An airborne radar signal anti-jamming processing method and system

Abstract

The application discloses an airborne radar signal anti-interference processing method and system, and relates to the technical field of radar signal anti-interference. The application provides an airborne radar signal anti-interference processing method, which comprises the following steps: calculating the eigenvalue variation gradient of an electromagnetic environment noise covariance matrix in real time, inserting a passive pure listening window between adjacent transmission pulses, and extracting an interference frequency band weighting vector; taking the interference frequency band weighting vector as a frequency domain stop band constraint condition to construct a multi-dimensional non-convex joint optimization objective function, generating a digital baseband waveform satisfying a constant modulus constraint; radiating the waveform to space through a radio frequency power amplifier; determining an interference incident direction, combining the sidelobe gain characteristics of the waveform in the interference incident direction, performing space-time cancellation processing on echo data in a target subband, and outputting pure radar target echo. The technical problem of the airborne radar in a complex and changeable electromagnetic environment, i.e., lagging behind in interference perception, declining target detection sensitivity and limited anti-interference capability, is solved.

Description

Technical Field

[0001] This application relates to the field of radar signal anti-jamming technology, and in particular to an airborne radar signal anti-jamming processing method and system. Background Technology

[0002] In the field of airborne radar detection and electronic reconnaissance, radar systems often need to perform air target search and tracking tasks in highly dynamic and dense artificial electromagnetic interference environments. Maintaining continuous and accurate situational awareness is the core key to ensuring the platform's survivability. With the continuous evolution of modern electromagnetic interference technology, interference signals exhibit multidimensional complexity in space, time, and frequency. They not only manifest as rapid frequency hopping or broadband suppression in frequency, but also have extremely strong non-uniformity in spatial distribution, accompanied by extremely high transient burst characteristics. This makes it difficult for traditional radar systems to achieve real-time deconstruction and acquisition of sudden interference electromagnetic environments during the active radiation signal period, resulting in the system being in a passive defense state for a long time and facing serious information acquisition blind spots. Summary of the Invention

[0003] The main purpose of this application is to provide an airborne radar signal anti-jamming processing method and system, which aims to solve the technical problems of airborne radar in complex and variable electromagnetic environments, such as delayed interference perception, decreased target detection sensitivity and limited anti-jamming capability.

[0004] To achieve the above objectives, in a first aspect, this application provides an airborne radar signal anti-jamming processing method, comprising: The gradient of eigenvalue changes of the electromagnetic environment noise covariance matrix obtained in the region without signal echo is calculated in real time. When it exceeds the preset transient rate of change threshold, a passive pure listening window is inserted between adjacent transmitted pulses, and the interference frequency band weighted vector is extracted through the passive pure listening window. The interference frequency band weighting vector is used as a frequency domain stopband constraint to construct a multidimensional non-convex joint optimization objective function. The convergence threshold of the alternating direction multiplier method is dynamically configured according to the real-time computing power load rate of the current radar processor. Based on the objective function and the convergence threshold, a digital baseband waveform that satisfies the constant modulus constraint is obtained. The digital baseband waveform is subjected to nonlinear predistortion compensation and then transmitted via an RF power amplifier; In response to the received echo data, the echo data is divided into multiple sub-band echo channels by a multiphase filter bank. The receiving array performs spatial spectrum estimation on the echo data to determine the interference incident direction. Combining the sidelobe gain characteristics of the transmitted waveform in the interference incident direction, the echo data is subjected to space-time cancellation processing of the target sub-band to output a clean radar target echo.

[0005] Optionally, the step of inserting a passive pure listening window between adjacent transmitted pulses and extracting the interference frequency band weighting vector through the passive pure listening window includes: During the insertion of the passive listening window, the radar transmitter is controlled to be in a physical silence state, and the radar receiver is turned on to passively receive spatial electromagnetic signals across the entire frequency band. The center frequency and bandwidth of the interference signal in the current space are extracted from the passively detected spatial electromagnetic signal. Based on the extracted center frequency and bandwidth, the corresponding interference band weighting vector is constructed.

[0006] Optionally, the step of constructing a multidimensional non-convex joint optimization objective function using the interference frequency band weighting vector as a frequency domain stopband constraint includes: Obtain a reference waveform with ideal autocorrelation characteristics preset by the radar system; By using the mean square error between the waveform to be synthesized and the reference waveform, combined with the scalar penalty factor preset by the system and the spectral constraint penalty term of each of the extracted interference frequency band weighting vectors for the waveform to be synthesized, the multidimensional non-convex joint optimization objective function is constructed so that the waveform to be synthesized forms an energy null trap in the frequency band corresponding to the interference frequency band weighting vector.

[0007] Optionally, the step of dynamically configuring the convergence threshold of the alternating direction multiplier method based on the current radar processor's real-time computing power load rate, and generating a digital baseband waveform that satisfies the constant modulus constraint based on the objective function, includes: Real-time reading of the current computing power load rate of the radar processor and the moving angular velocity of the passively detected interference source; When the computing power load rate is greater than the preset high load threshold or the angular velocity of the interference source is greater than the high dynamic threshold, the maximum number of iterations of the alternating direction multiplier method is reduced and the convergence threshold is relaxed. When the computing power load rate is not greater than the preset high load threshold and the moving angular velocity of the interference source is not greater than the high dynamic threshold, the convergence threshold is tightened, and iterative calculations are performed under the dynamically configured convergence threshold to output the digital baseband waveform.

[0008] Optionally, the step of performing nonlinear predistortion compensation on the generated digital baseband waveform and radiating the waveform into space via an RF power amplifier includes: Before the digital baseband waveform is input to the digital-to-analog converter, the phase and amplitude compensation calculations are performed on the digital baseband waveform to address the inherent amplitude and phase nonlinear distortion effects of the RF power amplifier operating in the saturation region. The waveform after inverse compensation calculation is converted by the digital-to-analog converter and the radio frequency power amplifier to suppress nonlinear distortion, so as to radiate electromagnetic waves carrying specific frequency domain concave characteristics into space.

[0009] Optionally, the step of the receiving array performing spatial spectrum estimation on the echo data to determine the interference incident direction, and combining the sidelobe gain characteristics of the transmitted waveform in the interference incident direction, includes: The space-time incident direction of the residual non-uniform interference is determined based on spatial spectrum estimation. The space-time steering vector of the residual non-uniform interference is calculated by combining the sidelobe distribution characteristics of the emitted waveform in the space-time incident direction. Based on the space-time steering vector, a projection operator is constructed to project the signal components onto the interference subspace.

[0010] Optionally, the projection operator is applied to the received echo data to extract the interference component, and the difference operation is performed between the echo data and the interference component. By removing the projection component belonging to the interference subspace in the echo data and retaining the remaining null space component, the spatiotemporal cancellation processing of the target subband is completed.

[0011] Optionally, the step of performing space-time cancellation processing on the echo data for the target subband includes: A low-pass prototype filter is obtained, and the coefficients of the low-pass prototype filter are decimated at equal intervals according to a preset number of sub-bands to obtain multiple parallel multiphase branch filters. The echo data is converted from serial to parallel using a multi-channel delay commutator so that the data in each parallel channel generates a sequentially increasing unit delay, and is downsampled to a low data rate corresponding to the number of sub-bands. The downsampled data from each channel is input into the corresponding multiphase branch filter for parallel convolution filtering. At each downsampling output moment, a fast Fourier transform is performed on the output data of all the multiphase branch filters. By rotating the phase, the signals of each channel are modulated onto the corresponding physical frequency band and synthesized into multiple independent and continuously spliced ​​subband data. The sub-band data whose frequency range overlaps with or falls within the frequency band corresponding to the interference frequency band weighting vector is identified as the target sub-band.

[0012] Secondly, this application provides an airborne radar signal anti-jamming processing system, characterized in that it includes: The interference frequency band weighted vector acquisition module is configured to: calculate the gradient of eigenvalue changes in the electromagnetic environment noise covariance matrix in real time; when the gradient exceeds a preset transient rate of change threshold, insert a passive pure listening window between adjacent transmitted pulses; and extract the interference frequency band weighted vector through the passive pure listening window. The digital baseband waveform acquisition module is configured to: construct a multidimensional non-convex joint optimization objective function by using the interference frequency band weighting vector as a frequency domain stopband constraint condition; dynamically configure the convergence threshold of the alternating direction multiplier method based on the current radar processor's real-time computing power load rate; and generate a digital baseband waveform that satisfies the constant modulus constraint based on the objective function. A radiation module is configured to perform nonlinear predistortion compensation on the generated digital baseband waveform and radiate the waveform into space via an RF power amplifier. The clean radar target echo module is configured to: in response to received echo data, divide the echo data into multiple sub-band echo channels through a multiphase filter bank; perform spatial spectrum estimation on the echo data to determine the interference incident direction; combine the sidelobe gain characteristics of the transmitted waveform in the interference incident direction; perform space-time cancellation processing on the echo data of the target sub-band; and output a clean radar target echo.

[0013] Optionally, the interference frequency band weighted vector acquisition module is further configured to: During the insertion of the passive listening window, the radar transmitter is controlled to be in a physical silence state, and the radar receiver is turned on to passively receive spatial electromagnetic signals across the entire frequency band. The center frequency and bandwidth of the interference signal in the current space are extracted from the passively detected spatial electromagnetic signal. Based on the extracted center frequency and bandwidth, the corresponding interference band weighting vector is constructed.

[0014] The beneficial effects that this application can achieve are: This application proposes an airborne radar signal anti-jamming processing method and system. By dynamically inserting passive listening windows between adjacent transmitted pulses in real time, it overcomes the lag problem of traditional methods being unable to detect transient sudden interference in real time, achieving accurate capture of the electromagnetic situation. Based on non-convex joint optimization waveform design of interference information, a high-depth spectral null is generated in a specific interference frequency band while ensuring transmitter efficiency, solving the problem that traditional waveforms cannot effectively avoid interference under hardware constraints. The introduction of nonlinear predistortion compensation technology effectively offsets the spectral sidelobe recovery effect generated by the high-power amplifier in the saturation region, physically protecting the carefully designed deep null characteristics from being destroyed, and solving the problem of severe null degradation of radiated signals in the prior art. Attached Figure Description

[0015] Figure 1 This is a flowchart illustrating the anti-interference processing method according to an embodiment of this application; Figure 2 This is a detailed flowchart illustrating step S1 in an embodiment of this application. Figure 3 This is a detailed flowchart illustrating step S2 in an embodiment of this application. Figure 4 This is a detailed flowchart illustrating step S3 in an embodiment of this application. Figure 5 This is a detailed flowchart illustrating step S4 in an embodiment of this application.

[0016] The realization of the purpose, functional features and advantages of this application will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0017] The technical solutions of 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 a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0018] It should be noted that all directional indications (such as up, down, left, right, front, back, etc.) in the embodiments of the present invention are only used to explain the relative positional relationship and movement of each component in a certain specific posture (as shown in the figure). If the specific posture changes, the directional indication will also change accordingly.

[0019] In this invention, unless otherwise explicitly specified and limited, the terms "connection," "fixed," etc., should be interpreted broadly. For example, "fixed" can mean a fixed connection, a detachable connection, or an integral part; it can mean a mechanical connection or an electrical connection; it can mean a direct connection or an indirect connection through an intermediate medium; it can mean the internal communication of two components or the interaction between two components, unless otherwise explicitly limited. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0020] Furthermore, if the embodiments of this invention involve descriptions such as "first" or "second," these descriptions are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined with "first" or "second" may explicitly or implicitly include at least one of those features. Additionally, the meaning of "and / or" throughout the text includes three parallel solutions; for example, "A and / or B" includes solution A, solution B, or a solution where both A and B are satisfied simultaneously. Furthermore, the technical solutions of the various embodiments can be combined with each other, but this must be based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or impossible to implement, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by this invention.

[0021] This embodiment discloses an airborne radar signal anti-jamming processing method and system, wherein the method specifically includes: S1. Calculate the gradient of eigenvalue changes in the electromagnetic environment noise covariance matrix in real time. When it exceeds the preset transient rate of change threshold, insert a passive pure listening window between adjacent transmitted pulses and extract the interference frequency band weighted vector through the passive pure listening window.

[0022] S2. Construct a multidimensional non-convex joint optimization objective function by using the interference frequency band weighted vector as the frequency domain stopband constraint condition. Dynamically configure the convergence threshold of the alternating direction multiplier method through the real-time computing power load rate of the current radar processor. Based on the objective function, obtain the digital baseband waveform that satisfies the constant modulus constraint.

[0023] S3. Perform nonlinear predistortion compensation on the digital baseband waveform, and then transmit it through an RF power amplifier.

[0024] S4. In response to the received echo data, the receiving array performs spatial spectrum estimation on the echo data to determine the interference incident direction. Combining the sidelobe gain characteristics of the transmitted waveform in the interference incident direction, the array performs space-time cancellation processing on the echo data for the target subband and outputs a clean radar target echo.

[0025] It should be noted that in S1, the echo data is divided into multiple sub-band echo channels using a multiphase filter bank. To address the issue of radar's inability to monitor changes in active interference characteristics in real time under complex and variable electromagnetic environments, the gradient of eigenvalue changes in the electromagnetic environment noise covariance matrix obtained in the signal-free echo region is calculated in real time. This adaptively captures sudden transients of interference and dynamically inserts a passive pure listening window. This passive pure listening window extracts the interference frequency band weighting vector during the physical silence period, providing accurate frequency domain prior input for subsequent active transmission waveforms.

[0026] In S2, to address the issues of imprecise time-frequency domain constraints in waveform generation and computational complexity limited by hardware computing power, a multi-dimensional non-convex joint optimization objective function is constructed by using the extracted interference frequency band weighting vector as the stopband condition in the time-frequency optimization process. Simultaneously, by utilizing the real-time computing load rate of the current radar processor, the convergence accuracy threshold of the alternating direction multiplier method is adaptively adjusted when computing resources are limited, generating a digital baseband waveform with deep spectral nulls and meeting the hardware constant modulus requirement while ensuring real-time performance.

[0027] In S3, to address the issue that high-power RF power amplifiers operating in the nonlinear saturation region can cause spectral rise in the digital baseband waveform, thereby destroying its spectral null anti-interference characteristics, reverse amplitude and phase nonlinearity pre-distortion compensation is introduced in the baseband processing stage to counteract the nonlinear distortion effect of the RF power amplifier, so that the electromagnetic waveform radiated into space truly retains the specific frequency domain deep null characteristics.

[0028] In S4, to address the impact of residual non-uniform sidelobe interference outside the stopband of the transmitted waveform on echo quality, the beam sidelobe distribution characteristics formed by the transmitted waveform in the spatial domain of the interference source are analyzed. A mapping relationship between the residual interference in the spatial and frequency domains is established, and a projection operator is constructed. At the receiver, spatiotemporal projection cancellation is performed specifically on the interfered subbands, while the non-interfering subbands remain unchanged. This achieves lossless reception cancellation that balances interference suppression and target detection energy, outputting a clean radar target echo.

[0029] In one specific embodiment, S1 includes: S11. Real-time calculation of the gradient of eigenvalue changes in the electromagnetic environment noise covariance matrix; S12. Compare the gradient of the feature value change with a preset transient rate of change threshold. When it exceeds the preset transient rate of change threshold, insert a passive pure listening window between adjacent transmission pulses. S13. During the insertion of the passive pure listening window, control the radar transmitter to be in a physical silence state and turn on the radar receiver to passively receive spatial electromagnetic signals across the entire frequency band. S14. Extract the center frequency and bandwidth of the interference signal in the current space from the passively detected spatial electromagnetic signal; S15. Based on the extracted center frequency and bandwidth, construct the corresponding interference band weighting vector.

[0030] It should be noted that, for S11, the radar system acquires multiple background noise samples through the receiving channel in a state without transmitted signals during a specific background noise detection period, and calculates the electromagnetic environment noise covariance matrix obtained in the region without signal echo. The radar processor performs real-time eigenvalue decomposition on this covariance matrix, extracts the energy distribution of its largest eigenvalue or the first few principal eigenvalues, and calculates the energy change gradient of the eigenvalues ​​between adjacent processing cycles based on the first-order difference, thereby characterizing the severity of transient fluctuations in the spatial electromagnetic situation.

[0031] Furthermore, the process of obtaining the covariance matrix is ​​illustrated with the following example: During the background noise detection period determined by the system, all physical channels of the radar receiving antenna array are simultaneously activated. The RF front-end of each receiving channel, under conditions of no active radiation, captures weak background thermal noise and external residual interference signals in space. These analog signals, after down-conversion processing, are synchronously input by high-speed analog-to-digital converters distributed across different antenna channels. To ensure the consistency of spatial sampling, all analog-to-digital converters are connected to the same highly stable master clock source, performing synchronous coherent sampling of all physical channels at equal intervals. The processing system aggregates the data acquired by each channel at each sampling moment, forming a complex vector characterizing the spatial electromagnetic state at that moment. By continuously accumulating these vectors within a preset passive listening time window, the system constructs a noise data matrix containing both temporal and spatial dimensions in the buffer area of ​​the memory, thereby achieving a discretized mapping of the real physical spatial electromagnetic field at the digital level.

[0032] In the raw digital signal output by the analog-to-digital converter, due to the bias voltage in the analog hardware circuit and the temperature drift effect of components caused by changes in ambient temperature, the signal usually contains a DC component that does not change over time. To prevent these non-physical DC energies from introducing biases into subsequent calculations, the processor first calculates the arithmetic mean of the continuously acquired samples in each physical receiving channel. Subtracting this average value from each sampling point of that channel eliminates the DC bias, ensuring that the input matrix contains only pure electromagnetic fluctuation information. To compensate for the RF gain imbalance and phase inconsistency between channels due to differences in manufacturing processes, the system reads the channel calibration coefficient table pre-stored in read-only memory. These coefficients are used to perform amplitude and phase consistency correction on the de-DC data, ensuring that different antenna channels exhibit equivalent physical response strength under the same electromagnetic excitation, ultimately outputting a standardized noise sampling matrix.

[0033] After obtaining the standardized noise sampling matrix, the processing system initiates a spatial cross-correlation pipeline to measure the correlation of electromagnetic energy between different receiving channels, i.e., the spatial distribution characteristics of noise. The processor multiplies the preprocessed noise sampling matrix by its own conjugate transpose. This operation is equivalent to summing the outer products of all instantaneous noise vectors collected within the passive listening window. By accumulating these instantaneous outer product results, the system smooths the randomly fluctuating thermal noise over time and normalizes the energy by dividing by the total number of samples. Through this temporal averaging operation, incoherent thermal noise components are statistically compressed, while spatially correlated interference signal characteristics are highlighted in the calculation results, ultimately forming the original covariance matrix reflecting the spatial electromagnetic environment noise and interference distribution.

[0034] In actual airborne flight missions, the duration of passive listening windows is often short due to system real-time constraints, or insufficient data samples may result from partial obstruction of the antenna array by the fuselage structure. Consequently, the directly calculated original covariance matrix often exhibits mathematical ill-conditioning, meaning the matrix may be invertible or contain non-physical zero eigenvalues. This directly leads to computational overflow or oscillations in subsequent algorithms. To improve the robustness of the processing system, the processor executes a diagonal loading and reconstruction process. The average power level of all diagonal elements of the original matrix is ​​calculated, and a small subset of this level is selected as the loading noise power and uniformly superimposed onto the main diagonal elements of the matrix. This process physically equates to raising the basis of the background noise, ensuring that the covariance matrix mathematically maintains a strictly positive definite property. This not only eliminates the ill-conditioning risk in numerical calculations but also ensures stable convergence of the subsequent eigenvalue decomposition process, providing a reliable data foundation for the radar detection system.

[0035] For S12, the radar system incorporates a comparator in its underlying control loop. When the calculated gradient of the characteristic value change exceeds a preset transient rate of change threshold, a newly arrived, sudden electromagnetic interference source is identified in space. At this point, the control system interrupts the normal continuous transmission sequence and forcibly inserts a passive pure listening window between adjacent transmission pulses. This passive pure listening window avoids aliasing interference from the radar's active radiated signals in the extraction of spatial interference features, ensuring that the acquired interference spectrum information is pure and uncontaminated.

[0036] For S13, the radar controller sends a control word to the transmitter's RF waveform bias control terminal. During the passive pure listening window, it directly lowers the bias enable of the RF amplifier, thereby shutting down high-voltage modulation and putting the transmitter in a physically zero-radiation silent state. Simultaneously, the receiver's RF front-end multi-channel low-noise amplifier switches to a full-bandwidth, large instantaneous bandwidth reception mode, achieving passive detection of full-bandwidth spatial electromagnetic signals.

[0037] For S14, the radar signal processor transforms the received time-domain digital signal to the frequency domain using a fast Fourier transform. The processor searches for continuous frequency bands in the frequency domain where the energy spectral density exceeds the noise floor, calculates the geometric center position of these strong radiation bands and the corresponding equivalent power bandwidth, thereby obtaining the center frequency and bandwidth of the interference signal in the current space.

[0038] For S15, the radar signal processor constructs a frequency-domain stopband window based on the center frequency and bandwidth of each extracted interference signal. It sets the weight of the corresponding frequency grid index falling within the stopband to 1, and sets the weight of the remaining uninterrupted frequency bands to 0, thus generating an interference frequency band weighting vector. This vector serves as the constraint basis for subsequent frequency domain concavity design of the transmitted waveform.

[0039] In some optional embodiments, regarding step S1, it is assumed that the radar system is deployed on an airborne detection platform. Initially, the eigenvalues ​​of the electromagnetic environment noise covariance matrix are stationary. At a certain moment, the airborne electromagnetic sensor detects a sudden frequency-hopping interference in space. By estimating the covariance of the received data and extracting eigenvalues, the gradient of eigenvalue change is calculated to increase from 0.02 per millisecond in the stationary state to 1.85 per millisecond, exceeding the system's preset transient rate of change threshold. At this point, the system immediately inserts a passive listening window lasting 100 microseconds between the two transmitted pulses. Within this window, the transmitter's high voltage is completely shut off. The receiver captures a high-power interference signal across the entire frequency band. Through frequency domain analysis, the center frequency of the interference signal is calculated to be 9.6 GHz, and the bandwidth is 40 MHz. Based on these parameters, the system constructs an interference band weighted vector within the frequency range of 9.58 GHz to 9.62 GHz, with a weight of 1, to indicate the suppression of energy in this frequency band during subsequent waveform design.

[0040] The preset transient rate of change threshold is obtained based on a finite number of historical calibration data. Specifically, in an anechoic environment and a typical interference-free field airspace, the statistical fluctuations of the noise covariance matrix eigenvalues ​​caused by pure thermal noise and system background fluctuations are measured and recorded, along with the average and standard deviation of the gradient of the statistical eigenvalue changes. The average value is then multiplied by five times the standard deviation to define the corresponding preset transient rate of change threshold. For example, in this embodiment, the preset transient rate of change threshold is defined as 1.2.

[0041] In one specific implementation, S2 includes: S21. Obtain a reference waveform with ideal autocorrelation characteristics preset by the radar system; S22. By using the mean square error between the waveform to be synthesized and the reference waveform, combined with the scalar penalty factor preset by the system and the spectral constraint penalty term of the waveform to be synthesized by the weighted vector of each interference frequency band extracted, a multidimensional non-convex joint optimization objective function is constructed. S23. Real-time reading of the current radar processor's computing power load rate and the moving angular velocity of the passively detected interference source; S24. When the computing load rate is greater than the preset high load threshold, or the angular velocity of the interference source is greater than the high dynamic threshold, reduce the maximum number of iterations of the alternating direction multiplier method and relax the convergence threshold. S25. When the computing load rate is not greater than the preset high load threshold and the angular velocity of the interference source is not greater than the high dynamic threshold, tighten the convergence threshold. S26. Under the convergence threshold after dynamic configuration, perform iterative calculations using the alternating direction multiplier method based on the multidimensional non-convex joint optimization objective function to generate a digital baseband waveform that satisfies the constant modulus constraint.

[0042] In this embodiment, it should be noted that for S21, the non-volatile memory inside the radar pre-stores linear frequency modulated signal data with standard large time-width-bandwidth product and low range sidelobe characteristics as a reference waveform.

[0043] For S22, the mathematical optimization framework constructed by the radar processor aims to make the generated transmitted waveform as similar as possible to the reference waveform in the time domain to maintain excellent ranging and pulse compression performance, while having a near-zero energy response in the frequency domain stopband. This optimization problem is a non-convex problem, and the expression of its constructed multidimensional non-convex joint optimization objective function is as follows:

[0044] In the formula, This represents the multidimensional nonconvex joint optimization augmented Lagrangian objective function constructed by the alternating direction multiplier method in iterative calculations; Represents the column vector of the radar digital baseband waveform to be synthesized; This represents a pre-stored reference waveform column vector with ideal autocorrelation characteristics; The square operator represents the L2 norm of a complex vector, used to measure the mean square deviation between two vectors; represents the system's preset scalar penalty factor, used to adjust the physical balance between the frequency domain stopband suppression depth and waveform matching degree; F represents the Fourier transform matrix; The conjugate transpose operator for a matrix or vector; The diagonalization operator represents the method of constructing a diagonal matrix using the vectors within the parentheses as diagonal elements. This represents the interference frequency band weighted vector extracted and constructed from the passive pure listening window; This represents the second-order augmentation penalty constant introduced in the alternating direction multiplier method, used to constrain the consistency between the time-domain auxiliary variables and the waveform vector to be synthesized; This represents the introduced time-domain auxiliary column vector that satisfies the constant amplitude envelope physical constraint; This represents the introduced dual multiplier column vector.

[0045] against In this context, the primary task of a radar system when transmitting signals is to ensure it possesses good autocorrelation function sidelobe characteristics and matched filter gain in order to accurately measure target distance. In the formula... It is a pre-stored reference waveform column vector. This is the digital baseband waveform to be synthesized. The L2-squared difference between the two measures the mean square deviation of the synthesized waveform from the ideal waveform in the time domain. If nulls are extracted in the frequency domain solely for anti-jamming purposes, the waveform will be severely distorted, leading to a deterioration in the pulse compression main-sidelobe ratio and a decrease in range resolution of the radar receiver. Introducing this term as the primary driving force for optimization can mathematically constrain the synthesized waveform to closely adhere to the reference waveform, ensuring that the radar's ranging and detection capabilities do not suffer catastrophic degradation.

[0046] against This term maps the time-domain waveform to the frequency domain using a Fourier matrix and accurately extracts the specific frequency band where the jammer is located using a weighted diagonal matrix. During optimization, minimizing this term is equivalent to forcing the power spectral density of the waveform within that frequency band to approach zero. This is due to the introduction of... As a balancing parameter, designers can adjust its size to quantify the physical trade-off between the depth of anti-interference suppression and the waveform matching degree, so that the waveform can accurately form an energy null trap in the interference frequency band.

[0047] against To achieve maximum efficiency, the radio frequency power amplifier of airborne radar typically operates in the nonlinear saturation region, which requires the transmitted waveform to satisfy a constant amplitude envelope constraint, i.e., constant mode property. To handle this strongly nonlinear constraint within a nonconvex optimization framework, a time-domain auxiliary column vector is introduced. (Satisfying constant modulus constraints) and dual multiplier vectors It employs an augmented Lagrangian form using the alternating direction multiplier method, through a quadratic penalty constant. The constraints are transformed into part of the objective function. Directly solving an optimization problem with both frequency domain null constraints and time domain constant modulus constraints is a typical NP-hard non-convex problem. An auxiliary variable is introduced. The waveform synthesis and constant mode characteristics are mathematically decoupled. Through alternating iterations, the waveform is first solved in the frequency domain and linear space, and then projected onto the constant mode space. Parameters The convergence speed and penalty function strength of the auxiliary variable to approximate the real waveform are determined, thereby ensuring that the final output digital baseband waveform can avoid interference in the frequency domain and adapt to the linear operating range of the power amplifier in the time domain.

[0048] For S23, the task scheduler of the radar's embedded operating system polls the CPU usage of the processing core in real time and calculates and outputs the current computing load rate. Simultaneously, by analyzing the rate of change of the spatial angle of arrival of the interference source extracted within several consecutive passive listening windows, the angular velocity of the interference source relative to the radar detection platform is calculated.

[0049] For S24, if the current radar system is in a multi-task parallel phase involving multi-target tracking and dense signal sorting, and the computing load exceeds the preset high load threshold; or if the interference source is maneuvering at high speed in space, with its angular velocity exceeding the high dynamic threshold, it means that the transmitted waveform reconstruction cycle must be shortened to accommodate the rapid drift of the interference source's spatial position. By sacrificing the null depth of a single waveform optimization, the waveform update rate is matched with the rate of change of the spatial dynamic interference manifold, thereby avoiding Doppler modulation failure. In this case, the system control mechanism ensures that the system does not go out of control by sacrificing some waveform convergence accuracy, directly reducing the maximum number of iterations of the alternating direction multiplier method from the default value of 50 to 15, and amplifying the convergence threshold to 10 times the original threshold value.

[0050] For S25 and S26, when computing resources are sufficient and the interference source is relatively stationary or moving slowly, the system tightens the convergence threshold to a preset high-precision threshold in order to achieve the deepest frequency domain null. Under this dynamically configured parameter, the processor alternately updates the waveform vector, auxiliary variables, and dual multipliers. During the iteration process, the auxiliary variables are forcibly projected onto the unit circle in each update step to meet the requirement of constant amplitude, and finally outputs a digital baseband waveform that satisfies the constant modulus constraint.

[0051] In some alternative embodiments, it is assumed that the radar processor is currently processing multiple air defense surveillance missions. The processor task scheduler reports a computational load rate of 82%, exceeding the preset high-load threshold of 75%. At this point, the system determines that a low-load waveform reconstruction timing must be initiated. To this end, the convergence threshold of the alternating direction multiplier method is relaxed from 1.0e-5 to 1.0e-4, and the maximum allowed number of iterations is limited to 12. Under this tolerance threshold, the processor completes the waveform iteration in only 2.1 milliseconds, outputting a digital baseband waveform that meets the constant modulus physical requirements.

[0052] The preset high-load threshold is obtained based on a limited number of historical calibration data. Specifically, under full-load benchmark testing of the processor, the number of various high-concurrency data processing threads of the processor is gradually increased, and the critical load value at which the waveform generation thread experiences computational overflow or output timeout is observed. Multiple experiments show that the probability of overflow increases when the computing power load rate reaches 78% or higher. Therefore, for safety margin considerations, the above value is calibrated to 75%. The high dynamic threshold is also calibrated based on historical experimental data. Specifically, the geometric conversion between radar antenna beamwidth and angle update period is calculated by simulating the jammer's flight speed at different speeds from 500 m / s to 2000 m / s. Multiple simulations show that when the angular velocity of the jamming source exceeds 3 degrees per second, the waveform nulls at the normal update rate will not be able to align with the jammer, thus causing the system's anti-jamming to fail. Therefore, the high dynamic threshold is calibrated to 3.0 degrees per second.

[0053] In one specific implementation, S3 includes: S31. Input the generated digital baseband waveform into the pre-established power amplifier inverse nonlinear characteristic model; S32. Before the digital baseband waveform is input to the digital-to-analog converter, the phase and amplitude compensation of the digital baseband waveform is calculated in reverse by using the power amplifier's inverse nonlinear characteristic model to obtain the pre-distorted baseband signal, taking into account the inherent amplitude and phase nonlinear distortion effect of the RF power amplifier operating in the saturation region. S33. Input the pre-distorted baseband signal into a digital-to-analog converter and convert it to output an ultra-high frequency analog baseband signal; S34. The ultra-high frequency analog baseband signal is sent to the upconverter to be modulated to the working frequency band, and then input to the radio frequency power amplifier for power amplification to obtain a radio frequency transmission waveform that suppresses nonlinear distortion and radiates into space.

[0054] It should be noted that for the S31, the RF power amplifier of the airborne radar typically operates in the extremely saturated region to pursue maximum radiation efficiency. This leads to strong nonlinearity in the power amplifier, namely amplitude-amplitude distortion (AM-AM distortion) and amplitude-phase distortion (AM-PM distortion). This nonlinear effect physically causes severe sidelobe rise in the transmitted signal spectrum, thus filling the frequency domain dip null in the S2. To address this, the radar system extracts the input-output complex envelope data of the RF power amplifier in the saturated region through offline testing or online closed-loop feedback coupling. A forward nonlinear model of the power amplifier is established through polynomial fitting or memory polynomial fitting. Based on this, an inverse nonlinear characteristic model of the power amplifier is constructed through mathematical inversion or Taylor series inverse expansion. Its physical essence is the inverse function of the nonlinear transmission characteristics of the power amplifier.

[0055] For S32, during the time-domain digital processing stage, the radar signal processor inputs the digital baseband waveform generated in S2 into the power amplifier's inverse nonlinear characteristic model. This model calculates the correction amount for the amplitude and phase of each sampling point of the digital baseband waveform, and this correction amount is superimposed on the original sampling points to generate a predistorted baseband signal. This step artificially introduces a predistortion distortion before signal radiation, equal in magnitude but opposite in direction to the physical distortion of the RF power amplifier, giving the predistorted baseband signal complementary nonlinear characteristics to the power amplifier distortion before it is input into the power amplifier.

[0056] The power amplifier inverse nonlinear characteristic model of this application embodiment is an inverse function of nonlinear transmission characteristics constructed based on memory polynomial theory. To ensure that the deep null characteristics of the radar radiation waveform within the interference band are not lost due to the saturation nonlinearity effect of the RF power amplifier, this system has processed the construction and calibration of this model. Through discretization, the model has the following polynomial structure in the digital baseband processing module:

[0057] In the formula, This represents the nth sampling point of the predistorted baseband signal after inverse nonlinear compensation processing. This represents the sampling point of the digital baseband waveform input at time nd; It represents the magnitude of the digital baseband waveform sampling point, characterizing the instantaneous amplitude of the signal envelope; This represents a pre-stored memory polynomial coefficient matrix that maps the nonlinear inverse response characteristics of the RF power amplifier at that frequency and power level. The order of nonlinearity determines the precision of the model's compensation for AM-AM and AM-PM nonlinear distortion in the power amplifier. The depth of memory determines the model's ability to compensate for memory distortion caused by power amplifier thermal effects and parasitic parameters.

[0058] This is a drive signal with distortion characteristics pre-calculated by the digital baseband processing module before the input digital baseband waveform enters the digital-to-analog converter and RF power amplifier. The RF power amplifier has nonlinear transmission characteristics, which manifest as gain compression as input power increases. If an ideal waveform is directly input, severe nonlinear distortion will occur at the output after passing through the power amplifier, causing the energy null originally established in the interference band to be raised, thus losing its anti-interference capability. This is addressed by pre-applying a distortion in the digital domain that is "directly opposite" to the nonlinear characteristics of the power amplifier. When the signal passes through the power amplifier, the nonlinearity of the power amplifier just cancels out this pre-introduced distortion, thus restoring an ideal waveform without distortion at the output of the power amplifier.

[0059] against The nonlinearity of the power amplifier is not only related to the input amplitude at the current moment, but also affected by the thermal effect of the transistor, the parasitic parameters of the bias circuit, and the filtering characteristics of the broadband signal, thus exhibiting a memory effect. It is a set of complex weights, obtained through offline or online system calibration. It assigns precise amplitude and phase weights to components of different nonlinear orders q and different delay times d, enabling the predistortion model to adaptively inversely match the physical characteristics of the current power amplifier.

[0060] against If the order Q is too low, for example, only linear or third-order polynomials are considered, the strong nonlinear characteristics of the high-power region of the power amplifier cannot be adequately fitted; if the memory depth K is too small, the out-of-band spectral asymmetry caused by time lag cannot be eliminated. By introducing a double summation structure, this polynomial mathematically constitutes an engineering simplification of the Volterra series of a strongly nonlinear time-varying system that can approximate it with arbitrary precision, thus achieving a balance between computational complexity and compensation accuracy.

[0061] This formula incorporates the instantaneous amplitude nonlinear term. With historical time delay item By performing multidimensional product combinations, the inverse mapping of power amplifier nonlinearity and memory effect is mathematically reproduced. This polynomial operation generates the digital baseband waveform. When driving the power amplifier, since the polynomial is the mathematical inverse function of the power amplifier's transmission characteristics, the actual physical transmission curve of the power amplifier is linearly equivalent to the inverse function after being cascaded, thus ensuring that the output signal maintains the frequency domain dip characteristics designed in the design and reducing the failure of anti-interference performance caused by power amplifier saturation.

[0062] To ensure that the model can adapt to complex physical changes in the airborne environment, such as drastic temperature fluctuations and changes in antenna VSWR, the model coefficients in this system... Instead of static constants, the system dynamically indexes and fine-tunes itself based on the current radar operating status. During the offline calibration phase, the system simulates the full operating temperature range of the airborne radar in the laboratory, from -55°C to 85°C, and under different voltage supply levels. The input and output envelopes of the RF power amplifier are simultaneously measured using a power analyzer. The polynomial coefficient matrix for different operating conditions is calculated using the least squares method and stored in the non-volatile memory of the radar processor. A directional coupler is integrated into the transmitter link to capture the actual output power and waveform characteristics of the RF power amplifier in real time. The radar signal processor performs a real-time error comparison between the coupled-backed actual output waveform and the expected designed digital baseband waveform. If a shallowing of the null depth within the frequency band is detected, the processor automatically corrects the currently used coefficient matrix based on the error gradient. This allows for real-time tracking and adaptive calibration of the power amplifier's nonlinear behavior at the physical link layer. Existing technologies typically focus only on the overall linearization of the power amplifier's output amplitude and phase, while the core physical purpose of this system's model is to maintain a null in the frequency domain spectrum. Since the nonlinear distortion of the RF power amplifier causes out-of-band emission in the null region of the signal spectrum, this is equivalent to forcibly injecting spurious energy into the null center. This system uses the aforementioned model for pre-distortion processing, essentially pre-assigning negative distortion characteristics to the signal at the input, ensuring that the nonlinear distortion effectively cancels out the pre-set negative distortion after the signal passes through the power amplifier. This mechanism ensures that the energy of the radar-radiated electromagnetic waves within the interference band is at the physical noise floor level before entering space, thus achieving optimal electromagnetic interference immunity.

[0063] For S33 and S34, the predistorted baseband signal is converted by a high-precision digital-to-analog converter to output an analog baseband signal. Subsequently, it is up-converted by a mixer to the X-band where the radar operates. The analog signal at this point carries predistortion characteristics that complement those of the subsequent RF power amplifier. When this signal passes through the RF power amplifier, the amplifier's own nonlinear distortion cancels out the pre-set inverse distortion in the signal. Through this physical cancellation process, the RF transmission waveform output by the power amplifier is restored to a standard linear transmission state, retaining the spectral dip null feature deeper than -50dB within the interference band, radiating into space without distortion.

[0064] In some optional embodiments, regarding step S3, it is assumed that the maximum output power of the RF power amplifier is 1000 watts, operating in the saturation region. When the digital baseband waveform output from S2 is directly input into the power amplifier, due to AM-AM and AM-PM nonlinear effects, the null depth of the output signal in the 9.6 GHz interference band degrades from the designed -55 dB to -18 dB, failing to achieve the function of interference avoidance transmission. The system calls the internally integrated memory polynomial power amplifier inverse nonlinear characteristic model to perform time-domain multiplication and accumulation inverse nonlinear calculation on the digital baseband waveform, outputting a predistorted baseband signal. After this predistorted baseband signal is sent to the power amplifier, it is canceled by the power amplifier's physical nonlinearity, and the null depth of the actual RF transmission waveform output by the power amplifier at 9.6 GHz is restored to -52 dB, effectively protecting the radar transmission energy from leakage into the interference band, while not interfering with other friendly electromagnetic devices in the same frequency band in space.

[0065] In one specific implementation, S4 includes: S41. Receive antenna array to collect spatial echo data; S42. Spatial spectrum estimation is performed on the collected echo data through the radar receiving antenna array to determine the spatiotemporal incident direction of the residual non-uniform interference. The spatiotemporal incident direction is mapped and associated with the interference frequency band weighting vector to calculate the spatiotemporal steering array matrix of the residual non-uniform interference. S43. Based on the space-time steering array matrix, construct a projection operator that projects the signal components onto the interference subspace; S44. Perform a difference operation between the received echo data and the projection operator. By removing the projection components belonging to the interference subspace in the echo data and retaining the remaining null space components, the space-time cancellation processing of the target subband is completed, and a clean radar target echo is output. S45. The space-time cancellation processing of the target sub-band only applies to the interfering sub-bands identified through the passive pure listening window, and maintains the original echo characteristics within the non-interfering sub-band range to ensure target detection gain. The echo data of the target sub-band that has undergone space-time cancellation processing, along with the echo data of the uninterrupted sub-band that has not undergone projection cancellation operation, are input into the synthesis filter bank for sub-band splicing reconstruction to output a full-bandwidth pure radar target echo signal.

[0066] It should be noted that for S41, the radar receiving antenna array activates multiple receiving channels during its active duty cycle to synchronously and coherently sample the spatial reflected echoes and obtain time-domain echo data. At this time, although the transmitted waveform has a deep spectral null in the interference band, the strong interference signal radiated by the space jammer will still penetrate into the echo through the sidelobes of the receiving antenna. Furthermore, due to the multipath effect and the inconsistency of the array channels, this interference exhibits a non-uniform distribution in both the spatial and frequency domains.

[0067] For S42, the spatial spectrum of the acquired echo data is estimated using the radar receiving antenna array, such as the MUSIC or ESPRIT algorithm, to determine the spatiotemporal incident direction of the residual non-uniform interference. Based on this, and combined with the prior characteristics of the sidelobe gain of the transmitted beam in the incident direction, the coupling energy of the residual interference is calculated and a spatiotemporal steering matrix is ​​constructed. Since the spatial electromagnetic wave radiated by S3 has a specific physical radiation pattern and waveform characteristics, the system knows the energy attenuation of the transmitted waveform within a specific spatial azimuth angle and frequency domain stopband. The system processor uses the prior physical distribution of the sidelobes of the transmitted beam in the interference interception space to estimate the spatial azimuth of the incoming wave from the interference source by inverse estimation, and performs cross-correlation mapping with the interference frequency band weighted vector extracted in S1. Since the interference has a specific incident angle in space and a specific stopband bandwidth in the frequency domain, the processor calculates the Kronecker product of the spatial steering vector and the temporal steering vector of the residual interference, and then combines them to construct a spatiotemporal steering array matrix that can accurately characterize the electromagnetic distribution characteristics of the residual non-uniform interference.

[0068] For S43, the radar signal processor establishes the characteristic subspace of the interference using the space-time steering array matrix. To achieve lossless physical cancellation of the interference energy, the processor calculates an orthogonal projection matrix as a projection operator based on the matrix oblique projection or orthogonal projection theorem. This projection operator physically decomposes any input signal into a projection component of the interference subspace and a null space signal component orthogonal to it.

[0069] For S44, the step of performing space-time cancellation processing on the target subband of the echo data includes: A low-pass prototype filter is obtained, and the coefficients of the low-pass prototype filter are decimated at equal intervals according to a preset number of sub-bands to obtain multiple parallel multiphase branch filters. The echo data is converted from serial to parallel using a multi-channel delay commutator so that the data in each parallel channel generates a sequentially increasing unit delay, and is downsampled to a low data rate corresponding to the number of sub-bands. The downsampled data from each channel is input into the corresponding multiphase branch filter for parallel convolution filtering. At each downsampling output moment, a fast Fourier transform is performed on the output data of all the multiphase branch filters. By rotating the phase, the signals of each channel are modulated onto the corresponding physical frequency band and synthesized into multiple independent and continuously spliced ​​subband data. The sub-band data whose frequency range overlaps with or falls within the frequency band corresponding to the interference frequency band weighting vector is identified as the target sub-band.

[0070] Specifically, in order to reduce the system's computing power load while achieving precise isolation of interference frequency bands, this embodiment adopts a channelized architecture based on multiphase analysis filter banks to divide the radar full-bandwidth echo data into multiple independent sub-band channels.

[0071] Based on the system's preset number of subbands and the radar receiver's full-bandwidth sampling rate, a low-pass prototype filter is designed. The cutoff frequency of this prototype filter perfectly matches the bandwidth of a single subband. The impulse response coefficients of this prototype filter are then subjected to polyphase decomposition, with the number of decomposition paths matching the preset number of subbands. Specifically, the decomposition method involves using the number of subbands as the interval step size to decimate the coefficients of the prototype filter at equal intervals, thereby reconstructing the single high-order prototype filter into multiple parallel low-order polyphase branch filters. Each branch filter is responsible for the filtering coefficients of its corresponding channel.

[0072] The high-speed serial full-bandwidth echo sequence acquired by the radar receiver is first fed into a multi-channel delay commutator. This commutator rotates and switches according to the radar sampling rate, distributing the continuously input high-speed serial echo data sequentially to various parallel processing branches. Through this serial-to-parallel conversion, the data streams of each branch channel generate progressively increasing unit delays in time, while the data rate of each branch naturally decreases to a multiple of the original sampling rate. Physically, this achieves downsampling equivalent to a multiple of the sub-band size, reducing the throughput pressure on subsequent digital signal processing.

[0073] The downsampled data streams from each branch channel are input into their respective multiphase branch filters for parallel convolution filtering. This step suppresses spectral aliasing caused by downsampling and performs phase alignment on the signals from each branch using specific filter coefficients of each multiphase branch. After filtering, at each downsampled output time, the output data of all parallel branch filters are treated as a single vector and input into a Fast Fourier Transform (FFT) for multi-point FFT. This FFT physically acts as a digital phase modulator, applying equally distributed phase rotation to each branch to modulate and shift the baseband signal of each channel to its corresponding physical frequency band, thereby synthesizing the full-bandwidth echo into multiple independent and continuously stitched sub-band channel signals in the frequency domain.

[0074] Based on the center frequency and bandwidth of the interference source obtained during the passive situational awareness phase, the frequency range covered by the interference signal is calculated. This interference frequency range is then compared and mapped to the physical frequency domain boundaries of each segmented sub-band channel. All sub-band channels whose frequency range overlaps with or falls within the interference frequency range are marked and locked as target sub-band channels; other sub-band channels unaffected by interference are marked as non-interference sub-band channels. The data of the locked target sub-band channels will be sent separately to the subsequent adaptive space-time cancellation processor for interference cancellation, while the data of the non-interference sub-band channels will be directly bypassed and maintained.

[0075] For steps S44 and S45, the processor multiplies the received echo data with the projection operator, i.e., performs difference cancellation. This operation physically removes interference components from the echo data that coincide with the incident direction and the affected frequency band of the interference space. To avoid energy loss of normal target signals in non-interference frequency bands due to this forced cancellation operation, the space-time cancellation processing of this target sub-band is strictly limited to the polyphase filter channels corresponding to the interference sub-bands identified by the passive pure listening window in step S1. In the remaining uninterrupted sub-bands, the processor does not perform any projection cancellation operation and directly retains the received original echo data, thereby preventing the target detection gain loss caused by the projection operation and ensuring the target detection probability during full-band synthesis. The echo data of the target sub-band that has undergone space-time cancellation processing, along with the echo data of the uninterrupted sub-bands that have not undergone projection cancellation, are input to the synthesis filter bank for sub-band splicing and reconstruction to output a clean radar target echo signal with full bandwidth.

[0076] The interference subspace projection cancellation process constructed in this embodiment can be represented as follows:

[0077] In the formula, This represents the clean radar target echo vector output after cancellation processing; This represents the column vector of echo data containing residual non-uniform interference acquired by the receiving antenna array; This represents the orthogonal projection operator matrix constructed based on the space-time steering array matrix, used to accurately extract the projection components of the echo signal in the interference subspace; This represents the physical projection component of the echo data onto the interference subspace, i.e., the identified residual non-uniform interference component.

[0078] In one specific implementation, when airborne radar signal anti-jamming processing methods face non-uniform interference in the electromagnetic environment, the complex dynamic characteristics of non-uniform interference in both the frequency and time domains mean that a fixed projection operator cannot adjust the cancellation strength according to the real-time spectral distribution characteristics of the non-uniform interference. When performing fixed cancellation depth processing, airborne radar signal anti-jamming processing methods often suffer from the following drawbacks: when the spectral distribution of the non-uniform interference is relatively flat or the interference energy is low, an excessively strong fixed cancellation depth can cause the projection operator to overfit the airborne radar target echo signal, resulting in unnecessary damage to the amplitude and phase information of the airborne radar target echo signal, thus reducing the signal-to-noise ratio of the airborne radar target echo signal.

[0079] Therefore, before performing space-time cancellation processing of the target subband for residual non-uniform interference in the infiltrated echo data, the following steps are also included: Calculate the spectral entropy value of the target sub-band in real time, and construct an adaptive weighting factor based on the spectral entropy value; An adaptive weighting factor is applied to the projection operator, and the cancellation depth of the projection operator in the target subband is adjusted by the adaptive weighting factor to achieve fine suppression of interference energy.

[0080] Specifically, the airborne radar signal anti-jamming processing method introduces spectral entropy calculation at the receiver to quantify the complexity of residual interference within the target sub-band. For the j-th target sub-band channel, the airborne radar signal anti-jamming processing method statistically analyzes the power distribution of frequency points within the j-th target sub-band, letting... Indicates the j-th target subband. Power density at each frequency point, normalized power spectral density Represented as:

[0081] in, Indicates the j-th target subband. Normalized power spectral density at each frequency point; Indicates the j-th target subband. Power density at each frequency point; j represents the index of the target sub-band; L represents the frequency index within the target sub-band; L represents the total number of frequency points within the target sub-band.

[0082] Based on the above normalized power spectral density, the airborne radar signal anti-jamming processing method constructs the spectral entropy of the j-th target sub-band. for:

[0083] In the formula, This represents the spectral entropy value of the j-th target sub-band; The symbol represents the logarithmic operator with base 2.

[0084] Airborne radar signal anti-jamming processing method based on spectral entropy value Real-time construction of adaptive weighting factors The specific expression is:

[0085] In the formula, The variable represents the adaptive weighting factor for the j-th target sub-band, and exp represents the exponential function operator. This represents the preset sensitivity coefficient, with a value of 0.5.

[0086] Airborne radar signal anti-jamming processing method will use adaptive weighting factors By applying the original projection operator, an adaptively weighted projection operator is constructed: ,in, This represents the adaptively weighted projection operator; Let represent the original projection operator for the j-th target subband.

[0087] The airborne radar signal anti-jamming processing method uses an adaptively weighted projection operator to cancel the received signal, obtaining clean radar echo data.

[0088] In the formula, This represents the clean radar echo data of the j-th target sub-band. This represents the raw received signal data of the j-th target subband; This represents the adaptively weighted projection operator.

[0089] By introducing spectral entropy calculation and an adaptive weighting mechanism, a closed-loop adaptive processing method for non-uniform interference is achieved. The airborne radar signal anti-jamming processing method quantifies the disorder and complexity of the interference signal within the target sub-band by calculating the spectral entropy value of the target sub-band in real time. The method dynamically adjusts the cancellation depth of the projection operator within the target sub-band using an adaptive weighting factor, enabling it to change the cancellation intensity in real time according to the strength and distribution characteristics of the interference energy. When the interference signal is complex and has high energy, the adaptive weighting factor increases the projection depth to completely filter out the interference; when the interference signal is relatively stable, the adaptive weighting factor decreases the projection depth to reduce damage to the target signal.

[0090] In some optional embodiments, regarding step S4, the radar receiving antenna array acquires echo data containing residual non-uniform interference. The system identifies the interference as originating from a spatial azimuth angle of 15 degrees and an elevation angle of 2 degrees by analyzing the sidelobe distribution characteristics of the transmitted waveform in the interference source's spatial domain. Combining this with the interference frequency band weighting vector extracted in S1, the system calculates the two-dimensional joint space-time steering array matrix of the interference source in both the spatial and frequency domains.

[0091] The processor constructs a matrix of size based on this matrix. The projection operator matrix, where The total spatiotemporal dimension is defined as follows. Within the disturbed sub-band channel from 9.60 GHz to 9.64 GHz, the processor multiplies the echo vector of this channel by a projection operator to filter out interference energy. In the adjacent non-interference sub-band, the signal is output directly without passing through the projection operator. After coherent synthesis, the radar target detector successfully detects weak targets located against a strong interference background.

[0092] The interference interception spatial domain and sidelobe distribution characteristics are obtained based on a limited number of historical calibration data. Specifically, in a microwave anechoic chamber without backscattering, the radar antenna is mounted on a multi-degree-of-freedom high-precision turntable. The transmitter is controlled to radiate the digital baseband waveform generated by S2, and a standard receiving horn antenna is erected 10 meters in front of the antenna. The antenna is rotated in 0.1-degree steps by the turntable, and the sidelobe electromagnetic power of the antenna's radiation pattern in a 360-degree azimuth of the entire space is measured and recorded. Simultaneously, a standard jammer transmits interference signals of the same frequency band on a specific angular grid, calibrating the physical interception effectiveness of the radar antenna against interference at different angles. This establishes a mapping database between antenna sidelobe gain and spatial interference interception capability, serving as the offline calibration basis for calculating the space-time steering array matrix.

[0093] To enable those skilled in the art to more clearly understand and implement the signal anti-interference processing method of this invention, a quantitative analysis is presented in conjunction with a specific airborne detection application scenario, demonstrating the complete physical closed loop from passive situational awareness acquisition to active precise interference radiation avoidance, and finally to adaptive clutter filtering at the receiver. It is assumed that the airborne radar employs an 8-channel equally spaced uniform linear array, with each channel's RF front-end possessing an equivalent physical gain, and initiates environmental sensing during the passive silent period of the coherent processing interval. When the radar receiver detects sudden frequency-hopping interference in external space, a high-speed analog-to-digital converter synchronously and equally spacedly coherently samples the analog baseband noise signals of the 8 physical channels at a sampling rate of 200 MHz. Within a passive pure listening window lasting 100 microseconds, the analog-to-digital converter captures snapshot data at 20,000 sampling moments, with each moment's data quantized into an 8-dimensional complex instantaneous sampling column vector. These vectors are arranged and concatenated in horizontal order along the sampling time axis in the cache of a field-programmable gate array (FPGA) to construct an 8x20000-dimensional time-domain multi-channel noise sampling data matrix. This physical construction process satisfies a matrix mapping relationship, represented as follows: Among them, the temporal noise sampling data matrix The study fully recorded the spatiotemporal two-dimensional joint physical distribution of spatial electromagnetic noise in 8 channel dimensions and 20,000 time sampling dimensions, providing underlying digital discrete samples for subsequent estimation of the spatial electromagnetic situation.

[0094] After acquiring the time-domain noise sampling data matrix, the processor first performs DC removal and amplitude-phase mismatch correction preprocessing on it to obtain a normalized noise sampling matrix. To characterize the spatial correlation of noise and interference between different antenna channels, the processor multiplies the normalized matrix by its conjugate transpose, then divides by the total number of samples (20,000) and performs a statistical average to obtain an 8x8 dimensional original electromagnetic environment noise covariance matrix, the mathematical expression of which is: ,in, This represents the estimated electromagnetic environment noise covariance matrix. This represents the noise snapshot column vector at time s after preprocessing, i.e., removing DC bias and inter-channel amplitude-phase mismatch; It should be The conjugate transpose of is used to construct an outer product matrix by multiplying it with the original vector.

[0095] To ensure the robustness of matrix calculations in complex airborne environments, the system implemented diagonal loading and reconstruction, with the following physical form: in, This represents the modified covariance matrix generated after performing the diagonal loading operation. This matrix is ​​strictly positive definite in mathematical properties, ensuring numerical stability during subsequent eigenvalue decomposition or matrix inversion operations. This is the original statistical covariance matrix calculated above; This represents an artificially introduced diagonally loaded scalar constant, the value of which is equal to the equivalent fictitious thermal noise power in this environment. It is used to raise the minimum eigenvalue of the matrix and prevent singular matrices from causing computational oscillations. The dimension is The identity matrix has all 1s on its diagonal and all 0s on its off-diagonal. By multiplying it by the loaded power and adding it to the main diagonal of the original matrix, the ill-conditioned nature of the matrix is ​​repaired.

[0096] Due to the limited sampling window width, the number of independent snapshot samples is finite. To avoid ill-conditioned computational states in the matrix, the processor introduces a diagonal loading technique to calculate the average power of the main diagonal elements. After normalizing the original electromagnetic environment noise covariance matrix, the loading factor is set to -20 dB to determine the loaded noise power. The value is 0.01. This power is added to the main diagonal of the original matrix to achieve a positive definite physical reconstruction of the electromagnetic environment noise covariance matrix. The calculation formula is: ,in, The covariance matrix is ​​an 8x8 dimensional unit matrix. The processor performs first-order difference calculations on the diagonally loaded covariance matrix to extract the gradient of eigenvalue changes. When this gradient jumps from 0.1 to 4.5, exceeding the preset transient rate of change threshold of 1.2 calibrated through multiple measurements in an anechoic environment, a sudden interference is identified. The processor extracts the interference center frequency of 9.62 GHz and the bandwidth of 40 MHz from its frequency domain energy spectrum. Then, it sets the weights to 1 at the spectral grid indices within the frequency range of 9.6 GHz to 9.64 GHz, and sets the weights to 0 for the remaining frequency bands, thus constructing a 256-dimensional interference frequency band weighted vector. .

[0097] To generate an active transmit waveform capable of forming a deep null at 9.62 GHz, the system weights the interference band vector. As a stopband constraint in the time-frequency optimization process, a pre-stored linear frequency modulated signal with excellent autocorrelation characteristics is read as a reference waveform column vector. At this point, the system task scheduler detected that the radar processor's real-time computing load rate was 42%, lower than the preset high load threshold of 75%, and the calculated spatial relative angular velocity of the interference source was 0.8 degrees per second, lower than the high dynamic threshold of 3.0 degrees per second. Due to sufficient computing resources and the relatively slow movement of the interference source, the system initiated a high-precision reconstruction timing sequence, tightening the convergence threshold of the alternating direction multiplier method to 1.0e-6 and setting the maximum number of iterations to 45. Under these parameter constraints, the processor constructed a multidimensional non-convex joint optimization objective function, whose augmented Lagrangian objective function satisfies the formula: The scalar penalty factor here. Setting it to 10 adjusts the balance between waveform matching and frequency domain null depth; it is also the second-order augmentation penalty constant. Set it to 2 to constrain the time-domain auxiliary variable. With the waveform vector to be synthesized The phase and amplitude are identical, and the dual multiplier column vector is... By performing 45 alternating iterations at a convergence threshold of 1.0e-6, a digital baseband waveform column vector with a spectral null depth of up to -58 dB and satisfying a constant amplitude envelope constraint was finally generated within the interference band. .

[0098] Before the generated digital baseband waveform is sent to the high-speed digital-to-analog converter, to prevent nonlinear amplitude and phase distortion caused by the RF power amplifier operating under high power saturation, the system calls the memory polynomial predistortion compensation module preset in the digital signal processor to fill the designed spectral null. The polynomial coefficients of this nonlinear characteristic model were obtained during the system's factory calibration phase by performing input-output envelope tests on the power amplifier at an operating temperature of 55 degrees Celsius and a DC bias voltage of 28 volts, and then fitting and calibrating using a least-squares algorithm. The processor sets the model's nonlinear order Q to 5 and the memory depth K to 3, and performs inverse phase and amplitude compensation calculations on the baseband signal to be transmitted. The expression for this physical calculation process is as follows: ,in Indicates the first The magnitude of the digital baseband waveform sampling points input at any given time represents the instantaneous amplitude of the envelope. This is a pre-stored 5x3 three-dimensional predistortion compensation polynomial coefficient matrix. The predistortion baseband signal is calculated using the above formula. Including artificially introduced inverse distortion components, when it passes through the RF power amplifier, the power amplifier's own physical nonlinear distortion cancels out the pre-distortion components in the signal. Tests show that the RF transmission waveform radiated into space maintains a spectral null depth of -52 dB in the 9.6 GHz to 9.64 GHz interference band, avoiding null degradation to -18 dB, thus ensuring the effectiveness of the transmission anti-interference strategy.

[0099] During the radar's active duty cycle, the receiving antenna array collects echo signals reflected from spatial targets. An external active jammer continuously operates, causing high-power electromagnetic interference to infiltrate the echo through the sidelobes of the receiving antenna. The processor first reads the sidelobe distribution database of the transmitted waveform, which is obtained by calibrating the radar in an anechoic chamber using a high-precision turntable with a 0.1-degree step rotation. By comparing the electromagnetic energy of the received signals in different antenna channels, the processor calculates that the infiltrated residual interference source originates from a direction with a spatial azimuth angle of 15 degrees and an elevation angle of 2 degrees. The processor performs a spatiotemporal mapping correlation between this spatial incident direction and the 9.62 GHz interference frequency band identified during the passive phase, calculating the spatiotemporal two-dimensional joint steering vector of this angle and frequency band across the eight antenna channels and coherent pulse sequences. Multiple interference spatiotemporal steering vectors are combined to construct a spatiotemporal steering array matrix describing the spatial and frequency domain distribution of the residual interference electromagnetic spectrum. Based on this steering array matrix, an 8x8-dimensional orthogonal projection operator is calculated within the interference frequency domain sub-band, serving as the projection operator for subsequent steps.

[0100] To suppress interference without damaging normal target signals in the unaffected frequency band, the radar signal processor uses a polyphase filter bank to divide the received multi-channel time-domain echo data into multiple independent sub-band echo channels. For the affected sub-band channel (9.58 GHz to 9.62 GHz) identified through passive listening, the processor invokes the projection operator. Perform space-time orthogonal projection cancellation. The physical process involves extracting the interference projection component from the target echo that coincides with the incident direction and the disturbed frequency band of the interference space using a projection operator, and then subtracting this projection component from the total echo. This process satisfies the cancellation model, specifically expressed as follows: .in This represents an 8-dimensional echo data column vector containing residual non-uniform interference collected in the receiving channel of the disturbed subband. It physically includes real target echoes, strong interference, and thermal noise components. To calculate the interference subspace projection components, the two vectors are subtracted and their differences are canceled. The output is a pure disturbed subband target echo vector that forms an ultra-deep null in the interference angle and interference frequency band. Through the physical processing of the aforementioned formula, the interference-to-noise ratio in the disturbed sub-band adaptively decreases from 35 dB to 2 dB. Meanwhile, in the remaining clean sub-band channels that are not disturbed, the echo signal flows directly without passing through the projection operator, preventing energy loss in normal frequency band target detection caused by zero-space projection.

[0101] After each sub-band channel outputs its signal, the processor calls an adaptive phase and amplitude coherence compensation factor to weight and compensate for each sub-band signal. The value of this compensation factor is determined by the ratio of the center frequency of each sub-band filter to the actual physical bandwidth, and is used to physically align the phase reference of each sub-band signal, which suffers from phase and amplitude distortion due to non-uniform sub-band division. The phase-aligned sub-band signals are then coherently accumulated and synthesized in Doppler, outputting a coherently restored full-band reconstructed signal. Subsequently, the full-band reconstructed signal is fed into a two-dimensional unit average constant false alarm rate detector. The detector calculates an adaptive electromagnetic decision threshold that matches a preset false alarm probability by measuring the statistical fluctuations of the reference units around the target detection unit. When the electromagnetic energy amplitude of the full-band reconstructed signal exceeds this decision threshold, the presence of the target is determined. The processor locks onto the two-dimensional grid coordinates corresponding to the strongest energy peak, reads out the electromagnetic round-trip time delay of the target as 800 microseconds, and the Doppler frequency shift as 22.6 kHz. Based on the physical formula of radar ranging, the physical distance of the target is calculated to be 120 kilometers, and the physical velocity of the target is calculated to be 352.4 meters per second based on the Doppler effect formula. Thus, the physical closed loop of airborne radar anti-jamming processing and parameter inversion is completed.

[0102] This embodiment provides an airborne radar signal anti-jamming processing system, including: The interference frequency band weighted vector acquisition module is configured to: calculate the gradient of eigenvalue changes in the electromagnetic environment noise covariance matrix in real time; when the gradient exceeds a preset transient rate of change threshold, insert a passive pure listening window between adjacent transmitted pulses; and extract the interference frequency band weighted vector through the passive pure listening window. The digital baseband waveform acquisition module is configured to: construct a multidimensional non-convex joint optimization objective function by using the interference frequency band weighting vector as a frequency domain stopband constraint condition; dynamically configure the convergence threshold of the alternating direction multiplier method based on the current radar processor's real-time computing power load rate; and generate a digital baseband waveform that satisfies the constant modulus constraint based on the objective function. A radiation module is configured to perform nonlinear predistortion compensation on the generated digital baseband waveform and radiate the waveform into space via an RF power amplifier. The clean radar target echo module is configured to: receive echo data, and based on the distribution characteristics of the beam sidelobes formed by the radiated waveform in the interference interception space domain, perform space-time cancellation processing of the target subband for residual non-uniform interference penetrating into the echo data, so as to output a clean radar target echo.

[0103] In this embodiment, the interference band weighted vector acquisition module physically includes a multi-channel passive receiving unit in the antenna array, multiple high-sensitivity low-noise amplifiers, a high-speed analog-to-digital converter, and an eigenvalue calculation pipeline in the field-programmable gate array (FPGA). The FPGA in this module has pre-stored factory-calibrated thermal noise electromagnetic environment threshold values. During the rest period of the coherent processing interval of the airborne radar operation, the FPGA controls the receiver to switch to passive detection mode. At this time, the instantaneous electromagnetic energy of the receiving channel is monitored in real time through the analog-to-digital converter. Once it is detected that the instantaneous channel energy exceeds the factory-calibrated thermal noise electromagnetic environment threshold value for multiple consecutive sampling points, the timing control core of the FPGA will instantaneously send a high-level interrupt signal to the transmit timing generator. This interrupt signal will forcibly cut off the transmit trigger pulse of the transmitter's internal RF modulator, forcibly inserting a preset width of physical silence time period, i.e., a passive pure listening window, between adjacent transmit pulses. Within the passive pure listening window, the transmitter's high-voltage bias is completely turned off. A field-programmable gate array (FPGA) performs a multi-point fast Fourier transform on the time-domain electromagnetic data captured within the listening window to extract the electromagnetic environment noise covariance matrix. By performing real-time online power iteration on this covariance matrix, its maximum principal eigenvalue is quickly solved, and the first-order difference of this principal eigenvalue within adjacent sampling periods is calculated to obtain its eigenvalue change gradient. If this gradient exceeds a preset transient rate of change threshold, it is determined that there is strong sudden active interference in the current electromagnetic environment. Subsequently, the module locates the continuous spectrum grid index in the frequency domain where the power spectral density exceeds 20dB of the background noise floor, uses this as the stopband interval, assigns a weight of 1 to the corresponding frequency band, and assigns a weight of 0 to the non-interference frequency band, ultimately constructing a one-dimensional discretized interference frequency band weighted vector.

[0104] The digital baseband waveform acquisition module is physically deployed within a high-speed multi-core digital signal processor or a floating-point graphics processing unit. This module receives the interference band weighted vector in real-time via a bus interface and reads a pre-stored reference waveform with ideal autocorrelation characteristics from an on-chip cache. The processor uses the interference band weighted vector as a constraint to construct a multi-dimensional non-convex joint optimization objective function as described above. To ensure the real-time performance of radar calculations under complex multi-task situations, the task scheduler within this module reads the overall computing load rate of the radar processor (i.e., the percentage of computing core occupancy) every working cycle, such as 10 milliseconds. Simultaneously, it calculates the angular velocity of the interference source relative to the radar platform axis using Doppler multi-round estimation. When the computing load rate exceeds a preset high load threshold, or the angular velocity of the interference source exceeds a high dynamic threshold, to prevent radar data stream congestion due to excessive waveform calculation time, the processor automatically limits the maximum number of iterations of the alternating direction multiplier method to a low constant value, such as 10 to 15 times, and correspondingly widens the iteration convergence threshold to 1.0e-4. Conversely, when the processor is running under low load and the interference source moves slowly, in order to pursue the ultimate frequency domain interference avoidance characteristics, the processor will adaptively tighten the convergence threshold to 1.0e-6 and allow the algorithm to run up to the set maximum number of iterations, such as 50 times. Through high-precision iterative calculations, it outputs a digital baseband waveform with continuous phase and constant amplitude.

[0105] The radiation module physically comprises a predistortion digital processing unit, a high-bandwidth digital-to-analog converter (DAC), an up-conversion mixer, and a gallium nitride (GaN) power amplifier. Because the GaN power amplifier exhibits intrinsic nonlinear distortion when operating at maximum efficiency, the radiation module invokes a pre-defined inverse nonlinear characteristic model of the power amplifier within the predistortion digital processing unit (e.g., a hard-core arithmetic block in an FPGA or DSP) before the digital baseband waveform is fed into the DAC. This model performs high-speed inverse nonlinear predistortion compensation calculations on the digital baseband waveform. The compensated predistortion baseband signal is then input to the DAC to reconstruct an ultra-high frequency analog waveform, which is then up-converted to the operating X-band and finally input to the GaN power amplifier. Since inverse distortion has been pre-introduced into the baseband signal, this distortion precisely cancels out its inherent AM-AM and AM-PM nonlinear responses when passing through the GaN power amplifier. This ensures that the RF transmission waveform output by the amplifier perfectly reproduces the designed frequency domain stopband dip, accurately radiating electromagnetic waves with spectral null physical characteristics into space.

[0106] The clean radar target echo module and target parameter inversion module are deployed in a general-purpose processor or dedicated signal processing board at the radar backend. When the antenna array receives mixed echo data containing target reflection and residual interference, this module reads the distribution database of beam sidelobes in the interference interception space domain during the transmission of the radiating module. Based on the a priori gain distribution of the transmission pattern, the spatial direction angle of arrival of the residual non-uniform interference is calculated. The processor performs a spatiotemporal joint mapping of this spatial direction angle of arrival with the stopband frequency band corresponding to the interference frequency band weighting vector to calculate the spatiotemporal steering array matrix of the residual non-uniform interference. Based on this matrix, an orthogonal projection operator for the interference subspace, which combines spatial and frequency domains, is constructed using the orthogonal projection principle. Subsequently, the processor performs a difference cancellation operation on the echo data and the orthogonal projection operator to completely remove the components belonging to the interference subspace from the echo data. During this cancellation process, the system controller controls the polyphase filter bank so that the projection cancellation operation only takes effect within the interfered subband channel identified by the passive pure listening window. In the other completely clean sub-band channels, the echo signal passes directly without any projection loss. Finally, all sub-bands are aligned after phase and amplitude compensation and then coherently synthesized across the entire frequency band. The synthesized signal is sent to a constant false alarm rate (CFAR) detector for target determination. When the signal amplitude exceeds the adaptive detection threshold, the presence of a target is determined, and the target's physical distance and radial velocity are calculated based on the peak coordinates and output to the radar terminal display.

[0107] The above are merely preferred embodiments of this application and do not limit the patent scope of this application. Any equivalent structural or procedural changes made based on the description and drawings of this application, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of this application.

Claims

1. A method for anti-jamming processing of airborne radar signals, characterized in that, include: The gradient of eigenvalue changes in the electromagnetic environment noise covariance matrix is ​​calculated in real time. When it exceeds a preset transient rate of change threshold, a passive pure listening window is inserted between adjacent transmitted pulses. The interference frequency band weighted vector is extracted through the passive pure listening window. The interference frequency band weighting vector is used as a frequency domain stopband constraint to construct a multidimensional non-convex joint optimization objective function. The convergence threshold of the alternating direction multiplier method is dynamically configured according to the real-time computing power load rate of the current radar processor. Based on the objective function and the convergence threshold, a digital baseband waveform that satisfies the constant modulus constraint is obtained. The digital baseband waveform is subjected to nonlinear predistortion compensation and then transmitted via an RF power amplifier; In response to the received echo data, the receiving array performs spatial spectrum estimation on the echo data to determine the interference incident direction. Combining the sidelobe gain characteristics of the transmitted waveform in the interference incident direction, it performs space-time cancellation processing on the echo data for the target subband and outputs a clean radar target echo.

2. The airborne radar signal anti-jamming processing method as described in claim 1, characterized in that, The step of inserting a passive listening window between adjacent transmitted pulses and extracting the interference frequency band weighting vector through the passive listening window includes: During the insertion of the passive listening window, the radar transmitter is kept in a physically silent state, and the radar receiver is turned on to passively receive spatial electromagnetic signals across the entire frequency band. The center frequency and bandwidth of the interference signal in the current space are extracted from the passively detected spatial electromagnetic signal. Based on the extracted center frequency and bandwidth, the corresponding interference band weighting vector is constructed.

3. The airborne radar signal anti-interference processing method as described in claim 2, characterized in that, The step of dynamically configuring the convergence threshold of the alternating direction multiplier method according to the current real-time computing power load rate of the radar processor, and obtaining the digital baseband waveform that satisfies the constant modulus constraint based on the objective function and the convergence threshold, includes: Real-time reading of the current radar processor's computing power load rate and the moving angular velocity of passively detected interference sources; When the computing power load rate is greater than the preset high load threshold or the angular velocity of the interference source is greater than the high dynamic threshold, the maximum number of iterations of the alternating direction multiplier method is reduced and the convergence threshold is relaxed. When the computing power load rate is not greater than the preset high load threshold and the moving angular velocity of the interference source is not greater than the high dynamic threshold, the convergence threshold is tightened, and iterative calculations are performed under the dynamically configured convergence threshold to output the digital baseband waveform.

4. The airborne radar signal anti-interference processing method as described in claim 1, characterized in that, The step of constructing a multidimensional non-convex joint optimization objective function by using the interference frequency band weighting vector as a frequency domain stopband constraint includes: Obtain a reference waveform with ideal autocorrelation characteristics preset by the radar system; By using the mean square error between the waveform to be synthesized and the reference waveform, combined with the scalar penalty factor preset by the system and the spectral constraint penalty term of each of the extracted interference frequency band weighting vectors for the waveform to be synthesized, the multidimensional non-convex joint optimization objective function is constructed so that the waveform to be synthesized forms an energy null trap in the frequency band corresponding to the interference frequency band weighting vector.

5. The airborne radar signal anti-jamming processing method as described in claim 1, characterized in that, The step of performing nonlinear predistortion compensation on the digital baseband waveform and transmitting it via an RF power amplifier includes: Before the digital baseband waveform is input to the digital-to-analog converter, the phase and amplitude compensation calculations are performed on the digital baseband waveform to address the inherent amplitude and phase nonlinear distortion effects of the RF power amplifier operating in the saturation region. The waveform after inverse compensation calculation is converted by the digital-to-analog converter and the radio frequency power amplifier to suppress nonlinear distortion, and then the electromagnetic wave carrying a specific frequency domain dip characteristic is emitted.

6. The airborne radar signal anti-jamming processing method as described in claim 1, characterized in that, The step of the receiving array performing spatial spectrum estimation on the echo data to determine the interference incident direction, and combining the sidelobe gain characteristics of the transmitted waveform in the interference incident direction, includes: The space-time incident direction of the residual non-uniform interference is determined based on spatial spectrum estimation. The space-time steering vector of the residual non-uniform interference is calculated by combining the sidelobe distribution characteristics of the emitted waveform in the space-time incident direction. Based on the space-time steering vector, a projection operator is constructed to project the signal components onto the interference subspace.

7. The airborne radar signal anti-interference processing method as described in claim 6, characterized in that, The projection operator is applied to the received echo data to extract the interference component, and the difference operation is performed between the echo data and the interference component. By removing the projection component belonging to the interference subspace in the echo data and retaining the remaining null space component, the spatiotemporal cancellation processing of the target subband is completed.

8. The airborne radar signal anti-jamming processing method as described in claim 1, characterized in that, The step of performing space-time cancellation processing on the echo data for the target subband includes: A low-pass prototype filter is obtained, and the coefficients of the low-pass prototype filter are decimated at equal intervals according to a preset number of sub-bands to obtain multiple parallel multiphase branch filters. The echo data is converted from serial to parallel using a multi-channel delay commutator so that the data in each parallel channel generates a sequentially increasing unit delay, and is downsampled to a low data rate corresponding to the number of sub-bands. The downsampled data from each channel is input into the corresponding multiphase branch filter for parallel convolution filtering. At each downsampling output moment, a fast Fourier transform is performed on the output data of all the multiphase branch filters. By rotating the phase, the signals of each channel are modulated onto the corresponding physical frequency band and synthesized into multiple independent and continuously spliced ​​subband data. The sub-band data whose frequency range overlaps with or falls within the frequency band corresponding to the interference frequency band weighting vector is identified as the target sub-band.

9. An airborne radar signal anti-jamming processing system, characterized in that, include: The interference frequency band weighted vector acquisition module is configured to: calculate the gradient of eigenvalue changes in the electromagnetic environment noise covariance matrix in real time; when the gradient exceeds a preset transient rate of change threshold, insert a passive pure listening window between adjacent transmitted pulses; and extract the interference frequency band weighted vector through the passive pure listening window. The digital baseband waveform acquisition module is configured to: construct a multidimensional non-convex joint optimization objective function by using the interference frequency band weighting vector as a frequency domain stopband constraint condition; dynamically configure the convergence threshold of the alternating direction multiplier method according to the current real-time computing power load rate of the radar processor; and obtain a digital baseband waveform that satisfies the constant modulus constraint based on the objective function and the convergence threshold. The radiation module is configured to perform nonlinear predistortion compensation on the generated digital baseband waveform and then transmit it via an RF power amplifier. The clean radar target echo module is configured to: in response to received echo data, the receiving array performs spatial spectrum estimation on the echo data to determine the interference incident direction, and, in combination with the sidelobe gain characteristics of the transmitted waveform in the interference incident direction, perform space-time cancellation processing on the echo data for the target subband, and output a clean radar target echo.

10. The airborne radar signal anti-jamming processing system as described in claim 9, characterized in that, The interference frequency band weighted vector acquisition module is further configured to: During the insertion of the passive listening window, the radar transmitter is kept in a physically silent state, and the radar receiver is turned on to passively receive spatial electromagnetic signals across the entire frequency band. The center frequency and bandwidth of the interference signal in the current space are extracted from the passively detected spatial electromagnetic signal. Based on the extracted center frequency and bandwidth, the corresponding interference band weighting vector is constructed.

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