Orbital angular momentum pattern recognition method based on complex field analysis

Abstract

The present application relates to a kind of track angular momentum mode recognition method based on composite domain analysis, belong to atmospheric channel optical signal transmission technical field.Establishes atmospheric turbulence light transmission simulation model, using the modeling idea of data-driven, constructs the track angular momentum mapping model based on penalty weighted extreme learning machine, the input of model considers the spatial information of light spot, frequency domain information, statistical domain information, realizes composite domain feature extraction by principal component analysis, the output of model is track angular momentum mode coding, realizes track angular momentum mode recognition function by optimal selection of mapping model parameter.The present application forms the track angular momentum mapping model based on penalty weighted extreme learning machine, breaks through the bottleneck of the calculation difficulty caused by physical model identification method, provides a solution for constructing track angular momentum identification under different turbulence intensity.

Description

Technical Field

[0001] This invention belongs to the field of atmospheric channel optical signal transmission technology, specifically relating to an orbital angular momentum pattern recognition method based on composite domain analysis. Background Technology

[0002] In space optical communication, the light beam, as the information carrier, is affected by atmospheric turbulence, leading to phenomena such as light intensity flicker, beam drift, beam spread, and fluctuations in angle of arrival, which become bottlenecks limiting the performance of wireless optical communication systems. Orbital angular momentum (OAM) is a unique physical property of a helical wavefront beam with a phase factor, containing rich beam information and is a key element in optical information transmission. Effective identification of orbital angular momentum has become an important support for optical information multiplexing, helping to improve the capacity and anti-interference capability of communication systems.

[0003] When OAM beams are used for multiplexing or encoding, model building and inversion calculations using physical methods can create bottlenecks that make modeling difficult or unsolvable. Since OAM beams in different superposition states exhibit different physical behaviors, pattern recognition can be performed using a data-driven approach. This method is applicable to orbital angular momentum optical signal processing techniques in various application scenarios and is of great significance for optical system design.

[0004] Chinese patent "Detection System for OAM Beam Topological Charge Number Identification Based on Signal Crosstalk Distribution Characteristics" (201711275118.5) proposes a statistical learning algorithm. It achieves orbital angular momentum multiplexing of vortex beams through an OAM multiplexing module, fully utilizing the topological charge number information contained in the crosstalk distribution to accelerate the detection rate. Chinese patent "Atmospheric Turbulence Loss Compensation System and Method in Orbital Angular Momentum Optical Transmission" (201910018132.X) proposes an atmospheric turbulence loss compensation system and method in orbital angular momentum optical transmission. It achieves signal beam pattern recognition through a polarization beam splitter, beam splitter, charge-coupled camera, and FPGA board, simplifying the structure of the compensation system. However, both methods are highly dependent on the selection of the correlation threshold, cannot calculate the generalization performance of the model, and the calculation results are only valid under specific assumptions.

[0005] Chinese patent "A Method and Apparatus for Processing OAM Messages" (201810252506.X) proposes an OAM type identification method and stores and controls the extracted OAM messages, improving RAM utilization. Chinese patent "A Vortex Beam Mode Recognition System and Method Based on Photonic Neural Network" (202011156823.5) discloses an integrated, efficient, and high-speed waveguide photonic neural network for vortex beam recognition, generating horizontally polarized modal vortex beams and loading phase information into the neural network, thus improving communication system performance. However, both methods do not consider the frequency domain and statistical domain information of the light intensity samples, and therefore cannot detect superposition-state OAM modes.

[0006] The published patent "High-Fidelity Holographic Orbital Angular Momentum Communication Method Based on Deep Learning" (202110613902.2) provides a holographic orbital angular momentum communication method that uses orbital angular momentum hologram encoding and deep learning decoding. High-quality images are obtained through image information encoding and hologram reconstruction. The published patent "A Coherent OAM Communication Demodulation System Based on Convolutional Neural Network" (201811346980.5) provides a method for classifying OAM coherent modulation signals, obtaining demodulated multi-channel OAM coherent modulation signals and improving the utilization rate of OAM optical carriers. However, both methods cannot express the analytical representation of the recognition model, increasing the potential probability of overfitting and making them difficult to apply to increasingly large sample sets. Summary of the Invention

[0007] This invention provides a method for recognizing orbital angular momentum patterns based on composite domain analysis. It fully analyzes composite domain information, balances approximation error and model complexity, improves generalization performance, and provides a solution for recognizing orbital angular momentum under different turbulence intensities.

[0008] The technical solution adopted by this invention includes the following steps:

[0009] (1) An atmospheric turbulent optical transmission simulation model was established. To simulate the propagation of the Laguerre-Gaussian beam under atmospheric turbulent conditions, a sequence of phase screens was formed by multiple intermediate planes. The expression for the Laguerre-Gaussian (LG) beam passing through each phase screen was obtained:

[0010]

[0011] Where U(r0) and U(r1) represent the light field intensity at the source and after propagation through a phase screen, respectively, U(r m () represents the light field intensity at the receiving plane. and Let r0 = (x0, y0), r1 = (x1, y1), ..., r2 = (x0, y0) / 2. m =(x m ,y m () represents the coordinates. Q Monte Carlo simulations are performed to obtain the light field intensity sample set D at the receiver. m×m,MT ={U1(r m ),U2(r m ),…,U MT (r m The entire sample set includes two main optical field intensity distribution states: single-state and superposition state. The OAM mode of the single-state beam is mainly reflected in the ring radius, while the OAM mode of the superposition beam is mainly reflected in different topological charges, forming different OAM modes.

[0012] (2) Extract features from the light field intensity samples to obtain spatial features SP. D Frequency domain characteristics FR D Statistical domain characteristics ST D The input parameter I is composed of the orbital angular momentum mode encoding, which is then used as the output parameter O.

[0013] The light field intensity sample set D m×m,Q Expanding this into vector form yields the light field intensity sample vector D. M,Q Where M = m × m, K samples are taken from Q sample sets to obtain K light field samples. Considering the cumulative effect of K light field samples, the light field intensity sample matrix segment D is obtained. M,K The expression is as follows:

[0014]

[0015] Where d M,K This represents the light intensity value at the M-th position of the K-th light field sample, for the light field intensity matrix segment D. M,K Each light intensity value in the data is standardized:

[0016]

[0017] Where, d t ′ ,k μ represents the standardized value of the intensity of the t-th light field in the k-th light field sample. t σ t Let D' represent the mean and variance of the k-th light field sample, respectively. After standardization, the standardized sampling matrix D′ of the light field intensity is obtained. M,K And calculate the eigenvalue λ of the light field intensity. D′,1 ,λ D′,2 ,…λD′,M The corresponding eigenvector η D′,1 ,η D′,2 ,…η D′,M When the contribution of the selected light field intensity eigenvalue is greater than the threshold θ1, the number of principal components Num1 is determined.

[0018]

[0019] Where m1 represents the light field intensity index within the range Num1, and the corresponding set of feature vectors is the spatial domain feature.

[0020] For light field intensity sample D m×m,Q Perform a Fourier transform to obtain the optical field frequency sample F. m×m,Q Vector expansion, standardization, and principal component analysis are performed to obtain the optical field frequency standardized sampling matrix F′. M,K Calculate the frequency eigenvalue λ of the light field. F′,1 ,λ F′,2 ,…λ F′,M The corresponding eigenvector η F′,1 ,η F′,2 ,…η F′,M Calculate the contribution of the eigenvalues. When the contribution of the selected eigenvalues ​​is greater than the threshold θ2, determine the number of principal components Num2.

[0021]

[0022] Where m2 represents the frequency index of the light field within the Num2 range, and the corresponding set of feature vectors is the frequency domain feature.

[0023] Calculate the light field intensity sample D m×m,Q The average value ξ1, variance ξ2, maximum value ξ3, and minimum value ξ4 are used to obtain the statistical domain vector S of the light field. D = (ξ1,ξ2,ξ3,ξ4), after standardization and principal component analysis, the standardized matrix S′ of the optical field statistical domain is obtained. M,K Calculate the eigenvalues ​​λ in the statistical domain of the light field. S′,1 ,λ S′,2 ,λ S′,3 ,λ S′,4 The corresponding eigenvector η S′,1 ,η S′,2 ,η S′,3 ,η S′,4 Calculate the contribution of eigenvalues ​​in the statistical domain of the light field. When the contribution of the selected eigenvalues ​​is greater than the threshold θ3, determine the number of principal components Num3.

[0024]

[0025] Where m3 represents the vector number of the statistical domain of the light field within the Num3 range, and the corresponding set of eigenvectors is the statistical domain feature ST. D =(η S′,1 ,η S′,2 ,η S′,3 ,η S′,4 );

[0026] The input parameter I of the orbital angular momentum identification model is the spatial feature SP. D Frequency domain characteristics FR D Statistical domain characteristics ST D The set, namely:

[0027] I = (SP) D ,FR D ST D )······················(7)

[0028] The output parameter is the orbital angular momentum mode code O;

[0029] (3) Using the data-driven approach, an orbital angular momentum mapping model based on penalized weighted extreme learning machine was established. By optimizing the parameters of the mapping model, the input weight a, input bias b, and output layer weight β of the mapping model were determined, and an orbital angular momentum pattern recognition model was obtained.

[0030] A three-layer neural network structure is constructed, consisting of an input layer, a hidden layer, and an output layer. The input layer has N nodes, the hidden layer has L nodes, and the output layer has 1 node. After sampling from the sample set, sample data is obtained, consisting of the input parameters I and the output parameters O of the orbital angular momentum mapping model. Forming a mapping model:

[0031]

[0032] Where a = [a1, a2, ..., a L ] T and b = [b1, b2, ..., b L ] T These are the input weights and biases, β = [β1, β2, ..., β2]. L ] T For the output layer weights, I j Represents the j-th input parameter of I, O j Represents the j-th output parameter of O. For the activation function, we choose the Sigmoid function, with the following expression:

[0033]

[0034] The entire mapping function satisfies the continuity condition, allowing for efficient calculation of the derivative at the poles. The hidden layer random matrix is ​​represented as:

[0035]

[0036] By adding a regularization term, the approximation error and complexity of the model are balanced. The regularization expression is the norm of the output layer weights, and the model optimization objective is obtained as follows:

[0037]

[0038] Where h(I) j ) is the feature mapping vector of the hidden layer, and the actual output value is h(I) j )β,ξ j For the expected prediction error, O j For the desired output, C is the regularization parameter, W represents the sample weights, and L... ELM To minimize the objective. According to the KKT (Karush-Kuhn-Tucker) principle, penalty-weighted optimization can be equivalent to the dual problem;

[0039]

[0040] Among them, the Lagrange multiplier α j Since it is a constant factor, the parameters can be solved using KKT optimization conditions. For the above multivariate equations, the partial derivatives of the undetermined variables are zero, resulting in the following relationship:

[0041]

[0042]

[0043]

[0044] Depending on the matrix structure, two forms of the output layer weight β can be obtained. From the theory of linear equations, it is known that if the number of samples in the current data segment is less than the number of hidden layer nodes, i.e., N... <L,WΗΗ T H is an N×N full-rank matrix; conversely, H T WH is an L×L full-rank matrix. A linear transformation of a full-rank matrix has an inverse matrix. Therefore, the expression for the output layer weights can be obtained as follows:

[0045]

[0046] Where E is the identity matrix, and O = (O1, O2, ..., O2) NLet I' be the output parameter vector. Substituting the input parameter I' into the orbital angular momentum recognition model, the orbital angular momentum pattern code O' can be calculated, thus achieving orbital angular momentum pattern recognition. The final output expression is:

[0047]

[0048] The penalized weighted extreme learning machine takes into account both training error and model structure, ensuring that the mapping model has good compactness.

[0049] (4) Extract features from the new light field intensity sample to obtain the new input parameter I″. Calculate the new orbital angular momentum code through the orbital angular momentum pattern recognition model to obtain the orbital angular momentum pattern code O″ of the current light field intensity sample, thus realizing orbital angular momentum pattern recognition.

[0050] The final orbital angular momentum pattern encoding expression is obtained by combining the output layer weights and the feature mapping vectors of the hidden layers:

[0051]

[0052] By extracting features from the new light field intensity sample, a new input parameter I″ is obtained. Through the orbital angular momentum pattern recognition model, the orbital angular momentum pattern code O″ of the current light field intensity sample can be obtained, thus realizing orbital angular momentum pattern recognition.

[0053] This invention establishes an atmospheric turbulent optical transmission simulation model. Through numerical simulation, it simulates the light field intensity distribution of a beam at the transmitter and receiver under atmospheric turbulence conditions, calculates the spot information received by a Laguerre-Gaussian beam under different atmospheric turbulence conditions, and obtains a light field intensity sample library. Based on the light field intensity sample set, training data and test data are formed, and a penalized weighted extreme learning machine mapping model is constructed. Spatial domain features, frequency domain features, and statistical domain features are input. By optimizing the model weights and biases, the orbital angular momentum identification result is obtained.

[0054] The advantages of this invention are:

[0055] (1) This invention considers the influence of atmospheric turbulence on optical parameters, simulates atmospheric turbulence conditions through a random phase screen, and obtains a sample library of optical field intensity. An orbital angular momentum mapping model based on a penalized weighted extreme learning machine is established using a data-driven approach, realizing orbital angular momentum pattern recognition and overcoming the bottleneck of computational difficulties caused by physical models.

[0056] (2) The model input considers the spatial, frequency, and statistical information of the light spot, and the feature extraction of the composite domain is achieved through principal component analysis. An orbital angular momentum mapping model is constructed to realize the analytical expression of the output parameters.

[0057] (3) By adding regularization terms, the approximation error and complexity of the model are balanced, the generalization ability of the orbital angular momentum identification model is improved, and the entire identification process does not require manual parameter adjustment, achieving full automation, which has good engineering application value for the information processing of complex systems. Attached Figure Description

[0058] Figure 1 This is a simulation model diagram of light transmission in atmospheric turbulence;

[0059] Figure 2 This is a flowchart of the OAM identification method;

[0060] Figure 3 This is a diagram of the orbital angular momentum mapping model;

[0061] Figure 4 This is a diagram showing the results of orbital angular momentum identification. Detailed Implementation

[0062] Includes the following steps:

[0063] (1) Establish an atmospheric turbulent optical transmission simulation model, use the Fourier transform method to generate a multi-phase screen, simulate the influence of Laguerre-Gaussian beams on atmospheric turbulent transmission through numerical simulation technology, calculate the spot information received by the Laguerre-Gaussian beams under different atmospheric turbulent conditions, and form a set of light field intensity samples.

[0064] (2) Extract features from the light field intensity samples to obtain spatial features SP. D Frequency domain characteristics FR D Statistical domain characteristics ST D The input parameter I is composed of the orbital angular momentum mode encoding, which is then used as the output parameter O.

[0065] (3) Using the data-driven approach, an orbital angular momentum mapping model based on penalized weighted extreme learning machine was established. By optimizing the parameters of the mapping model, the input weight a, input bias b, and output layer weight β of the mapping model were determined, and an orbital angular momentum pattern recognition model was obtained.

[0066] (4) Extract features from the new light field intensity sample to obtain the new input parameter I″. Calculate the new orbital angular momentum code through the orbital angular momentum pattern recognition model to obtain the orbital angular momentum pattern code O″ of the current light field intensity sample, thus realizing orbital angular momentum pattern recognition.

[0067] The atmospheric turbulence optical transmission simulation model in step (1) is as follows:

[0068] Specific forms such as Figure 1As shown, atmospheric turbulence conditions were simulated using a random phase screen. The light source information used was a Laguerre-Gaussian beam. The spot information received by the Laguerre-Gaussian beam under different atmospheric turbulence conditions was calculated to form a set of light field intensity samples.

[0069] To simulate the propagation of a Laguerre-Gaussian beam under atmospheric turbulence, a sequence of phase screens composed of multiple intermediate planes was used to obtain the expression for the Laguerre-Gaussian (LG) beam passing through each phase screen:

[0070]

[0071] Where U(r0) and U(r1) represent the light field intensity at the source and after propagation through a phase screen, respectively, U(r m () represents the light field intensity at the receiving plane. and Let r0 = (x0, y0), r1 = (x1, y1), ..., r2 = (x0, y0) / 2. m =(x m ,y m () represents the coordinates. Q Monte Carlo simulations are performed to obtain the light field intensity sample set D at the receiver. m×m,MT ={U1(r m ),U2(r m ),…,U MT (r m The entire sample set includes two main optical field intensity distribution states: single-state and superposition state. The OAM mode of the single-state beam is mainly reflected in the ring radius, while the OAM mode of the superposition beam is mainly reflected in different topological charges, forming different OAM modes.

[0072] The feature extraction method in step (2) is:

[0073] The light field intensity sample set D m×m,Q Expanding this into vector form yields the light field intensity sample vector D. M,Q Where M = m × m, K samples are taken from Q sample sets to obtain K light field samples. Considering the cumulative effect of K light field samples, the light field intensity sample matrix segment D is obtained. M,K The expression is as follows:

[0074]

[0075] Where d M,K This represents the light intensity value at the M-th position of the K-th light field sample, for the light field intensity matrix segment D. M,K Each light intensity value in the data is standardized:

[0076]

[0077] Where, d t ′ ,k μ represents the standardized value of the intensity of the t-th light field in the k-th light field sample. t σ t Let represent the mean and variance of the k-th light field sample, respectively. After standardization, the standardized light field intensity sampling matrix D′ is obtained. M,K And calculate the eigenvalue λ of the light field intensity. D′,1 ,λ D′,2 ,…λ D′,M The corresponding eigenvector η D′,1 ,η D′,2 ,…η D′,M When the contribution of the selected light field intensity eigenvalue is greater than the threshold θ1 = 0.85, the number of principal components Num1 is determined.

[0078]

[0079] Where m1 represents the light field intensity index within the range Num1, and the corresponding set of feature vectors is the spatial domain feature.

[0080] For light field intensity sample D m×m,Q Perform a Fourier transform to obtain the optical field frequency sample F. m×m,Q Vector expansion, standardization, and principal component analysis are performed to obtain the optical field frequency standardized sampling matrix F′. M,K Calculate the frequency eigenvalue λ of the light field. F′,1 ,λ F′,2 ,…λ F′,M The corresponding eigenvector η F′,1 ,η F′,2 ,…η F′,M Calculate the contribution of the eigenvalues. When the contribution of the selected eigenvalues ​​is greater than the threshold θ2 = 0.85, determine the number of principal components Num2.

[0081]

[0082] Where m2 represents the frequency index of the light field within the Num2 range, and the corresponding set of feature vectors is the frequency domain feature.

[0083] Calculate the light field intensity sample D m×m,Q The average value ξ1, variance ξ2, maximum value ξ3, and minimum value ξ4 are used to obtain the statistical domain vector S of the light field. D = (ξ1,ξ2,ξ3,ξ4), after standardization and principal component analysis, the standardized matrix S′ of the optical field statistical domain is obtained. M,KCalculate the eigenvalues ​​λ in the statistical domain of the light field. S′,1 ,λ S′,2 ,λ S′,3 ,λ S′,4 The corresponding eigenvector η S′,1 ,η S′,2 ,η S′,3 ,η S′,4 Calculate the contribution of the eigenvalues ​​in the statistical domain of the light field. When the contribution of the selected eigenvalues ​​is greater than the threshold θ3 = 0.85, determine the number of principal components Num3.

[0084]

[0085] Where m3 represents the vector number of the statistical domain of the light field within the Num3 range, and the corresponding set of eigenvectors is the statistical domain feature ST. D =(η S′,1 ,η S′,2 ,η S′,3 ,η S′,4 );

[0086] The input parameter I of the orbital angular momentum identification model is the spatial feature SP. D Frequency domain characteristics FR D Statistical domain characteristics ST D The set, namely:

[0087] I = (SP) D ,FR D ST D )·······················(7)

[0088] The output parameter is the orbital angular momentum mode code O;

[0089] In step (3), an orbital angular momentum mapping model is established, and the orbital angular momentum identification model is solved.

[0090] Construct a three-layer neural network structure consisting of an input layer, hidden layers, and an output layer, such as... Figure 3 As shown, the input layer is set to have N nodes, the hidden layer to have L = 20 nodes, and the output layer to have 1 node. After sampling from the sample set, sample data consisting of the input parameters I and output parameters O of the orbital angular momentum mapping model is obtained. Forming a mapping model:

[0091]

[0092] Where a = [a1, a2, ..., a L ] T and b = [b1, b2, ..., b L ] TThese are the input weights and biases, β = [β1, β2, ..., β2]. L ] T For the output layer weights, I j Represents the j-th input parameter of I, O j Represents the j-th output parameter of O. For the activation function, we choose the Sigmoid function, with the following expression:

[0093]

[0094] The entire mapping function satisfies the continuity condition, allowing for efficient calculation of the derivative at the poles. The hidden layer random matrix is ​​represented as:

[0095]

[0096] Perform data preprocessing. Normalize the input parameters so that all values ​​are within the range [0,1].

[0097] Calculate the hidden layer matrix, randomly select input layer weights a and biases b, and calculate the feature mapping vector h(I) of the hidden layer through nonlinear mapping. i );

[0098] By adding a regularization term, the approximation error and complexity of the model are balanced. The regularization expression is the norm of the output layer weights, and the model optimization objective is obtained as follows:

[0099]

[0100] Where h(I) j ) is the feature mapping vector of the hidden layer, and the actual output value is h(I) j )β,ξ j For the expected prediction error, O j For the desired output, C is the regularization parameter, W represents the sample weights, and L... ELM To minimize the objective, according to the KKT (Karush-Kuhn-Tucker) principle, penalized weighted optimization can be equivalent to the dual problem.

[0101]

[0102] Among them, the Lagrange multiplier α j It is a constant factor. The parameters can be solved using KKT optimization conditions. For the above multivariate equations, satisfying the condition that the partial derivatives of the undetermined variables are zero, we obtain the following relationship:

[0103]

[0104]

[0105]

[0106] Depending on the matrix structure, two forms of the output layer weight β can be obtained. From the theory of linear equations, it is known that if the number of samples in the current data segment is less than the number of hidden layer nodes, i.e., N... <L,WΗΗ T H is an N×N full-rank matrix; conversely, H T WH is an L×L full-rank matrix. A linear transformation of a full-rank matrix has an inverse matrix; therefore, the output layer weights can be expressed as follows:

[0107]

[0108] Where E is the identity matrix, and O = (O1, O2, ..., O2) N Let I' be the output parameter vector. Substituting the input parameter I' into the orbital angular momentum recognition model, we can calculate the orbital angular momentum pattern code O', thus achieving orbital angular momentum pattern recognition. The final output expression is:

[0109]

[0110] The penalized weighted extreme learning machine takes into account both training error and model structure, ensuring that the mapping model has good compactness.

[0111] In step (4), a new orbital angular momentum code is calculated using the orbital angular momentum pattern recognition model;

[0112] The final orbital angular momentum pattern encoding expression is obtained by combining the output layer weights and the feature mapping vectors of the hidden layers:

[0113]

[0114] By extracting features from the new light field intensity sample, a new input parameter I″ is obtained. Through the orbital angular momentum pattern recognition model, the orbital angular momentum pattern code O″ of the current light field intensity sample can be obtained, thus realizing orbital angular momentum pattern recognition.

[0115] The invention will be further illustrated below with examples.

[0116] like Figure 4 As shown, a set of light field intensity samples was obtained using an atmospheric turbulent light transmission simulation model. Some of the light field intensity samples are shown below. Figure 4 As shown in (a). After feature extraction, the orbital angular momentum pattern recognition model is used to calculate the output expression, thus obtaining the orbital angular momentum pattern encoding of the current light field intensity sample, as shown in (a). Figure 4 As shown in (b), O″=[1,2,4], thereby realizing orbital angular momentum pattern recognition.

Claims

1. A method for orbital angular momentum pattern recognition based on composite domain analysis, characterized in that, Includes the following steps: (1) Establish an atmospheric turbulent optical transmission simulation model, use the Fourier transform method to generate a multi-phase screen, simulate the influence of Laguerre-Gaussian beams on atmospheric turbulent transmission through numerical simulation technology, calculate the spot information received by the Laguerre-Gaussian beams under different atmospheric turbulent conditions, and form a set of light field intensity samples. (2) Extract features from the light field intensity samples to obtain spatial features. Frequency domain characteristics Statistical domain characteristics , forming input parameters Orbital angular momentum mode encoding is used as output parameter ; (3) Using a data-driven approach, an orbital angular momentum mapping model based on a penalized weighted extreme learning machine was established, and the input weights of the mapping model were determined. Input bias Output layer weights The orbital angular momentum pattern recognition model is obtained; the orbital angular momentum mapping model is: Construct a three-layer neural network structure consisting of an input layer, a hidden layer, and an output layer, and set the input layer as... There are 1 node, and the hidden layer is 1. The output layer has one node, and the input parameters of the orbital angular momentum mapping model are obtained after sampling from the sample set. and output parameters Composition of sample data This forms a mapping model: (8) in, and These are the input weights and the input bias, respectively. For output layer weights, represent The One input parameter, represent The One output parameter, The activation function is denoted as N, where N is the number of samples. The Sigmoid function is chosen, and its specific expression is: (9) The entire mapping function satisfies the continuity condition, and the derivative at the poles can be effectively obtained. The hidden layer random matrix is ​​represented as: (10) By adding a regularization term, the approximation error and complexity of the model are balanced. The regularization expression is the norm of the output layer weights, and the model optimization objective is obtained as follows: (11) in, It is the feature mapping vector of the hidden layer, and the actual output value is , The expected prediction error, For the desired output, For regularization parameters, Indicates sample weights, To minimize the objective, according to the KKT (Karush-Kuhn-Tucker) principle, penalty-weighted optimization can be equivalent to the dual problem; (12) Among them, the Lagrange multiplier Since it is a constant factor, the parameters are solved using the KKT optimization conditions. For the above multivariate equation, the partial derivatives of the undetermined variables are zero, resulting in the following relationship: (13) (14) (15) The output layer weights can be obtained based on different matrix structures. The two forms are known from the theory of linear equations: if the number of samples in the current data segment is less than the number of hidden layer nodes, i.e. , for A full-rank matrix; conversely, for Given a full-rank matrix, and the linear transformation of a full-rank matrix having an inverse matrix, the output layer weight expression is obtained as follows: (16) in, It is the identity matrix. The output parameter vector contains the input parameters. Substituting the values ​​into the orbital angular momentum identification model, the orbital angular momentum pattern code can be calculated. This achieves orbital angular momentum pattern recognition, and the final output expression is: (17) The penalized weighted extreme learning machine takes into account both the effects of training error and model structure, ensuring that the mapping model has good compactness. (4) Extract features from the new light field intensity samples to obtain new input parameters. By calculating the new orbital angular momentum code using the orbital angular momentum pattern recognition model, the orbital angular momentum pattern code of the current light field intensity sample can be obtained. To achieve orbital angular momentum pattern recognition.

2. The orbital angular momentum pattern recognition method based on composite domain analysis according to claim 1, characterized in that, The atmospheric turbulent light transmission simulation model in step (1) is as follows: To simulate the propagation of a Laguerre-Gaussian beam under atmospheric turbulence, a sequence of phase screens composed of multiple intermediate planes was used to obtain the expression for the Laguerre-Gaussian (LG) beam passing through each phase screen: (1) in and These represent the light field intensity at the source and after propagation through a phase screen, respectively. Indicates the light field intensity at the receiving plane. and These represent the Fourier transform and the inverse Fourier transform, respectively. Represents the imaginary unit. This represents the atmospheric turbulence transformation operator. The distance between each phase screen layer, , , , Represent coordinates, perform The Monte Carlo simulation yields a set of light field intensity samples at the receiver. The entire sample set includes two main optical field intensity distribution states: single-state and superposition state. The OAM mode of the single-state beam is mainly reflected in the ring radius, while the OAM mode of the superposition beam is mainly reflected in different topological charges, forming different OAM modes.

3. The orbital angular momentum pattern recognition method based on composite domain analysis according to claim 1, characterized in that, The feature extraction method in step (2) is: Set of light field intensity samples Expanding into vector form yields the light field intensity sample vector. ,in , Sampling from a sample set Next, get Considering a light field sample, The cumulative effect of individual light field samples yields a fragment of the light field intensity sample matrix. The expression is as follows: (2) in Indicates the first The light field sample of the first The light intensity value at each location corresponds to a segment of the light field intensity matrix. Each light intensity value in the data is standardized: (3) in, Indicates the first In the light field sample, the first The standardized value of the light field intensity, , They represent the first The mean and variance of each light field sample are normalized to obtain the normalized sampling matrix of light field intensity. And calculate the characteristic value of the light field intensity. corresponding feature vector When the contribution of the selected light field intensity eigenvalue is greater than the threshold When determining the number of principal components ; (4) in, express The set of eigenvectors corresponding to the light field intensity numbers within the range constitutes the spatial domain features. ; For light field intensity samples Perform a Fourier transform to obtain the optical field frequency samples. Vector expansion, standardization, and principal component analysis are performed to obtain the optical field frequency standardized sampling matrix. Calculate the frequency eigenvalues ​​of the light field corresponding feature vector Calculate the contribution of the eigenvalues; when the contribution of the selected eigenvalues ​​is greater than a threshold... When determining the number of principal components ; (5) in, express The set of eigenvectors corresponding to the frequency numbers of the light field within a given range constitutes the frequency domain features. ; Calculate light field intensity samples average ,variance Maximum value Minimum value The statistical domain vector of the light field is obtained. Standardization and principal component analysis were performed to obtain the standardized matrix of the optical field statistical domain. Calculate the eigenvalues ​​of the statistical domain of the light field corresponding feature vector Calculate the contribution of the eigenvalues ​​in the statistical domain of the light field. When the contribution of the selected eigenvalues ​​is greater than a threshold... When determining the number of principal components ; (6) in, express The set of eigenvectors corresponding to the statistical domain vectors of the light field within the specified range constitutes the statistical domain features. ; Orbital angular momentum identification model input parameters This refers to spatial characteristics. Frequency domain characteristics Statistical domain characteristics The set, namely: (7) The output parameters are the orbital angular momentum mode encoding. .

4. The orbital angular momentum pattern recognition method based on composite domain analysis according to claim 1, characterized in that, Step (4) involves calculating a new orbital angular momentum code using an orbital angular momentum pattern recognition model, including: The final orbital angular momentum pattern encoding expression is obtained by combining the output layer weights and the feature mapping vectors of the hidden layers: (18) New input parameters are obtained by extracting features from the new light field intensity samples. By using the orbital angular momentum pattern recognition model, the orbital angular momentum pattern encoding of the current light field intensity sample can be obtained. To achieve orbital angular momentum pattern recognition.

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