Non-uniform random waveform design method for suppressing the two-dimensional sidelobe of beamforming sar

Abstract

The application discloses a non-uniform random waveform design method for suppressing bunched SAR two-dimensional sidelobes, and belongs to the technical field of synthetic aperture radar. Firstly, the system key parameters are established; then, the nonlinear frequency modulation phase is characterized by using Fourier series in the azimuth direction, the equivalent mapping relationship between the nonlinear frequency modulation phase and the Doppler frequency is established, the non-uniform pulse repetition interval sequence is generated by iterative solution which satisfies the Nyquist sampling and the minimum distance requirement; meanwhile, the phase model is constructed by using random Fourier coefficients in the range direction, the parameter optimization of the coefficient distribution range is carried out based on the central limit theorem and the 3σ criterion, and the waveform spectrum compactness is ensured; finally, the non-uniform time reference and the random phase modulation are fused to generate the non-uniform random waveform with the pulse-to-pulse agility characteristic. Through the cooperative design of the azimuth non-uniform sampling and the range random modulation, the joint suppression of the two-dimensional sidelobes is effectively realized, the imaging quality is improved, and the spectrum utilization rate of the waveform and the feasibility of the engineering implementation are ensured.

Description

Technical Field

[0001] This invention relates to the field of synthetic aperture radar technology, specifically to a non-uniform random waveform design method for suppressing two-dimensional sidelobes in clustered SAR. Background Technology

[0002] Spotlight synthetic aperture radar (SAR) occupies a central position in high-resolution Earth observation, operating around the clock and in all weather conditions, due to its ability to perform long-term staring observations of specific areas. In such radar systems, the design of the transmitted waveform directly determines the processing efficiency and image quality of the final echo signal. Linear frequency modulated (LFM) signals are widely used due to their ease of generation and mature processing, but their inherently high sidelobe levels after matched filtering can easily cause sidelobe energy from strong scattering points to mask nearby weak targets, severely limiting the dynamic range and clarity of SAR images. Therefore, how to effectively suppress sidelobes through active waveform design without sacrificing main lobe resolution and signal-to-noise ratio has always been a research hotspot in the field of high-resolution radar imaging technology.

[0003] In existing technologies, to overcome the signal-to-noise ratio loss bottleneck caused by traditional windowing processing, researchers mainly explore two dimensions: nonlinear frequency modulation (NLFM) and random waveforms. NLFM technology reshapes the spectral energy distribution by constructing nonlinear frequency-time relationships such as an "S" shape, thereby reducing sidelobes at the physical level. Random waveform design, such as in noisy radar or random frequency modulation (RFM) technology, utilizes the non-periodic and random nature of waveforms to suppress range sidelobes by coherently superimposing a large number of pulses within the synthetic aperture time. Furthermore, with increased hardware flexibility, some technologies are beginning to combine azimuth-oriented non-uniform sampling mechanisms with waveform diversity techniques, attempting to leverage pulse agility characteristics in complex electromagnetic environments to improve radar anti-jamming capabilities and imaging performance.

[0004] However, despite the theoretical progress made by existing waveform design methods, they still face severe challenges in practical high-performance spotlight SAR applications. On the one hand, most existing random waveform design schemes mainly focus on one-dimensional sidelobe suppression in the range direction. A few schemes that attempt to combine non-uniform sampling in the azimuth direction often rely on traditional window function approximations, resulting in insufficient joint suppression depth of two-dimensional sidelobes, which makes it difficult to meet the requirements of extremely low sidelobe imaging. On the other hand, random frequency-modulated waveforms are prone to spectral energy leakage during generation, making it difficult to ensure both waveform randomness and excellent spectral compactness. Furthermore, many theoretical designs do not fully incorporate physical timing constraints such as the minimum detection range and Doppler bandwidth of the radar system into closed-loop considerations, resulting in generated waveform sequences that may not be directly adaptable to actual engineering hardware platforms due to time-domain overlap or frequency-domain aliasing. Summary of the Invention

[0005] To address the high sidelobe interference problem in existing focused synthetic aperture radar (SAR) imaging processes, this invention provides a non-uniform random waveform design method for suppressing two-dimensional sidelobes in focused SAR. This method introduces a non-uniform sampling mechanism in the azimuth direction and a random phase modulation technique in the range direction, achieving joint suppression of range and azimuth sidelobes while taking into account the spectral compactness of the transmitted waveform and the physical constraints of the system.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a non-uniform random waveform design method for suppressing two-dimensional sidelobes in clustered SAR, comprising the following steps:

[0007] Step 1: Determine system parameters: Identify and input the key parameters of the spotlight SAR system. The key parameters include at least the carrier center frequency, system velocity, synthetic aperture time, reference point position, initial number of pulse repetition intervals (PRI), bandwidth of random frequency modulated transmit waveform, and pulse width. Step 2: Generate a non-uniform PRI sequence: Based on the key parameters, construct a nonlinear frequency modulation characteristic in the azimuth Doppler frequency domain. By establishing the mapping relationship between the nonlinear frequency and the Doppler frequency and performing iterative solutions, a non-uniform PRI sequence that meets the preset constraints is obtained, which is used to achieve azimuth sidelobe suppression. Step 3: Optimize the random Fourier coefficients: Based on the bandwidth and pulse width in the key parameters, construct the phase model of the random frequency modulation waveform using the random Fourier coefficients, and optimize the distribution range of the random coefficients according to the spectral compactness requirements to obtain a set of random Fourier coefficients for range-directed sidelobe suppression. Step 4: Synthesize non-uniform random waveforms: Use the non-uniform PRI sequence obtained in Step 2 as the time reference for pulse transmission, and substitute the random Fourier coefficients obtained in Step 3 into the phase modulation of each pulse to generate a non-uniform random waveform sequence with pulse agility characteristics.

[0008] Furthermore, in step two, when constructing the nonlinear frequency modulation characteristics, a Fourier series model is used to characterize the phase of the azimuth nonlinear frequency modulation waveform at the reference point; the characterization process includes: setting the number of optimized Fourier coefficients, adjusting the phase curve shape by adjusting the numerical value of the Fourier coefficients, and thus determining the corresponding optimized nonlinear frequency curve.

[0009] Furthermore, in step two, the specific process of establishing the mapping relationship and performing iterative solution is as follows: Differentiate the phase with respect to time to obtain an optimized nonlinear frequency function with respect to time; consider only the quadratic term in the phase that varies with slow time to construct a Doppler frequency function that varies with slow time; establish an equivalent mapping equation between the optimized nonlinear frequency function and the Doppler frequency function, such that the optimized nonlinear frequency corresponding to the initial uniform sampling point is equal to the Doppler frequency corresponding to the slow time; solve for the slow time based on the equivalent mapping equation, and determine the specific value of each PRI based on the difference between adjacent slow times.

[0010] Furthermore, the preset constraint condition is that the value of PRI must simultaneously satisfy the requirements of the Nyquist sampling theorem and the minimum distance range requirement; specifically, each calculated PRI value must be greater than the minimum time interval determined by the minimum detection distance of the system, and at the same time, it must be less than the maximum time interval determined by the azimuth Doppler bandwidth.

[0011] Furthermore, the iterative solution process in step two specifically includes: determining the initial number of PRIs based on the set oversampling rate and generating initial azimuth uniform sampling points; calculating the corresponding slow time series and PRI value series based on the current number of PRIs using Doppler modulation frequency and mapping relationship; verifying the constraint conditions of the calculated PRI value series; if there are PRI values ​​greater than the maximum time interval, increasing the number of PRIs and recalculating; if there are PRI values ​​less than the minimum time interval, decreasing the number of PRIs and recalculating; repeating the above process until all calculated PRI values ​​fall within the range that satisfies the dual constraint conditions, and outputting the final non-uniform PRI sequence.

[0012] Furthermore, in step three, when constructing the phase model of the random frequency modulation waveform, a Fourier series form is adopted, in which the Fourier coefficients are set as independent and identically distributed uniform random variables within a specific interval range.

[0013] Furthermore, the specific logic for parameter optimization of the distribution range of random coefficients is as follows: based on the central limit theorem, the instantaneous frequency of the random frequency modulation waveform is determined to approximately follow a normal distribution; the 3σ criterion is introduced to constrain the frequency range of the normal distribution, so that a preset proportion of the power spectral density is concentrated within the target bandwidth; according to the constraint, a functional relationship is established between the uniform distribution range and the waveform bandwidth, pulse width, and number of coefficients, and the uniform distribution range value that meets the spectral compactness requirement is calculated accordingly.

[0014] Furthermore, in step four, the specific method for generating the non-uniform random waveform sequence is as follows: for each transmitted waveform in the sequence, the center time of the transmitted waveform is determined by accumulating the non-uniform PRI sequence output in step two; the phase information of the transmitted waveform is determined by the random Fourier coefficients determined in step three, and each transmitted waveform corresponds to a set of independent random Fourier coefficients; the pulse time range is limited by a rectangular window function, and finally, a transmitted signal with random characteristics in both time and frequency is generated by combining them.

[0015] The present invention also provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of the above-described method for designing a non-uniform random waveform to suppress two-dimensional sidelobes of clustered SAR.

[0016] The present invention also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of the above-described method for designing a non-uniform random waveform to suppress two-dimensional sidelobes of clustered SAR.

[0017] This invention provides a non-uniform random waveform design method for suppressing two-dimensional sidelobes in clustered SAR. It has the following beneficial effects: 1. By constructing a mapping relationship between nonlinear frequencies and Doppler frequencies in the azimuth direction to generate non-uniform PRI sequences, and combining it with phase modulation technology based on random Fourier coefficients in the range direction, non-uniform random waveforms with inter-pulse agility characteristics are generated. This design breaks the regularity of traditional periodic sampling and reshapes the two-dimensional sidelobe energy distribution, realizing the azimuth and range sidelobe collaborative suppression without increasing the system hardware complexity, thereby significantly improving the imaging contrast and clarity of the spotlight SAR system for point targets.

[0018] 2. This invention introduces a parameter optimization mechanism based on the central limit theorem and the 3σ criterion during the phase modeling stage of random frequency modulation waveforms. It establishes a quantitative constraint relationship between the uniform distribution range of random coefficients and the waveform bandwidth, pulse width, and number of coefficients. This enables precise control of the instantaneous frequency distribution range of random waveforms, thereby ensuring that most of the power spectral density is concentrated within the preset target bandwidth. This solves the spectral energy leakage problem that is common in random waveform design and ensures that the transmitted waveform has good spectral compactness while meeting the randomness requirements.

[0019] 3. This invention constructs an iterative solution process for the PRI sequence that includes dual constraints of the system's minimum detection range and azimuth Doppler bandwidth. During the waveform design stage, the numerical range of the pulse repetition interval is strictly limited and dynamically adjusted, thereby achieving dual avoidance of signal time-domain overlap and frequency-domain aliasing. This ensures that the generated non-uniform random waveform sequence can strictly adapt to the physical transmission and reception timing requirements of the spotlight SAR system, eliminating the engineering risks of theoretical waveforms not being effectively deployed on actual radar hardware and ensuring the stable operation of the system. Attached Figure Description

[0020] Figure 1 This is a flowchart illustrating the waveform design of the present invention. Figure 2 Example diagram of non-uniform PRI designed for this invention; Figure 3 This is an example diagram illustrating the frequency-normalized time relationship of a single RFM waveform based on random Fourier coefficients according to the present invention. Figure 4 This is a simulated image of a focused SAR point target using a non-uniform random agile RFM waveform designed in this invention. Figure 5 This is a azimuth slice of a clustered SAR point target simulation using a non-uniform PRI random agile RFM waveform designed in this invention. Figure 6 This is a range slice image of a clustered SAR point target simulation using a non-uniform PRI random agile RFM waveform designed in this invention. Detailed Implementation

[0021] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0022] Please see the appendix Figure 1-6 This invention provides a method for designing non-uniform random waveforms to suppress two-dimensional sidelobes in clustered SAR, specifically including: 1. Input the core system parameters: First, the key parameters of the spotlight SAR system are identified and input to provide constraints for subsequent waveform design. Specific input parameters include: carrier center frequency. SAR system velocity Synthesis pore size time Reference point location The initial number of pulse repetition intervals (PRI) Bandwidth of the random frequency modulated transmit waveform and pulse width .

[0023] 2. Non-uniform PRI design (azimuth sidelobe suppression core step) This step optimizes the design of the non-uniform PRI, effectively constructing nonlinear frequency modulation (NLFM) characteristics in the azimuth Doppler frequency domain, thereby achieving effective suppression of azimuth sidelobes. The specific process is as follows: 2.1 Determine the core parameters of the azimuth NLFM waveform The azimuth NLFM waveform to be optimized, its duration and synthetic aperture time. Equal to each other, its bandwidth is equal to the azimuth Doppler bandwidth. Doppler bandwidth The calculation formula is:

[0024] In the formula, At the speed of light, The distance coordinates are for the reference point.

[0025] 2.2 NLFM Waveform Phase Modeling To reduce the number of optimization parameters and improve design efficiency, an NLFM waveform model based on Fourier series is selected to characterize the azimuth phase. The expression is:

[0026] In the formula, To optimize the number of Fourier coefficients, For the first Each Fourier coefficient is optimized. The phase curve shape can be adjusted, thereby controlling the Doppler frequency characteristics.

[0027] 2.3 Derivation of the optimized nonlinear frequency For the above phase Regarding time Taking the derivative, we obtain the azimuth frequency corresponding to the optimized NLFM. The expression is:

[0028] The optimized Fourier coefficients Substituting into the above formula, we can obtain the optimized nonlinear frequency curve that achieves low sidelobes in the azimuth direction.

[0029] 2.4 Equivalent mapping between non-uniform PRI and NLFM set up For the sampling time in slow time, and (in , For the first (PRI). Considering only phase. Zhong Sui The changing quadratic term, at this time the phase It can be simplified to:

[0030] For the simplified phase mentioned above about Differentiate to obtain the Doppler frequency at the corresponding time. :

[0031] In the formula, To achieve the Doppler frequency modulation and realize the equivalence of non-uniform PRI to NLFM, the optimized nonlinear frequency needs to be adjusted. With Doppler frequency Establish a mapping relationship, that is, let ( (As initial uniform sampling points), by solving The specific value of PRI needs to be determined, and the number of PRI needs to be adjusted iteratively. ,make sure Within a reasonable range, to achieve Precise discretization.

[0032] 2.5 PRI Iterative Optimization (Satisfying Dual Constraints) 2.5.1 Constraints: The design of PRI must simultaneously satisfy the Nyquist-Shannon sampling theorem and the minimum distance range requirement. The specific constraint relationship is as follows:

[0033] In the formula, To minimize the system's detection range, the left-hand inequality ensures that the echo signal will not overlap with the subsequent transmitted signal, while the right-hand inequality ensures that the sampling frequency is greater than the Doppler bandwidth, thus avoiding azimuth signal aliasing.

[0034] 2.5.2 Iteration Process: Step 1, Initial parameter settings: Set the azimuth oversampling rate to 0.5%. PRI quantity The adjustment step size is The initial number of PRIs is determined based on the oversampling rate and Doppler bandwidth. ; The second step is to initialize uniform sampling points: based on the initial number of PRI points, generate azimuth uniform sampling points. (in ); The third step is to solve for the slow time. : Using the center point as a reference (i.e.) ), Substitute Combined with Doppler frequency modulation Solve The solution formula is:

[0035] Step 4, Constraint Verification and Parameter Adjustment: Based on the solution obtained... Calculate each PRI value and check if the above dual constraints are met; if the PRI is too high (exceeds the limit)... ), then let Increase the number of PRIs; if the PRIs are too small (less than) ), then let Reduce the number of PRIs; Step 5, Iterative convergence: Repeat steps 2 through 4, and re-discretize. And solve Continue with PRI until all PRI satisfy the constraints, then output the optimized non-uniform PRI sequence.

[0036] 2.5.3 Simulation Parameter Example: In a specific simulation, the SAR system velocity is set... carrier center frequency Synthesis pore size time Reference point location Through the above iterative optimization process, when the number of PRIs is set to 1024, a non-uniform PRI sequence that meets the constraints can be obtained.

[0037] 3. Random Fourier coefficient design (to ensure RFM waveform performance) This step generates a stochastic frequency modulation (RFM) waveform with constant amplitude, low sidelobes, and high spectral compactness by designing random Fourier coefficients, laying the foundation for range-direction sidelobe suppression. The specific process is as follows: 3.1 RFM Waveform Phase Modeling The phase of the RFM waveform is constructed based on the random Fourier coefficients. The expression is:

[0038] In the formula, The center frequency of the carrier. For waveform bandwidth, The pulse width. The number of random Fourier coefficients. For the first random Fourier coefficients; where Let them be independent and identically distributed uniform random variables, i.e. , The range is a uniformly distributed interval.

[0039] 3.2 Optimization of Spectral Compactness Parameters (Based on Central Limit Theorem and 3σ Criterion) 3.2.1 Application of the Central Limit Theorem: When the number of random Fourier coefficients... When it is larger (generally) Instantaneous frequency of the RFM waveform It approximately follows a normal distribution, and its probability density function is:

[0040] In the formula, It is the mean of a normal distribution (i.e., the carrier center frequency). The variance is the normal distribution.

[0041] 3.2.2 3σ Criterion Constraint: To ensure the spectral compactness of the RFM waveform and prevent spectral spread from exceeding the system bandwidth, the 3σ criterion is used to constrain the frequency distribution range. The power spectral density proportions within the frequency band corresponding to different σ multiples are: σ corresponds to 68.3%, 2σ corresponds to 95.5%, and 3σ corresponds to 99.7%. The formula for calculating the square root of the variance σ is:

[0042] 3.2.3 Parameter Determination: Taking the 2σ constraint (corresponding to 95.5% of the power spectral density concentrated within the target bandwidth) as an example, the parameters are set as follows: Substituting the formula for calculating σ into this constraint, we can derive:

[0043] In actual design, the frequency modulation speed required by the system should be determined first. ( The larger the value, the faster the frequency modulation speed, and the stronger the randomness and low interception probability of the RFM waveform. Combined with the above derivation formula, the corresponding value can be calculated. This achieves a balance between spectral compactness and randomness.

[0044] 3.2.4 Simulation Parameter Example: In a specific simulation, the bandwidth of the RFM waveform is set. pulse width Using 2σ constraints to ensure spectral compactness, select (satisfy (Substitute the conditions for applying the central limit theorem) It can be calculated Based on this parameter, a single RFM waveform with high spectral compactness can be generated, and the relationship between its frequency and normalized time meets the design requirements.

[0045] 4. Non-uniform random waveform generation By combining the non-uniform PRI and random Fourier coefficients obtained from the above optimization, a non-uniform random waveform for pulse agility is generated. The specific process is as follows: 4.1 Expression of a single transmitted waveform A spotlight SAR system transmits inter-pulse agile RFM waveforms under non-uniform PRI conditions. For the first The PRI corresponding to the _th transmitted waveform, then the _th One transmitted waveform The expression is:

[0046] The parameters in the formula are explained as follows: (1) This is a rectangular window function used to limit the time range of the pulse. And satisfy ; (2) For the first The formula for calculating the center time of each transmitted waveform is as follows:

[0047] In the formula, (Initial moment) The pulse width; (3) For the first The phase of each transmitted waveform (including random Fourier coefficients) is expressed as follows:

[0048] In the formula, For the first The first transmitted waveform A random Fourier coefficient, The number of random Fourier coefficients for a single RFM waveform.

[0049] 4.2 Fourier coefficient distribution characteristics If the number of PRIs is within one synthesis aperture time, Then the corresponding generation One RFM waveform (two adjacent PRIs correspond to one waveform, The PRI defines a total of (each waveform at a given moment). The random Fourier coefficients of all waveforms are independent random variables that follow a uniform distribution, i.e.:

[0050] In the formula, The range of uniformly distributed intervals is determined by step 3.2.3.

[0051] 4.3 Final Waveform Generation Substituting the non-uniform PRI sequence obtained from step 2 and the random Fourier coefficients designed in step 3 into the above single transmission waveform expression, a non-uniform random waveform sequence with pulse agility, non-uniform PRI, and high-spectral compactness can be generated. This waveform sequence can be directly used for transmission in a spotlight SAR system.

[0052] 5. Simulation and Verification of Spotlight SAR Imaging To verify the two-dimensional sidelobe suppression effect of the waveform designed in this invention, a improved back projection imaging algorithm was used to simulate focused SAR point target imaging. The specific process and verification results are as follows: 5.1 Construction of Point Target Echo Model Ignoring the effects of range and azimuth window functions, the echo signal of a point target The expression is:

[0053] The parameters in the formula are explained as follows: (1) The echo amplitude is determined by both the reflectivity of the point target and the signal propagation attenuation coefficient. (2) The transmitted waveform generated in step 4; (3) Slow time; (4) The speed of light; (5) For SAR transmitters and point targets The distance between them, combined with the SAR system velocity , The calculation formula is:

[0054] 5.2 Range-directed matched filtering Because this invention uses pulse-agile RFM waveforms, the transmit waveform corresponding to each PRI is different. Therefore, range-directed matched filtering needs to be performed separately for the waveform of each PRI. The system function of the matched filtering... (Consistent with the transmitted waveform of the corresponding PRI). Output of the range-direction matched filter. This is achieved through Fourier Transform (FFT) and Inverse Fourier Transform (IFFT), with the specific expression as follows:

[0055] Combined with the autocorrelation function of the RFM waveform (for time delay), and the number of sampling points in the azimuth direction PRI is The output of the above matched filter can be simplified to:

[0056] In the formula, For the first The autocorrelation function of an RFM waveform. The item includes azimuth modulation information and range migration effect caused by the motion of the SAR platform.

[0057] 5.3 Implementation of Back Projection Imaging Algorithm To adapt to the characteristics of non-uniform PRI and inter-pulse agility waveforms, a back projection algorithm is used for imaging. This eliminates the need for additional interpolation calculations and allows for direct range migration correction and azimuth pulse compression in the time domain. The specific process is as follows: The first step, grid generation: Range-compressed signals are sampled in the range dimension, and then an imaging grid is generated, with grid points set. The corresponding complex values ​​of the SAR image are ; The second step, azimuth coherent accumulation: The output signal after range matching filtering is coherently superimposed in the azimuth direction to complete range migration correction and azimuth pulse compression, ultimately obtaining the complex values ​​of the grid points. The expression is:

[0058] In the formula, This is the amplitude function after coherent accumulation in the azimuth direction. This process can simultaneously achieve two-dimensional sidelobe suppression in both the range and azimuth directions.

[0059] 5.4 Simulation Results and Performance Index Verification 5.4.1 Imaging Results: Through the above simulation process, the imaging results of the spotlight SAR point target are obtained, including the panoramic image of the point target, the azimuth slice image and the range slice image, which intuitively present the imaging effect and side lobe distribution of the target.

[0060] 5.4.2 Performance Indicator Comparison: The imaging performance of the non-uniform random waveform designed in this invention is compared with that of the traditional linear frequency modulation (LFM) waveform. The core performance indicators are as follows: (1) Traditional LFM waveform: peak sidelobe ratio -13.3dB, integral sidelobe ratio -9.8dB, 3dB normalized main lobe width 0.9; (2) The waveform designed in this invention is: azimuth peak sidelobe ratio -41.4dB, azimuth integral sidelobe ratio -36.1dB, azimuth 3dB normalized main lobe width 1.2; range peak sidelobe ratio -48.1dB, range integral sidelobe ratio -26.3dB, range 3dB normalized main lobe width 1.1.

[0061] Verification results show that the waveform designed in this invention achieves extremely low sidelobe suppression effect of less than -40dB in both range and azimuth directions, under the premise of only producing minimal main lobe widening. This is significantly better than the traditional LFM waveform and achieves the design goal of two-dimensional sidelobe synergistic suppression.

[0062] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for designing non-uniform random waveforms to suppress two-dimensional sidelobes in clustered SAR, characterized in that, Includes the following steps: Step 1: System Parameter Establishment: Identify and input the key parameters of the spotlight SAR system. The key parameters include at least the carrier center frequency, system velocity, synthetic aperture time, reference point position, initial number of pulse repetition intervals (PRI), bandwidth of random frequency modulated transmit waveform, and pulse width. Step 2: Non-uniform PRI sequence generation: Based on the key parameters, with the goal of constructing nonlinear frequency modulation characteristics in the azimuth Doppler frequency domain, a non-uniform PRI sequence that meets the preset constraints is obtained by establishing the mapping relationship between the nonlinear frequency and the Doppler frequency and performing iterative solution, which is used to achieve azimuth sidelobe suppression. Step 3: Random Fourier Coefficient Optimization: Based on the bandwidth and pulse width in the key parameters, a phase model of a random frequency-modulated waveform is constructed using random Fourier coefficients. The distribution range of the random coefficients is optimized according to the spectral compactness requirements to obtain a set of random Fourier coefficients for range-directed sidelobe suppression. Step 4: Non-uniform random waveform synthesis: The non-uniform PRI sequence obtained in Step 2 is used as the time reference for pulse transmission, and the random Fourier coefficients obtained in Step 3 are substituted into the phase modulation of each pulse to generate a non-uniform random waveform sequence with pulse agility characteristics.

2. The non-uniform random waveform design method for suppressing two-dimensional sidelobes in clustered SAR according to claim 1, characterized in that, In step two, when constructing the nonlinear frequency modulation characteristics, a Fourier series model is used to characterize the phase of the azimuth nonlinear frequency modulation waveform at the reference point. The characterization process includes: setting the number of optimized Fourier coefficients, adjusting the value of the Fourier coefficients to control the shape of the phase curve, and then determining the corresponding optimized nonlinear frequency curve.

3. The non-uniform random waveform design method for suppressing two-dimensional sidelobes in clustered SAR according to claim 1, characterized in that, In step two, the specific process of establishing the mapping relationship and performing iterative solution includes: Taking the derivative of the phase with respect to time yields an optimized nonlinear frequency function with respect to time; Considering only the quadratic term in the phase that varies with slow time, construct the Doppler frequency function that varies with slow time; An equivalent mapping equation is established between the optimized nonlinear frequency function and the Doppler frequency function, wherein the equivalent mapping equation represents that the optimized nonlinear frequency corresponding to the initial uniform sampling point is equal to the Doppler frequency corresponding to the slow time. The slow time is solved based on the equivalent mapping equation, and the specific value of each PRI is determined according to the difference between adjacent slow times.

4. The non-uniform random waveform design method for suppressing two-dimensional sidelobes in clustered SAR according to claim 1, characterized in that, In step two, the preset constraint is that the value of PRI must simultaneously satisfy the Nyquist-Shannon sampling theorem requirement and the minimum distance range requirement. Specifically, each calculated PRI value must be greater than the minimum time interval determined by the system's minimum detection distance, and simultaneously less than the maximum time interval determined by the azimuth Doppler bandwidth.

5. The non-uniform random waveform design method for suppressing two-dimensional sidelobes in clustered SAR according to claim 4, characterized in that, The iterative solution process in step two specifically includes: The initial number of PRIs is determined based on the set oversampling rate, and initial azimuth uniform sampling points are generated. Based on the current number of PRIs, the corresponding slow time series and PRI numerical series are calculated using Doppler modulation frequency and mapping relationship; The calculated PRI numerical sequence is subjected to constraint verification: if there is a PRI value greater than the maximum time interval, the number of PRI values ​​is increased and the calculation is recalculated; if there is a PRI value less than the minimum time interval, the number of PRI values ​​is decreased and the calculation is recalculated. Based on the adjusted number of PRIs, the steps of generating initial azimuth uniform sampling points, solving the corresponding slow time series and PRI numerical series, and verifying the constraints are repeated until all the calculated PRI values ​​fall within the range that satisfies the dual constraints, and the final non-uniform PRI sequence is output.

6. The non-uniform random waveform design method for suppressing two-dimensional sidelobes in clustered SAR according to claim 1, characterized in that, In step three, when constructing the phase model of the random frequency modulation waveform, a Fourier series form is adopted, in which the Fourier coefficients are set as independent and identically distributed uniform random variables that follow a specific interval range.

7. The method according to claim 6, characterized in that, In step three, the specific logic for optimizing the distribution range of the random coefficients is as follows: Based on the central limit theorem, it is determined that the instantaneous frequency of a random frequency modulated waveform approximately follows a normal distribution. The 3σ criterion is introduced to constrain the frequency range of the normal distribution, so that a preset proportion of the power spectral density is concentrated within the target bandwidth; Based on the constraints, a functional relationship is established between the uniform distribution range and the waveform bandwidth, pulse width, and number of coefficients, and the uniform distribution range value that meets the spectral compactness requirement is calculated accordingly.

8. The non-uniform random waveform design method for suppressing two-dimensional sidelobes in clustered SAR according to claim 1, characterized in that, In step four, the specific method for generating the non-uniform random waveform sequence is as follows: For each transmitted waveform in the sequence, the center time of the transmitted waveform is determined by accumulating the non-uniform PRI sequence output in step two; The phase information of the transmitted waveform is determined by the random Fourier coefficients determined in step three, and each transmitted waveform corresponds to a set of independent random Fourier coefficients. By limiting the pulse time range using a rectangular window function, a transmission signal with random characteristics in both time and frequency is finally generated.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the non-uniform random waveform design method for suppressing two-dimensional sidelobes of clustered SAR as described in any one of claims 1 to 8.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the non-uniform random waveform design method for suppressing two-dimensional sidelobes of clustered SAR as described in any one of claims 1 to 8.

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