Anti-interference design method based on multi-element mixed electromagnetic interference

Abstract

The application relates to the technical field of electronic signal processing, and discloses an anti-interference design method based on multi-element mixed electromagnetic interference, which establishes a mixed model of a useful signal static sparse dictionary and a parameterized atomic generating function of an interference signal; initial estimation of interference parameters is obtained by utilizing discrete anchor point dictionary matching; a joint optimization objective function containing a data fidelity term and a sparse constraint term is constructed; initial estimation values are used for initialization, and alternating iteration solving is executed based on a trust region constraint; useful signal sparse coefficients, interference parameter sets and amplitudes are alternately updated by minimizing the objective function, wherein the interference parameters are updated in a multi-element continuous parameter space containing time delay and frequency shift based on a trust region method to adaptively match waveform deformation; and finally, the useful signal is reconstructed according to the converged sparse coefficients and the static dictionary and is output. The application solves the problem of mixed interference separation under multi-system coexistence, and improves the parameter estimation precision and the reliability of algorithm convergence.

Description

Technical Field

[0001] This invention relates to the field of electronic signal processing technology, specifically to an anti-interference design method based on multi-electromagnetic interference. Background Technology

[0002] As smart home devices become increasingly integrated, composite electronic devices such as speakers, fans, and lights are becoming more common. These devices integrate motor and electronic control systems, audio power amplification systems, and Bluetooth or Wi-Fi wireless communication systems within a compact space. During operation, complex electromagnetic coupling phenomena exist between different subsystems. For example, high-order harmonic noise generated by variable frequency motor drives and in-band leakage of wireless radio frequency signals can interfere with the clarity of audio signals or the stability of communication links.

[0003] To address electromagnetic interference (EMI) issues in multi-system coexistence scenarios, existing technologies employ traditional frequency domain filters or signal processing methods based on fixed notch filters for suppression. However, in devices such as audio equipment, fans, and lights, changes in motor speed cause interference frequency drift, and near-field coupling effects between circuit boards can lead to nonlinear distortion and time-delay jitter in the interference waveform. Existing linear filtering methods struggle to establish accurate mathematical models to characterize these non-stationary interference signals with time-varying, frequency-shifting, and waveform-distorting characteristics. This results in insufficient fitting accuracy, incomplete interference cancellation, or unintended damage to the useful signal spectrum when dealing with dynamically changing interference from heterogeneous subsystems.

[0004] To address dynamic interference, existing technologies attempt to employ adaptive filtering algorithms for parameter tracking. However, when faced with a complex parameter space encompassing multiple dimensions such as time delay, frequency, and waveform shape, the constructed optimization objective function typically exhibits highly non-convex characteristics. Traditional gradient descent algorithms, lacking effective constraints, are prone to oscillations or even divergence during the search process in high-dimensional parameter spaces, making it difficult to guarantee the algorithm's convergence stability and thus unable to track and eliminate subtle waveform deformations in interference signals.

[0005] Furthermore, existing parameter estimation methods are highly sensitive to the selection of initial values. In low signal-to-interference ratio (SIR) environments with severe multi-system interference, the parameter search space is riddled with local extremum traps. Due to the lack of a mechanism combining global search and local refinement, existing algorithms are prone to getting trapped in local optima due to improper initial value selection, failing to lock onto the true interference parameters. This limits the reliability of signal separation and makes it difficult to meet the requirements of high-quality audio fans and lights for pure sound quality and stable control. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention provides an anti-interference design method based on multi-electromagnetic interference, which solves the problem that traditional methods are unable to accurately model and stably separate complex mixed interference with time-varying frequency shift and waveform deformation characteristics generated between multiple heterogeneous subsystems such as electronic control, audio, and wireless systems in compact integrated devices such as speakers, fans, and lights.

[0007] To achieve the above objectives, the present invention provides the following technical solution: An anti-interference design method based on multi-electromagnetic interference is proposed. This method first establishes a mathematical model of the mixed signal, representing the received signal as a linear superposition of a useful signal, a parameterized interference signal, and additive noise. For the useful signal, a static sparse dictionary is constructed, utilizing the sparsity characteristics of the useful signal in a specific transform domain for representation. For the parameterized interference signal, an atomic generating function is defined. This atomic generating function establishes a nonlinear mapping from the low-dimensional parameter space to the high-dimensional signal sample space based on a multi-electromagnetic continuous parameter space containing time delay, frequency shift, and waveform deformation dimensions.

[0008] To address the sensitivity of non-convex optimization problems to initial values, this invention utilizes atomic generating functions to construct a discrete anchor point dictionary. By calculating the correlation between the received signal and the anchor point dictionary, a gridded search is performed in the parameter space to obtain the initial estimate set of interference parameters and initial amplitude estimates. This process provides a reliable globally optimal attraction region for subsequent refined solutions.

[0009] Based on this, this invention establishes a joint optimization objective function comprising a data fidelity term and a useful signal sparsity constraint term. The data fidelity term measures the energy difference between the reconstructed signal and the received signal, while the sparsity constraint term constrains the sparsity of the useful signal. Initialization is performed using the aforementioned initial estimates, and alternating iterative solutions are executed based on trust region constraints. This solution process minimizes the joint optimization objective function, alternately updating the useful signal sparse coefficient vector, the interference parameter set, and the interference amplitude vector. The update of the interference parameter set is performed in a multivariate continuous parameter space based on the trust region method to adaptively match the waveform deformation of the interference. Finally, the useful signal estimate is reconstructed and output based on the final useful signal sparse coefficient vector after iterative convergence and combined with a static sparse dictionary.

[0010] Furthermore, the parameterized interference signal is modeled as a linear superposition of multiple interference components, each of which is uniquely determined by its corresponding complex amplitude and a parameter vector containing time delay, frequency shift, and waveform deformation dimensions. The static sparse dictionary is generated based on the physical layer parameters of the communication system and consists of basis vectors arranged in columns. The basis vectors can be selected from the inverse discrete Fourier transform matrix or an overcomplete Gabor frame. The useful signal is represented as a linear combination of this static sparse dictionary and the sparse coefficient vector.

[0011] To improve the efficiency and accuracy of initial parameter acquisition, this invention first determines the search space range of interference parameters and generates a grid set according to a preset resolution step size when acquiring the initial estimate. The grid points are mapped to normalized interference atom vectors using an atom generation function, forming an anchor point dictionary. The acquisition process employs a cyclic matching pursuit strategy: the received signal is initialized as a residual vector; the cross-correlation coefficient between the residual and the anchor point dictionary is calculated through vector inner product operation; the grid parameter at the point with the maximum cross-correlation modulus is selected as a coarse estimate of the current component; the initial complex amplitude is calculated based on orthogonal projection; and the reconstructed component is subtracted from the residual until all interference components are acquired.

[0012] In the alternating iterative solution phase, this invention employs a step-by-step optimization strategy. For updating the sparse coefficient vector of the useful signal, the interference parameters and amplitudes determined in the previous iteration are used to construct an equivalent observation vector after interference cancellation. Then, a coefficient vector that can approximate this equivalent observation vector and satisfy the sparsity constraint is searched within the spanned space of the static sparse dictionary.

[0013] For updating the set of interference parameters, this invention introduces a trust region mechanism to handle highly nonlinear parameter manifold optimization. Specifically, the sparse coefficients of the useful signal are fixed, and the interference observation residuals are calculated. For each interference component, a local quadratic approximation model is constructed in the neighborhood of the current parameter point, and the optimal correction step size, constrained by the trust region radius, is solved. Subsequently, the ratio of the actual decrease in the objective function to the model's predicted decrease is calculated, and the trust region radius is dynamically adjusted based on this ratio to determine whether to accept the correction step size. This mechanism effectively avoids the iteration process from getting trapped in local extrema or diverging, ensuring accurate tracking of time delay, frequency shift, and deformation parameters.

[0014] For updating the interference amplitude vector, this invention uses the updated parameter set to regenerate the time-domain waveform vector to construct a dynamic interference basis matrix. The interference observation residuals are orthogonally projected onto the subspace spanned by this dynamic basis matrix using the least squares principle. By solving the normal equation system, the complex amplitudes of all interference components are jointly corrected, thereby achieving the global optimum of amplitude estimation.

[0015] Finally, in the reconstruction output stage, after the iterative process meets the convergence condition, the final useful signal sparse coefficient vector is extracted, and matrix-vector multiplication is performed using a static sparse dictionary to reconstruct the useful signal time-domain waveform that only contains the characteristics of the static dictionary, thereby achieving effective filtering of multivariate mixed interference.

[0016] This invention provides an anti-interference design method based on multi-electromagnetic interference. It has the following beneficial effects: 1. This invention establishes a parameterized interference atom generation model by constructing a multivariate continuous parameter space that includes time delay, frequency shift, and waveform distortion dimensions. Compared with traditional filters or fixed notch filters, this technology can characterize complex interference signals with frequency drift (such as caused by motor speed change) and waveform distortion (such as caused by switching noise) inside the audio fan light, thus improving the fitting accuracy and cancellation capability of dynamic interference from electromechanical and power drive subsystems.

[0017] 2. This invention adopts an alternating iterative solution strategy based on trust region constraints. When updating the interference parameters, a local quadratic approximation model and an adaptive adjustment mechanism for the trust region radius are introduced to overcome the oscillation or divergence problems commonly encountered in the optimization process of high-dimensional parameter space. This ensures the convergence stability of the algorithm under a non-convex objective function, thereby enabling the tracking of subtle waveform deformations of the interference signal.

[0018] 3. This invention utilizes a discrete anchor point dictionary for coarse capture initialization of interference parameters, combined with subsequent continuous domain fine optimization, forming an estimation architecture that combines global search and local refinement. In complex parameter spaces with mixed interference from multiple systems, it can provide reliable initial values ​​within the globally optimal attraction domain for the iterative process, avoiding the algorithm from getting trapped in local extrema and ensuring the reliability of signal separation under low signal-to-interference ratio conditions. Attached Figure Description

[0019] Figure 1 A flowchart illustrating the overall process of an anti-interference method based on multi-electromagnetic interference provided in an embodiment of the present invention; Figure 2 This is a detailed flowchart of the coarse capture of interference parameters based on anchor point matching in an embodiment of the present invention; Figure 3 This is a schematic diagram of the alternating iterative solution logic based on trust region constraints in an embodiment of the present invention. Detailed Implementation

[0020] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0021] See attached document Figure 1This invention provides an anti-interference design method based on multi-electromagnetic interference, which operates in an electronic device including a radio frequency receiving front-end, an analog-to-digital converter (ADC), and a digital signal processing unit. The radio frequency receiving front-end is configured to capture analog signals in the electromagnetic environment, the ADC is configured to convert the analog signals into discrete digital signals, and the digital signal processing unit is configured to execute computer-readable instructions to implement the following steps. The method includes steps S1 to S5.

[0022] In step S1, a hybrid signal model and a hierarchical heterogeneous dictionary are constructed. The digital signal processing unit establishes a mathematical model of the received signal, which represents the received signal as a linear superposition of the useful signal, parameterized interference signal, and additive noise. For the useful signal, a static sparse dictionary is constructed according to a preset communication protocol, so that the useful signal is represented as a sparse coefficient vector under this dictionary. For the parameterized interference signal, an atom generation function based on a continuous parameter space is defined. The continuous parameter space includes time delay parameters, frequency shift parameters, and waveform deformation parameters. The interference signal is represented as a linear combination of multiple parameterized atoms generated by different parameters.

[0023] In step S2, coarse acquisition of interference parameters based on anchor point matching is performed. A discrete grid is generated within the continuous parameter space, and an anchor point dictionary containing multiple anchor point atoms is constructed based on the grid. The correlation between the received signal and each anchor point atom in the anchor point dictionary is calculated, and the parameters corresponding to the correlation peak are selected as the initial estimation set of the interference parameters. Simultaneously, initial amplitude estimates are obtained.

[0024] In step S3, a joint parameterized deformation optimization model is constructed. A joint optimization objective function is established, which includes a data fidelity term and a useful signal sparsity constraint term. The data fidelity term is used to measure the error between the received signal and the reconstructed signal, and the useful signal sparsity constraint term is used to constrain the sparsity of the useful signal under the static sparse dictionary.

[0025] In step S4, an alternating iterative solution is performed based on the trust region constraint. The useful signal sparse coefficient vector, the set of interference parameters, and the interference amplitude vector are updated alternately through iterative loops. In a single iteration, the set of interference parameters and the interference amplitude vector are first fixed, and the useful signal sparse coefficient vector is solved by minimizing the joint optimization objective function. Then, based on the current residual signal, the parameter update step size is solved within the trust region centered on the current interference parameter, and the trust region radius is adaptively adjusted according to the decrease in the objective function value, thereby updating the interference parameter set. Finally, based on the updated interference parameter set, the interference amplitude vector is updated using the least squares method. This process is repeated until the preset convergence condition is met.

[0026] In step S5, signal separation and reconstruction are performed. Based on the final useful signal sparse coefficient vector obtained after iterative convergence in step S4, the useful signal estimate is reconstructed. Based on the final interference parameter set and the final interference amplitude vector, the interference signal estimate is reconstructed. The digital signal processing unit outputs the useful signal estimate as the signal after anti-interference processing.

[0027] In step S1, the digital signal processing unit first performs mathematical modeling of the mixed signal. This process aims to abstract the complex electromagnetic environment signals received by the physical layer into a computable mathematical vector form, clarify the superposition relationship of each signal component, and provide a mathematical basis for subsequent signal separation. Specifically, the RF receiving front-end performs down-conversion and analog-to-digital conversion on the analog signal to generate a discrete-time baseband signal. The digital signal processing unit truncates the signal to a length of... The sampling sequence is used to construct the received signal vector. Received signal vector It is modeled as a linear superposition of the useful signal, heterogeneous interference signal, and environmental noise, and its mathematical expression is as follows: ; in, Represents the received signal vector, whose elements Corresponding to the Complex observations at each sampling time, .

[0028] This represents the desired received signal vector. This signal originates from the built-in wireless communication receiving subsystem of the speaker fan light (specifically, a Bluetooth audio receiving module or a Wi-Fi smart control module). Because this wireless communication receiving subsystem follows standard wireless transmission protocols, therefore... It has a predefined modulation format (such as GFSK for Bluetooth or OFDM for Wi-Fi) and a strict frame structure. In this embodiment, the useful signal vector It is assumed that it exhibits sparsity within a specific transform domain, meaning that its energy is concentrated on a small number of transform coefficients. This sparsity is the physical basis for subsequent extraction using a static dictionary.

[0029] This represents the interference signal vector originating from the electromechanical and power drive subsystems within the device (specifically, the brushless motor inverter drive unit or the Class D audio power amplifier unit). Unlike random noise, the interference signal vector... The waveform structure and mathematical laws are deterministic, but its specific parameters (such as arrival time, carrier frequency, modulation slope, etc.) are unknown at the receiving moment. The electromechanical and power drive subsystem and the wireless communication receiving subsystem operate in the same or overlapping frequency bands, leading to… and Aliasing occurs in both the time and frequency domains. Interference signal vector. The energy is usually higher than that of the useful signal vector. Its energy exhibits strong interference characteristics.

[0030] This represents an additive white Gaussian noise vector, used to characterize receiver thermal noise and background ambient noise. It is assumed that the noise components follow a zero mean and a variance of . The noise components are circularly symmetric complex Gaussian distributions, and the noise components between each sampling point are statistically independent.

[0031] By establishing the above model, this invention transforms the physical-level anti-interference problem into a mathematical signal decomposition problem, that is, under known... And only known and Given the structural characteristics (rather than specific numerical values), from Accurate recovery .

[0032] After completing the mixed-signal modeling, the digital signal processing unit performs the construction step of the static dictionary of useful signals. This step utilizes prior protocol information from the wireless communication receiving subsystem to construct vectors for sparse representation of useful signals. Static sparse dictionary .

[0033] Specifically, based on the preset physical layer parameters of the wireless communication receiving subsystem, including subcarrier spacing, symbol period, modulation scheme, and pilot distribution, a set of basis vectors is generated. These basis vectors are then arranged column-wise to form a static sparse dictionary. .in, The number of signal sampling points. This represents the total number of atoms in the dictionary. Each column vector of the static sparse dictionary... ( ) represents a predefined signal base waveform.

[0034] In this embodiment, for useful signals employing Orthogonal Frequency Division Multiplexing (OFDM), a static sparse dictionary is used. It is constructed as an inverse discrete Fourier transform (IDFT) matrix or an overcomplete Gabor framework. In this case, the column vectors of the dictionary correspond to the time-domain waveforms of subcarriers at different frequencies. Based on this static sparse dictionary, the useful signal vector... Represented as a linear combination of dictionary atoms: ; in, This represents a sparse coefficient vector. Because in actual transmission, some subcarriers are not activated (e.g., guard intervals), or the signal energy is concentrated in a specific transform domain (e.g., the time-frequency domain), the sparse coefficient vector... Satisfies the sparsity assumption, i.e. The number of non-zero elements in a numerator is much smaller than its total dimension. ( , (This indicates that the signal is much smaller than the target signal). This sparsity property is the mathematical basis for distinguishing useful signals from non-sparse noise and structured interference signals in subsequent joint optimization. Static sparse dictionary It remains constant throughout the signal processing process and does not update as the received signal changes.

[0035] After constructing the static dictionary of the useful signals, the digital signal processing unit further performs the parameterized manifold definition step for the interference signals. Unlike the representation method of the useful signals using a fixed discrete basis, this embodiment adopts a manifold modeling method based on a continuous parameter space to address the time-varying and parameter uncertainties of heterogeneous interference signals (especially dynamic harmonics generated by motor frequency conversion drives or switching transient noise of power amplifier circuits).

[0036] Specifically, the digital signal processing unit defines the atom generation function. This function establishes a nonlinear mapping from a low-dimensional parameter space to a high-dimensional signal sample space. The parameter space consists of continuously varying parameter vectors. Zhang Cheng, It includes three key dimensions that determine the physical characteristics of interference waveforms: Delay parameters : Indicates the arrival time or center position of the interference pulse within the observation time window, reflecting the translational characteristics of the interference in the time domain.

[0037] Frequency shift parameters This indicates the offset of the carrier frequency or center frequency of the interference signal, reflecting the shifting characteristics of the interference in the frequency domain.

[0038] Waveform deformation parameters This term describes the frequency modulation structure or envelope shape within an interference signal. It is used to describe pulse width modulation (PWM) interference or switching transient noise commonly found in audio fan and light applications. This can specifically refer to the duty cycle change rate of the PWM signal, the degree of nonlinear distortion at the pulse edges, or the attenuation factor of switching ringing. This differs from simply changing the signal position. and different, The changes reflect the distortion of the interference waveform shape caused by motor load fluctuations or the influence of circuit board distributed parameters.

[0039] Based on the above definition, the interference signal vector Modeled as The linear combination of the interference components has the following discrete-time mathematical expression: ; in, Sampling time; The sampling interval; For the first The complex amplitude of each interference component; For the first The parameter vector of each interference component.

[0040] To fully disclose this technical solution and support the claims, a typical dynamic frequency drift interference (such as frequency conversion noise generated during motor acceleration) is used as an example, and the atomic generation function is described. The specific mathematical form is defined as follows: ; in, Indicates by The generated interfering atoms at time Complex values; The time delay parameter represents the interference signal; The frequency shift parameter represents the interference signal; The waveform deformation parameter representing the interference signal; Indicates A normalized time-domain envelope function centered on the perturbed atom (e.g., a rectangular window function or a Gaussian window function) is used to limit the effective duration of the perturbed atom; Represented by natural constant An exponential function with base 0; Represents the imaginary unit, satisfying ; It represents pi (π).

[0041] Through this parameterization, all interfering atoms constitute a smooth manifold in the complex Hilbert space. The subsequent interference separation process is equivalent to searching for an optimal set of parameter points on this manifold. This allows the generated waveform to fit the interference components in the received signal to the greatest extent possible. A continuously varying waveform deformation parameter is introduced. This allows the model to cover disturbance patterns with arbitrary slopes or widths, thereby overcoming the basis mismatch problem caused by parameter discretization errors in traditional fixed-grid dictionaries.

[0042] See attached document Figure 2In step S2, to overcome the shortcomings of non-convex optimization problems, such as high sensitivity to initial values ​​and susceptibility to local extrema, the digital signal processing unit first performs the generation of a discrete anchor grid. This step aims to discretize the continuous infinite parameter space into a finite searchable set, thereby providing global guiding anchors for subsequent fine-grained optimization.

[0043] Specifically, the digital signal processing unit first determines the search space range of the interference parameters. This range is determined by the characteristics of the physical channel and prior knowledge. For the parameter vector... Its value boundaries are defined as follows: Delay parameters The range of values ​​is It covers the entire observation time window; Frequency shift parameters The range of values ​​is ,in The sampling rate covers the baseband bandwidth of the receiver; Waveform deformation parameters The range of values ​​is This range is set according to the electrical characteristics of the electronic control system (for example, the upper and lower limits are set according to the PWM carrier frequency variation range of the motor driver or the switching frequency jitter range of the audio power amplifier).

[0044] Subsequently, the digital signal processing unit searches the search space range according to a preset resolution step size. Perform gridded sampling. Define the time delay step as... The frequency shift step size is The deformation step size is The step size setting criterion is based on the fuzzy function characteristics of the interfering atoms, ensuring that the correlation between adjacent anchor points stored in the grid meets a preset threshold, so as to prevent real interference signals from falling into the grid gaps and causing missed capture.

[0045] Based on the above step size, construct a mesh set. : ; in, All are integer indices.

[0046] Using the atom generation function defined in step S1 , grid set Each parameter point in the vector is mapped to a corresponding normalized perturbation atom vector. All generated atom vectors constitute the anchor point dictionary. : ; in, This represents the total number of atoms in the anchor point dictionary (i.e., the total number of grid points). Corresponding to the Normalized anchor point vectors generated by grid parameters. Since the parameter space contains three dimensions, the anchor point dictionary... Typically, it is a highly overcomplete matrix. This anchor point dictionary is not merely a static set of waveforms, but a structured sampling representation of the parameter space, transforming the originally complex nonlinear parameter estimation problem into a linear search problem for discrete grid points.

[0047] After constructing the discrete anchor point grid, the digital signal processing unit performs an initial parameter matching and locking step. This step employs serial interference cancellation logic to strip away the strongest interference components one by one in the discrete anchor point space, thereby providing reliable initial parameter estimates for subsequent continuous domain fine-grained optimization.

[0048] Specifically, the digital signal processing unit first performs an initialization operation, defining a residual vector. And assign it the value of the original received signal vector. At the same time, an empty initial parameter set is established. and empty initial magnitude vector Subsequently, the invention initiates a cyclical process to capture them one by one. There are 1 interference component, of which This is the preset total number of interference components. In this loop, a variable is used... ( () refers to the currently being processed number ) Index of each interference component.

[0049] In response to the During the acquisition of each interference component, the digital signal processing unit calculates the residual vector from the previous stage. With anchor dictionary Each normalized anchor vector The cross-correlation coefficient. This calculation traverses the entire grid index. ( The aim is to find dictionary atoms that best match the current residual signal waveform structure. Anchor indices with the largest cross-correlation modulus values ​​are selected. The grid parameters corresponding to the index Locked as number Rough parameter estimates for each interference component .

[0050] After the parameters are locked, the digital signal processing unit calculates the complex amplitude of the interference component based on the principle of orthogonal projection. The initial complex amplitude of each interference component The calculation formula is as follows: ; in, Indicates the first The initial complex amplitude of each interference component; This represents the conjugate transpose operation, used to calculate the dot product of vectors; Indicates capturing the first The residual vector of the previous level before each interference component (when) At that time, it is the original received signal.

[0051] After obtaining the amplitude and waveform parameters, the digital signal processing unit updates the residual vector by subtracting the reconstructed first value from the current residual signal. The strong interference component is used to eliminate its influence on subsequent weak interference components (i.e., the first interference component). The masking effect of the search (including the first and subsequent interference components). The residual update formula is as follows: ; in, This represents the normalized anchor vector selected from the anchor dictionary that has the highest correlation with the current residual vector; Indicates capturing and stripping the first The updated residual vector output after each interference component.

[0052] Repeat the above process until... The digital signal processing unit locks all parameters Store in the initial parameter set All calculated amplitudes Store the initial amplitude vector Although the coarse parameters output in this step are limited by quantization errors due to grid resolution, they are close enough to the convex neighborhood of the global optimum, thus ensuring that subsequent algorithms can converge.

[0053] In step S3, the digital signal processing unit establishes a joint optimization objective function. This process aims to overcome the quantization error introduced by grid discretization in step S2, and simultaneously complete the sparse reconstruction of the useful signal and the fine fitting of the interference signal within the same mathematical framework.

[0054] Specifically, unlike traditional cascaded processing (i.e., filtering before reconstruction) which leads to useful signal impairment or residual interference, this invention proposes a joint parameterized deformation optimization strategy. This strategy transforms the received signal decomposition task into a hybrid optimization problem: For useful signals, find their place in the static sparse dictionary. The optimal sparse representation under the given conditions; For interference signals, find their optimal waveform parameter points on a continuous parametric manifold.

[0055] To achieve the above objectives, the digital signal processing unit constructs the following joint objective function. The function consists of a weighted average of a data fidelity term and a sparsity regularization term: ; in, This represents the minimization operation, which is to find the joint objective function. The set of variables that reaches its minimum value; The sparse coefficient vector represents the useful signal to be optimized, and its dimensions correspond to the static sparse dictionary. The number of columns; This represents the complex amplitude vector of the disturbance to be optimized. It contains amplitude information for all interference components; This represents the set of interference waveform parameters to be optimized. each of them Both are parameter vectors that take values ​​in the continuous real number field; This represents the original received signal vector; A static sparse dictionary representing the useful signals constructed in step S1; This represents the summation operator; The index variable represents the interference component, and its value ranges from 1 to... ; Indicates the total number of interference components; Indicates the first The complex amplitude variable of each interference component; This represents the vector generated by the parameterized atom generation function defined in step S1, i.e., the vector generated by the parameter vector. The decision One interference waveform vector; Representing vectors Norm (Euclidean norm); express The square of the norm, which here represents the residual energy, is used to measure the fitting error between the model-reconstructed signal and the actual observed signal. The regularization parameter is a non-negative real number used to balance the fitting error with the sparsity of the solution. Representing vectors Norm, which is the sum of the absolute values ​​of all elements in a vector, is used to induce sparse coefficient vectors. It exhibits sparse characteristics.

[0056] The construction of this objective function embodies the core idea of ​​this invention: to address the linear sparse coding problem (specifically for...) ) and the problem of estimating nonlinear manifold parameters (for The data fidelity term forces the model to interpret all energy in the received signal, while the sparsity regularization term uses prior knowledge to constrain the structure of the useful signal, forcing energy components that do not conform to the sparsity characteristics to be classified into categories defined by the data fidelity term. The interference terms described enable high-precision separation of signals and interference.

[0057] See attached document Figure 3 In step S4, to solve the non-convex joint objective function constructed in step S3, the digital signal processing unit adopts a block coordinate descent strategy to decompose the complex hybrid optimization problem into two simpler sub-problems for alternating solution. As the first step in this iterative process, the digital signal processing unit first updates the sparse coefficients of the useful signal while keeping the interference component parameters fixed.

[0058] Specifically, assuming we are currently in the th Alternating iterations ( The digital signal processing unit utilizes the previous iteration (i.e., the first iteration) The set of interference parameters obtained (time) and interference amplitude vector Construct the current equivalent observation vector after interference cancellation. This process is equivalent to temporarily stripping the currently estimated interference components from the original received signal in the time domain to reveal the potentially useful signal. The calculation formula is as follows: ; in, y represents the equivalent observation vector after removing the current estimated interference in the p-th alternation iteration; y represents the original received signal vector. This represents the summation operation; Indicates the first The 1st iteration (i.e., the previous round) obtained The complex amplitude of each interference component; Indicates according to the first The parameter vector estimated in the next iteration (i.e., the previous round). The generated first One interference waveform vector; Indices representing the interference components; This indicates the total number of interference components.

[0059] Obtain the equivalent observation vector Subsequently, the original joint optimization problem addresses the sparse coefficient vector. This degenerates into a standard convex optimization problem (i.e., a basis pursuit noise reduction problem or a LASSO problem). The digital signal processing unit needs a static sparse dictionary. Find a space within the span that can approximate the sum with minimum reconstruction error. And a sparse coefficient vector that satisfies the sparsity constraint The corresponding sub-objective function is expressed as: ; in, Indicates the first The sparse coefficient vector of the useful signal is updated in each alternating iteration step; This represents the variable minimization operator, which returns the variable values ​​(here, the sparse coefficient vector) that minimize the objective function within the parentheses. ); This represents the independent variable in the optimization process, i.e., the sparse coefficient vector to be solved. A static sparse dictionary representing useful signals; express The square of the norm, which here represents the fitting error term; The regularization parameter is a non-negative real number used to balance the fitting error with the sparsity of the solution. Representing vectors Norms are used to induce sparsity.

[0060] Given static sparse dictionaries (Such as Discrete Cosine Transform (DCT) or Discrete Fourier Transform (DFT) matrices) typically possess orthogonal or tight-frame properties. This embodiment employs a fast iterative shrinking threshold algorithm for solving this problem. During the solution process, by applying a soft thresholding operator, small energy fluctuations in the received signal that belong to interference residuals or Gaussian white noise are suppressed to zero, while obvious useful signal features are preserved. The resulting... This not only represents the best estimate of the useful signal at present, but also provides a cleaner residual background for fine-tuning the interference parameters in subsequent steps.

[0061] After updating the sparse coefficients of the useful signal, the digital signal processing unit then performs a fine-tuning update of the interference parameters. This process uses the trust region algorithm to fine-tune the nonlinear manifold based on the initial coarse parameters obtained in step S2 and the optimization results from the previous stage in step S4. This method effectively solves the problem of traditional gradient descent methods easily getting stuck at saddle points or having difficulty selecting step sizes on high-dimensional non-convex surfaces by constructing a quadratic approximation model in the neighborhood of the current parameter point, thereby accurately capturing the time-varying characteristics of the interference signal.

[0062] Specifically, in the first In each alternating iteration, the digital signal processing unit first fixes the sparse coefficient vector of the just-updated useful signal. Calculate the current residual of the interference observation. The residual represents the portion of the original received signal that, after removing the useful signal component, should be fully explained by the interference model. Its calculation formula is as follows: ; in, Represents the original received signal vector; A static sparse dictionary representing useful signals.

[0063] Subsequently, for each interference component ( The digital signal processing unit (DSP) is at the current parameter estimate. A local quadratic model is constructed in the vicinity of the parameter to find the optimal step size for parameter correction. This process is formulated as a constrained sub-optimization problem: ; in, Indicates the first The optimal correction step size for each interference component parameter (including increments in three dimensions: time delay, frequency shift, and deformation). This represents a local quadratic approximation model function established around the current parameter point; This represents the negative log-likelihood function or residual energy function with respect to the disturbance parameters (i.e., the original nonlinear objective function). This represents the result of the previous iteration. The parameter vector of each interference component; This represents the gradient vector of the objective function at the current parameter point; Represents the transpose operation of a vector or matrix; This represents the Hessian matrix or its approximation matrix (such as the approximation matrix generated using the BFGS algorithm) of the objective function at the current parameter point. The norm of a vector (usually the Euclidean norm); Indicates the first In the nth iteration The trust region radius of each interference component is used to limit the optimal correction step size. Size; This indicates that the condition is subject to constraints.

[0064] Find the optimal correction step size Subsequently, the digital signal processing unit (DSP) does not directly apply the update but needs to evaluate the effectiveness of the step size. The DSP calculates the ratio of the actual descent to the model-predicted descent. This is used as a basis for adjusting the trust region radius. The basis for this.

[0065] if A value close to 1 indicates that the local quadratic model is very accurate, and the digital signal processing unit accepts this step size to update the parameters (i.e., (and expand the trust region radius in the next round to accelerate convergence;) if A smaller or even negative value indicates that the local model has failed, and the digital signal processing unit rejects that step size (i.e., Furthermore, the trust region radius is reduced to limit the search range and ensure algorithm stability.

[0066] After completing the parameter vector After the update, the digital signal processing unit finally updates the complex amplitude of the interference component according to the least squares criterion. To ensure that the amplitude and phase of the interference waveform match the current interference observation residual. Achieving optimal matching. Through this dual update mechanism of parameter deformation and amplitude correction, the interference model can gradually approximate the real physical interference signal.

[0067] After updating the trust region deformation of the interference waveform parameters, the digital signal processing unit then performs least-squares correction of the interference amplitude. This step is crucial for ensuring algorithm convergence because the nonlinear adjustment of the waveform parameters in the preceding steps can alter the correlation between the interference components. Simple scalar updates cannot eliminate coupling errors caused by non-orthogonality between interference components. Therefore, this embodiment of the invention employs a global matrix projection method to update all... The complex amplitudes of each interference component are jointly corrected.

[0068] Specifically, the digital signal processing unit first utilizes the latest waveform parameter set updated in the previous stage. The time-domain waveform vectors of all interference components are regenerated. The digital signal processing unit arranges these waveform vectors column-wise to construct a dynamic interference basis matrix. Each column of this matrix represents a current interfering atom, and its physical meaning lies in constituting the subspace spanned by the interfering signal at the current iteration step.

[0069] Subsequently, the digital signal processing unit uses the least squares principle to process the interference observation residuals. (That is, the remaining part of the original signal after removing the useful signal) is orthogonally projected onto the subspace spanned by the dynamic interference basis matrix. All the... The optimal complex amplitude vector of each interference component This operation mathematically eliminates energy leakage caused by waveform overlap between various interference components, achieving optimal energy allocation in multi-interference scenarios. The calculation formula is as follows: ; in, Indicates the first In each alternating iteration, the complex amplitude vector of all disturbance components after joint correction (including...) (number of elements) Indicates the first The dynamic interference basis matrix constructed in each alternating iteration has the following dimensions: ( For signal length, (total number of interferences), its first Listed according to parameters The generated normalized waveform vector ; This represents the conjugate transpose operation of a matrix; This represents the inverse operation of a matrix; Indicates the first Interference observation residuals in alternating iterations; The Gram matrix represents the cross-correlation matrix between interference waveforms, which reflects the degree of non-orthogonality between different interference components. This represents the projection of the residual vector onto each interference basis vector (matched filter output).

[0070] After completing this step, the digital signal processing unit checks the iteration termination condition (such as whether the change in the objective function value between two consecutive iterations is less than a preset threshold, or whether the maximum number of iterations has been reached). If the termination condition is not met, then... The loop continues, returning to the step of updating the sparse coefficients of the useful signal; if the termination condition is met, the final sparse coefficient vector of the useful signal is output. By analyzing interference parameters, the signal separation task can be completed.

[0071] After completing the least-squares correction of the interference amplitude, the digital signal processing unit enters the decision-making stage of the alternating iteration process, namely, determining the iteration termination condition. This stage aims to balance the computational complexity of the algorithm with the accuracy of parameter estimation, ensuring that a convergent solution that meets the error requirements can be output within limited time resources.

[0072] Specifically, the digital signal processing unit first bases its signal on the current signal... All variables obtained from the next iteration update, including the sparse coefficient vector of the useful signal. Complex amplitude vector and the latest waveform parameter set Recalculate the numerical value of the joint objective function This value reflects the extent to which the current parameter configuration interprets the observed data and conforms to sparse priors.

[0073] Subsequently, the digital signal processing unit calculates the relative rate of change of the objective function value and compares it with a preset convergence threshold. (e.g., 10)-3 Or 10 -4 The comparison is performed. Simultaneously, the digital signal processing unit also checks the current iteration count. Has the preset maximum number of iterations been reached? The decision logic is shown in the following formula: ; in, Indicates the first The joint objective function value calculated at the end of the iteration; Indicates the first The joint objective function value at the end of the next iteration (i.e., the previous round); This indicates the absolute value operation; This represents the preset convergence threshold, used to determine whether the objective function has reached a stable state; This indicates the maximum number of iterations allowed by the digital signal processing unit, used to prevent the algorithm from getting stuck in an infinite loop under extreme non-convergence conditions; This represents the reconstructed useful signal vector of the final output.

[0074] If any of the above conditions are met, it indicates that the algorithm has converged to a local optimum or has exhausted the allowed computational budget. At this point, the digital signal processing unit determines that the iteration has terminated and performs the final signal reconstruction and output operations. The finally converged sparse coefficient vector is then... Substitute the useful signal model and perform matrix multiplication. Synthesize useful signals in the time domain to achieve complete removal of strong interference components and high-fidelity recovery of useful weak signals from the original mixed signals.

[0075] If none of the above conditions are met, it indicates that the current solution is still in a rapid descent phase and has not yet reached a stable state. At this point, the digital signal processing unit increments the iteration counter by one (i.e., sets...). The current parameter estimate is then used as the initial value for the next iteration, returning to the step of updating the sparse coefficients of the useful signal to continue the loop. Through this closed-loop feedback mechanism, the present invention ensures that the model can adaptively approximate the real physical structure of the signal under complex electromagnetic environments.

[0076] In step S5, once the iterative process in step S4 meets the termination condition, it indicates that the digital signal processing unit has obtained the optimal parameterized description of the current electromagnetic environment. At this point, the digital signal processing unit no longer performs update operations, but enters the final signal reconstruction stage, using the converged parameters to decompose a clean, useful signal and a high-precision copy of the interference.

[0077] Specifically, the digital signal processing unit first extracts the sparse coefficient vector of the last iteration output. Let be the optimal sparse coefficient vector. The static sparse dictionary of the useful signal pre-constructed in step S1 is used. The digital signal processing unit performs matrix-vector multiplication operations to reconstruct the useful time-domain signal in a generative manner. The calculation formula is as follows: ; in, This represents the final output, reconstructed useful signal vector after interference suppression and noise reduction processing; A static sparse dictionary representing the useful signals constructed in step S1; This represents the optimal sparse coefficient vector obtained after iterative convergence, where the non-zero elements correspond to the main features of the useful signal.

[0078] Meanwhile, in order to verify the separation effect or to monitor interference, the digital signal processing unit also extracts the optimal complex amplitude of the last iteration output. and optimal waveform parameters Using atomic generating functions, the digital signal processing unit synthesizes an estimate of the time-domain interference signal. : ; in, This represents the reconstructed time-domain interference signal estimate, used to assess the current interference environment intensity; This represents the summation operation; This indicates the total number of identified interference components; Indicates the 1st iteration after convergence. The optimal complex amplitude of each interference component; Indicates based on optimal waveform parameters (Including precise time delay, carrier frequency, etc.) The generated first The basis function waveforms of each interference component.

[0079] In this process, the core technical advantages of the present invention are fully demonstrated: First, the generated useful signal Not simply by obtaining the original received signal vector Subtracting interference from the middle yields (i.e.) While direct subtraction can remove interference, it retains Gaussian white noise and measurement errors in the original signal. In contrast, this invention employs... This method is essentially a nonlinear filtering process. Because... After Norm regularization and soft thresholding are applied, where the vast majority of the tiny coefficients corresponding to noise are set to zero. Therefore, the reconstructed... It not only eliminates strong interference, but also removes background noise, thus improving the output signal-to-noise ratio.

[0080] Secondly, this reconstruction method avoids the spectrum cancellation problem common in traditional frequency domain notch filtering techniques. In traditional methods, to suppress strong interference, the frequency band containing the interference needs to be forcibly set to zero. This leads to the loss of useful signal components overlapping with the interference spectrum and generates Gibbs phenomenon or waveform ringing in the time domain. However, this invention uses a static sparse dictionary... The sparse decomposition on the spectrum, utilizing the morphological differences between the signal and interference, can successfully preserve the energy of the useful signal that overlaps with the interference frequency band in the optimal sparse coefficient vector. This maximizes the preservation of the waveform integrity of the useful signal.

Claims

1. An anti-interference design method based on multi-electromagnetic interference, characterized in that, Includes the following steps: A mathematical model is established to represent the received signal as a hybrid signal consisting of a linear superposition of a useful signal, a parameterized interference signal, and additive noise. A static sparse dictionary is constructed for the useful signal, and an atomic generation function based on a multivariate continuous parameter space containing time delay, frequency shift, and waveform deformation dimensions is defined for the parameterized interference signal. A discrete anchor point dictionary is constructed using the atomic generation function. By calculating the correlation between the received signal and the anchor point dictionary, an initial set of interference parameter estimates and an initial amplitude estimate are obtained. Based on the aforementioned mixed-signal mathematical model, a joint optimization objective function is established, which includes data fidelity terms and useful signal sparsity constraints. Initialization is performed using the initial set of interference parameters and the initial amplitude estimate. Alternating iterative solution is performed based on trust region constraints. The sparse coefficient vector of the useful signal, the set of interference parameters, and the interference amplitude vector are alternately updated by minimizing the joint optimization objective function. The set of interference parameters is updated in the multivariate continuous parameter space based on the trust region method. The useful signal estimate is reconstructed and output based on the sparse coefficient vector of the final useful signal after iterative convergence and combined with the static sparse dictionary.

2. The anti-interference design method based on multi-electromagnetic interference according to claim 1, characterized in that, The parameterized interference signal originates from the electromechanical and power drive subsystem; The atom generating function establishes a nonlinear mapping from a low-dimensional parameter space to a high-dimensional signal sample space; The parameterized interference signal is composed of multiple interference components linearly superimposed. Each interference component is uniquely determined by its corresponding complex amplitude and a parameter vector containing time delay parameters, frequency shift parameters, and waveform deformation parameters.

3. The anti-interference design method based on multi-electromagnetic interference according to claim 1, characterized in that, The static sparse dictionary is generated based on the physical layer parameters of the wireless communication receiving subsystem. The static sparse dictionary is composed of basis vectors arranged in columns, and the basis vectors correspond to the inverse discrete Fourier transform matrix or the overcomplete Gabor frame. The useful signal is represented as a linear combination of the static sparse dictionary and the sparse coefficient vector of the useful signal.

4. The anti-interference design method based on multi-electromagnetic interference according to claim 1, characterized in that, Before obtaining the initial estimate set of interference parameters, the search space range of the interference parameters is determined; The search space is sampled in a grid pattern according to a preset resolution step size to generate a grid set; The atom generation function is used to map each parameter point in the mesh set to a corresponding normalized interference atom vector, thereby constructing the anchor point dictionary.

5. The anti-interference design method based on multi-electromagnetic interference according to claim 4, characterized in that, The initial set of estimates for the interference parameters and the initial magnitude estimates are obtained through a loop process: Initialize the received signal vector as a residual vector and perform iteration; The cross-correlation coefficient between the residual vector and each normalized anchor vector in the anchor dictionary is calculated by performing a vector inner product operation. The grid parameters corresponding to the anchor point index where the cross-correlation modulus value is the largest are selected as the coarse parameter estimates of the current interference component. The initial complex amplitude of the current interference component is calculated based on the principle of orthogonal projection; Subtract the reconstructed current disturbance component from the residual vector.

6. The anti-interference design method based on multi-electromagnetic interference according to claim 1, characterized in that, The joint optimization objective function is composed of a weighted sum of the data fidelity term and the useful signal sparse constraint term. The data fidelity term calculates the sum of squares of the magnitudes of the difference vector elements between the received signal vector and the reconstructed signal, wherein the reconstructed signal is composed of a sparse representation of the useful signal and a linear combination of parameterized atoms of all interference components. The useful signal sparse constraint term calculates the sum of the magnitudes of the elements of the useful signal sparse coefficient vector.

7. The anti-interference design method based on multi-electromagnetic interference according to claim 1, characterized in that, In the alternating iterative solution process, the step of alternately updating the sparse coefficient vector of the useful signal specifically includes: In a single iteration, the set of interference parameters and the interference amplitude vector obtained in the previous iteration are used to construct the equivalent observation vector after interference cancellation; Search within the spanned space of the static sparse dictionary for a sparse coefficient vector that approximates the equivalent observation vector and satisfies the sparse constraints.

8. The anti-interference design method based on multi-electromagnetic interference according to claim 7, characterized in that, In the alternating iterative solution process, the step of alternatingly updating the set of disturbance parameters specifically includes: The useful signal sparse coefficient vector is fixed and the interference observation residual is calculated by subtracting the currently reconstructed useful signal component from the received signal vector; For each interference component, a local quadratic approximation model is constructed in the neighborhood of the current parameter point; The solution is constrained by the optimal correction step size of the trust region radius; Calculate the ratio of the actual decrease in the objective function to the model-predicted decrease; The trust region radius is adjusted based on the ratio, and the optimal correction step size is determined to update the interference parameters.

9. The anti-interference design method based on multi-electromagnetic interference according to claim 8, characterized in that, In the alternating iterative solution process, the step of alternatingly updating the disturbance magnitude vector specifically includes: The time-domain waveform vectors of all interference components are regenerated using the updated set of interference parameters to construct a dynamic interference basis matrix; The interference observation residuals are orthogonally projected onto the subspace spanned by the dynamic interference basis matrix using the least squares principle; The complex amplitudes of all disturbance components are jointly corrected by solving the normal equations.

10. The anti-interference design method based on multi-element hybrid electromagnetic interference according to claim 1, characterized in that, When reconstructing the useful signal estimate, after determining that the iterative process meets the preset convergence condition, the final useful signal sparse coefficient vector is extracted. The time-domain useful signal estimate is reconstructed by performing matrix-vector multiplication operations using the static sparse dictionary and the final useful signal sparse coefficient vector. The time-domain useful signal estimate retains only the signal components that conform to the characteristics of the static sparse dictionary.

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