Low earth orbit satellite phased array multi-beam interference modeling and suppression method and system

Abstract

The invention relates to the technical field of satellite internet, and discloses a low-orbit satellite phased array multi-beam interference modeling and suppression method and system, and the method comprises the steps: selecting a Kaiser window as a core filtering method, and achieving the optimization of beam characteristics through the dynamic adjustment of a shape parameter beta; generating an initial beam directional diagram based on a digital phase matching method, and multiplying the Kaiser window function coefficient by the excitation weight of the 64-array-element linear array element by element to realize spatial domain weighted filtering; the method comprises the following steps: constructing a training data set containing multi-scene interference characteristics, calculating a corresponding covariance matrix and an accurate inverse matrix thereof to form a sample pair, designing a deep neural network architecture, inputting a flattened covariance matrix vector, and learning a complex nonlinear mapping relation from the covariance matrix to the inverse matrix through a multi-layer full-connection structure; a mean square error is used as a loss function to constrain network output precision, and a multi-beam interference system model is constructed; according to the invention, stable and efficient communication of the low-orbit satellite system in a complex electromagnetic environment and under rapid channel change is ensured.

Description

Technical Field

[0001] This invention relates to the field of satellite internet technology, specifically to a method and system for modeling and suppressing multi-beam interference in low-Earth orbit satellite phased arrays. Background Technology

[0002] In traditional LEO satellite channel modeling, it is often necessary to characterize the channel fading experienced by the transmitter and receiver in a certain region during the entire overpass. Therefore, it is necessary to implement staring beamforming based on this wavefront using a satellite phased array. For existing beamforming technologies, analog beamforming is relatively simple and has low hardware complexity, but its beam pointing flexibility and accuracy are low. For highly dynamic LEO satellite scenarios, it is often difficult to meet the requirements of high-precision beam control and cannot effectively cope with changing environments and rapidly changing channel conditions. Digital beamforming technology, on the other hand, can provide higher flexibility and accuracy, and can dynamically adjust the beam direction according to the real-time channel status, greatly improving signal quality and anti-interference capability. Therefore, digital beamforming technology has become a key technology for solving beam control and high-quality signal transmission in LEO satellite scenarios. In digital beamforming, considering factors such as limited onboard payload resources, the low-complexity and simple-to-implement digital phase matching method is widely used. However, this method results in a low main-sidelobe ratio after beamforming, which leads to high inter-beam interference. Therefore, it is necessary to design a beamforming technology with low complexity and high main-sidelobe ratio.

[0003] The high complexity of matrix inversion in traditional LCMV algorithms limits their application in scenarios with high real-time requirements. This problem is particularly prominent in low-Earth orbit satellite communication systems, where rapidly moving external interference sources (such as malicious jammers or other satellite signals) severely impact communication links. Due to the unknown and rapidly changing motion characteristics of these interference sources, traditional spatial interference suppression methods (such as fixed null design) struggle to track the interference direction in real time, leading to null offset and decreased suppression performance. Furthermore, while existing LCMV algorithms can form nulls in specified directions through constraint optimization, their computational complexity is high, and they are difficult to converge quickly in highly dynamic scenarios, failing to meet real-time requirements. Summary of the Invention

[0004] The purpose of this invention is to address the aforementioned problems by designing a method and system for modeling and suppressing multi-beam interference in low-Earth orbit (LEO) satellite phased arrays. Addressing the technical shortcomings of existing digital beamforming technologies in LEO satellite communication systems, this invention overcomes two main limitations: firstly, the traditional digital phase-coordinated beamforming method suffers from severe inter-beam interference due to its low main-sidelobe ratio, making it difficult to meet anti-interference requirements in high-dynamic scenarios; secondly, it overcomes the technical bottleneck of the traditional LCMV algorithm, which suffers from high matrix inversion computational complexity and slow convergence speed, hindering its ability to track high-speed moving interference sources in real time. Simultaneously considering the constraints of limited onboard payload resources, this invention proposes a collaborative optimization method that integrates low-complexity beamforming and dynamic interference suppression. This method simultaneously improves beam main-sidelobe ratio performance and dynamic interference suppression capabilities while reducing algorithm computational complexity, effectively solving the communication quality degradation problems caused by insufficient beam pointing accuracy and poor real-time interference suppression in high-dynamic satellite scenarios. This ensures stable and efficient communication for LEO satellite systems in complex electromagnetic environments and under rapid channel changes.

[0005] The first aspect of this invention provides a method for modeling and suppressing multi-beam interference in low-Earth orbit satellite phased arrays, the method comprising the following steps:

[0006] Step 1: Select the Kaiser window as the core filtering method and optimize beam characteristics by dynamically adjusting the shape parameter β;

[0007] Step 2: Generate the initial beam pattern based on the digital phase matching method, and multiply the Kaiser window function coefficients with the excitation weights of the 64-element linear array element by element to achieve spatial weighted filtering;

[0008] Step 3: Construct a training dataset containing interference features from multiple scenarios, randomly generate the direction, intensity and incident angle of the interference source, calculate the corresponding covariance matrix and its exact inverse matrix to form sample pairs, design a deep neural network architecture, with the input being a flattened covariance matrix vector, and learn the complex nonlinear mapping relationship from the covariance matrix to the inverse matrix through a multi-layer fully connected structure.

[0009] Step 4: Use mean squared error as the loss function to constrain the network output accuracy, and use an adaptive learning rate optimizer for iterative training to force the learning of interference coupling features in a 256-element multi-interference source scenario.

[0010] Step 5: A multi-beam interference system model was constructed. The transmitter used Kaiser window spatial filtering technology to balance sidelobe suppression and main lobe width at different elevation angles. After receiving a new signal, the covariance matrix was quickly calculated and input into the pre-trained network to directly output the approximate value of the inverse matrix, skipping the traditional inversion operation.

[0011] Optionally, in a first implementation of the first aspect of the present invention, the mathematical expression of the Kaiser window in step 1 is based on the zeroth-order modified Bessel function, defined as:

[0012]

[0013] Where I0 is a first-order zero-order modified Bessel function, and the length of the window function is L = N + 1. To obtain the Kaiser window of an FIR filter with sidelobe attenuation of α dB.

[0014] Optionally, in a second implementation of the first aspect of the present invention, the shape parameter β in step 1 can be expressed as:

[0015]

[0016] The shape parameter β determines the shape and performance of the window function. Increasing β will widen the main lobe and reduce the side lobe amplitude. When β = 0, the Kaiser window degenerates into a rectangular window. As β increases, the side lobe level gradually decreases, but the main lobe width will increase accordingly.

[0017] Optionally, in the third implementation of the first aspect of the present invention, in step 1, β is set to 6.5 for high elevation angle scenarios to control the main lobe width while ensuring sidelobe suppression capability, and β is increased to 10 for low elevation angle scenarios to actively widen the main lobe coverage range to reduce the beam tracking difficulty when the satellite is moving at high speed.

[0018] Optionally, in a fourth implementation of the first aspect of the present invention, the initial beam is generated in step 2 using a digital phase matching method, and the beam pointing of the 64-element linear array is controlled by phase offset.

[0019] Optionally, in a fifth implementation of the first aspect of the present invention, the covariance matrix R in step 3 can be calculated from the received signal sample matrix X, i.e.

[0020]

[0021] Where N is the number of samples, and the superscript H denotes the conjugate transpose. The formula for calculating the weight vector w is:

[0022]

[0023] Where C is the constraint vector, representing the steering vector of the desired signal.

[0024] Optionally, in the sixth implementation of the first aspect of the present invention, step 3 involves constructing a suitable training dataset and collecting the covariance matrices {R1, R2, ..., R} under different scenarios. M} and its corresponding inverse matrix Using the covariance matrix as input and the inverse matrix as output, a deep neural network is used for training. Let the deep neural network be a function f(R; θ), where R is the input covariance matrix and θ are the network parameters, including weights and biases. The network outputs the predicted inverse matrix based on the input R.

[0025] Optionally, in the seventh implementation of the first aspect of the present invention, step 3 involves measuring the predicted inverse matrix. With the true inverse matrix R -1 The error between them is calculated using the mean squared error loss function.

[0026] Optionally, in the eighth implementation of the first aspect of the present invention, after obtaining the trained deep neural network in step 4, it is applied to the improved LCMV algorithm when a new signal sample matrix X is received. new First, calculate the covariance matrix:

[0027]

[0028] Then, R new The input is fed into the trained deep neural network f(·θ) * In this process, an approximate inverse matrix is ​​obtained.

[0029]

[0030] Where, θ * These are the optimal parameters obtained after training.

[0031] A second aspect of the present invention provides a low-Earth orbit satellite phased array multi-beam interference modeling and suppression system, the system comprising:

[0032] The dynamic adjustment module is used to select the Kaiser window as the core filtering method and optimize beam characteristics by dynamically adjusting the shape parameter β.

[0033] The weighted filtering module is used to generate the initial beam pattern based on the digital phase matching method. It multiplies the Kaiser window function coefficients with the excitation weights of the 64-element linear array element by element to achieve spatial weighted filtering.

[0034] The computation module is used to construct a training dataset containing interference features from multiple scenarios, randomly generate the direction, intensity and incident angle of the interference source, calculate the corresponding covariance matrix and its exact inverse matrix to form sample pairs, design a deep neural network architecture, with the input being a flattened covariance matrix vector, and learn the complex nonlinear mapping relationship from the covariance matrix to the inverse matrix through a multi-layer fully connected structure.

[0035] The iterative training module is used to constrain the network output accuracy by using the mean squared error as the loss function and to perform iterative training using an adaptive learning rate optimizer. It forces the learning of interference coupling features in a 256-element multi-interference-source scenario.

[0036] The module is used to construct a multi-beam interference system model. The transmitter uses Kaiser window spatial filtering technology to balance sidelobe suppression and main lobe width at different elevation angles. After receiving a new signal, the covariance matrix is ​​quickly calculated and input into the pre-trained network to directly output the approximate value of the inverse matrix, skipping the traditional inversion operation.

[0037] The beneficial effects of the technical solution of this invention mainly include:

[0038] 1. This invention aims to significantly improve anti-interference performance by optimizing beam characteristics through a dynamically adjustable Kaiser window function. Specifically, the solution innovatively introduces a shape parameter adaptive adjustment mechanism for high-dynamic scenarios of low-Earth orbit satellites. At high elevation angles, it achieves sidelobe suppression while ensuring the main lobe width, and actively widens the main lobe at low elevation angles to reduce beam tracking difficulty. By multiplying the window function coefficients element-wise with the excitation weights of the 64-element linear array, this spatial filtering technique reduces the sidelobe level by more than 15dB, effectively suppressing interference from adjacent beams. Compared with traditional methods, the Kaiser window exhibits superior sidelobe attenuation characteristics at both high and low elevation angles, especially at low elevation angles where it can tolerate greater pointing deviations, avoiding communication link interruptions caused by high-speed satellite movement.

[0039] 2. This invention uses a deep neural network to replace the matrix inversion operation in the traditional LCMV algorithm. By establishing a high-precision mapping relationship between the covariance matrix and the inverse matrix, it achieves a breakthrough reduction in computational complexity in a 256-element multi-interference source scenario. The improved algorithm compresses computation time while increasing the depth of interference suppression, significantly improving real-time response capability. Combined with the system-level verification of the seven-beam coverage model, it systematically solves the signal quality degradation problem caused by insufficient main-sidelobe ratio and computational delay in traditional methods.

[0040] 3. Design a spatial filtering technology based on a dynamically adjustable Kaiser window to solve the inter-beam interference problem caused by the low main lobe-to-side lobe ratio in low-Earth orbit satellite multi-beam systems; dynamically configure the shape parameters of the Kaiser window according to different satellite elevation angles, balance side lobe suppression and main lobe width in high elevation angle scenarios, and widen the main lobe coverage in low elevation angle scenarios, reduce the beam tracking difficulty when the satellite is moving at high speed, and optimize the main lobe and side lobe performance of traditional digital beamforming under limited on-board resources.

[0041] 4. A real-time interference suppression method for LCMV based on deep neural networks is proposed, which breaks through the computational bottleneck of traditional matrix inversion. A multi-scenario interference training dataset is constructed, and the nonlinear mapping relationship from the covariance matrix to its inverse matrix is ​​learned by deep neural networks, directly outputting the approximate value of the inverse matrix. This method replaces the high-complexity matrix inversion operation of the traditional LCMV algorithm, significantly reducing the computational burden, realizing real-time tracking and suppression of high dynamic interference sources, while maintaining low sidelobe levels and beam pointing accuracy. Attached Figure Description

[0042] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention.

[0043] Figure 1 A flowchart of a method for modeling and suppressing multi-beam interference of low-Earth orbit satellite phased array provided in an embodiment of the present invention;

[0044] Figure 2 A comparison chart of the sidelobe reduction performance of the high elevation angle time window function provided in the embodiments of the present invention;

[0045] Figure 3 A comparison chart of the sidelobe reduction performance of the low elevation angle time window function provided in an embodiment of the present invention;

[0046] Figure 4 The RMSE and loss function iteration diagram provided in the embodiments of the present invention;

[0047] Figure 5 This is a performance comparison chart of LCMV and improved LCMV methods provided in an embodiment of the present invention;

[0048] Figure 6 This is a schematic diagram of the seven-beam coverage model terminal receiving SIR provided in an embodiment of the present invention;

[0049] Figure 7 This is a schematic diagram of the structure of the low-orbit satellite phased array multi-beam interference modeling and suppression system provided in an embodiment of the present invention. Detailed Implementation

[0050] The terms “first,” “second,” “third,” “fourth,” etc. (if present) in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms “comprising” or “having,” and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, apparatus, product, or device that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or devices.

[0051] For ease of understanding, the specific process of the embodiments of the present invention is described below. Please refer to [link / reference]. Figure 1 The method for modeling and suppressing multi-beam interference of low-Earth orbit satellite phased array provided in this embodiment of the invention specifically includes the following steps:

[0052] Step 1: Select the Kaiser window as the core filtering method and optimize beam characteristics by dynamically adjusting the shape parameter β: Set β to 6.5 for high elevation angle scenarios to control the main lobe width while ensuring sidelobe suppression capability; increase β to 10 for low elevation angle scenarios to actively widen the main lobe coverage range to reduce the difficulty of beam tracking when the satellite is moving at high speed.

[0053] Step 2: Generate the initial beam pattern based on the digital phase matching method, and multiply the Kaiser window function coefficients with the excitation weights of the 64-element linear array element by element to achieve spatial weighted filtering; this operation significantly reduces the sidelobe level by more than 15dB, effectively suppresses interference between adjacent beams, and can tolerate greater pointing deviations in low elevation angle scenarios to avoid communication link interruption.

[0054] Step 3: Construct a training dataset containing interference features from multiple scenarios, randomly generate the direction, intensity, and incident angle of the interference source, calculate the corresponding covariance matrix and its exact inverse matrix to form sample pairs; design a deep neural network architecture, with the input being a flattened covariance matrix vector, and learn the complex nonlinear mapping relationship from the covariance matrix to the inverse matrix through a multi-layer fully connected structure.

[0055] Step 4: The mean squared error is used as the loss function to constrain the network output accuracy, and an adaptive learning rate optimizer is used for iterative training; in the scenario of 256 array elements and multiple interference sources, interference coupling features are forced to be learned. After 50 rounds of training, the prediction error is reduced to the order of one-thousandth, indicating that the network has accurately mastered the matrix transformation rules.

[0056] Step 5: A multi-beam interference system model was constructed. The transmitter used Kaiser window spatial filtering technology to balance sidelobe suppression and main lobe width at different elevation angles. After receiving a new signal, the covariance matrix was quickly calculated and input into the pre-trained network to directly output the approximate value of the inverse matrix, skipping the traditional inversion operation.

[0057] The specific implementation process for each step is given below:

[0058] Step 1:

[0059] (1-1) Adding Kaiser window filtering to the transmitter to suppress interference.

[0060] The Kaiser window, also known as the Bessel window, is a window function widely used in digital signal processing and spectral analysis. Its mathematical expression is based on the zeroth-order modified Bessel function, defined as:

[0061]

[0062] Where I0 is a zeroth-order modified Bessel function of the first kind, and the length of the window function is L = N + 1. To obtain the Kaiser window of an FIR filter with sidelobe attenuation of α dB,

[0063] (1-2) The Kaiser window parameter β is flexibly adjusted to achieve an optimal balance between sidelobe suppression and main lobe width.

[0064] The shape parameter β can be expressed as

[0065]

[0066] The shape parameter β determines the shape and performance of the window function. Increasing β widens the main lobe and reduces the side lobe amplitude (i.e., increases attenuation). When β = 0, the Kaiser window degenerates into a rectangular window; as β increases, the side lobe level gradually decreases, but the main lobe width increases accordingly.

[0067] Step 2:

[0068] (2-1) Beam generation and simulation settings

[0069] The initial beam was generated using digital phase-coordinated array (DPA), and the beam pointing of a 64-element linear array was controlled by phase offset. Based on the high elevation angle simulation parameters shown in the table below, beamforming simulations were performed to compare the traditional DPA (without window), Hamming window, Chebyshev window, and Kaiser window algorithms. All simulation experiments used a linear array structure with 64 elements, an element spacing of half a wavelength (λ / 2), an operating frequency of 20 GHz, and a beam pointing angle of 0° elevation. The Kaiser window shape parameter β was set to 6.5 to balance the trade-off between sidelobe suppression and main lobe broadening.

[0070] Table 1 Simulation parameters for high elevation angle

[0071]

[0072] Table 2 Simulation parameters for low elevation angle

[0073]

[0074]

[0075] (2-2) Interference suppression effect

[0076] When the transmitter and receiver are at high elevation angles, and with similar sidelobe attenuation settings, the main lobe width of the Kaiser window is 2.7°, the Chebyshev window is 2.3°, and the Hamming window is 2.3°. Although the Chebyshev and Hamming windows can achieve narrower main lobe widths under the same sidelobe attenuation conditions, their lower sidelobe attenuation rates may lead to stronger far-field interference. In contrast, the Kaiser window maintains a lower sidelobe level while only slightly increasing the main lobe width, and its sidelobe attenuation rate is significantly better than the other two window functions.

[0077] like Figure 2-3 As shown, the Kaiser window effectively reduces sidelobe levels and, compared to other methods, better suppresses sidelobe interference. This is significant in low-elevation scenarios, as it reduces the impact of ground multipath reflections and other interference on satellite communication signals, improves signal purity and communication quality, and ensures a stable and efficient communication link between the satellite and users at low elevation angles.

[0078] Step 3:

[0079] (3-1) Dataset Generation

[0080] The traditional LCMV algorithm aims to minimize the variance of the output signal under specific constraints. Its core steps include calculating and inverting the covariance matrix R to obtain the weight vector w. Specifically, the covariance matrix R can be calculated from the received signal sample matrix X, i.e.

[0081]

[0082] Where N is the number of samples, and the superscript H denotes the conjugate transpose. The formula for calculating the weight vector w is:

[0083]

[0084] Here, C is the constraint vector, representing the steering vector of the desired signal. As mentioned earlier, the time complexity of matrix inversion is relatively high, O(N). 3 When the number of array elements is large or the interference environment changes rapidly, the amount of computation will increase sharply, resulting in a deterioration in the real-time performance of the algorithm.

[0085] To overcome this problem, this paper proposes a method using deep neural networks to learn the mapping relationship between the covariance matrix and its inverse matrix. First, a suitable training dataset is constructed, collecting covariance matrices {R1, R2, ..., R...} under different scenarios. M} and its corresponding inverse matrix The covariance matrix is ​​used as input, and the inverse matrix is ​​used as output. A deep neural network is then trained. Let the deep neural network be a function f(R; θ), where R is the input covariance matrix, and θ are the network parameters, including weights and biases. The network outputs the predicted inverse matrix based on the input R.

[0086] (3-2) Definition of loss function

[0087] To measure the inverse matrix of the prediction With the true inverse matrix R -1 The error between samples is calculated using the mean squared error (MSE) loss function. For a single sample... Its mean square error is defined as

[0088]

[0089] in, It is the prediction inverse matrix The element in the j-th row and k-th column, It is the true inverse matrix The element in the j-th row and k-th column of the dataset. For the entire training dataset, the total mean squared error loss function is...

[0090]

[0091] Step 4:

[0092] This paper employs the Adam optimizer, a variant of the stochastic gradient descent (SGD) method, to continuously adjust the network parameters θ, thereby minimizing the loss function L(θ).

[0093] After obtaining the trained deep neural network, it is applied to the improved LCMV algorithm. When a new signal sample matrix X is received... new First, calculate the covariance matrix.

[0094]

[0095] Then, R new The input is fed into the trained deep neural network f(·θ) * In this process, an approximate inverse matrix is ​​obtained.

[0096]

[0097] Where, θ * These are the optimal parameters obtained after training. Finally, the weight vector is calculated using the improved formula.

[0098]

[0099] Based on the neural network training parameters listed in the table, we conducted a systematic simulation comparison between the traditional Linear Constrained Minimum Variance (LCMV) algorithm and the improved method optimized by deep learning. In the simulation experiments, the array element count was set to 256, the target direction was fixed at 10°, and interference sources were introduced at -30° and 45° to verify the algorithm's performance in multi-interference scenarios. During training, the maximum number of training epochs was set to 50, and the number of training samples was 1000 to ensure sufficient model convergence.

[0100] Table 3. Neural Network Training Parameters

[0101]

[0102] like Figure 4 As shown, the blue curve represents the RMSE curve during training. With each training iteration, the RMSE value drops sharply from a high initial value, indicating that in the initial stage, the neural network can quickly learn the features of the data and reduce prediction errors. Later in training, the RMSE stabilizes, indicating that as the model continues to learn, the rate of error reduction gradually decreases, reaching a relatively stable state. This phenomenon suggests that after a certain amount of training, the model has essentially converged to a stable performance level. The orange curve in the figure above shows the change in training loss. Similar to the RMSE curve, the loss value also decreases rapidly in the early stages of training and then stabilizes in the later stages. This indicates that the network quickly optimizes model parameters by adjusting weights in the initial stage, reducing training errors. However, as training progresses, the rate of decrease in the loss value decreases, the model's optimization speed slows down, and it enters a plateau period. This phenomenon reflects that the model's learning effect gradually approaches saturation during training, leaving little room for further optimization.

[0103] like Figure 5 As shown in the simulation results, compared with the traditional LCMV method (blue curve), the improved LCMV method (orange curve) has a lower sidelobe level in its radiation pattern. Furthermore, in the two interference directions marked by the red dashed line in the figure, the gain of the improved LCMV is lower, reaching -59.26 dB, while the traditional LCMV method is -47.59 dB. Therefore, the improved method improves the interference suppression effect by 24.5% compared to the original method. In terms of computation time, the traditional method takes 0.1912 seconds, while the improved method takes 0.0958 seconds, representing a 49.9% reduction in computation time compared to the original method, equivalent to achieving a 2x speedup in real-time performance.

[0104] Step 5:

[0105] This study conducts simulation experiments on the multi-beam coverage and co-channel interference characteristics during the overhead transit phase of low-Earth orbit (LEO) satellites. In the simulation design, the ground coverage area of ​​the satellite-borne staring beam is kept statically distributed, and four typical elevation angles ({30°, 45°, 60°, 90°}) are selected to describe the entire overhead transit process. Next, using SIR, SNR, and SINR as simulation indicators, we quantify and calculate the electromagnetic environment parameters at any spatial location within the coverage area, and construct a spatial distribution contour map accordingly to visually characterize the coverage effectiveness boundary and interference suppression level of the multi-beam system.

[0106] like Figure 6 As shown, this set of simulation images illustrates the signal-to-interference ratio (SIR) distribution at different satellite elevation angles, measured in dB. Each sub-image corresponds to a specific satellite elevation angle, with the SIR distributions from left to right and top to bottom representing 30°, 45°, 60°, and 90° elevation angles, respectively. The colors in the images, ranging from yellow to blue, represent the intensity of the SIR, with yellow indicating a higher SIR value and blue indicating a lower SIR value.

[0107] When the satellite is at an elevation angle of 90°, that is, when the satellite is directly above the user, the SIR distribution among different users is uniform. The SIR of the outer beams is about 15dB, while the SIR of the center beam can reach a maximum of 5dB, indicating that the center beam is most affected by the six surrounding beams. As the satellite gradually moves away from the beam position and reaches elevation angles of 30°, 45°, and 60°, the SIR decreases with the decrease in elevation angle, and the SIR distribution among users becomes distorted and no longer uniform.

[0108] Unlike the Signal-to-Interference Ratio (SIR), which is susceptible to inter-beam interference, the SNR is relatively uniformly distributed among different users, and the beam shape is also relatively regular. When the satellite is at an elevation angle of 90°, all seven beams exhibit regular geometric shapes, with the highest SNR at the beam center, reaching 14dB, demonstrating good signal reception quality. As the satellite gradually moves away from the beam position, and the elevation angle decreases to 30°, 45°, and 60°, the SNR distribution of users undergoes slight distortion, but remains relatively uniform overall. Simultaneously, the SNR of each beam gradually decreases with the decrease in elevation angle; at 30° elevation angle, the SNR at the center of each beam is only 2dB, indicating a decline in signal quality.

[0109] Furthermore, the images also reveal that at different elevation angles, the SNR at the beam edge is relatively lower than that at the beam center, and the SNR difference between the beam edge and the center tends to increase as the elevation angle decreases. This means that in satellite communications, users at the beam edge may face worse signal reception conditions at low elevation angles.

[0110] Because SINR takes into account both noise and interference, its geometry is no longer regular. Compared to SIR, the SINR values ​​of each beam are lower at the same elevation angle. When the satellite is at a 90° elevation angle, the SINR of the center beam can reach a maximum of approximately 8.56 dB, while the SINR of the six surrounding beams can reach a maximum of 12.13 dB. As the satellite moves further away from the beam position, at elevation angles of 30°, 45°, and 60°, the user's SINR distribution becomes distorted, and the SINR values ​​of each beam gradually decrease with decreasing elevation angle. At a 30° elevation angle, the SINR at the center of each beam is only -4 dB, indicating that the signal quality at this point is poor due to the combined effects of noise and interference.

[0111] Furthermore, it can be observed that at different elevation angles, the SINR in the beam edge region is significantly lower than that in the beam center region, and this difference becomes more pronounced as the elevation angle decreases. This means that at low elevation angles, users located at the beam edge are more affected by noise and interference, and their communication quality is more easily affected. At the same time, the SINR transition region between adjacent beams also varies with the elevation angle, with more complex SINR changes in the transition region at low elevation angles.

[0112] Please see Figure 7 A schematic diagram of the structure of the low-Earth orbit satellite phased array multi-beam interference modeling and suppression system provided in this embodiment of the invention. The system includes:

[0113] The dynamic adjustment module is used to select the Kaiser window as the core filtering method and optimize beam characteristics by dynamically adjusting the shape parameter β.

[0114] The weighted filtering module is used to generate the initial beam pattern based on the digital phase matching method. It multiplies the Kaiser window function coefficients with the excitation weights of the 64-element linear array element by element to achieve spatial weighted filtering.

[0115] The computation module is used to construct a training dataset containing interference features from multiple scenarios, randomly generate the direction, intensity and incident angle of the interference source, calculate the corresponding covariance matrix and its exact inverse matrix to form sample pairs, design a deep neural network architecture, with the input being a flattened covariance matrix vector, and learn the complex nonlinear mapping relationship from the covariance matrix to the inverse matrix through a multi-layer fully connected structure.

[0116] The iterative training module is used to constrain the network output accuracy by using the mean squared error as the loss function and to perform iterative training using an adaptive learning rate optimizer. It forces the learning of interference coupling features in a 256-element multi-interference-source scenario.

[0117] The module is used to construct a multi-beam interference system model. The transmitter uses Kaiser window spatial filtering technology to balance sidelobe suppression and main lobe width at different elevation angles. After receiving a new signal, the covariance matrix is ​​quickly calculated and input into the pre-trained network to directly output the approximate value of the inverse matrix, skipping the traditional inversion operation.

[0118] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely preferred examples and are not intended to limit the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for modeling and suppressing multi-beam interference in low-Earth orbit satellite phased arrays, characterized in that, The method includes the following steps: Step 1: Select the Kaiser window as the core filtering method and optimize beam characteristics by dynamically adjusting the shape parameter β; Step 2: Generate the initial beam pattern based on the digital phase matching method, and multiply the Kaiser window function coefficients with the excitation weights of the 64-element linear array element by element to achieve spatial weighted filtering; Step 3: Construct a training dataset containing interference features from multiple scenarios, randomly generate the direction, intensity and incident angle of the interference source, calculate the corresponding covariance matrix and its exact inverse matrix to form sample pairs, design a deep neural network architecture, with the input being a flattened covariance matrix vector, and learn the complex nonlinear mapping relationship from the covariance matrix to the inverse matrix through a multi-layer fully connected structure. Step 4: Use mean squared error as the loss function to constrain the network output accuracy, and use an adaptive learning rate optimizer for iterative training to force the learning of interference coupling features in a 256-element multi-interference source scenario. Step 5: A multi-beam interference system model was constructed. The transmitter used Kaiser window spatial filtering technology to balance sidelobe suppression and main lobe width at different elevation angles. After receiving a new signal, the covariance matrix was quickly calculated and input into the pre-trained network to directly output the approximate value of the inverse matrix, skipping the traditional inversion operation.

2. The method for modeling and suppressing multi-beam interference of low-Earth orbit satellite phased array as described in claim 1, characterized in that, The mathematical expression for the Kaiser window in step 1 is based on the zeroth-order modified Bessel function, defined as: Where I0 is a first-order zero-order modified Bessel function, and the length of the window function is L = N + 1. To obtain the Kaiser window of an FIR filter with sidelobe attenuation of α dB.

3. The method for modeling and suppressing multi-beam interference of low-Earth orbit satellite phased array as described in claim 1, characterized in that, The shape parameter β in step 1 can be expressed as: The shape parameter β determines the shape and performance of the window function. Increasing β will widen the main lobe and reduce the side lobe amplitude. When β = 0, the Kaiser window degenerates into a rectangular window. As β increases, the side lobe level gradually decreases, but the main lobe width will increase accordingly.

4. The method for modeling and suppressing multi-beam interference of low-Earth orbit satellite phased array as described in claim 1, characterized in that, In step 1, β is set to 6.5 for high elevation angle scenarios to control the main lobe width while ensuring sidelobe suppression capability. For low elevation angle scenarios, β is increased to 10 to actively widen the main lobe coverage range and reduce the beam tracking difficulty when the satellite is moving at high speed.

5. The method for modeling and suppressing multi-beam interference of low-Earth orbit satellite phased array as described in claim 1, characterized in that, In step 2, the initial beam is generated using the digital phase matching method, and the beam pointing of the 64-element linear array is controlled by phase offset.

6. The method for modeling and suppressing multi-beam interference of low-Earth orbit satellite phased array as described in claim 1, characterized in that, In step 3, the covariance matrix R can be calculated from the received signal sample matrix X, that is... Where N is the number of samples, and the superscript H denotes the conjugate transpose. The formula for calculating the weight vector w is: Where C is the constraint vector, representing the steering vector of the desired signal.

7. The method for modeling and suppressing multi-beam interference of low-Earth orbit satellite phased array as described in claim 1, characterized in that, In step 3, a suitable training dataset is constructed, and the covariance matrices {R1, R2, ..., R} under different scenarios are collected. M } and its corresponding inverse matrix Using the covariance matrix as input and the inverse matrix as output, a deep neural network is used for training. Let the deep neural network be a function f(R; θ), where R is the input covariance matrix and θ are the network parameters, including weights and biases. The network outputs the predicted inverse matrix based on the input R.

8. The method for modeling and suppressing multi-beam interference of low-Earth orbit satellite phased array as described in claim 7, characterized in that, Step 3 is to measure the inverse matrix of the prediction. With the true inverse matrix R -1 The error between them is calculated using the mean squared error loss function.

9. The method for modeling and suppressing multi-beam interference of low-Earth orbit satellite phased array as described in claim 1, characterized in that, In step 4, after obtaining the trained deep neural network, it is applied to the improved LCMV algorithm. When a new signal sample matrix X is received... new First, calculate the covariance matrix: Then, R new The input is fed into the trained deep neural network f(·θ) * In this process, an approximate inverse matrix is ​​obtained. Where, θ * These are the optimal parameters obtained after training.

10. A system for modeling and suppressing multi-beam interference in low-Earth orbit satellite phased arrays, characterized in that, The system includes: The dynamic adjustment module is used to select the Kaiser window as the core filtering method and optimize beam characteristics by dynamically adjusting the shape parameter β. The weighted filtering module is used to generate the initial beam pattern based on the digital phase matching method. It multiplies the Kaiser window function coefficients with the excitation weights of the 64-element linear array element by element to achieve spatial weighted filtering. The computation module is used to construct a training dataset containing interference features from multiple scenarios, randomly generate the direction, intensity and incident angle of the interference source, calculate the corresponding covariance matrix and its exact inverse matrix to form sample pairs, design a deep neural network architecture, with the input being a flattened covariance matrix vector, and learn the complex nonlinear mapping relationship from the covariance matrix to the inverse matrix through a multi-layer fully connected structure. The iterative training module is used to constrain the network output accuracy by using the mean squared error as the loss function and to perform iterative training using an adaptive learning rate optimizer. It forces the learning of interference coupling features in a 256-element multi-interference-source scenario. The module is used to construct a multi-beam interference system model. The transmitter uses Kaiser window spatial filtering technology to balance sidelobe suppression and main lobe width at different elevation angles. After receiving a new signal, the covariance matrix is ​​quickly calculated and input into the pre-trained network to directly output the approximate value of the inverse matrix, skipping the traditional inversion operation.

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