Waveform generation method and device for fast time dimension frequency domain anti-clutter, equipment and medium

Abstract

The application relates to a fast time-domain frequency-domain anti-clutter waveform generation method, device, equipment and medium, a frequency-domain anti-clutter optimization problem model is established by taking the maximum frequency-domain signal-to-clutter ratio as a criterion, considering a waveform constant module constraint and a weighted integrated sidelobe level constraint, a penalty coefficient is introduced, the problem is converted into an optimization problem of minimizing clutter energy and a weighted integrated sidelobe level, a weight vector is introduced to convert the constraint optimization problem into an approximately equivalent problem model, the problem model is introduced into a complex circle flow space to convert the constraint optimization problem in the Euclidean space into an unconstrained optimization problem in the flow space, then, a Euclidean gradient and a Hessian matrix of the unconstrained optimization problem are calculated, based on a Riemannian gradient and a Riemannian Hessian matrix obtained through projection, the unconstrained optimization problem is subjected to a confidence interval descent in the Riemannian complex circle flow space, an iterative point is updated until convergence, and finally, a radar transmitting waveform is output. The method generates a radar transmitting waveform based on the difference between a target and clutter in the frequency domain, and can effectively suppress the clutter.

Description

Technical Field

[0001] This application relates to the field of radar anti-clutter technology, and in particular to a waveform generation method, apparatus, device and medium for fast time-dimensional frequency domain anti-clutter. Background Technology

[0002] Strong clutter on land and sea surfaces can overwhelm target echoes, making effective target detection impossible. While moving target indication and detection (MTI) can effectively suppress low-speed clutter, these methods are inapplicable to slow-moving or stationary targets. Therefore, detecting slow-moving or stationary targets on land and sea surfaces has always been a challenge for radar detection. Land and sea surface clutter can be viewed as the result of multiple scattering points superimposed, similar to targets, making effective suppression difficult using traditional range and velocity dimensions. Analysis of actual data reveals that clutter and targets typically exhibit significant differences in the frequency domain of the fast time dimension, allowing for clutter suppression from this perspective. This transforms the problem into a design problem for the fast time-dimensional spectrum.

[0003] Extensive research and achievements have been made by scholars both domestically and internationally regarding clutter suppression and spectral waveform design. The principles and limitations of these two approaches are mainly as follows: Traditional clutter suppression methods primarily consider the slow time dimension, utilizing the differences in range and velocity between the target and clutter to suppress the range-Doppler cell where the clutter resides, thereby highlighting the target and suppressing clutter. However, in reality, clutter is usually located in the same range cell as the target, and for low-speed (stationary) targets, it is difficult to distinguish between clutter and the target in the velocity cell. Therefore, clutter suppression from the slow time dimension can be seen as an extension of traditional moving target display and moving target detection, but its application scope in practical situations is relatively limited.

[0004] Traditional spectrum design initially addressed the problem of waveform interference in the frequency domain, typically requiring the complete suppression of the stopband. However, clutter is usually distributed across the entire frequency band, making it difficult to define the specific frequency range to be suppressed. This limits the direct application of traditional spectrum shaping-based waveform design methods to clutter suppression. However, clutter spectral distribution exhibits significant variations with frequency, so suppressing strong scattering points and enhancing weak scattering points can redistribute energy to suppress clutter. The complexity of the clutter spectral distribution leads to a complex target spectrum, and traditional spectrum shaping algorithms often struggle to achieve satisfactory results with complex-shaped spectra. Summary of the Invention

[0005] Therefore, it is necessary to provide a waveform generation method, apparatus, and medium that can effectively suppress clutter in the fast time-domain frequency domain to address the above-mentioned technical problems.

[0006] A fast time-domain frequency domain anti-clutter waveform generation method, the method comprising: Obtain the clutter signal to be suppressed, and construct a frequency domain clutter suppression objective function based on the clutter signal to be suppressed and with maximizing the signal-to-clutter-to-noise ratio as the criterion; By introducing the weighted integral sidelobe level into the objective function through a penalty factor, a constrained optimization problem model is constructed under constant modulus, weighted integral sidelobe level, and spectral constraints. By incorporating the spectrum and autocorrelation function weight vector into the objective function, an approximate equivalent problem model based on the weight vector is constructed. The approximate equivalent problem model based on the weight vector is extended by norm to obtain the extended frequency domain clutter suppression problem model; Transforming the extended frequency domain clutter suppression problem model in Euclidean space to Riemannian complex circular manifold space yields an unconstrained optimization problem. Solving the unconstrained optimization problem yields a constant-wave radar waveform for suppressing clutter signals.

[0007] In one embodiment, constructing the objective function for frequency domain anti-clutter based on the clutter signal to be countered and maximizing the signal-to-clutter-to-noise ratio includes: The initial objective function is constructed based on maximizing the signal-to-noise ratio. Based on the initial objective function and the clutter signal to be countered, an objective function that maximizes the frequency domain signal-to-clutter-to-noise ratio is constructed. The objective function of maximizing the frequency domain signal-to-clutter ratio is simplified to a frequency domain clutter energy minimization model, and this model is used as the objective function.

[0008] In one embodiment, the objective function is expressed as:

[0009] In the above formula, The frequency domain distribution characteristics of the clutter signal to be suppressed are represented by a complex vector. This represents the constant-wave radar waveform sequence to be solved. This represents the time-frequency domain transformation matrix.

[0010] In one embodiment, the constrained optimization problem model is represented as:

[0011] In the above formula, Indicates the penalty factor. This represents the waveform sequence emitted by the radar. Indicates the length of the sequence. Indicates size is Complex vectors, , Both represent time-frequency domain transformation matrices, where, , ; This represents the constant modulus constraint that the sequence design must satisfy. Indicates waveform sidelobe level constraint. This indicates the range of sidelobes that need to satisfy the constraints. Indicates the degree of constraint on the side lobes. This indicates a constraint on energy outside the radar frequency band. This indicates the range that needs to meet out-of-band spectral constraints. Indicates the degree of constraint on the spectrum; This represents the relationship between the autocorrelation function and the waveform. , representing the spectrum of the signal, This represents the modulo operation. This indicates the conjugate transpose operation.

[0012] In one embodiment, the unconstrained optimization problem is expressed as:

[0013] In the above formula, Representing variables The complex circular manifold space in which it is located This represents a weighting function that comprehensively considers both in-band and out-of-band frequencies. The weighted vector representing the sidelobe levels. express The value of the norm.

[0014] In one embodiment, solving the unconstrained optimization problem to obtain the constant-wave radar waveform for suppressing the clutter signal includes: Solve the Euclidean gradient and Euclidean Hessian matrix of the unconstrained optimization problem, and transform the Euclidean gradient and Euclidean Hessian matrix into Riemann gradient and Riemann Hessian matrix, respectively. Based on the Riemann gradient and Riemann-Hessian matrix of the unconstrained optimization problem, confidence interval descent is performed until the iteration cutoff condition is met, then the iteration stops and the constant wave radar waveform is output.

[0015] In one embodiment, the confidence interval descent based on the Riemann gradient and Riemann-Hessian matrix of the unconstrained optimization problem is performed until the iteration cutoff condition is met, at which point the iteration stops and the constant-wave radar waveform is output, including: Based on the Riemann gradient and Riemann-Hessian matrix of the unconstrained optimization problem, a local approximation function of the tangent space is constructed. Based on the local approximation function, a sub-problem to be solved in each iteration is constructed. The conjugate gradient algorithm is used to solve the sub-problem. The unconstrained optimization problem is solved by iterating step by step and updating the corresponding confidence interval.

[0016] A waveform generation device for fast time-domain frequency domain anti-clutter, the device comprising: The objective function construction module is used to obtain the clutter signal to be suppressed, and construct the frequency domain objective function for suppressing clutter based on the clutter signal to be suppressed and with maximizing the signal-to-clutter-to-noise ratio as the criterion. The constrained optimization problem construction module is used to introduce a penalty factor and construct a constrained optimization problem model under constant modulus, weighted integral sidelobe level and spectral constraints. The first transformation module of the problem model is used to transform the constrained optimization problem under constant modulus, weighted integral sidelobe level and spectral constraints into an approximate equivalent problem model based on weight vectors. The second transformation module of the problem model is used to extend the norm of the approximate equivalent problem model based on the weight vector to obtain an extended frequency domain clutter suppression problem model; The module for obtaining the unconstrained optimization problem is used to transform the extended frequency domain clutter suppression problem model in Euclidean space to Riemannian complex circular manifold space to obtain the unconstrained optimization problem. The anti-clutter waveform solving module is used to solve the unconstrained optimization problem and obtain a constant-wave radar waveform that suppresses the clutter signal to be suppressed.

[0017] A computer device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program performing the following steps: Obtain the clutter signal to be suppressed, and construct a frequency domain clutter suppression objective function based on the clutter signal to be suppressed and with maximizing the signal-to-clutter-to-noise ratio as the criterion; By introducing the weighted integral sidelobe level into the objective function through a penalty factor, a constrained optimization problem model is constructed under constant modulus, weighted integral sidelobe level, and spectral constraints. By incorporating the spectrum and autocorrelation function weight vector into the objective function, an approximate equivalent problem model based on the weight vector is constructed. The approximate equivalent problem model based on the weight vector is extended by norm to obtain the extended frequency domain clutter suppression problem model; Transforming the extended frequency domain clutter suppression problem model in Euclidean space to Riemannian complex circular manifold space yields an unconstrained optimization problem. Solving the unconstrained optimization problem yields a constant-wave radar waveform that suppresses the clutter signal to be suppressed.

[0018] A computer-readable storage medium having a computer program stored thereon, the computer program performing the following steps when executed by a processor: Obtain the clutter signal to be suppressed, and construct a frequency domain clutter suppression objective function based on the clutter signal to be suppressed and with maximizing the signal-to-clutter-to-noise ratio as the criterion; By introducing the weighted integral sidelobe level into the objective function through a penalty factor, a constrained optimization problem model is constructed under constant modulus, weighted integral sidelobe level, and spectral constraints. By incorporating the spectrum and autocorrelation function weight vector into the objective function, an approximate equivalent problem model based on the weight vector is constructed. The approximate equivalent problem model based on the weight vector is extended by norm to obtain the extended frequency domain clutter suppression problem model; Transforming the extended frequency domain clutter suppression problem model in Euclidean space to Riemannian complex circular manifold space yields an unconstrained optimization problem. Solving the unconstrained optimization problem yields a constant-wave radar waveform that suppresses the clutter signal to be suppressed.

[0019] The aforementioned fast-time-dimensional frequency domain clutter suppression waveform generation method, apparatus, equipment, and medium establish an optimization problem model for frequency domain clutter suppression by maximizing the frequency domain signal-to-clutter ratio (SNR) while considering both constant mode constraints and weighted integral sidelobe level constraints. A penalty coefficient is introduced to transform the objective function into an optimization problem that minimizes clutter energy and weighted integral sidelobe levels. A weight vector is introduced to approximate the constraint problem into an optimization problem model with only constant mode constraints. This model is then introduced into a complex circular manifold space to transform the constrained optimization problem in Euclidean space into an unconstrained optimization problem in the manifold space. The Euclidean gradient and Hessian matrix of the unconstrained optimization problem are calculated, and based on the Riemann gradient and Riemann-Hessian matrix obtained by projection, confidence interval descent is performed on the unconstrained optimization problem on the Riemann complex circular manifold, updating the iteration points until convergence, and outputting the final radar transmission waveform. This method generates radar transmission waveforms based on the frequency domain differences between the target and clutter, effectively suppressing clutter. Attached Figure Description

[0020] Figure 1 This is a flowchart illustrating a fast time-domain frequency domain anti-clutter waveform generation method in one embodiment; Figure 2 This is a graph showing the convergence curve of the objective function value in a simulation experiment. Figure 3 This is a graph showing the convergence curve of the gradient norm in a simulation experiment. Figure 4 The image shows the matched filtering results of a traditional linear frequency modulated signal under clutter interference for two targets with the same RCS in a simulation experiment. Figure 5The image shows the matched filtering result of the waveform designed using the RTR algorithm for two targets with the same RCS size in a simulation experiment under clutter interference. Figure 6 The image shows the matched filtering results of a traditional linear frequency modulated signal under clutter interference for two targets with different RCS sizes in a simulation experiment. Figure 7 The image shows the matched filtering results of the waveforms designed using the RTR algorithm for two targets with different RCS sizes in a simulation experiment under clutter interference. Figure 8 This is a structural block diagram of a waveform generation device for fast time-domain frequency domain anti-clutter in one embodiment; Figure 9 This is an internal structural diagram of a computer device in one embodiment. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0022] To address the difficulties of existing technologies in detecting low-speed (stationary) targets in the presence of clutter, and the challenges of designing complex spectra using classical spectral shaping techniques, such as... Figure 1 As shown, a fast time-domain frequency domain anti-clutter waveform generation method is provided, including the following steps: Step S100: Obtain the clutter signal to be suppressed, and construct the objective function for frequency domain clutter suppression based on the clutter signal to be suppressed and with maximizing the signal-to-clutter-to-noise ratio as the criterion.

[0023] Step S110: The weighted integral sidelobe level is introduced into the objective function through a penalty factor to construct a constrained optimization problem model under constant modulus, weighted integral sidelobe level, and spectral constraints.

[0024] Step S120: Introduce the spectrum and autocorrelation function weight vector into the objective function to construct an approximate equivalent problem model based on the weight vector.

[0025] Step S130: The approximate equivalent problem model based on the weight vector is extended by norm to obtain the extended frequency domain clutter suppression problem model.

[0026] Step S140: Transform the extended frequency domain clutter suppression problem model in Euclidean space to Riemannian complex circular manifold space to obtain an unconstrained optimization problem.

[0027] Step S150: Based on the Riemann gradient and Riemann-Hessen matrix of the unconstrained optimization problem, the confidence interval iterative descent algorithm is used to solve the problem to obtain the constant wave radar waveform for suppressing clutter signals.

[0028] In this embodiment, the difference between clutter and the target in the fast time frequency domain is fully utilized to achieve clutter suppression and improve detection performance.

[0029] In step S100, constructing the objective function for frequency domain clutter suppression based on the clutter signal to be suppressed and maximizing the signal-to-clutter-to-noise ratio (SNR) includes: firstly, constructing an initial objective function based on maximizing the SNR; then, constructing the objective function for maximizing the SNR in the frequency domain based on the initial objective function and the clutter signal to be suppressed; and finally, simplifying the objective function for maximizing the SNR in the frequency domain into a model for minimizing clutter energy in the frequency domain, and using this model as the objective function.

[0030] Specifically, the initial objective function is expressed as: (1) In formula (1), , , , representing the energy of the signal, clutter, and noise, respectively.

[0031] In practical working scenarios, the echo of clutter can be equivalent to the result of the superposition of waveform scattering by multiple small scatterers. For stationary (low-speed) targets, clutter and targets have basically the same characteristics in the range and velocity dimensions, but there are usually significant differences in the frequency domain. Therefore, in this method, the initial objective function is transformed to the frequency domain dimension.

[0032] The radar transmitted waveform sequence can be represented as: ,in, The frequency domain characteristics of clutter can be represented by the sequence length. Let be a complex vector. Therefore, the objective function for maximizing the frequency domain signal-to-clutter-to-noise ratio can be expressed as: (2) In formula (2), Represents the time-frequency domain transformation matrix. , Represents the L2 norm operation. Similarly, it represents the energy of the signal. This represents the energy of the clutter. The frequency domain distribution characteristics of the clutter signal to be suppressed are represented by a complex vector, and the clutter signal to be suppressed is the detected signal.

[0033] Considering the constant modulus constraint in waveform design, therefore, for waveforms with a fixed sequence length, For constants, noise and signal Irrelevant, therefore, maximize Equivalent to minimizing clutter energy, i.e., the objective function, it is expressed as: (3) In formula (3), The frequency domain distribution characteristics of the clutter signal to be suppressed are represented by a complex vector. This represents the constant-wave radar waveform sequence to be solved. This represents the time-frequency domain transformation matrix.

[0034] In step S110, a constrained optimization problem model can be constructed based on the criterion of minimizing the weighted integrated sidelobe levels (WISL) of the radar transmitted signal after passing through the matched filter: (4) In formula (4), This indicates the conversion relationship between sidelobe levels and signal sequences. This indicates a constraint on the sidelobe level. This indicates the magnitude of the weighted integral sidelobe level.

[0035] To achieve maximum And WISL is controlled by introducing a penalty factor. The overall constrained optimization problem model is constructed as follows: (5) In formula (5), Indicates the penalty factor. This represents the waveform sequence emitted by the radar. Indicates the length of the sequence. Indicates size is Complex vectors, , Both represent time-frequency domain transformation matrices, where, , ; This represents the constant modulus constraint that the sequence design must satisfy. Indicates waveform sidelobe level constraint. This indicates the range of sidelobes that need to satisfy the constraints. Indicates the degree of constraint on the side lobes. This indicates a constraint on energy outside the radar frequency band. This indicates the range that needs to meet out-of-band spectral constraints. Indicates the degree of constraint on the spectrum; This represents the conversion relationship between the autocorrelation function and the waveform. , representing the spectrum of the signal, This represents the modulo operation. This indicates the conjugate transpose operation.

[0036] Although the desired objective is effectively represented, the existence of constraints makes it difficult to solve the problem. Therefore, in step S120, an approximate equivalent transformation of the constraints is achieved by introducing a weight vector. The equivalent problem model can be expressed as: (6) In formula (6), This represents a weighting function that comprehensively considers both in-band and out-of-band frequencies. The weighted vector representing the sidelobe level, using and It can achieve equivalent control over the objective function and constraints, which can be specifically expressed as follows: (7) (8) In formulas (7) and (8), This indicates the search for the maximum value. and These represent the weight values ​​inside and outside the frequency band, respectively. This represents the desired weighted integral sidelobe level. This represents the inverse operation. and These represent the ranges of the side lobes and the main lobe, respectively.

[0037] The L2 norm can only constrain energy; for sidelobes, it can only guarantee the minimum overall energy. However, in practice, the condition to be met is the minimization of the maximum value, ensuring effective differentiation of neighboring targets within the required range. Therefore, in step S130, formula (6) is further generalized to obtain a result based on… p The generalized model of the norm is: (9) In formula (9), express The order of the norm, as Increasing the values ​​of the spectrum and sidelobe constraint range makes the corresponding image flatter, which can be achieved by adjusting... Adjust the waveform characteristics.

[0038] At this point, constant modulus constraints still exist in formula (9), and the search space of constant modulus constraints constitutes a complex circular manifold. Therefore, the constrained optimization problem in Euclidean space can be transformed into an unconstrained optimization problem in manifold space.

[0039] Specifically, the complex circular manifold space corresponding to the constant modulus constraint of the emitted waveform can be represented as: (10) In formula (10), express Restoring the European-style space This indicates the modulo operation.

[0040] Therefore, the extended problem model of frequency domain clutter suppression under constant modulus constraints can be transformed into an unconstrained optimization problem model on the Riemann complex circular manifold space, which can be expressed as: (11) In this embodiment, the solution to the unconstrained optimization problem model shown in formula (11) can be obtained by selecting a suitable algorithm from existing optimization algorithms based on experience or common sense, thereby obtaining a radar model that can suppress clutter.

[0041] In this embodiment, an algorithm based on Riemannian Trust-Region (RTR) is proposed to solve the unconstrained problem model shown in Equation (11). First, the Euclidean gradient and Euclidean Hessian matrix of the unconstrained optimization problem are solved. Then, the Euclidean gradient and Euclidean Hessian matrix are transformed into Riemann gradient and Riemann-Hessian matrix. Confidence interval descent is performed based on the Riemann gradient and Riemann-Hessian matrix until the iteration cutoff condition is met. Then, the iteration stops and the current waveform is output. This output waveform is the anti-clutter waveform that is finally required to be solved.

[0042] Furthermore, solving the unconstrained problem model The Euclidean gradient calculation process is as follows: (12) In formula (12) The objective function corresponding to the clutter spectrum is... This represents the objective function corresponding to the weighted integral sidelobe level. This represents the Euclidean gradient of the objective function.

[0043] and then and about The derivatives can be expressed as: (13) (14) Similarly, further solving can yield the unconstrained optimization problem. matrix: (15) In formula (15), The Euclidean Hess matrix representing the objective function. and about The Hess matrix can be represented as follows: (16) (17) In formula (17), Indicates the direction of descent.

[0044] In this embodiment, based on the projection relationship between the Riemann gradient and the Euclidean gradient, the unconstrained optimization objective function is applied to the Riemann complex circular manifold. Riemann gradient on Euclidean gradient on Euclidean space can be used Indicate: (18) In formula (18), This indicates the operation of taking the real part.

[0045] Based on the fundamental properties of Riemannian complex circular manifolds, the projection operator... It can be represented as: (19) In formula (19), and denote the tangent space on the Riemannian complex circular manifold.

[0046] Therefore, the Riemann gradient The objective function can be optimized by unconstrained optimization. about Represented by the Euclidean gradient: (20) Hessian matrix representation The second derivative of is a key variable in second-order optimization. The relationship between the Riemann-Hessian matrix and the Riemann gradient can be expressed as: (twenty one) In formula (21), The Levi-Civita link can be calculated based on the Euclidean descent direction of the tangent space. Indicates the direction of descent.

[0047] The Riemann-Hessian matrix can be further represented using the Euclidean gradient: (twenty two) In formula (22), and These represent the steepest descent directions of the Riemann gradient and the Euclidean gradient, respectively.

[0048] Based on Taylor expansion, the unconstrained problem model can be approximately represented as: (twenty three) Taking the derivative of the approximately unconstrained problem model, we can obtain: (twenty four) Setting the derivative to zero yields an approximate extreme point. Since the unconstrained problem model is an approximation, iterative solutions are required. The condition for the solution to the above equation to be an approximate extreme point is... It is a positive semi-definite matrix, but this condition may not necessarily hold. Therefore, the confidence interval method is used to solve the above problem.

[0049] The solution obtained First, it is pulled back to the manifold space through backtracking. ,in: (25) The rate of change of the iterations then needs to be calculated, i.e.: (26) Further determine whether to accept this iteration: (27) Next, update the confidence interval: (28) The process iterates continuously until the number of iterations reaches a preset maximum value, at which point the iteration stops and the current radar transmission waveform is output. .

[0050] Furthermore, the subproblem that is solved in each iteration can also be represented as: (29) In formula (29), Indicates the first The iteration vector The corresponding Riemann gradient, This represents the corresponding Riemann-Hessen matrix. express Located on the tangent space, express The solution needs to be found in the first... The confidence interval corresponding to the next iteration This subproblem can be solved using a typical conjugate gradient algorithm.

[0051] In this paper, simulation experiments are also used to demonstrate the effectiveness of the proposed method.

[0052] Experimental Scenario: The following experiments were conducted on a computer (2.30GHz i7-12700H core, 16.0GB RAM) using MATLAB version R2021b. During the experiments, the pulse width was set to... Bandwidth set to The total number of frequency points is sampling frequency , , The signal-to-noise ratio (SNR) is set to -15 dB, and the signal-to-noise ratio (SNR) is 0 dB. Penalty factor. The maximum number of iterations is set to 50. The initial waveform is a linear frequency modulated signal with an initial frequency of [frequency value missing]. Cutoff frequency is .

[0053] Using the simulation data described above, anti-clutter waveforms are generated according to the method proposed in this paper. During this process, such as... Figure 2 As shown, the curve of the objective function (i.e., the unconstrained optimization problem) value changing with the number of iterations is... Figure 2 As can be seen, the objective function value decreases monotonically as the iteration proceeds until the convergence condition is met, at which point the algorithm stops running. Since a quadratic descent algorithm is used, only a few iteration steps are needed to achieve a rapid decrease in the objective function. Figure 3 The curves showing the gradient norm as a function of iterations are presented, demonstrating that the gradient of the objective function using the quadratic algorithm also achieves a rapid decrease within a relatively small number of iterations. The Riemann confidence interval algorithm primarily aims to ensure that the objective function decreases monotonically, but the gradient may not necessarily decrease monotonically.

[0054] Assume that, in the presence of clutter, there exist two targets with the same RCS. Figure 4 The results of matched filtering using a linear frequency modulated signal are given. Due to the presence of clutter, the target was severely interfered with, and no target passed the threshold after CA-CFAR detection. Figure 5 The paper presents the matched filtering results for the waveforms designed using the proposed algorithm. The proposed algorithm can effectively suppress the influence of clutter, with both targets far exceeding the CA-CFAR detection threshold. The linear frequency modulated signal was affected by clutter, resulting in multiple sidelobes exceeding -7dB, while the proposed algorithm only had a few sidelobe energies slightly above -15dB, with a maximum of only -13.96dB. This demonstrates that the proposed algorithm can significantly suppress the adverse effects of clutter.

[0055] Suppose that there are two targets with different RCS in the presence of clutter. The conditions of target 1 are consistent with the problem statement, and the RCS of target 2 is half that of target 1. Figure 6The results of matched filtering using linear frequency modulated signals are given. Due to the presence of clutter, the target was severely affected. No target was detected by CA-CFAR, and smaller targets were completely covered by clutter. Figure 7 The paper presents the matched filtering results for the waveforms designed using the proposed algorithm. The proposed algorithm can effectively suppress clutter effects. Both targets far exceed the CA-CFAR detection threshold, and the energy of the smaller target (-5.92dB) still far exceeds the energy of the largest sidelobe (-16.78dB).

[0056] Experimental results show that this method effectively suppresses clutter, and has greater application value in radar cognitive active clutter suppression.

[0057] In the aforementioned fast-time-dimensional frequency domain clutter suppression waveform generation method, minimizing clutter energy and weighted integral sidelobe level are selected as optimization criteria. Simultaneously, to ensure radar transmitter efficiency, constant mode constraints are introduced, establishing a constrained optimization problem model in Euclidean space. To efficiently solve the established constrained optimization problem, the geometric properties of the constrained space are utilized to transform the Euclidean constrained optimization problem into an unconstrained optimization problem in Riemannian complex circular manifold space. An algorithm based on Riemannian Trust-Region (RTR) descent is proposed to solve the unconstrained optimization problem, ultimately achieving the design of the transmitted waveform. Compared to existing technologies, this method expands the clutter suppression approach: traditional clutter suppression algorithms mainly utilize the differences between the target and clutter in the range and velocity dimensions, while this invention considers the differences between the target and clutter in the fast-time-dimensional frequency domain, effectively improving the radar's detection capability for stationary (low-speed) targets. The design of the waveform spectrum is simplified: Traditional frequency domain waveform suppression algorithms are mainly based on spectrum shaping, and the setting of the spectrum directly affects the performance of the algorithm. When facing complex spectrum situations, setting the spectrum is quite complex and difficult. The algorithm in this paper only needs to perform simple processing on the prior clutter information to set the corresponding target weights, thereby achieving an equivalent design of the desired spectrum. The flexibility of waveform design is enhanced: Traditional algorithms usually apply the same norm constraint to the spectrum and sidelobes, which cannot effectively adapt to the needs of clutter suppression. The algorithm in this paper, by extending the model to… p The norm enables flexible control of the spectrum and sidelobes independently. Excellent clutter resistance: This invention proposes a transmit waveform design method based on the complex circular manifold Riemann confidence interval descent algorithm to effectively suppress clutter. Compared with classical methods, the proposed method has a faster convergence rate and superior clutter resistance.

[0058] It should be understood that, although Figure 1The steps in the flowchart are shown sequentially as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified herein, there is no strict order in which these steps are executed, and they can be performed in other orders. Figure 1 At least some of the steps in the process may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least some of the sub-steps or stages of other steps.

[0059] In one embodiment, such as Figure 8 As shown, a fast time-domain frequency domain anti-clutter waveform generation device is provided, comprising: an objective function construction module 200, a constrained optimization problem construction module 210, a first problem model transformation module 220, a second problem model transformation module 230, an unconstrained optimization problem acquisition module 240, and an anti-clutter waveform solution module 250, wherein: The objective function construction module 200 is used to acquire the clutter signal to be suppressed, and construct a frequency domain objective function for suppressing clutter based on the clutter signal to be suppressed and with maximizing the signal-to-clutter-to-noise ratio as the criterion. The constrained optimization problem construction module 210 is used to introduce a penalty factor and construct a constrained optimization problem model under constant modulus, weighted integral sidelobe level and spectral constraints. The first transformation module 220 of the problem model is used to transform the constrained optimization problem under constant modulus, weighted integral sidelobe level and spectrum constraints into an approximate equivalent problem model based on weight vectors; The second transformation module 230 of the problem model is used to extend the norm of the approximate equivalent problem model based on the weight vector to obtain an extended frequency domain clutter suppression problem model; Unconstrained optimization problem module 240 is used to transform the extended frequency domain clutter suppression problem model in Euclidean space to Riemannian complex circular manifold space to obtain an unconstrained optimization problem. The anti-clutter waveform solving module 250 is used to solve the unconstrained optimization problem to obtain a constant-wave radar waveform that suppresses the clutter signal to be suppressed.

[0060] Specific limitations regarding the waveform generation device for fast time-domain frequency domain clutter suppression can be found in the limitations of the waveform generation method for fast time-domain frequency domain clutter suppression described above, and will not be repeated here. Each module in the aforementioned fast time-domain frequency domain clutter suppression waveform generation device can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in hardware or independently of the processor in a computer device, or stored in software in the memory of a computer device, so that the processor can call and execute the corresponding operations of each module.

[0061] In one embodiment, a computer device is provided, which may be a terminal, and its internal structure diagram may be as follows: Figure 9 As shown, the computer device includes a processor, memory, network interface, display screen, and input devices connected via a system bus. The processor provides computing and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The network interface is used to communicate with external terminals via a network connection. When the computer program is executed by the processor, it implements a fast time-domain frequency domain anti-clutter waveform generation method. The display screen can be a liquid crystal display (LCD) or an e-ink display. The input devices can be a touch layer covering the display screen, buttons, a trackball, or a touchpad mounted on the computer device casing, or an external keyboard, touchpad, or mouse.

[0062] Those skilled in the art will understand that Figure 9 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0063] In one embodiment, a computer device is provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to perform the following steps: Obtain the clutter signal to be suppressed, and construct a frequency domain clutter suppression objective function based on the clutter signal to be suppressed and with maximizing the signal-to-clutter-to-noise ratio as the criterion; By introducing the weighted integral sidelobe level into the objective function through a penalty factor, a constrained optimization problem model is constructed under constant modulus, weighted integral sidelobe level, and spectral constraints. By incorporating the weight vectors of the spectrum and autocorrelation function into the objective function, an approximate equivalent problem model based on the weight vectors is constructed. The approximate equivalent problem model based on the weight vector is extended by norm to obtain the extended frequency domain clutter suppression problem model; Transforming the extended frequency domain clutter suppression problem model in Euclidean space to Riemannian complex circular manifold space yields an unconstrained optimization problem. Solving the unconstrained optimization problem yields a constant-wave radar waveform that suppresses the clutter signal to be suppressed.

[0064] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, the computer program performing the following steps when executed by a processor: Obtain the clutter signal to be suppressed, and construct a frequency domain clutter suppression objective function based on the clutter signal to be suppressed and with maximizing the signal-to-clutter-to-noise ratio as the criterion; By introducing the weighted integral sidelobe level into the objective function through a penalty factor, a constrained optimization problem model is constructed under constant modulus, weighted integral sidelobe level, and spectral constraints. By incorporating the spectrum and autocorrelation function weight vector into the objective function, an approximate equivalent problem model based on the weight vector is constructed. The approximate equivalent problem model based on the weight vector is extended by norm to obtain the extended frequency domain clutter suppression problem model; Transforming the extended frequency domain clutter suppression problem model in Euclidean space to Riemannian complex circular manifold space yields an unconstrained optimization problem. Solving the unconstrained optimization problem yields a constant-wave radar waveform that suppresses the clutter signal to be suppressed.

[0065] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in a variety of forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), RAMbus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0066] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0067] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A waveform generation method for fast time-domain frequency domain anti-clutter, characterized in that, The method includes: Obtain the clutter signal to be suppressed, and construct a frequency domain clutter suppression objective function based on the clutter signal to be suppressed and with maximizing the signal-to-clutter-to-noise ratio as the criterion; By introducing the weighted integral sidelobe level into the objective function through a penalty factor, a constrained optimization problem model is constructed under constant modulus, weighted integral sidelobe level, and spectral constraints. By incorporating the weight vectors of the spectrum and autocorrelation function into the objective function, an approximate equivalent problem model based on the weight vectors is constructed. The approximate equivalent problem model based on the weight vector is extended by norm to obtain the extended frequency domain clutter suppression problem model; Transforming the extended frequency domain clutter suppression problem model in Euclidean space to Riemannian complex circular manifold space yields an unconstrained optimization problem. Solving the unconstrained optimization problem yields a constant-wave radar waveform that suppresses the clutter signal to be suppressed.

2. The waveform generation method according to claim 1, characterized in that, The objective function for frequency domain anti-clutter based on the clutter signal to be countered and with maximizing the signal-to-clutter-to-noise ratio as the criterion includes: The initial objective function is constructed based on maximizing the signal-to-noise ratio. Based on the initial objective function and the clutter signal to be countered, an objective function that maximizes the frequency domain signal-to-clutter-to-noise ratio is constructed. The objective function of maximizing the frequency domain signal-to-clutter ratio is simplified to a frequency domain clutter energy minimization model, and this model is used as the objective function.

3. The waveform generation method according to claim 2, characterized in that, The objective function is expressed as: In the above formula, The frequency domain distribution characteristics of the clutter signal to be suppressed are represented by a complex vector. This represents the constant-wave radar waveform sequence to be solved. This represents the time-frequency domain transformation matrix.

4. The waveform generation method according to claim 3, characterized in that, The constrained optimization problem model is expressed as follows: In the above formula, Indicates the penalty factor. This represents the waveform sequence emitted by the radar. Indicates the length of the sequence. Indicates size is Complex vectors, , Both represent time-frequency domain transformation matrices, where, , ; This represents the constant modulus constraint that the sequence design needs to satisfy. Indicates waveform sidelobe level constraint. This indicates the range of sidelobes that need to satisfy the constraints. This indicates the degree of constraint on the side lobes. This indicates a constraint on energy outside the radar frequency band. This indicates the range that needs to meet out-of-band spectral constraints. Indicates the degree of constraint on the spectrum; This represents the conversion relationship between the autocorrelation function and the waveform. , representing the spectrum of the signal, This represents the modulo operation. This indicates the conjugate transpose operation.

5. The waveform generation method according to claim 4, characterized in that, The unconstrained optimization problem is expressed as: In the above formula, Representing variables The complex circular manifold space in which it is located This represents a weighting function that comprehensively considers both in-band and out-of-band frequencies. The weighted vector representing the sidelobe levels. express The order of the norm.

6. The waveform generation method according to claim 5, characterized in that, Solving the unconstrained optimization problem to obtain the constant-wave radar waveform for suppressing the clutter signal includes: Solve the Euclidean gradient and Euclidean Hessian matrix of the unconstrained optimization problem, and transform the Euclidean gradient and Euclidean Hessian matrix into Riemann gradient and Riemann Hessian matrix, respectively. Based on the Riemann gradient and Riemann-Hessian matrix of the unconstrained optimization problem, confidence interval descent is performed until the iteration cutoff condition is met, then the iteration stops and the constant wave radar waveform is output.

7. The waveform generation method according to claim 6, characterized in that, The confidence interval descent is performed based on the Riemann gradient and Riemann-Hessian matrix of the unconstrained optimization problem until the iteration cutoff condition is met. Then, the iteration stops and the constant-wave radar waveform is output, including: Based on the Riemann gradient and Riemann-Hessian matrix of the unconstrained optimization problem, a local approximation function of the tangent space is constructed. Based on the local approximation function, a sub-problem to be solved in each iteration is constructed. The conjugate gradient algorithm is used to solve the sub-problem. The unconstrained optimization problem is solved by iterating step by step and updating the corresponding confidence interval.

8. A waveform generation device for fast time-domain frequency domain anti-clutter, characterized in that, The device includes: The objective function construction module is used to obtain the clutter signal to be suppressed, and construct the frequency domain objective function for suppressing clutter based on the clutter signal to be suppressed and with maximizing the signal-to-clutter-to-noise ratio as the criterion. The constrained optimization problem construction module is used to introduce penalty factors and construct constrained optimization problem models under constant modulus, weighted integral sidelobe level and spectral constraints. The first transformation module of the problem model is used to transform the constrained optimization problem under constant modulus, weighted integral sidelobe level and spectral constraints into an approximate equivalent problem model based on weight vectors. The second transformation module of the problem model is used to extend the norm of the approximate equivalent problem model based on the weight vector to obtain an extended frequency domain clutter suppression problem model; The module for obtaining the unconstrained optimization problem is used to transform the extended frequency domain clutter suppression problem model in Euclidean space to Riemannian complex circular manifold space to obtain the unconstrained optimization problem. The anti-clutter waveform solving module is used to solve the unconstrained optimization problem and obtain a constant-wave radar waveform that suppresses the clutter signal to be suppressed.

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 method according to any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 7.

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