A method for designing SAR waveform driven by electromagnetic characteristics and K-means clustering

Abstract

The application relates to a SAR waveform design method combined with electromagnetic characteristics and K-means clustering, comprising the following steps: obtaining target scattering characteristic data based on a computational electromagnetic technique; constructing a signal model of a SAR one-dimensional range image based on the target scattering characteristic data; constructing a target function representing SAR waveform design by taking a signal-to-clutter ratio as an optimization criterion based on the signal model; constructing an original mathematical model of a SAR waveform design optimization problem by applying a constant modulus constraint and a similarity constraint to the target function; and converting the original mathematical model into a convex optimization problem and finally iteratively solving the convex optimization problem to obtain a SAR waveform. The application improves the dark weak target detection capability through azimuth angle domain scattering feature grouping and robust optimization.

Description

Technical Field

[0001] This invention relates to the field of synthetic aperture radar (SAR) signal processing technology, and in particular to a SAR waveform design method jointly driven by electromagnetic properties and K-means clustering. Background Technology

[0002] Synthetic aperture radar (SAR) is crucial for military reconnaissance and emergency response due to its advantages of all-weather, all-day operation, high penetration, and global coverage. However, target structure optimization and the application of new stealth materials have led to a reduction in the radar cross section (RCS), posing challenges to traditional SAR imaging. Since the transmitted waveform directly affects imaging quality, target detection, and anti-jamming performance, optimizing SAR waveform design has become a research hotspot for improving imaging quality.

[0003] Existing SAR waveforms are generally based on the assumption of ideal point targets, and their parameters are independent of the type of target being measured. Pulse compression through matched filtering can achieve a balance between point target resolution and signal-to-noise ratio. Although existing SAR waveform designs have been continuously optimized and improved in terms of performance indicators such as spatial resolution, sidelobe suppression, and point target detection, they generally lack the ability to adaptively adjust for specific targets, making it difficult to effectively highlight target scattering characteristics. As a result, the echo signals of many high-value weak targets are easily submerged by strong clutter, thereby reducing the system's target detection and imaging performance.

[0004] Although radar waveform studies for typical targets are commonplace, existing research generally assumes pre-existing electromagnetic scattering characteristics of the target. It fails to explain how these characteristics are acquired as supplementary knowledge. Constructing supplementary knowledge through electromagnetic scattering characteristic analysis is a primary condition for target-driven radar waveform design. Therefore, utilizing computational electromagnetics techniques to analyze target scattering characteristics, establishing supplementary knowledge for SAR waveform design, and subsequently proposing waveform design methods for faint targets and addressing the mismatch with actual environmental conditions, has significant application value. Summary of the Invention

[0005] To address the challenges of azimuth sensitivity and insufficient prior information matching in existing SAR waveform design methods for imaging faint targets, this invention proposes a SAR waveform design method jointly driven by electromagnetic properties and K-means clustering. Based on the FEKO electromagnetic simulation platform, multi-azimuth scattering characteristic data of the target are acquired. The scattering characteristics are automatically grouped using the K-means clustering algorithm, and typical azimuth domain features are extracted as prior information. An optimization model is then constructed with the objective of maximizing the worst-case signal-to-clutter ratio (SCR). Constant modulus constraints and similarity constraints are introduced to ensure waveform feasibility and high-resolution characteristics, and the Majorization-Minimization Algorithm (MM) is used for efficient solution. This method can achieve high resolution across a wide azimuth range. Internal matching of target scattering characteristics significantly improves the imaging quality of faint targets. To achieve the above objectives, the present invention provides the following solution: A SAR waveform design method jointly driven by electromagnetic properties and K-means clustering includes: Data on target scattering characteristics are obtained based on computational electromagnetics technology. Based on the target scattering characteristic data, a signal model of a one-dimensional SAR range profile is constructed; Based on the aforementioned signal model, the signal-to-noise ratio is used as the optimization criterion to construct an objective function characterizing SAR waveform design. By applying constant modulus constraints and similarity constraints to the objective function, the original mathematical model of the SAR waveform design optimization problem is constructed. The original mathematical model is transformed into a convex optimization problem, which is then solved iteratively to obtain the SAR waveform.

[0006] Optionally, based on computational electromagnetics techniques, obtaining target scattering characteristic data includes: Based on computational electromagnetics technology, the scattering characteristics of typical targets at different azimuth angles are obtained; The K-means clustering method is introduced to divide the scattering characteristics into angular domains. A representative set of data from each class is selected to approximate the overall characteristics of that class. At the same time, classes with coverage azimuth angles lower than the preset class are discarded, resulting in a set of representative target scattering characteristic data.

[0007] Optionally, obtaining the scattering characteristics of a typical target at different azimuth angles includes: Based on the target's geometric shape and material parameters, a target model is established; The target model is meshed according to its details and the incident wave wavelength, and the excitation source parameters are set to start the calculation task to obtain the electromagnetic scattering data of the target.

[0008] Optionally, the signal model is: in, The Toeplitz matrix constructed for the target scattering characteristic t. The Toeplitz matrix constructed for background scattering interference b. For noise, This is the transmitted waveform.

[0009] Optionally, the objective function characterizing SAR waveform design is: in, The target scattering characteristic matrix, The background scattering interference matrix, For the transmitted waveform, Represents convolution. Represents the conjugate transpose of a matrix or vector.

[0010] Optionally, the original mathematical model is: in, For the original mathematical model, This is a SAR waveform sequence. and These are the target scattering characteristic matrix and the background scattering interference matrix, respectively. The values ​​are obtained by K-means clustering of the target scattering characteristics corresponding to the azimuth angle. As a reference signal, parameters Used to control the degree of similarity between the optimized waveform and the reference signal. The number of elements in the target electromagnetic scattering property set. The first in the waveform The value of each code element, For the radar signal Each code element The length of the SAR transmitted signal.

[0011] Optionally, transforming the original mathematical model into a convex optimization problem includes: Introducing auxiliary variables The objective function of the original mathematical model is equivalently transformed into the form of the image above to obtain the first problem model. ; By enumerating all elements of the electromagnetic scattering characteristics, the worst-case performance constraint is equivalently transformed into a set of finite performance constraints, thus transforming the first problem model... The equivalent transformation yields the model for the second problem. ; The second problem model The non-convex constraints are transformed into convex constraints based on the MM algorithm, resulting in the third problem model. ; For the third problem model Introducing slack variables At the same time, a penalty item was added. This forces the convergence to satisfy the constant modulus constraint, resulting in the fourth problem model. ; By iteratively modeling the fourth problem To solve the original mathematical model The iteration continues until a preset stopping condition is met.

[0012] Optionally, the first problem model for: Second problem model for: in, express The set of possible values, For the signal at the 1st The scattering power of a target under specific electromagnetic scattering characteristics. The clutter power in the received signal; The third problem model for: Among them, let , for First-order Taylor expansion at the point, To extract the real part of the complex signal, Let be the complex conjugate value of the j-th signal symbol in the transmitted signal sequence determined by k iterations; The fourth problem model for: in, As a penalty item, These are slack variables.

[0013] Optionally, the preset stop condition is: in, It is a constant that is greater than and very close to 0.

[0014] The beneficial effects of this invention are as follows: This invention focuses on the adaptive optimization method of SAR waveform based on clustering of target scattering characteristics. By using FEKO to provide the electromagnetic scattering characteristics of typical targets, an optimization problem is established and a solution method is proposed. This method can effectively improve the imaging quality of synthetic aperture radar (SAR) for faint targets and alleviate the problem of poor matching between prior information and actual scene in traditional waveform design.

[0015] The SAR waveform adaptive optimization method based on target scattering characteristics proposed in this invention can be applied to the optimization design of other radar systems, providing ideas and preliminary theoretical basis for the simultaneous optimization of radar transmitter and receiver. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 This is a schematic diagram of a SAR waveform design method jointly driven by electromagnetic characteristics and K-means clustering according to an embodiment of the present invention. Figure 2 The diagram shows the clustered distribution of azimuth angles in each embodiment of the present invention. The radar operates in the X-band, with a frequency range of 8.75 GHz to 9.25 GHz and a step frequency of 2 MHz. The elevation angle of the plane wave source is fixed at 60°, and the azimuth angle traverses the range of -45° to 45° with a step size of 3°. Figure 3 This refers to the number of elements contained in each cluster in this embodiment of the invention; Figure 4 This is a schematic diagram of the system model of a SAR one-dimensional range image according to an embodiment of the present invention; Figure 5 The objective function of this invention embodiment With iteration step size A diagram illustrating the changes; Figure 6 This is a time-domain schematic diagram for verifying the similarity constraints between the design signal and the linear frequency modulated signal in an embodiment of the present invention, wherein (a) is a verification diagram of the real part similarity and (b) is a verification diagram of the imaginary part similarity. Figure 7 This is a schematic diagram showing the comparison results of a linear frequency modulated signal, a nonlinear frequency modulated signal, and the designed waveform signal-to-noise ratio (SCR) in an embodiment of the present invention. Figure 8 This is a schematic diagram of an aircraft model built based on FEKO according to an embodiment of the present invention; Figure 9 This is a schematic diagram of SAR images according to an embodiment of the present invention; wherein, (a) is the SAR image corresponding to the algorithm proposed in this invention, and (b) is the SAR image corresponding to the Chirp signal. Detailed Implementation

[0018] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only 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.

[0019] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0020] like Figure 1 As shown, this embodiment proposes a SAR waveform design method jointly driven by electromagnetic characteristics and K-means clustering, including: Data on target scattering characteristics are obtained based on computational electromagnetics technology. Based on the target scattering characteristic data, a signal model of a one-dimensional SAR range profile is constructed; Based on the aforementioned signal model, the signal-to-noise ratio is used as the optimization criterion to construct an objective function characterizing SAR waveform design. By applying constant modulus constraints and similarity constraints to the objective function, the original mathematical model of the SAR waveform design optimization problem is constructed. The original mathematical model is transformed into a convex optimization problem, which is then solved iteratively to obtain the SAR waveform.

[0021] Specifically, in this embodiment, the proposed SAR waveform design method driven by electromagnetic characteristics and K-means clustering includes: Step 1, obtaining the scattering characteristics of typical targets based on computational electromagnetics technology; Step 2, using K-means clustering to divide the scattering characteristics of targets at different azimuth angles into angular domains, selecting a representative set of data from each class to approximate the overall characteristics of that class. Simultaneously, classes with fewer covered azimuth angles are discarded, resulting in a set of representative target scattering characteristic data; Step 3, establishing a signal model for the SAR one-dimensional range profile based on the scattering model; Step 4, using the signal-to-clutter ratio (SCR) as the optimization criterion to analytically characterize the objective function for SAR waveform design; Step 5, applying constant mode constraints and similarity constraints; constant mode constraints ensure the radar amplifier is always in saturation, avoiding radar waveform amplitude modulation, while similarity constraints guarantee high resolution and low sidelobe characteristics. Combining the objective function and constraints, a mathematical model for the SAR waveform design optimization problem is constructed; Step 6, reconstructing the image of the original minimax fractional objective function, introducing auxiliary variables. As a lower bound for performance, the problem arises. Step 7: By enumerating the signal-to-clutter ratio (SCR) of representative target scattering data, the minimum value of the objective function is required to be no less than the lower performance bound. Transform the first constraint into an equivalent form, let , in This is the waveform we are looking for. It is a Toeplitz matrix composed of typical target scattering characteristics. The Toeplitz matrix, composed of background scattering characteristics, addresses the problem. The problem arises from equivalent transformation. Step 8, Problem It is non-convex; for further solution, let Constructing based on MM algorithm The lower bound convex function, similarly transforming the non-convex constraints in the constant modulus constraint into convex constraints based on the MM algorithm, yields the problem. Step 9: In the early stages of iteration, allow solutions to be searched within a more relaxed range to avoid getting trapped in local optima. Introduce slack variables. At the same time, a penalty item was added. This forces convergence while still satisfying the constant modulus constraint. The problem is... Step 10: Iterate through the problem To solve the problem Set iteration conditions when The iteration stops when the total difference between the generated signal and the constant-mode characteristic is less than a given value, and the SAR waveform is obtained.

[0022] To improve the imaging quality of synthetic aperture radar (SAR) for faint targets and alleviate the problem of poor matching between prior information and actual scene in traditional waveform design, a SAR waveform design method integrating electromagnetic properties and K-means clustering is proposed. This method enhances the detection capability of faint targets while ensuring constant modulus and similarity constraints. The implementation process is as follows: Figure 1 As shown, the specific steps include: Step 1: Obtain the scattering characteristics of typical targets based on computational electromagnetics techniques; First, using computational electromagnetic modeling tools, the target's geometry is created, establishing the target model. Ensure the model's size and shape conform to actual physical properties; this can be done by importing CAD models or drawing manually as needed. Target modeling should be as accurate as possible to approximate real target characteristics. For complex, electrically large targets, geometric simplification is also necessary to reduce computational burden. Configure appropriate material properties for each component module in the model, including electrical conductivity, dielectric constant, and magnetic permeability. Materials can be selected from an existing material library or new material properties can be defined. If it is a stealth target with coating, the electromagnetic parameters of the surface need to be defined.

[0023] Secondly, the geometric model is meshed, dividing it into multiple small units. The mesh size depends on the model's detail and the incident wave wavelength. A finer mesh yields higher computational accuracy but also increases the computational burden. Therefore, appropriate mesh optimization is needed in different regions of the model. The mesh should be refined in critical areas (such as edges and sharp points) to improve computational accuracy, while in simpler regions, the mesh can be coarsened to reduce the computational burden.

[0024] Next, set the excitation source parameters, including incident direction, frequency, incident angle, and polarization. Select an appropriate solution method based on the mesh size, computational resources, and frequency range. FEKO supports various solution methods, such as the Finite-Difference Time-Domain (FDTD), the Method of Moments (MoM), and multi-spectral methods. These methods offer different speeds and accuracies, suitable for various applications.

[0025] Finally, the computation task is initiated, the computation status is monitored, and the change of residuals with the number of iterations is observed to ensure the convergence of the computation process. After the computation is completed, the electromagnetic scattering data of the target is output as auxiliary knowledge for SAR waveform design.

[0026] Step 2: The K-means clustering method is introduced to divide the scattering characteristics of the target at different azimuth angles into angular domains, so as to obtain representative target scattering characteristics; K-means clustering is introduced to divide the scattering characteristics of the target at different azimuth angles into angular domains. A representative set of data from each class is selected to approximate the overall characteristics of that class. At the same time, classes with fewer azimuth angles are discarded. Figure 2 It describes the distribution of the angular family in each direction. Figure 3 This refers to the number of azimuth angles in each cluster. For example, groups 2, 6, and 7 cover a limited range of azimuth angles, so they are discarded, and groups 1, 3, 4, and 5 are retained.

[0027] Step 3: Establish a signal model for the SAR one-dimensional range profile based on the scattering model; The signal acquisition process of SAR one-dimensional range image is as follows Figure 4 As shown, the SAR transmitted waveform interacts with the target scattering characteristics and background scattering characteristics, producing an echo that is interfered with by noise, resulting in a one-dimensional range profile y, represented as: in The Toeplitz matrix is ​​constructed from the target scattering characteristics t. The Toeplitz matrix is ​​constructed from the background scattering interference b. It's noise. It is the transmitted waveform.

[0028] Step 4: Using the signal-to-noise ratio (SCR) as the optimization criterion, analyze the objective function characterizing the SAR waveform design; The signal-to-clutter ratio (SCR) directly quantifies the target signal's ability to counter clutter interference, determining the radar's detection performance in complex environments. Maximizing the SCR through waveform design can significantly improve the target detection probability. Therefore, the SCR is chosen as the optimization criterion. The SCR can be expressed as: in, It is the target scattering characteristic matrix. It is the background scattering interference matrix. It is the transmitted waveform. Represents the mathematical expectation. Represents the conjugate transpose of a matrix or vector.

[0029] Step 5: Apply constant modulus constraints and similarity constraints, and establish a mathematical model of the optimization problem in conjunction with the objective function; Constraints need to be introduced to ensure the SAR waveform is engineering-feasible and that the range direction has high resolution and low sidelobe characteristics. First, a constant mode constraint is added, namely... This ensures that the radar transmitter's amplifier operates at its optimal state, thereby achieving maximum transmit power; to guarantee high resolution and low sidelobe level in the SAR range direction, similarity constraints are introduced. Based on the objective function, an optimization problem is established. : Step 6: Reconstruct the upper view of the original minimax fractional objective function and introduce auxiliary variables. As a lower bound for performance, the problem arises. ; Here, through the transformation of the upper image, the objective function with difficult-to-handle fractional form and minimax structure is transformed into an easier-to-handle form. First, the worst-case SCR (Spectral Reduction) needs to be calculated for all possible electromagnetic scattering data, and then the waveform needs to be optimized to improve the performance in this worst-case scenario. This can be achieved by introducing auxiliary variables. As a lower bound for performance, the worst-case signal-to-noise ratio (SCR) is greater than [value missing]. Maximize this lower bound .

[0030] Step 7: By enumerating all elements in the electromagnetic scattering characteristics, the worst-case performance constraint is equivalently transformed into a finite set of deterministic performance constraints, let... , in This is the waveform we are looking for. It is a Toeplitz matrix composed of typical target scattering characteristics. The Toeplitz matrix, composed of background scattering characteristics, addresses the problem. The problem arises from equivalent transformation. ; Step 8, Questions It is non-convex; for further solution, let Constructing based on MM algorithm The lower bound convex function, similarly transforming the non-convex constraints in the constant modulus constraint into convex constraints based on the MM algorithm, yields the problem. ; For functions At any feasible point Taylor expansion, constructing a surrogate function, and the function at feasible points. The surrogate function has the same value as the original function, and at other points, the surrogate function is a lower bound of the original function. The Taylor expansion at the feasible point is: The gradient is: Substitute to get for: at this time about and All are convex functions.

[0031] The constant modulus constraint can be equivalent to: As it is a non-convex constraint, this embodiment uses the solution from the previous iteration. Perform a first-order Taylor expansion on it: Substituting this into the original non-convex constraint, we obtain a linear approximate constraint: Step 9: Introduce slack variables At the same time, a penalty item was added. This forces the problem to converge while satisfying the constant modulus constraint. ; Linear approximation constraints may be too strict, causing the feasible region of the optimization problem to be too small or even unsolvable in the early stages of iteration. Therefore, slack variables are introduced to address this. To relax the constraints: Slack variables The physical meaning of the first The value of the square of the amplitude of each signal point is less than 1. To prevent constraint failure, a penalty term is added to the objective function to penalize the slack variables. The objective function is: In the early stages of iteration, the penalty coefficient is extremely small, and the algorithm almost ignores the constant mode constraint. It prioritizes optimizing the waveform to maximize the worst signal-to-noise ratio (SCR), resulting in a significant improvement in waveform performance but a severe deviation from the constant mode. As the penalty coefficient gradually increases, the algorithm enters a trade-off mode, balancing the improvement of SCR with maintaining the constant mode, guiding the waveform to gradually converge from the high-performance region towards the feasible region of the constant mode. In the later stages of iteration, the penalty coefficient becomes extremely large, and the algorithm prioritizes strictly ensuring the constant mode property. Even a small deviation from the constant mode will cause a sharp drop in the objective function value. Therefore, it forces the waveform to tend towards the constant mode constraint boundary, thus outputting a solution that simultaneously guarantees a high SCR and approximates the constant mode constraint.

[0032] Step 10: Iterating through the problem To solve the problem Set iteration conditions; iteration stops when a stopping condition is met. The iteration condition is: When the sum of the constant modulus signal deviation at all points of the entire waveform is less than or equal to When the iteration stops, the SAR waveform is obtained.

[0033] This embodiment verifies the theoretical derivation and practical application involved in this embodiment through numerical experiments, including the convergence of the algorithm, the effectiveness of the constraints, and the ability to acquire information about the target under test. Furthermore, by simulating a simple airborne SAR system, it verifies whether this embodiment can improve the observation performance of imaging radar for typical targets.

[0034] 1. Algorithm convergence verification: set up , Reference signal For Chirp signals, different similarity parameters Different feasible regions are generated. After executing Algorithm 1, the objective function... With iteration step size Relationship such as Figure 5 As shown, in the initial iterations, due to the small penalty term, the optimization problem has a large feasible region, so the objective function sequence is monotonically increasing and gradually tends to plateau. As the iterations continue, the penalty term gradually increases, forcing the relaxed constraints to be satisfied, the feasible region decreases, the objective function decreases, and eventually plateaus, triggering the stopping condition. Meanwhile, Always greater than its lower bound ,and This is consistent with the description in the text.

[0035] 2. Similarity constraint verification: Verify the effectiveness of the similarity constraint. Figure 6 Draw the reference signal and the linear frequency modulated signal respectively. as well as The time-domain diagram of the designed waveform. Figure 6 (a) is the graph of the real part in the time domain. Figure 6 (b) is the diagram of the imaginary part in the time domain. It can be observed that... The smaller the value, the closer the time-domain waveform of the transmitted signal is to the reference signal. The more similar the time-domain waveforms are, the greater the degree of similarity, which is in line with expectations.

[0036] 3. Performance Evaluation: The performance of the design signal is evaluated using the signal-to-noise ratio (SRC). Figure 7By comparing the SCR values ​​of a linear frequency modulated (LFM) signal, an NLFM signal with the same parameters, and the designed signal within the azimuth angle range of -45° to 45°, it can be seen that the optimized waveform designed in this paper achieves a significant improvement in SCR over a wide 90° azimuth angle range. Compared with the other two comparison waveforms, the proposed method exhibits higher SCR at all azimuth angles. Compared with the Chirp signal with the same parameters, the minimum target SCR improvement can reach 2.4dB, demonstrating superior target enhancement capability and high robustness to azimuth angles.

[0037] 4. Applications in SAR: To verify whether the method proposed in this embodiment can be applied to SAR, SAR images of typical targets were obtained by simulating a simplified airborne SAR system. The basic parameters of the airborne SAR system are shown in Table 1.

[0038] Table 1 The B-2 bomber was selected as the target of the test, and a model of the aircraft was built based on FEKO, as follows: Figure 8 As shown. Step one obtains the radar cross section (RCS) of each frequency component of the target, serving as auxiliary knowledge for SAR joint design. Verification is based on real SAR images. A SAR image of a certain airport is used as the backscattering coefficient to form the scene to be tested. The scattering coefficient of B2 is generated through ISAR imaging. Assuming a B2 is parked at the airport, the echo signal is obtained through SAR system observation, and then a SAR image is generated through the RD imaging algorithm, as shown. Figure 9 As shown in (a)-(b).

[0039] Compared to images from linear frequency modulated signals, the SAR image corresponding to this embodiment has a greater contrast between the B2 bomber target and the background, resulting in the best visual effect. Furthermore, the aircraft target has a clear outline, which will be more helpful for subsequent target detection, recognition, and other applications of SAR images.

[0040] This embodiment proposes a SAR waveform design driven by electromagnetic properties and K-means clustering, provides a scheme for acquiring auxiliary knowledge in radar waveform design, establishes an optimization problem for the joint design, and designs a targeted solution method, which can effectively enhance the SAR's ability to acquire information about high-value targets, while also ensuring the constant magnitude, high resolution, and low sidelobe characteristics of the SAR waveform.

[0041] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A SAR waveform design method jointly driven by electromagnetic properties and K-means clustering, characterized in that, include: Data on target scattering characteristics are obtained based on computational electromagnetics technology. Based on the target scattering characteristic data, a signal model of a one-dimensional SAR range profile is constructed; Based on the aforementioned signal model, the signal-to-noise ratio is used as the optimization criterion to construct an objective function characterizing SAR waveform design. By applying constant modulus constraints and similarity constraints to the objective function, the original mathematical model of the SAR waveform design optimization problem is constructed. The original mathematical model is transformed into a convex optimization problem, which is then solved iteratively to obtain the SAR waveform.

2. The SAR waveform design method jointly driven by electromagnetic characteristics and K-means clustering according to claim 1, characterized in that, Based on computational electromagnetics technology, data on target scattering characteristics can be obtained, including: Based on computational electromagnetics technology, the scattering characteristics of typical targets at different azimuth angles are obtained; The K-means clustering method is introduced to divide the scattering characteristics into angular domains. A representative set of data from each class is selected to approximate the overall characteristics of that class. At the same time, classes with coverage azimuth angles lower than the preset class are discarded, resulting in a set of representative target scattering characteristic data.

3. The SAR waveform design method jointly driven by electromagnetic characteristics and K-means clustering according to claim 2, characterized in that, Obtaining the scattering characteristics of typical targets at different azimuth angles includes: Based on the target's geometric shape and material parameters, a target model is established; The target model is meshed according to its details and the incident wave wavelength, and the excitation source parameters are set to start the calculation task to obtain the electromagnetic scattering data of the target.

4. The SAR waveform design method jointly driven by electromagnetic characteristics and K-means clustering according to claim 1, characterized in that, The signal model is as follows: in, The Toeplitz matrix constructed for the target scattering characteristic t. The Toeplitz matrix constructed for background scattering interference b. For noise, This is the transmitted waveform.

5. The SAR waveform design method jointly driven by electromagnetic characteristics and K-means clustering according to claim 1, characterized in that, The objective function characterizing SAR waveform design is: in, The target scattering characteristic matrix, The background scattering interference matrix is... For the transmitted waveform, Represents convolution. Represents the conjugate transpose of a matrix or vector.

6. The SAR waveform design method jointly driven by electromagnetic characteristics and K-means clustering according to claim 5, characterized in that, The original mathematical model is as follows: in, The original mathematical model, and These are the target scattering characteristic matrix and the background scattering interference matrix, respectively. The values ​​are obtained by K-means clustering of the target scattering characteristics corresponding to the azimuth angle. As a reference signal, parameters Used to control the degree of similarity between the optimized waveform and the reference signal. The number of elements in the target electromagnetic scattering property set. The first in the waveform The value of each code element, For the radar signal Each code element The length of the SAR transmitted signal.

7. The SAR waveform design method jointly driven by electromagnetic characteristics and K-means clustering according to claim 6, characterized in that, Transforming the original mathematical model into a convex optimization problem includes: Introducing auxiliary variables The objective function of the original mathematical model is equivalently transformed into the form of the image above to obtain the first problem model. ; By enumerating all elements of the electromagnetic scattering characteristics, the worst-case performance constraint is equivalently transformed into a set of finite performance constraints, thus transforming the first problem model... The equivalent transformation yields the model for the second problem. ; The second problem model The non-convex constraints are transformed into convex constraints based on the MM algorithm, resulting in the third problem model. ; For the third problem model Introducing slack variables At the same time, a penalty item was added. This forces the convergence to satisfy the constant modulus constraint, resulting in the fourth problem model. ; By iteratively modeling the fourth problem To solve the original mathematical model The iteration continues until a preset stopping condition is met.

8. The SAR waveform design method jointly driven by electromagnetic characteristics and K-means clustering according to claim 7, characterized in that, The first problem model for: Second problem model for: in, express The set of possible values, For the signal at the 1st Target scattering power under various electromagnetic scattering characteristics The clutter power in the received signal; The third problem model for: Among them, let , for First-order Taylor expansion at the point, To extract the real part of the complex signal, for The transmitted signal sequence determined in the nth iteration is the 1st The complex conjugate value of each signal symbol; The fourth problem model for: in, As a penalty item, These are slack variables.

9. The SAR waveform design method jointly driven by electromagnetic characteristics and K-means clustering according to claim 8, characterized in that, The preset stop condition is: in, It is a constant that is greater than and very close to 0.

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