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

Abstract

The present application relates to the field of radar waveform design technology, and specifically to a NLFM waveform design method and device based on a single-parameter phase function. The method comprises the following steps: using a window function inverse method to obtain the minimum value of an initial phase function numerical sequence; introducing 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; designing an optimization function that minimizes the maximum sidelobe level while constraining the mainlobe width; based on the optimization function, using a genetic algorithm to optimize the exponential parameter in the single-parameter phase function to obtain the optimal parameter; substituting the optimal parameter into the single-parameter phase function to generate an NLFM waveform. The method can effectively reduce the sidelobe level of the waveform while reasonably constraining the mainlobe width. Compared with traditional waveform design methods, the method can improve waveform performance, reduce signal interference, and enhance the resolution and detection capability of signals in radar and other application scenarios.

Description

Technical Field

[0001] The present application relates to the technical field of radar waveform design, and in particular to a NLFM waveform design method and device based on a single-parameter phase function. Background Art

[0002] In the field of radar signal processing, waveform design is a crucial research topic, directly impacting radar system performance. In real-world radar detection environments, strong clutter and target interference energy often exist in adjacent range cells, severely impacting the radar's ability to accurately acquire and process target information. Low-sidelobe waveforms effectively suppress this interference energy and reduce sidelobe levels, significantly improving the radar's target detection capability, resolution, and anti-interference performance, ensuring stable and reliable operation in complex electromagnetic environments.

[0003] Currently, methods for designing nonlinear frequency modulation (NLFM) waveforms primarily include parametric frequency modulation, parametric phase function construction, and phase dwell methods based on frequency-domain window functions. The performance of the parametric phase function construction method is highly dependent on the construction of the parametric phase function, making the construction of a high-performance parametric phase function a key issue.

[0004] Currently, commonly used methods for constructing parameterized phase functions include polynomial phase encoding and random phase perturbation. Polynomial phase encoding faces difficulties in optimizing parameters to balance the mainlobe width and sidelobe level, making it difficult to simultaneously achieve the desired effects of low sidelobes and a narrow mainlobe. While NLFM waveforms designed using random phase perturbation can meet certain specific requirements to a certain extent, they have low Doppler tolerance. In the presence of Doppler shifts on targets, the waveform's performance degrades significantly, impacting the radar's ability to detect high-speed moving targets. Summary of the Invention

[0005] Aiming at the problem of low sidelobe NLFM waveform design, a low sidelobe NLFM waveform design method based on the single-parameter phase function construction method is proposed. This method can better balance the mainlobe width and sidelobe level. While the mainlobe and sidelobe performance are better than the NLFM waveform designed by the existing method, it also has good Doppler tolerance.

[0006] In a first aspect, the technical solution of the present invention provides a NLFM waveform design method based on a single-parameter phase function, comprising the following steps:

[0007] The minimum value of the initial phase function numerical sequence is obtained by using the window function inverse method;

[0008] 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.

[0009] Design an optimization function that minimizes the maximum sidelobe level while constraining the mainlobe width;

[0010] 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;

[0011] Substituting the optimal parameters into the single-parameter phase function, an NLFM waveform is generated.

[0012] By combining a window function inversion method with a single-parameter phase function construction method using an exponential parameter, and optimizing the exponential parameter using a genetic algorithm, a low-sidelobe NLFM waveform can be designed. This method comprehensively considers the waveform's sidelobe level and mainlobe width, effectively improving the radar system's anti-interference capability and target detection performance.

[0013] As a further limitation of the technical solution of the present invention, the step of obtaining the minimum value of the initial phase function numerical sequence by using the window function inverse method includes:

[0014] The Hamming window is used as the frequency domain window function, and the phase dwell method is used to derive the group delay function;

[0015] Based on the sampling rate and pulse width, the frequency points of the group delay function are discretized to obtain a sequence of the group delay function;

[0016] The 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.

[0017] Using a Hamming window as the frequency-domain window function and combining it with the phase dwell method to derive the group delay function more accurately describes the frequency-domain characteristics of the waveform. The numerical sequence of the initial phase function, obtained through cubic spline fitting and integration, provides a reliable foundation for the subsequent construction of a single-parameter phase function, helping to generate NLFM waveforms with better performance.

[0018] As a further limitation of the technical solution of the present invention, the step of discretizing the frequency points based on the sampling rate and the pulse width to obtain a sequence of group delay functions includes:

[0019] Calculate the number of sampling points within the pulse width based on the sampling rate and pulse width ;

[0020] Discretize the independent variable of the group delay function into frequency points;

[0021] Substituting the discretized frequency value into the group delay function, a sequence of group delay functions is obtained.

[0022] Discretizing the frequency points based on the sampling rate and pulse width allows for a more precise sequence of group delay functions, which in turn more accurately describes the waveform's time-frequency characteristics. This facilitates the calculation of the initial phase function and the construction of a single-parameter phase function in subsequent steps, improving the accuracy of NLFM waveform generation.

[0023] As a further limitation of the technical solution of the present invention, the group delay function is as follows:

[0024]

[0025] in, Therefore is the group delay function of the independent variable, is the bandwidth of the NLFM waveform, the independent variable The value range is , is the pulse width.

[0026] A specific expression for the group delay function is given, clarifying the relationship between its independent and dependent variables, as well as the 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 subsequent steps, facilitating the precise design of the NLFM waveform.

[0027] As a further limitation of the technical solution of the present invention, 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:

[0028]

[0029] in, is the exponential parameter, is the minimum value of the initial phase function numerical sequence.

[0030] By introducing an exponential parameter and the minimum value of the initial phase function numerical sequence, 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 mainlobe width, and helps to generate NLFM waveforms that meet specific performance requirements.

[0031] As a further limitation of the technical solution of the present invention, the step of designing an optimization function with the goal of minimizing the maximum sidelobe level while constraining the mainlobe width includes:

[0032] 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;

[0033] Perform pulse compression on the initial NLFM waveform and calculate the maximum sidelobe level and mainlobe width of the pulse compression result;

[0034] Design an optimization function based on the maximum sidelobe level and mainlobe width.

[0035] By generating an initial NLFM waveform and performing pulse compression, we can calculate the waveform's maximum sidelobe level and mainlobe width. Designing an optimization function based on these parameters can more accurately describe the waveform's performance indicators, providing a clear objective function for subsequent parameter optimization and helping to improve the quality of NLFM waveform generation.

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

[0037]

[0038] in, is an adjustable parameter, Indicates taking and The greater of the two, is the highest sidelobe level, is the main lobe width, is the required bandwidth of the NLFM waveform.

[0039] The specific expression of the optimization function is given, clarifying its variables such as adjustable parameters, maximum sidelobe level, mainlobe width, and required bandwidth. This optimization function comprehensively considers multiple waveform performance indicators and helps generate NLFM waveforms with better performance by minimizing the maximum sidelobe level while constraining the mainlobe width.

[0040] As a further limitation of the technical solution of the present invention, based on the optimization function, the step of optimizing the exponential parameter in the single-parameter phase function using a genetic algorithm to obtain the optimal parameter includes:

[0041] Substitute the highest sidelobe level and mainlobe width calculated based on the initial NLFM waveform into the optimization function;

[0042] 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.

[0043] By substituting the maximum sidelobe level and mainlobe width calculated based on the initial NLFM waveform into the optimization function and optimizing the exponential parameters using a genetic algorithm, the optimal parameters that minimize the fitness function can be found. This method automatically searches for the optimal solution, improving the efficiency and accuracy of parameter optimization and helping to generate NLFM waveforms that meet specific performance requirements.

[0044] As a further limitation of the technical solution of the present invention, the method further includes:

[0045] The obtained NLFM waveform is applied to the radar system.

[0046] Applying the resulting NLFM waveform to a radar system can directly improve the system's anti-interference capabilities and target detection performance. The low-sidelobe NLFM waveform helps reduce sidelobe interference, improving the radar's target resolution and detection accuracy, thereby enhancing the radar system's overall performance.

[0047] In a second aspect, the technical solution of the present invention further provides an NLFM waveform design device based on a single-parameter phase function, comprising a function value calculation module, a phase function construction module, an optimization function design module, a parameter optimization module, and a waveform generation module;

[0048] 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;

[0049] 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;

[0050] An optimization function design module is used to design an optimization function that aims to minimize the maximum sidelobe level while constraining the mainlobe width;

[0051] 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;

[0052] The waveform generation module is used to generate the NLFM signal according to the optimal parameters.

[0053] By designing a low-sidelobe NLFM waveform design device based on a single-parameter phase function, each step is modularized to achieve automated and intelligent 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. These modules work together to efficiently generate NLFM waveforms that meet specific performance requirements, improving the efficiency and accuracy of waveform design.

[0054] 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;

[0055] A group delay function derivation unit configures a Hamming window as a frequency domain window function and uses a phase dwell method to derive the group delay function;

[0056] A 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 a sequence of the group delay function;

[0057] 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.

[0058] 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.

[0059] As a further limitation of the technical solution of the present invention, the group delay function is as follows:

[0060]

[0061] in, Therefore is the group delay function of the independent variable, is the bandwidth of the NLFM waveform, the independent variable The value range is , is the pulse width.

[0062] As a further limitation of the technical solution of the present invention, the single-parameter phase function is as follows:

[0063]

[0064] in, is the exponential parameter, is the minimum value of the initial phase function numerical sequence.

[0065] 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;

[0066] an initial waveform generating unit for generating an initial NLFM waveform based on an initial value of the exponential parameter, a sampling rate, and a desired bandwidth and pulse width of the NLFM waveform;

[0067] a calculation unit, configured to perform pulse compression on the initial NLFM waveform and calculate a maximum sidelobe level and a mainlobe width of the pulse compression result;

[0068] The optimization function design unit is used to design an optimization function according to the maximum sidelobe level and the mainlobe width.

[0069] As a further limitation of the technical solution of the present invention, the optimization function is as follows:

[0070]

[0071] in, is an adjustable parameter, Indicates taking and The greater of the two, is the highest sidelobe level, is the main lobe width, is the required bandwidth of the NLFM waveform.

[0072] As a further limitation of the technical solution of the present invention, the parameter optimization module is specifically used to substitute the maximum sidelobe level and mainlobe width calculated based on the initial NLFM waveform into the optimization function; using the optimization function as the fitness function of the genetic algorithm, iteratively updating the parameters through selection, crossover and mutation, optimizing the exponential parameters, and returning the optimal parameters that minimize the fitness function.

[0073] As a further limitation of the technical solution of the present invention, the device also 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 units.

[0074] The above technical solution demonstrates the following advantages: By employing a 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 combined with a genetic algorithm for optimization, the NLFM waveform is finally generated. This process systematically combines multiple technical approaches to effectively reduce the waveform's sidelobe level while reasonably constraining the mainlobe width. Compared to traditional waveform design methods, this approach improves waveform performance, reduces signal interference, and enhances signal resolution and detection capabilities in applications such as radar. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] In order to more clearly illustrate the technical solution of the present application, the following is a brief introduction to the drawings required for the description. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0076] Figure 1 A flowchart of a method provided in an embodiment of the present invention.

[0077] Figure 2 A schematic diagram of a design method for a method provided in an embodiment of the present invention.

[0078] Figure 3The comparison chart of the windowed pulse compression output results of LFM waveform, NLFM0 waveform and NLFM1 waveform under no Doppler condition, where: Figure 3 (a) is the LFM waveform pulse pressure result, Figure 3 (b) is the NLFM0 waveform pulse pressure result. Figure 3 (c) is the NLFM1 waveform pulse pressure result. Figure 3 (d) is a comparison of the locally enlarged images of the pulse pressure results of the three waveforms.

[0079] Figure 4 The figure compares the windowed pulse pressure output of the NLFM1 waveform with and without target Doppler.

[0080] Figure 5 A block diagram of a device provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0081] The present invention provides a new low-sidelobe NLFM waveform design method, which combines the phase residence method based on the frequency domain window function and the parameterized phase function construction method. Starting from the inverse of the window function, mathematical fitting is used to construct a nonlinear single-parameter phase function, and an optimization function is designed with the goal of "minimizing the maximum sidelobe level while constraining the main lobe width". A genetic algorithm is used to optimize the parameters, and a NLFM waveform with low sidelobe performance and meeting the constraints is obtained. In order to make the purpose, features, and advantages of the present application more obvious and easy to understand, the technical solution protected by the present application will be clearly and completely described using specific embodiments and drawings. Obviously, the embodiments described below are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present application.

[0082] The purpose of the present invention is to provide a low sidelobe NLFM waveform design method based on a single-parameter phase function construction method to address the problem of low sidelobe NLFM waveform design. This method can better balance the mainlobe width and sidelobe level, and while the mainlobe and sidelobe performance are better than those of NLFM waveforms designed by existing methods, it also has better Doppler tolerance. Figure 1 As shown, an embodiment of the present invention provides a NLFM waveform design method based on a single-parameter phase function, comprising the following steps:

[0083] S1. Using the window function inverse method, obtain the minimum value of the initial phase function numerical sequence; specifically including:

[0084] S11. Use Hamming window as the frequency domain window function and use phase dwell method to derive group delay function;

[0085] The group delay function is as follows:

[0086]

[0087] in, Therefore is the group delay function of the independent variable, is the bandwidth of the NLFM waveform, the independent variable The value range is , is the pulse width.

[0088] S12. Calculate the number of sampling points within the pulse width based on the sampling rate and pulse width. ;

[0089]

[0090] Where, is the sampling rate.

[0091] S13. Discretize the independent variable of the group delay function into frequency points; among them, the interval between frequency points .

[0092] S14. Substitute the discretized frequency value into the group delay function to obtain a sequence of group delay functions.

[0093] S15. Using a cubic spline fitting method, a function with time as the independent variable and frequency as the dependent variable is obtained, and the function is integrated to obtain a numerical sequence of the initial phase function, thereby obtaining the minimum value of the numerical sequence of the initial phase function.

[0094] The frequency f Discretized into N points, the frequency point range is [− B / 2, B / 2]. Therefore, the discretized frequency points It can be expressed as:

[0095]

[0096] The discretized frequency points Substituting into the group delay function In the equation, we get the sequence of group delay functions :

[0097]

[0098] Using the cubic spline fitting method, the discrete group delay function Fitting to a continuous function ,int is a time variable. The specific steps are as follows:

[0099] Time t Divided into N nodes, and the node time interval is:

[0100]

[0101] Node Time for: ;

[0102] For each interval , construct a cubic polynomial , such that:

[0103]

[0104] And the continuity conditions of the first and second order derivatives are satisfied at the nodes.

[0105] By solving the tridiagonal linear equations, the cubic polynomial coefficients in each interval are obtained.

[0106] For spline functions Integrate to obtain the initial phase function. You can use numerical integration methods, such as the trapezoidal rule or Simpson's rule, to calculate each time point The phase values ​​at all time points are combined into a numerical sequence, and the minimum value of the sequence is calculated.

[0107] A Hamming window is used as the frequency domain window function, and the phase dwell method is used to derive the group delay function. A combination of cubic spline fitting and integration operations is used to obtain the minimum value of the initial phase function numerical sequence. This approach leverages the Hamming window's sidelobe suppression properties. Through rigorous mathematical derivation and processing, key information about the initial phase function can be accurately obtained, laying a solid foundation for subsequent phase function construction and enabling the subsequent waveform generation to have greater performance optimization potential.

[0108] The frequency points are discretized according to the sampling rate and pulse width, and the continuous group delay function is scientifically converted into a discrete sequence, which meets the requirements of digital signal processing and facilitates subsequent calculations and processing in digital systems such as computers. It ensures the accuracy and efficiency of signal processing, avoids signal distortion or error accumulation caused by unreasonable discretization, and helps to improve the reliability of waveform design.

[0109] 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;

[0110] The single-parameter phase function is as follows:

[0111]

[0112] in, is the exponential parameter, is the minimum value of the initial phase function numerical sequence.

[0113] A single-parameter phase function is constructed based on the minimum value of the initial phase function numerical sequence. The phase function is linked to waveform performance optimization by introducing an exponential parameter. This concise and reasonable function construction method allows for subsequent waveform optimization by adjusting the exponential parameter, providing a flexible adjustment method for waveform design and adapting to the waveform performance requirements of different application scenarios.

[0114] S3. Design an optimization function that minimizes the maximum sidelobe level while constraining the mainlobe width; specifically, the following steps are involved:

[0115] S31, 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;

[0116] S32, performing pulse compression on the initial NLFM waveform, and calculating the maximum sidelobe level and mainlobe width of the pulse compression result;

[0117] S33. Design an optimization function based on the maximum sidelobe level and the mainlobe width.

[0118] The optimization function is as follows:

[0119]

[0120] in, is an adjustable parameter, Indicates taking and The greater of the two, is the highest sidelobe level, is the main lobe width, is the NLFM waveform bandwidth.

[0121] By generating an initial NLFM waveform, performing pulse compression, and calculating relevant performance indicators, an optimization function is designed. This process closely integrates the actual performance of the waveform with the optimization goal. The optimization direction is designed based on the actual waveform effect, allowing the optimization function to more accurately reflect the waveform performance requirements. This provides a more realistic objective function for subsequent parameter optimization, improving optimization efficiency and waveform optimization quality.

[0122] S4. Based on the optimization function, a genetic algorithm is used to optimize the exponential parameter in the single-parameter phase function to obtain the optimal parameter; specifically, the following steps are included:

[0123] S41, substituting the highest sidelobe level and mainlobe width calculated based on the initial NLFM waveform into the optimization function;

[0124] S42: Using the optimization function as the fitness function of the genetic algorithm, iteratively update the parameters through selection, crossover, and mutation, optimize the exponential parameters, and return the optimal parameters that minimize the fitness function. The specific steps are as follows:

[0125] Initialize the population:

[0126] Determine index parameters The value range of , for example [0.1,1].

[0127] Randomly generate a set of parameters The initial value of , each parameter value is called an "individual". Population size P Usually chosen based on the problem size, e.g. P =50 or P =100.

[0128] Fitness function calculation:

[0129] The optimization function is used to evaluate the fitness of each individual. According to the problem description, the optimization function is:

[0130] For each individual in the population , calculate the corresponding NLFM waveform's highest sidelobe level and mainlobe width, and substitute them into the optimization function to calculate the fitness .

[0131] According to the fitness function value, the probability of each individual being selected is calculated. The lower the fitness (the smaller the optimization function value), the higher the probability of the individual being selected.

[0132] Calculate the fitness ratio of each individual:

[0133]

[0134] According to probability Randomly select individuals to generate a new population.

[0135] Randomly select two parent individuals and , at a random point k They exchange some of their genes to produce two offspring individuals.

[0136] The newly generated offspring individuals are randomly mutated, and the genes of the individuals are randomly changed with a certain probability (for example, 0.01).

[0137] Replace some or all individuals in the population with newly generated offspring individuals.

[0138] Repeat the fitness calculation, selection, crossover and mutation operations until the termination condition is met (for example, the maximum number of iterations is reached or the fitness no longer improves significantly). In the final population, the individual with the smallest fitness is selected as the optimal parameter.

[0139] Using the optimization function as the fitness function of the genetic algorithm to optimize the exponential parameters, this approach leverages the genetic algorithm's strengths in global optimization and can quickly find the exponential parameter values ​​that optimize waveform performance within a large parameter space. Compared to traditional optimization methods, the genetic algorithm's iterative update mechanism avoids falling into local optimal solutions, improving the accuracy and reliability of the optimization process and ultimately resulting in a more optimal NLFM waveform.

[0140] S5. Substitute the optimal parameters into a single-parameter phase function to generate an NLFM waveform.

[0141] By combining a window function inversion method with a single-parameter phase function construction method using an exponential parameter, and optimizing the exponential parameter using a genetic algorithm, a low-sidelobe NLFM waveform can be designed. This method comprehensively considers the waveform's sidelobe level and mainlobe width, effectively improving the radar system's anti-interference capability and target detection performance.

[0142] In some embodiments, the method further comprises:

[0143] The obtained NLFM waveform is applied to the radar system.

[0144] The designed NLFM waveform is applied to a radar system, fully leveraging the advantages of the low-sidelobe NLFM waveform in radar detection. This low-sidelobe characteristic reduces sidelobe interference in target echo signals, improving the radar's target resolution and detection probability, and enhancing the radar system's anti-interference capability and operational stability, thereby improving the radar system's overall performance and application value.

[0145] Refer to the attached Figure 2 The specific implementation of the method provided by the present invention is divided into the following steps:

[0146] (1) Using the window function inverse method, the minimum value of the initial phase function numerical sequence is obtained;

[0147] (2) Introducing exponential parameters to construct a new single-parameter phase function based on quadratic functions;

[0148] (3) Design an optimization function with the goal of “minimizing the maximum sidelobe level while constraining the mainlobe width”, and use genetic algorithm to optimize the parameters to obtain the optimal parameters, and then generate the NLFM waveform.

[0149] The following is a detailed explanation of the above steps:

[0150] When designing NLFM waveform, the NLFM waveform parameters determined by the system include pulse width ,bandwidth and sampling rate ; The NLFM waveform to be designed is recorded as ,in is the phase function to be designed, the time variable The value range is , is the pulse width of the waveform;

[0151] (1) Using the window function inverse method, the minimum value of the initial phase function numerical sequence is obtained;

[0152] First, the Hamming window is used as the frequency domain window function, and the phase dwell method is used to derive its group delay function.

[0153]

[0154] in, Therefore The group delay function of the independent variable , is the bandwidth of the NLFM waveform, the independent variable The value range is ;

[0155] Then, based on the sampling rate and pulse width The number of sampling points in the pulse obtained , the independent variable Discretized into frequency points, the discreteness is ;Will Substitute the discrete values ​​of The sequence of group delay functions is obtained from the function; the time-dependent As the independent variable, with frequency is a function of the dependent variable ,in The discreteness is ;

[0156] Finally, yes Perform integration operation to obtain the numerical sequence of the initial phase function , , Calculate as follows The minimum value of ,

[0157]

[0158] (2) Introducing exponential parameters to construct a new single-parameter phase function based on quadratic functions;

[0159] Introducing the exponential parameter, construct the single-parameter phase function as shown below:

[0160]

[0161] in is the exponential parameter to be optimized, which controls the steepness of the frequency change. The optimal interval is ;set up Initial value of .

[0162] (3) Design an optimization function with the goal of "minimizing the maximum sidelobe level while constraining the mainlobe width" and use genetic algorithm to optimize the parameters to obtain the optimal parameters , and then generate NLFM waveform;

[0163] Step 3.1, calculate the maximum sidelobe level and main lobe width

[0164] The initial phase function parameters And the waveform parameters determined by the system 、 and Import the genetic algorithm to generate NLFM waveform, perform pulse compression, and calculate the maximum sidelobe level , calculate the main lobe width The order of implementation is as follows, and we get and The value of Indicates the main lobe width corresponding to the pulse compression output result at -4dB;

[0165] Step 3.2, design optimization function

[0166] To achieve low sidelobes, the goal must be to minimize the maximum sidelobe level of the pulse compression output. At the same time, in order to ensure the range resolution of the pulse compression output, the mainlobe width is increased as a penalty term. As the reference value of the main lobe width; considering the above conditions, the design optimization function is:

[0167]

[0168] in, It is an adjustable parameter with a value of 10 3 Magnitude; Indicates taking and the greater of the two;

[0169] Step 3.3: Genetic algorithm optimization to generate optimized NLFM waveform

[0170] The result obtained in step 3.1 and The value is substituted into the optimization function, and the optimization function is used as the fitness function of the genetic algorithm. Optimize and get the optimal parameters , and then construct the phase function to generate the NLFM waveform .

[0171] The following is a design case. The waveform parameters determined by the system are 、 and ; Obtained from step (1) ; The NLFM waveform obtained from step (3) is as follows:

[0172] , ,

[0173] A scenario was designed that included two targets, one large and one small, and a noisy background. The amplitudes of the two targets were 1000 and 1, respectively, with a difference of 60 dB.

[0174] Figure 3 The LFM waveform without Doppler is given ( Figure 3 (a) is marked as LFM waveform), NLFM waveform obtained by phase dwell method based on frequency domain window function ( Figure 3 (b) is marked as NLFM0 waveform) and the NLFM waveform obtained by the present invention ( Figure 3 (c) is the NLFM1 waveform) in the windowed pulse compression output comparison chart. Figure 3 (d) A comparison of the pulse compression results for the three waveforms is shown in a zoomed-in image. The NLFM1 waveform has significantly lower pulse compression sidelobes than the LFM and NLFM0 waveforms, and its improvement at small targets is also significantly better than the other two waveforms. Furthermore, with windowed pulse compression, the range resolution achieved with the LFM waveform is 7.5 meters, the NLFM0 waveform is 12 meters, and the NLFM1 waveform is 13.5 meters.

[0175] Figure 4This is a comparison chart of the windowed pulse compression output results of the NLFM1 waveform under two conditions: with and without target Doppler. The black line shows the situation where the main lobe of the pulse compression output of the NLFM1 waveform obtained by the present invention has just been deformed under the conditions of a target speed of 200 m / s and a waveform carrier frequency of 9.5 GHz. The red line shows the pulse compression output result of the NLFM1 waveform under the condition of no target Doppler, which shows that the Doppler tolerance of the NLFM1 waveform is about 200 m / s.

[0176] like Figure 5 As shown, an embodiment of the present invention further provides an NLFM waveform design device based on a single-parameter phase function, comprising a function value calculation module, a phase function construction module, an optimization function design module, a parameter optimization module, and a waveform generation module;

[0177] 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;

[0178] 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;

[0179] An optimization function design module is used to design an optimization function that aims to minimize the maximum sidelobe level while constraining the mainlobe width;

[0180] 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;

[0181] The waveform generation module is used to generate the NLFM signal according to the optimal parameters.

[0182] By designing a NLFM waveform design device based on a single-parameter phase function, each step is modularized to achieve automated and intelligent 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. These modules work together to efficiently generate NLFM waveforms that meet specific performance requirements, improving the efficiency and accuracy of waveform design.

[0183] 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;

[0184] A group delay function derivation unit configures a Hamming window as a frequency domain window function and uses a phase dwell method to derive the group delay function;

[0185] A 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 a sequence of the group delay function;

[0186] 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.

[0187] In some embodiments, the group delay function sequence acquisition unit is specifically configured 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.

[0188] As a further limitation of the technical solution of the present invention, the group delay function is as follows:

[0189]

[0190] in, Therefore is the group delay function of the independent variable, is the bandwidth of the NLFM waveform, the independent variable The value range is , is the pulse width.

[0191] The single-parameter phase function is as follows:

[0192]

[0193] in, is the exponential parameter, is the minimum value of the initial phase function numerical sequence.

[0194] In some embodiments, the optimization function design module includes an initial waveform generation unit, a calculation unit, and an optimization function design unit;

[0195] an initial waveform generating unit for generating an initial NLFM waveform based on an initial value of the exponential parameter, a sampling rate, and a desired bandwidth and pulse width of the NLFM waveform;

[0196] a calculation unit, configured to perform pulse compression on the initial NLFM waveform and calculate a maximum sidelobe level and a mainlobe width of the pulse compression result;

[0197] The optimization function design unit is used to design an optimization function according to the maximum sidelobe level and the mainlobe width.

[0198] The optimization function is as follows:

[0199]

[0200] in, is an adjustable parameter, Indicates taking and The greater of the two, is the highest sidelobe level, is the main lobe width, is the required bandwidth of the NLFM waveform.

[0201] In some embodiments, the parameter optimization module is specifically used to substitute the maximum sidelobe level and mainlobe width calculated based on the initial NLFM waveform into the optimization function; use the optimization function as the fitness function of the genetic algorithm, update the parameters through selection, crossover and mutation iteratively, optimize the exponential parameters, and return the optimal parameters that minimize the fitness function.

[0202] In some embodiments, the apparatus further includes an application module configured to apply the obtained low sidelobe NLFM waveform to a radar system to suppress strong clutter and strong target interference energy from adjacent range cells.

[0203] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention is not limited to the embodiments shown herein but is intended to conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A NLFM waveform design method 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. in, is the exponential parameter, is the minimum value of the initial phase function numerical sequence; Design an optimization function that minimizes the maximum 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 a single-parameter phase function to generate an NLFM waveform; The steps for designing an optimization function that minimizes the maximum 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 mainlobe width of the pulse compression result; Design an optimization function based on the maximum sidelobe level and mainlobe width; The optimization function is as follows: in, is an adjustable parameter, Indicates taking and The greater of the two, is the highest sidelobe level, The width of the main lobe.

2. The NLFM waveform design method based on a single-parameter phase function according to claim 1, characterized in that: 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 phase dwell method is used to derive the group delay function; Based on the sampling rate and pulse width, the frequency points of the group delay function are discretized to obtain a sequence of the group delay function; The 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, characterized in that: The steps of discretizing the frequency points based on the sampling rate and 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 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 group delay functions is obtained.

4. The NLFM waveform design method based on a single-parameter phase function according to claim 3, characterized in that: The group delay function is as follows: in, Therefore is the group delay function of the independent variable, is the bandwidth of the NLFM waveform, the independent variable The value range is , 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 optimization function, the genetic algorithm is used to optimize the exponential parameter in the single-parameter phase function. The steps to obtain 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.

6. The NLFM waveform design method based on a single-parameter phase function according to claim 5, characterized in that: The method further comprises: The obtained NLFM waveform is applied to the radar system.

7. A NLFM waveform design device based on a single-parameter phase function, characterized in that: It includes function value calculation module, phase function construction module, optimization function design module, parameter optimization module and 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; in, is the exponential parameter, is the minimum value of the initial phase function numerical sequence; The optimization function design module is used to design an optimization function that aims to minimize the maximum sidelobe level while constraining the mainlobe width. Specifically, it 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; perform pulse compression on the initial NLFM waveform, and calculate the maximum sidelobe level and mainlobe width of the pulse compression result; and design an optimization function based on the maximum sidelobe level and mainlobe width. The optimization function is as follows: in, is an adjustable parameter, Indicates taking and The greater of the two, is the highest sidelobe level, is 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.

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