Waveform optimization method of self-ambiguity function under comprehensive weight distribution

Abstract

The invention discloses a waveform optimization method for a self-ambiguity function under comprehensive weight distribution, and the method comprises the following steps: 1, analyzing a game model of a radar, a target and a jammer based on a long-distance support jamming scene; 2, designing a self-fuzzy function template under weight distribution; 3, constructing a zero-sum game model between a radar party and an interference party under weight distribution; and step 4, improving and designing a simplified model based on the zero-sum game model. According to the waveform design method under the prior information facing the self-ambiguity function, the optimal transmitted waveform and the matched waveform can be efficiently obtained through a reverse iteration method, and therefore the anti-interference capacity of a radar system is improved.

Description

Technical Field

[0001] The invention belongs to the technical field of radar waveform design, and in particular relates to a waveform optimization method of a self-fuzzy function under comprehensive weight distribution. Background Art

[0002] Radar waveform design is a very important part of the radar system, which aims to improve the performance of the radar system by selecting and optimizing the characteristics of the transmitted signal. The design of the radar waveform directly affects many aspects such as target detection, distance and speed measurement, and anti-interference ability. The radar system detects and identifies targets by emitting specific electromagnetic waveforms, while dealing with various complex electromagnetic environments and hostile interference. Traditional waveform design methods often rely on fixed waveform patterns or empirical designs. Although these designs meet the basic detection needs to a certain extent, their performance and effects are significantly limited when facing a changing electromagnetic environment and strong electronic warfare interference.

[0003] Commonly used waveform design methods are as follows: 1. Linear frequency modulation (LFM) signal: use the frequency of the signal to change linearly over time. It has good distance resolution and Doppler tolerance, suitable for multi-target detection. 2. Phase coded signal: Encode information by changing the phase of the signal, strong anti-interference ability, suitable for complex electromagnetic environment. 3. Frequency Agility signal: Rapidly change the frequency of the transmitted signal in a short time. Improve anti-interference ability and reduce the risk of being intercepted by enemy radar. 4. Doppler shift compensation signal: By adjusting the frequency of the signal, compensate for the influence of Doppler shift. Improve the accuracy of target detection, especially in the detection of high-speed moving targets. 5. Orthogonal frequency division multiplexing (OFDM) signal: Divide the signal into multiple orthogonal subcarriers, each subcarrier transmits different data, has strong anti-multipath interference ability, and is suitable for complex propagation environment. 6. Random waveform: Use random or pseudo-random signals to improve anti-interference ability and confidentiality, strong anti-interference ability, and difficult to be intercepted and analyzed. 7. Compressed Sensing Signal: Using sparse representation and compressed sensing theory, the signal is reconstructed through a small amount of measurement data, reducing the amount of data transmission and improving signal processing efficiency.

[0004] In traditional waveform design, researchers usually rely on mathematical models and simulation tools to evaluate the performance of different waveform schemes. These models involve the propagation characteristics of radar signals, target feature extraction methods, and interference suppression techniques. With the improvement of computing power and algorithm optimization, modern waveform design increasingly adopts methods based on statistical learning and optimization theory, and maximizes the signal processing efficiency in dynamic scenarios through big data analysis and adaptive algorithms.

[0005] As an important part of modern radar system performance optimization, waveform design is constantly driven and influenced by technological innovation and scientific research. Future development directions include more intelligent waveform adaptive design, integrated multi-sensor collaboration, and adaptability to extreme conditions in complex electromagnetic environments. These technological advances will further enhance the wide application and actual 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 of a self-fuzzy function under a comprehensive weight distribution. Based on the 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 greatest extent when receiving target signals, and can suppress interference to the greatest extent when facing interference signals, thereby ensuring the stability and performance of the system.

[0007] The object of the present invention is achieved through the following technical solution, a comprehensive mutual fuzzy function loop optimization method based on determined information, the method comprising the following steps:

[0008] Step 1: Analyze the game model among radar, target and jammer based on the long-distance support jamming scenario;

[0009] Step 2, designing a self-fuzzy function template under weight distribution;

[0010] Step 3: construct a zero-sum game model between the radar party and the jammer under weight distribution;

[0011] Step 4: Based on the zero-sum game model, improve and design a simplified model.

[0012] Furthermore, the long-distance support interference scenario is:

[0013] The radar is located at the origin of the coordinate system, forming a spherical envelope and a burn-through envelope B(0,R max ),B(0,R min ), R max is the maximum range of radar and anti-missile system, R min is the burn-through distance of the radar, in the burn-through envelope B(0,R max ), it is impossible to effectively detect and threaten the target and jammer. min ) can accurately detect the target; the distance between the jammer and the radar is R1. The meaning of long-distance support interference is that the jammer does not enter the spherical envelope to avoid risks, but interferes near the spherical envelope, so R1>R max ,R1=R max +δ,δ is the relative safety distance; the jammer is located in envelope B(0,R max+δ) and B(0,R max ); the current target is located in 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 Represents the characteristic set 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 is uncertain, according to Q target ,Q jammer The probability distribution on

[0016]

[0017] α k,p is the probability that the kth element in the target feature set is selected under the pth condition, β k,p is the probability that the kth element in the interference source feature set is selected under the pth condition; k is the identifier of different targets or interference sources, and p is the condition associated with each target or interference source;

[0018] To determine the fuzzy function template g k,p ,(k,p)∈T×F corresponding weight

[0019]

[0020] α k′,p′ is the probability that the kth element in the target feature set under the fuzzy function template is selected under the pth condition, β k′,p′ is the probability that the kth element in the interference source feature set under the fuzzy function template is selected under the pth condition, k′ is the identifier of the target or interference source under the fuzzy function template, p′ is the condition associated with each target or interference source under the fuzzy function template, Q zero is a feature set in which the weights of the elements contained in it are uniformly set to 1.

[0021] Furthermore, the zero-sum game model between the radar party and the jammer is:

[0022] The template spaces of radar self-ambiguity function and mutual ambiguity function are

[0023] M radar,auto ,M radar,cross

[0024] The jammer’s interference pattern space is

[0025] M jammer,j∈M jammer

[0026] represents a certain interference pattern. So the first level of game between radar and jammer is in M auto ,M cross ,M jammer The real target and interference energy distribution area are However, the target and interference energy areas designed by template d are The distance or coverage measure between regions is dist, so the conceptual model of the first-level game is as follows:

[0027] For the jammer:

[0028]

[0029] std∈M auto oeLh cross ,j∈M jammer

[0030] For radar:

[0031]

[0032] std∈M auto oeLh cross ,j∈M jammer

[0033] If the area determined by the template d has a probability distribution, then the above model can be constructed as a random model. The expectation in the following model is to find the expectation of the area with probability distribution:

[0034] For the jammer:

[0035]

[0036] std∈M auto oeLh cross ,j∈M jammer

[0037] For radar:

[0038]

[0039] std∈M auto oeLh cross ,j∈M jammer .

[0040] Furthermore, for the first-level game, the backward induction method is first applied to solve the extended game problem of template selection and interference pattern selection under complete information conditions, and then the perfect Bayesian Nash equilibrium method is applied to solve the Bayesian extended game problem of template selection and interference pattern without complete information.

[0041] Furthermore, if the choice of the first-level game has been determined, that is, the template d of the fuzzy function and the interference pattern j of the jammer have been determined, then the second-level parameter fine-tuning differential game stage is entered:

[0042] Radar control function: (S radar (t),W match∨mis (t)) is the amplitude, frequency, and phase modulation function, denoted as

[0043] u radar (t)=(S radar (t),W match∨mis (t); a m,n (t),f m,n (t),θ m,n (t))

[0044] 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;

[0045] Jammer control function: parameter control in deception forwarding jamming mode, including delay and Doppler shift modulation, recorded as:

[0046] v jammer (t)=(t jammer ,f d,jammer )

[0047] t jammer is the delay, f d,jammer is Doppler shift modulation, d is the template;

[0048] State space: The state space of the game is the real-time evolution of the local signal-to-noise ratio on the range-Doppler plane;

[0049] Target function: the difference between the template set by the fuzzy function and the true fuzzy function of the transmitted waveform;

[0050] Construct a conceptual model of differential game with parameter modulation under deterministic information mode and uncertain information mode.

[0051] Furthermore, the differential game model under the deterministic information mode is constructed as follows:

[0052] For radar:

[0053]

[0054] For the jammer:

[0055]

[0056] Among them, Q target and Q jammer Represents the characteristic set of target and interference source respectively, g k,p is a discrete template of the mutual ambiguity function, which is used to describe the characteristics of the signal in the 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 mutual fuzzy function and its expected value, χ auto∨cross,S,W (τ, f) are the 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 They represent the local signal-to-noise ratio and interference-to-noise ratio respectively, and their dynamic changes are determined by the internal state of the system and the external control input u radar (t) and v jammer (t ) Determined, and It is a function that describes the dynamic evolution and is used to calculate the rate of change of the local signal-to-noise ratio and interference-to-noise ratio.

[0057] Furthermore, the differential game model under the uncertain information mode is constructed as follows. Here, the uncertain information mode is uncertain about the distance area and Doppler frequency shift area of ​​the target, so the expectation in the following model is to find the expectation of the area with probability distribution:

[0058] For radar:

[0059]

[0060] For the jammer:

[0061]

[0062] Compared with the existing methods, the advantage of the method of the present invention is that network game is a research hotspot in recent years. However, traditional game solving algorithms are extremely difficult to solve in large-scale networks. The present invention provides a waveform design method under prior information for self-fuzzy functions. Through the reverse iteration method, the optimal transmission waveform and matching waveform can be efficiently obtained, thereby improving the anti-interference ability of the radar system. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 A schematic diagram of a process flow of an embodiment of the present invention is shown;

[0064] Figure 2 The range Doppler diagram of the target echo and the interference before optimization in the embodiment of the present invention is shown;

[0065] Figure 3 A 2D mutual ambiguity function diagram of a transmission waveform before optimization according to an embodiment of the present invention is shown;

[0066] Figure 4 The optimized range Doppler diagram of the target echo and interference according to the embodiment of the present invention is shown. DETAILED DESCRIPTION

[0067] The present invention is further described below in conjunction with the accompanying drawings, but the present invention is not limited in any way. Any changes or substitutions made based on the teachings of the present invention belong to the protection scope of the present invention.

[0068] In this embodiment, linear frequency modulation is adopted to add noise and interference to the waveform, and the effectiveness of the method is verified by comparing the signal-to-interference-noise ratio before and after optimization.

[0069] like Figure 1 As shown, a comprehensive mutual fuzzy function loop optimization method based on determined information includes expressing

[0070] Step 1: Analyze the game model among radar, target and jammer based on the long-distance support jamming scenario;

[0071] Step 2, designing a self-fuzzy function template under weight distribution;

[0072] Step 3: construct a zero-sum game model between the radar party and the jammer under weight distribution;

[0073] Step 4: Based on the zero-sum game model, improve and design a simplified model;

[0074] Specifically, the long-distance support interference scenario is:

[0075] Radar, target, and jammer constitute the three players in the long-distance support jamming scenario under the background of air defense and anti-missile. The radar stands at the origin of the coordinate system, and its maximum range of action in coordination with the anti-missile system is R max , with the radar as the center, R max The radius forms the air defense and anti-missile sphere envelope B(0,R max), any hostile aircraft entering this envelope is extremely risky. If a hostile aircraft, that is, a target, wants to penetrate into the envelope space, the target's own interference stealth capability is relatively weak, and at this time, another jammer is needed to provide long-distance cover for it. The distance between the jammer and the radar is R1. The meaning of long-distance support jamming is that the jammer does not enter the spherical envelope to avoid risks, but performs jamming near the spherical envelope, so R1>R max ,R1=R max +δ,δ is a relatively small safe distance. The jammer’s cover for the target is not absolute. When the distance between the target and the radar is close enough, the jammer loses its interference significance, and the radar can definitely detect the target clearly. This distance is called the radar’s burn-through distance, recorded as R min , which constitutes the burn-through envelope of the radar system, denoted as B(0,R min ). So the jammer's cover for the target occurs at B(0,R max ), B(0,R min ) this area.

[0076] In summary, in the long-distance support interference scenario under the background of air defense and anti-missile, 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 ), it is impossible to effectively detect and threaten the target and jammer. min ), occupying an absolute advantage and being able to accurately detect the target; the jammer is located in envelope B(0,R max +δ) and B(0,R max ); the current target is located in the envelope B(0,R max ) and B(0,R min )between.

[0077] Furthermore, the self-fuzzy function is:

[0078] The so-called uncertain information mode refers to the radar's response to Q target ,Q jammer is uncertain, so the discrete template g of the designed self-fuzzy function k,p is not accurate enough, we need to target ,Q jammer The probability distribution above

[0079]

[0080] To determine the fuzzy function template g k,p ,(k,p)∈T×F corresponding weight

[0081]

[0082] Probability distribution essentially needs to be converted into weights, so it is possible to directly give weight distribution instead of probability distribution, which also reflects uncertainty.

[0083] Furthermore, the zero-sum game model between the radar party and the jammer is:

[0084] We denote the template space of radar self-ambiguity function and mutual ambiguity function as

[0085] M radar,auto ,M radar,cross

[0086] We denote the jammer's interference pattern space as

[0087] M jammer ,j∈M jammer

[0088] represents a certain interference pattern. So the first level of game between radar and jammer is in M auto ,M cross ,M jammer The game on assuming that the real target and the interference energy distribution area are However, the target and interference energy areas designed by template d are The distance or coverage measure between regions is dist, so the conceptual model of the first-level game is as follows.

[0089] For the jammer:

[0090]

[0091] std∈M auto oeLh cross ,j∈M jammer

[0092] For radar:

[0093]

[0094] std∈M auto oeLh cross ,j∈M jammer

[0095] If the area determined by the template d has a probability distribution, then the above model can be constructed as a random model, and the expectation in the following model is to find the expectation of the area with probability distribution.

[0096] For the jammer:

[0097]

[0098] std∈M auto oeLh cross ,j∈M jammer

[0099] For radar:

[0100]

[0101] std∈M auto oeLh cross ,j∈M jammer

[0102] For the first-level game, we first need to study the extended game problem of template selection and interference pattern selection under complete information conditions, and then study the Bayesian extended game problem of template selection and interference pattern selection without complete information.

[0103] If the choice of the first-level game has been determined, that is, the template d of the fuzzy function and the interference pattern j of the jammer have been determined, then the second-level parameter fine-tuning differential game stage is entered.

[0104] Radar control function: (S radar (t),W match∨mis (t)) is the amplitude, frequency, and phase modulation function, denoted as

[0105] u radar (t)=(S radar (t),W match∨mis (t); a m,n (t),f m,n (t),θ m,n (t))

[0106] Jammer control function: parameter control under a certain jamming mode. This topic mainly focuses on deception forwarding jamming, mainly delay and Doppler shift modulation, recorded as

[0107] v jammer (t)=(t jammer ,f d,jammer )

[0108] State Space: The state space of the game is the real-time evolution of the local signal-to-noise ratio on the range-Doppler plane.

[0109] Target function: The difference between the template set by the fuzzy function and the true fuzzy function of the transmitted waveform (filter).

[0110] Therefore, we can construct a conceptual model of differential game with parameter modulation under deterministic information mode and uncertain information mode.

[0111] First, the differential game model under the deterministic information mode is constructed as follows.

[0112] For radar:

[0113]

[0114] For the jammer:

[0115]

[0116] Secondly, the differential game model under the uncertain information mode is constructed as follows. Here, the uncertain information mode mainly has uncertainty in the distance area and Doppler frequency shift area of ​​the target, so the expectation in the following model is to find the expectation of the area with probability distribution.

[0117] For radar:

[0118]

[0119] For the jammer:

[0120]

[0121] Therefore, we constructed a two-layer game model of the game between radar, target and jammer. The first layer is a coarse-grained fuzzy function template and jammer interference mode selection game model based on extended game. It mainly determines the template type and interference mode through game. According to the different information modes, two types of deterministic and uncertain types can be constructed. The second layer is a fine-grained parameter modulation game model based on differential game on the basis of the first layer. It mainly determines the radar's transmission waveform and matching and mismatch filter waveforms through game. The above model is a conceptual model and a continuous model. Modern radar systems are mainly digital systems. Digital systems have discrete characteristics. The model is a discrete model based on the conceptual model.

[0122] According to the above content, the range Doppler image before optimization in this embodiment is as follows: Figure 2 As shown, the mutual fuzzy function diagram before optimization is as follows Figure 3As shown. To optimize the waveform, first, the radar initial waveform, filter and other necessary parameters are given. The two-dimensional color map and three-dimensional function map of the fuzzy function of the initial waveform and filter are calculated. According to the model of the target and interference, a range Doppler image is formed, and the local signal-to-interference-noise ratio of the target unit is calculated. The initial waveform and filter of the radar are modulated using the fuzzy function-based model and algorithm in the previous article, and the waveform and filter are output. The two-dimensional color map and three-dimensional function map of the fuzzy function of the modulated waveform and filter are calculated. Again, according to the signal model of the target and interference, a range Doppler image is formed, and the local signal-to-interference-noise ratio of the target unit is calculated. Compare the shapes of the fuzzy functions before and after, and compare the clarity and local signal-to-interference-noise ratio of the target units before and after. The optimized range Doppler map is shown as follows. Figure 4 shown.

[0123] The present invention provides a waveform design method under prior information facing a self-fuzzy function, and can efficiently obtain an optimal transmission waveform and a matching waveform through a reverse iteration method, thereby improving the anti-interference capability of a radar system.

[0124] As used herein, the word "preferred" is intended to be used as an example, instance, or illustration. Any aspect or design described herein as "preferred" is not necessarily to be construed as being more advantageous than other aspects or designs. On the contrary, the use of the word "preferred" is intended to present concepts in a specific way. The term "or" as used in this application is intended to mean an inclusive "or" rather than an exclusive "or". That is, unless otherwise specified or clear from the context, "X uses A or B" means any one of the naturally included 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.

[0125] Moreover, although the present disclosure has been shown and described with respect to one or implementations, those skilled in the art will think of equivalent variations and modifications based on the reading and understanding of this specification and the accompanying drawings. The present 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 above-mentioned components (such as elements, etc.), the terms used to describe such components are intended to correspond to any component (unless otherwise indicated) that performs the specified function of the component (such as it is functionally equivalent), even if the structure is not equivalent to the disclosed structure of the function in the exemplary implementation of the present disclosure shown herein. In addition, although the specific features of the present disclosure have been disclosed with respect to only one of several implementations, such features can be combined with one or other features of other implementations that may be desired and advantageous for a given or specific application. Moreover, insofar as the terms "including", "having", "containing" or their variations are used in specific embodiments or claims, such terms are intended to be included in a manner similar to the term "comprising".

[0126] The functional units in the embodiments of the present invention may be integrated into a processing module, or each unit may exist physically separately, or multiple or more units may be integrated into one module. The above-mentioned integrated module may be implemented in the form of hardware or in the form of a software functional module. If the integrated module is implemented in the form of a software functional module and sold or used as an independent product, it may also be stored in a computer-readable storage medium. The above-mentioned storage medium may be a read-only memory, a disk or an optical disk, etc. The above-mentioned devices or systems may execute the storage method in the corresponding method embodiment.

[0127] To sum up, the above embodiment is an implementation mode of the present invention, but the implementation mode of the present invention is not limited by the embodiment. Any other changes, modifications, substitutions, combinations, and simplifications that deviate from the spirit and principles of the present invention should be equivalent replacement methods and are included in the protection scope of the present invention.

Claims

1. A waveform optimization method for a self-fuzzy function under comprehensive weight distribution, characterized in that: The following steps are involved: Step 1: Analyze the game model among radar, target and jammer based on the long-distance support jamming scenario; Step 2, designing a self-fuzzy function template under weight distribution; Step 3: construct a zero-sum game model between the radar party and the jammer under weight distribution; Step 4: Based on the zero-sum game model, improve and design a simplified model.

2. The waveform optimization method of the self-fuzzy function under comprehensive weight distribution according to claim 1 is characterized in that: The long-distance support interference scenario is: The radar is located at the origin of the coordinate system, forming a spherical envelope and a burn-through envelope B(0,R max ),B(0,R min ), R max is the maximum range of radar and anti-missile system, R min is the burn-through distance of the radar, in the burn-through envelope B(0,R max ), it is impossible to effectively detect and threaten the target and jammer. min ) can accurately detect the target; the distance between the jammer and the radar is R1. The meaning of long-distance support interference is that the jammer does not enter the spherical envelope to avoid risks, but interferes near the spherical envelope, so R1>R max ,R1=R max +δ,δ is the relative safety distance; the jammer is located in envelope B(0,R max +δ) and B(0,R max ); the current target is located in the envelope B(0,R max ) and B(0,R min )between.

3. The waveform optimization method of the self-fuzzy function under comprehensive weight distribution according to claim 1 is characterized in that: The self-fuzzy function is: Q target and Q jammer Represents the characteristic set 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 is uncertain, according to Q target ,Q jammer The probability distribution on α k,p is the probability that the kth element in the target feature set is selected under the pth condition, β k,p is the probability that the kth element in the interference source feature set is selected under the pth condition; k is the identifier of different targets or interference sources, and p is the condition associated with each target or interference source; T and F are the index sets of time delay and frequency offset, which determine the fuzzy function template g k,p ,(k,p)∈T×F corresponding weight α k′,p′ is the probability that the kth element in the target feature set under the fuzzy function template is selected under the pth condition, β k′,p′ is the probability that the kth element in the interference source feature set under the fuzzy function template is selected under the pth condition, k′ is the identifier of the target or interference source under the fuzzy function template, p′ is the condition associated with each target or interference source under the fuzzy function template, Q zero is a feature set in which the weights of the elements contained in it are uniformly set to 1.

4. The waveform optimization method of the self-fuzzy function under comprehensive weight distribution according to claim 1 is characterized in that: The zero-sum game model between the radar party and the jammer is: The template spaces of radar self-ambiguity function and mutual ambiguity function are M radar,auto ,M radar,cross The jammer’s interference pattern space is M jammer ,j∈M jammer represents a certain interference mode; so the first level of game between radar and jammer is in M auto ,M cross ,M jammer The real target and interference energy distribution area are However, the target and interference energy areas designed by template d are The distance or coverage measure between regions is dist, so the conceptual model of the first-level game is as follows: For the jammer: s.t.d∈M auto orM cross ,j∈M jammer For radar: s.t.d∈M auto orM cross ,j∈M jammer If the area determined by the template d has a probability distribution, then the above model can be constructed as a random model. The expectation in the following model is to find the expectation of the area with probability distribution: For the jammer: s.t.d∈M auto orM cross ,j∈M jammer For radar: s.t.d∈M auto orM cross ,j∈M jammer 。 5. The waveform optimization method of the self-fuzzy function under comprehensive weight distribution according to claim 4 is characterized in that: For the first-level game, the backward induction method is first applied to solve the extended game problem of template selection and interference pattern selection under complete information conditions, and then the perfect Bayesian Nash equilibrium method is applied to solve the Bayesian extended game problem of template selection and interference pattern without complete information.

6. The waveform optimization method of the self-fuzzy function under comprehensive weight distribution according to claim 5 is characterized in that: If the choice of the first-level game has been determined, that is, the template d of the fuzzy function and the interference pattern j of the jammer have been determined, then the second-level parameter fine-tuning differential game stage is entered: Radar control function: (S radar (t),W match∨mis (t)) is the amplitude, frequency, and phase modulation function, 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; Jammer control function: parameter control in deception forwarding jamming mode, including delay and Doppler shift modulation, recorded as: v jammer (t)=(t jammer ,f d,jammer ) t jammer is the delay, f d,jammer is Doppler shift modulation, d is the template; State space: The state space of the game is the real-time evolution of the local signal-to-noise ratio on the range-Doppler plane; Target function: the difference between the template set by the fuzzy function and the true fuzzy function of the transmitted waveform; Construct a conceptual model of differential game with parameter modulation under deterministic information mode and uncertain information mode.

7. The waveform optimization method of the self-fuzzy function under comprehensive weight distribution according to claim 6 is characterized in that: The differential game model under the deterministic information mode is constructed as follows: For radar: For the jammer: Among them, Q target and Q jammer Represents the characteristic set of target and interference source respectively, g k,p is a discrete template of the mutual ambiguity function, which is used to describe the characteristics of the signal in the 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 mutual fuzzy function and its expected value, χ auto∨cross,S,W (τ, f) are the 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 They represent the local signal-to-noise ratio and interference-to-noise ratio respectively, and their dynamic changes are determined by the internal state of the system and the external control input u radar (t) and v jammer (t) determined by and It is a function that describes the dynamic evolution and is used to calculate the rate of change of the local signal-to-noise ratio and interference-to-noise ratio.

8. The waveform optimization method of the self-fuzzy function under comprehensive weight distribution according to claim 7 is characterized in that: The differential game model under the uncertain information mode is constructed as follows. Here, the uncertain information mode is uncertain about the distance area and Doppler frequency shift area of ​​the target, so the expectation in the following model is to find the expectation of the area with probability distribution: For radar: For the jammer:

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