A Waveform Optimization Method for Self-Fuzzy Functions under Integrated Weight Distribution

Abstract

This invention discloses a waveform optimization method for a self-fuzzy function under a comprehensive weight distribution, comprising the following steps: Step 1, analyzing the game model among radar, target, and jammer based on a long-range support jamming scenario; Step 2, designing a self-fuzzy function template under the weight distribution; Step 3, constructing a zero-sum game model between the radar and jammer under the weight distribution; Step 4, improving and designing a simplified model based on the zero-sum game model. This invention provides a waveform design method based on prior information for self-fuzzy functions. Through a reverse iterative method, the optimal transmitted waveform and 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 optimization method for a self-fuzzy function under a comprehensive weight distribution. Background Technology

[0002] Radar waveform design is a crucial aspect of radar systems, aiming to improve system performance by selecting and optimizing the characteristics of the transmitted signal. Radar waveform design directly impacts target detection, range and velocity measurement, and anti-jamming capabilities. 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] Commonly used waveform design methods are as follows: 1. Linear Frequency Modulation (LFM) signal: Utilizes the linear change of signal frequency over time. It has good range resolution and Doppler tolerance, suitable for multi-target detection. 2. Phase-coded signal: Encodes information by changing the phase of the signal. It has strong anti-interference capabilities and is suitable for complex electromagnetic environments. 3. Frequency Agility signal: Quickly changes the frequency of the transmitted signal in a short time. Improves anti-interference capabilities and reduces the risk of being intercepted by enemy radar. 4. Doppler Shift Compensated signal: Compensates for the effects of Doppler shift by adjusting the signal frequency. Improves the accuracy of target detection, especially in the detection of high-speed moving targets. 5. Orthogonal Frequency Division Multiplexing (OFDM) signal: Divides the signal into multiple orthogonal subcarriers, each transmitting different data. It has strong anti-multipath interference capabilities and is suitable for complex propagation environments. 6. Random waveform: Uses random or pseudo-random signals to improve anti-interference capabilities and confidentiality. It has strong anti-interference capabilities and is difficult to intercept and analyze. 7. Compressive Sensing: Using sparse representation and compressed sensing theory, signals are reconstructed with a small amount of measurement data, reducing the amount of data transmitted and improving signal processing efficiency.

[0004] 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.

[0005] 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

[0006] In view of this, the present invention discloses a waveform optimization method for a self-fuzzy function under a comprehensive weight distribution. Based on existing target and interference signal models, a series of waveform templates or optimization 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.

[0007] The objective of this invention is achieved through the following technical solution: a comprehensive mutual fuzzy function cyclic optimization method based on deterministic information, the method comprising the following steps:

[0008] Step 1: Based on the long-range support jamming scenario, analyze the game model among radar, target, and jammer;

[0009] Step 2: Design a self-fuzzy function template under the weight distribution;

[0010] Step 3: Construct a zero-sum game model between the radar side and the jamming side under the weight distribution;

[0011] Step 4: Based on the zero-sum game model, a simplified model is designed.

[0012] Furthermore, the aforementioned long-range support jamming scenario is as follows:

[0013] The radar is located at the origin, forming a spherical envelope and a burn-through envelope B(0,R). max ),B(0,R min ), R max R represents the maximum effective range of the radar and anti-missile system working together. min The radar's burn-through range is defined within the burn-through envelope B(0,R). max Beyond this, it cannot effectively detect or threaten targets and jammers within the envelope B(0,R). min Within a certain range, it can accurately detect targets; the distance between the jammer and the radar is R1. Long-range jamming support means that the jammer does not enter the spherical envelope to avoid risks, but performs jamming near the spherical envelope. Therefore, R1 > R max R1=R max +δ, where δ represents the relative safe distance; the jammer is located within the envelope B(0,R). max+δ) and B(0,R) max The current target is located within the envelope B(0,R). max ) and B(0,R min )between.

[0014] Furthermore, the self-fuzzy function is:

[0015] Q target and Q jammer These represent the sets of characteristics of the target and the interference source, respectively. The so-called uncertain information mode refers to the radar's response to Q. target Q jammer It is uncertain, according to Q. target Q jammer probability distribution on

[0016]

[0017] α k,p β is the probability that the k-th element in the target feature set is selected under the p-th condition. k,p It is the probability that the k-th element in the set of interference source characteristics is selected under the p-th condition; k is the identifier of the different target or interference source, and p is the condition associated with each target or interference source.

[0018] Determine the fuzzy function template g k,p The weights corresponding to (k,p)∈T×F

[0019]

[0020] α k′,p′ β is the probability that the k-th element in the target feature set under the fuzzy function template is selected under the p-th condition. k′,p′ Q represents the probability that the k-th element in the set of interference source characteristics under the fuzzy function template is selected under the p-th condition, where k′ is the identifier of the target or interference source under the fuzzy function template, and p′ is the condition associated with each target or interference source under the fuzzy function template. zero It is a set of features, in which the weight of each element is uniformly set to 1.

[0021] Furthermore, the zero-sum game model between the radar side and the jamming side is as follows:

[0022] The template spaces for radar self-ambiguity functions and mutual ambiguity functions are respectively

[0023] M auto M cross

[0024] The jamming mode space of the jammer is

[0025] M jammer,j∈M jammer

[0026] This indicates a certain jamming mode. Therefore, the first layer of the game between radar and jammer is...

[0027] M auto M cross M jammer In the game above, the actual target and the distribution area of ​​interference energy are However, the target and interference energy region of template d design are... If the distance or coverage metric between regions is dist, then the conceptual model of the first-level game is as follows:

[0028] For jammers:

[0029]

[0030] For radar:

[0031]

[0032] If the region defined by template d has a probability distribution, then the above model can be constructed as a stochastic model. The expectation in the model below is the expectation of the region with a probability distribution:

[0033] For jammers:

[0034]

[0035] For radar:

[0036]

[0037] Furthermore, 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.

[0038] Furthermore, 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 pattern j of the interference machine have been determined, then we enter the second layer of parameter fine-tuning differential game stage:

[0039] Radar control function: (S radar (t),W match∨mis The amplitude, frequency, and phase modulation function of (t) is denoted as

[0040] u radar (t)=(S radar (t),W match∨mis (t); a m,n(t),f m,n (t),θ m,n (t))

[0041] 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, W march∨mis (t) is the output of the matched filter;

[0042] The jammer's control function: parameter control in deception-forwarding jamming mode, including time delay and Doppler shift modulation, denoted as:

[0043] v jammer (t)=(t jammer ,f d,jammer )

[0044] t jammer It's a time delay, f d,jammer It is Doppler translation modulation, where d is the template;

[0045] 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;

[0046] Objective function: The difference between the template set by the fuzzy function and the actual fuzzy function of the transmitted waveform;

[0047] Construct a differential game concept model of parameter modulation under deterministic and uncertain information modes.

[0048] Furthermore, the differential game model under the deterministic information model is constructed as follows:

[0049] For radar:

[0050]

[0051] For jammers:

[0052]

[0053] 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, and d auto∨cross (τ,f) is the error between the discrete template of the mutually ambiguous function and its expected value, χ auto∨cross,S,W(τ,f) are self-ambiguity and mutual ambiguity functions used to describe the correlation between signals S and W under time delay τ and 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 the external control input u. radar (t) and v jammer Determined by (t), 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.

[0054] 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:

[0055] For radar:

[0056]

[0057] For jammers:

[0058]

[0059] Compared with existing methods, the advantages of the method of this invention are that network game theory is a research hotspot in recent years. However, traditional game theory solving algorithms are extremely difficult to solve in large-scale networks. This invention provides a waveform design method based on prior information of self-fuzzy functions. Through the inverse iterative method, the optimal transmission waveform and matching waveform can be obtained efficiently, thereby improving the anti-jamming capability of the radar system. Attached Figure Description

[0060] Figure 1 A flowchart illustrating an embodiment of the present invention is shown;

[0061] 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;

[0062] 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;

[0063] 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

[0064] 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.

[0065] 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.

[0066] like Figure 1 As shown, a comprehensive mutual fuzzy function iterative optimization method based on deterministic information includes a representation of...

[0067] Step 1: Based on the long-range support jamming scenario, analyze the game model among radar, target, and jammer;

[0068] Step 2: Design a self-fuzzy function template under the weight distribution;

[0069] Step 3: Construct a zero-sum game model between the radar side and the jamming side under the weight distribution;

[0070] Step 4: Based on the zero-sum game model, a simplified model is designed;

[0071] Specifically, the long-range support jamming scenario is as follows:

[0072] Radar, targets, and jamming mechanisms have become the three key players in a long-range support jamming scenario within the broader context of air defense and missile defense. The radar, positioned at the origin, has a maximum effective range of R in conjunction with the missile defense system. max With the radar as the center, R max The radius constitutes the envelope B(0,R) of the air defense and anti-missile sphere. max Any hostile aircraft entering this envelope faces significant risks. If a hostile aircraft, or target, attempts to penetrate the envelope, its own jamming and stealth capabilities are relatively weak. Therefore, a separate jamming aircraft is needed to provide long-range cover. The distance between the jamming aircraft and the radar is R1. Long-range jamming support means that the jamming aircraft does not enter the spherical envelope to avoid risk, but rather performs jamming close to the envelope. Therefore, R1 > R. max R1=R max +δ, where δ represents a smaller relative safe distance. The jammer's protection of the target is not absolute. When the target is close enough to the radar, the jammer loses its jamming effect, and the radar can clearly detect the target. This distance is called the radar's burn-through distance, denoted as R. min This constitutes the burn-through envelope of the radar system, denoted as B(0,R). min Therefore, the jammer's cover for the target occurs at B(0,R). max B(0,R) min This area.

[0073] In summary, in the long-range support and jamming scenario under the broader context of air defense and missile defense, the radar is located at the origin of the coordinate system, forming two envelopes B(0,R).max ),B(0,R min ), in the envelope B(0,R) max Beyond this, it cannot effectively detect or threaten targets and jammers within the envelope B(0,R). min Within the envelope B(0,R), it holds an absolute advantage and can accurately detect targets; the jammer is located within the envelope B(0,R). max +δ) and B(0,R) max The current target is located within the envelope B(0,R). max ) and B(0,R min )between.

[0074] Furthermore, the self-fuzzy function is:

[0075] The so-called uncertain information mode refers to the radar's response to Q. target Q jammer It is uncertain, so the discrete template g of the designed self-fuzzy function is... k,p It's not precise enough; we need to use Q. target Q jammer The above probability distribution

[0076]

[0077] Determine the fuzzy function template g k,p The weights corresponding to (k,p)∈T×F

[0078]

[0079] The probability distribution is essentially transformed into weights, so the fact that the weight distribution can be given directly without specifying the probability distribution also reflects uncertainty.

[0080] Furthermore, the zero-sum game model between the radar side and the jamming side is as follows:

[0081] Let the template spaces of the radar self-ambiguity function and the mutual ambiguity function be respectively...

[0082] M auto M cross

[0083] We denote the jamming mode space of the jammer as...

[0084] M jammer ,j∈M jammer

[0085] This indicates a certain jamming mode. Therefore, the first layer of the game between radar and jammer is...

[0086] M auto M cross M jammerIn the game above, assuming the actual target and interference energy distribution areas are... However, the target and interference energy region of template d design are... If the distance or coverage metric between regions is dist, then the conceptual model of the first-level game is as follows.

[0087] For jammers:

[0088]

[0089]

[0090] For radar:

[0091]

[0092] 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.

[0093] For jammers:

[0094]

[0095] For radar:

[0096]

[0097] 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.

[0098] 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 pattern j of the interference machine have been determined, then we enter the second layer of parameter fine-tuning differential game stage.

[0099] Radar control function: (S radar (t),W match∨mis The amplitude, frequency, and phase modulation function of (t) is denoted as

[0100] u radar (t)=(S radar (t),W match∨mis (t); a m,n (t),f m,n (t),θ m,n (t))

[0101] The control function of the jammer: parameter control under a certain jamming mode. This project mainly focuses on deception and forwarding jamming, primarily time delay and Doppler shift modulation, denoted as...

[0102] v jammer (t)=(t jammer ,f d,jammer )

[0103] 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.

[0104] Objective function: The difference between the template set by the fuzzy function and the actual fuzzy function of the transmitted waveform (filtered).

[0105] Therefore, we can construct a conceptual model of differential game with parameter modulation under deterministic and uncertain information modes.

[0106] First, the differential game model under deterministic information mode is constructed as follows.

[0107] For radar:

[0108]

[0109] For jammers:

[0110]

[0111] 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.

[0112] For radar:

[0113]

[0114] For jammers:

[0115]

[0116] 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.

[0117] 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.

[0118] This invention provides a waveform design method based on prior information of self-fuzzy functions. By using an inverse iterative method, the optimal transmitted waveform and the matching waveform can be obtained efficiently, thereby improving the anti-jamming capability of the radar system.

[0119] 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.

[0120] 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.”

[0121] 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.

[0122] 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 optimization method for a self-fuzzy function under a comprehensive weight distribution, characterized in that, Includes the following steps: Step 1: Based on the long-range support jamming scenario, analyze the game model among radar, target, and jammer; Step 2: Design a self-fuzzy function template under the weight distribution; Step 3: Construct a zero-sum game model between the radar side and the jamming side under the weight distribution; Step 4: Based on the zero-sum game model, a simplified model is designed; The aforementioned long-range support jamming scenario is: The radar is located at the origin, forming a spherical envelope and a burn-through envelope B(0,R). max ),B(0,R min ), R max R represents the maximum effective range of the radar and anti-missile system working together. min The radar's burn-through range is defined within the burn-through envelope B(0,R). max Beyond this, it cannot effectively detect or threaten targets and jammers within the envelope B(0,R). min Within a certain range, it can accurately detect targets; the distance between the jammer and the radar is R1. Long-range jamming support means that the jammer does not enter the spherical envelope to avoid risks, but performs jamming near the spherical envelope. Therefore, R1 > R max R1=R max +δ, where δ represents the relative safe distance; the jammer is located within the envelope B(0,R). max +δ) and B(0,R) max The current target is located within the envelope B(0,R). max ) and B(0,R min )between; The self-fuzzy function is: Q target and Q jammer These represent the sets of characteristics of the target and the interference source, respectively. The so-called uncertain information mode refers to the radar's response to Q. target Q jammer It is uncertain, according to Q. target Q jammer probability distribution on α k,p β is the probability that the k-th element in the target feature set is selected under the p-th condition. k,p It is the probability that the k-th element in the set of interference source characteristics is selected under the p-th condition; k is the identifier of the different target or interference source, and p is the condition associated with each target or interference source. T and F are sets of indices for time delay and frequency offset, which determine the fuzzy function template g. k,p The weights corresponding to (k,p)∈T×F α k′,p′ β is the probability that the k-th element in the target feature set under the fuzzy function template is selected under the p-th condition. k′,p′ Q represents the probability that the k-th element in the set of interference source characteristics under the fuzzy function template is selected under the p-th condition, where k′ is the identifier of the target or interference source under the fuzzy function template, and p′ is the condition associated with each target or interference source under the fuzzy function template. zero It is a set of features, in which the weight of each element is uniformly set to 1.

2. The waveform optimization method for a self-fuzzy function under a comprehensive weight distribution according to claim 1, characterized in that, The zero-sum game model between the radar side and the jamming side is as follows: The template spaces for radar self-ambiguity functions and mutual ambiguity functions are respectively M auto ,M cross The jamming mode space of the jammer is M jammer ,j∈M jammer This represents a certain jamming mode; therefore, the first level of the game between the radar and the jammer is in M. auto M cross M jammer In the game above, the actual target and the distribution area of ​​interference energy are However, the target and interference energy region of template d design are... If the distance or coverage metric between regions is dist, then the conceptual model of the first-level game is as follows: For jammers: s.t.d∈M auto or M cross ,j∈M jammer For radar: s.t.d∈M auto or M cross ,j∈M jammer If the region defined by template d has a probability distribution, then the above model can be constructed as a stochastic model. The expectation in the model below is the expectation of the region with a probability distribution: For jammers: s.t.d∈M auto or M cross ,j∈M jammer For radar: s.t.d∈M auto or M cross ,j∈M jammer 。 3. The waveform optimization method for a self-fuzzy function under a comprehensive weight distribution according to claim 2, characterized in that, For the first level of the 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.

4. The waveform optimization method for a self-fuzzy function under a comprehensive weight distribution according to claim 3, characterized in that, If the choices in the first layer of the game are already determined, that is, the template d of the fuzzy function and the jamming pattern j of the jammer are already determined, then we enter the second layer of parameter fine-tuning differential game stage: the radar control function: (S radar (t),W match∨mis The amplitude, frequency, and phase modulation function of (t) is denoted as u radar (t)=(S radar (t),W match∨mis (t);a m,n (t),f m,n (t),θ m,n (t)) 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, W march∨mis (t) is the output of the matched filter; The jammer's control function: parameter control in deception-forwarding jamming mode, including time delay and Doppler shift modulation, denoted as: v jammer (t)=(t jammer ,f d,jammer ) 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; Construct a differential game concept model of parameter modulation under deterministic and uncertain information modes.

5. The waveform optimization method for a self-fuzzy function under a comprehensive weight distribution according to claim 4, 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, and d auto∨cross (τ,f) is the error between the discrete template of the mutually ambiguous function and its expected value, χ auto∨cross,S,W (τ,f) are self-ambiguity and mutual ambiguity functions used to describe the correlation between signals S and W under time delay τ and 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 the external control input u. radar (t) and v jammer Determined by (t), 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.

6. The waveform optimization method for a self-fuzzy function under a comprehensive weight distribution according to claim 5, 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:

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