Satellite communication anti-interference method and system based on kernel method and FastICA

Abstract

The invention relates to the technical field of satellite communication, and particularly discloses a satellite communication anti-interference method and system based on a kernel method and FastICA, and the method comprises the steps: building a post-nonlinear hybrid model, so as to simulate the nonlinear signal distortion caused by an amplitude limiter in satellite communication, the post-nonlinear mixing model comprises a linear mixing stage and a nonlinear compression stage; a kernel method is adopted to map observation signals to a high-dimensional regeneration kernel Hilbert space, nonlinear features are represented through a quartic polynomial kernel function, and a nonlinear mixing problem is converted into a linear separable form; in a high-dimensional kernel space, based on a FastICA algorithm, a communication signal and an interference signal are separated through a non-Gaussian criterion of maximizing negentropy; in combination with regularization pre-whitening processing and a symmetric fixed point iterative optimization strategy, a separation matrix is updated; and outputting the separated communication signal to realize nonlinear interference suppression.

Description

Technical Field

[0001] This invention relates to the field of satellite communication technology, and specifically to a satellite communication anti-interference method and system based on the kernel method and FastICA. Background Technology

[0002] With the development of satellite communication technology, the global coverage, dynamic deployment, and high-frequency data collection capabilities of low Earth orbit (LEO) satellites make them a key carrier for future Internet of Things (IoT), emergency communication, and remote sensing. However, satellite communication systems generally face the challenge of complex interference environments. Especially under nonlinear channel conditions, the presence of nonlinear devices such as power amplifiers and limiters in satellite links can easily lead to signal distortion, rendering traditional linear anti-interference techniques ineffective. Furthermore, satellite-to-ground links are highly exposed and extremely vulnerable to intentional or unintentional interference attacks, which is particularly serious in military, emergency, or remote satellite application scenarios. Therefore, researching efficient anti-interference methods adaptable to nonlinear mixed signal environments has become a key focus in the current satellite communication field.

[0003] Currently, much research on anti-jamming mainly focuses on spread spectrum technology, adaptive beamforming, and frequency hopping communication. For example, some literature proposes spread spectrum-based anti-jamming mechanisms that improve anti-jamming capabilities by expanding bandwidth; other studies utilize blind source separation (BSS) technology to extract target signals from mixed signals to mitigate interference effects. In recent years, some research has also attempted to apply Fast Independent Component Analysis (FastICA) to satellite communication systems to separate different source signals, improve the signal-to-noise ratio, and reduce interference impact. However, when facing nonlinear mixed problems, the linear independence assumption upon which FastICA relies significantly reduces its separation effectiveness. Furthermore, some studies have attempted to combine neural networks or deep learning techniques to handle blind source separation problems, but their high computational complexity and energy consumption are unsuitable for resource-constrained satellite platforms.

[0004] The aforementioned existing technologies generally suffer from two core problems: first, they ignore the complexity of nonlinear signal mixing in satellite communication, resulting in poor performance of anti-interference algorithms in actual deployment; second, the algorithms have a large computational load, and the training and inference processes place high demands on computing resources and energy consumption, which is not suitable for the real-time and low-power requirements of low-Earth orbit satellite systems. Summary of the Invention

[0005] This invention aims to alleviate the problems of low separation accuracy and poor real-time performance of traditional blind source separation algorithms in scenarios with nonlinear distortion and high computational complexity. To achieve the purpose of this invention, this application provides a satellite communication anti-interference method based on kernel methods and FastICA, comprising: Step S1: Construct a post-nonlinear hybridization model to simulate the nonlinear signal distortion caused by the limiter in satellite communication. The post-nonlinear hybridization model includes a linear hybridization stage and a nonlinear compression stage. Step S2: The observed signal is mapped to a high-dimensional regenerative kernel Hilbert space using the kernel method. The nonlinear characteristics are characterized by a fourth-order polynomial kernel function, which transforms the nonlinear mixed problem into a linearly separable form. Step S3: In the high-dimensional kernel space, based on the FastICA algorithm, the communication signal and the interference signal are separated by maximizing the non-Gaussianity criterion of negative entropy; Step S4: Combine regularized pre-whitening processing with symmetric fixed-point iterative optimization strategy to update the separation matrix; Step S5: Output the separated communication signal to achieve nonlinear interference suppression.

[0006] In some specific embodiments, step S1 includes: The linear mixing stage uses the channel transmission matrix to linearly mix the source signals to generate a mixed signal; the nonlinear compression stage uses the hyperbolic tangent function to simulate the nonlinear distortion of the limiter to generate the observation signal.

[0007] In some specific embodiments, in step S2, the fourth-order polynomial kernel function is determined according to the following formula: ; In the formula, x1 represents the first dimension component of the received signal vector, and x2 represents the second dimension component of the received signal vector.

[0008] In some specific embodiments, in step S3, the non-Gaussianity criterion for maximizing negative entropy is determined by the following objective function: ; In the formula, This represents a nonlinear function used to measure non-Gaussianity. Let v represent the row vector of the unmixing vector separation matrix, used to extract independent components, and v denote a standard Gaussian random variable. Indicates a normal distribution. Represents the mathematical expectation. This represents the eigenvector after kernel mapping.

[0009] In some specific embodiments, step S4 includes the following: The covariance matrix of the kernel-mapped signal is estimated, and a regularization term is introduced to suppress small eigenvalue perturbations. The signal is whitened by constructing a whitening matrix through eigenvalue decomposition.

[0010] To achieve the same inventive objective, this application also provides a satellite communication anti-jamming system based on a kernel method and FastICA, comprising: Signal acquisition module: used to construct a post-nonlinear mixing model to simulate the nonlinear signal distortion caused by the limiter in satellite communication. The post-nonlinear mixing model includes a linear mixing stage and a nonlinear compression stage. Kernel mapping module: Used to map observed signals to a high-dimensional regenerative kernel Hilbert space using kernel methods, characterizing nonlinear features through a quartic polynomial kernel function, and transforming nonlinear mixed problems into linearly separable forms; Signal separation module: used to separate communication signals from interference signals in a high-dimensional kernel space based on the FastICA algorithm and by maximizing the non-Gaussianity criterion of negative entropy; Optimization processing module: used to update the separation matrix by combining regularized pre-whitening processing with symmetric fixed-point iterative optimization strategy; Signal output module: Used to output the separated communication signal and achieve nonlinear interference suppression.

[0011] In some specific embodiments, the signal acquisition module is used for: The linear mixing stage uses the channel transmission matrix to linearly mix the source signals to generate a mixed signal; the nonlinear compression stage uses the hyperbolic tangent function to simulate the nonlinear distortion of the limiter to generate the observation signal.

[0012] In some specific embodiments, the fourth-order polynomial kernel function in the kernel mapping module is determined according to the following formula: ; In the formula, x1 represents the first dimension component of the received signal vector, and x2 represents the second dimension component of the received signal vector.

[0013] In some specific embodiments, the non-Gaussianity criterion for maximizing negative entropy in the signal separation module is determined by the following objective function: ; In the formula, This represents a nonlinear function used to measure non-Gaussianity. Let v represent the row vector of the unmixing vector separation matrix, used to extract independent components, and v denote a standard Gaussian random variable. Indicates a normal distribution. Represents the mathematical expectation. This represents the eigenvector after kernel mapping.

[0014] In some specific embodiments, the regularization pre-whitening process in the optimization processing module includes: The covariance matrix of the kernel-mapped signal is estimated, and a regularization term is introduced to suppress small eigenvalue perturbations. The signal is whitened by constructing a whitening matrix through eigenvalue decomposition.

[0015] The beneficial effects of the above technical solution are as follows: This application presents a satellite communication anti-jamming method based on kernel methods and FastICA. By modeling nonlinear interference in satellite communication as a post-nonlinear hybrid model, it more accurately simulates and compensates for nonlinear signal distortion in satellite communication. A kernel method is introduced to map the original nonlinear problem to a high-dimensional regenerative kernel Hilbert space. Furthermore, a fast independent component analysis algorithm is used in this space for blind source separation of the signal. An optimization strategy combining regularized pre-whitening and symmetric fixed-point iteration is proposed to avoid the high computational complexity and slow convergence of traditional methods when dealing with nonlinear interference. The final result is a computationally efficient and highly accurate anti-jamming method that effectively enhances the robustness of satellite communication systems in complex electromagnetic environments, providing a reliable reference for real-time anti-jamming technology for spaceborne platforms. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 A flowchart illustrating a satellite communication anti-jamming method based on kernel method and FastICA is provided as an embodiment of the present invention. Figure 2 A schematic diagram of a satellite communication anti-jamming system based on kernel methods and FastICA is provided as an embodiment of the present invention; Figure 3 A block diagram of a nonlinear blind source separation signal processing system based on a satellite communication anti-interference method using kernel methods and FastICA is provided as an embodiment of the present invention. Detailed Implementation

[0018] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0019] Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar symbols denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the invention, and should not be construed as limiting the invention.

[0020] Example 1 In satellite communication systems, nonlinear distortion is one of the key factors restricting signal separation and interference suppression performance. This type of distortion mainly originates from limiters in the RF receiver front-end used to protect high-sensitivity devices. To prevent high-power interference signals from damaging critical components such as power amplifiers (PAs) and analog-to-digital converters (ADCs), limiters are typically placed at the front end of the signal link to limit the input signal amplitude within a preset threshold range. However, when the received signal power exceeds the linear operating range of the limiter, its nonlinear compression effect significantly disrupts the linear superposition characteristics of the signal. This distortion not only interferes with subsequent signal processing but also weakens the effectiveness of traditional blind source separation methods (such as FastICA). To address the nonlinear distortion problem introduced by the limiter, this invention employs a post-nonlinear (PNL) mixing model to model the signal mixing process. This model divides the signal propagation process into two stages: first, the source signals are mixed through a linear mixing matrix; subsequently, the mixed signal is processed by a nonlinear function to simulate the distortion effect of the limiter. Unlike traditional pre-nonlinear models, the PNL model better reflects the physical characteristics of satellite communication systems, i.e., the nonlinear effect of the limiter acts after the linear mixing stage. This modeling approach can accurately characterize the signal distortion mechanism under amplitude compression conditions.

[0021] One embodiment of the present invention provides a satellite communication anti-jamming method based on kernel methods and FastICA, referring to... Figure 1 As shown, it includes: Step S1: Construct a post-nonlinear hybridization model to simulate the nonlinear signal distortion caused by the limiter in satellite communication. The post-nonlinear hybridization model includes a linear hybridization stage and a nonlinear compression stage. In one specific embodiment of the present invention, step S1 includes: The linear mixing stage uses the channel transmission matrix to linearly mix the source signals to generate a mixed signal; the nonlinear compression stage uses the hyperbolic tangent function to simulate the nonlinear distortion of the limiter to generate the observation signal.

[0022] Specifically, there are two source signals. It uses a linear hybrid matrix (i.e., a channel transmission matrix). The signals are mixed to generate the antenna receiving signal. : (1) in, Let represent the communication signal and the interference signal, respectively, and n(t) be the additive noise of the receiving antenna. Indicates the source signal Through channel transmission matrix The resulting linear mixed signal (without noise components).

[0023] The mixed signal is then subjected to a nonlinear transformation caused by the nonlinear distortion characteristics of the device (such as a limiter), ultimately yielding the observed signal. : (2) Among them, the function This is used to simulate the nonlinear distortion introduced by the limiter. In this invention, the hyperbolic tangent function is selected. As a nonlinear approximation function, i.e. (3) This function exhibits smooth, continuous, and differentiable asymptotic saturation characteristics, maintaining linear gain in the low-power region while simulating the nonlinear response of a soft limiter through progressive amplitude compression in the overload region. Furthermore, its characteristics significantly suppress out-of-band radiation while preserving signal envelope information, thus meeting the synergistic optimization requirements of modern satellite communication systems for limiting distortion and spectral efficiency.

[0024] The main idea of ​​the anti-interference method based on nonlinear blind source separation is to design a nonlinear unmixing system. This causes nonlinear distortion signals After processing by this system, the estimated value of the output source signal is... ,Right now (4) The goal of interference suppression is to accurately estimate the communication signal. A block diagram of a nonlinear blind source separation signal processing system is shown below. Figure 3 As shown.

[0025] Step S2: The observed signal is mapped to a high-dimensional regenerative kernel Hilbert space using the kernel method. The nonlinear characteristics are characterized by a fourth-order polynomial kernel function, which transforms the nonlinear mixed problem into a linearly separable form. In a specific embodiment of the present invention, in step S2, the fourth-order polynomial kernel function is determined according to the following formula: ; In the formula, x1 represents the first dimension component of the received signal vector, and x2 represents the second dimension component of the received signal vector.

[0026] Specifically, based on the post-nonlinear hybrid model established in the system model, the core objective of Blind Source Separation (BSS) is to separate communication signals from interference signals using only observed signals without prior information, thereby obtaining a clean communication signal and suppressing interference. Due to the influence of nonlinear devices such as amplitude limiters during signal transmission, traditional linear model-based blind source separation methods fail in this scenario. Therefore, it is urgent to construct a BSS framework suitable for nonlinear hybrids. Addressing the dual challenges of channel distortion and interference coupling in satellite communication, this invention proposes a kernel-based fast independent component analysis algorithm (Kernel-FastICA), which adopts a two-stage architecture of "nonlinear mapping-linear separation".

[0027] The core step of the kernel method lies in nonlinear mapping, which aims to transform the nonlinear hybrid structure in the original observed signal into a linearly separable form through feature space transformation. Specifically, for the observed signal x... Through mapping function This is projected onto a high-dimensional reproducing kernel Hilbert space (RKHS)Γ. In this space, complex nonlinear mixing relationships can be approximated as a linear superposition model, thus providing theoretical feasibility for the subsequent FastICA algorithm. The kernel function is defined in this process as the inner product operation of data points in the feature space: (5) in, These are the sample points from the original input space. The kernel function is an implicit mapping function. According to Mercer's theorem, the positive definiteness of the kernel function can implicitly construct a high-dimensional feature space, avoiding the curse of dimensionality while preserving the statistical independence of the signal. To improve nonlinear separation capability, this invention uses a quartic polynomial kernel mapping to explicitly construct the feature space: (6) Among them, the input signal The dimension is expanded to 15 dimensions through a fourth-order polynomial. Compared to low-order polynomial kernels, the fourth-order kernel can effectively capture nonlinear characteristics such as power amplifier limiting distortion and cross-modulation interference, while avoiding the dimension explosion problem of high-order kernels. Compared to Gaussian kernels that require parameter adjustment, polynomial kernels are more suitable for the deterministic modulation modes of satellite communication, balancing algorithm efficiency and robustness.

[0028] Step S3: In the high-dimensional kernel space, based on the FastICA algorithm, the communication signal and the interference signal are separated by maximizing the non-Gaussianity criterion of negative entropy; In a specific embodiment of the present invention, in step S3, the non-Gaussianity criterion for maximizing negative entropy is determined by the following objective function: ; In the formula, This represents a nonlinear function used to measure non-Gaussianity. Let v represent the row vector of the unmixing vector separation matrix, used to extract independent components, and v denote a standard Gaussian random variable. Indicates a normal distribution. Represents the mathematical expectation. This represents the eigenvector after kernel mapping.

[0029] In a high-dimensional kernel feature space, this invention employs the Fast Independent Component Analysis (FastICA) algorithm to extract independent source signals by maximizing the non-Gaussianity criterion. The theoretical basis of FastICA lies in the non-Gaussianity measure, which assumes that the stronger the non-Gaussianity of the source signal, the higher the statistical independence. This invention chooses Negentropy as the non-Gaussianity indicator: (7) In the formula, For signal Shannon entropy, For signal Shannon entropy, To and The reference variable is a Gaussian distribution with homoscedasticity. According to information theory, a Gaussian distribution has maximum entropy, therefore negative entropy. The nonnegativity of the expression quantifies the degree to which the signal deviates from a Gaussian distribution. By iteratively optimizing and maximizing the negative entropy, the algorithm can gradually approximate the real independent source signal. To approximate the calculation of the negative entropy, a Gaussian nonlinear function is used. Define the optimization goal: (8) The gradient update rule can be obtained by taking the derivative of the objective function: (9) In the formula, , β represents the scaling factor for gradient updates. Let u represent the mathematical expectation, and let u represent the nonlinear function. The input variables are denoted by e, representing the natural constant, and w, representing the unmixing vector, i.e., the row vector of the separation matrix. To avoid the local convergence problem of the gradient descent method, a symmetric fixed-point iterative method is used to update the separation matrix W. Its core iterative formula is: (10) The iteration termination condition is set to the maximum number of iterations. Or convergence threshold To improve numerical stability, the algorithm pre-whitens the kernel mapping signal and introduces a regularization term in the covariance matrix estimation. : (11) In the formula, T Let I be the number of sampling points, and let I be the identity matrix. The regularization term is used to suppress small eigenvalue perturbations and ensure matrix invertibility.

[0030] Step S4: Combining regularized pre-whitening processing with symmetric fixed-point iterative optimization strategy, update the separation matrix, suppress small eigenvalue perturbations, and improve the convergence stability of the algorithm; In a specific embodiment of the present invention, step S4, the regularization pre-whitening process includes: The covariance matrix of the kernel-mapped signal is estimated, and a regularization term is introduced to suppress small eigenvalue perturbations. The signal is whitened by constructing a whitening matrix through eigenvalue decomposition.

[0031] Step S5: Output the separated communication signal to achieve nonlinear interference suppression.

[0032] This invention provides a satellite anti-jamming method for nonlinear blind source separation based on kernel learning and fast independent component analysis. By modeling nonlinear interference in satellite communication as a post-nonlinear hybrid model and introducing a kernel method to map the original nonlinear problem to a high-dimensional regenerative kernel Hilbert space, a fast independent component analysis algorithm is further employed in this space to separate the signal's blind sources. An optimization strategy combining regularized pre-whitening and symmetric fixed-point iteration is proposed to avoid the high computational complexity and slow convergence issues of traditional methods when dealing with nonlinear interference. Ultimately, a computationally efficient and highly accurate anti-jamming method is obtained, effectively enhancing the robustness of satellite communication systems in complex electromagnetic environments and providing a reliable reference for real-time anti-jamming technology on spaceborne platforms.

[0033] Example 2 One embodiment of the present invention provides a satellite communication anti-jamming system based on kernel methods and FastICA, referring to... Figure 2 As shown, it includes: Signal acquisition module 10: used to construct a post-nonlinear mixing model to simulate the nonlinear signal distortion caused by the limiter in satellite communication. The post-nonlinear mixing model includes a linear mixing stage and a nonlinear compression stage. Kernel Mapping Module 20: Used to map the observed signal to a high-dimensional regenerating kernel Hilbert space using the kernel method, and to characterize the nonlinear features through a quartic polynomial kernel function, so that the nonlinear mixed problem is transformed into a linearly separable form; Signal separation module 30: used to separate communication signals from interference signals in a high-dimensional kernel space based on the FastICA algorithm and by maximizing the non-Gaussianity criterion of negative entropy; Optimization processing module 40: It is used to combine regularized pre-whitening processing and symmetric fixed-point iterative optimization strategy to update the separation matrix, suppress small eigenvalue perturbations and improve the convergence stability of the algorithm; Signal output module 50: Used to output the separated communication signal to achieve nonlinear interference suppression.

[0034] In some specific embodiments, the signal acquisition module 10 is used for: The linear mixing stage uses the channel transmission matrix to linearly mix the source signals to generate a mixed signal; the nonlinear compression stage uses the hyperbolic tangent function to simulate the nonlinear distortion of the limiter to generate the observation signal.

[0035] In some specific embodiments, in the kernel mapping module 20, the fourth-order polynomial kernel function is determined according to the following formula: ; In the formula, x1 represents the first dimension component of the received signal vector, and x2 represents the second dimension component of the received signal vector.

[0036] In some specific embodiments, in the signal separation module 30, the non-Gaussianity criterion for maximizing negative entropy is determined by the following objective function: ; In the formula, This represents a nonlinear function used to measure non-Gaussianity. Let v represent the row vector of the unmixing vector separation matrix, used to extract independent components, and v denote a standard Gaussian random variable. Indicates a normal distribution. Represents the mathematical expectation. This represents the eigenvector after kernel mapping.

[0037] In some specific embodiments, the regularization pre-whitening process in the optimization processing module 40 includes: The covariance matrix of the kernel-mapped signal is estimated, and a regularization term is introduced to suppress small eigenvalue perturbations. The signal is whitened by constructing a whitening matrix through eigenvalue decomposition.

[0038] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

[0039] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. The embodiments of the present invention are described with reference to flowchart illustrations and / or block diagrams of methods, terminal devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing terminal device to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing terminal device, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 The computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing terminal device to operate in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The functions specified in one or more boxes. These computer program instructions may also be loaded onto a computer or other programmable data processing terminal equipment to cause a series of operational steps to be performed on the computer or other programmable terminal equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable terminal equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1The steps of the functions specified in one or more boxes. Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of the embodiments of the invention. Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or terminal device that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or terminal device. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or terminal device that includes said element.

[0040] The methods and apparatus provided by the present invention have been described in detail above. Specific examples have been used to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of the present invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of the present invention. Therefore, the content of this specification should not be construed as a limitation of the present invention.

[0041] In the description of this specification, references to terms such as "an embodiment," "some embodiments," "example," "specific example," or "a specific embodiment" or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, illustrative expressions of terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0042] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A satellite communication anti-jamming method based on kernel method and FastICA, characterized in that, include: Step S1: Construct a post-nonlinear hybridization model to simulate the nonlinear signal distortion caused by the limiter in satellite communication. The post-nonlinear hybridization model includes a linear hybridization stage and a nonlinear compression stage. Step S2: The observed signal is mapped to a high-dimensional regenerative kernel Hilbert space using the kernel method. The nonlinear characteristics are characterized by a fourth-order polynomial kernel function, which transforms the nonlinear mixed problem into a linearly separable form. Step S3: In the high-dimensional kernel space, based on the FastICA algorithm, the communication signal and the interference signal are separated by maximizing the non-Gaussianity criterion of negative entropy; Step S4: Combine regularized pre-whitening processing with symmetric fixed-point iterative optimization strategy to update the separation matrix; Step S5: Output the separated communication signal to achieve nonlinear interference suppression.

2. The satellite communication anti-interference method based on kernel method and FastICA according to claim 1, characterized in that, Step S1 includes: The linear mixing stage uses the channel transmission matrix to linearly mix the source signals to generate a mixed signal; the nonlinear compression stage uses the hyperbolic tangent function to simulate the nonlinear distortion of the limiter to generate the observation signal.

3. The satellite communication anti-interference method based on kernel method and FastICA according to claim 1, characterized in that, In step S2, the fourth-order polynomial kernel function is determined according to the following formula: ； In the formula, x1 represents the first dimension component of the received signal vector, and x2 represents the second dimension component of the received signal vector.

4. The satellite communication anti-interference method based on kernel method and FastICA according to claim 1, characterized in that, In step S3, the non-Gaussianity criterion for maximizing negative entropy is determined by the following objective function: ； In the formula, Represents a nonlinear function. Let v represent the row vector of the unmixing vector separation matrix, and v represent the standard Gaussian random variable. Indicates a normal distribution. Represents the mathematical expectation. This represents the eigenvector after kernel mapping.

5. The satellite communication anti-interference method based on kernel method and FastICA according to claim 1, characterized in that, In step S4, the regularization pre-whitening process includes: The covariance matrix of the kernel-mapped signal is estimated, and a regularization term is introduced to suppress small eigenvalue perturbations. The signal is whitened by constructing a whitening matrix through eigenvalue decomposition.

6. A satellite communication anti-jamming system based on kernel methods and FastICA, characterized in that, include: Signal acquisition module: used to construct a post-nonlinear mixing model to simulate the nonlinear signal distortion caused by the limiter in satellite communication. The post-nonlinear mixing model includes a linear mixing stage and a nonlinear compression stage. Kernel mapping module: Used to map observed signals to a high-dimensional regenerative kernel Hilbert space using kernel methods, characterizing nonlinear features through a quartic polynomial kernel function, and transforming nonlinear mixed problems into linearly separable forms; Signal separation module: used to separate communication signals from interference signals in a high-dimensional kernel space based on the FastICA algorithm and by maximizing the non-Gaussianity criterion of negative entropy; Optimization processing module: used to update the separation matrix by combining regularized pre-whitening processing with symmetric fixed-point iterative optimization strategy; Signal output module: Used to output the separated communication signal and achieve nonlinear interference suppression.

7. The satellite communication anti-jamming system based on kernel method and FastICA according to claim 6, characterized in that, The signal acquisition module is used for: The linear mixing stage uses the channel transmission matrix to linearly mix the source signals to generate a mixed signal; the nonlinear compression stage uses the hyperbolic tangent function to simulate the nonlinear distortion of the limiter to generate the observation signal.

8. The satellite communication anti-jamming system based on kernel method and FastICA according to claim 6, characterized in that, In the kernel mapping module, the fourth-order polynomial kernel function is determined according to the following formula: ； In the formula, x1 represents the first dimension component of the received signal vector, and x2 represents the second dimension component of the received signal vector.

9. The satellite communication anti-jamming system based on kernel method and FastICA according to claim 6, characterized in that, In the signal separation module, the non-Gaussianity criterion for maximizing negative entropy is determined by the following objective function: ； In the formula, Represents a nonlinear function. Let v represent the row vector of the unmixing vector separation matrix, and v represent the standard Gaussian random variable. Indicates a normal distribution. Represents the mathematical expectation. This represents the eigenvector after kernel mapping.

10. The satellite communication anti-jamming system based on kernel method and FastICA according to claim 6, characterized in that, In the optimization processing module, the regularization pre-whitening processing includes: The covariance matrix of the kernel-mapped signal is estimated, and a regularization term is introduced to suppress small eigenvalue perturbations. The signal is whitened by constructing a whitening matrix through eigenvalue decomposition.

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