NLFM waveform design method and device based on two-parameter phase function

Abstract

The invention relates to the field of radar waveform design, in particular to an NLFM waveform design method and device based on a two-parameter phase function, and the method comprises the steps: introducing a bandwidth control parameter and an index parameter, and constructing a two-parameter phase function based on a quadratic function; by taking minimization of the highest sidelobe level as a target, constraining a main lobe width and a signal bandwidth at the same time, and designing an optimization function; optimizing bandwidth control parameters and index parameters in the two-parameter phase function by using a genetic algorithm to obtain an optimal parameter group; and substituting the optimal parameter group into the two-parameter phase function to generate a low sidelobe NLFM waveform. By constructing a two-parameter phase function, an optimization function is designed by taking minimization of the highest sidelobe level as a target, and the waveform performance can be effectively balanced; and optimizing by using a genetic algorithm to generate an NLFM waveform meeting the requirement. The waveform with good performance can be obtained in the radar system, the sidelobe level can be reduced, and the target detection and resolution capability of the radar system can be improved.

Description

Technical Field

[0001] This application relates to the technical field of radar waveform design, and particularly to a method and device for designing an NLFM waveform based on a two-parameter phase function. Background Art

[0002] Waveform design is an important research content in the field of radar signal processing. The design of low sidelobe waveforms is an important research direction in radar waveform design. Low sidelobe waveforms are of great significance for suppressing strong clutter and strong target interference energy from adjacent range cells.

[0003] Traditional methods for designing non-linear frequency modulation (NLFM) waveforms include parametric frequency modulation method, parametric phase function construction method, and phase stationary method based on frequency domain window function. The parametric frequency modulation method is relatively intuitive and easy to implement, but the optimization of high-order parameters is complex, and it can only meet the design requirements of simple NLFM; the phase stationary method based on frequency domain window function can only approximately solve the inverse function of the group delay function, so the sidelobes of the obtained NLFM waveform are relatively high; while the parametric phase function construction method has strong flexibility and can approximate the global optimum, but the key lies in how to construct a parametric phase function with good performance. Commonly used parametric phase function construction methods include polynomial phase coding and random phase perturbation, etc. The former has difficulties in optimizing parameters to balance the main lobe width and sidelobe level, and the Doppler tolerance of the NLFM waveform designed by the latter is relatively low.

[0004] In view of this, it is necessary to design a method for designing a low sidelobe NLFM waveform based on a two-parameter phase function, which can better balance the main lobe width and sidelobe level, is superior to existing methods in both main lobe and sidelobe performance while maintaining the set signal bandwidth, and also has good Doppler tolerance. Summary of the Invention

[0005] The purpose of the present invention is to provide a method for designing a low sidelobe NLFM waveform based on a two-parameter phase function construction method for the problem of designing a low sidelobe NLFM waveform. This method can better balance the main lobe width and sidelobe level, is superior to existing methods in both main lobe and sidelobe performance while maintaining the set signal bandwidth, and also has good Doppler tolerance.

[0006] In a first aspect, the technical solution of the present invention provides a method for designing an NLFM waveform based on a two-parameter phase function, including the following steps: Introduce a bandwidth control parameter and an exponential parameter, and construct a two-parameter phase function based on a quadratic function; Taking the minimization of the highest sidelobe level as the goal and constraining the main lobe width and signal bandwidth at the same time, design an optimization function; Based on the optimization function, use the genetic algorithm to optimize the bandwidth control parameter and the exponential parameter in the two-parameter phase function to obtain an optimal parameter group; Substitute the optimal parameter set into the two-parameter phase function to generate a low sidelobe NLFM waveform.

[0007] As a further limitation of the technical solution of the present invention, in the step of constructing the two-parameter phase function based on the quadratic function by introducing the bandwidth control parameter and the exponential parameter, the two-parameter phase function is as follows:

[0008] In the formula, is the bandwidth control parameter, is the exponential parameter.

[0009] Based on the specific expression of the two-parameter phase function of the quadratic function, the function has an exact mathematical definition, providing a clear basis for subsequent waveform design and performance analysis based on this function, ensuring the accuracy and consistency of the design process, and helping to accurately understand and apply this phase function for low sidelobe NLFM waveform design.

[0010] As a further limitation of the technical solution of the present invention, the steps of designing the optimization function with the goal of minimizing the highest sidelobe level while constraining the main lobe width and the signal bandwidth include: Generate an NLFM waveform based on the initial values of the bandwidth control parameter and the exponential parameter; Perform pulse compression on the generated NLFM waveform, and calculate the highest sidelobe level and the main lobe width of the pulse compression result; Perform FFT transformation on the generated NLFM waveform, and calculate the actual bandwidth of the signal; Design the optimization function according to the highest sidelobe level, the main lobe width and the actual bandwidth of the signal.

[0011] By first generating a waveform based on the parameter initial values, then performing pulse compression and FFT transformation to calculate the relevant performance indicators, and finally designing the optimization function according to these indicators, the construction process of the optimization function is scientific, reasonable and highly operable. This way of constructing the optimization function based on the actual waveform performance indicators can ensure that the optimization function truly reflects the actual requirements of the waveform, thus more effectively guiding the parameter optimization process and improving the quality of waveform design.

[0012] As a further limitation of the technical solution of the present invention, the formulas for calculating the highest sidelobe level and the main lobe width are as follows:

[0013] Where represents the main lobe peak value, and the interval is the main lobe protection range, ; is the highest sidelobe level, is the main lobe width, This is the result of pulse compression.

[0014] Specific formulas for calculating the highest sidelobe level and main lobe width are given, providing clear criteria and methods for calculating these two key performance indicators, and avoiding ambiguity and arbitrariness in calculations. During the waveform design process, based on these precise calculation methods, the waveform performance can be more accurately evaluated, and then the parameters can be adjusted through the optimization function to achieve precise optimization of the waveform performance.

[0015] As a further limitation of the technical solution of the present invention, the steps for performing FFT transformation on the generated NLFM waveform and calculating the actual bandwidth of the signal include: Perform FFT transformation on the NLFM waveform to find the position of the spectral peak; Extend from the spectral peak to both sides until the spectral power drops to a set percentage of the peak, obtaining two points; Obtain the frequency range between the two points, which is the actual bandwidth of the signal.

[0016] By performing FFT transformation on the NLFM waveform and determining the bandwidth based on the spectral power characteristics, a reliable method for accurately obtaining the signal bandwidth is provided. Accurate bandwidth calculation is crucial for reasonably constraining the signal bandwidth when designing the optimization function, helping to ensure that the designed waveform not only meets the performance requirements but also conforms to the bandwidth limit conditions, improving the practicality of waveform design.

[0017] As a further limitation of the technical solution of the present invention, the optimization function is as follows:

[0018] The calculation formula of is:

[0019] Wherein, and are both penalty coefficients, represents taking and the larger of the two; is the highest sidelobe level, is the main lobe width, and B is the bandwidth required by the design.

[0020] This optimization function comprehensively considers key factors such as the highest sidelobe level, main lobe width, and signal bandwidth, and penalizes the cases that do not meet the constraint conditions through penalty coefficients, enabling the optimization function to comprehensively and effectively balance all aspects of waveform performance. During the genetic algorithm optimization process, this optimization function can guide the algorithm to search in the direction of meeting the requirements of low sidelobes, appropriate main lobe width, and bandwidth, improving the accuracy and effectiveness of optimization.

[0021] As a further limitation of the technical solution of the present invention, the steps of using a genetic algorithm to optimize the bandwidth control parameter and the exponential parameter in the two-parameter phase function to obtain an optimal parameter set include: Substitute the calculated values of the highest sidelobe level, the main lobe width, and the actual bandwidth of the signal into the optimization function. Using the optimization function as the fitness function of the genetic algorithm, optimize the bandwidth control parameter and the exponential parameter to obtain the optimal bandwidth control parameter and the optimal exponential parameter .

[0022] As a further limitation of the technical solution of the present invention, in the step of substituting the optimal parameter set into the two-parameter phase function to generate a low-sidelobe NLFM waveform, the generated low-sidelobe NLFM waveform:

[0023] wherein, is the optimal bandwidth control parameter, is the optimal exponential parameter.

[0024] Substituting the optimal parameter set into the specific form of the two-parameter phase function to generate the NLFM waveform, so that the generated waveform has a clear mathematical expression, which is convenient to accurately generate the required low-sidelobe NLFM waveform in practical applications, provides an accurate waveform generation basis for subsequent application of the waveform to the radar system, and ensures the consistency and reliability of waveform generation.

[0025] As a further limitation of the technical solution of the present invention, the method further includes: Apply the obtained low-sidelobe NLFM waveform to the radar system to suppress strong clutter and strong target interference energy from adjacent range cells.

[0026] Apply the designed NLFM waveform to the radar system to suppress strong clutter and strong target interference energy from adjacent range cells, expand the application scenario of the low-sidelobe NLFM waveform, give full play to the advantages of this waveform in the radar system, improve the target detection ability and anti-interference performance of the radar system in complex environments, and enhance the practicability and reliability of the radar system.

[0027] In a second aspect, the technical solution of the present invention further provides an NLFM waveform design device based on a two-parameter phase function, including a phase function construction module, an optimization function design module, a genetic algorithm optimization module, and a waveform generation module; The phase function construction module is used to introduce a bandwidth control parameter and an exponential parameter to construct a two-parameter phase function based on a quadratic function; The optimization function design module is used to design an optimization function with the goal of minimizing the highest sidelobe level while constraining the main lobe width and the signal bandwidth; A genetic algorithm optimization module, which is used to optimize the bandwidth control parameter and the exponential parameter in the two-parameter phase function by using the genetic algorithm to obtain an optimal parameter group; A waveform generation module, which is used to substitute the optimal parameter group into the two-parameter phase function to generate a low sidelobe NLFM waveform.

[0028] Modularize each key step in the waveform design process, realizing the systematization and process of waveform design. Each module has a clear division of labor and cooperates with each other. Compared with the traditional waveform design method, it improves the design efficiency and accuracy, and is convenient for the maintenance and upgrade of the device.

[0029] As a further limitation of the technical solution of the present invention, the two-parameter phase function is as follows:

[0030] In the formula, is the bandwidth control parameter, is the exponential parameter.

[0031] As a further limitation of the technical solution of the present invention, the optimization function design module includes an initialization unit, a first calculation and processing unit, a second calculation and processing unit, and an optimization function design unit; The initialization unit is used to generate an NLFM waveform based on the initial values of the bandwidth control parameter and the exponential parameter; The first calculation and processing unit is used to perform pulse compression on the generated NLFM waveform and calculate the highest sidelobe level and the main lobe width of the pulse compression result; The second calculation and processing unit is used to perform FFT transformation on the generated NLFM waveform and calculate the actual bandwidth of the signal; The optimization function design unit is used to design an optimization function according to the highest sidelobe level, the main lobe width, and the actual bandwidth of the signal.

[0032] As a further limitation of the technical solution of the present invention, the formulas for the first calculation and processing unit to calculate the highest sidelobe level and the main lobe width are as follows:

[0033] Where represents the main lobe peak value, and the interval is the main lobe protection range, ; is the highest sidelobe level, is the main lobe width.

[0034] As a further limitation of the technical solution of the present invention, the second calculation and processing unit is specifically configured to perform FFT transformation on the NLFM waveform to find the position of the spectral peak; extend from the spectral peak to both sides until the spectral power drops to a set percentage of the peak to obtain two points; and acquire the frequency range between the two points, i.e., the actual bandwidth of the signal.

[0035] As a further limitation of the technical solution of the present invention, the optimization function is as follows:

[0036] The calculation formula of is:

[0037] Wherein, and are both penalty coefficients, represents taking and the larger value of the two; is the highest sidelobe level, is the main lobe width.

[0038] As a further limitation of the technical solution of the present invention, the genetic algorithm optimization module is specifically configured to substitute the calculated values of the highest sidelobe level, the main lobe width, and the actual bandwidth value of the signal into the optimization function, and use the optimization function as the fitness function of the genetic algorithm to optimize the bandwidth control parameter and the exponential parameter to obtain the optimal bandwidth control parameter and the optimal exponential parameter .

[0039] As a further limitation of the technical solution of the present invention, the low sidelobe NLFM waveform generated by the waveform generation module:

[0040] In the formula, is the optimal bandwidth control parameter, is the optimal exponential parameter.

[0041] As a further limitation of the technical solution of the present invention, the device further includes an application module for applying the obtained low sidelobe NLFM waveform to a radar system to suppress strong clutter and strong target interference energy from adjacent range cells.

[0042] Adding an application module to the design device, which is specifically used to apply the obtained NLFM waveform to the radar system to suppress interference, enables the device to not only have the waveform design function but also achieve a close combination with the radar system application, forming a complete chain from waveform design to actual application. This design further improves the practicality and functionality of the device, can better meet the application requirements of the radar system for low sidelobe waveforms, and enhances the performance and competitiveness of the entire system.

[0043] As can be seen from the above technical solutions, the present application has the following advantages: This method uses the parametric phase function construction method to construct a non-linear two-parameter phase function, and designs an optimization function with the goal of "minimizing the highest sidelobe level while constraining the main lobe width and signal bandwidth", and uses the genetic algorithm for parameter optimization to obtain an NLFM waveform with low sidelobe performance and meeting the constraint conditions. Specifically, by introducing a bandwidth control parameter and an exponential parameter to construct a two-parameter phase function, it provides a basis for flexible adjustment of waveform design; with the goal of minimizing the highest sidelobe level and simultaneously constraining the main lobe width and signal bandwidth to design an optimization function, it can effectively balance the waveform performance; using the genetic algorithm for optimization can quickly and accurately find the optimal parameter group, thereby generating a low sidelobe NLFM waveform that meets the requirements. Compared with the traditional waveform design method, it improves the efficiency of waveform design and the optimization degree of waveform performance, and enhances the anti-interference ability and detection performance of the radar system. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] In order to more clearly illustrate the technical solutions of the present application, the following will briefly introduce the drawings required in the description. Obviously, the drawings in the following description are only some embodiments of the present application. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0045] Figure 1 It is a schematic flowchart of the method provided by the embodiment of the present invention.

[0046] Figure 2 It is a principle block diagram of the low sidelobe NLFM waveform design method provided by the embodiment of the present invention.

[0047] Figure 3 It is a spectrogram of NLFM1 waveform and LFM waveform.

[0048] Figure 4 It is a comparison diagram of the windowed pulse compression output results of LFM waveform, NLFM0 waveform and NLFM1 waveform under the condition of no Doppler, Figure 4 where (a) is the pulse compression result diagram of LFM waveform, Figure 4 where (b) is the pulse compression result diagram of NLFM0 waveform, Figure 4Among them, (c) is the pulse compression result diagram of the NLFM1 waveform, Figure 4 Among them, (d) is the local enlarged view comparison diagram of the pulse compression results of the three waveforms.

[0049] Figure 5 It is a comparison diagram of the windowed pulse compression output results of the NLFM1 waveform under two conditions of with / without target Doppler.

[0050] Figure 6 It is the block diagram of the device provided by the embodiment of the present invention. Detailed implementation manners

[0051] Aiming at the problem of high pulse compression sidelobes of the NLFM waveform obtained by the existing NLFM waveform design method, the present invention provides a low-sidelobe NLFM waveform design method based on the two-parameter phase function construction method. First, introduce the bandwidth control parameter and the exponential parameter, and construct a two-parameter phase function based on the quadratic function; then, design an optimization function with the goal of minimizing the highest sidelobe level while constraining the main lobe width and the signal bandwidth, and use the genetic algorithm for parameter optimization to obtain the optimal parameters, and then generate the NLFM waveform. Compared with the LFM waveform and the NLFM waveform obtained by the phase stationary method based on the frequency domain window function, the pulse compression sidelobe performance and the improvement effect at small targets of the NLFM waveform obtained by the present invention are significantly better than these two waveforms. In order to make the application purpose, features, and advantages of the present application more obvious and understandable, the following will use specific embodiments and drawings to clearly and completely describe the technical solutions protected by the present application. Obviously, the embodiments described below are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative work fall within the scope of protection of the present application.

[0052] As Figure 1 shown, the embodiment of the present invention provides a NLFM waveform design method based on a two-parameter phase function, including the following steps: S1. Introduce the bandwidth control parameter and the exponential parameter, and construct a two-parameter phase function based on the quadratic function; specifically including: Introduce the bandwidth control parameter and the exponential parameter, and construct the following two-parameter phase function:

[0053] Among them, is the bandwidth control parameter to be optimized, the search interval of is Set the initial value of to be is the exponential parameter to be optimized, which controls the steepness of the frequency change, The optimization interval of is set with the initial value of .

[0054] Construct the specific form of the two-parameter phase function based on the quadratic function, introducing the bandwidth control parameter and the exponential parameter. This provides a specific mathematical expression for the construction of the two-parameter phase function, making the design of the phase function clearer and more operable, and laying a foundation for subsequent optimization and waveform generation.

[0055] S2. With the goal of minimizing the highest sidelobe level while constraining the main lobe width and the signal bandwidth, design the optimization function; specifically including: S21. Calculate the highest sidelobe level and the main lobe width ; The initial phase function parameter group is combined with and the waveform parameters , and determined by the system and imported into the genetic algorithm. Implement them in sequence according to generating the NLFM waveform, performing pulse compression to obtain the pulse compression result , calculating the highest sidelobe level , calculating the main lobe width to obtain the and values, where represents the main lobe width corresponding to -4dB of the pulse compression output result, and the calculation formula of is

[0056] where, represents the main lobe peak value, the interval is the main lobe protection range, .

[0057] This provides an objective and accurate calculation method, which can accurately quantify the sidelobe level and the main lobe width of the waveform, providing a reliable basis for the design of the optimization function and parameter optimization, and helping to improve the optimization accuracy and performance of the waveform.

[0058] Step S22. Calculate the actual bandwidth of the signal; The initial phase function parameter group is combined with and the waveform parameters , and determined by the system and imported into the genetic algorithm. Implement them in sequence according to generating the NLFM waveform, performing the FFT transformation, and calculating the signal bandwidth to obtain The value, where represents the frequency width corresponding to -4 dB of the FFT transform output result of the NLFM waveform.

[0059] Through the methods of FFT transform and spectrum analysis, the actual bandwidth of the signal can be accurately determined, ensuring that the signal is optimized under the condition of meeting the bandwidth constraint, avoiding the signal bandwidth exceeding the expected range, and guaranteeing the normal operation of the radar system.

[0060] Step S23, design the optimization function; To achieve low sidelobes, it is necessary to aim at minimizing the maximum sidelobe level of the pulse compression output result; at the same time, to ensure the range resolution of the pulse compression output result, the main lobe width is increased as a penalty term for constraint; at the same time, to ensure the signal bandwidth of the optimized waveform is equal to the bandwidth required by the design , the judgment coefficient of whether the bandwidths are equal is increased for constraint; combining the above conditions, the designed optimization function is

[0061] where and are both penalty coefficients and are adjustable parameters, The value of 7 is of the order of 10 The value of 4 is of the order of 10 represents taking and the larger of the two; The calculation formula of

[0062] In the formula, B is the bandwidth required by the design.

[0063] Generate the NLFM waveform, perform pulse compression and FFT transform, and design the optimization function according to the calculation results. By comprehensively considering multiple factors such as the highest sidelobe level, main lobe width, and signal bandwidth to design the optimization function, the performance of the waveform can be more comprehensively measured and optimized, ensuring that the generated waveform can meet the requirements on multiple key indicators.

[0064] The optimization function comprehensively considers multiple objectives such as the highest sidelobe level, main lobe width, and bandwidth, and punishes the cases that do not meet the constraint conditions through the penalty coefficient, which can guide the genetic algorithm to move in the direction of meeting all constraint conditions and minimizing the highest sidelobe level during the optimization process, improving the effectiveness of the optimization algorithm and the performance of the waveform.

[0065] S3. Optimize the bandwidth control parameter and the exponential parameter in the two-parameter phase function by using the genetic algorithm based on the optimization function to obtain the optimal parameter group; Substitute the value obtained in S21 and the value obtained in S22 into the optimization function. Use the optimization function in S23 as the fitness function of the genetic algorithm to optimize the parameters and to obtain the optimal group and . During the iterative optimization process of the optimization function, according to the parameter group and obtained in each iteration and the waveform parameters , and determined by the system, calculate the corresponding , and values according to the methods in S21 and S22 for the next iterative optimization.

[0066] The process of using the genetic algorithm for optimization in this step is as follows: Initialize the population: Set the initial value of the bandwidth control parameter to , and the optimization interval of ; is the exponential parameter, which controls the steepness of the frequency change. and the optimization interval of is . Set the initial value of . Initialize the population of the genetic algorithm, including multiple individuals, and each individual contains a set of parameters ([[]] , ). Encode the parameter group to be optimized ([[]] , ) as a chromosome. Real number encoding can be used, and directly use ([[]] , ) as the gene value.

[0067] Fitness function design: Use the optimization function as the fitness function and calculate the fitness value of each individual according to the fitness function formula. The calculation process is as follows: Generate the NLFM waveform , according to the current parameters ([[]] ). Perform pulse compression on to obtain the output . Extract from , (Width at -4 dB). For perform FFT and calculate the actual bandwidth (Frequency width at -4 dB). Substitute into the fitness function to calculate the fitness value of the current individual.

[0068] Select individuals for reproduction according to the fitness value. Select excellent individuals probabilistically according to the fitness value. The smaller the fitness value (the better the performance), the higher the probability of being selected. Perform crossover operations on the selected individuals to generate new individuals. Crossover operations can be achieved by exchanging some parameters of two individuals. Perform mutation operations on the newly generated individuals to randomly change the parameter values of the individuals with a set probability to increase the diversity of the population. For each individual in the newly generated population, recalculate its fitness value. Repeat the selection, crossover, mutation, and evaluation steps until a predetermined number of iterations is reached or the fitness value converges to a certain threshold. After the iteration ends, select the individual with the lowest fitness value, and its corresponding parameter group ( , ) is the optimal parameter group.

[0069] S4. Substitute the optimal parameter group into the two-parameter phase function to generate a low sidelobe NLFM waveform.

[0070] The generated NLFM waveform:

[0071] In the formula, is the optimal bandwidth control parameter, is the optimal exponential parameter.

[0072] By introducing specific parameters to construct the phase function and designing an optimization function to find the optimal solution using the genetic algorithm to generate the waveform. It provides a systematic and effective method for the design of low sidelobe NLFM waveforms, helps to obtain waveforms with good performance in radar systems, reduces the sidelobe level, and improves the target detection and resolution capabilities of radar systems. The specific method for generating the final NLFM waveform is given, enabling the optimal parameters obtained through the previous optimization process to be effectively transformed into actual waveforms, providing directly applicable signal waveforms for radar systems.

[0073] As Figure 2 shown, the embodiment of the present invention provides a method for designing an NLFM waveform based on a two-parameter phase function, including the following processes: (1) The NLFM waveform parameters determined by the system include the pulse width , bandwidth and sampling rate ; Denote the NLFM waveform to be designed as , where is the phase function to be designed, and the time variable has a value range of , is the pulse width of the waveform; (2) Introduce the bandwidth control parameter and the exponential parameter, and construct a two-parameter phase function based on the quadratic function; (3) Design an optimization function with the goal of "constraining the main lobe width and the signal bandwidth while minimizing the highest sidelobe level", and use the genetic algorithm to optimize the parameters to obtain the optimal parameters, and then generate the NLFM waveform.

[0074] The above steps are elaborated in detail as follows: In step (2), introduce the bandwidth control parameter and the exponential parameter, and construct a two-parameter phase function based on the quadratic function; specifically including: Introduce the bandwidth control parameter and the exponential parameter, and construct the two-parameter phase function as follows:

[0075] Among them, is the bandwidth control parameter to be optimized, The optimization interval of is , set The initial value of is ; is the exponential parameter to be optimized, which controls the steepness of the frequency change, The optimization interval of is , set The initial value of is .

[0076] In step (3), with the goal of minimizing the highest sidelobe level and constraining the main lobe width and the signal bandwidth at the same time, design the optimization function; specifically including: (31) Calculate the highest sidelobe level and the main lobe width ; Put the initial phase function parameter group together with and the waveform parameters determined by the system , and import into the genetic algorithm, and implement them in the order of generating the NLFM waveform, performing pulse compression to obtain the pulse compression result , calculating the highest sidelobe level , calculating the main lobe width in turn, and obtain and The values of, where represents the main lobe width corresponding to -4 dB of the pulse compression output result, The calculation formula of is,

[0077] Among them, represents the main lobe peak value, and the interval is the main lobe protection range, .

[0078] (32) Calculate the actual bandwidth of the signal ; Input the initial phase function parameter group and as well as the waveform parameters determined by the system , and into the genetic algorithm, and implement them in sequence according to the order of generating the NLFM waveform, performing FFT transformation, and calculating the signal bandwidth, to obtain the value, where represents the frequency width corresponding to -4 dB of the FFT transformation output result of the NLFM waveform; (33) Design the optimization function; To achieve low sidelobes, it is necessary to aim at minimizing the maximum sidelobe level of the pulse compression output result; at the same time, to ensure the range resolution of the pulse compression output result, the main lobe width is increased as a penalty term for constraint; at the same time, to ensure that the signal bandwidth of the optimized waveform is equal to the bandwidth required by the design, a judgment coefficient for whether the bandwidths are equal is added for constraint; considering the above conditions, the designed optimization function is

[0079] Among them, and are both penalty coefficients and are adjustable parameters, takes a value of 10 7 order of magnitude, takes a value of 10 4 order of magnitude; means taking and the larger of the two; The calculation formula of

[0080] In the formula, B is the bandwidth required by the design.

[0081] (34) Use the genetic algorithm to optimize the bandwidth control parameter and the exponential parameter in the two-parameter phase function to obtain the optimal parameter group; Input the , values obtained in step (31) and the The values are substituted into the optimization function, and the optimization function in step (33) is used as the fitness function of the genetic algorithm to optimize the parameters and to obtain the optimal group and . During the iterative optimization process of the optimization function, it is necessary to calculate the corresponding and obtained in each iteration, as well as the waveform parameters , and determined by the system, and calculate the corresponding , and values according to the methods in step (31) and step (32) for the next iterative optimization.

[0082] (35) Substitute the optimal parameter group into the two-parameter phase function to generate a low sidelobe NLFM waveform.

[0083] The generated low sidelobe NLFM waveform:

[0084] In the formula, is the optimal bandwidth control parameter, and is the optimal exponential parameter.

[0085] The following provides a design case. The waveform parameters determined by the system are , and ; the NLFM waveform obtained from the above steps is as follows: , ,

[0086] A scenario including two targets of different sizes and a noise background is designed, where the amplitudes of the two targets are 1000 and 1 respectively, with a difference of 60 dB between them; Figure 3 The spectra of the NLFM waveform obtained by the present invention and the spectra of the LFM waveform for comparison are given. Figure 3 Among them, the frequency width at -4 dB is exactly equal to the bandwidth design value required by the system.

[0087] Figure 4 gives, in the case of no Doppler, the LFM waveform ( Figure 4 (a) in, marked as the LFM waveform), the NLFM waveform obtained by the phase dwell method based on the frequency domain window function ( Figure 4 (b) in, marked as the NLFM0 waveform), and the NLFM waveform obtained by the present invention ( Figure 4In (c) thereof, it is a comparison diagram of the windowed pulse compression output results marked as the NLFM1 waveform Figure 4 In (d) thereof, it is a comparison diagram of the partial enlarged views of the pulse compression results of three waveforms. This Figure 4 Indicates that the pulse compression sidelobes of the NLFM1 waveform are significantly lower than those of the LFM waveform and the NLFM0 waveform, and the improvement effect at small targets is also significantly better than these two waveforms; in addition, in the case of windowed pulse compression, the range resolution obtained by the LFM waveform is 45 meters, the range resolution obtained by the NLFM0 waveform is 75 meters, and the range resolution obtained by the NLFM1 waveform is 42 meters, which indicates that the range resolution of the NLFM waveform obtained in this application is also better than these two waveforms being compared.

[0088] Figure 5 It is a comparison diagram of the windowed pulse compression output results of the NLFM1 waveform under two conditions of with / without target Doppler. Among them, the black line shows the situation where the main lobe of the pulse compression output of the NLFM1 waveform obtained in this application just starts to deform under the conditions of a target speed of 100 m / s and a waveform carrier frequency of 9.5 GHz, and the red line is the pulse compression output result of the NLFM1 waveform under the condition of no target Doppler. This indicates that the Doppler tolerance of the NLFM1 waveform is about 100 m / s.

[0089] In some embodiments, the method further includes: Applying the obtained low-sidelobe NLFM waveform to a radar system to suppress strong clutter and strong target interference energy from adjacent range cells.

[0090] Applying the low-sidelobe NLFM waveform to a radar system requires the following steps: According to the design requirements of the radar system, determine parameters such as pulse width, bandwidth, and sampling rate. Design the low-sidelobe NLFM waveform using the two-parameter phase function construction method, and determine the optimal bandwidth control parameters and exponential parameters through an optimization function and a genetic algorithm. Load the designed low-sidelobe NLFM waveform into the radar transmitter to transmit the signal. Receive the target echo signal and perform pulse compression processing. During the pulse compression process, utilize the low-sidelobe characteristics of the low-sidelobe NLFM waveform to reduce the interference of clutter and strong target echoes. Further improve the target detection performance through signal processing algorithms (such as the constant false alarm rate detection algorithm). Evaluate the detection performance of the radar system, including indicators such as target detection probability, false alarm rate, and range resolution. According to the evaluation results, further optimize the waveform parameters to improve the overall performance of the radar system.

[0091] Applying the low sidelobe NLFM waveform to a radar system has the following beneficial effects: The low sidelobe NLFM waveform can effectively reduce the interference of clutter and strong target echoes, improving the radar's detection ability and detection accuracy for small targets. By optimizing the waveform parameters, the low sidelobe NLFM waveform can enhance the radar signal's anti-interference ability, ensuring the stable operation of the radar in a complex electromagnetic environment. The design of the low sidelobe NLFM waveform can improve the overall performance of the radar system, reducing the probability of misjudgment and missed detection, thereby enhancing the system's reliability. The low sidelobe NLFM waveform has good Doppler tolerance, capable of adapting to the target detection requirements in a dynamic environment and improving the adaptability of the radar system.

[0092] It is proposed to apply the obtained NLFM waveform to a radar system to suppress the strong clutter and strong target interference energy from adjacent range cells. Combining the designed waveform with the actual application scenario fully exploits the advantages of the low sidelobe NLFM waveform in suppressing clutter and interference, improving the radar system's target detection ability and anti-interference ability in a complex environment, and enhancing the practicality and reliability of the radar system.

[0093] As Figure 6 shown, an embodiment of the present invention also provides an NLFM waveform design device based on a two-parameter phase function, including a phase function construction module, an optimization function design module, a genetic algorithm optimization module, and a waveform generation module; The phase function construction module is used to introduce a bandwidth control parameter and an exponential parameter to construct a two-parameter phase function based on a quadratic function; The optimization function design module is used to design an optimization function with the goal of minimizing the highest sidelobe level while constraining the main lobe width and the signal bandwidth; The genetic algorithm optimization module is used to optimize the bandwidth control parameter and the exponential parameter in the two-parameter phase function using the genetic algorithm to obtain the optimal parameter group; The waveform generation module is used to substitute the optimal parameter group into the two-parameter phase function to generate a low sidelobe NLFM waveform.

[0094] Implementing the low sidelobe NLFM waveform design method in the form of a device makes the design process more automated and standardized, improving the design efficiency and the waveform generation quality, and facilitating integration and promotion in radar system development and application.

[0095] The two-parameter phase function is as follows:

[0096] In the formula, is the bandwidth control parameter, is the exponential parameter.

[0097] In some embodiments, the optimization function design module includes an initialization unit, a first calculation processing unit, a second calculation processing unit, and an optimization function design unit; The initialization unit is configured to generate an NLFM waveform based on the initial values of the bandwidth control parameter and the exponential parameter; The first calculation processing unit is configured to perform pulse compression on the generated NLFM waveform and calculate the highest sidelobe level and the main lobe width of the pulse compression result; The second calculation processing unit is configured to perform FFT transformation on the generated NLFM waveform and calculate the actual bandwidth of the signal; The optimization function design unit is configured to design an optimization function according to the highest sidelobe level, the main lobe width, and the actual bandwidth of the signal.

[0098] The formulas for the first calculation processing unit to calculate the highest sidelobe level and the main lobe width are as follows:

[0099] Where represents the main lobe peak, and the interval is the main lobe protection range, ; is the highest sidelobe level, is the main lobe width.

[0100] The second calculation processing unit is specifically configured to perform FFT transformation on the NLFM waveform, find the position of the spectral peak; extend from the spectral peak to both sides until the spectral power drops to a set percentage of the peak, obtaining two points; obtain the frequency range between the two points, which is the actual bandwidth of the signal.

[0101] The optimization function is as follows:

[0102] The calculation formula of

[0103] is: and are both penalty coefficients, represents taking and the larger of the two; is the highest sidelobe level, is the main lobe width.

[0104] In some embodiments, the genetic algorithm optimization module is specifically configured to substitute the calculated values of the highest sidelobe level and the main lobe width and the value of the actual bandwidth of the signal into the optimization function, use the optimization function as the fitness function of the genetic algorithm, and optimize the bandwidth control parameter and the exponential parameter to obtain the optimal bandwidth control parameter and the optimal exponential parameter . The specific process is as follows: Initializing the population: Set the initial value of the bandwidth control parameter to be , the optimization interval of is . is an exponential parameter that controls the steepness of the frequency change. the optimization interval of is Set the initial value of to be . Initialize the population of the genetic algorithm, including multiple individuals, and each individual contains a set of parameters ( ). Encode the parameter group to be optimized ( , ) into chromosomes. Real number encoding can be used, and directly use ( , ) as the gene value.

[0105] Fitness function design: Use the optimization function as the fitness function, and calculate the fitness value of each individual according to the fitness function formula. The calculation process is as follows: Generate the NLFM waveform , ) according to the current parameters ( . Perform pulse compression on to obtain the output . Extract from , (width at -4dB). Perform FFT on to calculate the actual bandwidth (frequency width at -4dB). Substitute into the fitness function to calculate the fitness value of the current individual.

[0106] Select individuals for reproduction according to the fitness value. Select excellent individuals according to the fitness value with probability. The smaller the fitness value (the better the performance), the higher the probability of being selected. Perform crossover operations on the selected individuals to generate new individuals. The crossover operation can be achieved by exchanging some parameters of two individuals. Perform mutation operations on the newly generated individuals to randomly change the parameter values of the individuals with a set probability to increase the diversity of the population. For each individual in the newly generated population, recalculate its fitness value. Repeat the steps of selection, crossover, mutation, and evaluation until the predetermined number of iterations is reached or the fitness value converges to a certain threshold. After the iteration ends, select the individual with the lowest fitness value, and its corresponding parameter group ( , ) is the optimal parameter group.

[0107] The low sidelobe NLFM waveform generated by the waveform generation module:

[0108] wherein is the optimal bandwidth control parameter, is the optimal exponential parameter.

[0109] In some embodiments, the device further includes an application module for applying the obtained low sidelobe NLFM waveform to a radar system to suppress strong clutter and strong target interference energy from adjacent range cells.

[0110] Adding an application module to the designed device, which is specifically used to apply the obtained NLFM waveform to the radar system to suppress interference, enables the device to not only have the waveform design function but also achieve a close combination with the application of the radar system, forming a complete chain from waveform design to actual application. This design further improves the practicability and functionality of the device, can better meet the application requirements of the radar system for low sidelobe waveforms, and enhances the performance and competitiveness of the entire system.

[0111] The device further includes an application module for applying the obtained low sidelobe NLFM waveform to a radar system to suppress strong clutter and strong target interference energy from adjacent range cells. This further emphasizes the practicability of the device. By directly applying the designed waveform to the radar system through the application module, a closed-loop from waveform design to actual application is achieved, which can quickly and effectively improve the performance of the radar system and meet the actual engineering requirements.

[0112] An embodiment of the present invention further provides an electronic device, which includes: a processor, a communication interface, a memory, and a communication bus. Among them, the processor, the communication interface, and the memory complete mutual communication through the communication bus. The communication bus can be used for information transmission between the electronic device and the sensor. The processor can call the logical instructions in the memory to execute the following method: introduce a bandwidth control parameter and an exponential parameter, construct a two-parameter phase function based on a quadratic function; design an optimization function with the goal of minimizing the highest sidelobe level while constraining the main lobe width and the signal bandwidth; use a genetic algorithm to optimize the bandwidth control parameter and the exponential parameter in the two-parameter phase function to obtain an optimal parameter group; substitute the optimal parameter group into the two-parameter phase function to generate a low sidelobe NLFM waveform.

[0113] In addition, when the logic instructions in the above-mentioned memory can be implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on such an understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or a part of this technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in various embodiments of the present invention. The aforementioned storage medium includes: various media such as USB flash drives, mobile hard disks, read-only memories (ROM, Read-Only Memory), random access memories (RAM, Random Access Memory), magnetic disks, or optical discs that can store program codes.

[0114] An embodiment of the present invention provides a non-transitory computer-readable storage medium. The non-transitory computer-readable storage medium stores computer instructions, and these computer instructions cause the computer to execute the method provided in the above method embodiment. For example, it includes: introducing a bandwidth control parameter and an exponential parameter, constructing a two-parameter phase function based on a quadratic function; taking minimizing the highest sidelobe level as the goal while constraining the main lobe width and the signal bandwidth, and designing an optimization function; using a genetic algorithm to optimize the bandwidth control parameter and the exponential parameter in the two-parameter phase function to obtain an optimal parameter group; substituting the optimal parameter group into the two-parameter phase function to generate a low-sidelobe NLFM waveform.

[0115] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present invention. Various modifications to these embodiments will be obvious to those skilled in the art. The general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to these embodiments shown herein, but rather will be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for designing NLFM waveforms based on a two-parameter phase function, characterized in that, It includes the following steps: Introduce a bandwidth control parameter and an exponential parameter, and construct a two-parameter phase function based on a quadratic function; Design an optimization function with the goal of minimizing the highest sidelobe level while constraining the main lobe width and signal bandwidth; Based on the optimization function, use the genetic algorithm to optimize the bandwidth control parameter and exponential parameter in the two-parameter phase function to obtain the optimal parameter group; Substitute the optimal parameter group into the two-parameter phase function to generate a low-sidelobe NLFM waveform.

2. The NLFM waveform design method based on the dual-parameter phase function according to claim 1, wherein In the step of introducing a bandwidth control parameter and an exponential parameter and constructing a two-parameter phase function based on a quadratic function, the two-parameter phase function is as follows: In the formula, is the bandwidth control parameter, is the exponential parameter.

3. The NLFM waveform design method based on the two-parameter phase function according to claim 2, wherein The steps of designing an optimization function with the goal of minimizing the highest sidelobe level while constraining the main lobe width and signal bandwidth include: Generate an NLFM waveform based on the initial values of the bandwidth control parameter and exponential parameter; Perform pulse compression on the generated NLFM waveform, and calculate the highest sidelobe level and main lobe width of the pulse compression result; Perform FFT transformation on the generated NLFM waveform, and calculate the actual bandwidth of the signal; Design an optimization function according to the highest sidelobe level, main lobe width and actual bandwidth of the signal.

4. The NLFM waveform design method based on the double-parameter phase function according to claim 3, wherein, The formulas for calculating the highest sidelobe level and main lobe width are as follows: Among them, represents the main lobe peak value, and the interval is the main lobe protection range, ; is the highest sidelobe level, is the main lobe width, is the pulse compression result.

5. The NLFM waveform design method based on the two-parameter phase function according to claim 4, characterized in that The steps of performing FFT transformation on the generated NLFM waveform and calculating the actual bandwidth of the signal include: Perform FFT transformation on the NLFM waveform to find the position of the spectral peak; Extend from the spectral peak to both sides until the spectral power drops to a set percentage of the peak to obtain two points; Obtain the frequency range between the two points, which is the actual bandwidth of the signal.

6. The NLFM waveform design method based on the two-parameter phase function according to claim 5, wherein The optimization function is as follows: The calculation formula is as follows: Among them, and are both penalty coefficients, means taking and the larger of the two; is the highest sidelobe level, is the main lobe width, and B is the bandwidth.

7. The NLFM waveform design method based on the dual-parameter phase function according to claim 6, wherein In the step of substituting the optimal parameter group into the two-parameter phase function to generate a low-sidelobe NLFM waveform, the generated low-sidelobe NLFM waveform: In the formula, is the optimal bandwidth control parameter, is the optimal exponential parameter.

8. The NLFM waveform design method based on the two-parameter phase function according to claim 7, wherein The method further includes: Apply the obtained low-sidelobe NLFM waveform to the radar system to suppress clutter and target interference energy from adjacent range cells.

9. An NLFM waveform design device based on a two-parameter phase function, characterized in that It includes a phase function construction module, an optimization function design module, a genetic algorithm optimization module and a waveform generation module; The phase function construction module is used to introduce a bandwidth control parameter and an exponential parameter, and construct a two-parameter phase function based on a quadratic function; The optimization function design module is used to design an optimization function with the goal of minimizing the highest sidelobe level while constraining the main lobe width and signal bandwidth; The genetic algorithm optimization module is used to optimize the bandwidth control parameter and exponential parameter in the two-parameter phase function based on the optimization function by using the genetic algorithm to obtain the optimal parameter group; The waveform generation module is used to substitute the optimal parameter group into the two-parameter phase function to generate a low-sidelobe NLFM waveform.

10. The NLFM waveform design device based on the dual-parameter phase function according to claim 9, characterized in that, The device further includes an application module, which is used to apply the obtained low-sidelobe NLFM waveform to the radar system to suppress clutter and target interference energy from adjacent range cells.

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