Waveform Design Method Based on Prior Information of Self-Fuzzy Function

Abstract

This invention discloses a waveform design method based on prior information and a self-fuzzy function, comprising the following steps: Step 1, determining the radar target and the jamming target based on prior information; Step 2, designing a self-fuzzy function template based on the prior information; Step 3, constructing a zero-sum game model between the radar and the jamming party; Step 4, generating the optimized waveform based on an iterative method derived from the model. This invention provides a waveform design method based on prior information and a self-fuzzy function. Through a reverse iterative method, the optimal transmitted waveform and the matching waveform can be obtained efficiently, thereby improving the anti-jamming capability of the radar system.

Description

Technical Field

[0001] This invention belongs to the field of radar waveform design technology, and particularly relates to a waveform design method based on prior information oriented towards self-fuzzy functions. Background Technology

[0002] In modern radar systems, waveform design is one of the key technologies affecting their performance and effectiveness. Radar systems detect and identify targets by emitting specific electromagnetic waveforms, while simultaneously dealing with various complex electromagnetic environments and hostile interference. Traditional waveform design methods often rely on fixed waveform patterns or empirical designs. While these designs may meet basic detection requirements to some extent, their performance and effectiveness are significantly limited when facing variable electromagnetic environments and intense electronic warfare interference.

[0003] The development of modern radar technology has driven the continuous evolution and optimization of waveform design methods. Based on advanced signal processing techniques and mathematical modeling methods, the new generation of radar waveform design aims to improve the performance of radar systems in target detection, tracking, and anti-jamming capabilities by optimizing the energy distribution, spectral characteristics, and spatiotemporal characteristics of the waveform.

[0004] The background technology of waveform design encompasses several aspects: First, it requires a comprehensive understanding and analysis of the radar's operating environment and usage scenarios. Different mission requirements may pose different challenges to the waveform design of radar systems, such as the identification of high-resolution targets, the realization of low-probability interception, and effective signal transmission in complex electromagnetic environments. Second, waveform design also needs to consider the actual characteristics and limitations of radar hardware, such as the frequency response, power output capability, and signal processing speed of the transmitter and receiver.

[0005] In traditional waveform design, researchers typically rely on mathematical models and simulation tools to evaluate the performance of different waveform schemes. These models involve radar signal propagation characteristics, target feature extraction methods, and interference suppression techniques. With advancements in computing power and algorithm optimization, modern waveform design increasingly employs methods based on statistical learning and optimization theory, leveraging big data analysis and adaptive algorithms to maximize signal processing efficiency in dynamic scenarios.

[0006] Waveform design, as a crucial component of modern radar system performance optimization, is continuously driven and influenced by technological innovation and scientific research. Future development directions include more intelligent adaptive waveform design, integrated multi-sensor collaborative operation, and adaptability to extreme conditions in complex electromagnetic environments. These technological advancements will further enhance the widespread application and practical effectiveness of radar systems in military, civilian, and scientific research fields. Summary of the Invention

[0007] In view of this, the present invention discloses a waveform design method based on prior information for self-fuzzy functions. Based on existing target and interference signal models, a series of waveform templates or optimized parameters are designed so that the radar system can extract target features to the maximum extent when receiving target signals, and suppress interference to the maximum extent when facing interference signals, thereby ensuring the stability and performance of the system.

[0008] The objective of this invention is achieved through the following technical solution: a waveform design method based on prior information of a self-fuzzy function, the method comprising...

[0009] Step 1: Determine the radar target and the jamming target based on prior information;

[0010] Step 2: Design a self-fuzzy function template based on prior information;

[0011] Step 3: Construct a zero-sum game model between the radar operator and the jammer.

[0012] Step 4: Based on the iterative method derived from the model, generate the optimized radar waveform.

[0013] Specifically, the radar target is characterized by the local signal-to-interference-plus-noise ratio (SIR / NDR) of the target echo signal:

[0014]

[0015] Local represents the region or potential region where the target is located on the range-Doppler plane. This represents the signal-to-interference-plus-noise ratio (SIR) of the local area where the target is located.

[0016] The target of the interference is expressed by the local interference noise ratio of the interference signal:

[0017]

[0018] This refers to the false target region on the range-Doppler plane.

[0019] In summary, the game objective of radar is a bi-objective function.

[0020]

[0021] The game objective of the jammer is a bi-objective function.

[0022]

[0023] The relationship between radar and jamming is a zero-sum game.

[0024] Specifically, the self-fuzzy function is:

[0025]

[0026] It is a signal, where t is time. Indicates signal The complex conjugate, The parameter represents the time delay, and f represents the frequency offset. It is a combination of frequency offset f and time delay. The complex exponential function is used to introduce the corresponding phase shift, and the infinitesimal integral dt represents the integration of the signal over time.

[0027] It has the following mathematical properties:

[0028]

[0029] in, Indicates the self-fuzzy function in The amplitude at point S, where Energy(S) represents the energy of the signal S. and These represent the self-fuzzy function in and The range at that point, The double integral symbol represents the integral over the entire time delay. Integrate over the range of frequency offset f. Let represent the square of the modulus of the self-fuzzy function, and let represent the energy density. Indicates time delay The infinitesimal element df represents the infinitesimal element of the frequency offset f, indicating that the self-ambiguity function has a certain degree of ambiguity with respect to the frequency offset f. Symmetry;

[0030] Based on prior knowledge and the correspondence between the energy distribution in the distance-Doppler plane and the fuzzy function, a self-fuzzy function template is obtained:

[0031]

[0032] Where E is the energy constraint of the transmitted waveform, therefore the template design satisfies the energy constraint, that is... .

[0033] Furthermore, the zero-sum game model between the radar side and the jamming side is as follows:

[0034] The template spaces for radar self-ambiguity functions and mutual ambiguity functions are respectively

[0035]

[0036] The jamming mode space of the jammer is

[0037]

[0038] This indicates a certain jamming mode, so the first layer of the game between the radar and the jammer is between the radar, the target, and the jammer. In the game above, the actual target and the distribution area of ​​interference energy are The target region and interference energy region of template d are as follows: The distance or coverage metric between regions is The conceptual model of the first-level game is as follows.

[0039] For jammers:

[0040]

[0041] For radar:

[0042]

[0043] If the region defined by template d has a probability distribution, then the above model is a stochastic model, and the expectation in the model below is the expectation of the region with the probability distribution:

[0044] For jammers:

[0045]

[0046] For radar:

[0047]

[0048] For the first-level game, we first apply backward induction to solve the extended game problem of template selection and interference mode selection under the condition of complete information, and then apply the perfect Bayesian Nash equilibrium method to solve the Bayesian extended game problem of template selection and interference mode selection without complete information. The first-level game is a coarse-grained fuzzy function template and interference mode selection game model based on extended game. Through the game, the template type and interference mode are determined. According to the different information modes, two types are constructed: deterministic and uncertain.

[0049] If the choices in the first layer of the game have been determined, that is, the template d of the fuzzy function and the interference mode j of the interference machine have been determined, then we enter the second layer of parameter fine-tuning differential game stage.

[0050] Furthermore, in the second-layer parameter fine-tuning differential game stage,

[0051] Radar control functions: The amplitude, frequency, and phase modulation function is denoted as...

[0052]

[0053] It is an amplitude function. It is a frequency function. It is a phase modulation function. It is the time-domain waveform of the radar signal. It is the output of the matched filter;

[0054] Control functions of the jammer: parameter control under time delay and Doppler shift modulation

[0055]

[0056] It's a time delay. It is Doppler translation modulation, where d is the template;

[0057] State space: The state space of a game is the real-time evolution of the local signal-to-noise ratio on the distance-Doppler plane;

[0058] Objective function: The difference between the template set by the fuzzy function and the actual fuzzy function of the transmitted waveform.

[0059] Furthermore, in the second-layer parameter fine-tuning differential game stage, a conceptual model of differential game with parameter modulation under deterministic and uncertain information modes is constructed.

[0060] Furthermore, the differential game model under the deterministic information model is constructed as follows:

[0061] For radar:

[0062]

[0063] For jammers:

[0064]

[0065] in, and These represent the sets of characteristics of the target and the interference source, respectively. It is a discrete template of the mutual ambiguity function, used to describe the characteristics of signals in a radar system, where k and p are the discretized time delay and frequency offset indices. It is the error between the discrete template of the mutually fuzzy function and its expected value. These are self-ambiguity and mutual ambiguity functions used to describe the time delay of signals S and W. Correlation with frequency offset f and These represent the local signal-to-noise ratio and the interference noise ratio, respectively, and their dynamic changes are determined by the system's internal state and external control inputs. and The decision, and It is a function that describes dynamic evolution and is used to calculate the rate of change of local signal-to-noise ratio and interference-to-noise ratio.

[0066] Furthermore, the differential game model under the uncertain information mode is constructed as follows. Here, the uncertain information mode has uncertainty in the distance region and Doppler shift region of the target. Therefore, the expectation in the following model is the expectation of the region with a probability distribution:

[0067] For radar:

[0068]

[0069] For jammers:

[0070]

[0071] The second-level game is based on the first-level game. It uses a fine-grained parameter modulation game model based on differential game theory to determine the radar's transmitted waveform and the matching and mismatch filtering waveforms through game theory.

[0072] Furthermore, based on the waveforms of the first-level and second-level games, the discretization model is designed as follows:

[0073]

[0074] Represents the expression for variables and Perform a minimize operation. Represents a set of indices for time delay and frequency offset. Summation, A discrete template representing a mutually ambiguous function, describing the signal with time delay. and frequency offset The following characteristics, The modulus representing the expected value of the mutual ambiguity function template. express The conjugate transpose of . Complex representation of a mutually ambiguous function template. This represents the received signal processing vector in the optimization model;

[0075] First, derive the objective function.

[0076]

[0077] in

[0078]

[0079] The last term of the expansion of the objective function

[0080] Using loop iteration, based on

[0081]

[0082] Iteration produces two sequences

[0083]

[0084] The iterative method is as follows:

[0085] Step 1: Randomly initialize and generate the first element of two sequences according to the constraints of vector X. and ;

[0086] Step 2: For a fixed sequence and sequence Calculations yielded

[0087]

[0088] And update , yes;

[0089] Step 3: Calculate the phase offset after a fixed iteration. and sequence Calculations yielded

[0090]

[0091] m and n are the row and column indices of matrix X, respectively. Representation matrix In the first iteration, the value of the element at position m, n It represents the value of the element at position m, N+l during the first iteration.

[0092] Step 4: For fixed and Calculations yielded

[0093]

[0094] Step 5: Repeat steps 2, 3, and 4 until the convergence threshold is met.

[0095] Compared with existing methods, the advantage of the method of the present invention is that it can efficiently obtain the optimal transmission waveform and matching waveform through reverse iteration, thereby improving the anti-jamming capability of the radar system. Attached Figure Description

[0096] Figure 1A flowchart illustrating an embodiment of the present invention is shown;

[0097] Figure 2 The image shows the range Doppler plots of the target echo and interference before optimization according to an embodiment of the present invention;

[0098] Figure 3 The diagram shows a 2D mutual ambiguity function plot of the transmitted waveform before optimization according to an embodiment of the present invention;

[0099] Figure 4 The optimized range Doppler plots of the target echo and interference according to an embodiment of the present invention are shown. Detailed Implementation

[0100] The present invention will be further described below with reference to the accompanying drawings, but this is not intended to limit the present invention in any way. Any modifications or substitutions made based on the teachings of the present invention shall fall within the protection scope of the present invention.

[0101] In this embodiment, linear frequency modulation is used to add noise and interference to the waveform. The effectiveness of the method is verified by comparing the signal-to-interference-plus-noise ratio before and after optimization.

[0102] like Figure 1 As shown, a waveform design method based on prior information of a self-fuzzy function is described, the method comprising:

[0103] Step 1: Determine the targets of radar and jamming based on prior information;

[0104] Step 2: Design a self-fuzzy function template based on prior information;

[0105] Step 3: Construct a zero-sum game model between the radar operator and the jammer.

[0106] Step 4: Based on the iterative method derived from the model, generate the optimized waveform;

[0107] The deterministic information refers to the radar's precise knowledge of the target's time delay. Doppler shift of the target The jamming mode of the jammer (assuming it is forwarding deception jamming), and the time delay modulation of the jammer based on the target's time delay. The jammer modulates the target's Doppler frequency shift. Information such as...

[0108] Specifically, the target of the radar is:

[0109] Based on prior knowledge, the area where the target is located or the possible area is located on the range-Doppler plane. The interference and noise in the signal are suppressed, while the target echo is highlighted. We can characterize this using the local signal-to-interference-plus-noise ratio (SNR) of the target echo signal.

[0110]

[0111] The target of the interference is:

[0112] Based on prior knowledge, in certain regions of the distance-Doppler plane ( The jammer creates false targets to cover up the real targets. The local interference-to-noise ratio (RIN) of the jamming signal can be used to represent the jammer's target.

[0113]

[0114] In summary, the game objective of radar is a bi-objective function.

[0115]

[0116] The game objective of the jammer is also a bi-objective function.

[0117]

[0118] The relationship between radar and jamming is a zero-sum game.

[0119] Furthermore, the self-fuzzy function is:

[0120] Fuzzy function: The definition of a self-fuzzy function is...

[0121]

[0122] It has the following mathematical properties

[0123]

[0124] Fuzzy Function Template: Based on prior knowledge and the correspondence between the energy distribution of the distance-Doppler plane and fuzzy functions, a self-fuzzy function template is designed.

[0125]

[0126] Where E is the energy constraint of the transmitted waveform. Therefore, the template design must satisfy the energy constraint, that is...

[0127]

[0128] The template for the fuzzy function must be designed based on prior knowledge. Therefore, from the perspective of the fuzzy function template, the radar should design an accurate template as much as possible, while the jammer should make the template as inaccurate as possible.

[0129] Furthermore, the zero-sum game model between the radar side and the jamming side is as follows:

[0130] Let the template spaces of the radar self-ambiguity function and the mutual ambiguity function be respectively...

[0131]

[0132] Let the jamming mode space of the jammer be .

[0133] This indicates a certain jamming mode. Therefore, the first layer of the game between radar and jammer is... In the game above, assuming the actual target and interference energy distribution areas are... However, the target and interference energy regions of template d are... The distance or coverage metric between regions is The conceptual model of the first-level game is as follows.

[0134] For jammers:

[0135]

[0136] For radar:

[0137]

[0138] If the region defined by template d has a probability distribution, then the above model can be constructed as a stochastic model, and the expectation in the model below is the expectation of the region with a probability distribution.

[0139] For jammers:

[0140]

[0141] For radar:

[0142]

[0143] For first-level games, we should first study the extended game problem of template selection and interference mode selection under the condition of complete information, and then study the Bayesian extended game problem of template selection and interference mode selection without complete information.

[0144] If the choices in the first layer of the game have been determined, that is, the template d of the fuzzy function and the interference mode j of the interference machine have been determined, then we enter the second layer of parameter fine-tuning differential game stage.

[0145] Radar control functions: The amplitude, frequency, and phase modulation function is denoted as...

[0146]

[0147] The control function of the jammer: parameter control under a certain jamming mode. This invention is mainly aimed at deception and forwarding jamming, primarily time delay and Doppler shift modulation, denoted as...

[0148]

[0149] State space: The state space of a game is the real-time evolution of the local signal-to-noise ratio on the distance-Doppler plane.

[0150] Objective function: The difference between the template set by the fuzzy function and the actual fuzzy function of the transmitted waveform (filtered).

[0151] Therefore, we can construct a conceptual model of differential game with parameter modulation under deterministic and uncertain information modes.

[0152] First, the differential game model under deterministic information mode is constructed as follows.

[0153] For radar:

[0154]

[0155] For jammers:

[0156]

[0157] Secondly, the differential game model under the uncertain information mode is constructed as follows. Here, the uncertain information mode mainly involves uncertainty about the distance region and Doppler shift region of the target. Therefore, the expectation in the model below is the expectation of the region with a probability distribution.

[0158] For radar:

[0159]

[0160] For jammers:

[0161]

[0162] Therefore, we constructed a two-layer game theory model involving the radar, target, and jammer. The first layer is a coarse-grained fuzzy function template and jammer jamming mode selection game model based on extended game theory. This model primarily determines the template type and jamming mode through game theory, and can construct deterministic and uncertain types depending on the information mode. The second layer, based on the first layer, is a fine-grained parameter modulation game model based on differential game theory. This model primarily determines the radar's transmitted waveform and matched / mismatched filtering waveforms through game theory. The above model is a conceptual model and a continuous model. Modern radar systems are primarily digital systems, which have discretized characteristics; therefore, the model is a discretized model based on the conceptual model.

[0163] Furthermore, the derivation is as follows:

[0164] For the model

[0165]

[0166] First, derive the objective function.

[0167]

[0168] in

[0169]

[0170] Observe the last term of the objective function expansion

[0171]

[0172] In order to use the loop iteration technique, we based on

[0173]

[0174] Iteration produces two sequences

[0175]

[0176] The iterative method is as follows:

[0177] Step 1: Randomly initialize and generate vectors according to the constraints of vector $X$. and .

[0178] Step 2: For fixed... and Calculations yielded

[0179]

[0180] And update

[0181] Step 3: For fixed... and Calculations yielded

[0182]

[0183] Step 4: For fixed and Calculations yielded

[0184]

[0185] Step 5: Repeat steps 2, 3, and 4 until the convergence threshold is met.

[0186] Output: Final .

[0187] Based on the above, the distance Doppler image before optimization in this embodiment is as follows: Figure 2 As shown, the mutual fuzziness function graph before optimization is as follows: Figure 3 As shown. To optimize this waveform, firstly, given the initial radar waveform, filtering, and other necessary parameters, calculate the two-dimensional color map and three-dimensional function map of the ambiguity function for the initial waveform and the filter. Based on the target and interference models, form a range Doppler image and calculate the local signal-to-interference-plus-noise ratio (SNR) of the target element. Modulate the initial radar waveform and filter using the ambiguity function-based model and algorithm described above, outputting the waveform and filter. Calculate the two-dimensional color map and three-dimensional function map of the ambiguity function for the modulated waveform and the filter. Again, based on the target and interference signal models, form a range Doppler image and calculate the local SNR of the target element. Compare the shapes of the ambiguity functions before and after, compare the clarity of the target element and the local SNR before and after, and the optimized range Doppler image is shown below. Figure 4 As shown.

[0188] Compared with existing methods, the advantage of the method of the present invention is that it can efficiently obtain the optimal transmission waveform and matching waveform through reverse iteration, thereby improving the anti-jamming capability of the radar system.

[0189] As used herein, the term "preferred" is meant as an example, illustration, or illustration. Any aspect or design described herein as "preferred" need not be construed as being more advantageous than other aspects or designs. Rather, the use of the term "preferred" is intended to present the concept in a specific manner. As used in this application, the term "or" is intended to mean an inclusive "or" rather than an exclusionary "or." That is, unless otherwise specified or clear from the context, "X uses A or B" naturally includes either of the permutations. That is, if X uses A; X uses B; or X uses both A and B, then "X uses A or B" is satisfied in any of the foregoing examples.

[0190] Furthermore, although this disclosure has been shown and described with respect to one or more implementations, equivalent variations and modifications will occur to those skilled in the art based on a reading and understanding of this specification and the accompanying drawings. This disclosure includes all such modifications and variations and is limited only by the scope of the appended claims. In particular, with respect to the various functions performed by the aforementioned components (e.g., elements, etc.), the terminology used to describe such components is intended to correspond to any component (unless otherwise indicated) that performs the specified function of said component (e.g., is functionally equivalent to it), even if structurally not equivalent to the disclosed structure performing the functions in the exemplary implementations of this disclosure shown herein. Moreover, although specific features of this disclosure have been disclosed with respect to only one of several implementations, such features may be combined with one or more features of other implementations that may be desirable and advantageous for a given or particular application. Furthermore, with regard to the use of the terms “comprising,” “having,” “containing,” or variations thereof in the Detailed Description or claims, such terms are intended to be included in a manner similar to the term “including.”

[0191] The functional units in this invention embodiment can be integrated into a processing module, or each unit can exist physically separately, or multiple units can be integrated into a module. The integrated module can be implemented in hardware or as a software functional module. If the integrated module is implemented as a software functional module and sold or used as an independent product, it can also be stored in a computer-readable storage medium. The storage medium mentioned above can be a read-only memory, a disk, or an optical disk, etc. The aforementioned devices or systems can execute the storage methods in the corresponding method embodiments.

[0192] In summary, the above embodiments are one implementation of the present invention, but the implementation of the present invention is not limited to the embodiments described above. Any changes, modifications, substitutions, combinations, or simplifications made that deviate from the spirit and principle of the present invention should be considered equivalent substitutions and are included within the protection scope of the present invention.

Claims

1. A waveform design method based on prior information of self-fuzzy functions, characterized in that, Includes the following steps: Step 1: Determine the radar target and the jamming target based on prior information; Step 2: Design a self-fuzzy function template based on prior information; Step 3: Construct a zero-sum game model between the radar operator and the jammer. Step 4: Generate the optimized radar waveform based on the iterative method derived from the model; The self-fuzzy function is as follows: S(t) is the signal, t is time, and S * (t) represents the complex conjugate of the signal S(t). The parameter represents the time delay, and f represents the frequency offset. It is a combination of frequency offset f and time delay. The complex exponential function is used to introduce the corresponding phase shift, and the infinitesimal integral dt represents the integration of the signal over time. It has the following mathematical properties: in, Indicates the self-fuzzy function in The amplitude at point S, where Energy(S) represents the energy of the signal S. and These represent the self-fuzzy function in and The range at that point, The double integral symbol represents the integral over the entire time delay. Integrate over the range of frequency offset f. Let represent the square of the modulus of the self-fuzzy function, and let represent the energy density. Indicates time delay The infinitesimal element df represents the infinitesimal element of the frequency offset f, indicating that the self-ambiguity function has a certain degree of ambiguity with respect to the frequency offset f. Symmetry; Based on prior knowledge and the correspondence between the energy distribution in the distance-Doppler plane and the fuzzy function, a self-fuzzy function template is obtained: Where E is the energy constraint of the transmitted waveform, therefore the template design satisfies the energy constraint, that is...

2. The waveform design method based on prior information of self-fuzzy functions according to claim 1, characterized in that, The radar target is characterized by the local signal-to-interference-plus-noise ratio (SIR / NDR) of the target echo signal. Q′ target Local represents the region or potential region where the target is located on the range-Doppler plane. This represents the signal-to-interference-plus-noise ratio (SIR) of the local area where the target is located. The target of the interference is expressed by the local interference noise ratio of the interference signal: Q′ jammer This refers to the false target region on the range-Doppler plane. In summary, the game objective of radar is a bi-objective function. The game objective of the jammer is a bi-objective function. The relationship between radar and jamming is a zero-sum game.

3. The waveform design method based on prior information of self-fuzzy functions according to claim 2, characterized in that, The zero-sum game model of the radar and jammer is as follows: The template spaces for the radar self-ambiguity function and the mutual ambiguity function are M and M, respectively. radar,auto M radar,cross The jamming mode space of the jammer is M jammer ,j∈M jammer This indicates a certain jamming mode, so the first layer of the game between the radar and the jammer is between the radar, the target, and the jammer M. auto M cross M jammer In the game above, the actual target and the distribution area of ​​interference energy are The target region and interference energy region of the template d design are as follows: If the distance or coverage metric between regions is dist, then the conceptual model of the first-level game is as follows: For jammers: For radar: If the region defined by template d has a probability distribution, then the above model is a stochastic model, and the expectation in the model below is the expectation of the region with the probability distribution: For jammers: For radar: For the first-level game, we first apply backward induction to solve the extended game problem of template selection and interference mode selection under the condition of complete information, and then apply the perfect Bayesian Nash equilibrium method to solve the Bayesian extended game problem of template selection and interference mode selection without complete information. The first-level game is a coarse-grained fuzzy function template and interference mode selection game model based on extended game. Through the game, the template type and interference mode are determined. According to the different information modes, two types are constructed: deterministic and uncertain. If the choices in the first layer of the game have been determined, that is, the template d of the fuzzy function and the interference mode j of the interference machine have been determined, then we enter the second layer of parameter fine-tuning differential game stage.

4. The waveform design method based on prior information for self-fuzzy functions according to claim 3, characterized in that, In the second layer of parameter fine-tuning differential game stage Radar control functions: The amplitude, frequency, and phase modulation function is denoted as... a m，n (t) is the amplitude function, f m，n (t) is the frequency function, θ m，n (t) is the phase modulation function, S radar (t) is the time-domain waveform of the radar signal. It is the output of the matched filter; Control functions of the jammer: parameter control under time delay and Doppler shift modulation t jammer It's a time delay, f d，jammer It is Doppler translation modulation, where d is the template; State space: The state space of a game is the real-time evolution of the local signal-to-noise ratio on the distance-Doppler plane; Objective function: The difference between the template set by the fuzzy function and the actual fuzzy function of the transmitted waveform.

5. The waveform design method based on prior information for self-fuzzy functions according to claim 4, characterized in that, In the second-level parameter fine-tuning differential game stage, a conceptual model of differential game with parameter modulation under deterministic and uncertain information modes is constructed.

6. The waveform design method based on prior information of self-fuzzy functions according to claim 5, characterized in that, The differential game model under deterministic information is constructed as follows: For radar: For jammers: Among them, Q target and Q jammer G represents the sets of characteristics of the target and the interference source, respectively. k，p It is a discrete template of the mutual ambiguity function, used to describe the characteristics of signals in a radar system, where k and p are the discretized time delay and frequency offset indices. It is the error between the discrete template of the mutually fuzzy function and its expected value. These are self-ambiguity and mutual ambiguity functions used to describe the time delay of signals S and W. Correlation with frequency offset f and These represent the local signal-to-noise ratio and the interference noise ratio, respectively, and their dynamic changes are determined by the system's internal state and external control inputs. and The decision, and It is a function that describes dynamic evolution and is used to calculate the rate of change of local signal-to-noise ratio and interference-to-noise ratio.

7. The waveform design method based on prior information for self-fuzzy functions according to claim 6, characterized in that, The differential game model under the uncertain information mode is constructed as follows. Here, the uncertain information mode has uncertainty in the distance region and the Doppler shift region of the target. Therefore, the expectation in the model below is the expectation of the region with a probability distribution: For radar: For jammers: The second-level game is based on the first-level game. It uses a fine-grained parameter modulation game model based on differential game theory to determine the radar's transmitted waveform and the matching and mismatch filtering waveforms through game theory.

8. The waveform design method based on prior information for self-fuzzy functions according to claim 7, characterized in that, Based on the waveforms of the first-level and second-level games, the discretization model is designed as follows: min X,Y This indicates a minimization operation on variables X and Y. This represents the summation of the index set T×F over time delay and frequency offset, g kp The discrete template representing the mutual ambiguity function describes the characteristics of the signal under time delay k and frequency offset p. X represents the modulus of the expected value of the mutual fuzzy function template. H J represents the conjugate transpose of X. kp Let X represent the complex representation of the mutual ambiguity function template, and let X represent the received signal processing vector in the optimization model. This represents the phase offset, where m and n are the row and column indices of X, respectively. First, derive the objective function. in The last term Re(X) in the expansion of the objective function H AX) Using loop iteration, based on Iteration produces two sequences The iterative method is as follows: Step 1: Randomly initialize and generate the first element of two sequences according to the constraints of vector X. and X (0) ; Step 2: For a fixed sequence and sequence X (.) Calculations yielded And update A (.) A (.) yes; Step 3: Calculate the phase offset after a fixed iteration. and sequence X (.) Calculations yielded m and n are the row and column indices of matrix X, respectively. Representation matrix In the first iteration, the value of the element at position m, n It represents the value of the element at position m, N+l during the first iteration. Step 4: For fixed and Calculated Step 5: Repeat steps 2, 3, and 4 until the convergence threshold is met; Finally, output the final X. (.) .

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