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

Abstract

The invention relates to the technical field of radar waveform design, in particular to an NLFM waveform design method and device based on a single-parameter phase function, and the method comprises the following steps: obtaining a minimum value of an initial phase function numerical sequence through employing a window function reverse calculation method; based on the minimum value of the initial phase function numerical sequence, introducing an index parameter, and constructing a single-parameter phase function based on a quadratic function; designing an optimization function which aims at minimizing the highest sidelobe level and constrains the width of a main lobe; based on the optimization function, optimizing index parameters in the single-parameter phase function by using a genetic algorithm to obtain optimal parameters; and substituting the optimal parameter into a single-parameter phase function to generate an NLFM waveform. The method can effectively reduce the sidelobe level of the waveform, reasonably restrains the width of the main lobe, and can improve the performance of the waveform, reduce the signal interference, and improve the resolution and detection capability of signals in radar and other application scenes compared with a traditional waveform design method.

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 single-parameter phase function. Background Art

[0002] In the field of radar signal processing, waveform design is a crucial research content, which is directly related to the performance of the radar system. In the actual radar detection environment, strong clutter and strong target interference energy often exist in adjacent range cells, and these interferences will seriously affect the accurate acquisition and processing of target information by the radar. The low sidelobe waveform can effectively suppress this interference energy and reduce the sidelobe level, thereby significantly improving the radar's target detection ability, resolution, and anti-interference performance, ensuring that the radar can still work stably and reliably in a complex electromagnetic environment.

[0003] Currently, the methods for designing non-linear frequency modulation (NLFM) waveforms mainly include parametric frequency modulation method, parametric phase function construction method, and phase stationary method based on frequency domain window function. Among them, the performance of the parametric phase function construction method highly depends on the construction of the parametric phase function, and how to construct a parametric phase function with good performance becomes a key issue.

[0004] The currently commonly used parametric phase function construction methods mainly include polynomial phase coding and random phase perturbation, etc. Polynomial phase coding faces difficulties in optimizing parameters to balance the main lobe width and sidelobe level, and it is difficult to achieve the ideal effects of both low sidelobes and narrow main lobes simultaneously. Although the NLFM waveform designed by random phase perturbation can meet certain specific requirements to a certain extent, its Doppler tolerance is relatively low. In the case where the target has a Doppler frequency shift, the performance of the waveform will decrease significantly, affecting the radar's detection ability for high-speed moving targets. Summary of the Invention

[0005] Aiming at the problem of designing a low sidelobe NLFM waveform, a method for designing a low sidelobe NLFM waveform based on a single-parameter phase function construction method is provided. This method can better balance the main lobe width and sidelobe level, and while the performance of both the main lobe and sidelobe is better than that of the NLFM waveform designed by the existing methods, it also has better Doppler tolerance.

[0006] In the first aspect, the technical solution of the present invention provides a method for designing an NLFM waveform based on a single-parameter phase function, including the following steps: Using the window function inverse method, obtain the minimum value of the initial phase function numerical sequence; Based on the minimum value of the initial phase function numerical sequence, introduce an exponential parameter to construct a single-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; Based on the optimization function, the genetic algorithm is used to optimize the exponential parameter in the single-parameter phase function to obtain the optimal parameter; Substitute the optimal parameter into the single-parameter phase function to generate the NLFM waveform.

[0007] By adopting the window function inverse method combined with the construction method of the single-parameter phase function introduced by the exponential parameter, and using the genetic algorithm to optimize the exponential parameter, an NLFM waveform with low sidelobe characteristics can be designed. This method comprehensively considers the sidelobe level and main lobe width of the waveform, effectively improving the anti-interference ability and target detection performance of the radar system.

[0008] As a further limitation of the technical solution of the present invention, the steps of obtaining the minimum value of the initial phase function numerical sequence by using the window function inverse method include: Adopt the hamming window as the frequency-domain window function and use the phase stationary method to deduce the group delay function; Based on the sampling rate and pulse width, discretize the frequency points of the group delay function to obtain the sequence of the group delay function; Use the cubic spline fitting method to obtain a function with time as the independent variable and frequency as the dependent variable, and integrate this function to obtain the numerical sequence of the initial phase function, and then obtain the minimum value of the initial phase function numerical sequence.

[0009] Adopting the hamming window as the frequency-domain window function and combining with the phase stationary method to deduce the group delay function can more accurately describe the frequency-domain characteristics of the waveform. Obtaining the numerical sequence of the initial phase function through cubic spline fitting and integration provides a reliable basis for the subsequent construction of the single-parameter phase function, which helps to generate an NLFM waveform with better performance.

[0010] As a further limitation of the technical solution of the present invention, the steps of discretizing the frequency points based on the sampling rate and pulse width to obtain the sequence of the group delay function include: According to the sampling rate and pulse width, calculate the number of sampling points within the pulse width ; Discretize the independent variable of the group delay function into frequency points; Substitute the discretized frequency values into the group delay function to obtain the sequence of the group delay function.

[0011] Discretizing the frequency points based on the sampling rate and pulse width can more accurately obtain the sequence of the group delay function, so as to more accurately describe the time-frequency characteristics of the waveform. This helps the calculation of the initial phase function and the construction of the single-parameter phase function in the subsequent steps, improving the generation accuracy of the NLFM waveform.

[0012] As a further limitation of the technical solution of the present invention, the group delay function is as follows:

[0013] Among them, is the group delay function with as the independent variable, is the bandwidth of the NLFM waveform, and the independent variable has a value range of , is the pulse width.

[0014] The specific expression of the group delay function is given, clarifying the relationship between its independent variable and dependent variable, as well as the value range of the independent variable. This provides a clear mathematical basis for the calculation of the group delay function and the generation of the initial phase function in the subsequent steps, and helps to achieve the precise design of the NLFM waveform.

[0015] As a further limitation of the technical solution of the present invention, in the step of introducing an exponential parameter and constructing a single-parameter phase function based on a quadratic function based on the minimum value of the numerical sequence of the initial phase function, the single-parameter phase function is as follows:

[0016] Among them, is the exponential parameter, is the minimum value of the numerical sequence of the initial phase function.

[0017] By introducing the exponential parameter and the minimum value of the numerical sequence of the initial phase function, a single-parameter phase function based on a quadratic function is constructed. This construction method can flexibly adjust the phase characteristics of the waveform, thereby effectively controlling the sidelobe level and main lobe width, and helping to generate an NLFM waveform that meets specific performance requirements.

[0018] As a further limitation of the technical solution of the present invention, the steps of designing an optimization function with the goal of minimizing the highest sidelobe level while constraining the main lobe width include: Generating an initial NLFM waveform based on the initial value of the exponential parameter, the sampling rate, and the required bandwidth and pulse width of the NLFM waveform; Performing pulse compression on the initial NLFM waveform and calculating the highest sidelobe level and main lobe width of the pulse compression result; Designing an optimization function according to the highest sidelobe level and main lobe width.

[0019] By generating an initial NLFM waveform and performing pulse compression, the highest sidelobe level and main lobe width of the waveform can be calculated. Designing an optimization function based on these parameters can more accurately describe the performance indicators of the waveform, provide a clear objective function for subsequent parameter optimization, and help improve the generation quality of the NLFM waveform.

[0020] As a further limitation of the technical solution of the present invention, the optimization function is as follows:

[0021] Wherein, is an adjustable parameter, means taking and the larger of the two, is the highest sidelobe level, is the main lobe width, is the required bandwidth of the NLFM waveform.

[0022] The specific expression of the optimization function is given, clarifying the variables such as the adjustable parameters, the highest sidelobe level, the main lobe width, and the required bandwidth it contains. This optimization function can comprehensively consider multiple performance indicators of the waveform. By minimizing the highest sidelobe level and simultaneously constraining the main lobe width, it helps to generate an NLFM waveform with better performance.

[0023] As a further limitation of the technical solution of the present invention, based on the optimization function, the steps of using the genetic algorithm to optimize the exponential parameter in the single-parameter phase function to obtain the optimal parameter include: Substitute the highest sidelobe level and the main lobe width calculated based on the initial NLFM waveform into the optimization function; Use the optimization function as the fitness function of the genetic algorithm, and optimize the exponential parameter by iteratively updating the parameters through selection, crossover, and mutation, and return the optimal parameter that minimizes the fitness function.

[0024] By substituting the highest sidelobe level and the main lobe width calculated based on the initial NLFM waveform into the optimization function and using the genetic algorithm to optimize the exponential parameter, the optimal parameter that minimizes the fitness function can be found. This method can automatically search for the optimal solution, improve the efficiency and accuracy of parameter optimization, and help generate an NLFM waveform that meets specific performance requirements.

[0025] As a further limitation of the technical solution of the present invention, the method further includes: Apply the obtained NLFM waveform to the radar system.

[0026] Applying the obtained NLFM waveform to the radar system can directly improve the anti-jamming ability and target detection performance of the radar system. The NLFM waveform with low sidelobe characteristics helps to reduce sidelobe interference, improve the radar's target resolution ability and detection accuracy, thereby enhancing the overall performance of the radar system.

[0027] In a second aspect, the technical solution of the present invention also provides a NLFM waveform design device based on a single-parameter phase function, including a function value calculation module, a phase function construction module, an optimization function design module, a parameter optimization module and a waveform generation module; A function value calculation module is used to perform a window function inverse method to calculate the minimum value of the initial phase function numerical sequence; A phase function construction module is used to introduce an exponential parameter based on the minimum value of the initial phase function numerical sequence to construct a single-parameter phase function based on a quadratic function; An optimization function design module, used to design an optimization function with the goal of minimizing the highest sidelobe level while constraining the main lobe width; The parameter optimization module configures the genetic algorithm optimizer to optimize the exponential parameters in the single-parameter phase function to obtain the optimal parameters; The waveform generation module is used to generate the NLFM signal according to the optimal parameters.

[0028] By designing a low sidelobe NLFM waveform design device based on a single-parameter phase function, each step is modularized to achieve automation and intelligence of waveform design. The device includes a function value calculation module, a phase function construction module, an optimization function design module, a parameter optimization module and a waveform generation module. Each module works together to efficiently generate an NLFM waveform that meets specific performance requirements, thereby improving the efficiency and accuracy of waveform design.

[0029] As a further limitation of the technical solution of the present invention, the function value calculation module includes a group delay function derivation unit, a group delay function sequence acquisition unit, and a minimum value calculation unit; A group delay function derivation unit, which configures a hamming window as a frequency domain window function and uses a phase dwell method to derive a group delay function; A group delay function sequence acquisition unit, used for discretizing the frequency points of the group delay function based on the sampling rate and the pulse width to obtain a sequence of the group delay function; The minimum value calculation unit is used to obtain a function with time as the independent variable and frequency as the dependent variable by using a cubic spline fitting method, and to integrate the function to obtain a numerical sequence of the initial phase function, thereby obtaining the minimum value of the numerical sequence of the initial phase function.

[0030] As a further limitation of the technical solution of the present invention, the group delay function sequence acquisition unit is specifically used to calculate the number of sampling points within the pulse width according to the sampling rate and the pulse width. ; Discretize the independent variable of the group delay function into frequency points; substitute the discretized frequency values ​​into the group delay function to obtain a sequence of group delay functions.

[0031] As a further limitation of the technical solution of the present invention, the group delay function is as follows:

[0032] Wherein, is the group delay function with as the independent variable, is the bandwidth of the NLFM waveform, and the independent variable has a value range of , is the pulse width.

[0033] As a further limitation of the technical solution of the present invention, the single-parameter phase function is as follows:

[0034] Wherein, is the exponential parameter, is the minimum value of the numerical sequence of the initial phase function.

[0035] As a further limitation of the technical solution of the present invention, the optimization function design module includes an initial waveform generation unit, a calculation unit, and an optimization function design unit; The initial waveform generation unit is used to generate an initial NLFM waveform based on the initial value of the exponential parameter, the sampling rate, and the required bandwidth and pulse width of the NLFM waveform; The calculation unit is used to perform pulse compression on the initial NLFM waveform and calculate the highest sidelobe level and main lobe width of the pulse compression result; The optimization function design unit is used to design an optimization function according to the highest sidelobe level and main lobe width.

[0036] As a further limitation of the technical solution of the present invention, the optimization function is as follows:

[0037] Wherein, is an adjustable parameter, represents taking and the larger of the two, is the highest sidelobe level, is the main lobe width, is the required bandwidth of the NLFM waveform.

[0038] As a further limitation of the technical solution of the present invention, the parameter optimization module is specifically used to substitute the highest sidelobe level and main lobe width calculated based on the initial NLFM waveform into the optimization function; use the optimization function as the fitness function of the genetic algorithm, and iteratively update the parameters through selection, crossover, and mutation to optimize the exponential parameter, and return the optimal parameter that minimizes the fitness function.

[0039] 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.

[0040] From the above technical solutions, it can be seen that the present application has the following advantages: By using the window function inverse method to determine the minimum value of the initial phase function numerical sequence, introducing an exponential parameter to construct a single-parameter phase function, and designing an optimization function to combine with the genetic algorithm for optimization, finally generating the NLFM waveform. This process systematically combines a variety of technical means, which can effectively reduce the sidelobe level of the waveform, while reasonably restricting the main lobe width. Compared with the traditional waveform design method, it can improve the performance of the waveform, reduce signal interference, and enhance the resolution and detection ability of signals in application scenarios such as radar. Description of the Drawings

[0041] In order to more clearly illustrate the technical solutions of the present application, the drawings required for description will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present application. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0042] Figure 1 It is a schematic flowchart of the method provided by the embodiment of the present invention.

[0043] Figure 2 It is a schematic diagram of the design method of the method provided by the embodiment of the present invention.

[0044] Figure 3 It is a comparison chart of the windowed pulse compression output results of the LFM waveform, NLFM0 waveform, and NLFM1 waveform under the non-Doppler condition. Among them, Figure 3 in (a) is the pulse compression result of the LFM waveform, Figure 3 in (b) is the pulse compression result of the NLFM0 waveform, Figure 3 in (c) is the pulse compression result of the NLFM1 waveform, Figure 3 in (d) is a comparison of the local enlarged views of the pulse compression results of the three waveforms.

[0045] Figure 4 It is a comparison chart of the windowed pulse compression output results of the NLFM1 waveform under two conditions of with / without target Doppler.

[0046] Figure 5 It is a block diagram of the device provided by the embodiment of the present invention. Detailed Embodiments

[0047] The present invention provides a new method for designing a low sidelobe NLFM waveform. This method combines the phase dwell method based on the frequency domain window function and the parametric phase function construction method. Starting from the inverse solution of the window function, a non-linear single-parameter phase function is constructed using mathematical fitting, and an optimization function with the goal of "minimizing the highest sidelobe level while constraining the main lobe width" is designed. The genetic algorithm is used for parameter optimization to obtain an NLFM waveform with low sidelobe performance and meeting the constraint conditions. To make the application purpose, features, and advantages of the present application more obvious and understandable, the technical solutions protected by the present application will be clearly and completely described below by using specific embodiments and accompanying drawings. 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 efforts belong to the scope protected by the present application.

[0048] The purpose of the present invention is to provide a method for designing a low sidelobe NLFM waveform based on the parametric phase function construction method for the problem of designing a low sidelobe NLFM waveform. This method can better balance the main lobe width and the sidelobe level, and while the main lobe and sidelobe performances are better than those of the NLFM waveforms designed by existing methods, it also has better Doppler tolerance. As Figure 1 shown, the embodiment of the present invention provides a method for designing an NLFM waveform based on a single-parameter phase function, including the following steps: S1. Using the window function inverse solution method, obtain the minimum value of the initial phase function numerical sequence; specifically including: S11. Use the hamming window as the frequency domain window function, and use the phase dwell method to deduce the group delay function; The group delay function is as follows:

[0049] Among them, is the group delay function with as the independent variable, is the bandwidth of the NLFM waveform, and the independent variable has a value range of , is the pulse width.

[0050] S12. According to the sampling rate and the pulse width, calculate the number of sampling points within the pulse width;

[0051] In the formula, is the sampling rate.

[0052] S13. Discretize the independent variable of the group delay function into frequency points; where the interval between the frequency points .

[0053] S14. Substitute the discretized frequency values into the group delay function to obtain a sequence of the group delay function.

[0054] S15. Use the cubic spline fitting method to obtain a function with time as the independent variable and frequency as the dependent variable, integrate this function to obtain a numerical sequence of the initial phase function, and further obtain the minimum value of the numerical sequence of the initial phase function.

[0055] The frequency f is discretized into N points, and the value range of the frequency points is [− B / 2, B / 2]. Therefore, the discretized frequency points can be expressed as:

[0056] Substitute the discretized frequency points into the group delay function to obtain a sequence of the group delay function :

[0057] Using the cubic spline fitting method, fit the discrete group delay function into a continuous function , where t is the time variable. The specific steps are as follows: Divide the time t into N nodes, and the node time interval is:

[0058] The node time is: ; For each interval , construct a cubic polynomial such that:

[0059] And satisfy the continuity conditions of the first and second derivatives at the nodes.

[0060] By solving the tridiagonal linear equations, obtain the coefficients of the cubic polynomial in each interval.

[0061] Integrate the spline function to obtain the initial phase function. Numerical integration methods such as the trapezoidal rule or Simpson's rule can be used to calculate each time point The phase values at all time points are used to form a numerical sequence, and the minimum value of this sequence is calculated.

[0062] The Hamming window is used as the frequency-domain window function, and the group delay function is derived using the phase dwell method. By combining cubic spline fitting and integration operations, the minimum value of the initial phase function numerical sequence is obtained. This method utilizes the characteristics of the Hamming window in suppressing sidelobes and, through rigorous mathematical derivation and processing methods, can accurately obtain the key information of the initial phase function, laying a solid foundation for constructing the subsequent phase function and enabling the generated waveform to have better potential for performance optimization.

[0063] The frequency points are discretized according to the sampling rate and pulse width. Scientifically converting the continuous group delay function into a discrete sequence meets the requirements of digital signal processing, facilitates subsequent calculations and processing in digital systems such as computers, ensures the accuracy and efficiency of signal processing, avoids signal distortion or error accumulation caused by unreasonable discretization, and helps improve the reliability of waveform design.

[0064] S2. Based on the minimum value of the initial phase function numerical sequence, an exponential parameter is introduced to construct a single-parameter phase function based on a quadratic function; The single-parameter phase function is as follows:

[0065] where, is the exponential parameter, is the minimum value of the initial phase function numerical sequence.

[0066] Constructing a single-parameter phase function based on the minimum value of the initial phase function numerical sequence links the phase function with waveform performance optimization by introducing an exponential parameter. This simple and reasonable function construction method enables subsequent optimization of the waveform by adjusting the exponential parameter, providing a flexible adjustment means for waveform design and being able to meet the requirements of waveform performance in different application scenarios.

[0067] S3. Design an optimization function with the goal of minimizing the highest sidelobe level while constraining the main lobe width; specifically including: S31. Generate an initial NLFM waveform based on the initial value of the exponential parameter, the sampling rate, and the required bandwidth and pulse width of the NLFM waveform; S32. Perform pulse compression on the initial NLFM waveform and calculate the highest sidelobe level and main lobe width of the pulse compression result; S33. Design an optimization function based on the highest sidelobe level and main lobe width.

[0068] The optimization function is as follows:

[0069] Among them, is an adjustable parameter, represents taking and the larger value of the two, is the highest sidelobe level, is the main lobe width, is the bandwidth of the NLFM waveform.

[0070] By generating an initial NLFM waveform, performing pulse compression and calculating relevant performance indicators, an optimization function is then designed. This process closely combines the actual performance of the waveform with the optimization goal, designs the optimization direction starting from the actual waveform effect, enables the optimization function to more accurately reflect the waveform performance requirements, provides a more practical objective function for subsequent parameter optimization, and improves the optimization efficiency and waveform optimization quality.

[0071] S4. Based on the optimization function, use the genetic algorithm to optimize the exponential parameter in the single-parameter phase function to obtain the optimal parameter; specifically including: S41. Substitute the highest sidelobe level and main lobe width calculated based on the initial NLFM waveform into the optimization function; S42. Use the optimization function as the fitness function of the genetic algorithm, and optimize the exponential parameter by iteratively updating the parameters through selection, crossover, and mutation, and return the optimal parameter that minimizes the fitness function. The specific steps are as follows: Initialize the population: Determine the value range of the exponential parameter , for example, [0.1, 1].

[0072] Randomly generate a set of initial values of the parameter , and each parameter value is called an "individual". The population size P is usually selected according to the problem scale, for example P = 50 or P = 100.

[0073] Fitness function calculation: The optimization function is used to evaluate the fitness of each individual. According to the problem description, the optimization function is:

[0074] For each individual in the population , calculate the highest sidelobe level and main lobe width of the corresponding NLFM waveform, and substitute them into the optimization function to calculate the fitness

[0075] Calculate the selection probability of each individual according to the fitness function value. The lower the fitness (the smaller the optimization function value), the higher the selection probability of the individual.

[0076] Calculate the fitness proportion of each individual:

[0077] According to the probability Randomly select individuals to generate a new population.

[0078] Randomly select two parent individuals and , and exchange part of their genes at a certain random point k to generate two offspring individuals.

[0079] Perform random mutation on the newly generated offspring individuals, and randomly change the genes of the individuals with a certain probability (e.g., 0.01).

[0080] Replace part or all of the individuals in the population with the newly generated offspring individuals.

[0081] Repeat the operations of calculating fitness, selection, crossover, and mutation until the termination condition is met (e.g., reaching the maximum number of iterations or the fitness no longer improves significantly). In the final population, select the individual with the minimum fitness as the optimal parameter.

[0082] Use the optimization function as the fitness function of the genetic algorithm to optimize the exponential parameter. By making full use of the global optimization advantage of the genetic algorithm, it can quickly find the exponential parameter value that makes the waveform performance optimal in a large parameter space. Compared with traditional optimization methods, the iterative update mechanism of the genetic algorithm can avoid falling into local optimal solutions, improve the accuracy and reliability of optimization, and thus obtain an NLFM waveform with better performance.

[0083] S5. Substitute the optimal parameter into the single-parameter phase function to generate the NLFM waveform.

[0084] By adopting the window function inverse method combined with the construction method of the single-parameter phase function introduced by the exponential parameter, and using the genetic algorithm to optimize the exponential parameter, an NLFM waveform with low sidelobe characteristics can be designed. This method comprehensively considers the sidelobe level and main lobe width of the waveform, and effectively improves the anti-jamming ability and target detection performance of the radar system.

[0085] In some embodiments, the method further includes: Apply the obtained NLFM waveform to the radar system.

[0086] The designed NLFM waveform is applied to the radar system, giving full play to the advantages of the low-sidelobe NLFM waveform in radar detection. The low-sidelobe characteristic can reduce the sidelobe interference in the target echo signal, improve the radar's target resolution ability and detection probability, enhance the radar system's anti-interference ability and working stability, thereby improving the overall performance and application value of the radar system.

[0087] Refer to the attached Figure 2 , the specific implementation of the method provided by the present invention is divided into the following steps: (1) Using the window function inverse method, obtain the minimum value of the initial phase function numerical sequence; (2) Introduce an exponential parameter to construct a new single-parameter phase function based on a quadratic function; (3) Design an optimization function with the goal of "minimizing the highest sidelobe level while constraining the main lobe width", and use the genetic algorithm for parameter optimization to obtain the optimal parameters, and then generate the NLFM waveform.

[0088] The above steps are elaborated in detail as follows: When designing the NLFM waveform, 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 ranges from , is the pulse width of the waveform; (1) Using the window function inverse method, obtain the minimum value of the initial phase function numerical sequence; First, use the hamming window as the frequency-domain window function, and use the phase stationary method to deduce its group delay function,

[0089] Among them, is the group delay function with as the independent variable , is the bandwidth of the NLFM waveform, and the independent variable ranges from ; Then, based on the sampling rate and the pulse width to obtain the number of in-pulse sampling points , discretize the independent variable into frequency points, and the discretization degree is ; Substitute Substitute the discrete values into the function to obtain a sequence of group delay functions; Use cubic spline fitting technology to obtain a function with time as the independent variable and frequency as the dependent variable, where the dispersion of is Finally, perform an integration operation on to obtain a numerical sequence of the initial phase function , , . Calculate the minimum value of according to the following formula, denoted as ,

[0090] (2) Introduce an exponential parameter to construct a new single-parameter phase function based on a quadratic function; Introduce an exponential parameter to construct the following single-parameter phase function

[0091] where is the exponential parameter to be optimized, which controls the steepness of the frequency change. The optimization interval of is ; Let the initial value of .

[0092] (3) Design an optimization function with the goal of "minimizing the highest sidelobe level while constraining the main lobe width", and use the genetic algorithm to perform parameter optimization to obtain the optimal parameter , and then generate the NLFM waveform; Step 3.1, calculate the highest sidelobe level and the main lobe width

[0093] Import the initial phase function parameters and the waveform parameters determined by the system , and into the genetic algorithm, and implement them in the order of generating the NLFM waveform, performing pulse compression, calculating the highest sidelobe level , calculating the main lobe width to obtain and values, where represents the main lobe width corresponding to -4 dB of the pulse compression output result; Step 3.2, 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, in order to ensure the range resolution of the pulse compression output result, the main lobe width is increased as a penalty term for constraint, where is selected as the reference value of the main lobe width; considering the above conditions, the optimization function is designed as:

[0094] where, is an adjustable parameter with a value of 10 3 orders of magnitude; means taking and the larger of the two; Step 3.3, genetic algorithm optimization to generate an optimized NLFM waveform Substitute the and values obtained in Step 3.1 into the optimization function. Using the optimization function as the fitness function of the genetic algorithm, optimize the parameter to obtain the optimal parameter , and then construct the phase function to generate the NLFM waveform .

[0095] The following provides a design example. The waveform parameters determined by the system are , and ; from step (1), is obtained; from step (3), the NLFM waveform is as follows: , ,

[0096] 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 comparison diagram of the windowed pulse compression output results of the LFM waveform (the (a) in Figure 3 is marked as the LFM waveform), the NLFM waveform obtained by the phase dwell method based on the frequency domain window function (the (b) in Figure 3 is marked as the NLFM0 waveform), and the NLFM waveform obtained by the present invention (the (c) in Figure 3 is marked as the NLFM1 waveform) without Doppler is given, Figure 3Local enlarged view comparison of the pulse compression results of the three waveforms in (d). 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 the other two. In addition, in the case of windowed pulse compression, the range resolution obtained by the LFM waveform is 7.5 meters, the range resolution obtained by the NLFM0 waveform is 12 meters, and the range resolution obtained by the NLFM1 waveform is 13.5 meters.

[0097] Figure 4 Figure Figure 4 is a comparison diagram of the windowed pulse compression output results of the NLFM1 waveform under two conditions of with / without target Doppler. The black line shows the case where the main lobe of the pulse compression output of the NLFM1 waveform obtained by the present invention just starts to deform under the conditions of a target speed of 200 m / s and a waveform carrier frequency of 9.5 GHz. The red line is the pulse compression output result of the NLFM1 waveform under the condition of no target Doppler, which indicates that the Doppler tolerance of the NLFM1 waveform is about 200 m / s.

[0098] As Figure 5 shown, the embodiment of the present invention also provides an NLFM waveform design device based on a single-parameter phase function, including a function value calculation module, a phase function construction module, an optimization function design module, a parameter optimization module, and a waveform generation module; The function value calculation module is used to execute the window function inverse method to calculate the minimum value of the initial phase function numerical sequence; The phase function construction module is used to introduce an exponential parameter based on the minimum value of the initial phase function numerical sequence to construct a single-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; The parameter optimization module is configured to optimize the exponential parameter in the single-parameter phase function using a genetic algorithm optimizer to obtain the optimal parameter; The waveform generation module is used to generate an NLFM signal according to the optimal parameter.

[0099] By designing an NLFM waveform design device based on a single-parameter phase function and modularizing each step, the automation and intelligence of waveform design are realized. The device includes a function value calculation module, a phase function construction module, an optimization function design module, a parameter optimization module, and a waveform generation module. Each module works together to efficiently generate an NLFM waveform that meets specific performance requirements, improving the efficiency and accuracy of waveform design.

[0100] In some embodiments, the function value calculation module includes a group delay function derivation unit, a group delay function sequence acquisition unit, and a minimum value calculation unit; The group delay function derivation unit configures a Hamming window as the frequency domain window function and derives the group delay function using the phase stationary method; The group delay function sequence acquisition unit is used to discretize the frequency points of the group delay function based on the sampling rate and the pulse width to obtain the sequence of the group delay function; The minimum value calculation unit is used to obtain a function with time as the independent variable and frequency as the dependent variable by using the cubic spline fitting method, integrate the function to obtain the numerical sequence of the initial phase function, and further obtain the minimum value of the numerical sequence of the initial phase function.

[0101] In some embodiments, the group delay function sequence acquisition unit is specifically used to calculate the number of sampling points within the pulse width according to the sampling rate and the pulse width ; discretize the independent variable of the group delay function into frequency points; substitute the discretized frequency values into the group delay function to obtain the sequence of the group delay function.

[0102] As a further limitation of the technical solution of the present invention, the group delay function is as follows:

[0103] Wherein, is the group delay function with as the independent variable, is the bandwidth of the NLFM waveform, and the value range of the independent variable is , is the pulse width.

[0104] The single-parameter phase function is as follows:

[0105] Wherein, is the exponential parameter, is the minimum value of the numerical sequence of the initial phase function.

[0106] In some embodiments, the optimization function design module includes an initial waveform generation unit, a calculation unit, and an optimization function design unit; The initial waveform generation unit is used to generate an initial NLFM waveform based on the initial value of the exponential parameter, the sampling rate, and the required bandwidth and pulse width of the NLFM waveform; The calculation unit is used to perform pulse compression on the initial NLFM waveform and calculate the highest sidelobe level and the main lobe width of the pulse compression result; The optimization function design unit is used to design an optimization function according to the highest sidelobe level and the main lobe width.

[0107] The optimization function is as follows:

[0108] Among them, is an adjustable parameter, represents taking and the larger value of the two, is the highest sidelobe level, is the main lobe width, is the required bandwidth of the NLFM waveform.

[0109] In some embodiments, the parameter optimization module is specifically configured to substitute the highest sidelobe level and the main lobe width calculated based on the initial NLFM waveform into the optimization function; use the optimization function as the fitness function of the genetic algorithm, iteratively update the parameters through selection, crossover, and mutation to optimize the exponential parameter, and return the optimal parameter that minimizes the fitness function.

[0110] 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.

[0111] 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 apparent to those skilled in the art, and 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 the embodiments shown herein, but rather to the broadest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for designing an NLFM waveform based on a single-parameter phase function, characterized in that, The steps include: The minimum value of the initial phase function numerical sequence is obtained by using the window function inverse method; Based on the minimum value of the initial phase function numerical sequence, an exponential parameter is introduced to construct a single-parameter phase function based on a quadratic function. Design an optimization function that minimizes the highest sidelobe level while constraining the mainlobe width; Based on the optimization function, the genetic algorithm is used to optimize the exponential parameter in the single-parameter phase function and obtain the optimal parameter; Substituting the optimal parameters into the single-parameter phase function, the NLFM waveform is generated.

2. The NLFM waveform design method based on a single-parameter phase function according to claim 1, wherein The steps of obtaining the minimum value of the initial phase function numerical sequence by using the window function inverse method include: The Hamming window is used as the frequency domain window function, and the group delay function is derived using the phase dwell method. Based on the sampling rate and the pulse width, the frequency points of the group delay function are discretized to obtain a sequence of the group delay function; A cubic spline fitting method is used to obtain a function with time as the independent variable and frequency as the dependent variable, and the numerical sequence of the initial phase function is obtained by integrating the function, and then the minimum value of the numerical sequence of the initial phase function is obtained.

3. The NLFM waveform design method based on a single-parameter phase function according to claim 2, wherein The steps of discretizing the frequency points based on the sampling rate and the pulse width to obtain a sequence of group delay functions include: Calculate the number of sampling points within the pulse width based on the sampling rate and the pulse width ; Discretize the independent variable of the group delay function into frequency points; Substituting the discretized frequency value into the group delay function, a sequence of the group delay function is obtained.

4. The NLFM waveform design method based on a single-parameter phase function according to claim 3, wherein The group delay function is as follows: Among them, is the group delay function with as the independent variable, is the bandwidth of the NLFM waveform, and the independent variable , is the pulse width.

5. The NLFM waveform design method based on a single-parameter phase function according to claim 4, characterized in that, Based on the minimum value of the initial phase function numerical sequence, an exponential parameter is introduced to construct a single-parameter phase function based on a quadratic function. The single-parameter phase function is as follows: Among them, is an exponential parameter, is the minimum value of the numerical sequence of the initial phase function.

6. The NLFM waveform design method based on a single-parameter phase function according to claim 5, wherein The steps of designing an optimization function with the goal of minimizing the highest sidelobe level while constraining the mainlobe width include: generating an initial NLFM waveform based on an initial value of an exponential parameter, a sampling rate, and a desired bandwidth and pulse width of the NLFM waveform; Perform pulse compression on the initial NLFM waveform and calculate the maximum sidelobe level and main lobe width of the pulse compression result; Design an optimization function based on the maximum sidelobe level and main lobe width.

7. The NLFM waveform design method based on a single-parameter phase function according to claim 6, wherein The optimization function is as follows: wherein, is an adjustable parameter, means taking and the larger value of the two, is the highest sidelobe level, is the main lobe width.

8. The NLFM waveform design method based on a single-parameter phase function according to claim 7, wherein Based on the optimization function, the genetic algorithm is used to optimize the exponential parameter in the single-parameter phase function. The steps of obtaining the optimal parameter include: Substitute the highest sidelobe level and mainlobe width calculated based on the initial NLFM waveform into the optimization function; The optimization function is used as the fitness function of the genetic algorithm. The parameters are updated iteratively through selection, crossover and mutation to optimize the exponential parameters and return the optimal parameters that minimize the fitness function.

9. The NLFM waveform design method based on a single-parameter phase function according to claim 8, characterized in that, The method further comprises: The obtained NLFM waveform is applied in the radar system.

10. An NLFM waveform design device based on a single-parameter phase function, characterized in that, It includes a function value calculation module, a phase function construction module, an optimization function design module, a parameter optimization module and a waveform generation module; A function value calculation module is used to perform a window function inverse method to calculate the minimum value of the initial phase function numerical sequence; A phase function construction module is used to introduce an exponential parameter based on the minimum value of the initial phase function numerical sequence to construct a single-parameter phase function based on a quadratic function; An optimization function design module, used to design an optimization function with the goal of minimizing the highest sidelobe level while constraining the main lobe width; The parameter optimization module configures the genetic algorithm optimizer to optimize the exponential parameters in the single-parameter phase function to obtain the optimal parameters; A waveform generation module for generating an NLFM signal according to optimal parameters.

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