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

Abstract

The present application relates to the field of radar waveform design, and specifically to a NLFM waveform design method and device based on a dual-parameter phase function. The method comprises: introducing a bandwidth control parameter and an exponential parameter to construct a dual-parameter phase function based on a quadratic function; designing an optimization function with the goal of minimizing the maximum sidelobe level while constraining the mainlobe width and signal bandwidth; optimizing the bandwidth control parameter and the exponential parameter in the dual-parameter phase function using a genetic algorithm to obtain an optimal parameter set; substituting the optimal parameter set into the dual-parameter phase function to generate a low-sidelobe NLFM waveform. By constructing a dual-parameter phase function and designing an optimization function with the goal of minimizing the maximum sidelobe level, waveform performance can be effectively balanced; optimizing using a genetic algorithm to generate an NLFM waveform that meets the requirements. This method helps to obtain a waveform with good performance in a radar system, reduce the sidelobe level, and improve the target detection and resolution capabilities of the radar system.

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 dual-parameter phase function. Background Art

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

[0003] Traditional methods for designing nonlinear frequency modulation (NLFM) waveforms include parametric frequency modulation, parametric phase function construction, and phase dwell methods based on frequency-domain window functions. Parametric frequency modulation is relatively intuitive and easy to implement, but high-order parameter optimization is complex and can only meet the design requirements of simple NLFM. The phase dwell method based on frequency-domain window functions can only approximately solve the inverse function of the group delay function, resulting in high sidelobes in the resulting NLFM waveform. Parametric phase function construction methods offer greater flexibility and can approach global optimization, but the key lies in constructing a high-performance parametric phase function. Common parametric phase function construction methods include polynomial phase encoding and random phase perturbation. The former presents difficulties in optimizing parameters to balance mainlobe width and sidelobe level, while the latter results in NLFM waveforms with low Doppler tolerance.

[0004] In view of this, it is necessary to design a low sidelobe NLFM waveform design method based on a dual-parameter phase function, which can better balance the mainlobe width and sidelobe level. While the mainlobe and sidelobe performance are better than the existing methods and the set signal bandwidth is maintained, it also has good Doppler tolerance. Summary of the Invention

[0005] The purpose of the present invention is to provide a low sidelobe NLFM waveform design method based on a dual-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 has better mainlobe and sidelobe performance than existing methods while maintaining the set signal bandwidth and having good Doppler tolerance.

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

[0007] The bandwidth control parameter and exponential parameter are introduced to construct a two-parameter phase function based on the quadratic function.

[0008] Design an optimization function with the goal of minimizing the maximum sidelobe level while constraining the mainlobe width and signal bandwidth;

[0009] Based on the optimization function, the genetic algorithm is used to optimize the bandwidth control parameters and exponential parameters in the dual-parameter phase function to obtain the optimal parameter group;

[0010] Substituting the optimal parameter set into the two-parameter phase function, a low-sidelobe NLFM waveform is generated.

[0011] As a further limitation of the technical solution of the present invention, a bandwidth control parameter and an exponential parameter are introduced to construct a dual-parameter phase function based on a quadratic function. The dual-parameter phase function is as follows:

[0012]

[0013] Where, is the bandwidth control parameter, is the exponential parameter.

[0014] The specific expression of the two-parameter phase function based on the quadratic function gives the function a precise mathematical definition, providing a clear basis for subsequent waveform design and performance analysis based on this function, ensuring the accuracy and consistency of the design process, and helping to accurately understand and apply this phase function for low-sidelobe NLFM waveform design.

[0015] 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 maximum sidelobe level while constraining the mainlobe width and signal bandwidth include:

[0016] generating an NLFM waveform based on initial values ​​of a bandwidth control parameter and an exponential parameter;

[0017] Perform pulse compression on the generated NLFM waveform and calculate the maximum sidelobe level and mainlobe width of the pulse compression result;

[0018] Perform FFT transformation on the generated NLFM waveform to calculate the actual bandwidth of the signal;

[0019] Design an optimization function based on the maximum sidelobe level, mainlobe width and actual signal bandwidth.

[0020] By first generating a waveform based on initial parameter values, then performing pulse compression and FFT transforms to calculate relevant performance indicators, and finally designing an optimization function based on these indicators, the construction process of the optimization function is scientific, rational, and highly operational. This approach of constructing the optimization function based on actual waveform performance indicators ensures that the optimization function truly reflects the actual waveform requirements, thereby more effectively guiding the parameter optimization process and improving the quality of waveform design.

[0021] As a further limitation of the technical solution of the present invention, the formula for calculating the maximum sidelobe level and the mainlobe width is as follows:

[0022]

[0023] in Indicates the main lobe peak, interval The main lobe protection range is ; is the highest sidelobe level, is the main lobe width, is the pulse compression result.

[0024] Specific formulas for calculating the maximum sidelobe level and mainlobe width are provided, providing clear standards and methods for calculating these two key performance indicators, avoiding ambiguity and arbitrariness. During the waveform design process, these precise calculation methods enable more accurate assessment of waveform performance, allowing parameters to be adjusted through optimization functions to achieve precise optimization of waveform performance.

[0025] As a further limitation of the technical solution of the present invention, the step of performing FFT transformation on the generated NLFM waveform to calculate the actual bandwidth of the signal includes:

[0026] Perform FFT transformation on the NLFM waveform to find the location of the spectrum peak;

[0027] Extend from the spectrum peak to both sides until the spectrum power drops to the set percentage of the peak, and obtain two points;

[0028] Get the frequency range between the two points, which is the actual bandwidth of the signal.

[0029] By performing an FFT transform on the NLFM waveform and determining the bandwidth based on its spectral power characteristics, this method provides a reliable method for accurately determining the signal bandwidth. Accurate bandwidth calculation is crucial for properly constraining the signal bandwidth when designing optimization functions. This helps ensure that the designed waveform meets both performance requirements and bandwidth constraints, thus improving the practicality of waveform design.

[0030] As a further limitation of the technical solution of the present invention, the optimization function is as follows:

[0031]

[0032] The calculation formula is:

[0033] in, and These are penalty coefficients. Indicates taking and the greater of the two; is the highest sidelobe level, is the main lobe width, and B is the bandwidth required by the design.

[0034] This optimization function comprehensively considers key factors such as maximum sidelobe level, mainlobe width, and signal bandwidth, and uses a penalty coefficient to penalize situations where constraints are not met, enabling the optimization function to comprehensively and effectively balance all aspects of waveform performance. During the genetic algorithm optimization process, this optimization function guides the algorithm toward the direction that meets the requirements of low sidelobe, appropriate mainlobe width, and bandwidth, improving the accuracy and effectiveness of the optimization.

[0035] As a further limitation of the technical solution of the present invention, the steps of optimizing the bandwidth control parameter and the exponential parameter in the dual-parameter phase function using a genetic algorithm to obtain the optimal parameter set include:

[0036] Substitute the calculated values ​​of the highest sidelobe level and mainlobe width and the actual bandwidth of the signal into the optimization function, use the optimization function as the fitness function of the genetic algorithm, optimize the bandwidth control parameters and exponential parameters, and obtain the optimal bandwidth control parameters and the optimal index parameter .

[0037] As a further limitation of the technical solution of the present invention, in the step of substituting the optimal parameter group into the dual-parameter phase function to generate a low-sidelobe NLFM waveform, the generated low-sidelobe NLFM waveform is:

[0038]

[0039] Where, is the optimal bandwidth control parameter, is the optimal index parameter.

[0040] The optimal parameter group is substituted into the two-parameter phase function to generate the specific form of the NLFM waveform, so that the generated waveform has a clear mathematical expression, which facilitates the accurate generation of the required low-sidelobe NLFM waveform in practical applications, provides an accurate waveform generation basis for the subsequent application of the waveform in the radar system, and ensures the consistency and reliability of the waveform generation.

[0041] As a further limitation of the technical solution of the present invention, the method further includes:

[0042] The obtained low sidelobe NLFM waveform is applied in radar system to suppress strong clutter and strong target interference energy from adjacent range cells.

[0043] The designed NLFM waveform is applied to the radar system to suppress strong clutter and strong target interference energy in adjacent range cells, expanding the application scenarios of the low-sidelobe NLFM waveform, giving full play to the advantages of this waveform in the radar system, improving the target detection capability and anti-interference performance of the radar system in complex environments, and enhancing the practicality and reliability of the radar system.

[0044] In a second aspect, the technical solution of the present invention further provides an NLFM waveform design device based on a dual-parameter phase function, comprising a phase function construction module, an optimization function design module, a genetic algorithm optimization module, and a waveform generation module;

[0045] Phase function construction module, used to introduce bandwidth control parameters and exponential parameters to construct a two-parameter phase function based on a quadratic function;

[0046] An optimization function design module is used to design an optimization function with the goal of minimizing the maximum sidelobe level while constraining the mainlobe width and signal bandwidth;

[0047] A genetic algorithm optimization module is used to optimize the bandwidth control parameter and the exponential parameter in the dual-parameter phase function using a genetic algorithm to obtain the optimal parameter group;

[0048] The waveform generation module is used to substitute the optimal parameter group into the two-parameter phase function to generate a low-sidelobe NLFM waveform.

[0049] By modularizing each key step in the waveform design process, we achieve a systematic and streamlined waveform design process. Each module has a clear division of labor and collaborates with each other. Compared to traditional waveform design methods, this improves design efficiency and accuracy, and facilitates device maintenance and upgrades.

[0050] As a further limitation of the technical solution of the present invention, the two-parameter phase function is as follows:

[0051]

[0052] Where, is the bandwidth control parameter, is the exponential parameter.

[0053] As a further limitation of the technical solution of the present invention, the optimization function design module includes an initialization unit, a first calculation processing unit, a second calculation processing unit and an optimization function design unit;

[0054] an initialization unit for generating an NLFM waveform based on initial values ​​of a bandwidth control parameter and an exponential parameter;

[0055] A first calculation processing unit is used to perform pulse compression on the generated NLFM waveform and calculate the maximum sidelobe level and mainlobe width of the pulse compression result;

[0056] A second calculation processing unit is used to perform FFT transformation on the generated NLFM waveform to calculate the actual bandwidth of the signal;

[0057] The optimization function design unit is used to design the optimization function according to the highest sidelobe level, the mainlobe width and the actual bandwidth of the signal.

[0058] As a further limitation of the technical solution of the present invention, the formula for calculating the maximum sidelobe level and the mainlobe width by the first calculation processing unit is as follows:

[0059]

[0060] in Indicates the main lobe peak, interval The main lobe protection range is ; is the highest sidelobe level, The width of the main lobe.

[0061] As a further limitation of the technical solution of the present invention, the second computing and processing unit is specifically used to perform an FFT transform on the NLFM waveform to find the position of the spectrum peak; extend from the spectrum peak to both sides until the spectrum power drops to a set percentage of the peak, to obtain two points; and obtain the frequency range between the two points, that is, the actual bandwidth of the signal.

[0062] As a further limitation of the technical solution of the present invention, the optimization function is as follows:

[0063]

[0064] The calculation formula is:

[0065] in, and These are penalty coefficients. Indicates taking and the greater of the two; is the highest sidelobe level, The width of the main lobe.

[0066] As a further limitation of the technical solution of the present invention, the genetic algorithm optimization module is specifically used to substitute the calculated values ​​of the highest sidelobe level and the mainlobe width and the actual bandwidth value of the signal into the optimization function, and use the optimization function as the fitness function of the genetic algorithm to optimize the bandwidth control parameters and the exponential parameters to obtain the optimal bandwidth control parameters. and the optimal index parameter .

[0067] As a further limitation of the technical solution of the present invention, the low sidelobe NLFM waveform generated by the waveform generation module is:

[0068]

[0069] Where, is the optimal bandwidth control parameter, is the optimal index parameter.

[0070] 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.

[0071] By adding an application module to the design device, specifically for applying the resulting NLFM waveform to radar system interference suppression, the device not only possesses waveform design capabilities but also achieves close integration with radar system applications, forming a complete chain from waveform design to practical application. This design further enhances the device's practicality and functionality, better meeting the radar system's application requirements for low-sidelobe waveforms and enhancing the performance and competitiveness of the entire system.

[0072] It can be seen from the above technical solutions that the present application has the following advantages: the method adopts a parameterized phase function construction method to construct a nonlinear dual-parameter phase function, and designs an optimization function with the goal of "minimizing the maximum sidelobe level while constraining the mainlobe width and signal bandwidth". The genetic algorithm is used to optimize the parameters, and a NLFM waveform with low sidelobe performance and meeting the constraints is obtained. Specifically, by introducing bandwidth control parameters and exponential parameters to construct a dual-parameter phase function, a flexible adjustment basis is provided for waveform design; the optimization function is designed with the goal of minimizing the maximum sidelobe level while constraining the mainlobe width and signal bandwidth, which can effectively balance the waveform performance; the genetic algorithm is used to optimize, and the optimal parameter group can be quickly and accurately found, thereby generating a low-sidelobe NLFM waveform that meets the requirements. Compared with traditional waveform design methods, the efficiency of waveform design and the degree of optimization of waveform performance are improved, and the anti-interference ability and detection performance of the radar system are enhanced. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] 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.

[0074] Figure 1 A flowchart of a method provided in an embodiment of the present invention.

[0075] Figure 2 This is a principle block diagram of the low sidelobe NLFM waveform design method provided by an embodiment of the present invention.

[0076] Figure 3 The spectrum diagram of NLFM1 waveform and LFM waveform.

[0077] Figure 4 The following is a comparison of the windowed pulse compression output results of the LFM waveform, NLFM0 waveform, and NLFM1 waveform under no Doppler conditions. Figure 4 (a) is the LFM waveform pulse pressure result diagram, Figure 4 (b) is the NLFM0 waveform pulse pressure result diagram, Figure 4 (c) is the NLFM1 waveform pulse pressure result diagram. Figure 4 (d) in the figure is a comparison of the locally enlarged images of the pulse pressure results of the three waveforms.

[0078] Figure 5 The figure compares the windowed pulse pressure output of the NLFM1 waveform with and without target Doppler.

[0079] Figure 6 A block diagram of a device provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0080] To address the problem of high pulse pressure sidelobes in NLFM waveforms generated by existing NLFM waveform design methods, the present invention provides a low-sidelobe NLFM waveform design method based on a dual-parameter phase function construction method. First, a bandwidth control parameter and an exponential parameter are introduced to construct a dual-parameter phase function based on a quadratic function. Then, an optimization function is designed to minimize the maximum sidelobe level while constraining the mainlobe width and signal bandwidth. A genetic algorithm is used to optimize the parameters to obtain the optimal parameters, thereby generating an NLFM waveform. Compared with LFM waveforms and NLFM waveforms generated by a phase dwell method based on a frequency-domain window function, the NLFM waveform obtained by the present invention significantly outperforms both LFM waveforms and NLFM waveforms generated by the phase dwell method based on a frequency-domain window function in terms of pulse pressure sidelobe performance and improvement at small targets. To make the objectives, features, and advantages of this application more apparent and understandable, the technical solutions protected by this application will be clearly and completely described below using specific embodiments and accompanying figures. It should be noted that the embodiments described below represent only some, and not all, of the embodiments of this application. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of this application without inventive effort are intended to fall within the scope of protection of this application.

[0081] like Figure 1 As shown, an embodiment of the present invention provides a NLFM waveform design method based on a dual-parameter phase function, comprising the following steps:

[0082] S1. Introducing bandwidth control parameters and exponential parameters to construct a two-parameter phase function based on a quadratic function; specifically including:

[0083] Introducing bandwidth control parameters and exponential parameters, constructing the two-parameter phase function shown below:

[0084]

[0085] in, is the bandwidth control parameter to be optimized, The optimal interval is ,set up The initial value is ; is the exponential parameter to be optimized, which controls the steepness of the frequency change. The optimal interval is ,set up The initial value is .

[0086] A specific form of a two-parameter phase function based on a quadratic function is constructed, introducing bandwidth control parameters and exponential parameters. This provides a specific mathematical expression for the construction of the two-parameter phase function, making the design of the phase function clearer and more operational, laying the foundation for subsequent optimization and waveform generation.

[0087] S2. Design an optimization function with the goal of minimizing the maximum sidelobe level while constraining the mainlobe width and signal bandwidth. Specifically, it includes:

[0088] S21, calculate the maximum sidelobe level and main lobe width ;

[0089] The initial phase function parameter group and And the waveform parameters determined by the system 、 and Import the genetic algorithm, generate NLFM waveform, perform pulse compression and obtain the pulse compression result , 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. The calculation formula is,

[0090]

[0091] in, Indicates the main lobe peak, interval The main lobe protection range is .

[0092] It provides an objective and accurate calculation method that can accurately quantify the sidelobe level and mainlobe width of the waveform, providing a reliable basis for the design of optimization functions and parameter optimization, and helping to improve the optimization accuracy and performance of the waveform.

[0093] Step S22: Calculate the actual bandwidth of the signal ;

[0094] The initial phase function parameter group and And the waveform parameters determined by the system 、 and Import the genetic algorithm and implement it in the order of generating NLFM waveform, performing FFT transformation and calculating signal bandwidth to obtain The value of Indicates the frequency width corresponding to the -4dB position of the NLFM waveform FFT transform output result.

[0095] Through FFT transformation and spectrum analysis methods, the actual bandwidth of the signal can be accurately determined, ensuring that the signal is optimized under the condition of meeting the bandwidth constraint, avoiding the signal bandwidth exceeding the expected range, and ensuring the normal operation of the radar system.

[0096] Step S23, designing an optimization function;

[0097] 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 distance resolution of the pulse compression output, the mainlobe width is increased as a penalty term to constrain it; at the same time, in order to ensure the signal bandwidth of the optimized waveform Equal to the bandwidth required by the design , increase the judgment coefficient of whether the bandwidth is equal Constraints are made; based on the above conditions, the optimization function is designed as follows:

[0098]

[0099] in, and Are penalty coefficients, and are adjustable parameters, The value is 10 7 Magnitude, The value is 10 4 Magnitude; Indicates taking and the greater of the two; The calculation formula is:

[0100]

[0101] Where B is the bandwidth required by the design.

[0102] Generate an NLFM waveform, perform pulse compression and FFT transformation, and design an optimization function based on the calculated results. By comprehensively considering multiple factors such as maximum sidelobe level, mainlobe width, and signal bandwidth, the optimization function can more comprehensively measure and optimize waveform performance, ensuring that the generated waveform meets requirements across multiple key indicators.

[0103] The optimization function comprehensively considers multiple objectives such as the maximum sidelobe level, mainlobe width and bandwidth, and penalizes situations that do not meet the constraints through a penalty coefficient. It can guide the genetic algorithm in the direction of satisfying all constraints and minimizing the maximum sidelobe level during the optimization process, thereby improving the effectiveness of the optimization algorithm and the performance of the waveform.

[0104] S3. Based on the optimization function, a genetic algorithm is used to optimize the bandwidth control parameter and the exponential parameter in the dual-parameter phase function to obtain the optimal parameter group;

[0105] The S21 obtained 、 The value and S22 are obtained The value is substituted into the optimization function, and the optimization function of S23 is used as the fitness function of the genetic algorithm. and Search for the best combination and , the optimization function needs to be optimized according to the parameter set obtained in each iteration during the iterative optimization process. and And the waveform parameters determined by the system 、 and , calculate the corresponding 、 and value, which is used for the next iterative optimization.

[0106] The optimization process using genetic algorithm in this step is as follows:

[0107] Initialize the population: set bandwidth control parameters The initial value is , The optimal interval is ; is an exponential parameter that controls the steepness of the frequency change. The optimal interval is ,set up The initial value is Initialize the population of the genetic algorithm, including multiple individuals, each of which contains a set of parameters ( 、 ). The parameter group to be optimized ( 、 ) is encoded as chromosome. Real number encoding can be used, directly as ( 、 ) as the gene value.

[0108] Fitness function design: Take the optimization function as the fitness function and calculate the fitness value of each individual according to the fitness function formula. The calculation process is as follows: According to the current parameters ( 、 ) Generate NLFM waveform .right Perform pulse compression to obtain the output .from Extract 、 (-4dB width). Do FFT and calculate actual bandwidth (-4dB frequency width). Substitute into the fitness function to calculate the fitness value of the current individual.

[0109] Individuals are selected for reproduction based on fitness values. Excellent individuals are selected according to probability based on fitness values. Individuals with smaller fitness values ​​(better performance) have higher probability of being selected. Crossover operation is performed on the selected individuals to generate new individuals. Crossover operation can be achieved by exchanging some parameters of two individuals. Mutation operation is performed on the newly generated individuals to randomly change the parameter values ​​of the individuals with a set probability to increase the diversity of the population. For each individual in the newly generated population, its fitness value is recalculated. The selection, crossover, mutation and evaluation steps are repeated until the predetermined number of iterations is reached or the fitness value converges to a certain threshold. After the iteration, the individual with the lowest fitness value is selected, and its corresponding parameter group ( , ) is the optimal parameter group.

[0110] S4. Substitute the optimal parameter set into the two-parameter phase function to generate a low-sidelobe NLFM waveform.

[0111] Generated NLFM waveform:

[0112]

[0113] Where, is the optimal bandwidth control parameter, is the optimal index parameter.

[0114] By introducing specific parameters to construct a phase function and designing an optimization function, a genetic algorithm is used to generate the waveform. This provides a systematic and effective approach for low-sidelobe NLFM waveform design, helping to obtain waveforms with good performance in radar systems, reduce sidelobe levels, and improve target detection and resolution capabilities. A specific method for generating the final NLFM waveform is presented, allowing the optimal parameters obtained through the previous optimization process to be effectively converted into an actual waveform, providing a directly applicable signal waveform for radar systems.

[0115] like Figure 2 As shown, an embodiment of the present invention provides a NLFM waveform design method based on a dual-parameter phase function, including the following process:

[0116] (1) 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;

[0117] (2) Introducing bandwidth control parameters and exponential parameters to construct a two-parameter phase function based on a quadratic function;

[0118] (3) Design an optimization function with the goal of “minimizing the maximum sidelobe level while constraining the mainlobe width and signal bandwidth”, and use genetic algorithm to optimize the parameters to obtain the optimal parameters, and then generate the NLFM waveform.

[0119] The following is a detailed explanation of the above steps:

[0120] In step (2), a bandwidth control parameter and an exponential parameter are introduced to construct a two-parameter phase function based on a quadratic function; specifically, the following steps are involved:

[0121] Introducing bandwidth control parameters and exponential parameters, constructing the two-parameter phase function shown below:

[0122]

[0123] in, is the bandwidth control parameter to be optimized, The optimal interval is ,set up The initial value is ; is the exponential parameter to be optimized, which controls the steepness of the frequency change. The optimal interval is ,set up The initial value is .

[0124] In step (3), the optimization function is designed with the goal of minimizing the maximum sidelobe level while constraining the mainlobe width and signal bandwidth. Specifically, it includes:

[0125] (31) Calculate the maximum sidelobe level and main lobe width ;

[0126] The initial phase function parameter group and And the waveform parameters determined by the system 、 and Import the genetic algorithm, generate NLFM waveform, perform pulse compression and obtain the pulse compression result , 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. The calculation formula is,

[0127]

[0128] in, Indicates the main lobe peak, interval The main lobe protection range is .

[0129] (32) Calculate the actual bandwidth of the signal ;

[0130] The initial phase function parameter group and And the waveform parameters determined by the system 、 and Import the genetic algorithm and implement it in the order of generating NLFM waveform, performing FFT transformation and calculating signal bandwidth to obtain The value of Indicates the frequency width corresponding to the -4dB position of the NLFM waveform FFT transform output result;

[0131] (33) Design optimization function;

[0132] 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 distance resolution of the pulse compression output, the mainlobe width is increased as a penalty term to constrain it; at the same time, in order to ensure the signal bandwidth of the optimized waveform Equal to the bandwidth required by the design , increase the judgment coefficient of whether the bandwidth is equal Constraints are made; based on the above conditions, the optimization function is designed as follows:

[0133]

[0134] in, and Are penalty coefficients, and are adjustable parameters, The value is 10 7 Magnitude, The value is 10 4 Magnitude; Indicates taking and the greater of the two; The calculation formula is:

[0135]

[0136] Where B is the bandwidth required by the design.

[0137] (34) Genetic algorithm is used to optimize the bandwidth control parameters and exponential parameters in the two-parameter phase function to obtain the optimal parameter set;

[0138] The obtained step (31) 、 The values ​​and steps (32) are obtained The value is substituted into the optimization function, and the optimization function of step (33) is used as the fitness function of the genetic algorithm. and Search for the best combination and , the optimization function needs to be optimized according to the parameter set obtained in each iteration during the iterative optimization process. and And the waveform parameters determined by the system 、 and , calculate the corresponding 、 and value, which is used for the next iterative optimization.

[0139] (35) Substituting the optimal parameter set into the two-parameter phase function, a low-sidelobe NLFM waveform is generated.

[0140] The resulting low-sidelobe NLFM waveform is:

[0141]

[0142] Where, is the optimal bandwidth control parameter, is the optimal index parameter.

[0143] The following is a design example. The waveform parameters determined by the system are 、 and The NLFM waveform obtained from the above steps is as follows:

[0144] , ,

[0145] 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.

[0146] Figure 3 The spectrum of the NLFM waveform obtained by the present invention and the spectrum of the LFM waveform for comparison are given. Figure 3 The frequency width at -4dB is exactly equal to the bandwidth design value required by the system. .

[0147] Figure 4 The LFM waveform without Doppler is given ( Figure 4 (a), marked as LFM waveform), NLFM waveform obtained by phase dwell method based on frequency domain window function ( Figure 4 (b), marked as NLFM0 waveform) and the NLFM waveform obtained by the present invention ( Figure 4 (c) in the figure, marked as NLFM1 waveform) windowed pulse compression output results comparison chart, Figure 4 (d) is a comparison of the local enlarged graph of the three waveform pulse pressure results. Figure 4 It shows that the pulse pressure sidelobe of the NLFM1 waveform is significantly lower than that of the LFM waveform and the NLFM0 waveform, and the improvement effect at small targets is also significantly better than those of the two waveforms; in addition, under the condition of windowed pulse compression, the distance resolution obtained by the LFM waveform is 45 meters, the distance resolution obtained by the NLFM0 waveform is 75 meters, and the distance resolution obtained by the NLFM1 waveform is 42 meters, which shows that the distance resolution of the NLFM waveform obtained in this application is also better than the two waveforms compared.

[0148] Figure 5This is a comparison chart of the windowed pulse compression output results of the NLFM1 waveform under the two conditions of 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 in this application has just been deformed under the conditions of a target speed of 100m / s and a waveform carrier frequency of 9.5GHz. The red line is 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 100m / s.

[0149] In some embodiments, the method further comprises:

[0150] The obtained low sidelobe NLFM waveform is applied in radar system to suppress strong clutter and strong target interference energy from adjacent range cells.

[0151] Applying a low-sidelobe NLFM waveform to a radar system requires the following steps: Determine parameters such as pulse width, bandwidth, and sampling rate based on the radar system's design requirements. Design the low-sidelobe NLFM waveform using a two-parameter phase function construction method. Optimize the bandwidth control parameters and exponent parameters using an optimization function and genetic algorithm. Load the designed low-sidelobe NLFM waveform into the radar transmitter and transmit the signal. Receive the target echo signal and perform pulse compression. During the pulse compression process, the low-sidelobe characteristics of the NLFM waveform are utilized to reduce interference from clutter and strong target echoes. Target detection performance is further improved using signal processing algorithms (such as a constant false alarm rate (CFAR) detection algorithm). Evaluate the radar system's detection performance, including metrics such as target detection probability, false alarm rate, and range resolution. Based on the evaluation results, further optimize the waveform parameters to improve the overall performance of the radar system.

[0152] Applying a low-sidelobe NLFM waveform to radar systems has the following beneficial effects: It effectively reduces interference from clutter and strong target echoes, improving the radar's ability to detect small targets and its accuracy. By optimizing waveform parameters, the low-sidelobe NLFM waveform enhances the radar signal's anti-interference capability, ensuring stable operation in complex electromagnetic environments. The design of a low-sidelobe NLFM waveform improves the overall performance of the radar system, reducing the probability of false and missed detections, thereby enhancing system reliability. The low-sidelobe NLFM waveform also exhibits excellent Doppler tolerance, adapting to target detection requirements in dynamic environments and improving the adaptability of the radar system.

[0153] The resulting NLFM waveform is proposed for use in radar systems to suppress strong clutter and strong target interference energy from adjacent range cells. By combining the designed waveform with practical application scenarios, the advantages of the low-sidelobe NLFM waveform in suppressing clutter and interference are fully utilized, improving the radar system's target detection and anti-interference capabilities in complex environments, and enhancing the radar system's practicality and reliability.

[0154] like Figure 6 As shown, an embodiment of the present invention further provides an NLFM waveform design device based on a dual-parameter phase function, comprising a phase function construction module, an optimization function design module, a genetic algorithm optimization module, and a waveform generation module;

[0155] Phase function construction module, used to introduce bandwidth control parameters and exponential parameters to construct a two-parameter phase function based on a quadratic function;

[0156] An optimization function design module is used to design an optimization function with the goal of minimizing the maximum sidelobe level while constraining the mainlobe width and signal bandwidth;

[0157] A genetic algorithm optimization module is used to optimize the bandwidth control parameter and the exponential parameter in the dual-parameter phase function using a genetic algorithm to obtain the optimal parameter group;

[0158] The waveform generation module is used to substitute the optimal parameter group into the two-parameter phase function to generate a low-sidelobe NLFM waveform.

[0159] Implementing the low sidelobe NLFM waveform design method in the form of a device makes the design process more automated and standardized, improves the design efficiency and waveform generation quality, and facilitates integration and promotion in radar system development and application.

[0160] The two-parameter phase function is as follows:

[0161]

[0162] Where, is the bandwidth control parameter, is the exponential parameter.

[0163] In some embodiments, the optimization function design module includes an initialization unit, a first calculation processing unit, a second calculation processing unit, and an optimization function design unit;

[0164] an initialization unit for generating an NLFM waveform based on initial values ​​of a bandwidth control parameter and an exponential parameter;

[0165] A first calculation processing unit is used to perform pulse compression on the generated NLFM waveform and calculate the maximum sidelobe level and mainlobe width of the pulse compression result;

[0166] A second calculation processing unit is used to perform FFT transformation on the generated NLFM waveform to calculate the actual bandwidth of the signal;

[0167] The optimization function design unit is used to design the optimization function according to the highest sidelobe level, the mainlobe width and the actual bandwidth of the signal.

[0168] The formula for calculating the maximum sidelobe level and the mainlobe width by the first calculation processing unit is as follows:

[0169]

[0170] in Indicates the main lobe peak, interval The main lobe protection range is ; is the highest sidelobe level, The width of the main lobe.

[0171] The second computing unit is specifically used to perform an FFT transform on the NLFM waveform to find the location of the spectrum peak; extend from the spectrum peak to both sides until the spectrum power drops to a set percentage of the peak, obtaining two points; and obtain the frequency range between the two points, namely the actual bandwidth of the signal.

[0172] The optimization function is as follows:

[0173]

[0174] The calculation formula is:

[0175] in, and These are penalty coefficients. Indicates taking and the greater of the two; is the highest sidelobe level, The width of the main lobe.

[0176] In some embodiments, the genetic algorithm optimization module is specifically used to substitute the calculated values ​​of the maximum sidelobe level and the mainlobe width and the actual bandwidth of the signal into the optimization function, and use the optimization function as the fitness function of the genetic algorithm to optimize the bandwidth control parameters and the exponential parameters to obtain the optimal bandwidth control parameters. and the optimal index parameter The specific process is as follows:

[0177] Initialize the population: set bandwidth control parameters The initial value is , The optimal interval is ; is an exponential parameter that controls the steepness of the frequency change. The optimal interval is ,set up The initial value is Initialize the population of the genetic algorithm, including multiple individuals, each of which contains a set of parameters ( 、 ). The parameter group to be optimized ( 、 ) is encoded as chromosome. Real number encoding can be used, directly as ( 、 ) as the gene value.

[0178] Fitness function design: Take the optimization function as the fitness function and calculate the fitness value of each individual according to the fitness function formula. The calculation process is as follows: According to the current parameters ( 、 ) Generate NLFM waveform .right Perform pulse compression to obtain the output .from Extract 、 (-4dB width). Do FFT and calculate actual bandwidth (-4dB frequency width). Substitute into the fitness function to calculate the fitness value of the current individual.

[0179] Individuals are selected for reproduction based on fitness values. Excellent individuals are selected according to probability based on fitness values. Individuals with smaller fitness values ​​(better performance) have higher probability of being selected. Crossover operation is performed on the selected individuals to generate new individuals. Crossover operation can be achieved by exchanging some parameters of two individuals. Mutation operation is performed on the newly generated individuals to randomly change the parameter values ​​of the individuals with a set probability to increase the diversity of the population. For each individual in the newly generated population, its fitness value is recalculated. The selection, crossover, mutation and evaluation steps are repeated until the predetermined number of iterations is reached or the fitness value converges to a certain threshold. After the iteration, the individual with the lowest fitness value is selected, and its corresponding parameter group ( , ) is the optimal parameter group.

[0180] The low sidelobe NLFM waveform generated by the waveform generation module:

[0181]

[0182] Where, is the optimal bandwidth control parameter, is the optimal index parameter.

[0183] 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.

[0184] By adding an application module to the design device, specifically for applying the resulting NLFM waveform to radar system interference suppression, the device not only possesses waveform design capabilities but also achieves close integration with radar system applications, forming a complete chain from waveform design to practical application. This design further enhances the device's practicality and functionality, better meeting the radar system's application requirements for low-sidelobe waveforms and enhancing the performance and competitiveness of the entire system.

[0185] The device also includes an application module for applying the resulting low-sidelobe NLFM waveform to a radar system, suppressing strong clutter and strong target interference energy from adjacent range cells. Further emphasizing the device's practicality, the application module allows the designed waveform to be directly applied to the radar system, completing a closed-loop process from waveform design to practical application. This can quickly and effectively improve radar system performance and meet practical engineering requirements.

[0186] An embodiment of the present invention further provides an electronic device, comprising: a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other via the communication bus. The communication bus can be used to transmit information between the electronic device and the sensor. The processor can call the logic instructions in the memory to execute the following method: introduce bandwidth control parameters and exponential parameters to construct a two-parameter phase function based on a quadratic function; design an optimization function with the goal of minimizing the maximum sidelobe level while constraining the mainlobe width and signal bandwidth; use a genetic algorithm to optimize the bandwidth control parameters and exponential parameters in the two-parameter phase function to obtain an optimal parameter set; substitute the optimal parameter set into the two-parameter phase function to generate a low-sidelobe NLFM waveform.

[0187] Furthermore, the logical instructions in the aforementioned memory can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the portion that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in various embodiments of the present invention. The aforementioned storage media include various media capable of storing program code, such as USB flash drives, mobile hard drives, read-only memories (ROMs), random access memories (RAMs), magnetic disks, or optical disks.

[0188] An embodiment of the present invention provides a non-transitory computer-readable storage medium, which stores computer instructions. The computer instructions enable a computer to execute the method provided by the above-mentioned method embodiment, for example, including: introducing a bandwidth control parameter and an exponential parameter to construct a two-parameter phase function based on a quadratic function; designing an optimization function with the goal of minimizing the maximum sidelobe level while constraining the mainlobe width and signal bandwidth; using a genetic algorithm to optimize the bandwidth control parameter and the exponential parameter in the two-parameter phase function to obtain an optimal parameter group; substituting the optimal parameter group into the two-parameter phase function to generate a low-sidelobe NLFM waveform.

[0189] 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 dual-parameter phase function, characterized in that: The steps include: The bandwidth control parameter and exponential parameter are introduced to construct a two-parameter phase function based on the quadratic function. Design an optimization function with the goal of minimizing the maximum sidelobe level while constraining the mainlobe width and signal bandwidth; Based on the optimization function, the genetic algorithm is used to optimize the bandwidth control parameters and exponential parameters in the dual-parameter phase function to obtain the optimal parameter group; Substituting the optimal parameter set into the two-parameter phase function, a low-sidelobe NLFM waveform is generated; Introducing bandwidth control parameters and exponential parameters, in the steps of constructing a two-parameter phase function based on a quadratic function, the two-parameter phase function is as follows: Where, is the bandwidth control parameter, is the exponential parameter, is the time variable; With the goal of minimizing the maximum sidelobe level while constraining the mainlobe width and signal bandwidth, the steps for designing the optimization function include: generating an NLFM waveform based on initial values ​​of a bandwidth control parameter and an exponential parameter; Perform pulse compression on the generated NLFM waveform and calculate the maximum sidelobe level and mainlobe width of the pulse compression result; Perform FFT transformation on the generated NLFM waveform to calculate the actual bandwidth of the signal; Design an optimization function based on the maximum sidelobe level, mainlobe width and actual signal bandwidth; The optimization function is as follows: The calculation formula is: in, and These are penalty coefficients. is the highest sidelobe level, is the main lobe width, B is the bandwidth, is the actual bandwidth.

2. The NLFM waveform design method based on a dual-parameter phase function according to claim 1, characterized in that: The formulas for calculating the maximum sidelobe level and mainlobe width are as follows: in, Indicates the main lobe peak, interval The main lobe protection range is ; is the highest sidelobe level, is the main lobe width, is the pulse compression result.

3. The NLFM waveform design method based on a dual-parameter phase function according to claim 2, characterized in that: The steps for performing FFT transformation on the generated NLFM waveform and calculating the actual bandwidth of the signal include: Perform FFT transformation on the NLFM waveform to find the location of the spectrum peak; Extend from the spectrum peak to both sides until the spectrum power drops to the set percentage of the peak, and obtain two points; Get the frequency range between the two points, which is the actual bandwidth of the signal.

4. The NLFM waveform design method based on a dual-parameter phase function according to claim 3, characterized in that: Substitute the optimal parameter set into the two-parameter phase function to generate a low-sidelobe NLFM waveform. The generated low-sidelobe NLFM waveform is: Where, is the optimal bandwidth control parameter, is the optimal index parameter, is the time variable.

5. The NLFM waveform design method based on a dual-parameter phase function according to claim 4, characterized in that: The method further comprises: The obtained low sidelobe NLFM waveform is applied in radar system to suppress clutter and target interference energy from adjacent range cells.

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

7. The NLFM waveform design device based on a dual-parameter phase function according to claim 6, characterized in that: The device also includes an application module for applying the obtained low sidelobe NLFM waveform to a radar system to suppress clutter and target interference energy from adjacent range cells.

Images