Self-ambiguity function-oriented waveform design method under prior information

Abstract

The invention discloses a self-ambiguity function-oriented waveform design method under prior information. The method comprises the following steps of 1, determining a radar target and an interference target according to the prior information; step 2, designing a self-fuzzy function template under prior information; step 3, constructing a zero-sum game model of a radar party and an interference party; and 4, generating an optimized waveform according to a model derivation iteration method. 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 design method under prior information facing a self-fuzzy function. Background Art

[0002] In modern radar systems, waveform design is one of the key technologies related to its performance and effectiveness. Radar systems detect and identify 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 basic detection needs to a certain extent, their performance and effectiveness are significantly limited when faced with changing electromagnetic environments and strong 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 technology 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-interference capabilities by optimizing the energy distribution, spectrum characteristics and spatiotemporal characteristics of the waveform.

[0004] The background technology of waveform design covers many aspects: first, a comprehensive understanding and analysis of the radar working environment and usage scenarios. Different mission requirements may pose different challenges to the waveform design of the radar system, such as high-resolution target recognition, low-probability interception, and effective signal transmission in complex electromagnetic environments. Secondly, waveform design also needs to take into account 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 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.

[0006] 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

[0007] In view of this, the present invention discloses a waveform design method under prior information for self-fuzzy functions. 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.

[0008] The object of the present invention is to achieve a waveform design method under prior information of a self-fuzzy function through the following technical scheme, the method comprising:

[0009] Step 1, determine the radar target and the jamming target based on prior information;

[0010] Step 2, designing a self-fuzzy function template under prior information;

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

[0012] Step 4: Generate optimized radar waveform based on the model derivation iterative method.

[0013] Specifically, the target of the radar is characterized by the local signal-to-interference-noise ratio of the target echo signal:

[0014]

[0015] Q t ' arget is the area or possible area where the target is located on the range-Doppler plane. Local means local. Indicates the signal-to-interference-noise ratio of the local area where the target is located;

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

[0017]

[0018] Q j ' ammer is the false target area on the range-Doppler plane;

[0019] In summary, the radar game goal is a dual objective function.

[0020]

[0021] The game objective of the jammer is a dual objective function

[0022]

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

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

[0025]

[0026] S(t) is the signal, t is the time, S * (t) represents the complex conjugate of the signal S(t), τ represents the time delay parameter, f represents the frequency offset parameter, It is a complex exponential function containing frequency offset f and time delay τ, which is used to introduce the corresponding phase shift, dt differential integration, which means integrating the signal in time;

[0027] It has the following mathematical properties:

[0028] | auto,S (0,0)|=Energy(S)

[0029] | auto,S (-τ,-f)|=|χ auto,S (τ,f)|

[0030]

[0031] Among them, |χ auto，S (0, 0)| represents the amplitude of the self-blurring function at (τ, f) = (0, 0), Energy(S) represents the energy of the signal S, |χ auto，S (-τ, -f)| and |χ auto，S (τ, f)| represents the amplitude of the self-blur function at (-τ, -f) and (τ, f), respectively. represents the double integral symbol, indicating that the integration is performed over the entire range of time delay τ and frequency offset f, |χ auto，S (τ, f)| 2 represents the square of the modulus of the self-ambiguity function, represents the energy density, dτ represents the infinitesimal element of the time delay τ, and df represents the infinitesimal element of the frequency shift f, indicating that the self-ambiguity function has symmetry about (τ, f);

[0032] Based on the prior knowledge and the corresponding law between the energy distribution in the range-Doppler plane and the fuzzy function, the self-fuzzy function template is obtained:

[0033]

[0034] Where E is the energy constraint of the emission waveform, so the template design satisfies the energy constraint, that is,

[0035]

[0036] Furthermore, the zero-sum game model between the radar party and the jammer is:

[0037] The template spaces of radar self-ambiguity function and mutual ambiguity function are

[0038] M radar,auto ,M radar,cross

[0039] The jammer’s interference pattern space is

[0040] M jammer ,j∈M jammer

[0041] represents a certain interference mode, so the first level of game between radar and jammer is between radar, target, and jammer M auto ,M cross ,M jammer The real target and interference energy distribution area are The target area and interference energy area 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.

[0042] For the jammer:

[0043]

[0044] For radar:

[0045]

[0046] If the area determined by the template d has a probability distribution, then the above model is constructed as a random model, and the expectation in the following model is to find the expectation of the area with probability distribution:

[0047] For the jammer:

[0048]

[0049] For radar:

[0050]

[0051] For the first-level game, the backward induction method is first used to solve the extended game problem of template selection and interference mode selection under complete information conditions, and then the perfect Bayesian Nash equilibrium method is used to solve the Bayesian extended game problem of template selection and interference mode without complete information; the first-level game is a coarse-grained fuzzy function template and jammer interference mode selection game model based on the extended game. Through the game, the template type and interference mode are determined, and two types of deterministic and uncertain types are constructed according to different information modes;

[0052] 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.

[0053] Furthermore, in the second-layer parameter fine-tuning differential game stage,

[0054] Radar control function: (S radar (t),W match∨mis (t)) is the amplitude, frequency, and phase modulation function, denoted as

[0055] u radar (t)=(S radar (t),W match∨mis (t); a m,n (t),f m,n (t),θ m,n (t))

[0056] 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;

[0057] Jammer control function: parameter control under delay and Doppler shift modulation

[0058] v jammer (t)=(t jammer ,f d,jammer )

[0059] t jammer is the delay, f d,jammer is Doppler shift modulation, d is the template;

[0060] 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;

[0061] Target function: The difference between the template set by the fuzzy function and the true fuzzy function of the transmitted waveform.

[0062] Furthermore, in the second-level parameter fine-tuning differential game stage, a differential game conceptual model of parameter modulation under deterministic information mode and uncertain information mode is constructed.

[0063] Furthermore, the differential game model under the deterministic information mode is constructed as follows:

[0064] For radar:

[0065]

[0066] For the jammer:

[0067]

[0068] 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.

[0069] 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:

[0070] For radar:

[0071]

[0072] For the jammer:

[0073]

[0074] The second-level game is based on the first-level game and is a fine-grained parameter modulation game model based on differential game. Through the game, the radar's transmitting waveform and matching and mismatching filter waveforms are determined.

[0075] Furthermore, the discretization model is designed based on the waveforms of the first-layer game and the second-layer game as follows:

[0076]

[0077] min X,Y It indicates that the variables X and Y are minimized. represents the sum of the index set T×F of time delay and frequency offset, g kp Represents the discrete template of the mutual ambiguity function, describing the characteristics of the signal under time delay k and frequency offset p, represents the modulus of the expected value of the mutual fuzzy function template, X H represents the conjugate transpose of X, J kp represents the complex number representation of the mutual ambiguity function template, Y represents the received signal processing vector in the optimization model;

[0078] First derive the objective function

[0079]

[0080] in

[0081]

[0082] The last term Re(X H AX)

[0083] Use loop iteration, according to

[0084]

[0085] Iteration produces two sequences

[0086]

[0087] The iterative method is:

[0088] Step 1: Generate the first elements of the two sequences by random initialization according to the constraints of vector X and X (0) ;

[0089] Step 2: For a fixed sequence and sequence X (.) , calculated

[0090]

[0091] And update A (.) , A (.) yes;

[0092] Step 3: For a fixed phase shift after iteration and sequence X (.) , calculated

[0093]

[0094] m, n are the row index and column index of matrix X respectively, Representation Matrix At the first iteration, the value of the element at position m,n, is the value of the element at position m,N+l at the first iteration,

[0095] Step 4: For fixed and Calculated

[0096]

[0097] Step 5: Repeat steps 2, 3, and 4 until the convergence threshold is met.

[0098] Compared with the existing methods, the method of the present invention has the advantage that the optimal transmission waveform and matching waveform can be efficiently obtained through the reverse iteration method, thereby improving the anti-interference ability of the radar system. BRIEF DESCRIPTION OF THE DRAWINGS

[0099] Figure 1 A schematic diagram of a process flow of an embodiment of the present invention is shown;

[0100] Figure 2 The range Doppler diagram of the target echo and the interference before optimization in the embodiment of the present invention is shown;

[0101] Figure 3 A 2D mutual ambiguity function diagram of a transmission waveform before optimization according to an embodiment of the present invention is shown;

[0102] 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

[0103] 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.

[0104] 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.

[0105] like Figure 1 As shown, a waveform design method based on prior information of a self-fuzzy function comprises:

[0106] Step 1, determine the radar and jamming targets based on prior information;

[0107] Step 2, designing a self-fuzzy function template under prior information;

[0108] Step 3: Construct a zero-sum game model between the radar party and the jammer;

[0109] Step 4, deriving an iterative method based on the model to generate an optimized waveform;

[0110] The deterministic information indicates the time delay t at which the radar accurately knows the target. target 、The Doppler shift of the target f d,target , the jammer's jamming pattern (assumed to be forwarding deception jamming), the jammer's delay modulation based on the target delay t jammer , the Doppler frequency shift modulation of the jammer based on the target Doppler frequency shift f d,jammer And other information.

[0111] Specifically, the target of the radar is:

[0112] According to prior knowledge, the target area or possible area (Q t ' arget ) suppresses the interference and noise in the target echo and highlights the target echo. We can use the local signal-to-interference-noise ratio of the target echo signal to characterize

[0113]

[0114] The targets of the interference are:

[0115] According to a priori knowledge, in certain areas on the range-Doppler plane (Q j ' ammer ) forms a false target to cover the real target. The local interference-to-noise ratio of the jammer can be used to express the target of the jammer.

[0116]

[0117] In summary, the radar game goal is a dual objective function.

[0118]

[0119] The game objective of the jammer is also a dual objective function

[0120]

[0121] The game between radar and jamming is a zero-sum game.

[0122] Furthermore, the self-fuzzy function is:

[0123] Fuzzy function: The self-fuzzy function is defined as

[0124]

[0125] It has the following mathematical properties

[0126] |auto,S (0,0)|=Energy(S)

[0127] | auto,S (-τ,-f)|=|χ auto,S (τ,f)|

[0128]

[0129] Fuzzy function template: Based on prior knowledge and the corresponding law between the energy distribution of the range-Doppler plane and the fuzzy function, such a self-fuzzy function template is designed

[0130]

[0131] Where E is the energy constraint of the emission waveform. Therefore, the template design must satisfy the energy constraint, that is,

[0132]

[0133] The template of the fuzzy function must be designed based on a priori. So from the perspective of the fuzzy function template, the radar should design an accurate template as much as possible, and the jammer should make the template as inaccurate as possible.

[0134] Furthermore, the zero-sum game model between the radar party and the jammer is:

[0135] The template spaces of radar self-ambiguity function and mutual ambiguity function are respectively

[0136] M radar,auto ,M radar,cross

[0137] The interference pattern space of the jammer is

[0138] M jammer ,j∈M jammer

[0139] 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.

[0140] For the jammer:

[0141]

[0142] For radar:

[0143]

[0144] 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.

[0145] For the jammer:

[0146]

[0147] For radar:

[0148]

[0149] 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.

[0150] 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.

[0151] Radar control function: (S radar (t),W match∨mis (t)) is the amplitude, frequency, and phase modulation function, denoted as

[0152] u radar (t)=(S radar (t),W match∨mis (t); a m,n (t),f m,n (t),θ m,n (t))

[0153] Jammer control function: parameter control under a certain jamming mode. The present invention is mainly aimed at deceptive forwarding jamming, mainly time delay and Doppler shift modulation, recorded as

[0154] v jammer (t)=(t jammer ,f d,jammer )

[0155] 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.

[0156] Target function: The difference between the template set by the fuzzy function and the true fuzzy function of the transmitted waveform (filter).

[0157] Therefore, a conceptual model of differential game with parameter modulation under deterministic information mode and uncertain information mode can be constructed.

[0158] First, the differential game model under the deterministic information mode is constructed as follows.

[0159] For radar:

[0160]

[0161] For the jammer:

[0162]

[0163] 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.

[0164] For radar:

[0165]

[0166] For the jammer:

[0167]

[0168] 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.

[0169] Furthermore, the derivation is:

[0170] For the model

[0171]

[0172] First derive the objective function

[0173]

[0174] in

[0175]

[0176] Observe the last term of the objective function expansion

[0177] Re(X H AX)

[0178] To use the loop iteration technique, we follow

[0179]

[0180] Iteration produces two sequences

[0181]

[0182] The iterative method is:

[0183] Step 1: Generate random initialization according to the constraints of vector $X$ and X (0) .

[0184] Step 2: For fixed and X (.) , calculated

[0185]

[0186] And update A (.)

[0187] Step 3: For fixed and X (.) , calculated

[0188]

[0189] Step 4: For fixed and Calculated

[0190]

[0191] Step 5: Repeat steps 2, 3, and 4 until the convergence threshold is met.

[0192] Output: Final X (.) .

[0193] 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.

[0194] Compared with the existing methods, the method of the present invention has the advantage that the optimal transmission waveform and matching waveform can be efficiently obtained through the reverse iteration method, thereby improving the anti-interference ability of the radar system.

[0195] 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.

[0196] 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".

[0197] 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.

[0198] 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 design method based on prior information of a self-fuzzy function, characterized in that: The following steps are involved: Step 1, determine the radar target and the jamming target based on prior information; Step 2, designing a self-fuzzy function template under prior information; Step 3: Construct a zero-sum game model between the radar party and the jammer; Step 4: Generate optimized radar waveform based on the model derivation iterative method.

2. The waveform design method based on prior information of self-fuzzy function according to claim 1 is characterized in that: The target of the radar is characterized by the local signal-to-interference-to-noise ratio of the target echo signal: Q t ' arget is the area or possible area where the target is located on the range-Doppler plane. Local means local. Indicates the signal-to-interference-noise ratio of the local area where the target is located; The interference target is expressed by the local interference-to-noise ratio of the interference signal: Q j ' ammer is the false target area on the range-Doppler plane; In summary, the radar game goal is a dual objective function. The game objective of the jammer is a dual objective function The game between radar and jamming is a zero-sum one.

3. The waveform design method based on prior information of self-fuzzy function according to claim 2, characterized in that: The self-fuzzy function is: S(t) is the signal, t is time, S * (t) represents the complex conjugate of the signal S(t), τ represents the time delay parameter, f represents the frequency offset parameter, It is a complex exponential function containing frequency offset f and time delay τ, which is used to introduce the corresponding phase shift, dt differential integration, which means integrating the signal in time; It has the following mathematical properties: |x auto，S (0,0)|=Energy(S) |x auto，S (-τ,-f)|=|χ auto，S (t, f)| Among them, |χ auto，S (0,0)|: represents the amplitude of the self-blurring function at (τ, f) = (0, 0), Energy(S) represents the energy of signal S, |χ auto，S (-τ, -f)| and |χ auto，S (τ, f)| represents the amplitude of the self-blur function at (-τ, -f) and (τ, f), respectively. represents the double integral symbol, indicating that the integration is performed over the entire range of time delay τ and frequency offset f, |χ auto，S (τ, f)| 2 represents the square of the modulus of the self-ambiguity function, represents the energy density, dτ represents the infinitesimal element of the time delay τ, and df represents the infinitesimal element of the frequency shift f, indicating that the self-ambiguity function has symmetry about (τ, f); Based on the prior knowledge and the corresponding law between the energy distribution in the range-Doppler plane and the fuzzy function, the self-fuzzy function template is obtained: Where E is the energy constraint of the emission waveform, so the template design satisfies the energy constraint, that is, 4. The waveform design method under prior information for self-fuzzy function according to claim 3 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 between radar, target, and jammer M auto ,M cross ,M jammer The real target and interference energy distribution area are The target area and interference energy area 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 is constructed as a random model, and 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 For the first-level game, the backward induction method is first used to solve the extended game problem of template selection and interference mode selection under complete information conditions, and then the perfect Bayesian Nash equilibrium method is used to solve the Bayesian extended game problem of template selection and interference mode without complete information; the first-level game is a coarse-grained fuzzy function template and jammer interference mode selection game model based on the extended game. Through the game, the template type and interference mode are determined, and two types of deterministic and uncertain types are constructed according to different information modes; 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.

5. The waveform design method based on prior information of self-fuzzy function according to claim 4 is characterized in that: In the second layer of parameter fine-tuning differential game stage, 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 under delay and Doppler shift modulation 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.

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

7. The waveform design method based on prior information of self-fuzzy function according to claim 6, 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 design method based on prior information of self-fuzzy function according to claim 7, 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: The second-level game is based on the first-level game and is a fine-grained parameter modulation game model based on differential game. Through the game, the radar's transmitting waveform and matching and mismatching filter waveforms are determined.

9. The waveform design method based on prior information of self-fuzzy function according to claim 8, characterized in that: According to the waveform design of the first-level game and the second-level game, the discretization model is: min X,Y It indicates that the variables X and Y are minimized. represents the sum of the index set T×F of time delay and frequency offset, g kp Represents the discrete template of the mutual ambiguity function, describing the characteristics of the signal under time delay k and frequency offset p, represents the modulus of the expected value of the mutual fuzzy function template, X H represents the conjugate transpose of X, J kp represents the complex number representation of the mutual ambiguity function template, Y represents the received signal processing vector in the optimization model; First derive the objective function in The last term Re(X H AX) Use loop iteration, according to Iteration produces two sequences The iterative method is: Step 1: Randomly initialize the first elements of the two sequences according to the constraints of vector X and X (0) ; Step 2: For a fixed sequence and sequence X (.) , calculated And update A (.) , A (.) yes; Step 3: For a fixed phase shift after iteration and sequence X (.) , calculated m, n are the row index and column index of matrix X respectively, Representation Matrix At the first iteration, the value of the element at position m,n, is the value of the element at position m,N+l at the first iteration, Step 4: For fixed and Calculated Step 5: Repeat steps 2, 3, and 4 until the convergence threshold is met.

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