Metasurface two-dimensional high-resolution signal source positioning method based on deep learning aided design

Abstract

The invention belongs to the field of metasurface electromagnetic signal processing, and particularly relates to a deep learning aided design-based metasurface two-dimensional high-resolution signal source positioning method. The super-surface two-dimensional high-resolution signal source positioning method based on deep learning aided design comprises a matched filtering algorithm and an image denoising algorithm. The method comprises the following steps: firstly, performing principle analysis and mathematical modeling on a metasurface two-dimensional signal source positioning function based on a ray tracing method and metasurface physical parameters to obtain a matrix equation; secondly, performing matrix inverse operation on the equality by adopting a matched filtering algorithm, preliminarily estimating two-dimensional position information of the signal source, and outputting the two-dimensional position information in an image form; and finally, inputting image information into the image denoising deep neural network by adopting an image denoising algorithm, and finally realizing two-dimensional high-resolution signal source positioning. According to the high-resolution signal source positioning method, multiple times of simulation and experiments are carried out on the basis of the two-dimensional gradient programmable metasurface platform, and a large number of data results prove that the method has the advantages of high resolution, low complexity and the like.

Description

Technical Field

[0001] The present invention belongs to the field of metasurface electromagnetic signal processing, specifically a deep learning-assisted design method that can achieve two-dimensional high-resolution signal source positioning on metasurfaces, mainly involving matched filtering algorithms and image denoising algorithms. Background Art

[0002] Radar applications in the microwave field can operate around the clock and penetrate a wide range of media, including paper, plastic, and glass, offering broad application prospects. In recent years, metasurfaces, due to their flexible electromagnetic wave control, ease of deployment, and low cost, have begun to replace traditional phased array antennas for signal source localization, a process known as signal source location. However, at present, most of the signal source positioning functions assisted by metasurfaces can only perform positioning estimation of azimuth or pitch angles. Therefore, in order to obtain more information such as signal source polarization and frequency, it is necessary to rely on more powerful metasurface devices to achieve it; secondly, from the perspective of implementation methods, there are three main methods for recovering signal source position information, namely compressed sensing, traditional algorithms and machine learning. However, these methods all have some problems. Among them, taking the orthogonal matching pursuit (OMP) algorithm as an example, the compressed sensing method has a large number of adjustable parameters, which makes it difficult to quickly achieve accurate signal source positioning, and it is easy to cause confusion and overlap in positioning results due to insufficient physical resolution; taking the multiple signal classification (MUSIC) algorithm as an example, the traditional algorithm needs to determine the number information of the signal source in advance and is greatly affected by environmental interference factors; taking the classification algorithm as an example, the machine learning method relies on the data set obtained in a certain situation. When facing changes in internal structure or external environment, the accuracy of signal source positioning will be greatly reduced. Summary of the Invention

[0003] To address these issues, the present invention combines matched filtering and deep learning methods. By introducing a deep neural network for image denoising, a deep learning-assisted metasurface two-dimensional high-resolution signal source localization method is established. This method transforms the data optimization process into image processing, ultimately achieving high-resolution signal source localization. Multiple simulations and experiments have been conducted on this method based on the existing metasurface platform to verify its effectiveness, which has important potential applications in the fields of national defense and information communications.

[0004] The present invention discloses a method for positioning a two-dimensional high-resolution signal source on a hypersurface using deep learning-assisted design. The method comprises the following steps:

[0005] Step 1: Based on the ray tracing method and the physical parameters of the metasurface, the principle analysis and mathematical modeling of the two-dimensional signal source positioning function are carried out to obtain the received signal;

[0006] Step 2: Based on the matched filtering algorithm, the two-dimensional position information of the signal source is preliminarily estimated by the received signal, and the two-dimensional position information is converted into an image;

[0007] Step 3: Process the two-dimensional position information image through an image denoising deep neural network to obtain two-dimensional high-resolution signal source positioning.

[0008] Furthermore, in step 1, for N unknown signal sources incident on the metasurface, the electric field intensity at each unit is Expressed as:

[0009]

[0010] Among them, φ n is the pitch angle, θ n is the azimuth angle, m and n represent the metasurface unit number and the signal source number at different positions, respectively, k is the free space wave number, x m and y m Represents the coordinate values ​​of the mth unit along the x and y axes, E n Represents the initial information of the electric field of the nth unknown signal source.

[0011] Furthermore, in step 1, the phase response of each metasurface unit to the electromagnetic wave is assigned a random value between 180° and 0°, and the received signal s of the receiving antenna at a certain moment can be obtained as:

[0012]

[0013] x r ,y r , z r is the receiving antenna position, and A m They represent the phase and amplitude responses of the mth metasurface unit to the reflected electromagnetic wave, respectively. The phase responses of 180° and 0° correspond to the coding states of 1 and 0, respectively. The coding states of all units together constitute the coded aperture of the metasurface.

[0014] Furthermore, in step 1, by configuring the metasurface coded aperture L times and sampling the receiving horn L times, the final matrix equation is obtained:

[0015]

[0016] Where, s=[s1s2…s L ] T is the result of L sampling times, F is an L×N measurement matrix, where L is the number of samples of the coded aperture configuration, N is the number of potential signal source positions, and FL (θ N ,φ N ) represents the electric field strength of the Nth potential signal source in the direction of the receiving antenna under the Lth coded aperture, e is the target vector containing the initial information of the signal source at N positions, E N Represents the initial information of the electric field of the Nth unknown signal source. The purpose of signal processing is to estimate this vector, where is the Gaussian white noise associated with the Lth sample.

[0017] Furthermore, in step 2, the far-field pattern under a specific coding matrix is ​​obtained according to the far-field formula of the plane wave angular spectrum theory.

[0018]

[0019] represents the electric field intensity in a specific direction (defined by the angles θ and φ in the spherical coordinate system) in the far field region, is the azimuth angle in the spherical coordinate system, θ is the pitch angle in the spherical coordinate system, and Corresponding to the unit vector in the direction of angles θ and φ. x (α,β) and F y (α, β)] represents the Fourier transform of the metasurface aperture field distribution in the x and y directions;

[0020] The parameters were substituted into the simulation software and the electric field distribution at different azimuths and elevation angles under 100 coding matrices was calculated to realize the construction of the final measurement matrix F.

[0021] Furthermore, in step 2, the target vector e is solved using a matched filter algorithm based on the measurement matrix F:

[0022] e=F H ·s

[0023] F H represents the conjugate transpose of the measurement matrix F.

[0024] Furthermore, in step 2, the target vector e is converted into an image, including the following steps:

[0025] The ranges of azimuth and elevation angles are determined and the angle grid is divided into N θ ×N φ signal source locations;

[0026] The signal strength estimate corresponding to each element in the target vector e is respectively θ ×N φ There is a one-to-one correspondence between discrete angle points;

[0027] This one-dimensional target vector e is converted into θ ×N φ Rearrange into a two-dimensional matrix;

[0028] The intensity of the signal corresponding to each element in the target vector e is mapped to the grayscale value or pseudo-color value of the pixel at the corresponding position in the two-dimensional matrix.

[0029] Furthermore, in step 3, the image denoising deep neural network includes an encoder, a decoder, and a generator;

[0030] The encoder consists of three convolutional network modules and two maximum pooling layers. The image passes through the first convolutional network module, the first maximum pooling layer, the second convolutional network module, the second maximum pooling layer, and the third convolutional network module in sequence to output low-dimensional features.

[0031] The decoder's structure is mirror-symmetrical to the encoder, consisting of three deconvolutional network modules and two depooling layers. The low-dimensional features are sequentially passed through the first deconvolutional network module, the first depooling layer, the second deconvolutional network module, the second demax pooling layer, and the third deconvolutional network module to output the final features.

[0032] The generator contains only a single convolutional layer, which fuses the input image with the high-dimensional features obtained by the decoder and outputs a high-resolution two-dimensional signal source localization result.

[0033] Furthermore, in step 3, the two unpooling layers are connected to the two max-pooling layers in the corresponding encoder respectively;

[0034] The two unpooling layers expand the feature map dimensions through the index information output by the corresponding maximum pooling layer.

[0035] Furthermore, in step 3, the original data input into the first convolutional network module is concatenated with the output data of the third deconvolutional network module to form a fused feature map with more channels.

[0036] The feature maps input to the first maximum pooling layer, the second convolutional network module, the second maximum pooling layer, and the third convolutional network module are respectively subjected to element-by-element multiplication calculation with the feature maps input to the first depooling layer, the second deconvolutional network module, the second demax pooling layer, and the third deconvolutional network module.

[0037] The beneficial effects achieved by the present invention are:

[0038] By combining the matched filtering algorithm with the image denoising algorithm, the problem of insufficient resolution of the current metasurface signal source localization method is solved in a simple way;

[0039] By introducing an image denoising neural network, the method of achieving two-dimensional signal source localization on metasurfaces is transformed from data optimization to image processing;

[0040] The metasurface device uses a two-dimensional gradient programmable metasurface, which solves the problem that most metasurfaces can only be used for azimuth or pitch angle positioning estimation, and realizes two-dimensional signal source positioning at the hardware level. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 Diagram of the working principle for locating two-dimensional signal sources on the metasurface;

[0042] Figure 2 The calculation results of electric field distribution at different azimuth and elevation angles under 8 different coding matrices are shown;

[0043] Figure 3 Deep neural network architecture for image denoising;

[0044] Figure 4 The simulation results of two-dimensional signal source localization on a metasurface under a single signal source are shown. (a) Signal source localization results using the image denoising algorithm; (b) Signal source localization results using the matched filtering algorithm.

[0045] Figure 5 The simulation results of two-dimensional signal source localization on the metasurface under two signal sources. (a) Signal source localization result under the image denoising algorithm; (b) Signal source localization result under the matched filtering algorithm;

[0046] Figure 6 The simulation results of two-dimensional signal source positioning on the metasurface under a single signal source are shown. (a) Signal source positioning results obtained by the two algorithms when the signal source incident angle is (40°, 40°); (b) Signal source positioning results obtained by the two algorithms when the signal source incident angle is (40°, -40°); (c) Signal source positioning results obtained by the two algorithms when the signal source incident angle is (-40°, 40°); (d) Signal source positioning results obtained by the two algorithms when the signal source incident angle is (-40°, -40°);

[0047] Figure 7 The experimental setup for one-dimensional metasurface signal source localization based on a far-field test platform. (a) Rear view of the experimental setup; (b) Side view of the experimental setup.

[0048] Figure 8The experimental results of one-dimensional metasurface signal source positioning based on the far-field test platform. (a) Positioning result when the incident angle of the signal source is -45°; (b) Positioning result when the incident angle of the signal source is -30°; (c) Positioning result when the incident angle of the signal source is -15°; (d) Positioning result when the incident angle of the signal source is 15°; (e) Positioning result when the incident angle of the signal source is 30°; (b) Positioning result when the incident angle of the signal source is 45°;

[0049] Figure 9 Experimental setup for signal source localization on a novel two-dimensional metasurface. (a) Side view of the experimental setup; (b) Back view of the experimental setup.

[0050] Figure 10 Experimental results of two-dimensional metasurface signal source positioning under a single signal source. (a) Positioning results obtained by the two algorithms when the signal source incident angle is (45°, 0°); (b) Positioning results obtained by the two algorithms when the signal source incident angle is (-25°, 0°); (c) Positioning results obtained by the two algorithms when the signal source incident angle is (-25°, 10°);

[0051] Figure 11 Experimental results of 2D metasurface signal source localization using a single signal source. (a) Localization results obtained by the two algorithms when the signal source incident angles are (-15°, 25°); (b) Localization results obtained by the two algorithms when the signal source incident angles are (-15°, 35°); (c) Localization results obtained by the two algorithms when the signal source incident angles are (-15°, 50°). DETAILED DESCRIPTION

[0052] The present invention will be further described below with reference to specific embodiments, and the advantages and features of the present invention will become clearer as the description proceeds. However, these embodiments are merely exemplary and do not constitute any limitation to the scope of the present invention. It should be understood by those skilled in the art that the details and forms of the technical solutions of the present invention may be modified or replaced without departing from the spirit and scope of the present invention, and such modifications and replacements fall within the scope of protection of the present invention.

[0053] The purpose of the present invention is to propose a deep learning-assisted design method for two-dimensional high-resolution signal source localization on a hypersurface.

[0054] The present invention obtains a matrix equation based on the ray tracing method. The physical process is as follows: when the signal source incidents an electromagnetic wave onto the metasurface from a specific angle, a randomly scattered electromagnetic wave is formed after being regulated by the metasurface, and a receiving antenna is used to receive the electromagnetic wave signal, which is finally converted into a digital signal that can be processed by a computer. The electromagnetic wave signal is a broadband signal, which contains amplitude, phase and frequency information. By processing the amplitude and phase data of the signal at each frequency, the position information of the signal source can be obtained. Generally, the result is most accurate at the center frequency point. Based on the above matrix equation, the two-dimensional signal source positioning problem is converted into an inverse matrix solution problem, where the measurement matrix is ​​represented by the far-field pattern under a specific coded aperture, and the final measurement matrix result is obtained by substituting the specific physical parameters of the metasurface into the calculation.

[0055] In order to achieve a better-performing two-dimensional signal source positioning function, it is first necessary to ensure that the orthogonality of the above-mentioned final measurement matrix is ​​strong. Therefore, the mutual correlation coefficient of the measurement matrix under 100 sets of coding matrices adopted in the present invention is 0.127, that is, there are large differences between the far-field radiation patterns of the metasurface under different coding matrices, and the same algorithm has better signal source positioning accuracy; secondly, the matched filtering algorithm is used to restore the electromagnetic wave signal to the position information of the signal source, and the position information is converted into an image result; finally, the image denoising algorithm is used to input the image result obtained by the matched filtering algorithm into the image denoising deep neural network, and the network finally outputs a high-resolution result.

[0056] According to the requirements of two-dimensional high-resolution signal source positioning on the metasurface, the present invention combines the matched filtering algorithm with the image denoising algorithm. The specific steps are as follows:

[0057] Step 1: Based on the ray tracing method and the physical parameters of the metasurface, the principle analysis and mathematical modeling of the two-dimensional signal source positioning function are carried out to obtain the received signal;

[0058] Based on electromagnetic field strength prediction algorithms such as ray tracing, the principle analysis and mathematical modeling of the two-dimensional signal source positioning function are carried out. The center of the metasurface is taken as the origin, and the receiving antenna is placed at any position in space and aligned with the center of the metasurface. First, assume that there are N unknown signal sources in space with arbitrary azimuth angles θ n and pitch angle φ n The electric field intensity at each unit is Expressed as:

[0059]

[0060] Among them, m and n represent the metasurface unit number and the signal source number at different positions, respectively, k is the free space wave number, and x is the m and y m Represents the coordinate values ​​of the mth unit along the x and y axes, E n Represents the initial information of the electric field of the nth unknown signal source.

[0061] Further assume that the receiving antenna is located at (x r ,y r , z r ), and the phase response of each metasurface unit to the electromagnetic wave is assigned a random value between 180° and 0°, then the received signal s of the receiving antenna at a certain moment can be obtained as:

[0062]

[0063] here and A m Represent the phase and amplitude responses of the mth metasurface unit to the reflected electromagnetic wave, respectively. The phase responses of 180° and 0° correspond to the coding states of 1 and 0, respectively. The coding states of all units together constitute the coded aperture of the metasurface. Formula (2) describes the coding state of all M units when the metasurface is in a specific coded aperture configuration (i.e., and the amplitude response A m are determined), the single sampled signal s received by the receiving antenna. In order to effectively distinguish N potential signal sources from different directions and accurately locate them, it is necessary to configure the coded aperture of the metasurface L times and perform L corresponding signal sampling through the receiving antenna. For each (lth, where l = 1, ..., L) coded aperture configuration, each unit m (m = 1, ..., M) of the metasurface has its specific phase response under this configuration (given by , where the superscript l refers to the lth configuration) and the amplitude response A m . Combined with the formula (1) The definition of , formula (2) can be expressed more finely as for the l-th sampling signal s l In the form of:

[0064]

[0065] The L sampling signals s1, s2, ..., s L Collect them together and finally get the sorted matrix equation:

[0066]

[0067] Where, s=[s1 s2 … s L ] Tis the result of L times sampling, F L (θ N ,φ N ) is the electric field strength in the direction of the receiving antenna corresponding to the Nth potential signal source under the Lth metasurface coded aperture configuration (given by the azimuth angle θ N and pitch angle φ N Definition), e is the target vector containing the initial information of N position signal sources, E N Represents the initial information of the electric field of the Nth unknown signal source. The purpose of signal processing is to estimate this vector, where is the Gaussian white noise associated with the Lth sample. In practice, this term can be weakened and ignored by optimizing the experimental conditions.

[0068] Its general expression is:

[0069]

[0070] Finally, based on the above formula, the problem of metasurface two-dimensional signal source positioning is transformed into a matrix inverse solution problem. However, the matrix F is usually irreversible, and specific methods are needed to deal with this inverse problem, such as pseudo-inverse matrix, compressed sensing, and deep learning.

[0071] It is worth noting that to achieve this patented two-dimensional high-resolution metasurface signal source localization method, the metasurface structure must be composed of a large number of independently programmable units and be a planar structure capable of two-dimensional dynamic control of the phase (and possibly amplitude) of electromagnetic waves at the target operating frequency. By changing the encoding state of each unit, this metasurface can exhibit different electromagnetic scattering characteristics as a whole, thereby achieving unique responses to different incident signals, laying the physical foundation for subsequent signal processing and high-resolution localization.

[0072] Step 2: Based on the matched filtering algorithm, the two-dimensional position information of the signal source is preliminarily estimated by the received signal, and the two-dimensional position information is converted into an image;

[0073] According to formula (4), in order to recover the target vector e from the received electric field information s, it is necessary to use Figure 1 The working principle shown here constructs the measurement matrix F. Assume that the receiving antenna is located at (0mm, 0mm, 147mm) and according to the far field formula of the plane wave angular spectrum theory

[0074] The far-field pattern F(θ,φ) under a specific coding matrix is ​​obtained, which is specifically expressed as the electric field distribution under different azimuths and elevation angles. Here, the physical parameters involved (including the geometric parameters of the metasurface unit, the number of units, the type of metasurface coding matrix, the operating frequency, and the position of the receiving antenna) are substituted into the MATLAB simulation software and the electric field distribution under different azimuths and elevation angles under 100 coding matrices is calculated to achieve the construction of the final measurement matrix F, and 8 of the calculation results are given, as shown in the figure. Figure 2 To characterize the characteristics of the measurement matrix F, the cross-correlation coefficient is defined to determine the orthogonality between different column vectors of the measurement matrix. Its expression is as follows:

[0075]

[0076] in, is the normalized measurement matrix, C is the number of columns of the measurement matrix, μ g is the cross-correlation coefficient of the measurement matrix F, and i and j are the indices of the column vectors in the measurement matrix F. Based on the above formula, the cross-correlation coefficient of the measurement matrix F can be calculated to be 0.127, indicating that there are significant differences in the electric field distribution under different encoding matrices. This also means that the same algorithm can achieve better two-dimensional signal source localization accuracy.

[0077] After obtaining the measurement matrix F, the matched filter algorithm is used to solve the target vector e:

[0078] e=F H ·s (7)

[0079] F H represents the conjugate transpose operation on the measurement matrix.

[0080] The process of converting the position vector e into an image can be understood as follows:

[0081] Establishment of angle grid: Before locating the signal source, the two-dimensional space to be detected (defined by azimuth and elevation) is usually discretized to form an angle grid. The range of both angles is determined and the angle grid is divided with a predetermined angle as the step size. If the azimuth angle θ and the elevation angle φ are divided in this way, assuming that there are N azimuth angles θ discrete points, the pitch angle is N φ discrete points, then there are a total of N=N θ ×N φ possible signal source positions (angle combinations).

[0082] The correspondence between vector e and angle grid: the length of target vector e is N (or contains N elements E1, E2, ..., E N). These N elements are the same as the above N θ ×N φ That is, each element value in the vector e represents the signal strength estimate at the corresponding angle grid point.

[0083] Reshape into a two-dimensional matrix: This one-dimensional vector e (length N θ ×N φ ) is rearranged or "reshaped" into a two-dimensional matrix with dimension N θ ×N φ (or N φ ×N θ , depending on how the rows and columns of the image are defined).

[0084] Matrix-to-image mapping: Each element value of this two-dimensional matrix (from vector e) can be mapped to the intensity value of the pixel at the corresponding position in the image (such as grayscale value or pseudo-color value). The rows and columns of the matrix correspond to the discretized azimuth and elevation axes, respectively. In this way, the signal strength information contained in vector e at different angles is intuitively displayed in the form of an image. Brighter (or specific color) areas in the image indicate that there is an estimated strong signal source in that angle direction.

[0085] Step 3: Process the two-dimensional position information image through an image denoising deep neural network to obtain two-dimensional high-resolution signal source positioning.

[0086] For the matched filter algorithm, due to its inherently high sidelobe level, it is sensitive to model errors. The coupling noise caused by the non-ideal orthogonality of the waveform will have a significant impact on the results, thus significantly reducing its two-dimensional signal source positioning performance. To solve this problem, the nonlinear fitting ability of the deep learning network is utilized to reduce the impact of the non-ideal orthogonal waveform on the results, thereby improving the accuracy and resolution of two-dimensional signal source positioning. The proposed method first obtains a low-resolution result through the matched filter algorithm, which is then input into the image denoising deep neural network and finally outputs a high-resolution result. Therefore, the algorithm constructed based on this network can be called an image denoising algorithm, and its process can be simply expressed as:

[0087] e out =D(e) (8)

[0088] Where, e represents the input target vector, e out Denotes the output target vector, and D(·) represents the image denoising deep neural network. The network structure is as follows Figure 3As shown. It mainly includes three modules: encoder, decoder and generator. It is worth emphasizing that the input image processed by the image denoising deep neural network in the present invention (converted from the target vector e in step 2) is not a noisy image in the general sense, but a two-dimensional angular spectrum estimation map with its special physical connotation and specific artifact characteristics. The image originates from a specially designed two-dimensional gradient programmable metasurface (whose characteristics have been characterized by parameters such as the mutual correlation coefficient μg=0.127) to receive the signal and undergo matched filtering processing. Therefore, the "noise" in the image is mainly manifested as structured artifacts such as high sidelobes, broadened mainlobes and potential pseudo-peaks caused by the non-ideal orthogonality of the measurement matrix F and the inherent characteristics of the matched filtering algorithm, rather than the random noise commonly seen in traditional images. The core task of this neural network is to specifically suppress these structured artifacts that are closely related to the physical properties of the metasurface and the signal processing process, and significantly improve the angular resolution of the real signal source, which is essentially different from conventional image denoising or super-resolution tasks.

[0089] The algorithm's specific process is as follows: First, the low-resolution image result obtained by the matched filtering algorithm, with dimensions of 64×64×2 (height × width × number of channels), is input to the encoder. The encoder includes three convolutional network (CNN) modules and two maximum pooling layers (MaxPool). Each CNN module consists of a convolution layer (Convolution, Conv), a batch normalization layer (BN), and an activation layer (ReLU). Through this encoder, the input low-resolution result is encoded and feature extracted layer by layer, obtaining its low-dimensional features and entering the decoder.

[0090] Specifically, in the first convolutional module (Conv+BN+ReLU) of the encoder, the input feature map has a size of 64x64 and a number of channels of 2. This convolutional layer uses a 5x5 convolution kernel, a stride of 1, no padding (padding=0), and the number of output channels is set to 32. After this convolution operation, the size of the output feature map becomes 60x60 with a number of channels of 32. Subsequently, a maximum pooling layer (MaxPool 1) using a 2x2 pooling kernel and a stride of 2 is used to reduce the feature map dimension from 60x60x32 to 30x30x32. Next, the second convolutional module (CNN Block 2, which includes a convolutional layer, a batch normalization layer, and a ReLU activation layer) receives a 30x30x32 feature map. This convolutional layer uses a 3x3 convolution kernel, a stride of 1, no padding, and 64 output channels. After processing, the feature map dimension becomes 28x28x64. Then, after a maximum pooling layer (MaxPool 2), using the same 2x2 pooling kernel and stride of 2, the feature map dimension is further reduced from 28x28x64 to 14x14x64. Finally, the third convolutional module (CNNBlock 3, which includes a convolutional layer, a batch normalization layer, and a ReLU activation layer) processes the 14x14x64 feature map. This convolutional layer uses a 3x3 convolution kernel, a stride of 1, no padding, and maintains the number of output channels at 64. After processing, the feature map dimension becomes 12x12x64, which is the low-dimensional feature output by the encoder.

[0091] The decoder's structure is symmetrical to the encoder's. The convolutional layers and maximum pooling layers in the decoder are replaced by deconvolutional layers (Convolution Transpose, ConvTrans) and unpooling layers (MaxUnpool), respectively. The decoder decodes and transforms feature maps layer by layer, yielding high-dimensional features from low-resolution results.

[0092] Specifically, after the input feature map passes through MaxUnpool 1 (using the index of encoder MaxPool 2), its dimension should be restored to 14×14×64; after MaxUnpool 2 (using the index of encoder MaxPool 1), the feature map dimension should be restored to 28×28×64; after passing through the corresponding CNN Block (ConvTrans+BN+ReLU), the feature map dimension becomes 30×30×32 (the number of channels is reduced from 64 to 32); after similar unpooling operations and CNN Block (ConvTrans+BN+ReLU), the feature map dimension becomes 60×60×32, and is finally adjusted to the dimension of the adaptation generator input, for example Figure 3The final features of the decoder part in the path description (or the features to be fused with the original input) have a dimension of 64×64×(a certain number of channels). The generator contains only a single convolutional layer, which fuses the input image with the high-dimensional features obtained by the decoder and outputs a high-resolution two-dimensional signal source localization result. Specifically, the fusion feature dimension input to the generator is: according to Figure 3 The path is described as 64×64×4. This is the result of concatenating the original input image (64×64×2) and the decoder output features (resized to 64×64×2) along the channel dimension. After passing through the convolutional layer of the generator, the output is a high-resolution image with dimensions of 64×64×1 (a single-channel image representing the localization result).

[0093] It should be noted that the proposed image denoising deep neural network realizes information transfer and feature fusion between shallow features and deep features through three methods, mainly including: (1) Pool Index Passing: when performing pooling operation, the extracted maximum value index is passed to the corresponding unpooling layer to retain key information; (2) Dot Product: during the encoding-decoding process, feature transfer is achieved while maintaining the sparsity of features; (3) Concatenating: the original data and output features are fused by channel concatenation.

[0094] The specific implementation methods of the three features are as follows.

[0095] First, there is index transfer: (1) When the maximum pooling layer (MaxPool) in the encoder downsamples the input feature map, it not only outputs the maximum value in each pooling window, but also records the position index of this maximum value within the window (for example, in a 2×2 window, the maximum value is located in one of the four positions: upper left, upper right, lower left, and lower right). Therefore, these index information will be saved. (2) When the unpooling layer (MaxUnpool or upsampling layer) in the decoder works, it will use these index information passed from the corresponding layer of the encoder. Specifically, the unpooling layer creates an output feature map with a larger size than the input feature map (usually the inverse size of the pooling operation), and then places the element values ​​of the input feature map at the position specified by the "index" in this larger feature map. Other positions not specified by the index are usually filled with zeros. (3) In this way, the position information lost in the pooling operation can be accurately restored during the decoding process, which helps to generate clearer and sharper-edged reconstructed images because it preserves important spatial structure information.

[0096] The second is the dot product connection: (1) "Dot product connection" in neural networks usually refers to the element-wise multiplication of two feature maps of the same dimension. Suppose we have two feature maps A and B, both of which are of shape H×W×C, then their dot product connection result C is also a feature map of H×W×C, where C[i,j,k]=A[i,j,k]×B[i,j,k]. (2) In the encoder-decoder structure, dot product connection is often implemented as a "skip connection" or "gating mechanism". Specifically, the output feature map of a certain layer in the encoder (shallow features) will be fused with the feature map of the corresponding symmetric layer (or later layer) in the decoder (features generated by deep features during decoding) through a dot product operation. (3) This connection method allows the detailed information captured by the encoder (such as edges, textures) to be passed to the decoder to assist in reconstruction. If one of the feature maps involved in the dot product is sparse, then the result of the element-wise multiplication will also tend to remain sparse, because any number multiplied by zero will be zero. This helps the model learn more robust or more focused feature representations.

[0097] Finally, there is concatenation: (1) “Concatenation” or “channel concatenation” refers to stacking two or more feature maps (usually with the same height and width) along the channel dimension to form a feature map with more channels. (2) Assuming that the “original data” (i.e., the low-resolution image input to the entire neural network, for example, the dimensions are H×W×C in ) and "output features" (here refers to the feature map finally output by the decoder, whose spatial dimension should also be H×W, assuming the number of channels is C dec ) for splicing. The dimension of the feature map after splicing will be H×W×(C in +C dec ). (3) This splicing operation usually occurs at the key node of feature fusion. In the description of this patent, it occurs after the decoder output and before the generator module input. Figure 3 As shown (combined with the previous round of Figure 3 The original 64×64×2 input image is concatenated with the 64×64×2 feature map output by the decoder to form a 64×64×4 feature map. This fused feature map, which contains the original information and the decoded deep features, is then fed into the “generator” module (usually one or more convolutional layers) to produce the final high-resolution output image. (4) The concatenated connection allows the network to utilize the deep semantic features that have undergone multiple layers of abstraction and processing when generating the output in the final stage, while also directly referencing the detailed information of the original input image, which helps to improve the fidelity and detail recovery of the final result.

[0098] In addition, the training data set of the image denoising deep neural network is generated by a large number of simulations (or combined experiments) on the specific two-dimensional gradient programmable metasurface platform adopted by the present invention. The training sample pairs include the low-resolution, artifact-containing angular spectrogram output by the matched filtering algorithm and the corresponding real high-resolution signal source position map. This means that the parameters and performance of the neural network are end-to-end optimized and adapted for the specific metasurface hardware characteristics, specific encoding strategies and specific signals and artifact patterns generated therefrom of the present invention, rather than a general image processing network that is unrelated to the specific physical front end. This deep coupling and collaborative optimization with the specific physical perception front end is the key to the present invention to achieve high-resolution, high-robustness signal source positioning, and constitutes an important aspect that distinguishes it from existing general deep learning technologies.

[0099] Comparison between simulation and results

[0100] First, the positioning performance of the two methods is verified and analyzed through simulation. First, it is assumed that the incident angle (θ, φ) of the signal source is (30°, 60°) and is located in the radiation far field relative to the metasurface. At the same time, the range of the two angles is determined to be ±90° and the angle grid is divided with a step size of 5°. Then, a simulation program is used to generate a large number of target vectors e and received signals s as labels and data sets for training the network model. A total of 10,000 sets of training data and 1,000 sets of test data are generated, and they are input into the image denoising deep neural network for training and testing. Finally, the matched filtering algorithm and image denoising algorithm are used to obtain the final estimated simulation results, as shown in the figure. Figure 4 As shown in the figure, it can be observed that although the matched filter algorithm can also locate the position of the signal source well, its sidelobe level is high, which is manifested as a more obvious artifact effect on the image. When there are multiple signal sources with similar angles, it is impossible to restore the position information of all signal sources well.

[0101] To prove the above conclusion, assume that there are two signal sources with incident angles (θ, φ) of (30°, 20°) and (30°, 40°) respectively. The same two algorithms are used for simulation. The results are as follows: Figure 5 As shown in the figure, it can be seen that the angular position information of the two signal sources obtained by the matched filtering algorithm has overlapping sidelobes, which makes it difficult to distinguish the actual angular position information of the two signal sources. However, the image denoising algorithm can well distinguish and estimate the angular position information of the two signal sources.

[0102] In order to prove the superiority of the image denoising algorithm, the root mean square error value is used as an indicator to evaluate the performance of the two algorithms, which is defined as:

[0103]

[0104] Where Monte is the number of Monte Carlo trials, θ ′ k,n and φ ′ k,n are the pitch angle and azimuth angle estimation results obtained from the nth experiment of the kth signal source, θ k and φ k are the actual elevation angles and azimuth angles of the k signal sources respectively.

[0105] Here, taking the simulation results under a single signal source as an example, the incident angles (θ, φ) of the signal source are assumed to be (40°, 40°), (-40°, 40°), (40°, -40°) and (-40°, -40°) and simulations are performed to obtain the image results as shown below: Figure 6 As shown in the figure, the simulation results of absolute error and root mean square error are calculated at the same time. The absolute error results of the matched filtering algorithm are (0.09, 0.39), (0.46, 0.07), (0.02, 0.67), and (0.47, 0.25), respectively; the absolute error results of the image denoising algorithm are (0.05, 0.02), (0.03, 0.02), (0.00, 0.09), and (0.08, 0.04), respectively. After further conversion to root mean square error, the root mean square errors of the matched filtering algorithm are 0.38, 0.47, 0.67, and 0.53, respectively; and the root mean square errors of the image denoising algorithm are 0.05, 0.04, 0.09, and 0.09, respectively. It can be found that when the signal source is at different incident angles, the adopted methods can all obtain the angular position information of the signal source very well. The average root mean square error result under the matched filtering algorithm is 0.51, while the corresponding result under the image denoising algorithm is 0.07. Its accuracy is improved by more than 7 times compared with the former. From a simulation perspective, it is proved that the proposed image denoising algorithm can achieve high-resolution two-dimensional signal source positioning.

[0106] Comparison of experiments and results

[0107] After simulating and verifying the two-dimensional signal source positioning function of the metasurface under the two algorithms, the present invention further verifies the effectiveness and superiority of the proposed invention method through experimental tests. The experimental setting is consistent with the simulation setting. The receiving antenna is placed 147mm in front of the center of the metasurface antenna, and 100 sets of random coding matrices consistent with the simulation are used. First, the target positioning device is placed on the far-field test platform to realize one-dimensional signal source positioning. The experimental setting is as follows: Figure 7 A computer and a portable vector network analyzer were used to automatically obtain 100 sets of received signal test results under random coding matrices. The TCP / IP protocol was used for communication between them, and a far-field test platform was used to precisely control the pitch angle of the signal source relative to the center of the metasurface, with the azimuth angle at 0°.

[0108] After obtaining the test results of the received signal, the angle estimation of the signal source under different incident angles is obtained through the matched filtering algorithm. The results are as follows: Figure 8 As shown in the figure, similar to the simulation results, the matched filter algorithm can well estimate the incident angle of the actual signal source, but there are large sidelobes, confirming that the target positioning device has the ability to locate the signal source. However, due to the complex environment and the lack of absorbing materials to improve the experimental conditions, the multipath effect is affected, resulting in an average error of 1.4°. Furthermore, the signal source cannot set its two-dimensional incident angle under this experimental setup, making it difficult to achieve two-dimensional signal source positioning. A more complete experimental setup is urgently needed.

[0109] After using the far-field test platform to verify the feasibility of the signal source positioning function of the hardware platform, due to its large error and the inability to continue to rely on the platform for two-dimensional signal source positioning experiments, it was transferred to the ground plane. The signal source can be placed at any pitch and azimuth angles, and a large amount of absorbing sponge material is used to build an experimental environment similar to a small microwave darkroom to make it as consistent as possible with the simulation conditions, so that it can be better used to verify the accuracy of different wave arrival angle estimation methods. The new experimental settings are as follows: Figure 9 shown.

[0110] According to the optimal focal ratio, the receiving antenna is placed 147mm in front of the center of the metasurface, the signal source is placed at a position that meets the far-field conditions, and the pitch and azimuth angles (θ, φ) are set to (45°, 0°), (-25°, 0°), (-25°, 10°), (-15°, 25°), (-15°, 35°) and (-15°, 50°). Two algorithms are used to conduct two-dimensional signal source positioning experiments. The results are shown in the figure. Figure 10 and Figure 11As shown in the figure, the simulation results of absolute error and root mean square error are calculated at the same time. The absolute error results under the matched filtering algorithm are (0.42, 1.16), (0.35, 0.22), (0.89, 1.03), (0.16, 0.86), (0.14, 1.87), and (0.81, 1.89); the absolute error results under the image denoising algorithm are (0.11, 0.04), (0.04, 0.07), (0.08, 0.16), (0.03, 0.15), (0.02, 0.91), and (0.05, 0.75). After further conversion to root mean square error (RMS), the RMS errors for the matched filtering algorithm were 1.23, 0.41, 1.36, 0.87, 1.88, and 2.06, respectively; and the RMS errors for the image denoising algorithm were 0.12, 0.08, 0.18, 0.15, 0.91, and 0.75, respectively. It can be seen that the inventive method used in the experimental environment can also effectively obtain the angular position information of the signal source. The average RMS error result for the matched filtering algorithm was 1.3, while the corresponding result for the image denoising algorithm was 0.37, which is more than three times the accuracy of the former.

[0111] The above are only specific steps of the present invention and do not constitute any limitation to the scope of protection of the present invention; any technical solutions formed by equivalent transformation or equivalent replacement fall within the scope of protection of the present invention; the parts not elaborated in detail in the present invention belong to the common knowledge of those skilled in the art.

Claims

1. A deep learning-assisted design method for high-resolution two-dimensional signal source localization on a metasurface, characterized by: The deep learning-assisted design method for two-dimensional high-resolution signal source localization on a hypersurface comprises the following steps: Step 1: Based on the ray tracing method and the physical parameters of the metasurface, the principle analysis and mathematical modeling of the two-dimensional signal source positioning function are carried out to obtain the received signal; Step 2: Based on the matched filtering algorithm, the two-dimensional position information of the signal source is preliminarily estimated by the received signal, and the two-dimensional position information is converted into an image; Step 3: Process the two-dimensional position information image through an image denoising deep neural network to obtain two-dimensional high-resolution signal source positioning.

2. The method for two-dimensional high-resolution signal source localization on a hypersurface designed with deep learning assistance according to claim 1, characterized in that: In step 1, for N unknown signal sources incident on the metasurface, the electric field intensity at each unit is Expressed as: Among them, φ n is the pitch angle, θ n is the azimuth angle, m and n represent the metasurface unit number and the signal source number at different positions, respectively, k is the free space wave number, x m and y m Represents the coordinate values ​​of the mth unit along the x and y axes, E n Represents the initial information of the electric field of the nth unknown signal source.

3. The method for two-dimensional high-resolution signal source localization on a hypersurface designed with deep learning assistance according to claim 2, characterized in that: In step 1, the phase response of each metasurface unit to the electromagnetic wave is assigned a random value between 180° and 0°, so that the received signal s of the receiving antenna at a certain moment can be obtained as: x r ,y r , z r is the receiving antenna position, and A m They represent the phase and amplitude responses of the mth metasurface unit to the reflected electromagnetic wave, respectively. The phase responses of 180° and 0° correspond to the coding states of 1 and 0, respectively. The coding states of all units together constitute the coded aperture of the metasurface.

4. The method for two-dimensional high-resolution signal source localization on a hypersurface designed with deep learning assistance according to claim 3 is characterized in that: In step 1, by configuring the metasurface coded aperture L times and sampling the receiving horn L times, the final matrix equation is obtained: Where, s=[s1s2…s L ] T is the result of L sampling times, F is an L×N measurement matrix, where L is the number of samples of the coded aperture configuration, N is the number of potential signal source positions, and F L (θ N ,φ N ) represents the electric field strength of the Nth potential signal source in the direction of the receiving antenna under the Lth coded aperture, e is the target vector containing the initial information of the signal source at N positions, E N Represents the initial information of the electric field of the Nth unknown signal source. The purpose of signal processing is to estimate this vector, where is the Gaussian white noise associated with the Lth sample.

5. The method for two-dimensional high-resolution signal source localization on a hypersurface designed with deep learning assistance according to claim 4 is characterized in that: In step 2, the far-field pattern under a specific coding matrix is ​​obtained according to the far-field formula of plane wave angular spectrum theory represents the electric field intensity in a specific direction (defined by the angles θ and φ in the spherical coordinate system) in the far field region, is the azimuth angle in the spherical coordinate system, θ is the pitch angle in the spherical coordinate system, and Corresponding to the unit vector in the direction of angles θ and φ. x (α,β) and F y (α, β)] represents the Fourier transform of the metasurface aperture field distribution in the x and y directions; The parameters were substituted into the simulation software and the electric field distribution at different azimuths and elevation angles under 100 coding matrices was calculated to realize the construction of the final measurement matrix F.

6. The method for two-dimensional high-resolution signal source localization on a hypersurface designed with deep learning assistance according to claim 5, characterized in that: In step 2, the target vector e is solved using the matched filter algorithm based on the measurement matrix F: e=F H ·s F H represents the conjugate transpose of the measurement matrix F.

7. The method for two-dimensional high-resolution signal source localization on a hypersurface designed with deep learning assistance according to claim 5, characterized in that: In step 2, the target vector e is converted into an image, which includes the following steps: The ranges of azimuth and elevation angles are determined and the angle grid is divided into N θ ×N φ signal source locations; The signal strength estimate corresponding to each element in the target vector e is respectively θ ×N φ There is a one-to-one correspondence between discrete angle points; This one-dimensional target vector e is converted into θ ×N φ Rearrange into a two-dimensional matrix; The intensity of the signal corresponding to each element in the target vector e is mapped to the grayscale value or pseudo-color value of the pixel at the corresponding position in the two-dimensional matrix.

8. The method for two-dimensional high-resolution signal source localization on a hypersurface designed with deep learning assistance according to claim 1, characterized in that: In step 3, the image denoising deep neural network includes an encoder, a decoder, and a generator; The encoder consists of three convolutional network modules and two maximum pooling layers. The image passes through the first convolutional network module, the first maximum pooling layer, the second convolutional network module, the second maximum pooling layer, and the third convolutional network module in sequence to output low-dimensional features. The decoder structure is mirror-symmetric to the encoder, consisting of three deconvolutional network modules and two depooling layers. The low-dimensional features are sequentially output through the first deconvolution network module, the first depooling layer, the second deconvolution network module, the second demax pooling layer, and the third deconvolution network module to output the final features; The generator contains only a single convolutional layer, which fuses the input image with the high-dimensional features obtained by the decoder and outputs a high-resolution two-dimensional signal source localization result.

9. The method for two-dimensional high-resolution signal source localization on a hypersurface designed with deep learning assistance according to claim 8, characterized in that: In step 3, the two unpooling layers are connected to the two maximum pooling layers in the corresponding encoder respectively; The two unpooling layers expand the feature map dimensions through the index information output by the corresponding maximum pooling layer.

10. The method for two-dimensional high-resolution signal source localization on a hypersurface designed with deep learning assistance according to claim 8, characterized in that: In step 3, the original data input into the first convolutional network module is spliced ​​with the output data of the third deconvolutional network module to form a fused feature map with more channels; The feature maps input to the first maximum pooling layer, the second convolutional network module, the second maximum pooling layer, and the third convolutional network module are respectively subjected to element-by-element multiplication calculation with the feature maps input to the first depooling layer, the second deconvolutional network module, the second demax pooling layer, and the third deconvolutional network module.

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