A complex electromagnetic environment simulation method based on FPGA

Abstract

The present invention discloses a complex electromagnetic environment simulation method based on FPGA, including adopting a kernel density estimation method to construct a multidimensional probability distribution model; performing layered parameter sampling to obtain a sampling parameter set; applying a spatiotemporal sequence prediction model to adjust the sampling parameter set; grouping the optimized parameter set to obtain a clustering result; realizing intra-group competition units and dynamic weight adjustment; performing digital waveform generation and realizing digital pulse modulation to obtain a modulated signal sequence; calculating and superimposing a signal spectrum to obtain a comprehensive spectrum; based on the comprehensive spectrum, sequentially performing real-time feature distribution verification and distribution deviation correction mechanisms, and finally outputting a corrected signal sequence; sequentially performing a parallel signal processing pipeline and digital beam synthesis to obtain a final filtered analog signal. The method improves the authenticity, dynamic adaptability and processing efficiency of electromagnetic environment simulation.

Description

Technical Field

[0001] The invention belongs to the field of electronic countermeasures and discloses a complex electromagnetic environment simulation method based on FPGA. Background Art

[0002] FPGA-based complex electromagnetic environment simulation methods are key technologies in the fields of electronic countermeasures, communication system testing, and electromagnetic compatibility research. With the rapid development of modern electronic equipment and the increasing complexity of the electromagnetic environment, high-precision and high-efficiency electromagnetic environment simulation has become an urgent need. Complex electromagnetic environment simulation can not only provide an important reference for electronic system design and optimization, but also significantly reduce actual testing costs and accelerate product development cycles. Therefore, the study of FPGA-based complex electromagnetic environment simulation methods has a far-reaching impact on promoting the development of electronic information technology.

[0003] At present, the research on complex electromagnetic environment simulation mainly focuses on signal generation, channel simulation and receiver simulation. Traditional methods are usually implemented by software simulation or dedicated hardware, but they face many challenges when dealing with complex scenarios with high dynamics and multiple signal sources. Although software simulation has high flexibility, its real-time performance is poor and it is difficult to meet the needs of high-speed signal processing. Although dedicated hardware has superior performance, it is expensive and lacks flexibility. In recent years, FPGA-based simulation methods have attracted widespread attention due to their high performance, reconfigurability and cost-effectiveness. Current research mainly uses digital signal processing technology, such as direct digital frequency synthesis (DDS) and digital up-conversion, to achieve basic signal generation and modulation. In terms of channel simulation, lookup tables (LUTs) and simple mathematical models are mainly used to simulate attenuation, multipath effects, etc. Receiver simulation mainly focuses on the realization of basic functions such as digital down-conversion and baseband signal processing.

[0004] However, there are still some technical problems in the existing FPGA-based complex electromagnetic environment simulation methods. First, in terms of parameter generation and optimization, the existing methods mostly use fixed-bandwidth kernel density estimation, which is difficult to adapt to complex multimodal distributions, resulting in the lack of authenticity and dynamics of the generated electromagnetic environment parameters. Secondly, signal grouping and scheduling algorithms generally use simple priority queues or polling methods, which cannot effectively handle highly dynamic and diverse signal scenarios, affecting the simulation system's ability to respond quickly to the actual electromagnetic environment. Furthermore, spectrum analysis and synthesis techniques are mostly limited to traditional fast Fourier transform (FFT) methods, which have obvious deficiencies in processing non-stationary signals and transient events, affecting the accuracy of spectrum simulation. In addition, the existing beamforming algorithms mostly use fixed weights or simple adaptive methods, which are difficult to cope with complex interference environments and dynamically changing signal scenarios, limiting the authenticity of spatial electromagnetic environment simulation. Finally, FPGA resource allocation strategies often use static configurations and lack the ability to dynamically adapt to changes in the complexity of the electromagnetic environment, resulting in low efficiency in hardware resource utilization and affecting the overall performance and scalability of the system. The existence of these technical problems seriously restricts the performance and application scope of FPGA-based complex electromagnetic environment simulation systems, and new technical solutions are urgently needed to solve them. Summary of the invention

[0005] The purpose of the invention is to propose a complex electromagnetic environment simulation method based on FPGA to solve the above problems existing in the prior art.

[0006] Technical solution, a complex electromagnetic environment simulation method based on FPGA, including the following steps:

[0007] S1. Read the initial electromagnetic environment parameter set from the external database, and use the kernel density estimation method to build a multidimensional probability distribution model; based on the initial electromagnetic environment parameter set, build a parameter dependency graph and generate a parameter dependency tree; based on the parameter dependency tree and the multidimensional probability distribution model, perform hierarchical parameter sampling to obtain a sampled parameter set; apply the spatiotemporal sequence prediction model to adjust the sampled parameter set to obtain an optimized parameter set;

[0008] S2. Group the optimized parameter set to obtain clustering results; based on the clustering results, construct an intra-group competition unit for each cluster, and implement an inter-group competition unit to obtain an output signal; based on the output signal, execute a dynamic weight adjustment algorithm, implement an adaptive time window mechanism, and output a reorganized signal sequence;

[0009] S3. Based on the reorganized signal sequence, generate a corresponding digital waveform and implement digital pulse modulation to obtain a modulated signal sequence; based on the modulated signal sequence, calculate the signal spectrum and superimpose it to obtain a comprehensive spectrum; based on the comprehensive spectrum, sequentially execute real-time feature distribution verification and distribution deviation correction mechanism, and finally output the corrected signal sequence;

[0010] S4. Read the current electromagnetic environment complexity index, dynamically adjust the FPGA resource allocation, and obtain the optimal resource allocation plan; based on the optimal resource allocation plan and the corrected signal sequence, execute the parallel signal processing pipeline and digital beam synthesis in sequence to obtain the beam synthesis signal; based on the beam synthesis signal, perform digital-to-analog conversion and output the final filtered analog signal.

[0011] Beneficial effects: The present invention not only improves the efficiency of signal processing, but also enhances the system's ability to respond to rapid changes in the electromagnetic environment, ensuring that the statistical characteristics of the analog signal are highly consistent with the actual environment; at the same time, it also improves the authenticity and reliability of the analog signal, improves the efficiency and flexibility of FPGA resource allocation, and enhances the system's ability to adapt to changes in the complexity of the electromagnetic environment, providing efficient hardware support for the entire simulation system, which has an important impact on the overall performance and scalability of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 It is a flow chart of the present invention.

[0013] Figure 2 This is a flow chart of step S1 of the present invention.

[0014] Figure 3 This is a flow chart of step S2 of the present invention.

[0015] Figure 4 This is a flow chart of step S3 of the present invention.

[0016] Figure 5 This is a flow chart of step S4 of the present invention.

[0017] Figure 6 This is a principle block diagram of a complex electromagnetic environment simulation based on FPGA according to an embodiment of the present invention.

[0018] Figure 7 The figure is a principle block diagram of a single radar signal generating module according to an embodiment of the present invention.

[0019] Figure 8 FIG. 4 is a schematic diagram of a video pulse competition timing sequence according to an embodiment of the present invention. DETAILED DESCRIPTION

[0020] like Figure 1As shown, this application proposes a complex electromagnetic environment simulation method based on FPGA, comprising the following steps:

[0021] S1. Read the initial electromagnetic environment parameter set from the external database, and use the kernel density estimation method to build a multidimensional probability distribution model; based on the initial electromagnetic environment parameter set, build a parameter dependency graph and generate a parameter dependency tree; based on the parameter dependency tree and the multidimensional probability distribution model, perform hierarchical parameter sampling to obtain a sampled parameter set; apply the spatiotemporal sequence prediction model to adjust the sampled parameter set to obtain an optimized parameter set;

[0022] S2. Group the optimized parameter set to obtain clustering results; based on the clustering results, construct an intra-group competition unit for each cluster, and implement an inter-group competition unit to obtain an output signal; based on the output signal, execute a dynamic weight adjustment algorithm, implement an adaptive time window mechanism, and output a reorganized signal sequence;

[0023] S3. Based on the reorganized signal sequence, generate a corresponding digital waveform and implement digital pulse modulation to obtain a modulated signal sequence; based on the modulated signal sequence, calculate the signal spectrum and superimpose it to obtain a comprehensive spectrum; based on the comprehensive spectrum, sequentially execute real-time feature distribution verification and distribution deviation correction mechanism, and finally output the corrected signal sequence;

[0024] S4. Read the current electromagnetic environment complexity index, dynamically adjust the FPGA resource allocation, and obtain the optimal resource allocation plan; based on the optimal resource allocation plan and the corrected signal sequence, execute the parallel signal processing pipeline and digital beam synthesis in sequence to obtain the beam synthesis signal; based on the beam synthesis signal, perform digital-to-analog conversion and output the final filtered analog signal.

[0025] like Figure 2 As shown, according to one aspect of the present application, step S1 is further:

[0026] S11, reading an initial electromagnetic environment parameter set from an external database, preprocessing the initial electromagnetic environment parameter set, including data cleaning and standardization, to obtain a preprocessed initial electromagnetic environment parameter set; wherein the initial electromagnetic environment parameter set includes parameter sets of a predetermined number of radars, each parameter set including repetition period, pulse width, carrier frequency, amplitude and phase information;

[0027] S12. Based on the preprocessed initial electromagnetic environment parameter set, calculate the kernel density estimation value of each sample point, accumulate the kernel density estimation value of each sample point, and obtain the accumulated result; based on the accumulated result, calculate the probability density estimation, and construct a complete multidimensional probability distribution model;

[0028] S13. Based on the preprocessed initial electromagnetic environment parameter set, calculate the mutual information value of each pair of parameters; based on the mutual information value, construct the joint probability distribution and the edge probability distribution; calculate the mutual information of the joint probability distribution and the edge probability distribution as the edge weight of the graph; based on the mutual information, use the maximum spanning tree algorithm to construct a parameter dependency tree;

[0029] S14, starting from the root node of the parameter dependency tree, using the inverse transform sampling method to generate a candidate value set; based on the candidate value set, obtaining the parent node; combining the parent node and the multidimensional probability distribution model to generate a sampling parameter set;

[0030] S15. Based on the sampling parameter set, use the preconfigured time series model to obtain the time prediction result; based on the sampling parameter set, perform spatial autocorrelation analysis to calculate the spatial distribution pattern of the parameters; combine the time prediction result and the spatial distribution pattern to fine-tune each parameter of the sampling parameter set to obtain the optimized parameter set.

[0031] According to one aspect of the present application, step S12 further includes applying an adaptive bandwidth selection algorithm to optimize the multidimensional probability distribution model, specifically:

[0032] S12a. Based on the multidimensional probability distribution model, calculate the cross-validation score of each sample point; accumulate the cross-validation scores of each sample point and take the average value as the final cross-validation score;

[0033] S12b, obtaining the current bandwidth value, optimizing the bandwidth value using the gradient descent method to minimize the final cross-validation score, repeating the optimization process until convergence or reaching the maximum number of iterations, and obtaining the optimized bandwidth value;

[0034] S12c. Based on the optimized bandwidth value, the multidimensional probability distribution model is optimized to obtain an optimized multidimensional probability distribution model.

[0035] In one embodiment of the present application, an initial electromagnetic environment parameter set is read from an external database, the set including parameter sets of multiple radars, each parameter set including information such as repetition period, pulse width, carrier frequency, amplitude and phase. The read initial electromagnetic environment parameter set is preprocessed, including data cleaning and standardization. The preprocessed initial electromagnetic environment parameter set is stored in the internal memory of the FPGA.

[0036] Read the preprocessed initial electromagnetic environment parameter set stored in the internal memory of the FPGA, and use the kernel density estimation method to build a multidimensional probability distribution model: for each parameter dimension, calculate the kernel density estimate and select the Gaussian kernel function; initialize the bandwidth parameter, traverse all sample points, and accumulate the kernel function value corresponding to each sample; divide the accumulated result by the number of samples and the bandwidth to obtain the probability density estimate. Repeat this process for all parameter dimensions to build a complete multidimensional probability distribution model. Store the multidimensional probability distribution model in the internal memory of the FPGA.

[0037] Read the multidimensional probability distribution model from the internal memory of the FPGA and apply the adaptive bandwidth selection algorithm for optimization: initialize the bandwidth value of each dimension, and for each dimension, calculate the cross-validation score; the score is calculated by the leave-one-out method, that is, remove one sample point at a time, use the remaining samples to estimate the probability density, and then evaluate the density value at the removed sample point. Repeat this process for all samples and take the average as the cross-validation score. Use the gradient descent method to optimize the bandwidth value to minimize the cross-validation score, and repeat the optimization process until convergence or the maximum number of iterations is reached. Store the optimized bandwidth value in the register of the FPGA.

[0038] Read the preprocessed initial electromagnetic environment parameter set and construct a parameter dependency graph: calculate the mutual information value between each pair of parameters, construct a joint probability distribution and an edge probability distribution for each pair of parameters, calculate the entropy and mutual information of these distributions, and use the mutual information value as the edge weight of the graph; apply the maximum spanning tree algorithm to construct a parameter dependency tree: initialize an empty tree structure, start from the edge with the largest mutual information, and gradually add edges to the tree. Each time an edge is added, ensure that no loop is formed. Repeat this process until all nodes are connected, and store the parameter dependency tree in the internal memory of the FPGA.

[0039] Read the parameter dependency tree from the internal memory of the FPGA, and perform hierarchical parameter sampling based on the parameter dependency tree: starting from the root node of the tree, use the inverse transform sampling method to generate the value of the parameter; for each child node in the tree, generate the parameter value based on the value of its parent node and the conditional probability distribution; read the multidimensional probability distribution model to obtain the conditional probability information; repeat this process until all nodes of the tree are assigned values. Store the generated complete parameter set in the FPGA cache.

[0040] Read the complete parameter set in the FPGA cache and adjust the complete parameter set using the spatiotemporal series prediction model: construct a time series model, such as an autoregressive integrated moving average model; train the model using historical data to predict short-term parameter change trends; perform spatial autocorrelation analysis to calculate the spatial distribution pattern of the parameters; combine the time prediction results and the spatial distribution pattern to fine-tune each parameter in the complete parameter set. Store the adjusted complete parameter set in the FPGA output buffer. At the same time, store the multidimensional probability distribution model in the FPGA output buffer.

[0041] In another embodiment of the present application, an initial electromagnetic environment parameter set E={e1, e2, ..., e n}, where e i Represents the parameter set of the i-th radar, including repetition period (PRF), pulse width (PW), carrier frequency (CF), amplitude (A) and phase (φ).

[0042] Read the parameter set E and use the kernel density estimation (KDE) method to construct a multidimensional probability distribution model P(E): For each parameter dimension d, construct a multidimensional probability distribution model: P(E d )=1 / (nh)*Σ i=1 n K((E d -e i，d ) / h), where K is the kernel function (such as Gaussian kernel), h is the bandwidth parameter, n is the number of samples, and E d Represents the value of the dth dimension in the parameter set E, e i，d Represents the value of the ith sample in the dth dimension. The constructed multidimensional probability distribution model P(E) is stored in the internal memory of the FPGA.

[0043] Read the multidimensional probability distribution model P(E) and apply the adaptive bandwidth selection algorithm for optimization. Initialize the bandwidth vector H={h1, h2, ..., h D}, D is the parameter dimension. For each dimension d, calculate the cross-validation score: CV(h d ) =1 / n*Σ i=1 n [Pi(e i，d )-2 / (n-1)*Σ j≠i K((e i，d -e j，d ) / h d )], where Pi is the KDE estimate after removing the i-th sample. H is optimized using the gradient descent method to minimize the cross-validation score CV(H). The optimized bandwidth vector H is stored in the register of the FPGA for subsequent parameter generation.

[0044] Read the initial parameter set E and construct the parameter dependency graph G(V, E). The vertex set V represents the dimensions of each parameter. The edge set E represents the correlation between parameters, and the edge weight is calculated using mutual information (MI): MI(X, Y) = Σ(x, y)P(x, y)*log(P(x, y) / (P(x)P(y))). Apply the maximum spanning tree algorithm to obtain the parameter dependency tree T. Store the parameter dependency tree T in the internal memory of the FPGA.

[0045] Read the parameter dependency tree T and perform hierarchical parameter sampling based on T. Starting from the root of the tree, use the inverse transform sampling method to generate the root parameter value. For each child node, generate a parameter value based on the parent node value and the conditional probability distribution. Repeat until a complete parameter set S = {s1, s2, ..., s m}, m is the number of radars to be simulated. The generated parameter set S is stored in the cache of the FPGA.

[0046] Read parameter set S and adjust it by applying the spatiotemporal series prediction model. Build the time series model ARIMA(p, d, q) to predict the short-term parameter change trend. Use spatial autocorrelation analysis (such as Moran's I) to identify the spatial distribution pattern of the parameters. Combine the temporal and spatial prediction results to fine-tune the parameter set S to obtain the final parameter set S'. Output the final parameter set S' and the multidimensional probability distribution model P(E) to the output buffer of the FPGA.

[0047] This embodiment realizes efficient and accurate generation and optimization of electromagnetic environment parameters. The kernel density estimation method is used to construct a multidimensional probability distribution model, which can better capture the true distribution of parameters in a complex electromagnetic environment and avoid the deviation that may be caused by the traditional parameterization method. By introducing an adaptive bandwidth selection algorithm, the accuracy and robustness of the probability distribution model are further improved, and the bandwidth can be dynamically adjusted according to the local characteristics of the data. It performs well when processing heterogeneous data and effectively reduces the risk of overfitting or underfitting. By constructing a parameter dependency graph and generating a parameter dependency tree, the complex interaction between electromagnetic environment parameters is successfully captured. It can not only reflect the direct relationship between parameters, but also reveal potential indirect dependencies, providing more accurate guidance for subsequent parameter sampling. The application of hierarchical parameter sampling technology improves sampling efficiency and sample quality. By sampling according to the structure of the parameter dependency tree, the generated samples are more in line with the characteristics of the actual electromagnetic environment and reduce the generation of unreasonable samples. The introduction of the spatiotemporal series prediction model enables the generated parameter set to reflect the dynamic change characteristics of the electromagnetic environment, not only considering the change trend of the time dimension, but also incorporating the spatial distribution pattern, so that the evolution process of the complex electromagnetic environment can be more accurately simulated. The entire process is implemented on FPGA, making full use of the parallel processing capabilities and flexible hardware architecture of FPGA to improve computing efficiency. For example, computationally intensive tasks such as kernel density estimation and adaptive bandwidth selection can be implemented with high-speed computing through the parallel processing unit of FPGA. The construction and traversal of parameter dependency trees can be optimized using the flexible logic resources of FPGA to achieve fast graph structure operations. Hierarchical parameter sampling and spatiotemporal series prediction can be implemented through the pipeline architecture of FPGA, further improving processing speed. In addition, the on-chip storage resources of FPGA are fully utilized, such as storing intermediate results such as multidimensional probability distribution models and parameter dependency trees in internal memory, reducing external memory access and improving data access speed. This FPGA-based implementation not only improves the overall computing efficiency, but also enhances the real-time performance of the system, enabling the simulation of complex electromagnetic environments to be performed with higher accuracy and faster speed, providing high-quality input data for subsequent signal processing and analysis.

[0048] According to one aspect of the present application, the optimization of the multidimensional probability distribution model is specifically as follows: Read the multidimensional probability distribution model. Initialize a bandwidth value set for each dimension, where each dimension contains multiple bandwidth values ​​of different scales. For the i-th dimension, initialize the bandwidth set H i ={h i1 ,h i2 , ..., h iL}, where L is the preset number of scales. The initialized bandwidth value set is stored in the temporary memory of the FPGA. For each dimension, the multi-scale cross-validation score is calculated: the bandwidth value set is read from the temporary memory of the FPGA, and the cross-validation score is calculated for the bandwidth value of each scale using the leave-one-out method. The specific process is: remove one sample point each time, estimate the probability density using the remaining samples and the bandwidth value of the current scale, and then evaluate the density value at the removed sample point. Repeat this process for all samples and take the average as the cross-validation score for the scale. The cross-validation scores of each scale are stored in the scoring matrix of the FPGA.

[0049] Implement adaptive scale fusion. Read the cross-validation scores of each scale from the FPGA scoring matrix. Use the softmax function to calculate the weight of each scale: w ij =exp(-CV ij ) / Σ k exp(-CV ik ), where CV ij is the cross-validation score of the jth scale in the i-th dimension, and exp( ) represents the exponential function. Calculate the fusion bandwidth value of each dimension: h i =Σ j w ij *h ij The fused bandwidth value is stored in the intermediate result buffer of the FPGA.

[0050] Perform multi-dimensional collaborative optimization. Read the fused bandwidth values ​​from the intermediate result cache of the FPGA. Construct a bandwidth covariance matrix to capture the correlation between bandwidths of different dimensions. Decompose the covariance matrix using the singular value decomposition (SVD) method to extract the main correlation patterns. Co-adjust the bandwidth values ​​based on the extracted correlation patterns. Store the adjusted bandwidth values ​​in the optimization result cache of the FPGA.

[0051] Implement an iterative optimization process. Read the current bandwidth value from the optimization result cache of the FPGA. Calculate the objective function value, which takes into account the cross-validation score and bandwidth smoothness. Update the bandwidth value using the improved particle swarm optimization algorithm. Each particle in the particle swarm represents a set of possible bandwidth values. Update the position and velocity of the particle to find the optimal solution. Repeat this process until convergence or the maximum number of iterations is reached. Store the final optimized bandwidth value in the register of the FPGA. Apply the optimized bandwidth value to rebuild the kernel density estimation model. Read the optimized bandwidth value from the register of the FPGA. Use these bandwidth values ​​to recalculate the kernel density estimate for each dimension. Traverse all sample points and accumulate the kernel function value corresponding to each sample. Divide the accumulated result by the number of samples and the optimized bandwidth to obtain an updated probability density estimate. Store the updated multidimensional probability distribution model in the internal memory of the FPGA.

[0052] This embodiment improves the accuracy and robustness of kernel density estimation by implementing a multi-scale adaptive bandwidth selection algorithm. The multi-scale method allows data features to be captured at different granularities, effectively coping with complex multimodal distributions. The adaptive bandwidth selection mechanism can dynamically adjust the bandwidth according to the local data density, and performs well in processing non-uniform distributions. By introducing the softmax function for scale fusion, the contribution of different scales can be automatically balanced, enhancing the adaptability of the model. The multi-dimensional collaborative optimization technology takes into account the correlation between different dimensions and improves the accuracy of high-dimensional data processing. The iterative optimization process uses an improved particle swarm algorithm to effectively avoid local optimal traps and improve global search capabilities. The optimized bandwidth is used to reconstruct the kernel density estimation model to ensure the high quality of the final model. The entire process is implemented on FPGA, and the flexible architecture of FPGA allows dynamic adjustment of computing resource allocation to adapt to data distributions of different complexities. It not only improves the quality of kernel density estimation, but also lays a solid foundation for subsequent parameter sampling and signal processing, which has a key impact on the performance of the entire electromagnetic environment simulation system.

[0053] According to one aspect of the present application, step S14 is further:

[0054] S141, read the parameter dependency tree structure from the internal memory of the FPGA. Initialize the sampling parameter set S to an empty set. Create a priority queue Q for storing the tree nodes to be sampled. Add the root node of the tree to the queue Q, and assign an importance weight to each node in the cache of the FPGA, with the initial value set to 1.

[0055] S142, take out the node N with the highest importance weight from the priority queue Q, read the edge distribution corresponding to the node N in the multidimensional probability distribution model, and use the inverse transform sampling method to generate a candidate value set {v1, v2, ..., v k}. The candidate value set is stored in a temporary buffer of the FPGA.

[0056] S143, for each generated candidate value v i , calculate its conditional probability density p(v i | Parent node value): Read the sampled value of the parent node from the FPGA cache, combine it with the multidimensional probability distribution model, and use the Monte Carlo integration method to estimate the conditional probability density. Store the calculated conditional probability density value in the FPGA probability cache.

[0057] S144, read the conditional probability density value, and implement adaptive importance resampling: calculate the importance weight w of each candidate value i = p(v i |parent node value) / q(v i), where q(v i ) is the probability density of the proposed distribution; these weights are used for weighted random sampling to select the final sampled value v*. The sampled value v* is added to the sampling parameter set S and stored in the result buffer of the FPGA.

[0058] S145. Update the importance weight of the child node of node N. Read the current importance weight of the child node from the cache of the FPGA, calculate the new importance weight based on the sampling value v* of the parent node and the edge distribution of the child node; update the importance weight of the child node using the exponential moving average method. Store the updated importance weight back into the cache of the FPGA.

[0059] S146, add all child nodes of node N to the priority queue Q. Read the current sampling parameter set S from the result cache of the FPGA to check whether all nodes have been sampled. If not completed, return to step S142 to continue the sampling process. If completed, store the final sampling parameter set S in the cache of the FPGA.

[0060] S147, perform post-sampling processing. Read the sampling parameter set S from the FPGA cache, calculate the final importance weight of each sampling point, and comprehensively consider the conditional probabilities of all ancestor nodes. Use these weights to resample the sampling set to obtain an equal-weighted sampling set S'. Store S' in the output buffer of the FPGA.

[0061] This embodiment implements adaptive hierarchical importance sampling based on parameter dependency tree, which improves sampling efficiency and sample quality. By constructing a priority queue and assigning dynamic weights, the most important parameters can be intelligently selected for sampling, effectively reducing the waste of computing resources. The application of the inverse transform sampling method ensures the consistency of the generated samples with the target distribution. The Monte Carlo integral estimation of the conditional probability density improves the sampling process's ability to capture complex dependencies. The adaptive importance resampling mechanism not only improves the sampling probability of rare events, but also balances the representativeness of the samples. The dynamic update strategy of the importance weights of subnodes enhances the algorithm's adaptability to dynamic changes in parameter space. Importance resampling in post-sampling processing further optimizes the quality of the sample set and ensures the unbiasedness and representativeness of the final sample. The conditional probability density calculation can be executed in parallel on multiple processing units, which improves the calculation speed. The flexible architecture of FPGA also allows dynamic adjustment of the sampling strategy to adapt to parameter dependencies of different complexities. Not only does it improve the sampling efficiency, but it also enhances the quality and diversity of the generated samples, providing high-quality input data for subsequent electromagnetic environment simulation, which has a decisive impact on the simulation accuracy of the entire system.

[0062] According to one aspect of the present application, step S15 is further:

[0063] S151, read the complete parameter set from the FPGA cache, and decompose the parameter set into two parts: time series and spatial distribution. Use wavelet transform to perform multi-scale decomposition on the time series data to obtain different frequency components. Store the decomposed time series data in the time series cache of the FPGA. Grid the spatial distribution data to generate a regular grid data structure. Store the gridded spatial data in the spatial data cache of the FPGA.

[0064] S152, read the decomposed time series data in the FPGA time series cache, and apply the long short-term memory network (LSTM) to each frequency component for time series prediction: prepare training data using the sliding window method, and adjust the window size adaptively according to the frequency component. Train the LSTM model, use the mean square error as the loss function, and apply the Adam optimizer to update the parameters. Store the trained LSTM model parameters in the model parameter memory of the FPGA.

[0065] S153, read the gridded spatial data from the FPGA spatial data cache, build a spatial autoregressive model (SAR), calculate the spatial weight matrix, and use the inverse distance weighting method. Construct the design matrix and dependent variable vector of the SAR model. Use the maximum likelihood estimation method to estimate the SAR model parameters. Store the estimated SAR model parameters in the model parameter memory of the FPGA.

[0066] S154, read the LSTM model parameters and SAR model parameters in the FPGA model parameter memory, build a spatiotemporal coupling layer, and fuse the output of the LSTM with the prediction results of the SAR model. Use the attention mechanism to calculate the weights of the temporal and spatial prediction results. Implement weighted summation to obtain preliminary spatiotemporal fusion prediction results. Store the fusion prediction results in the intermediate result cache of the FPGA.

[0067] S155. Read the spatiotemporal fusion prediction results from the intermediate result cache of the FPGA, and apply the integrated learning method to correct the prediction results: build a random forest model, use the historical prediction errors as training data; train the random forest model to predict and correct the deviation of the fusion results; store the trained random forest model parameters in the model parameter memory of the FPGA.

[0068] S156, read the fusion prediction results in the FPGA intermediate result cache and the random forest model parameters in the model parameter memory, use the random forest model to perform deviation correction on the fusion prediction results, and generate the final spatiotemporal prediction results. Compare the final prediction results with the original parameter set and calculate the adjustment amount. Apply the calculated adjustment amount to the original parameter set to generate an adjusted complete parameter set. Store the adjusted complete parameter set in the output buffer of the FPGA.

[0069] S157, read the adjusted complete parameter set from the FPGA output buffer, and perform uncertainty quantification of the prediction results: use the Monte Carlo random dropout method to make multiple predictions for the LSTM and random forest models. Calculate the confidence interval of the prediction results. Append the uncertainty information to the adjusted parameter set. Store the final parameter set and its uncertainty information together in the FPGA output buffer for use in subsequent processing steps.

[0070] This embodiment implements a multimodal fusion spatiotemporal series prediction model, which improves the accuracy and robustness of electromagnetic environment parameter prediction. The application of wavelet transform enables the model to capture the multi-scale characteristics of time series and effectively handle non-stationarity. The introduction of LSTM network enhances the model's learning ability for long-term dependencies and improves the accuracy of time series prediction. The integration of spatial autoregressive model enables the prediction process to consider spatial correlation and enhances the spatial perception ability of the model. The design of spatiotemporal coupling layer, combined with attention mechanism, realizes the effective fusion of time and space information and improves the comprehensiveness of prediction. The application of integrated learning methods, especially the use of random forest model, enhances the stability and generalization ability of prediction results. The introduction of Monte Carlo dropout technology enables the model to quantify the uncertainty of prediction and provide more information for decision-making. The whole process is implemented on FPGA, making full use of hardware acceleration capabilities. For example, the calculation of wavelet transform and LSTM network can be executed in parallel to improve processing speed. The reconfigurable characteristics of FPGA allow the model structure to be dynamically adjusted to adapt to spatiotemporal patterns of different complexity. It not only improves the accuracy of the prediction, but also enhances the model's adaptability to changes in complex electromagnetic environments, provides high-quality parameter predictions for the system, and has an important impact on the dynamics and authenticity of the entire electromagnetic environment simulation.

[0071] like Figure 3 As shown, according to one aspect of the present application, step S2 is further:

[0072] S21, initialize K cluster centers, and for each signal in the optimized parameter set, calculate the Euclidean distance between it and each cluster center; based on the Euclidean distance, assign each signal to the cluster center with the nearest distance to obtain the assignment result; based on the assignment result, recalculate the center point of each cluster, repeat the assignment and center point calculation process until the clustering result converges or reaches the maximum number of iterations, and output the final clustering result;

[0073] S22. Based on the clustering result, using the priority queue data structure, construct an intra-group competition unit for each cluster to form a priority queue set;

[0074] S23, based on the priority queue set, calculating the selection probability of each group; based on the selection probability, using the roulette wheel selection method to obtain the selected group; obtaining the head element of the priority queue of the selected group as the output signal of the current time step;

[0075] S24, based on the output signal, calculating the output frequency distribution of each group of signals within a predetermined time window; calculating the Kullback-Leibler divergence between the output frequency distribution and the multidimensional probability distribution model; using the gradient descent method to update the weight of each group of signals to minimize the Kullback-Leibler divergence, and obtaining the output signal after the weight is updated;

[0076] S25. Based on the output signal after the weights are updated, the short-time signal density is calculated using a sliding window method; based on the short-time signal density, the time window is adjusted to obtain adjusted time window parameters; based on the adjusted time window parameters, the output signal after the weights are updated is reorganized to obtain a reorganized signal sequence.

[0077] In one embodiment of the present application, the optimized radar parameter set and multidimensional probability distribution model are read from the output buffer of the FPGA. The signals in the radar parameter set are grouped using the K-means clustering algorithm: K cluster centers are initialized, and the K value is dynamically determined according to the complexity of the current simulation scene; for each signal, the Euclidean distance between it and each cluster center is calculated, and it is assigned to the cluster with the closest distance, and the center point of each cluster is recalculated; the assignment and center point calculation process are repeated until the clustering results converge or the maximum number of iterations is reached. The clustering results are stored in the internal memory of the FPGA.

[0078] Read the clustering results stored in the internal memory of the FPGA. Build an intra-group competition unit for each cluster, and each intra-group competition unit is implemented using a priority queue data structure. Read the real-time radar signal pulse sequence from the input buffer of the FPGA. For each input pulse, insert it into the corresponding priority queue according to the cluster it belongs to. The priority is determined based on the timestamp and signal priority of the pulse. Store all priority queues in the cache of the FPGA.

[0079] Read the priority queue set stored in the FPGA cache to implement the inter-group competition unit: Use a random selection algorithm based on the Softmax function to decide which group's signal should be output at each time step. For each group, calculate its selection probability. The selection probability calculation takes into account the group weight and queue characteristic functions (such as queue length or queue head element priority). Use the roulette wheel selection method to select a group based on the calculated probability. Pop the head element from the priority queue of the selected group as the output signal of the current time step. Store the output signal in the output buffer of the FPGA.

[0080] Read the output signal and multidimensional probability distribution model stored in the FPGA output buffer to implement the dynamic weight adjustment algorithm: calculate the output frequency distribution of each group of signals in a time window, calculate the Kullback-Leibler divergence between the output frequency distribution and the ideal distribution (i.e., the multidimensional probability distribution model), and use the gradient descent method to update the weight of each group. The goal of the weight update is to minimize the Kullback-Leibler divergence. Store the updated weight in the FPGA register.

[0081] Read the output signal sequence stored in the FPGA output buffer and implement the adaptive time window mechanism: Use the sliding window method to calculate the short-term signal density. When the signal density exceeds the preset threshold, reduce the contention time window size. When the signal density is lower than the threshold, increase the contention time window size. Use similar methods to adjust the waiting time window and the protection time window. Store the adjusted time window parameters in the control register of the FPGA. Read the output signal sequence from the FPGA output buffer and reorganize the signal sequence according to the adjusted time window parameters. Store the reorganized signal sequence in the FPGA output buffer.

[0082] In another embodiment of the present application, the final parameter set S' and the multidimensional probability distribution model P(E) are read from the output buffer of the FPGA. The radar signals in the final parameter set S' are grouped using the K-means clustering algorithm: K cluster centers C={c1, c2, ..., c K}, where the K value is dynamically determined according to the complexity of the current simulation scenario. i , calculate the distance d(s) between it and each cluster center i , c j ) and assign it to the cluster with the closest distance. Repeat the calculation of cluster centers and reallocation until convergence or the maximum number of iterations is reached. Store the clustering results in the internal memory of the FPGA.

[0083] Read the clustering results and design an intra-group competition unit for each cluster. Each intra-group competition unit is implemented using a priority queue data structure. Read the real-time radar signal pulse sequence I={i1, i2, ..., i n}. For each input pulse i j , according to the cluster k to which it belongs, insert it into the corresponding priority queue Q k The priority is determined based on the timestamp of the pulse and the signal priority. All priority queues Q = {Q1, Q2, ..., Q K}Stored in the FPGA's cache.

[0084] Read the priority queue set Q to implement the inter-group competition unit. Use a random selection algorithm based on the Softmax function to decide which group's signal should be output at each time step. For each group k, calculate its selection probability: P(k)=exp(w k *f(Q k )) / Σ i=1 K exp(w i *f(Q i )), where w k is the group weight, f(Q k ) is the queue Q k A certain characteristic function of the queue (such as queue length or the priority of the first element in the queue). Use the roulette wheel selection method to select a group according to the calculated probability. Pop the first element of the queue from the priority queue of the selected group as the output signal of the current time step. Store the output signal in the output buffer of the FPGA.

[0085] Read the output signal and the multidimensional probability distribution model P(E) to implement the dynamic weight adjustment algorithm. Calculate the output frequency distribution F={f1, f2, ..., f K}. Calculate the Kullback-Leibler divergence between the output frequency distribution F and the ideal distribution P(E): DKL(P||F)=Σ k=1 K P(k)*log(P(k) / F(k)). Use gradient descent to update the weight of each group: w k =w k -η*ΨDKL / Ψw k , where η is the learning rate and Ψ is the partial derivative. The updated weights W={w1, w2, ..., w K}Stored in the FPGA register for inter-group competition.

[0086] Read the output signal sequence to implement the adaptive time window mechanism. Use the sliding window method to calculate the short-time signal density ρ(t). When the short-time signal density ρ(t) exceeds the preset threshold θ, reduce the contention time window size Tc: Tc =Tc*(1-α*(ρ(t)-θ) / θ), where α is the adjustment coefficient. When the short-time signal density ρ(t) is lower than the threshold, increase the contention time window size Tc. Similarly, adjust the waiting time window Tw and the protection time window Tp. Store the adjusted time window parameters {Tc, Tw, Tp} in the control register of the FPGA to control the signal output timing.

[0087] This embodiment realizes efficient and intelligent radar signal processing and dynamic adjustment. The K-means clustering algorithm is used to group radar signals. This unsupervised learning method can automatically identify and classify different types of signals in complex electromagnetic environments, providing a structured basis for subsequent signal processing. The clustering process is implemented on the FPGA, and its parallel computing capability is used to improve the processing speed of large-scale signal data. The intra-group competition unit designed for each cluster adopts a priority queue data structure. This efficient data organization method can quickly respond to the real-time input radar signal pulse sequence, ensuring the system's rapid adaptability to high-dynamic electromagnetic environments. The inter-group competition unit introduces a random selection algorithm based on the Softmax function, which not only considers the weights of each group, but also introduces randomness, effectively simulating the random characteristics and dynamic changes of priorities of signals in complex electromagnetic environments. The application of the dynamic weight adjustment algorithm realizes the adaptive adjustment of the system to changes in the electromagnetic environment by calculating the Kullback-Leibler divergence between the output signal distribution and the ideal distribution, and using the gradient descent method to update the weights. This closed-loop feedback mechanism ensures that the statistical characteristics of the simulated signal continue to match the real electromagnetic environment. The introduction of the adaptive time window mechanism further enhances the dynamic adaptability of the system. By calculating the short-term signal density in real time and dynamically adjusting the size of the contention time window, waiting time window, and protection time window, the system can accurately capture the instantaneous changes in the electromagnetic environment and improve the time resolution and accuracy of the simulation. The entire process is implemented on the FPGA, making full use of the parallel processing capability and reconfigurable characteristics of the FPGA. For example, the K-means clustering algorithm can achieve high-speed clustering calculations through the parallel processing unit of the FPGA, reducing the processing time. The priority queue of the intra-group competition unit can be optimized using the dedicated storage resources of the FPGA to achieve fast insertion and pop-up operations. The Softmax function and random selection algorithm of the inter-group competition unit can be efficiently implemented through the lookup table (LUT) and dedicated mathematical operation unit of the FPGA, ensuring real-time performance. The gradient descent method in the dynamic weight adjustment algorithm can use the FPGA's DSP module for parallel calculation to accelerate the convergence process. The adaptive time window mechanism can be implemented through the dynamic partial reconstruction function of the FPGA, allowing the system to dynamically adjust the processing logic according to the signal characteristics during operation. In addition, the on-chip storage resources of the FPGA are fully utilized, such as storing the clustering results, weight information, and time window parameters in the internal memory, reducing the external memory access delay. This FPGA-based implementation not only improves the overall signal processing efficiency, but also enhances the real-time adaptability of the system, enabling the simulation of complex electromagnetic environments to respond to environmental changes with higher accuracy and faster speed, providing a highly dynamic and precise control mechanism for subsequent signal generation and analysis.

[0088] According to one aspect of the present application, step S21 may also be processed using an adaptive density-aware hierarchical clustering algorithm, specifically:

[0089] S211, read the optimized radar parameter set from the output buffer of the FPGA, and calculate the local density of each data point in the parameter set. Use the Gaussian kernel function to estimate the local density value of each point, select an adaptive bandwidth parameter, and dynamically adjust the bandwidth value according to the k-nearest neighbor distance of the data point. Store the calculated local density value in the density buffer of the FPGA.

[0090] S212, read the local density value in the FPGA density cache, and construct a k-nearest neighbor graph of the data point: use the KD tree algorithm to accelerate the k-nearest neighbor search process, calculate the distance between each pair of k-nearest neighbor data points, combine the distance value with the corresponding local density value, and calculate the edge weight. The edge weight calculation takes into account the distance and density differences. The constructed k-nearest neighbor graph structure is stored in the graph structure cache of the FPGA.

[0091] S213, read the k-nearest neighbor graph from the graph structure cache of the FPGA, perform the graph cut operation, and preliminarily divide the data points. Use the spectral clustering method to calculate the Laplacian matrix of the graph; solve the eigenvalues ​​and eigenvectors of the Laplacian matrix; select the top-k eigenvectors to form a low-dimensional embedding space; apply the mean shift algorithm in the embedding space to identify the center of the initial cluster. Store the initial clustering results in the clustering result cache of the FPGA.

[0092] S214, read the initial clustering results in the FPGA clustering result cache, and implement the adaptive cluster merging process: calculate the inter-cluster similarity matrix, consider the density distribution and shape characteristics of the clusters; use the dynamic programming algorithm to find the optimal cluster merging sequence; perform the cluster merging operation, and update the cluster statistics. Store the updated clustering results back in the FPGA clustering result cache.

[0093] S215, read the updated clustering results from the FPGA clustering result cache, perform outlier detection and reallocation: calculate the Mahalanobis distance from each data point to the center of the cluster to which it belongs; identify outliers, i.e., points whose distance exceeds a preset threshold; perform reallocation on outliers, assign them to the next closest cluster or form a new cluster; update the statistical information and boundaries of the cluster. Store the adjusted clustering results in the intermediate result cache of the FPGA.

[0094] S216, read the adjusted clustering results in the FPGA intermediate result cache, and perform intra-cluster density balancing operations: calculate the density distribution of each cluster; apply an adaptive splitting strategy to clusters with uneven density; use principal component analysis (PCA) to determine the best splitting direction; divide the uneven cluster into two sub-clusters along the splitting direction; repeat this process until a preset uniformity threshold is reached. Store the clustering results after density balancing in the final result cache of the FPGA.

[0095] S217, read the clustering result after density equalization from the FPGA final result cache, and evaluate the clustering quality: calculate the clustering effectiveness indicators such as the silhouette coefficient and the Calinski-Harabasz index. If the quality indicator does not reach the preset threshold, adjust the algorithm parameters (such as k value, density estimation bandwidth, etc.), and return to step S211 to re-execute the clustering process. If the quality requirement or the maximum number of iterations is met, terminate the iteration. Store the final clustering result in the internal memory of the FPGA for use in subsequent processing steps.

[0096] This embodiment improves the accuracy and efficiency of radar signal grouping. The local density calculation uses adaptive bandwidth parameters to enhance the algorithm's sensitivity to density changes at different scales. The k-nearest neighbor graph construction combined with the KD tree algorithm improves the efficiency of high-dimensional data processing. The application of spectral clustering methods, especially the use of mean shift algorithm in low-dimensional embedding space, effectively identifies cluster structures of complex shapes. The adaptive cluster merging process takes into account the density distribution and shape characteristics of the cluster, improving the rationality of the clustering results. The outlier detection and redistribution mechanism enhances the robustness of the algorithm and reduces the impact of outliers on clustering quality. The intra-cluster density balancing operation effectively handles the internal inhomogeneity problem through an adaptive splitting strategy. Clustering quality assessment uses multiple indicators to ensure the reliability of the results. The entire process is implemented on FPGA, making full use of the hardware parallel processing capabilities. For example, local density calculation and k-nearest neighbor search can be executed in parallel on multiple processing units to improve the calculation speed. The flexible architecture of FPGA also allows dynamic adjustment of clustering parameters to adapt to signal distributions of different complexities. It not only improves the accuracy and efficiency of clustering, but also enhances the algorithm's adaptability to diverse signal characteristics in complex electromagnetic environments, provides high-quality grouping results for subsequent signal processing and analysis, and has an important impact on the performance and decision-making ability of the entire system.

[0097] According to one aspect of the present application, step S23 is further:

[0098] S231. Based on the priority queue set, calculate the feature vector of each queue, and use the exponential sliding average method to update the historical feature statistics of each queue; wherein the feature vector includes the queue length, the priority of the first element in the queue, and the variance of the priority of the queue elements;

[0099] S232. Based on the feature vector and historical feature statistical information of each queue, a multi-criteria decision matrix is ​​constructed; based on the multi-criteria decision matrix, a normalized decision value is calculated; based on the normalized decision value, an entropy weight method is used to calculate the weight of each criterion; wherein the multi-criteria decision matrix includes signal priority, queue load balancing, and spectrum utilization;

[0100] S233. Based on the multi-criteria decision matrix and the weight of each criterion, the improved TOPSIS method is applied to calculate the comprehensive score of each queue, specifically: construct a weighted standardized decision matrix, and determine the ideal solution and the negative ideal solution; calculate the distance of each queue to the ideal solution and the negative ideal solution; based on the distance of each queue to the ideal solution and the negative ideal solution, calculate the relative proximity as the comprehensive score;

[0101] S234. Use the Softmax function to convert the comprehensive score into a selection probability; based on the selection probability, execute the Monte Carlo tree search optimization selection strategy to obtain the search result; based on the search result, determine the selected priority queue, and obtain the head element from the selected priority queue as the output signal of the current time step.

[0102] In one embodiment of the present application, an adaptive softening selection mechanism is implemented based on the comprehensive score: the comprehensive score is converted into a selection probability using a Softmax function, a temperature parameter is introduced to adjust the smoothness of the probability distribution, the temperature parameter is dynamically adjusted according to the current state of the system, and the calculated selection probability is stored in the probability cache of the FPGA. Based on the selection probability, a Monte Carlo tree search (MCTS) is performed to optimize the selection strategy. A search tree is constructed, where each node represents a possible selection sequence; an upper confidence bound (UCB) algorithm is used to balance exploration and utilization. A multi-step selection process is simulated to evaluate long-term benefits. Node values ​​and access times are updated. The search results of MCTS are stored in the strategy cache of the FPGA.

[0103] Read the MCTS search results in the FPGA policy cache, combine the short-term selection probability and long-term policy evaluation to make the final decision; use the threshold method to handle extreme cases to ensure fairness and system stability; pop the first element from the selected priority queue as the output signal of the current time step; store the output signal in the FPGA output buffer. Read the output signal, perform post-decision evaluation and learning: calculate the deviation between the actual output and the expected target; use the reinforcement learning method to update the decision model parameters, apply the policy gradient algorithm, and adjust the decision weight according to the accumulated reward; store the updated model parameters in the FPGA model parameter memory for the next round of decision optimization.

[0104] Read the updated decision model parameters and perform regular meta-learning processes: collect decision data and system performance indicators over a period of time, use meta-learning algorithms to automatically adjust the hyperparameters of the decision framework, such as the search depth of MCTS and the learning rate of reinforcement learning; store the optimized hyperparameter configuration in the configuration register of the FPGA to guide subsequent decision-making processes.

[0105] This embodiment implements a multi-criteria adaptive inter-group competition selection algorithm, which improves the intelligence and flexibility of signal selection. The dynamic calculation of feature vectors and the historical statistical update mechanism enhance the sensitivity of the algorithm to changes in signal characteristics. The construction of the multi-criteria decision matrix, combined with the entropy weight method to determine the criterion weights, improves the comprehensiveness and objectivity of the decision. The improved TOPSIS method effectively balances the weights between different criteria on the basis of comprehensive consideration of multiple decision factors. The adaptive softening selection mechanism flexibly controls the randomness and certainty of the selection strategy by dynamically adjusting the temperature parameters. The introduction of Monte Carlo tree search improves the long-term strategy planning ability of the algorithm and effectively avoids short-sighted decisions. The application of reinforcement learning methods enables the algorithm to learn from historical decisions and continuously optimize the selection strategy. The implementation of the meta-learning process further enhances the algorithm's adaptive ability and can dynamically adjust the hyperparameters of the decision framework according to system performance. The entire process is implemented on FPGA, making full use of hardware acceleration capabilities. For example, feature calculation and decision matrix construction can be executed in parallel to increase processing speed. The reconfigurable nature of FPGA allows dynamic adjustment of computing resource allocation to adapt to decision scenarios of different complexities. It not only improves the quality and efficiency of signal selection, but also enhances the system's ability to adapt to dynamic changes in complex electromagnetic environments, providing high-quality input for subsequent signal processing.

[0106] According to one aspect of the present application, step S24 is further:

[0107] S241, read the output signal sequence from the FPGA output buffer, and calculate the output frequency distribution of each group of signals in a sliding time window. Use the exponentially weighted moving average method to smooth the frequency distribution data. Based on the multidimensional probability distribution model, calculate the Wasserstein distance between the actual output frequency distribution and the ideal distribution. Store the calculated frequency distribution and Wasserstein distance in the distribution buffer of the FPGA.

[0108] S242. Read the frequency distribution and Wasserstein distance to build a multi-level error evaluation model. At the micro level, calculate the output deviation of each signal group; at the meso level, evaluate the balance between signal groups; at the macro level, analyze the deviation of the overall distribution; use the self-organizing map (SOM) algorithm to map the multi-level errors to a two-dimensional plane. Store the mapping results in the error mapping cache of the FPGA.

[0109] S243, read the multi-level error mapping results, and apply the fuzzy reasoning system to make weight adjustment decisions. Define a fuzzy rule set, including rules such as "if the error is large and changes quickly, adjust the weight significantly". Use the Mamdani reasoning method to calculate the activation of each rule. Defuzzify using the centroid method to obtain a preliminary weight adjustment. Store the preliminary adjustment in the FPGA's adjustment cache.

[0110] S244, read the initial weight adjustment amount and implement the adaptive learning rate mechanism. Construct a meta-learner, use the system performance index as input, and predict the optimal learning rate. Use the Bayesian optimization algorithm to search the learning rate hyperparameter space. Apply the Gaussian process regression model to estimate the performance surface. Select the learning rate that maximizes the performance expectation. Store the selected learning rate in the learning rate cache of the FPGA.

[0111] S245. Read the adaptive learning rate and read the preliminary weight adjustment from the adjustment cache. Perform the gradient projection method to update the weights. Calculate the gradient direction of the weight update. Use the L1 regularization term to maintain the sparsity of the weights. Apply the Nesterov momentum method to accelerate the convergence process; perform gradient projection to ensure that the updated weights meet the constraint of summing to 1. Store the updated weights in the intermediate weight cache of the FPGA.

[0112] S246. Read the updated weights and implement the weight smoothing strategy. Use the Kalman filter to suppress noise and predict trends in the weight sequence. Build a state space model and treat the weights as hidden states. Perform the prediction and update steps to obtain smoothed weight estimates. Apply an adaptive forgetting factor to balance the impact of historical information and new observations. Store the smoothed weights in the smoothed weight cache of the FPGA.

[0113] S247. Read the smoothed weights and perform stability analysis and constraint processing. Construct a Lyapunov function to evaluate the impact of weight adjustment on system stability. If potential instability is detected, apply convex optimization techniques to fine-tune the weights. Ensure that the rate of change of weights does not exceed the preset threshold. Apply box constraints to the weights to limit them to a valid range. Store the final adjusted weights in the final weight cache of the FPGA.

[0114] S248, read the adjusted weights, perform performance evaluation and adaptive adjustment. Calculate system performance indicators before and after the adjustment, such as signal coverage, spectrum utilization efficiency, etc. Use the multi-armed bandit algorithm to dynamically allocate computing resources and optimize the number of attempts for different adjustment strategies. Update the strategy value estimate to guide the future weight adjustment direction. Store the evaluation results and the optimized adjustment strategy in the FPGA's strategy cache to guide the next round of weight adjustment process.

[0115] This embodiment implements a multi-level adaptive dynamic weight adjustment algorithm, which improves the accuracy of weight adjustment and system adaptability. The application of sliding time window and exponential weighted moving average method enhances the algorithm's ability to smooth short-term fluctuations. The use of Wasserstein distance provides a more accurate distribution similarity measure. The introduction of a multi-level error evaluation model enables the algorithm to evaluate system performance from multiple levels, including micro, meso and macro, and improves the comprehensiveness of the adjustment. The application of the self-organizing map algorithm realizes the effective visualization of high-dimensional error data, which is convenient for pattern recognition. The use of fuzzy inference system enhances the decision-making ability of the algorithm in complex scenarios. The adaptive learning rate mechanism, combined with Bayesian optimization, improves the efficiency and stability of weight update. The application of gradient projection method and Nesterov momentum accelerates the weight convergence process. The introduction of Kalman filter effectively suppresses the noise of weight sequence and improves the smoothness and accuracy of estimation. Lyapunov stability analysis ensures the stability of the system during weight adjustment. The use of multi-armed tiger machine algorithm optimizes the allocation of computing resources and improves the exploration efficiency of different adjustment strategies. The whole process is implemented on FPGA, making full use of the hardware parallel processing capability. For example, multi-level error evaluation and fuzzy reasoning can be performed in parallel on multiple processing units to improve the calculation speed. The flexible architecture of FPGA also allows dynamic adjustment of weight update strategies to adapt to electromagnetic environments of different complexities. This not only improves the accuracy and efficiency of weight adjustment, but also enhances the system's ability to adapt to dynamic changes in complex electromagnetic environments, providing a more accurate and stable control mechanism for the entire simulation system.

[0116] like Figure 4 As shown, according to one aspect of the present application, step S3 is further:

[0117] S31, generating a corresponding digital waveform using direct digital synthesis technology based on the parameters of the reorganized signal sequence;

[0118] S32, reading the pulse width and repetition period parameters corresponding to the digital waveform, generating a rectangular function and a comb function; multiplying the digital waveform with the rectangular function and the comb function to obtain a modulated signal sequence;

[0119] S33, based on the modulated signal sequence, segmenting each signal to obtain predetermined segment data; applying a fast Fourier transform algorithm to each segment data to calculate spectrum data; averaging all spectrum data to obtain power spectrum density; superimposing the power spectrum densities of all signals to obtain a comprehensive spectrum;

[0120] S34, converting the integrated spectrum into a discrete probability distribution using an adaptive binning algorithm; calculating the Wasserstein distance between the discrete probability distribution and the frequency dimension distribution in the multidimensional probability distribution model;

[0121] S35. Determine whether the Wasserstein distance exceeds a preset threshold. If so, use the optimal transmission theory to calculate a transmission plan from the current distribution to the target distribution. According to the transmission plan, fine-tune each signal in the modulated signal sequence to obtain a corrected signal sequence. If not, no correction is performed and the modulated signal sequence is directly output.

[0122] In one embodiment of the present application, a radar signal sequence is read. For each signal, a corresponding digital waveform is generated using direct digital synthesis technology according to its parameters (carrier frequency, phase, amplitude, etc.). For each sampling point, the sine function value is calculated, and the amplitude, frequency and phase parameters are substituted into the calculation formula. The generated digital waveform sequence is stored in the waveform buffer of the FPGA.

[0123] Read the digital waveform sequence to implement digital pulse modulation. For each waveform, read its corresponding pulse width and repetition period parameters; generate a rectangular function whose width is equal to the pulse width; generate a comb function whose period is equal to the repetition period; multiply the original waveform with the rectangular function and the comb function to obtain the modulated signal. Store the modulated signal sequence in the output buffer of the FPGA.

[0124] Read the modulated signal sequence and use the fast Fourier transform algorithm to calculate the spectrum of each signal: for each signal, divide its time domain data into segments and apply the fast Fourier transform (FFT) algorithm to each segment of data. Average the obtained spectrum data to obtain the power spectrum density estimate of the signal. Superimpose the power spectrum densities of all signals to obtain the comprehensive spectrum. Store the comprehensive spectrum in the spectrum analysis cache of the FPGA.

[0125] Read the comprehensive spectrum and multi-dimensional probability distribution model to realize real-time feature distribution verification. Use the adaptive binning algorithm to convert the comprehensive spectrum into a discrete probability distribution; calculate the Wasserstein distance between the discrete probability distribution and the frequency dimension distribution in the multi-dimensional probability distribution model. The Wasserstein distance calculation process includes constructing a transmission matrix and solving a linear programming problem. Store the calculated Wasserstein distance in the state register of the FPGA.

[0126] Read the Wasserstein distance to implement the distribution deviation correction mechanism. Determine whether the Wasserstein distance exceeds the preset threshold. If it exceeds the threshold, trigger the correction process. Use the optimal transmission theory to calculate the transmission plan from the current distribution to the target distribution. Read the modulated signal sequence and fine-tune each signal according to the transmission plan. The fine-tuning includes adjusting the amplitude, frequency or phase of the signal. Store the corrected signal sequence in the output buffer of the FPGA and replace the original sequence. If the Wasserstein distance does not exceed the threshold, no correction is performed and the signal sequence is directly copied to the output buffer.

[0127] In another embodiment of the present application, the radar signal sequence O={o1, o2, . . . , o m}. For each signal o i , according to its parameters (carrier frequency, phase, amplitude, etc.), the corresponding digital waveform is generated. Use direct digital synthesis (DDS) technology to realize waveform generation: s(t)=A*sin(2πft+φ), where A is the amplitude, f is the carrier frequency, and φ is the initial phase. The generated digital waveform sequence S={s1(t), s2(t), ..., s m (t)} is stored in the waveform buffer of the FPGA.

[0128] Read the digital waveform sequence S to implement digital pulse modulation. For each waveform s i (t), according to its corresponding pulse width PW i and repetition period PRF i , generating the modulated signal: x i (t) = s i (t)*rect(t / PW i )*comb(t*PRF i ), where rect() is a rectangular function and comb() is a comb function. m (t)} is stored in the output buffer of the FPGA.

[0129] Read the modulated signal sequence X and use the fast Fourier transform (FFT) to calculate the spectrum of each signal: X i (f) = FFT{x i (t)}. The spectrum of all signals is superimposed to obtain the comprehensive spectrum: X total (f) =Σ i=1 m X i (f). The comprehensive spectrum X total (f) Stored in the spectrum analysis buffer of the FPGA.

[0130] Read comprehensive spectrum X total (f) and multi-dimensional probability distribution model P(E) to achieve real-time feature distribution verification. The comprehensive spectrum X is divided into total (f) is converted to a discrete probability distribution Q(f). The Wasserstein distance between the discrete probability distribution Q(f) and the frequency dimension distribution P(f) in the multidimensional probability distribution model P(E) is calculated: W(P, Q) = inf{E[d(X, Y)]: X ~ P, Y ~ Q}, where d is the Euclidean distance and inf is the infimum. The calculated Wasserstein distance W is stored in the state register of the FPGA.

[0131] Read the Wasserstein distance W to implement the distribution deviation correction mechanism. If the distance W exceeds the preset threshold ε, the correction process is triggered. Use the optimal transmission theory to calculate the transmission plan T from the discrete probability distribution Q to the multidimensional probability distribution model P. According to the transmission plan T, fine-tune the modulated signal sequence X: x' i (t)=x i (t)+δ(T,x i ), where δ is an adjustment function based on the transmission plan. The corrected signal sequence X'={x'1(t), x'2(t), ..., x' m (t)} is stored back to the FPGA output buffer, replacing the original sequence X.

[0132] This embodiment realizes high-fidelity radar signal generation and dynamic correction. The digital waveform is generated by direct digital synthesis (DDS) technology, which can accurately control the frequency, phase and amplitude of the signal, providing a high-quality basic waveform for subsequent signal processing. The application of digital pulse modulation technology realizes the accurate simulation of the time domain characteristics of the radar signal, including key parameters such as pulse width and repetition period, by multiplying the original waveform with carefully designed rectangular functions and comb functions. The application of fast Fourier transform (FFT) algorithm enables the system to efficiently calculate the spectral characteristics of the signal. By superimposing the power spectral density of multiple signals to generate a comprehensive spectrum, it not only improves the accuracy of spectrum analysis, but also reflects the characteristics of multi-signal interaction in a complex electromagnetic environment. The introduction of the real-time feature distribution verification mechanism uses an adaptive binning algorithm to convert the comprehensive spectrum into a discrete probability distribution, and calculates the Wasserstein distance between the ideal distribution, providing a mathematically rigorous metric for signal quality assessment. The application of the distribution deviation correction mechanism calculates the transmission plan based on the optimal transmission theory and fine-tunes the signal to ensure the consistency of the statistical characteristics of the generated signal with the target distribution. This closed-loop correction mechanism improves the authenticity and reliability of the simulated signal. The entire process is implemented on FPGA, making full use of the high-performance computing capabilities and flexible hardware architecture of FPGA. For example, direct digital synthesis (DDS) technology can be implemented through the dedicated DDS IP core of FPGA to provide a high-precision, low-phase noise basic waveform. Digital pulse modulation can use the DSP module of FPGA to perform high-speed multiplication operations to achieve accurate time domain modulation. The FFT algorithm can be implemented through the parallel processing unit and dedicated FFT IP core of FPGA to improve the speed of spectrum calculation. The Wasserstein distance calculation in real-time feature distribution verification can use the parallel processing capabilities of FPGA to achieve efficient calculation through the optimized linear programming solver. The optimal transmission plan calculation in the distribution deviation correction mechanism can be implemented through the reconfigurable logic resources of FPGA, allowing the correction strategy to be dynamically adjusted according to different deviation conditions. In addition, the on-chip storage resources of FPGA are fully utilized, such as storing intermediate results such as waveform cache and spectrum analysis cache in internal memory, reducing external memory access and improving data processing speed. The high-speed I / O interface of FPGA is also fully utilized to achieve high-speed digital-to-analog conversion and analog signal output. This embodiment not only improves the overall signal generation and processing efficiency, but also enhances the real-time correction capability of the system, so that the simulation of complex electromagnetic environments can be performed with higher fidelity and faster speed. The system can dynamically respond to environmental changes and adjust signal characteristics in real time, providing a highly realistic and controllable signal source for subsequent electromagnetic environment analysis and testing.

[0133] According to one aspect of the present application, step S33 is further:

[0134] S331. Use an adaptive basis function selection algorithm to select a basis function from a predefined wavelet basis function library; based on the modulated signal sequence and the basis function, calculate the wavelet packet coefficients of the signal at different scales and frequency subbands; based on a preset optimal threshold, perform soft threshold processing on the wavelet packet coefficients to obtain the denoised coefficients; the optimal threshold can be calculated using the Stein's Unbiased Risk Estimate (SURE) criterion for each subband, and then use the cyclic shift technique to reduce the pseudo-Gibbs phenomenon;

[0135] S332, based on the denoised coefficients, calculate the energy distribution of each frequency subband; based on the energy distribution, use the information entropy criterion to evaluate the importance of the subband; decompose the subbands whose importance is higher than the preset threshold to improve the frequency resolution; merge the subbands whose importance is lower than the preset threshold to reduce redundancy; generate an optimized time-frequency representation based on the decomposed subbands and the merged subbands;

[0136] S333. Based on the optimized time-frequency representation, a parameterized autoregressive model is used to calculate the power spectrum density of each subband; based on the power spectrum density, multi-resolution spectrum fusion is performed to obtain a fused multi-resolution spectrum; super-resolution technology is used to improve the frequency resolution of the multi-resolution spectrum to obtain an enhanced multi-resolution spectrum; based on the enhanced multi-resolution spectrum, a deep learning model is used to generate a refined high-resolution spectrum;

[0137] S334, based on the refined high-resolution spectrum, using wavelet Rayleigh entropy, extracting key texture features; based on the key texture features, calculating the shape factor and inter-peak relationship of the spectrum peak; based on the shape factor and inter-peak relationship of the spectrum peak, applying a support vector machine to classify the high-resolution spectrum to obtain a classification result;

[0138] S335. Based on the classification result, select a template spectrum from a pre-trained spectrum template library; use a dynamic time warping algorithm to align the pre-stored observation spectrum and the template spectrum; based on the aligned observation spectrum and template spectrum, calculate the weighted average to obtain a fused spectrum; use an adaptive filter to process the fused spectrum to obtain a final integrated spectrum.

[0139] In this embodiment, after reading the optimized time-frequency representation, adaptive spectrum estimation is implemented. A parameterized autoregressive model is applied to each subband, and the autoregressive coefficients are estimated using the Levinson-Durbin algorithm. The power spectral density estimate of each subband is calculated.

[0140] Based on the power spectral density estimation of each subband, perform multi-resolution spectrum fusion: construct a spectrum fusion tree, where the leaf nodes correspond to the finest subband spectrum estimation, and use the maximum mutual information criterion to merge adjacent nodes from bottom to top; at each non-leaf node, apply an adaptive weighting scheme to fuse the sub-node spectrum estimation. Store the fused multi-resolution spectrum in the fused spectrum cache of the FPGA. Read the multi-resolution fused spectrum. Implement spectrum enhancement and refinement: Use super-resolution technology to improve the frequency resolution of the spectrum; apply deep learning models, such as generative adversarial networks (GANs), to learn the features of high-resolution spectra; use the model to generate refined high-resolution spectrum estimates. Store the enhanced spectrum in the enhanced spectrum cache of the FPGA.

[0141] This embodiment implements an adaptive multi-resolution spectrum analysis and fusion algorithm, and improves the accuracy and adaptability of spectrum analysis. The wavelet packet transform combined with the adaptive basis function selection enhances the adaptability of the algorithm to different signal features. The adaptive threshold denoising technology, especially the application of the SURE criterion, effectively improves the signal-to-noise ratio and retains the key features of the signal. The adaptive frequency resolution optimization dynamically adjusts the sub-band division according to the information entropy criterion, and realizes the efficient use of spectrum resources. The introduction of the parameterized autoregressive model improves the accuracy of power spectrum density estimation. The multi-resolution spectrum fusion technology, combined with the maximization mutual information criterion, effectively integrates spectrum information of different scales. The application of super-resolution technology and deep learning models improves the resolution and detail retention of the spectrum. The introduction of spectral feature extraction and classification enhances the algorithm's ability to recognize different signal types. The adaptive spectrum correction and synthesis process, combined with the dynamic time warping algorithm, improves the accuracy and reliability of the final spectrum estimation. The entire process is implemented on the FPGA, making full use of the hardware acceleration capability. For example, the wavelet packet transform and the autoregressive model estimation can be executed in parallel, which improves the processing speed. The reconfigurable characteristics of the FPGA allow the dynamic adjustment of computing resource allocation to adapt to spectrum analysis tasks of different complexity. It not only improves the quality and efficiency of spectrum analysis, but also enhances the system's adaptability to diverse signal characteristics in complex electromagnetic environments, providing high-quality spectrum information for subsequent signal recognition and classification.

[0142] According to one aspect of the present application, step S34 is further:

[0143] S341, calculating the local density change of the integrated spectrum; determining the high-density area and the low-density area based on the local density change; in the high-density area, performing fine-grained binning on the corresponding integrated spectrum, and in the low-density area, performing coarse-grained binning on the corresponding integrated spectrum to obtain a discrete probability distribution;

[0144] S342, performing multi-scale decomposition on the discrete probability distribution using discrete wavelet transform to obtain wavelet coefficients after multi-scale decomposition;

[0145] S343. Based on the wavelet coefficients after multi-scale decomposition, construct the optimal transmission problem; use the Sinkhorn algorithm to solve the regularized optimal transmission problem to obtain the transmission plan and transmission cost; based on the transmission plan and transmission cost, calculate the Wasserstein distance at each scale.

[0146] In one embodiment of the present application, the comprehensive spectrum and the multidimensional probability distribution model are read, and the comprehensive spectrum is converted into a discrete probability distribution using an adaptive binning algorithm; the local density change of the spectrum is calculated, and fine-grained binning is used in high-density areas and coarse-grained binning is used in low-density areas. The binned discrete probability distribution is stored in the distribution cache of the FPGA.

[0147] Read the discrete probability distribution and multidimensional probability distribution models and perform multiscale decomposition: Use discrete wavelet transform to perform multiscale decomposition on the two distributions, select Daubechies wavelet as the basis function, and set the decomposition level to log2(N), where N is the number of sampling points of the distribution. Store the decomposed wavelet coefficients in the wavelet coefficient cache of the FPGA.

[0148] Read the wavelet coefficients after multi-scale decomposition and calculate the local Wasserstein distance at each scale. For each scale, construct the optimal transmission problem. Use the Sinkhorn algorithm to solve the regularized optimal transmission problem. Calculate the Wasserstein distance at each scale. Store the Wasserstein distance of each scale in the distance cache of the FPGA. Read the Wasserstein distance of each scale to achieve adaptive scale fusion. Construct a fusion weight learning model and use the adaptive boost (AdaBoost) algorithm to learn the optimal scale fusion weights using the distribution similarity labels in the historical data as the training set. Apply the learned weights and calculate the weighted average to obtain a preliminary global similarity measure. Store the preliminary global similarity measure in the similarity cache of the FPGA.

[0149] Read the preliminary global similarity measure and perform nonlinear correction. Build a radial basis function (RBF) network model. Use cross validation to select the optimal RBF kernel width. Train the RBF network to map the preliminary similarity measure to a more accurate similarity estimate. Store the corrected similarity measure in the corrected similarity buffer on the FPGA.

[0150] Read the corrected similarity metric and perform uncertainty quantification. Use the Monte Carlo dropout method to sample the RBF network multiple times and calculate the mean and variance of the similarity estimate. Construct a Bayesian confidence interval to quantify the uncertainty of the similarity estimate. Store the similarity estimate and its uncertainty information in the uncertainty buffer of the FPGA.

[0151] Read similarity estimates and their uncertainty information and perform adaptive threshold setting. Use extreme value theory to build a dynamic threshold model. Fit the generalized extreme value distribution based on historical data. Calculate the dynamic threshold at a given confidence level. Store the calculated dynamic threshold in the threshold cache of the FPGA. Read the similarity estimates in the dynamic threshold and uncertainty cache and perform decision making and feedback. Compare the similarity estimate with the dynamic threshold to determine if the distribution is significantly different. If so, trigger the distribution deviation correction mechanism, calculate the time series of similarity metrics, and detect trends and periodic patterns. Store the decision results and time series analysis results in the decision cache of the FPGA to guide subsequent distribution adjustments and system optimization.

[0152] This embodiment implements a multi-scale adaptive distribution similarity measurement algorithm, which improves the accuracy and robustness of distribution comparison. The application of the adaptive binning algorithm enables the discretization process to better retain the local characteristics of the distribution. The multi-scale decomposition technology, especially the use of discrete wavelet transform, enables the algorithm to capture the characteristics of the distribution at different scales. The calculation of the local Wasserstein distance, combined with the Sinkhorn algorithm, provides a more accurate and efficient local similarity measurement. The adaptive scale fusion mechanism learns the optimal fusion weight through the AdaBoost algorithm, which enhances the algorithm's adaptive ability to the importance of different scales. The nonlinear correction process uses the RBF network to effectively handle the nonlinear relationship in the similarity measurement. The introduction of uncertainty quantification technology, especially the Monte Carlo dropout method, provides a reliable confidence interval for similarity estimation. The adaptive threshold setting, based on extreme value theory, improves the robustness of the algorithm in different scenarios. The implementation of the decision-making and feedback mechanism enables the system to trigger correction in time according to the similarity analysis results and provide a basis for long-term optimization. The entire process is implemented on the FPGA, making full use of the hardware parallel processing capabilities. For example, multi-scale decomposition and local Wasserstein distance calculation can be performed in parallel on multiple processing units, which improves the calculation speed. The flexible architecture of FPGA also allows dynamic adjustment of computing resource allocation to adapt to distribution comparison tasks of different complexity. It not only improves the accuracy and efficiency of distribution similarity measurement, but also enhances the system's ability to adapt to dynamic changes in complex electromagnetic environments, providing a reliable basis for real-time distribution deviation detection and correction.

[0153] like Figure 5 As shown, according to one aspect of the present application, step S4 is further:

[0154] S41. Based on the short-time signal density and Wasserstein distance, the current electromagnetic environment complexity index is calculated; based on the electromagnetic environment complexity index, a resource allocation optimizer based on a genetic algorithm is used to dynamically adjust FPGA resource allocation to obtain an optimal resource allocation solution;

[0155] S42, dividing the corrected signal sequence into a predetermined number of subsequences according to the optimal resource allocation scheme; performing digital up-conversion, power control and waveform shaping in parallel on each subsequence to obtain a processed signal sequence;

[0156] S43, reading pre-stored antenna pattern data, and calculating the complex weight vector of each signal in the processed signal sequence based on the antenna pattern data and the preset target direction using the phased array antenna model; multiplying each signal in the processed signal sequence by its corresponding complex weight vector to obtain an input signal of each antenna array element; superimposing all input signals on each antenna array element to obtain a beamforming signal; wherein the number of elements of the complex weight vector is equal to the number of antenna array elements;

[0157] S44. Use a pre-stored nonlinear characteristic model of the digital-to-analog converter to calculate the pre-distortion value of the beamforming signal to obtain a pre-distorted beamforming signal; input the pre-distorted beamforming signal into a high-speed digital-to-analog converter to obtain an analog signal; use an analog low-pass filter to remove high-frequency spurs in the analog signal to obtain a filtered analog signal.

[0158] In one embodiment of the present application, the current electromagnetic environment complexity index is read, which is calculated based on the signal density and distribution deviation. A resource allocation optimizer based on a genetic algorithm is used to dynamically adjust FPGA resource allocation. An objective function is defined, which takes into account resource utilization, processing performance, and power consumption. The population is initialized, and each individual represents a resource allocation scheme. Selection, crossover, and mutation operations are performed to iteratively optimize the population. The fitness of each individual is evaluated, and the optimal individual is selected as the final resource allocation scheme. The optimal resource allocation scheme is written into the configuration register of the FPGA.

[0159] The resource allocation scheme and the corrected signal sequence are read to implement a parallel signal processing pipeline. According to the resource allocation scheme, the signal sequence is divided into several subsequences; for each subsequence, digital up-conversion, power control and waveform shaping are performed in parallel; digital up-conversion is implemented using complex sine multiplication to multiply the baseband signal with the local oscillator signal; power control is implemented using digital automatic gain control to adjust the signal amplitude according to the target power level. Waveform shaping is implemented using a finite impulse response filter to convolve the signal with the preset filter coefficients. The processed signal sequence is stored in the output buffer of the FPGA.

[0160] Read the processed signal sequence to implement digital beamforming. Use the phased array antenna model to assign a complex weight vector to each signal. The number of elements in the complex weight vector is equal to the number of antenna elements. Read the pre-stored antenna pattern data and calculate the complex weight vector for each signal based on the target direction. Multiply each signal with its corresponding complex weight vector to obtain the input signal for each antenna element. Superimpose all signals on each element to obtain the beamforming output. Store the beamforming output in the FPGA's digital-to-analog conversion buffer.

[0161] Read the digital signal and use digital pre-distortion technology to compensate for the nonlinear distortion of the digital-to-analog converter. Read the pre-stored nonlinear characteristic model of the digital-to-analog converter and calculate the pre-distortion value of the input signal based on the nonlinear characteristic model. Input the pre-distorted digital signal into the high-speed digital-to-analog converter. The digital-to-analog converter converts the digital signal into an analog signal. Use an analog low-pass filter to remove the high-frequency spurious generated during the conversion process. Send the filtered analog signal to the subsequent RF front-end circuit through the analog output interface of the FPGA.

[0162] Read the analog signal and perform real-time signal quality monitoring. Use an analog-to-digital converter to sample the output signal. Calculate the key performance indicators of the signal, such as signal-to-noise ratio, spurious suppression ratio, and phase noise. Compare the calculated performance indicators with the preset thresholds. If the performance indicators exceed the thresholds, trigger the adaptive correction mechanism. The adaptive correction mechanism adjusts the digital signal processing parameters in step S42, such as filter coefficients, gain control parameters, etc. Write the adjusted parameters to the control register of the FPGA for the next round of signal processing. Output the final analog radar signal to the external RF system.

[0163] In another embodiment of the present application, the current electromagnetic environment complexity index C is read from the state register of the FPGA, and the index is calculated based on the signal density ρ(t) and the distribution deviation W. The FPGA resource allocation is dynamically adjusted according to the electromagnetic environment complexity index C. A resource allocation optimizer based on a genetic algorithm is used to define an objective function F=αR+βP-γL, where R is resource utilization, P is processing performance, L is power consumption, and α, β, and γ are weight coefficients. The genetic algorithm is run to obtain the optimal resource allocation scheme A. A is written into the configuration register of the FPGA to reconfigure the allocation of logic units and storage units.

[0164] Read the resource allocation scheme A and the corrected signal sequence X' to implement a parallel signal processing pipeline. According to the resource allocation in the resource allocation scheme A, the corrected signal sequence X' is divided into several subsequences {X'1, X'2, ..., X' n}. For each subsequence X' i, performing digital up-conversion, power control, and waveform shaping in parallel. Digital up-conversion is implemented using complex sine multiplication: i (t) = x' i (t)*exp(j2πfct), where fc is the center frequency. Power control is implemented using digital automatic gain control (AGC): i (t)=G*y i (t), where G is the gain factor. Waveform shaping is achieved using a finite impulse response (FIR) filter: i (t)=z i (t)*h(t), where h(t) is the filter impulse response. The processed signal sequence W={w1(t), w2(t),...,w n (t)} is stored in the output buffer of the FPGA.

[0165] Read the processed signal sequence W to implement digital beamforming. Using the phased array antenna model, for each signal w i (t) Assign a complex weight vector a i = [a i1 , a i2 , ..., a iM ], where M is the number of antenna elements. Calculate the beamforming output: b(t)=Σ i=1 n Σ j=1 M a ij *w i (t). The synthesized signal b(t) is sent to the digital-to-analog converter (DAC) module of the FPGA.

[0166] Receive the digital signal b(t) and convert it into an analog signal s(t) through a high-speed DAC. Use digital pre-distortion technology to compensate for the nonlinear distortion of the DAC: b'(t)=F -1 [b(t)], where F is the nonlinear characteristic function of DAC, F -1 The inverse function of the compensation function is given by inputting the compensated digital signal b'(t) into the DAC to obtain the analog signal s(t). The analog signal s(t) is sent to the subsequent RF front-end circuit through the analog output interface of the FPGA.

[0167] This embodiment realizes highly flexible and high-performance signal processing and output control. The application of the resource allocation optimizer based on the genetic algorithm enables the system to dynamically adjust the FPGA resource allocation according to the complexity of the current electromagnetic environment. This adaptive optimization method takes into account multiple factors such as resource utilization, processing performance and power consumption, ensuring that the system can maintain optimal performance under different working conditions. The implementation of the parallel signal processing pipeline fully utilizes the parallel computing capability of the FPGA and improves the throughput of signal processing. The parallel execution of processing steps such as digital up-conversion, power control and waveform shaping not only improves the processing speed, but also enhances the system's ability to process complex signals. The application of digital beamforming technology, by simulating the working principle of phased array antennas, realizes precise control of the spatial characteristics of the signal, can flexibly adjust the directivity of the signal, and provides a powerful tool for simulating complex spatial electromagnetic environments. The introduction of digital pre-distortion technology effectively compensates for the nonlinear distortion in the digital-to-analog conversion process and improves the quality and fidelity of the output signal. The application of real-time signal quality monitoring and adaptive correction mechanism ensures the long-term stability and reliability of the system output by continuously monitoring key performance indicators and dynamically adjusting processing parameters. The system's ability to adapt to external environmental changes and internal performance drift is enhanced. The entire process is implemented on the FPGA, giving full play to the hardware advantages of the FPGA. For example, the resource allocation optimizer based on the genetic algorithm can take advantage of the reconfigurable characteristics of the FPGA to dynamically adjust the hardware resource allocation at runtime to achieve optimal utilization of computing resources. The parallel signal processing pipeline can be implemented through a large number of programmable logic units and DSP modules of the FPGA, and a dedicated hardware accelerator can be designed for each processing step to improve the processing speed. Digital beam synthesis can use the FPGA's multiplication and addition operator array to efficiently implement complex matrix operations and achieve real-time beam control. Digital pre-distortion technology can achieve high-speed, low-latency nonlinear correction through the FPGA's lookup table (LUT) and DSP module. Real-time signal quality monitoring and adaptive correction mechanisms can use the FPGA's parallel processing capabilities to calculate and evaluate multiple performance indicators at the same time, achieving a millisecond response time. In addition, the FPGA's high-speed interface resources are fully utilized, such as the high-speed digital-to-analog converter (DAC) interface to achieve high-bandwidth, low-latency analog signal output. The on-chip storage resources of FPGA are also optimized, such as storing key parameters such as beamforming weights and pre-distortion correction coefficients in internal memory, reducing external memory access latency. This FPGA-based implementation not only improves the efficiency and flexibility of signal processing and output, but also enhances the system's real-time adaptability and output quality control. The system can adjust the processing strategy and output characteristics in real time according to the dynamic changes of the complex electromagnetic environment, providing a highly realistic, controllable and high-performance signal source for electromagnetic environment simulation.

[0168] According to one aspect of the present application, step S41 is further:

[0169] S411. Based on the short-time signal density and Wasserstein distance, calculate the current electromagnetic environment complexity index; read the current resource utilization, processing performance and power consumption data, and construct a multi-objective optimization problem. The objective function includes maximizing resource utilization, maximizing processing performance and minimizing power consumption. Store the multi-objective optimization problem in the problem definition cache of the FPGA.

[0170] S412, read the multi-objective optimization problem and implement the improved non-dominated sorting genetic algorithm (NSGA-III). Initialize the population, and each individual represents a resource allocation scheme. The encoding scheme uses real number encoding to represent the resource proportion of each functional module. Calculate the objective function value of each individual. Perform non-dominated sorting and divide the population into different fronts. Store the initial population and its evaluation results in the population cache of the FPGA.

[0171] S413, read the current population and its evaluation results, and perform an adaptive crossover operation. Use an adaptive fuzzy controller to dynamically adjust the crossover probability. Design fuzzy rules based on population diversity and convergence degree, and apply simulated binary crossover (SBX) to generate offspring for the selected parent individual pairs. Store the generated offspring individuals in the offspring cache of the FPGA.

[0172] S414, read the offspring individuals and perform adaptive mutation operations. Construct a Gaussian process regression model to predict the impact of mutation on individual fitness. Adaptively adjust the mutation probability and mutation intensity based on the prediction results. Perform a polynomial mutation operation on each offspring individual. Store the mutated individuals back into the offspring cache of the FPGA.

[0173] S415, read the mutated offspring individuals, read the parent individuals from the population cache, and perform reference point-based selection operations. Generate a uniformly distributed reference point set in the target space, and calculate the distance from each individual to the nearest reference point. Combine the non-dominated sorting results and reference point association information to select the next generation population. Store the selected new generation population in the new population cache of the FPGA.

[0174] S416, read the new generation population and perform local search optimization. Use the Pareto local search (PLS) algorithm to perform neighborhood search for solutions on the Pareto frontier. Evaluate the objective function value of the neighborhood solution. Update the Pareto solution set. Store the optimized population back into the population cache of the FPGA.

[0175] S417, read the optimized population and implement dynamic constraint processing. Read the hardware constraint information and use the adaptive penalty function method to handle constraint violations. Dynamically adjust the penalty coefficient to balance feasibility and optimization goals. Re-evaluate the fitness of individuals in the population. Store the population evaluation results after processing constraints in the evaluation cache of the FPGA.

[0176] S418. Read the population evaluation results and perform convergence and diversity analysis. Calculate the hypervolume index to evaluate the convergence and diversity of the solution set; use the adaptive termination criterion to decide whether to continue iteration based on the hypervolume improvement rate and computing budget; if the termination condition is met, select the final Pareto optimal solution set. Write the optimal resource allocation plan into the configuration register of the FPGA and reconfigure the allocation of logic units and storage units. Store the statistical information of the convergence process in the optimization history cache of the FPGA for adaptive adjustment of subsequent optimization processes.

[0177] This embodiment implements a multi-objective adaptive resource allocation optimization algorithm, which improves the efficiency and flexibility of FPGA resource utilization. The construction of the multi-objective optimization problem takes into account key factors such as resource utilization, processing performance and power consumption, ensuring the comprehensiveness of the optimization. The application of the improved NSGA-III algorithm effectively handles the multi-objective optimization problem and converges quickly to the Pareto frontier while maintaining population diversity. Adaptive crossover operations and mutation operations enhance the exploration ability of the algorithm and improve the coverage of the search space. The reference point-based selection operation ensures the uniform distribution of the solution set in the target space and improves the diversity of decisions. The introduction of Pareto local search further optimizes the Pareto solution set and improves the quality of the solution. The dynamic constraint processing mechanism, especially the adaptive penalty function method, effectively balances feasibility and optimization objectives. Convergence and diversity analysis, combined with the hypervolume indicator, provide a reliable termination criterion and avoid unnecessary waste of computing resources. The entire process is implemented on the FPGA, making full use of the hardware acceleration capability. For example, population evaluation and local search can be executed in parallel, which improves the optimization speed. The reconfigurable nature of the FPGA allows the optimization strategy to be dynamically adjusted to adapt to resource allocation scenarios of different complexities. It not only improves the efficiency and flexibility of FPGA resource allocation, but also enhances the system's ability to adapt to changes in the complexity of the electromagnetic environment, provides efficient hardware support for the entire simulation system, and has an important impact on the overall performance and scalability of the system.

[0178] According to one aspect of the present application, step S43 is further:

[0179] S431, reading pre-stored antenna array geometric parameters and element characteristic data, constructing an antenna array response matrix based on the antenna array geometric parameters, element characteristic data and the processed signal sequence; decomposing the antenna array response matrix using a singular value decomposition method to obtain a decomposition result, including a left singular vector, a singular value matrix and a right singular vector;

[0180] S432, based on the decomposition result, calculate a projection matrix; apply the projection matrix to the processed signal sequence to obtain a projected signal;

[0181] S433, constructing a constraint matrix and a response vector based on the projected signal to form a multi-constraint optimization problem; solving the multi-constraint optimization problem using a Lagrange multiplier method to obtain an optimal weight vector;

[0182] S434, detecting a strong interference source in the processed signal sequence, and updating a constraint matrix based on the strong interference source; repeating step S433 based on the updated constraint matrix to obtain an updated weight vector; constructing a covariance matrix based on the updated weight vector; constructing a convex optimization problem based on the covariance matrix, and solving to obtain a robust weight vector;

[0183] S435, read the real-time signal data, perform weighted summation on each signal of the real-time signal data based on a robust weight vector to obtain a sum signal; based on the sum signal, use a time domain filter to process it to obtain a beamforming signal.

[0184] In one embodiment of the present application, the processed signal sequence and the pre-stored antenna array geometric parameters and element characteristic data are read to construct the antenna array response matrix A. The matrix A is decomposed using the singular value decomposition (SVD) method to obtain its left singular vector U, singular value matrix Σ and right singular vector V. The decomposition result is stored in the matrix decomposition cache of the FPGA.

[0185] Read the decomposition result and perform subspace projection. Use the orthogonality of matrix U to project the signal space into the noise subspace. Calculate the projection matrix P = I - UU H , where I is the identity matrix, H Represents conjugate transpose. Apply the projection matrix P to the input signal to suppress correlation interference. Store the projected signal in the projection signal buffer of the FPGA.

[0186] Read the projected signal and construct a multi-constraint optimization problem. Define the beam direction vector d(θ, φ), where θ and φ are the elevation angle and azimuth angle, respectively. Set the main lobe pointing constraint, null constraint, and side lobe level constraint. Construct the constraint matrix C and the response vector f. Formulate the optimization problem as minw H Rw,st C Hw=f, where w is the weight vector and R is the signal covariance matrix. The optimization problem is stored in the constrained optimization cache of the FPGA.

[0187] Read the optimization problem and solve it using the Lagrange multiplier method. Construct the Lagrange function L(w,λ)=w H Rw+λ H (C H wf), where λ represents the Lagrange multiplier. Calculate ΨL / Ψw and ΨL / Ψλ and set them to zero. Solve for the optimal weight vector w opt =R -1 C(C H R -1 C) -1 f. Use Cholesky decomposition to accelerate the matrix inversion operation. Store the calculated optimal weight vector in the FPGA weight cache.

[0188] Read the optimal weight vector w opt , perform adaptive beam nulling. Detect strong interference sources in the input signal. Update the constraint matrix C and add nulling constraints in the direction of the interference source. Repeat the optimization process to obtain the updated weight vector. Store the updated weight vector back to the FPGA weight cache.

[0189] Read the updated weight vector and perform robustness enhancement. Consider array errors and channel uncertainties to construct the covariance matrix of the weight vector. Apply convex optimization methods to minimize the worst-case performance loss. Solve the convex optimization problem to obtain a robust weight vector. Store the robust weight vector in the robust weight cache of the FPGA.

[0190] Read the robust weight vector and perform adaptive beamforming. Read the real-time signal data in the FPGA input buffer. Apply the robust weight vector to each signal sample for weighted summation. Implement a time domain filter to compensate for frequency selective fading. Store the beamformed output signal in the FPGA's beam output buffer.

[0191] Read the beamforming output signal and perform performance evaluation and adaptive adjustment. Calculate the signal-to-noise ratio (SNR) and signal-to-interference-plus-noise ratio (SINR) of the output signal. Compare with the preset threshold to determine the beamforming effect. If the performance does not meet the requirements, adjust the constraints of the optimization problem and return to the previous steps to re-execute the optimization. Store the performance evaluation results and adjustment parameters in the FPGA's performance log cache for long-term performance optimization and algorithm adaptation. Transmit the final beamforming output signal to the FPGA's digital-to-analog conversion (DAC) module for subsequent processing.

[0192] This embodiment implements an adaptive multi-constraint digital beamforming algorithm, which improves the accuracy and flexibility of beamforming. The application of singular value decomposition provides efficient decomposition of the antenna array response matrix, laying the foundation for subsequent processing. The subspace projection technology effectively suppresses correlation interference and improves the quality of signal processing. The construction of multi-constraint optimization problems takes into account key factors such as main lobe pointing, nulling and side lobe level, ensuring the comprehensiveness of beamforming. The application of Lagrange multiplier method provides an efficient method for solving constrained optimization problems. Adaptive beam nulling technology enhances the system's ability to suppress strong interference sources. Robustness enhancement processing takes into account array errors and channel uncertainties, improving the reliability of beamforming in actual environments. The introduction of time domain filters effectively compensates for frequency selective fading and improves signal quality. Performance evaluation and adaptive adjustment mechanisms ensure continuous optimization of beamforming effects. The entire process is implemented on FPGA, making full use of hardware parallel processing capabilities. For example, matrix operations and beamforming can be performed in parallel on multiple DSP units, improving the calculation speed. The reconfigurable nature of FPGA allows dynamic adjustment of beamforming strategies to adapt to electromagnetic environments of different complexities. This optimization not only improves the accuracy and efficiency of digital beamforming, but also enhances the system's ability to adapt to dynamic changes in complex electromagnetic environments, provides high-quality spatial filtering output for subsequent signal processing, and has a key impact on the performance and authenticity of the entire electromagnetic environment simulation system.

[0193] like Figure 6 As shown, according to one aspect of the present application, a complex electromagnetic environment simulation system based on FPGA, by constructing a single radar signal simulation module, each radar independently simulates the signal, and each radar competes with each other through the pulse rising edge within the competition time window of the comparison window to obtain the actual output signal pulse sequence. The FPGA includes a radar parameter modeling unit, a video pulse signal generation unit, a phase accumulator unit, a video pulse competition unit, a digital waveform output unit, and a microwave control unit.

[0194] like Figure 7As shown in the figure, the radar parameter modeling unit analyzes and calculates the modulation characteristics of the radar signal, and generates pulse stream data including repetition, pulse width, first pulse occurrence time, carrier frequency, amplitude, and intra-pulse modulation in real time; the video pulse signal generation unit generates a video pulse signal according to the three parameters of first pulse occurrence time, pulse width, and repetition in the full pulse description word after the start instruction is issued; the phase accumulator unit performs continuous phase accumulation on the radar signal according to the intra-pulse modulation information; the intra-pulse modulation information includes frequency and phase; the video pulse competition unit determines that the pulse leading edge that arrives first in the competition time window of the comparison window is the winning pulse, and the corresponding radar signal is the actual output signal at this moment; the comparison window is now transferred to the waiting time window, and when the pulse falls, the comparison window is transferred to the protection time window, and after the protection time is reached, it is transferred to the competition time window again, and the final output signal sequence is obtained by repeating the cycle; the digital waveform output unit obtains the digitalized sine wave amplitude by corresponding the radar signal phase accumulation result to the sine wave lookup table, and converts it into a usable radar intermediate frequency analog signal through a high-speed D / A converter; the microwave control unit generates a frequency synthesis and amplitude control signal according to the carrier frequency and amplitude information.

[0195] A signal simulation module is established for a single radiation source, including modeling of full pulse data, generation of video pulse signals and continuous phase accumulation. Multiple radar radiation source signals call multiple radar signal generation modules to simulate the signals of each radar in parallel. In the competition time window, the leading edge of the video pulse of each radar competes to determine the radar serial number of the current output, and the radar is used for the current microwave control and radar intermediate frequency signal output.

[0196] In another embodiment of the present application, a complex electromagnetic environment simulation method based on FPGA includes the following steps:

[0197] Step 1: The host computer sets the radar signal parameters, which include: repetition rate, pulse width, first pulse occurrence time, carrier frequency, amplitude, and intra-pulse modulation information. The host computer transmits the parameters to the FPGA through the Ethernet port;

[0198] Step 2, the radar parameter modeling unit performs radiation source first pulse preprocessing on the single radar signal parameters sent down, including calculating the carrier frequency, repetition rate, pulse width, amplitude and other parameters of the first pulse, and sends the preprocessing results of repetition rate and pulse width and the time of occurrence of the first pulse to the video pulse signal generation unit; after receiving the start signal, the radar parameter modeling unit waits for the video pulse signal generation unit to output the video pulse signal (including an original pulse and a delayed modulated pulse signal), the rising edge of the delayed modulated pulse signal triggers the simulation calculation of the pulse modulation parameters, and the falling edge of the original pulse signal triggers the simulation calculation of the carrier frequency, repetition rate, pulse width, amplitude and other parameters of the next pulse: when the pulse modulation parameters change linearly, the parameters can be updated once every clock cycle, and when the pulse modulation parameters change nonlinearly, the parameters can be updated once in the shortest 5 clock cycles. In this project, the internal operating clock of the FPGA uses 156.25MHz, and each cycle is 6.4ns. This indicator meets the system requirements.

[0199] Step 3, the video pulse signal generation unit receives the pulse width and repetition simulation results of step 2, generates the original video pulse according to the first pulse occurrence time and pulse width and repetition parameters after receiving the start signal, and stores the current pulse width and repetition parameters on the rising edge of the original video pulse for use by the pulse generation state machine; since the pulse width and repetition parameters of the next pulse are simulated after the falling edge of the current pulse, and the simulation calculation can be completed within 5 clock cycles, it is necessary to ensure that the repetition should be greater than the pulse width plus 5 clock cycles. In this project, the internal operating clock of the FPGA uses 156.25MHz, and each cycle is 6.4ns, which means that the pulse interval must be greater than 32ns, which meets the system requirements.

[0200] Step 4, the phase accumulator unit receives the simulation results of the intra-pulse frequency and phase modulation parameters in step 2, and performs continuous phase accumulation on the radar under the time domain control of the delayed modulated video pulse output in step 3, thereby ensuring the coherence of the radar signal;

[0201] Step 5. The video pulse competition unit receives the original video pulse signal output in step 3. The radar signal simulator of this project can simulate a maximum of 64 radar signals. Radars are numbered according to their priorities. Serial number 0 represents the highest priority, and serial number 63 represents the lowest priority. If the radars have the same priority, they are sorted by weight. Radars with smaller weights have higher numbers than radars with larger weights. Each radar corresponds to a video pulse signal. If the number of radars simulated in the scene is less than 64, the video pulse signals output by the radar signal generation modules of the insufficient number will always be at a low level. Figure 8As shown, after receiving the start signal, the video pulse competition unit enters the competition time window, in which the rising edges of 64 video pulse signals are compared in parallel pipelines, the leading edge of the pulse that arrives first is obtained, and the corresponding radar serial number is recorded and output. The radar signal is the radar intermediate frequency analog signal that should be actually output at present; once the winning pulse is obtained, it enters the waiting time window, the size of which is equal to the pulse width of the winning pulse; after the falling edge of the winning pulse arrives, it enters the protection time window, the window time is equal to the frequency synthesis switching time of the microwave system, and the protection time window is set to 1us in this project; after the protection time window ends, it enters the competition time window again to find the radar signal to be output at the next moment, and the window switching is repeated according to this process;

[0202] Step 6, the digital waveform output unit reads the phase accumulation result of step 4 corresponding to the radar serial number output in step 5, addresses the waveform memory through the phase code and outputs the corresponding amplitude code, obtains the corresponding signal waveform through the digital-to-analog conversion of the DA chip, and finally obtains the required radar intermediate frequency signal through the low-pass filter;

[0203] Step 7, the microwave control unit reads the corresponding carrier frequency and amplitude information calculated in step 2 according to the radar serial number output in step 5, and generates a frequency synthesis control code and an amplitude control code;

[0204] In step 5, pulse competition follows the following principles:

[0205] a) Based on the time of the first radar pulse, competition is based on the principle of first come first served;

[0206] b) When two or more radars appear at the same time and different radars have priority requirements, ensure that the radar with higher priority appears first in the competition process, and the others are discarded;

[0207] c) When multiple radar signals with the same priority compete at the same time, the pulse with the smallest repetition period is retained and the others are discarded;

[0208] d) In the protection time window, no competition comparison is performed on the rising edge of the arriving pulse. The protection time window is the minimum switching time of the digital frequency synthesis.

[0209] When the simulation scenario includes multiple radar radiation source signals, multiple radar signal generation modules are called, and the simulation processing of steps 2 to 4 is performed in parallel to independently generate the signals of each radar; in the video pulse competition unit, the front edge of each radar video pulse within the competition time window competes to determine the radar serial number currently output, and the parameters of the radar are used for the current microwave control and radar intermediate frequency signal output.

[0210] In one embodiment of the present application, taking the generation of 8 special-system radar signals as an example, the repetition period of each radar is set to 12μs, the pulse width is 0.5μs, the first pulse appearance time is 0μs, 1.5μs, 3μs, 4.5μs, 6μs, 7.5μs, 9μs, and 10.5μs respectively, and the output frequency is arbitrarily selected within the range of 0.3-18GHz and 33-40GHz. The special-system signal patterns are two intra-pulse frequency modulations, two intra-pulse phase modulations, one with staggered repetition frequency, one with agile carrier frequency, one with pulse width jitter, and one with amplitude scanning. The output RF signal is split into two paths. One path is connected to a spectrum analyzer to test the frequency, bandwidth and power of the output signal. The other path is connected to a real-time spectrum analyzer to test the repetition, pulse width, carrier frequency, amplitude, intra-pulse characteristics and pulse flow density of the output signal. The measured radar signal parameters are consistent with the set radar signal parameters. Tested by the real-time spectrum analyzer, the minimum pulse interval is 1μs, and the pulse flow density of the generated special system radar signal reaches 667,000 pulses / second.

[0211] In another embodiment of the present application, taking the generation of 64 radar signals (64 special systems) as an example, the repetition period of each radar is set to 32μs, the pulse width is 0.6μs, the first pulse appearance time is n (n from 0 to 31)μs, and the output frequency is arbitrarily selected in the range of 0.3-18GHz and 33-40GHz. The radar signal style can be arbitrarily selected between pulse width modulation, carrier frequency agility, phase modulation, nonlinear frequency modulation, linear frequency modulation and antenna amplitude scanning. The output RF signal is split into two paths, one connected to a spectrum analyzer to test the frequency, bandwidth and power of the output signal; the other connected to a real-time spectrum analyzer to test the repetition period, pulse width, carrier frequency, amplitude, intra-pulse characteristics and pulse flow density of the output signal. The measured radar signal parameters are consistent with the set radar signal parameters. Through the real-time spectrum analyzer test, all 64 radars have no lost output, the style is accurate, and the radar signal pulse flow density reaches 1 million pulses / second.

[0212] This embodiment does not need to generate the actual output pulse stream through the traditional sorting algorithm, but uses the rising edges of radar video pulses to compete with each other to determine the actual radar signal currently released. It can easily generate radar coherent signals with high pulse flow density in large-scale scenarios, which more truly reflects the characteristics of modern electromagnetic environment, which is dense, complex, interlaced and changeable. The modular operation of this method is convenient for expanding the scale of radar radiation source simulation. The competitive output mode of video pulses can improve the pulse flow density. The independent phase accumulator ensures the phase continuity of each radar signal, which provides a guarantee for the development, testing, performance evaluation, delivery acceptance and finalization of jamming equipment.

[0213] The present invention realizes high-fidelity generation and dynamic optimization of electromagnetic environment parameters. Through the comprehensive application of technologies such as kernel density estimation, adaptive bandwidth selection, parameter dependency tree construction and hierarchical parameter sampling, the system can accurately capture the true distribution and interdependence of parameters in complex electromagnetic environments. The introduction of the spatiotemporal series prediction model further enhances the system's ability to simulate dynamic changes in the electromagnetic environment. This parameter generation and optimization method not only improves the accuracy of the simulation, but also enhances the system's adaptability to complex and dynamic electromagnetic environments.

[0214] An efficient multi-level signal competition and dynamic adjustment mechanism is implemented. Through the application of technologies such as K-means clustering, in-group and out-group competition units, dynamic weight adjustment, and adaptive time windows, the system can intelligently process and dispatch a large number of complex radar signals. This multi-level competition mechanism not only improves the efficiency of signal processing, but also enhances the system's ability to respond to rapid changes in the electromagnetic environment, ensuring that the statistical characteristics of the simulated signal are highly consistent with the actual environment.

[0215] High-fidelity radar signal generation and real-time correction are achieved. Through the comprehensive application of technologies such as direct digital synthesis, digital pulse modulation, fast Fourier transform, real-time feature distribution verification and distribution deviation correction, the system can generate highly realistic radar signals and perform quality assessment and correction in real time. This closed-loop correction mechanism improves the authenticity and reliability of the analog signal and provides a high-quality signal source for subsequent electromagnetic environment analysis and testing.

[0216] Highly flexible and high-performance signal processing and output control are achieved. Through the application of genetic algorithm-based resource allocation optimization, parallel signal processing pipeline, digital beamforming, digital pre-distortion and real-time signal quality monitoring, the system can dynamically adjust the processing strategy according to the complexity of the electromagnetic environment to achieve efficient and accurate signal processing and output control. This adaptive processing and control mechanism not only improves the processing performance of the system, but also enhances the quality and reliability of the output signal.

[0217] The present invention makes full use of the hardware advantages of FPGA, such as parallel processing capability, reconfigurable characteristics, dedicated computing units (such as DSP modules, FFT IP cores) and on-chip storage resources. This FPGA-based implementation not only improves the computing efficiency and real-time performance of the overall system, but also enhances the flexibility and scalability of the system. The system can quickly adjust the hardware resource allocation and processing strategy according to different application requirements and electromagnetic environment characteristics to achieve the optimal balance between performance and power consumption.

[0218] The present invention successfully solves the key challenges in complex electromagnetic environment simulation. It can simulate various complex electromagnetic environments in a highly realistic, dynamically adjustable and efficient manner, providing strong technical support for applications such as radar system testing, electromagnetic compatibility analysis, and electronic countermeasure training. The modular design and FPGA-based implementation also make the system scalable and maintainable, and can be easily upgraded and optimized according to future needs. This comprehensive performance improvement has promoted the development of electromagnetic environment simulation technology and opened up new possibilities for research and application in related fields.

[0219] The preferred embodiments of the present invention are described in detail above; however, the present invention is not limited to the specific details in the above embodiments. Within the technical concept of the present invention, various equivalent transformations can be made to the technical solutions of the present invention, and these equivalent transformations all belong to the protection scope of the present invention.

Claims

1. A complex electromagnetic environment simulation method based on FPGA, characterized in that: The steps include: S1. Read the initial electromagnetic environment parameter set from the external database, and use the kernel density estimation method to build a multidimensional probability distribution model; based on the initial electromagnetic environment parameter set, build a dependency relationship diagram between parameters and generate a parameter dependency tree; Based on the parameter dependency tree and multidimensional probability distribution model, hierarchical parameter sampling is performed to obtain a sampling parameter set; the sampling parameter set is adjusted using the spatiotemporal sequence prediction model to obtain an optimized parameter set; S2, grouping the optimized parameter set to obtain clustering results; Based on the clustering results, an intra-group competition unit is constructed for each cluster, and an inter-group competition unit is implemented to obtain an output signal; Based on the output signal, a dynamic weight adjustment algorithm is executed, and an adaptive time window mechanism is implemented to output a reorganized signal sequence; S3. Based on the reorganized signal sequence, generate a corresponding digital waveform and implement digital pulse modulation to obtain a modulated signal sequence; based on the modulated signal sequence, calculate the signal spectrum and superimpose it to obtain a comprehensive spectrum; based on the comprehensive spectrum, sequentially execute real-time feature distribution verification and distribution deviation correction mechanism, and finally output the corrected signal sequence; S4, read the current electromagnetic environment complexity index, dynamically adjust FPGA resource allocation, and obtain the optimal resource allocation plan; Based on the optimal resource allocation scheme and the corrected signal sequence, the parallel signal processing pipeline and digital beamforming are sequentially executed to obtain a beamforming signal; based on the beamforming signal, digital-to-analog conversion is performed to output a final filtered analog signal; Step S1 is further as follows: S11, reading an initial electromagnetic environment parameter set from an external database, preprocessing the initial electromagnetic environment parameter set, including data cleaning and standardization, to obtain a preprocessed initial electromagnetic environment parameter set; wherein the initial electromagnetic environment parameter set includes parameter sets of a predetermined number of radars, each parameter set including repetition period, pulse width, carrier frequency, amplitude and phase information; S12, based on the preprocessed initial electromagnetic environment parameter set, calculating the kernel density estimation value of each sample point, accumulating the kernel density estimation value of each sample point, and obtaining an accumulation result; Based on the accumulated results, the probability density estimate is calculated and a complete multi-dimensional probability distribution model is constructed; S13. Based on the preprocessed initial electromagnetic environment parameter set, calculate the mutual information value of each pair of parameters; based on the mutual information value, construct the joint probability distribution and the edge probability distribution; calculate the mutual information of the joint probability distribution and the edge probability distribution as the edge weight of the graph; based on the mutual information, use the maximum spanning tree algorithm to construct a parameter dependency tree; S14, starting from the root node of the parameter dependency tree, using the inverse transform sampling method to generate a set of candidate values; Based on the candidate value set, the parent node is obtained; the sampling parameter set is generated by combining the parent node and the multidimensional probability distribution model; S15, based on the sampling parameter set, using a preconfigured time series model to obtain a time prediction result; Based on the sampling parameter set, spatial autocorrelation analysis is performed to calculate the spatial distribution pattern of the parameters; combining the time prediction results and the spatial distribution pattern, each parameter of the sampling parameter set is fine-tuned to obtain the optimized parameter set.

2. The complex electromagnetic environment simulation method based on FPGA according to claim 1 is characterized in that: Step S2 is further as follows: S21, initializing K cluster centers, and calculating the Euclidean distance between each signal in the optimized parameter set and each cluster center; based on the Euclidean distance, assigning each signal to the cluster center closest to it to obtain an assignment result; Based on the allocation results, the center point of each cluster is recalculated, and the allocation and center point calculation process is repeated until the clustering results converge or the maximum number of iterations is reached, and the final clustering results are output; S22. Based on the clustering result, using the priority queue data structure, construct an intra-group competition unit for each cluster to form a priority queue set; S23. Calculate the selection probability of each group based on the priority queue set; Based on the selection probability, the roulette wheel selection method is used to obtain the selected group; the head element of the priority queue of the selected group is obtained as the output signal of the current time step; S24, based on the output signal, calculating the output frequency distribution of each group of signals within a predetermined time window; calculating the Kullback-Leibler divergence between the output frequency distribution and the multidimensional probability distribution model; using the gradient descent method to update the weight of each group of signals to minimize the Kullback-Leibler divergence, and obtaining the output signal after the weight is updated; S25, based on the output signal after the weight is updated, using a sliding window method to calculate the short-term signal density; Based on the short-time signal density, the time window is adjusted to obtain an adjusted time window parameter; Based on the adjusted time window parameters, the output signal after the weight update is reorganized to obtain a reorganized signal sequence.

3. The complex electromagnetic environment simulation method based on FPGA according to claim 2 is characterized in that: Step S3 is further as follows: S31, generating a corresponding digital waveform using direct digital synthesis technology based on the parameters of the reorganized signal sequence; S32, reading the pulse width and repetition period parameters corresponding to the digital waveform, generating a rectangular function and a comb function; multiplying the digital waveform with the rectangular function and the comb function to obtain a modulated signal sequence; S33, based on the modulated signal sequence, segmenting each signal to obtain predetermined segment data; applying a fast Fourier transform algorithm to each segment data to calculate spectrum data; averaging all spectrum data to obtain power spectrum density; superimposing the power spectrum densities of all signals to obtain a comprehensive spectrum; S34, converting the integrated spectrum into a discrete probability distribution using an adaptive binning algorithm; calculating the Wasserstein distance between the discrete probability distribution and the frequency dimension distribution in the multidimensional probability distribution model; S35, determining whether the Wasserstein distance exceeds a preset threshold, and if so, using the optimal transmission theory to calculate a transmission plan from the current distribution to the target distribution, and fine-tuning each signal in the modulated signal sequence according to the transmission plan to obtain a corrected signal sequence; If it does not exceed, no correction is performed and the modulated signal sequence is directly output.

4. The complex electromagnetic environment simulation method based on FPGA according to claim 3 is characterized in that: Step S4 is further as follows: S41. Based on the short-time signal density and Wasserstein distance, the current electromagnetic environment complexity index is calculated; based on the electromagnetic environment complexity index, a resource allocation optimizer based on a genetic algorithm is used to dynamically adjust FPGA resource allocation to obtain an optimal resource allocation solution; S42, dividing the corrected signal sequence into a predetermined number of subsequences according to the optimal resource allocation scheme; performing digital up-conversion, power control and waveform shaping in parallel on each subsequence to obtain a processed signal sequence; S43, reading pre-stored antenna pattern data, and calculating the complex weight vector of each signal in the processed signal sequence based on the antenna pattern data and the preset target direction using the phased array antenna model; multiplying each signal in the processed signal sequence by its corresponding complex weight vector to obtain an input signal of each antenna array element; superimposing all input signals on each antenna array element to obtain a beamforming signal; The number of elements in the complex weight vector is equal to the number of antenna array elements; S44. Use a pre-stored nonlinear characteristic model of the digital-to-analog converter to calculate the pre-distortion value of the beamforming signal to obtain a pre-distorted beamforming signal; input the pre-distorted beamforming signal into a high-speed digital-to-analog converter to obtain an analog signal; use an analog low-pass filter to remove high-frequency spurs in the analog signal to obtain a filtered analog signal.

5. The complex electromagnetic environment simulation method based on FPGA according to claim 4 is characterized in that: Step S23 is further as follows: S231. Based on the priority queue set, calculate the feature vector of each queue, and use the exponential sliding average method to update the historical feature statistics of each queue; wherein the feature vector includes the queue length, the priority of the first element in the queue, and the variance of the priority of the queue elements; S232. Based on the feature vector and historical feature statistical information of each queue, a multi-criteria decision matrix is ​​constructed; based on the multi-criteria decision matrix, a normalized decision value is calculated; based on the normalized decision value, an entropy weight method is used to calculate the weight of each criterion; wherein the multi-criteria decision matrix includes signal priority, queue load balancing, and spectrum utilization; S233. Based on the multi-criteria decision matrix and the weight of each criterion, a weighted standardized decision matrix is ​​constructed, and an ideal solution and a negative ideal solution are determined; the distance from each queue to the ideal solution and the negative ideal solution is calculated; based on the distance from each queue to the ideal solution and the negative ideal solution, a relative proximity is calculated as a comprehensive score; S234. Use the Softmax function to convert the comprehensive score into a selection probability; based on the selection probability, execute the Monte Carlo tree search optimization selection strategy to obtain the search result; based on the search result, determine the selected priority queue, and obtain the head element from the selected priority queue as the output signal of the current time step.

6. The complex electromagnetic environment simulation method based on FPGA according to claim 4 is characterized in that: Step S12 also includes applying an adaptive bandwidth selection algorithm to optimize the multidimensional probability distribution model, specifically: S12a. Based on the multidimensional probability distribution model, calculate the cross-validation score of each sample point; accumulate the cross-validation scores of each sample point and take the average value as the final cross-validation score; S12b, obtaining the current bandwidth value, optimizing the bandwidth value using the gradient descent method to minimize the final cross-validation score, repeating the optimization process until convergence or reaching the maximum number of iterations, and obtaining the optimized bandwidth value; S12c. Based on the optimized bandwidth value, the multidimensional probability distribution model is optimized to obtain an optimized multidimensional probability distribution model.

7. The complex electromagnetic environment simulation method based on FPGA according to claim 4 is characterized in that: Step S33 is further as follows: S331, using an adaptive basis function selection algorithm to select a basis function from a predefined wavelet basis function library; based on the modulated signal sequence and the basis function, calculating the wavelet packet coefficients of the signal at different scales and frequency subbands; based on a preset optimal threshold, performing soft threshold processing on the wavelet packet coefficients to obtain denoised coefficients; S332, calculating the energy distribution of each frequency subband based on the denoised coefficients; Based on the energy distribution, the importance of the subband is evaluated using the information entropy criterion; Decompose subbands whose importance is higher than a preset threshold to improve frequency resolution; Merge subbands whose importance is lower than a preset threshold to reduce redundancy; generate optimized time-frequency representation based on the decomposed subbands and the merged subbands; S333, based on the optimized time-frequency representation, using a parameterized autoregressive model, calculating the power spectral density of each subband; Based on the power spectral density, multi-resolution spectrum fusion is performed to obtain a fused multi-resolution spectrum; super-resolution technology is used to improve the frequency resolution of the multi-resolution spectrum to obtain an enhanced multi-resolution spectrum; based on the enhanced multi-resolution spectrum, a deep learning model is used to generate a refined high-resolution spectrum; S334, based on the refined high-resolution spectrum, using Wavelet Rayleigh entropy to extract key texture features; Based on the key texture features, the shape factor and inter-peak relationship of the spectrum peaks are calculated; based on the shape factor and inter-peak relationship of the spectrum peaks, the support vector machine is used to classify the high-resolution spectrum to obtain the classification results; S335, selecting a template spectrum from a pre-trained spectrum template library based on the classification result; A dynamic time warping algorithm is used to align the pre-stored observed spectrum and template spectrum; based on the aligned observed spectrum and template spectrum, a weighted average is calculated to obtain a fused spectrum; an adaptive filter is used to process the fused spectrum to obtain the final integrated spectrum.

8. The complex electromagnetic environment simulation method based on FPGA according to claim 4, characterized in that: Step S34 is further as follows: S341, calculating the local density change of the integrated spectrum; determining the high-density area and the low-density area based on the local density change; in the high-density area, performing fine-grained binning on the corresponding integrated spectrum, and in the low-density area, performing coarse-grained binning on the corresponding integrated spectrum to obtain a discrete probability distribution; S342, performing multi-scale decomposition on the discrete probability distribution using discrete wavelet transform to obtain wavelet coefficients after multi-scale decomposition; S343. Based on the wavelet coefficients after multi-scale decomposition, construct the optimal transmission problem; use the Sinkhorn algorithm to solve the regularized optimal transmission problem to obtain the transmission plan and transmission cost; based on the transmission plan and transmission cost, calculate the Wasserstein distance at each scale.

9. The complex electromagnetic environment simulation method based on FPGA according to claim 4, characterized in that: Step S43 is further as follows: S431, reading pre-stored antenna array geometric parameters and element characteristic data, and constructing an antenna array response matrix based on the antenna array geometric parameters, element characteristic data and the processed signal sequence; Decomposing the antenna array response matrix using a singular value decomposition method to obtain decomposition results including left singular vectors, singular value matrices and right singular vectors; S432, based on the decomposition result, calculate and obtain a projection matrix; Applying the projection matrix to the processed signal sequence to obtain a projected signal; S433, constructing a constraint matrix and a response vector based on the projected signal to form a multi-constraint optimization problem; The Lagrange multiplier method is used to solve the multi-constrained optimization problem and obtain the optimal weight vector; S434, detecting a strong interference source in the processed signal sequence, and updating a constraint matrix based on the strong interference source; Based on the updated constraint matrix, repeat step S433 to obtain an updated weight vector; based on the updated weight vector, construct a covariance matrix; Based on the covariance matrix, a convex optimization problem is constructed and the robust weight vector is obtained by solving it. S435, reading the real-time signal data, and performing weighted summation on each signal of the real-time signal data based on a robust weight vector to obtain a summation signal; Based on the summed signal, a time domain filter is used for processing to obtain a beamforming signal.

Images