonics (such as ±2nd order) form interference enhancement at the preset spatial position, while suppressing the sidelobe energy of redundant harmonics. The accompanying FPGA control circuit achieves dynamic refreshing of the states of thousands of metasurface units through nanosecond timing synchronization, ensuring phase consistency of spatiotemporal modulation.

[0045] 2) Electromagnetic metasurface sparse signal control: The low-dimensional measurement matrix of the signal is generated by using metasurface spatial encoding. The modulation of the incident wave by the metasurface array element with coordinates (i, j) can be expressed as:

[0046]

[0047] In formula (1), T (i,j) The transmission matrix, which depends on the incident angle θ and frequency ω of the electromagnetic metasurface, dynamically reconstructs the sparse signal through PIN diodes or varactor diodes. The metasurface encoding mechanism is further designed, and the metasurface unit phase distribution φ(x,y) is designed so that the transmitted / reflected field forms a random phase plate spatial encoding pattern, which is equivalent to constructing the measurement matrix Φ of the sparse signal.

[0048] Step S2: Solving the signal sparse prior knowledge under the constraints of the electromagnetic constitutive equation

[0049] Based on the sparse signal measurement matrix obtained from the electromagnetic metasurface, the physical laws of the electromagnetic field are further combined with the sparse signal optimization objectives, and the signal sparse prior knowledge is solved under the constraints of Maxwell's electromagnetic constitutive equations.

[0050] 1) Electromagnetic constitutive equation modeling: The sparse signal measurement matrix is expressed as E = ψs (s is the sparse coefficient) under the frequency domain sparse basis ψ, and is subject to the curl equation K = CurlCurl-ω 2μεI and the divergence equation D = diag(ε) Div constraints, the curl constraint ensures that the electromagnetic field E satisfies the frequency domain Maxwell equations, and the divergence constraint eliminates the pseudo-solutions in the sparse signal representation model solution process, ensuring the physical rationality of the solution results. The sparse signal electromagnetic constitutive equation is expressed as:

[0051]

[0052] In formula (2), Curl is the discrete matrix of the curl operator, ω is the angular frequency, μ and ε are the medium parameters, and I corresponds to the electromagnetic wave source term. Div is the divergence operator, and the constraint The objective function ||s||1 makes the coefficients sparse, which is consistent with the sparsity prior of the signal in the transform domain.

[0053] 2) Solving the signal sparse prior knowledge: We further introduce a multi-scale Gaussian mixture model to approximate and solve the sparse signal distribution function expression of the channel with electromagnetic wave vector characteristics and multipath effects, and obtain an approximate finite mixture model of the distribution function of the nonlinear propagation channel signal with arbitrary parameters, which is expressed as:

[0054]

[0055] In formula (3), K is the component order of the multi-scale Gaussian mixture model, Represents the mixing weight coefficient of the i-th component and satisfies represents the distribution function of the i-th component, μ i represents the mean of the i-th component, In summary, the solution of signal sparse prior knowledge under the constraints of electromagnetic constitutive equations is completed.

[0056] Step S3: Mapping signal sparse prior knowledge to Riemannian manifold space

[0057] In order to intuitively characterize the sparse characteristics of electromagnetic signals, the nonlinear sparse signal prior knowledge is mapped to the Riemannian manifold space based on information geometry theory. The elements in the manifold space are parameterized as coordinates, and the signal differences are projected as information distances between the manifold space coordinates through the statistical moment model. The mapping relationship between the signal data statistical moment model and the global coordinate system of the manifold space is analyzed. The sparse signal distribution function is deformed and calculated, and the signal sparse prior knowledge x is obtained. i The corresponding probability density function is:

[0058]

[0059] In formula (4), x i and As coordinate variables on the Riemannian manifold space, their coefficients are the unit vectors of the coordinate variables. Further, multiple parameters are constructed based on the coordinate variables, which are defined as:

[0060] First parameter: r i1 =x i (5)

[0061] Second parameter:

[0062] The third parameter:

[0063] Fourth parameter:

[0064] Fifth parameter:

[0065] Furthermore, the received signal of the metasurface receiving unit is projected as the coordinates in the Riemannian manifold space The corresponding distribution function is expressed as Complete the coordinate system construction and representation of sparse signals in Riemannian manifold space.

[0066] Step S4: Sparse signal modeling of electromagnetic metasurface

[0067] Using electromagnetic constitutive equations as physical constraints and combining them with prior knowledge of sparse signals, a sparse signal representation method is constructed in a Riemannian manifold space coordinate system. This allows for the construction of high-precision electromagnetic field distribution or medium parameter models from finite sparse signals. The core idea is to enhance the robustness of signal modeling through sparse regularization (such as the L1 norm) while simultaneously leveraging the electromagnetic constitutive equations to constrain the physical consistency of the modeling results.

[0068] According to formula (4) combined with formulas (5), (6), (7), (8) and (9), the signal electromagnetic field manifold embedding model after the sparse signal based on the electromagnetic metasurface is mapped in the Riemann space is obtained as follows:

[0069]

[0070] In formula (10), K is the component order of the Gaussian mixture model. The signal electromagnetic field manifold embedding model is suitable for sparse signal processing scenarios based on electromagnetic metasurfaces. It can be used to model signals using a combination of sparse prior knowledge and electromagnetic physical constraints, even in the context of small amounts of data where data acquisition is difficult. This provides theoretical support for electromagnetic field reconstruction.

[0071] The embodiments of the present invention have the following innovations:

[0072] 1. Dynamically adjustable metasurface encoding and sparse signal acquisition

[0073] Design a programmable electromagnetic metasurface array driven by FPGA. Dynamically control the unit phase distribution through nonlinear coding sequence to generate pseudo-random measurement matrix, thus achieving low-dimensional sparse sampling of high-dimensional electromagnetic signals.

[0074] A mapping model between harmonic components and phase gradient distribution is proposed, and the gradient descent feedback algorithm is combined to optimize the coding sequence, suppress redundant harmonics and enhance the target harmonic interference, thereby improving the efficiency of sparse signal acquisition.

[0075] 2. Metasurface sparse signal modeling by integrating electromagnetic physics laws with sparse priors

[0076] It is proposed to use Maxwell's electromagnetic constitutive equations as electromagnetic physics constraints and jointly model them with prior knowledge of signal sparsity, breaking through the limitations of the traditional method of separating data-driven and physical models, and significantly improving the physical consistency and noise resistance of sparse signal modeling; introducing the curl equation (Maxwell's equations in the frequency domain) and divergence equation constraints in solving the sparse signal measurement matrix to eliminate pseudo-solutions and ensure the physical rationality of the electromagnetic field distribution.

[0077] 3. Solving sparse signal prior knowledge under the constraints of electromagnetic constitutive equations

[0078] Combined with the multi-scale Gaussian mixture model, the sparse signal distribution function of the electromagnetic wave vector characteristics and the multipath effect channel is approximated and solved to obtain sparse signal prior knowledge, thereby enhancing the model's adaptability to complex propagation scenarios.

[0079] 4. Nonlinear representation of sparse signals based on Riemannian manifold space

[0080] Based on the theory of information geometry, the prior knowledge of sparse signals is mapped to the Riemannian manifold space. The statistical characteristics of the signal are analyzed through the statistical moment model and information distance, and the geometric characteristics of the manifold space are used to solve the problem of nonlinear sparse signal modeling. A joint optimization model based on electromagnetic constitutive equations and manifold embedding is constructed to achieve high-precision signal modeling of the metasurface with a small amount of data.

[0081] Example 2:

[0082] An embodiment of the present invention further provides an electromagnetic metasurface sparse signal modeling device, comprising:

[0083] A first processing module is used to obtain a sparse electromagnetic signal of the electromagnetic metasurface;

[0084] The second processing module is used to solve the signal sparse prior knowledge under the constraints of the electromagnetic constitutive equation to obtain the sparse signal distribution function;

[0085] The third processing module is used to obtain a coordinate system representation of the sparse signal in the Riemannian manifold space according to the sparse signal distribution function;

[0086] The fourth processing module is used to obtain a signal electromagnetic field manifold embedding model after the sparse signal is mapped in the Riemannian space based on the electromagnetic metasurface according to the coordinate system representation of the sparse signal in the Riemannian manifold space.

[0087] As an implementation method of an embodiment of the present invention, the first processing module obtains the sparse electromagnetic signal of the electromagnetic metasurface based on a dynamic modulation method.

[0088] As an implementation method of an embodiment of the present invention, the sparse signal distribution function is:

[0089]

[0090] Where K is the component order of the multi-scale Gaussian mixture model; Represents the mixing weight coefficient of the i-th component and satisfies represents the distribution function of the i-th component; μ i represents the mean of the i-th component; represents the variance of the i-th component.

[0091] As an implementation method of an embodiment of the present invention, the signal electromagnetic field manifold embedding model after the sparse signal based on the electromagnetic metasurface is mapped in the Riemann space is expressed as:

[0092]

[0093] in,

[0094] The embodiments described above are merely descriptions of preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by persons skilled in the art should fall within the scope of protection defined by the claims of the present invention.

Claims

1. A method for modeling sparse signals on electromagnetic metasurfaces, characterized in that: include: Step S1, obtaining a sparse electromagnetic signal of an electromagnetic metasurface; Step S2, solving the signal sparse priori knowledge under the constraints of the electromagnetic constitutive equation to obtain a sparse signal distribution function; Step S3: obtaining a coordinate system representation of the sparse signal in the Riemannian manifold space according to the sparse signal distribution function; Step S4: According to the coordinate system representation of the sparse signal in the Riemannian manifold space, a signal electromagnetic field manifold embedding model of the sparse signal after the sparse signal is mapped in the Riemannian space based on the electromagnetic metasurface is obtained.

2. The electromagnetic metasurface sparse signal modeling method according to claim 1, wherein: In step S1, a sparse electromagnetic signal of the electromagnetic metasurface is acquired based on a dynamic modulation method.

3. The electromagnetic metasurface sparse signal modeling method according to claim 2, wherein: The sparse signal distribution function is: Where K is the component order of the multi-scale Gaussian mixture model; Represents the mixing weight coefficient of the i-th component and satisfies represents the distribution function of the i-th component; μ i represents the mean of the i-th component; represents the variance of the i-th component.

4. The electromagnetic metasurface sparse signal modeling method according to claim 3, wherein: The electromagnetic field manifold embedding model of the sparse signal based on the electromagnetic metasurface after mapping in the Riemann space is expressed as: in, q∈(1,2).

5. An electromagnetic metasurface sparse signal modeling device, characterized in that: include: A first processing module is used to obtain a sparse electromagnetic signal of the electromagnetic metasurface; The second processing module is used to solve the signal sparse prior knowledge under the constraints of the electromagnetic constitutive equation to obtain the sparse signal distribution function; The third processing module is used to obtain a coordinate system representation of the sparse signal in the Riemannian manifold space according to the sparse signal distribution function; The fourth processing module is used to obtain a signal electromagnetic field manifold embedding model after the sparse signal is mapped in the Riemannian space based on the electromagnetic metasurface according to the coordinate system representation of the sparse signal in the Riemannian manifold space.

6. The electromagnetic metasurface sparse signal modeling device according to claim 5, wherein: The first processing module obtains the sparse electromagnetic signal of the electromagnetic metasurface based on a dynamic modulation method.

7. The electromagnetic metasurface sparse signal modeling device according to claim 6, wherein: The sparse signal distribution function is: Where K is the component order of the multi-scale Gaussian mixture model; Represents the mixing weight coefficient of the i-th component and satisfies represents the distribution function of the i-th component; μ i represents the mean of the i-th component; represents the variance of the i-th component.

8. The electromagnetic metasurface sparse signal modeling device according to claim 7, wherein: The electromagnetic field manifold embedding model of the sparse signal based on the electromagnetic metasurface after mapping in the Riemann space is expressed as: in, q∈(1,2).

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