NLFM signal optimization method based on asymmetric PWL function and simulated annealing algorithm

Abstract

The embodiment of the invention relates to the technical field of signal processing, in particular to an NLFM signal optimization method based on an asymmetric PWL function and a simulated annealing algorithm, and the method comprises the steps: generating an initial NLFM signal through employing a method based on analysis fitting; dividing the time-frequency derivative model based on the asymmetric PWL function into 2n + 2 segments, performing secondary interpolation segmentation, and combining the initial NLFM signal to obtain an optimized signal generation model; based on a cooling process of an energy object in physics, generating an enhanced simulated annealing optimization model suitable for time-frequency derivative control point optimization; and constructing an objective function based on the peak sidelobe ratio, the IRW ultra-wide penalty factor and the bandwidth ultra-wide penalty factor, performing iterative optimization based on the constructed objective function, the enhanced simulated annealing optimization model and the optimized signal generation model, and finally generating an optimized NLFM signal. The method corresponds to smaller main lobe width, lower cost and simpler design steps, and can efficiently generate the optimized NLFM signal with high quality.

Description

Technical Field

[0001] Embodiments of the present application relate to the technical field of signal processing, and particularly to an NLFM signal optimization method based on an asymmetric PWL function and an simulated annealing algorithm. Background Art

[0002] The design of NLFM (Nonlinear Frequency Modulation signal) based on PWL (Piecewise Linear Function) is a method that divides the time axis of a signal into several segments and designs different frequency change rules within each segment to achieve complex nonlinear frequency modulation characteristics. This design has been widely used in systems such as radar, sonar, and communication to optimize the pulse compression performance (such as low sidelobes, high resolution) and Doppler tolerance of signals.

[0003] Compared with linear frequency modulation, the currently proposed PWL-based nonlinear frequency modulation signal design method can significantly reduce the sidelobe level of the intermediate frequency response and has no adverse effects on the signal-to-noise ratio and main lobe width. However, due to its symmetric characteristics, the optimization space of this design is not large, and the design freedom is not high enough.

[0004] In the face of this situation, Wei et al. proposed a design method based on genetic algorithm constraint optimization. This method uses the third-order polynomial phase function method proposed by Sandia Laboratories to generate an initial comparison NLFM signal. By using the opposite change of the window function shape as the instantaneous frequency modulation function model and combining the integral of the frequency modulation function as the bandwidth, the frequency modulation function converges after several iterations, and then an initial NLFM signal is generated. Then, all the frequency modulation control point sets on the positive and negative axes after the PWL function is segmented are input into the matlab optimization toolbox, and the genetic algorithm is used to optimize the optimal solution. The population size, crossover factor, and mutation factor are set to 100, 0.8, and 0.2 respectively. To avoid the situation that the spectrum exceeds the bandwidth limit during the optimization process, the bandwidth within the time interval is also set for the signal frequency modulation control points. The first group of experiments is optimized based on the LFM signal. Since the initial main lobe width of the LFM is 0.89, the main lobe constraint is also set to 0.89. In the second group of simulation experiments, a 3rd-order NLFM signal designed by the high-order polynomial phase function method proposed by Sandia Laboratories is used as the initial signal, and the experimental results all show the sidelobe suppression effect.

[0005] However, this method has three main deficiencies.

[0006] First, the number of segments of this method is small, and the optimization freedom is not high.

[0007] Second, in the process of evolution, the genetic algorithm may have the premature convergence situation where individuals with high fitness over-reproduce while the population size is limited, resulting in a rapid reduction in the diversity of the population and unable to generate the optimal solution that meets the constraints.

[0008] Thirdly, genetic algorithms usually need to maintain an entire population, and in each generation, fitness calculation, selection, crossover, and mutation operations are performed on the individuals in the population, which results in very high computational complexity and cost for this method. Summary of the Invention

[0009] In view of this, embodiments of the present application propose an NLFM signal optimization method based on an asymmetric PWL function and a simulated annealing algorithm, corresponding to a smaller main lobe width, lower design cost, and more concise design steps. There will be a greater chance of jumping out of local optima during the search process, so as to be able to explore more widely in space and finally generate optimized NLFM signals efficiently and with high quality.

[0010] In a first aspect, embodiments of the present application propose an NLFM signal optimization method based on an asymmetric PWL function and a simulated annealing algorithm, which is applicable to generating optimized NLFM signals. The method includes: generating an initial NLFM signal using an analytical formula fitting method; dividing the time-frequency derivative model based on the asymmetric PWL function into 2n + 2 segments and then performing quadratic interpolation segmentation, and then combining with the initial NLFM signal to obtain an optimized signal generation model, where n is an integer greater than 0; generating a strengthened simulated annealing optimization model suitable for optimizing the time-frequency derivative control points of the signal based on the cooling process of energy objects in physics; constructing an objective function based on the peak sidelobe ratio, IRW ultra-wide penalty factor, and bandwidth ultra-wide penalty factor, and performing iterative optimization based on the constructed objective function, strengthened simulated annealing optimization model, and optimized signal generation model to finally generate optimized NLFM signals.

[0011] Optionally, the initial NLFM signal is designed as a U-shaped waveform. The initial NLFM signal is generated using an analytical formula fitting method, which is achieved through the following formula: ; where represents the bandwidth of the initial NLFM signal, represents the pulse width of the initial NLFM signal, is the preset number of segments on the positive change rate side or negative change rate side, represents the initial NLFM signal.

[0012] Optionally, dividing the time-frequency derivative model based on the asymmetric PWL function into 2n + 2 segments and then performing quadratic interpolation segmentation, and then combining with the initial NLFM signal to obtain an optimized signal generation model includes: The positive change rate side and the negative change rate side are respectively split into n + 1 line segments. Each of the n + 1 line segments on each side corresponds to 2n + 2 time-frequency derivative control points. There are a total of 4n + 4 time-frequency derivative control points on both the positive change rate side and the negative change rate side. The duration of each line segment is designed to be a fixed value; Set the first line segment starting from the time axis of 0 as , and the second line segment as , and so on. Denote the set of 2n + 2 line segments as , ; Start counting the time-frequency derivative control points from the time axis of 0. Let The time-frequency derivative control points on the left and right sides be respectively and . Let The time-frequency derivative control points on the left and right sides be respectively and , and so on. Denote the set of 4n + 4 time-frequency derivative control points as , .

[0013] Optionally, the general analytical expression of the time-frequency derivative function is: ; ; ; where, represents the duration of the th line segment; Integrate the time-frequency derivative function to obtain the instantaneous frequency function of the constructed initial NLFM signal. The expression of the instantaneous frequency function is: ; ; ; ; where, , , are all instantaneous frequency function coefficients; Integrate the instantaneous frequency function to obtain the phase function , The expression of is: Based on the phase function , an optimized signal generation model is obtained , .

[0014] Optionally, based on the process of temperature reduction of an energy object in physics, a reinforcement simulated annealing optimization model applicable to the optimization of time-frequency derivative control points of signals is generated, including: Assume that the previous crystal state is , according to a preset index, the crystal state becomes , correspondingly, the crystal energy changes from to ; where the preset index is temperature decrease or temperature increase; Define the acceptance probability of changing from to as , and the expression of the acceptance probability is: ; Among them, is the initial temperature, is the current temperature; If the change in the crystal state results in a decrease in the crystal energy, the transfer is directly accepted, that is, ; If the change in the crystal state results in an increase in the crystal energy, it means that the crystal is deviating from the global optimal solution. At this time, a random number between 0 and 1 is generated and compared with . If , the state transfer is accepted. If , the state transfer is rejected; The acceptance probability is dynamically generated based on the energy change amount and . During the process of temperature decrease and state transfer acceptance, three principles need to be followed; The first principle is that as the temperature decreases, the probability of accepting a solution that makes the objective function increase gradually decreases; The second principle is that when the temperature approaches zero, only solutions that make the objective function decrease can be accepted; The third principle is that at a fixed temperature, the probability of accepting a candidate solution that makes the objective function decrease is greater than the probability of accepting a candidate solution that makes the objective function increase; The basic simulated annealing optimization model is expressed by the formula: ; Among them, is the parameter vector to be optimized, is the objective function, matrix and matrix are the coefficient matrix of the linear inequality equation and the coefficient matrix of the linear equality equation, respectively, and the vectors and the vector are the constraint vector of the linear inequality equation and the constraint vector of the linear equality equation, respectively. The functions and the function are the non - linear inequality constraint term and the linear inequality constraint term, respectively. and are the lower limit and the upper limit of respectively; Since at the start and end of the chirp signal pulse, a higher frequency change rate can reduce the Fresnel ripples in the waveform spectrum, thereby reducing the sidelobes to a certain extent. Therefore, in order to increase the degree of freedom of optimization, the upper and lower limit threshold coefficients are defined. The upper and lower limit threshold coefficients change the calculation expressions of and in the simulated annealing algorithm. The calculation expressions of and are as follows: ; ; Among them, is a function to generate a matrix or array of all 1s; The autocorrelation function of the ideal NLFM signal after matched filtering should have as low a peak sidelobe ratio as possible and as narrow a - 3dB main lobe width as possible. Therefore, it is also necessary to limit the signal bandwidth beyond the set spectral bandwidth range, that is , , represents the time interval between every two time - frequency derivative control points; Based on this, the enhanced annealing optimization model can be obtained. The enhanced simulated annealing optimization model is expressed by the formula: ; Among them, represents the impulse response width obtained when using the current time - frequency derivative control point, is the main lobe width constraint value.

[0015] Optionally, the objective function constructed based on the peak sidelobe ratio, IRW over - width penalty factor, and bandwidth over - width penalty factor is expressed by the following formula: ; Among them, represents the peak sidelobe ratio obtained when the optimized signal uses the current time - frequency derivative control point, is the main lobe width penalty coefficient, is the bandwidth penalty coefficient, is the objective function.

[0016] Optionally, iterative optimization is performed based on the constructed objective function, enhanced simulated annealing optimization model, and optimization signal generation model, and finally an optimized NLFM signal is generated, including: Calculate the objective function value, and determine whether the value of the objective function decreases; If the value of the objective function decreases, directly perform state transition, generate a new NLFM signal, and re - perform quadratic interpolation segmentation; If the value of the objective function does not decrease, calculate and determine whether the temperature drops to 0 degrees; If the temperature drops to 0 degrees, heat it to a certain temperature and continue optimization, and re - perform quadratic interpolation segmentation; If the temperature does not drop to 0 degrees, continue to determine whether the temperature remains unchanged for a certain number of generations; If the temperature remains unchanged for a certain number of generations, output the time - frequency derivative control points, end the optimization, and output the optimized NLFM signal; If the temperature does not remain unchanged for a certain number of generations, determine whether to perform state transition through parameter - calculated probability, and calculate the value of the objective function again.

[0017] An NLFM signal optimization method based on an asymmetric PWL function and simulated annealing algorithm proposed in this application first generates an initial NLFM signal using an analytical - formula fitting - based method, divides the time - frequency derivative model based on the asymmetric PWL function into 2n + 2 segments and then performs quadratic interpolation segmentation to obtain an optimization signal generation model. Subsequently, based on the process of the temperature drop of an energy object in physics, an enhanced simulated annealing optimization model suitable for optimizing the time - frequency derivative control points of the signal is generated. Then, an objective function is constructed based on the peak sidelobe ratio, IRW ultra - width penalty factor, and bandwidth ultra - width penalty factor. Finally, iterative optimization is performed based on the constructed objective function, enhanced simulated annealing optimization model, and optimization signal generation model to generate an optimized NLFM signal. This method can be applied to all NLFM signal models generated based on time - frequency derivatives. When the main lobe of the NLFM signal is significantly broadened, the bandwidth exceeds the planned range, or the maximum sidelobe value of the signal is relatively high, this method can be used to perform a large - degree - of - freedom optimization design on the initial signal. If the designer does not have a basic signal, the initial NLFM expression designed by this method can be used for experiments and optimization. This method has great design flexibility. For signals with specific parameter requirements, the penalty factors and threshold parameters can also be appropriately changed. It has a wide range of engineering applications and low optimization costs, and finally can efficiently and high - quality generate optimized NLFM signals.

[0018] Second aspect, an embodiment of the present application provides an NLFM signal optimization system based on an asymmetric PWL function and a simulated annealing algorithm, which is applicable to generating an optimized NLFM signal. The system includes: an initialization module for generating an initial NLFM signal using an analytical formula fitting method; a segmentation module for dividing the time-frequency derivative model based on the asymmetric PWL function into 2n + 2 segments, performing quadratic interpolation segmentation, and then combining with the initial NLFM signal to obtain an optimized signal generation model, where n is an integer greater than 0; a strengthened simulated annealing construction module for generating a strengthened simulated annealing optimization model applicable to optimizing the time-frequency derivative control points of the signal based on the cooling process of an energy object in physics; an objective function construction module for constructing an objective function based on the peak sidelobe ratio, IRW ultra-wide penalty factor, and bandwidth ultra-wide penalty factor; and an optimization generation module for performing iterative optimization based on the constructed objective function, strengthened simulated annealing optimization model, and optimized signal generation model, and finally generating an optimized NLFM signal.

[0019] Third aspect, an embodiment of the present application provides an electronic device, including: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, and when the instructions are executed by the at least one processor, the at least one processor is enabled to execute an NLFM signal optimization method based on an asymmetric PWL function and a simulated annealing algorithm as described in the first aspect above.

[0020] Fourth aspect, an embodiment of the present application provides a computer-readable storage medium storing a computer program, which when executed by a processor, can implement an NLFM signal optimization method based on an asymmetric PWL function and a simulated annealing algorithm as described in the first aspect above.

[0021] It can be understood that the beneficial effects of the second to fourth aspects above can refer to the relevant descriptions in the first aspect above, and will not be elaborated here. Description of the Drawings

[0022] To more clearly illustrate the embodiments of the present application or the technical solutions in the related art, the following will briefly introduce the drawings required for use in the description of the embodiments of the present application or the related technical solutions. Obviously, the drawings in the following description are only some embodiments of the present application, and for those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0023] Figure 1 It is a flowchart of an NLFM signal optimization method based on an asymmetric PWL function and a simulated annealing algorithm provided in an embodiment of the present application; Figure 2 It is a schematic diagram of the time-frequency derivative function optimization model provided in an embodiment of the present application; Figure 3 It is the generation structure diagram of the NLFM signal provided in an embodiment of the present application; Figure 4 It is the flow chart of optimization using the enhanced simulated annealing algorithm provided in an embodiment of the present application; Figure 5 It is the schematic structural diagram of an NLFM signal optimization system based on the asymmetric PWL function and the simulated annealing algorithm provided in another embodiment of the present application; Figure 6 It is the schematic structural diagram of an electronic device provided in another embodiment of the present application. Detailed implementation manners

[0024] To make the objectives, technical solutions, and advantages of the embodiments of the present application clearer, the embodiments of the present application will be described in detail below with reference to the accompanying drawings. In various embodiments of the present application, many technical details are proposed for readers to better understand the present application. However, even without these technical details and various changes and modifications based on the following embodiments, the technical solutions required to be protected by the present application can be implemented. The division of the following embodiments is only for convenient description and should not constitute any limitation to the specific implementation manners of the present application. The various embodiments can be combined and cross-referenced with each other on the premise of no conflict.

[0025] An embodiment of the present application proposes an NLFM signal optimization method based on the asymmetric PWL function and the simulated annealing algorithm for generating an optimized NLFM signal, which is applied to an electronic device. The electronic device can be a terminal or a server. In this embodiment and the following embodiments, the electronic device is described by taking the server as an example. The implementation details of an NLFM signal optimization method based on the asymmetric PWL function and the simulated annealing algorithm proposed in this embodiment are specifically described below. The following content is only the implementation details provided for convenient understanding and is not necessary for implementing this solution.

[0026] The specific process of an NLFM signal optimization method based on the asymmetric PWL function and the simulated annealing algorithm proposed in this embodiment can be as Figure 1 shown and includes: Step 101, generating an initial NLFM signal using an analytic formula fitting-based method.

[0027] In a specific implementation, the server first needs to generate an initial NLFM signal using an analytical formula fitting method. The sidelobe level of the initially generated NLFM signal is not as low as that of the signal generated based on the POSP principle and the high-order polynomial phase function method. However, correspondingly, it brings a smaller main lobe width, a lower design cost, and a simpler design procedure.

[0028] In one example, the initial NLFM signal is designed as a U-shaped waveform. The initial NLFM signal is generated using an analytical formula fitting method, which is implemented through the following formula: ; where represents the bandwidth of the initial NLFM signal, represents the pulse width of the initial NLFM signal, is the preset number of segments on the positive or negative rate-of-change side, represents the initial NLFM signal.

[0029] Step 102: Divide the time-frequency derivative model based on the asymmetric PWL function into 2n + 2 segments, perform quadratic interpolation on the segments, and then combine it with the initial NLFM signal to obtain an optimized signal generation model.

[0030] In a specific implementation, after obtaining the initial NLFM signal, the server needs to divide the time-frequency derivative model based on the asymmetric PWL function into 2n + 2 segments, perform quadratic interpolation on the segments, and then combine it with the initial NLFM signal to obtain an optimized signal generation model. Here, n is an integer greater than 0.

[0031] In one example, the server divides the positive rate-of-change side and the negative rate-of-change side into n + 1 line segments respectively. Each of the n + 1 line segments on each side corresponds to 2n + 2 time-frequency derivative control points. Considering a greater design freedom, the time-frequency derivative function optimization model is designed as an asymmetric structure here. Therefore, a total of 4n + 4 time-frequency derivative control points are set on both the positive rate-of-change side and the negative rate-of-change side, and the duration of each line segment is designed to be a fixed value.

[0032] In one example, the time-frequency derivative function optimization model can be as Figure 2 shown.

[0033] In one example, the server sets the first line segment starting from the time axis of 0 as , the second line segment as , and so on. The set of 2n + 2 line segments is denoted as , . At the same time, starting from the time axis of 0, the time-frequency derivative control points are counted. Let the time-frequency derivative control points on the left and right sides of be respectively and , let The time-frequency derivative control points on the left and right sides are respectively and , and so on. The set composed of 4n + 4 time-frequency derivative control points is denoted as , .

[0034] Based on this, the general analytical expression of the time-frequency derivative function can be written as: ; ; ; where represents the duration of the th line segment.

[0035] Next, perform integral processing on the time-frequency derivative function , and the instantaneous frequency function of the constructed initial NLFM signal can be obtained. Since the time-frequency derivative is piecewise, the calculation method is to sum first and then multiply by the unit time. Correspondingly, the expression of the instantaneous frequency function can be written as: ; ; ; ; where , , are all instantaneous frequency function coefficients.

[0036] It should be noted that the setting of the instantaneous frequency function coefficient is based on the characteristics of the continuity and differentiability of the time-frequency function. Since the time-frequency function needs to be continuously differentiable, the continuity and differentiability of the function should be considered after integrating the time-frequency derivative. It is expressed by the formula as: .

[0037] So far, all the coefficients of the instantaneous frequency function have been determined. Integrate the instantaneous frequency function , and the phase function can be obtained. The expression of can be written as: .

[0038] Based on the phase function , the optimized signal generation model can be obtained. .

[0039] In one example, the NLFM signal can be generated by a cascader or an accumulator, and its specific structural diagram can be as Figure 3 shown.

[0040] Step 103: Based on the process of the temperature drop of an energy object in physics, generate a strengthened simulated annealing optimization model suitable for optimizing the time-frequency derivative control points of the signal.

[0041] In a specific implementation, the optimization of this embodiment designs a strengthened simulated annealing optimization algorithm, which needs to be implemented by generating a strengthened simulated annealing optimization model suitable for optimizing the time-frequency derivative control points of the signal based on the process of the temperature drop of an energy object in physics.

[0042] In one example, the server assumes that the previous crystal state is , and according to the preset index, the crystal state becomes , and correspondingly, the crystal energy changes from to . Among them, the preset index is a temperature drop or a temperature rise.

[0043] Define the acceptance probability of changing from to as , and the acceptance probability is expressed as: ; Among them, is the initial temperature, and is the current temperature.

[0044] If the change in the crystal state results in a decrease in the crystal energy, the transfer is directly accepted, that is, .

[0045] If the change in the crystal state results in an increase in the crystal energy, it means that the crystal is deviating from the global optimal solution. At this time, a random number between 0 and 1 is generated and compared with . If , the state transfer is accepted. If , the state transfer is rejected.

[0046] It should be noted that the acceptance probability is dynamically generated based on the energy change amount and . During the process of temperature drop and state transfer acceptance, three principles need to be followed.

[0047] The first principle is that as the temperature drops, the probability of accepting a solution that makes the objective function increase gradually decreases.

[0048] The second principle is that when the temperature approaches zero, only solutions with a decreasing objective function can be accepted.

[0049] The third principle is that at a fixed temperature, the probability of accepting a candidate solution that decreases the objective function is greater than the probability of accepting a candidate solution that increases the objective function.

[0050] Based on this, the basic simulated annealing optimization model can be expressed by the formula: ; where, is the parameter vector to be optimized, is the objective function, the matrix and the matrix are the coefficient matrix of the linear inequality equation and the coefficient matrix of the linear equality equation respectively, the vector and the vector are the constraint vector of the linear inequality equation and the constraint vector of the linear equality equation respectively, the function and the function are the non - linear inequality constraint term and the linear inequality constraint term respectively, and are respectively 's lower and upper limits.

[0051] Since at the beginning and end of the chirp signal pulse, a higher frequency change rate can reduce the Fresnel ripples in the waveform spectrum, thereby reducing the sidelobes to a certain extent. Therefore, in order to increase the degree of freedom of optimization, the upper and lower limit threshold coefficients are defined. The upper and lower limit threshold coefficients change the calculation expressions of and in the simulated annealing algorithm. The calculation expressions of and are as follows: ; ; where, is a function to generate a matrix or array of all 1s.

[0052] The autocorrelation function of the ideal NLFM signal after matched filtering should have as low a peak sidelobe ratio as possible and as narrow a - 3dB main lobe width as possible. Therefore, it is also necessary to limit the signal bandwidth to exceed the set spectral bandwidth range, that is , , represents the time interval between every two time - frequency derivative control points.

[0053] Based on this, the enhanced annealing optimization model can be obtained. The enhanced simulated annealing optimization model is expressed by the formula: ; Among them, represents the impulse response width obtained when using the current time-frequency derivative control point, is the main lobe width constraint value.

[0054] Step 104: Construct an objective function based on the peak sidelobe ratio, IRW ultra-wide penalty factor, and bandwidth ultra-wide penalty factor, and perform iterative optimization based on the constructed objective function, enhanced simulated annealing optimization model, and optimized signal generation model, and finally generate an optimized NLFM signal.

[0055] In a specific implementation, after obtaining the enhanced simulated annealing optimization model, the server needs to construct an objective function based on the peak sidelobe ratio, IRW ultra-wide penalty factor, and bandwidth ultra-wide penalty factor, and then perform iterative optimization based on the constructed objective function, enhanced simulated annealing optimization model, and optimized signal generation model, and finally generate an optimized NLFM signal.

[0056] In an example, the objective function constructed by the server based on the peak sidelobe ratio, IRW ultra-wide penalty factor, and bandwidth ultra-wide penalty factor can be expressed by the following formula: ; Among them, represents the peak sidelobe ratio obtained when the optimized signal uses the current time-frequency derivative control point, is the main lobe width penalty coefficient, is the bandwidth penalty coefficient, is the objective function.

[0057] In an example, the process of the server performing iterative optimization based on the constructed objective function, enhanced simulated annealing optimization model, and optimized signal generation model to finally generate an optimized NLFM signal can be as Figure 4 shown.

[0058] The server first calculates the value of the objective function , and judges whether the value of the objective function decreases.

[0059] If the value of the objective function decreases, then directly perform a state transition, generate a new NLFM signal, and re-perform quadratic interpolation segmentation.

[0060] If the value of the objective function does not decrease, then calculate and judge whether the temperature has dropped to 0 degrees.

[0061] If the temperature has dropped to 0 degrees, then heat it to a certain temperature to continue optimization, and re-perform quadratic interpolation segmentation.

[0062] If the temperature does not drop to 0 degrees, continue to determine whether the temperature remains unchanged for a certain number of generations.

[0063] If the temperature remains unchanged for a certain number of generations, output the time-frequency derivative control point, end the optimization, and output the optimized NLFM signal.

[0064] If the temperature does not remain unchanged for a certain number of generations, determine whether to perform a state transition through parameter calculation probability, and calculate the value of the objective function again. value.

[0065] An NLFM signal optimization method based on an asymmetric PWL function and a simulated annealing algorithm proposed in this embodiment first generates an initial NLFM signal using an analytical formula fitting method. After dividing the time-frequency derivative model based on the asymmetric PWL function into 2n + 2 segments, quadratic interpolation segmentation is performed to obtain an optimized signal generation model. Subsequently, based on the cooling process of energy objects in physics, a strengthened simulated annealing optimization model suitable for optimizing the time-frequency derivative control point of the signal is generated. Then, an objective function is constructed based on the peak sidelobe ratio, IRW ultra-wide penalty factor, and bandwidth ultra-wide penalty factor. Finally, iterative optimization is performed based on the constructed objective function, strengthened simulated annealing optimization model, and optimized signal generation model to generate an optimized NLFM signal. This method corresponds to a smaller main lobe width, lower design cost, and simpler design steps. The probability of accepting a worse solution is relatively large, and it can jump out of the local optimal solution. It can be applied to all NLFM signal models generated based on time-frequency derivatives. When the main lobe of the NLFM signal is widened significantly, the bandwidth exceeds the planned range, or the maximum sidelobe value of the signal is high, this method can be used to perform a large-degree-of-freedom optimization design on the initial signal. If the designer does not have a basic signal, the initial NLFM expression designed by this method can be used for experiments and optimization. This method has great design flexibility. For signals with specific parameter requirements, the penalty factor and threshold parameter can be appropriately changed. This method has wide engineering applications and low optimization costs, and finally can generate optimized NLFM signals efficiently and with high quality.

[0066] The step division of the above various methods is only for clear description. When implemented, they can be combined into one step, or some steps can be split, or decomposed into multiple steps. As long as they include the same logical relationship, they are all within the protection scope of this application; adding insignificant modifications to the algorithm or process or introducing insignificant designs, but not changing the core design of the algorithm and process, are all within the protection scope of this application.

[0067] Another embodiment of the present application proposes an NLFM signal optimization system based on an asymmetric PWL function and a simulated annealing algorithm, which is applicable to generating optimized NLFM signals. The implementation details of an NLFM signal optimization system based on an asymmetric PWL function and a simulated annealing algorithm proposed in this embodiment will be specifically described below. The following content is only the implementation details provided for convenience of understanding and is not necessary for implementing this example. Figure 5 FIG. Figure 5 is a schematic structural diagram of an NLFM signal optimization system based on an asymmetric PWL function and a simulated annealing algorithm proposed in this embodiment. The system includes: an initialization module 201, a segmentation module 202, a strengthened simulated annealing construction module 203, an objective function construction module 204, and an optimization generation module 205.

[0068] The initialization module 201 is configured to generate an initial NLFM signal using an analytical formula fitting-based method.

[0069] The segmentation module 202 is configured to divide the time-frequency derivative model based on the asymmetric PWL function into 2n + 2 segments, perform quadratic interpolation segmentation, and then combine with the initial NLFM signal to obtain an optimized signal generation model, where n is an integer greater than 0.

[0070] The strengthened simulated annealing construction module 203 is configured to generate a strengthened simulated annealing optimization model applicable to optimizing time-frequency derivative control points of a signal based on the cooling process of an energy object in physics.

[0071] The objective function construction module 204 is configured to construct an objective function based on the peak sidelobe ratio, the IRW ultra-wide penalty factor, and the bandwidth ultra-wide penalty factor.

[0072] The optimization generation module 205 is configured to perform iterative optimization based on the constructed objective function, the strengthened simulated annealing optimization model, and the optimized signal generation model, and finally generate an optimized NLFM signal.

[0073] It is worth mentioning that each module mentioned in this embodiment is a logical module. In practical applications, a logical unit can be a physical unit, a part of a physical unit, or a combination of multiple physical units. In addition, in order to highlight the innovative part of the present application, units not closely related to solving the technical problems proposed in the present application are not introduced in this embodiment, but this does not mean that there are no other units in this embodiment.

[0074] It is not difficult to find that this embodiment is a system embodiment corresponding to the above method embodiment. This embodiment can be implemented in cooperation with the above method embodiment. The relevant technical details and technical effects mentioned in the above method embodiments are still valid in this embodiment. To avoid repetition, they will not be elaborated here. Correspondingly, the relevant technical details mentioned in this embodiment can also be applied to the above method embodiments.

[0075] Another embodiment of the present application proposes an electronic device, and the specific structure of the electronic device is as Figure 6 shown, including: at least one processor 301; and a memory 302 communicatively connected to the at least one processor 301; wherein, the memory 302 stores instructions executable by the at least one processor 301, and the instructions are executed by the at least one processor 301 to enable the at least one processor 301 to execute an NLFM signal optimization method based on an asymmetric PWL function and a simulated annealing algorithm as described in the above method embodiments.

[0076] Among them, the memory and the processor can be connected in a bus manner. The bus can include any number of interconnected buses and bridges, and the bus connects various circuits of one or more processors and memories together. The bus can also connect various other circuits such as peripheral devices, voltage regulators, and power management circuits together, which are well known in the art and will not be further described herein. The bus interface is responsible for providing an interface between the bus and the transceiver. The transceiver can be an element or multiple elements, such as multiple receivers and transmitters, and provides a unit for communicating with various other devices on the transmission medium.

[0077] The processor is responsible for managing the bus and general processing, and can also provide various functions, including timing, peripheral interface, voltage regulation, power management, and other control functions. The memory can be used to store data used by the processor when executing operations.

[0078] Another embodiment of the present application proposes a computer-readable storage medium, in which a computer program is stored. When the computer program is executed by a processor, it can implement an NLFM signal optimization method based on an asymmetric PWL function and a simulated annealing algorithm as described in the above method embodiments.

[0079] That is, those skilled in the art can understand that all or part of the steps in the methods of the above embodiments can be completed by instructing relevant hardware through a program. The program is stored in a storage medium, including several instructions to enable a device (such as a single-chip microcomputer, a chip, etc.) or a processor to execute all or part of the steps of the methods described in the various embodiments of the present application. The aforementioned storage medium includes: various media that can store program codes, such as USB flash drives, mobile hard disks, ROM (Read-Only Memory), RAM (Random Access Memory), magnetic disks, or optical discs.

[0080] Those of ordinary skill in the art can understand that the above embodiments are specific embodiments for implementing the technical solutions of the present application. In actual applications, various changes can be made to them in form and details without departing from the spirit and scope of the present application.

Claims

1. A NLFM signal optimization method based on an asymmetric PWL function and a simulated annealing algorithm, suitable for generating an optimized NLFM signal, characterized in that: include: Generate the initial NLFM signal using an analytical fitting-based method; The time-frequency derivative model based on the asymmetric PWL function is divided into 2n+2 segments and then segmented by secondary interpolation, and then combined with the initial NLFM signal to obtain the optimized signal generation model; wherein n is an integer greater than 0; Based on the cooling process of energy objects in physics, an enhanced simulated annealing optimization model suitable for signal time-frequency derivative control point optimization is generated; An objective function is constructed based on the peak-to-sidelobe ratio, IRW over-wide penalty factor and bandwidth over-wide penalty factor. Iterative optimization is performed based on the constructed objective function, enhanced simulated annealing optimization model and optimized signal generation model to finally generate an optimized NLFM signal.

2. The NLFM signal optimization method based on an asymmetric PWL function and a simulated annealing algorithm according to claim 1, characterized in that: The initial NLFM signal is designed as a U-shaped waveform and is generated using an analytical fitting-based method, which is implemented using the following formula: ； in, represents the bandwidth of the initial NLFM signal, represents the pulse width of the initial NLFM signal, is the preset number of segments on the positive or negative rate of change side, represents the initial NLFM signal.

3. The NLFM signal optimization method based on an asymmetric PWL function and a simulated annealing algorithm according to claim 2, characterized in that: The time-frequency derivative model based on the asymmetric PWL function is divided into 2n+2 segments and then segmented by secondary interpolation. Then, combined with the initial NLFM signal, the optimized signal generation model is obtained, including: The positive rate of change side and the negative rate of change side are split into n+1 line segments respectively. Each n+1 line segment on each side corresponds to 2n+2 time-frequency derivative control points. There are a total of 4n+4 time-frequency derivative control points on both sides of the positive rate of change side and the negative rate of change side. The duration of each line segment is designed to be a constant value. Set the first line segment starting from time axis 0 to , the second line segment is set to , and so on, the set of 2n+2 line segments is recorded as , ; Starting from time axis 0, count the time-frequency derivative control points, set The time-frequency derivative control points on the left and right sides are and ,set up The time-frequency derivative control points on the left and right sides are and , and so on, the set of 4n+4 time-frequency derivative control points is recorded as , .

4. The NLFM signal optimization method based on an asymmetric PWL function and a simulated annealing algorithm according to claim 3, characterized in that: Time-frequency derivative function The general analytical expression of is: ； ； ； in, Indicates The duration of the line segment; Time-frequency derivative function Perform integration processing to obtain the instantaneous frequency function of the constructed initial NLFM signal , instantaneous frequency function The expression is: ； ； ； ； in, , , All are instantaneous frequency function coefficients; Function of instantaneous frequency Integrate to get the phase function , The expression is: ； Based on the phase function , and obtain the optimized signal generation model , .

5. The NLFM signal optimization method based on an asymmetric PWL function and a simulated annealing algorithm according to claim 4, characterized in that: Based on the cooling process of energy objects in physics, an enhanced simulated annealing optimization model suitable for signal time-frequency derivative control point optimization is generated, including: Assume that the previous crystal state is , according to the preset index, the crystal state becomes , and accordingly, the crystal energy is given by becomes ; Among them, the preset indicator is temperature drop or temperature rise; Defined by becomes The acceptance probability is , acceptance probability The expression is: ； in, is the initial temperature, is the current temperature; If the change in crystal state results in a decrease in crystal energy, the transfer is directly accepted, i.e. ; If the change in the crystal state causes the crystal energy to increase, it means that the crystal is deviating from the global optimal solution. At this time, a random number between 0 and 1 is generated. and Compare, if , then accept this state transfer, if , then reject this state transfer; Probability of acceptance is based on the energy change and Dynamically generated, during the temperature drop and state transfer acceptance process, three principles need to be followed; The first principle is that as the temperature decreases, the probability of accepting a solution that increases the objective function gradually decreases; The second principle is that when the temperature approaches zero, only solutions that decrease the objective function are acceptable; The third principle is that, at a fixed temperature, the probability of accepting a candidate solution that reduces the objective function is greater than the probability of accepting a candidate solution that increases the objective function; The basic simulated annealing optimization model is expressed by the formula: ； in, is the parameter vector to be optimized, is the objective function, the matrix and matrix are the coefficient matrices of linear inequality equations and linear equality equations, respectively, and the vector and vector are the constraint vectors of the linear inequality equation and the linear equality equation respectively, and the function and function are the nonlinear inequality constraints and the linear inequality constraints respectively, and They are The lower and upper limits of Since the higher frequency change rate of the linear frequency modulation signal pulse at the beginning and end can reduce the sidelobes to a certain extent by reducing the Fresnel ripples in the waveform spectrum, in order to increase the degree of freedom of optimization, the upper and lower threshold coefficients are defined. , upper and lower threshold coefficients Changed the simulated annealing algorithm and The calculation expression of and The calculation expression is as follows: ； ； in, A function that generates a matrix or array of all 1s; The autocorrelation function of an ideal NLFM signal after matched filtering should have a peak-to-sidelobe ratio as low as possible and a -3dB mainlobe width as narrow as possible. Therefore, it is also necessary to limit the bandwidth of the signal to not exceed the set spectrum bandwidth range, that is, , , Represents the time interval between every two time-frequency derivative control points; Based on this, the enhanced annealing optimization model can be obtained, and the enhanced simulated annealing optimization model is expressed by the formula: ； in, represents the impulse response width obtained when the current time-frequency derivative control point is used, is the main lobe width constraint value.

6. The NLFM signal optimization method based on an asymmetric PWL function and a simulated annealing algorithm according to claim 5, characterized in that: The objective function constructed based on the peak sidelobe ratio, the IRW over-wide penalty factor, and the bandwidth over-wide penalty factor is expressed by the following formula: ； in, It represents the peak sidelobe ratio obtained when the optimized signal adopts the current time-frequency derivative control point. is the main lobe width penalty coefficient, is the bandwidth penalty coefficient, is the objective function.

7. The NLFM signal optimization method based on an asymmetric PWL function and a simulated annealing algorithm according to claim 6, characterized in that: Based on the constructed objective function, enhanced simulated annealing optimization model and optimized signal generation model, iterative optimization is performed to finally generate the optimized NLFM signal, including: Calculate the objective function The value of the objective function Whether the value of decreases; If the objective function If the value of decreases, the state transfer is performed directly to generate a new NLFM signal and re-perform the secondary interpolation segmentation; If the objective function If the value of does not decrease, then the calculation determines whether the temperature is about to reach 0 degrees; If the temperature is about to reach 0 degrees, then heat it to a certain temperature and continue to optimize, and re-perform secondary interpolation segmentation; If the temperature does not drop to 0 degrees, continue to determine whether the temperature remains constant for a certain number of generations; If the temperature remains constant within a certain algebra, the time-frequency derivative control point is output, the optimization ends, and the optimized NLFM signal is output; If the temperature does not remain constant for a certain number of generations, the probability is calculated by the parameters to determine whether the state is transferred, and the objective function is calculated again The value of .

8. A NLFM signal optimization system based on an asymmetric PWL function and a simulated annealing algorithm, suitable for generating an optimized NLFM signal, characterized in that: include: An initialization module, used to generate an initial NLFM signal using an analytical fitting-based method; A segmentation module is used to divide the time-frequency derivative model based on the asymmetric PWL function into 2n+2 segments and then perform secondary interpolation segmentation, and then combine the initial NLFM signal to obtain an optimized signal generation model; wherein n is an integer greater than 0; Enhanced simulated annealing building block, used to generate enhanced simulated annealing optimization models suitable for signal time-frequency derivative control point optimization based on the cooling process of energy objects in physics; An objective function building module, used for building an objective function based on a peak sidelobe ratio, an IRW over-wide penalty factor, and a bandwidth over-wide penalty factor; The optimization generation module is used to perform iterative optimization based on the constructed objective function, enhanced simulated annealing optimization model and optimization signal generation model, and finally generate an optimized NLFM signal.

9. An electronic device, characterized in that: include: at least one processor; and, a memory communicatively coupled to the at least one processor; The memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can execute an NLFM signal optimization method based on an asymmetric PWL function and a simulated annealing algorithm as described in any one of claims 1 to 7.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, it can implement a NLFM signal optimization method based on an asymmetric PWL function and a simulated annealing algorithm as described in any one of claims 1 to 7.

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