A cyclic optimization method for comprehensive mutual fuzzy functions based on certain information

Abstract

The present invention discloses a method for optimizing a comprehensive mutual fuzzy function loop based on deterministic information, comprising the following steps: Step 1: Designing a discrete template for the mutual fuzzy function to determine information; Step 2: Determining a zero-sum game model between the radar and the interference party; Step 3: Improving the zero-sum game model based on the template model to construct a model that does not rely on the template; Step 4: Degenerating code elements into pulses, constructing a computationally feasible special model, and designing a radar waveform based on the special model. Through a reverse iterative method, the present invention can efficiently obtain the optimal transmission waveform and matching waveform, thereby improving the radar system's anti-interference capability and effectively solving the computational efficiency problem of attack and defense strategy selection in large-scale networks.

Description

Technical Field

[0001] The present invention belongs to the technical field of radar waveform design, and in particular relates to a comprehensive mutual fuzzy function cyclic optimization method based on certain information. Background Art

[0002] In modern radar systems, waveform design is a key technology for their performance and effectiveness. Radar systems detect and identify targets by emitting specific electromagnetic waveforms while simultaneously navigating complex electromagnetic environments and hostile interference. Traditional waveform design methods often rely on fixed waveform patterns or empirically derived designs. While these designs meet basic detection requirements to a certain extent, their performance and effectiveness are significantly limited when faced with changing electromagnetic environments and intense electronic warfare interference.

[0003] The development of modern radar technology is driving the continuous evolution and optimization of waveform design methods. Based on advanced signal processing techniques and mathematical modeling, the next-generation radar waveform design aims to enhance radar system performance in target detection, tracking, and anti-interference capabilities by optimizing the waveform's energy distribution, spectral characteristics, and spatiotemporal characteristics.

[0004] The technical background for waveform design encompasses multiple aspects. First, a comprehensive understanding and analysis of the radar's operating environment and usage scenarios is essential. Different mission requirements can present varying challenges for radar system waveform design, such as high-resolution target identification, achieving low-probability interception, and effective signal transmission in complex electromagnetic environments. Second, waveform design must also consider the actual characteristics and limitations of radar hardware, such as transmitter and receiver frequency response, power output capability, and signal processing speed.

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

[0006] Waveform design, a crucial component of optimizing modern radar system performance, is continually driven and influenced by technological innovation and scientific research. Future developments 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 widespread application and practical effectiveness of radar systems in military, civilian, and scientific research fields. Summary of the Invention

[0007] In view of this, a comprehensive mutual ambiguity function loop optimization method based on deterministic information is disclosed. 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 at the same time, 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 achieved by the following technical solution, which is a method for optimizing a comprehensive mutual fuzzy function loop based on certain information, comprising the following steps:

[0009] Step 1: Design a discrete template of mutual fuzzy functions to determine information;

[0010] Step 2: Determine the zero-sum game model between the radar party and the jammer;

[0011] Step 3: Improve the zero-sum game model based on the template model and build a model that does not rely on the template;

[0012] Step 4: degenerate the code element into pulses, construct a computationally feasible special model, and design the radar waveform based on the special model;

[0013] The determined information at least includes the time delay t for the radar to accurately know the target target , the Doppler shift of the target f d,target , jammer's jamming pattern, jammer's delay modulation based on target delay jammer , Doppler frequency shift modulation of the jammer based on the target Doppler frequency shift f d,jammer one.

[0014] Preferably, the mutual ambiguity function is defined as:

[0015]

[0016] Among them, χ cross,S,W (τ, f) is the mutual ambiguity function, which is a function of time delay τ and frequency offset f, where τ represents the time delay parameter and f represents the frequency offset parameter. Indicates the double integral symbol, S(t) and W(t) are two different signals, t is time, S * (t) represents the complex conjugate of the signal S(t), W(t) is another signal that performs mutual fuzzy operation with the signal S(t), It is a complex exponential function containing frequency offset f and time delay τ, which is used to introduce the corresponding phase shift. The differential integral of dt represents the integration of the signal in time.

[0017] The mutual ambiguity function has the following properties:

[0018]

[0019] |χ cross,S,W (-τ,-f)|=|χ cross,S,W (τ,f)|;

[0020]

[0021] Among them, |χ cross,S,W (0,0)| represents the amplitude of the mutual ambiguity function at (τ,f)=(0,0), represents the square root of the energy of the signal S, represents the square root of the energy of the signal W, |χ cross，S，W (τ, f)| and |χ cross,S,W (-τ,-f)| represents the amplitude of the mutual ambiguity 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 cross,S,W (τ,f)| 2 represents the square of the modulus of the mutual 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 offset f, indicating that the mutual ambiguity function has symmetry about (τ, f).

[0022] Preferably, the zero-sum game model between the radar party and the jammer is:

[0023] Radar stated the following:

[0024]

[0025] The interfering party is represented as follows:

[0026]

[0027] 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, 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;

[0028] The zero-sum game model is established as follows:

[0029]

[0030] Among them, min X,Y 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, 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 representation of the mutual ambiguity function template, and Y represents the received signal processing vector in the optimization model;

[0031] Equivalent to

[0032]

[0033] in, Represents the variables X, Y and phase angle φ k,p Perform the minimize operation. Represents a complex exponential function, introducing a phase angle φ kp The phase shift, φ k,p Represents the phase angle, which is used to describe the phase shift of the signal.

[0034] Preferably, the standard model form of the zero-sum game model is:

[0035]

[0036] Among them, min means minimizing the objective function, represents the sum of the index set T×F of time delay and frequency offset, |X k | represents the modulus of the kth element in X,

[0037] m∈[1,2,…,M],n∈[1,2,…,N] means to constrain all indexes k that meet the conditions, and st means the constraints. represents the square root of MN, φ kp ∈[0,2π) represents the phase angle φ kp The value range constraints.

[0038] Preferably, the simplified model of the zero-sum game model is as follows:

[0039] Determine the symbol vector of the first pulse

[0040]

[0041] The following M-1 pulse symbol vectors are derived from the symbol vector of the first pulse.

[0042]

[0043] Then at this time

[0044]

[0045] Get a simplified model

[0046]

[0047] Among them, min means that the goal is to minimize the subsequent expression, 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 a complex exponential function, introducing a phase angle φ kp The phase shift, φ kp Indicates the phase angle, which is used to describe the phase shift of the signal. H represents the conjugate transpose of X, J kp represents the complex representation of the mutual ambiguity function template, Y represents the received signal processing vector in the optimization model, st represents the constraint condition, |X 1,n |=1 indicates a constraint condition, ensuring that the first element in X 1,n The modulus is 1, for all n, |ρ m |=1 indicates the constraint condition, ensuring ρ m The modulus is 1, for all m, X m,n =ρ m X 1,n Represents constraints that describe how the subsequent parts of X are constructed, where X m,n By ρ m Multiply by X 1,n Get, X m,N+l =0 represents the constraint condition, ensuring that some elements in X are zero. Represents a constraint condition, ensuring that the modulus of Y is φ kp ∈[0,2π) represents the constraint condition, limiting the phase angle φ kp The value range of .

[0048] Preferably, the template-independent model is:

[0049]

[0050] Among them, min means that the goal is to minimize the subsequent expression, X H represents the conjugate transpose of X, J kp The complex form of the mutual ambiguity function template is described, which is related to the time delay k and the frequency offset p. Y is the received signal processing vector in the optimization model, st represents the constraint condition, |X k |=1 constraint, ensuring that the modulus of the kth row in X is 1, where k=(m,n), m represents the pulse index, n represents the code element index, and X k = 0 constraint, ensuring that the elements at specific positions in X are zero, where k = (m, N + l), m represents the pulse index, and l represents the additional index offset. Constraints ensure that the modulus of Y is Where M and N represent the size of time and frequency dimensions respectively, kp ∈[0,2π) constraint, limiting the phase angle φ kp The value range of , where (k, p) represents the combination of time delay and frequency offset;

[0051] The model is written in standard model form as:

[0052]

[0053] Preferably, in the computationally feasible special model, when N+L=1, the code element degenerates into a pulse, and one pulse repetition period is one code element. At this time, the phase coding degenerates into the initial phase modulation of the pulse:

[0054] X=(X1,X2,…,X m ,…,X M ) T It is the initial phase modulation of M pulses, and the model becomes

[0055]

[0056] At this time, the index set is T=[-M,…,0,…,M], min means that the goal is to minimize the subsequent expression, 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 a complex exponential function, introducing a phase angle φ kp The phase shift, φ kp Indicates the phase angle, which is used to describe the phase shift of the signal. H represents the conjugate transpose of X, J kprepresents the complex representation of the mutual ambiguity function template, Y represents the received signal processing vector in the optimization model, st represents the constraint condition, |X m |=1 represents the constraint condition, ensuring that the modulus of the mth row in X is 1, for all m, Represents a constraint condition, ensuring that the modulus of Y is φ kp ∈[0,2π) represents the constraint condition, limiting the phase angle φ kp The value range of .

[0057] Compared with existing methods, the advantage of the method of the present invention is that network games have been 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 network game solving method based on a greedy algorithm. This method gradually approaches the global optimal solution through local optimal selection, effectively solving the computational efficiency problem of attack and defense strategy selection in large-scale networks. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 A schematic diagram of a process flow of an embodiment of the present invention is shown;

[0059] Figure 2 shows the range Doppler diagram of the target echo and interference before optimization according to an embodiment of the present invention;

[0060] Figure 3 FIG. 2 shows a 2D mutual ambiguity function diagram of a transmit waveform before optimization according to an embodiment of the present invention;

[0061] 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

[0062] The present invention will be further described below with reference to 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 fall within the scope of protection of the present invention.

[0063] 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.

[0064] like Figure 1 As shown, a comprehensive mutual fuzzy function loop optimization method based on determined information includes expressing

[0065] Step 1: Design a discrete template of mutual fuzzy functions to determine information;

[0066] Step 2: Determine the zero-sum game model between the radar party and the jammer;

[0067] Step 3: Improve the zero-sum game model based on the template model and construct and design a model that does not rely on the template;

[0068] Step 4: degenerate the code elements into pulses and construct a computationally feasible special model.

[0069] The above-mentioned information is an ideal model, which means that the radar knows the target's delay t accurately. target , the Doppler shift of the target f d,target , the jammer's jamming pattern (assuming forwarding deception jamming), the jammer's delay modulation t based on the target delay jammer , Doppler frequency shift modulation of the jammer based on the target Doppler frequency shift f d,jammer and other information.

[0070] Specifically, the mutual fuzzy function is defined as

[0071]

[0072] Among them, χ cross,S,W (τ,f) is the mutual ambiguity function, which is a function of time delay (τ) and frequency offset (f), where τ represents the time delay parameter and f represents the frequency offset parameter. Indicates the double integral symbol, S(t) and W(t) are two signals, S * (t) represents the complex conjugate of the signal S(t), W(t) is another signal that performs mutual fuzzy operation with the signal S(t), 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 integral represents the integration of the signal over time.

[0073] It has properties similar to self-fuzzifying functions:

[0074]

[0075] |χ cross,S,W (-τ,-f)|=|χ cross,S,W (τ,f)|;

[0076]

[0077] Among them, |χ cross,S,W (0,0)| represents the amplitude of the mutual ambiguity function at (τ,f)=(0,0), represents the square root of the energy of the signal S, represents the square root of the energy of the signal W,

[0078] |χ cross,S,W (-τ,-f)| represents the magnitude of the mutual ambiguity function at (τ,f) and (-τ,-f), represents the double integral symbol, indicating that the integration is performed over the entire range of time delay τ and frequency offset f, |χ cross,S,W (τ,f)| 2 represents the square of the modulus of the mutual 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 offset f, indicating that the mutual ambiguity function has symmetry about (τ, f).

[0079] Furthermore, the zero-sum game model between the radar party and the jammer is as follows:

[0080] The so-called deterministic information mode refers to the radar's target ,Q jammer is certain, so the discrete template g of the designed mutual fuzzy function k,p It is relatively accurate, then we can use the zero-sum game model of deterministic information pattern + mismatch filter + self-fuzzy function

[0081] Radar said

[0082]

[0083] The interfering party stated

[0084]

[0085] 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, 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;

[0086] Can build models

[0087]

[0088] Among them, min X,YIndicates that the variables X and Y are minimized.

[0089] (Tex translation failed) means summing 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, 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 representation of the mutual ambiguity function template, and Y represents the received signal processing vector in the optimization model;

[0090] Equivalent to

[0091]

[0092] in, Represents the variables X, Y and phase angle φ k,p Perform the minimize operation. Represents a complex exponential function, introducing a phase angle φ kp The phase shift, φ k,p Represents the phase angle, which is used to describe the phase shift of the signal;

[0093] Written in standard model form, we can get

[0094]

[0095] Among them, min means minimizing the objective function, represents the sum of the index set T×F of time delay and frequency offset, |X k | represents the modulus of the kth element in X,

[0096] m∈[1,2,…,M],n∈[1,2,…,N] means to constrain all indexes k that meet the conditions, and st means the constraints. represents the square root of MN, φ kp ∈[0,2π) represents the phase angle φ kp The value range constraint of ;

[0097] Many simplified models can be established. For example, we determine the code element vector of the first pulse

[0098]

[0099] The following M-1 pulse symbol vectors are derived from the symbol vector of the first pulse.

[0100]

[0101] Then at this time

[0102]

[0103] A simplified model can be obtained

[0104]

[0105] Among them, min means that the goal is to minimize the subsequent expression, 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 a complex exponential function, introducing a phase angle φ kp The phase shift, φ kp Indicates the phase angle, which is used to describe the phase shift of the signal. H represents the conjugate transpose of X, J kp represents the complex representation of the mutual ambiguity function template, Y represents the received signal processing vector in the optimization model, st represents the constraint condition, |X 1,n |=1 indicates a constraint condition, ensuring that the first element in X 1,n The modulus is 1, for all n, |ρ m |=1 indicates the constraint condition, ensuring ρ m The modulus is 1, for all m, X m,n =ρ m X 1,n Represents constraints that describe how the subsequent parts of X are constructed, where X m,n By ρ m Multiply by X 1,n Get, X m,N+l =0 represents the constraint condition, ensuring that some elements in X are zero. Represents a constraint condition, ensuring that the modulus of Y is φ kp ∈[0,2π) represents the constraint condition, limiting the phase angle φ kp The value range of .

[0106] In one embodiment, the code element vectors of the first and second pulses of the transmitted waveform are further optimized. Other pulse code element vectors are based on the code elements of the first and second pulses through the overall initial phase modulation. Through this idea, a large number of sub-models can be established, and a special model that is computationally feasible can also be constructed. That is, when N+L=1, the code element degenerates into a pulse, and one pulse repetition period is one code element. At this time, the phase coding degenerates into the initial phase modulation of the pulse.

[0107] X=(X1,X2,…,X m ,…,XM ) T

[0108] It is the initial phase modulation of M pulses, and the model becomes

[0109]

[0110] At this time, the index set is T=[-M,…,0,…,M], min means that the goal is to minimize the subsequent expression, 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 a complex exponential function, introducing a phase angle φ kp The phase shift, φ kp Indicates the phase angle, which is used to describe the phase shift of the signal. H represents the conjugate transpose of X, J kp represents the complex representation of the mutual ambiguity function template, Y represents the received signal processing vector in the optimization model, st represents the constraint condition, |X m |=1 represents the constraint condition, ensuring that the modulus of the mth row in X is 1, for all m, Represents a constraint condition, ensuring that the modulus of Y is φ kp ∈[0,2π) represents the constraint condition, limiting the phase angle φ kp The value range of .

[0111] Furthermore, the template-independent model is represented by

[0112] The design of the template requires considerable accuracy to achieve good results, which requires the help of intelligent technology. We can improve the above model based on the template model and build and design a model that does not rely on the template.

[0113]

[0114] Among them, min means that the goal is to minimize the subsequent expression, X H represents the conjugate transpose of X, J kp The complex form of the mutual ambiguity function template is described, which is related to the time delay k and the frequency offset p. Y is the received signal processing vector in the optimization model, st represents the constraint condition, |X k |=1 constraint, ensuring that the modulus of the kth row in X is 1, where k=(m,n), m represents the pulse index, n represents the code element index, and X k = 0 constraint, ensuring that the elements at specific positions in X are zero, where k = (m, N + l), m represents the pulse index, and l represents the additional index offset. Constraints ensure that the modulus of Y is Where M and N represent the size of time and frequency dimensions respectively, kp ∈[0,2π) constraint, limiting the phase angle φ kp The value range of , where (k, p) represents the combination of time delay and frequency offset;

[0115] It must be noted that the indicator set here

[0116]

[0117] It is a proper subset of the original index, because if the proper subset is not selected, then according to the law of conservation of energy, there is

[0118]

[0119] Then the optimization loses its meaning.

[0120] Model

[0121]

[0122] Written in standard model form, we can get

[0123]

[0124] Many simplified models can be established. For example, we determine the code element vector of the first pulse

[0125]

[0126] The following M-1 pulse symbol vectors are derived from the symbol vector of the first pulse.

[0127]

[0128] Then at this time

[0129]

[0130] A simplified model can be obtained

[0131]

[0132] Among them, min means that the goal is to minimize the subsequent expression, X H represents the conjugate transpose of X, J kp The complex form of the mutual ambiguity function template is described, which is related to the time delay k and the frequency offset p. Y is the received signal processing vector in the optimization model, st represents the constraint condition, |X 1,n |=1 constraint, ensuring that the first element in X 1,nThe modulus is 1, for all n, |ρ m |=1 constraint, ensuring ρ m The modulus is 1, for all m, ρ m is the complex scaling factor of the symbol vector, X m,n =ρ m X 1,n Constraints that describe how the subsequent parts of X are constructed, where X m,n By ρ m Multiply by X 1,n Get, X m,N+l =0 constraint, ensuring that some elements in X are zero, Constraints ensure that the modulus of Y is Where M and N represent the size of time and frequency dimensions respectively;

[0133] We can also optimize the code element vectors of the first and second pulses. The other pulse code element vectors are based on the code elements of the first and second pulses through the overall initial phase modulation. With this idea, we can establish a large number of sub-models.

[0134] Furthermore, the computationally feasible special model refers to the representation

[0135] When N+L=1, the code element degenerates into a pulse, and one pulse repetition period is one code element. The phase coding at this time degenerates into the initial phase modulation of the pulse X=(X1, X2,…, X m ,…,X M ) T It is the initial phase modulation of M pulses, and the model becomes

[0136]

[0137] Among them, min means that the goal is to minimize the subsequent expression, X H represents the conjugate transpose of X, J kp The complex form of the mutual ambiguity function template is described, which is related to the time delay k and the frequency offset p. Y is the received signal processing vector in the optimization model, st represents the constraint condition, |X m |=1 constraint, ensuring that the modulus of the mth row in X is 1, where m represents the pulse index, Constraints ensure that the modulus of Y is Where M represents the number of pulses.

[0138] At this time, the indicator set is

[0139]

[0140] These metrics describe the range of time delays and frequency offsets, ensuring that the model operates effectively under the specific conditions encountered in radar signal processing.

[0141] 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 3 As shown. To optimize the waveform, first, the radar initial waveform, filter and other necessary parameters are given. Calculate the two-dimensional color map and three-dimensional function map of the fuzzy function of the initial waveform and filter. According to the model of the target and interference, form a range Doppler image, and calculate the local signal to noise ratio of the target unit. Use the fuzzy function-based model and algorithm mentioned above to modulate the initial waveform and filter, and output the waveform and filter. Calculate the two-dimensional color map and three-dimensional function map of the fuzzy function of the modulated waveform and filter. Again, based on the signal model of the target and interference, form a range Doppler image, and calculate the local signal to noise ratio of the target unit. Compare the shapes of the fuzzy functions before and after, and compare the clarity and local signal to noise ratio of the target units before and after. The optimized range Doppler map is shown as follows. Figure 4 shown.

[0142] Traditional game-solving algorithms are extremely difficult to solve in large-scale networks. Compared with existing methods, the present invention can efficiently obtain the optimal transmission waveform and matching waveform through a reverse iterative method, thereby improving the anti-interference capability of the radar system.

[0143] As used herein, the word "preferred" is intended to serve as an example, instance, or illustration. Any aspect or design described herein as "preferred" is not necessarily to be construed as advantageous over other aspects or designs. Rather, the use of the word "preferred" is intended to present concepts in a concrete manner. As used in this application, the term "or" is intended to mean an inclusive "or" rather than an exclusive "or." That is, unless otherwise specified or clear from the context, "X employs A or B" is intended to mean any of the naturally inclusive permutations. That is, if X employs A; X employs B; or X employs both A and B, then "X employs A or B" is satisfied in any of the foregoing examples.

[0144] Moreover, although the present disclosure has been shown and described with respect to one or implementation, those skilled in the art will think of equivalent variations and modifications based on 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 structurally different from the disclosed structure that performs 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 can 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".

[0145] In summary, the above embodiment is one implementation method of the present invention, but the implementation method of the present invention is not limited to the described 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 scope of protection of the present invention.

Claims

1. A method for optimizing the comprehensive mutual fuzzy function loop based on certain information, characterized in that: The following steps are involved: Step 1: Design a discrete template of mutual fuzzy functions to determine information; Step 2: Determine the zero-sum game model between the radar party and the jammer; Step 3: Improve the zero-sum game model based on the template model and build a model that does not rely on the template; Step 4: degenerate the code element into pulses, construct a computationally feasible special model, and design the radar waveform based on the special model; The information indicates that the radar knows the target's delay t accurately. target , the Doppler shift of the target f d,target , jammer's jamming pattern, jammer's delay modulation based on target delay jammer , Doppler frequency shift modulation of the jammer based on the target Doppler frequency shift f d,jammer one; The zero-sum game model in step 2 is as follows: Among them, min X,Y Indicates minimization of variables X and Y. 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, 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 representation of the mutual ambiguity function template, and Y represents the received signal processing vector in the optimization model; The template-independent model described in step 3 is: Among them, min means that the goal is to minimize the subsequent expression, X H represents the conjugate transpose of X, J kp The complex form of the template describing the mutual ambiguity function, which is related to the time delay k and the frequency offset p, is the received signal processing vector in the Y optimization model; In the computationally feasible special model, N represents the size of the time and frequency dimensions. When N+L=1, the code element degenerates into a pulse, and one pulse repetition period is one code element. At this time, the phase coding degenerates into the initial phase modulation of the pulse: X=(X1,X2,…,X m ,…,X M ) T It is the initial phase modulation of M pulses.

2. The method for optimizing the comprehensive mutual fuzzy function loop based on the determined information according to claim 1, characterized in that: The mutual ambiguity function is defined as: Among them, χ cross,S,W (τ, f) is the mutual ambiguity function, which is a function of time delay τ and frequency offset f, where τ represents the time delay parameter and f represents the frequency offset parameter. Indicates the integral symbol, S(t) and W(t) are two different signals, t is time, S * (t) represents the complex conjugate of the signal S(t), W(t) is another signal that performs mutual fuzzy operation with the signal S(t), It is a complex exponential function containing frequency offset f and time delay τ, which is used to introduce the corresponding phase shift. The differential integral of dt represents the integration of the signal in time. The mutual ambiguity function has the following properties: |x cross,S,W (-τ,-f)|=|χ cross,S，W (t,f)|; Among them, |χ cross,S,W (0,0)| represents the amplitude of the mutual ambiguity function at (τ,f)=(0,0), represents the square root of the energy of the signal S, represents the square root of the energy of the signal W, |χ cross,S,W (τ,f)| 2 and |χ cross,S,W (-τ,-f)| represents the amplitude of the mutual ambiguity 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 cross,S,W (τ,f)| 2 represents the square of the modulus of the mutual 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 offset f, indicating that the mutual ambiguity function has symmetry about (τ, f).

3. The method for optimizing the comprehensive mutual fuzzy function loop based on the determined information according to claim 2, characterized in that: The zero-sum game model between the radar party and the jammer is: Radar stated the following: The interfering party is represented as follows: 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, 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. st represents the constraint condition. The zero-sum game model established is equivalent to in, Represents the variables X, Y and phase angle φ k,p Perform the minimize operation. Represents a complex exponential function, introducing a phase angle φ kp The phase shift, φ k,p Represents the phase angle, which is used to describe the phase shift of the signal.

4. The method for optimizing the comprehensive mutual fuzzy function loop based on the determined information according to claim 3, characterized in that: The standard model form of the zero-sum game model is: Among them, min means minimizing the objective function, represents the sum of the index set T×F of time delay and frequency offset, |X k | represents the modulus of the kth element in X, Indicates that all indexes k that meet the conditions are constrained, st represents the constraint conditions, represents the square root of MN, φ kp ∈[0,2π) represents the phase angle φ kp The value range constraints.

5. The method for optimizing the comprehensive mutual fuzzy function loop based on the determined information according to claim 4, characterized in that: The simplified model of the zero-sum game model is as follows: Determine the symbol vector of the first pulse The following M-1 pulse symbol vectors are derived from the symbol vector of the first pulse. Then at this time Get a simplified model Among them, min means that the goal is to minimize the subsequent expression, 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 a complex exponential function, introducing a phase angle φ kp The phase shift, φ kp Indicates the phase angle, which is used to describe the phase shift of the signal. H represents the conjugate transpose of X, J kp represents the complex representation of the mutual ambiguity function template, Y represents the received signal processing vector in the optimization model, st represents the constraint condition, |X 1,n |=1 indicates a constraint condition, ensuring that the first element in X 1,n The modulus is 1, for all n, |ρ m |=1 indicates the constraint condition, ensuring ρ m The modulus is 1, for all m, X m,n =ρ m X 1,n Represents constraints that describe how the subsequent parts of X are constructed, where X m,n By ρ m Multiply by X 1,n Get, X m,N+l =0 represents the constraint condition, ensuring that some elements in X are zero. Represents a constraint condition, ensuring that the modulus of Y is φ kp ∈[0,2π) represents the constraint condition, limiting the phase angle φ kp The value range of .

6. The method for optimizing the comprehensive mutual fuzzy function loop based on certain information according to claim 5, characterized in that: The template-independent model is written in standard model form as follows: st represents the constraint condition, |X k |=1 constraint, ensuring that the modulus of the kth row in X is 1, where k=(m,n), m represents the pulse index, n represents the code element index, and X k = 0 constraint, ensuring that the elements at specific positions in X are zero, where k = (m, N + l), m represents the pulse index, and l represents the additional index offset. Constraints ensure that the modulus of Y is Where M and N represent the size of time and frequency dimensions respectively, kp ∈[0,2π) constraint, limiting the phase angle φ kp The value range of (k, p) is where (k, p) represents the combination of time delay and frequency offset.

7. The method for optimizing the comprehensive mutual fuzzy function loop based on the determined information according to claim 6, characterized in that: The simplified model of the model that does not rely on templates is: Determine the symbol vector of the first pulse The following M-1 pulse symbol vectors are derived from the symbol vector of the first pulse. Then at this time Get a simplified model Among them, min means that the goal is to minimize the subsequent expression, X H represents the conjugate transpose of X, J kp The complex form of the mutual ambiguity function template is described, which is related to the time delay k and the frequency offset p. Y is the received signal processing vector in the optimization model, st represents the constraint condition, |X 1,n |=1 constraint, ensuring that the first element in X 1,n The modulus is 1, for all n, |ρ m |=1 constraint, ensuring ρ m The modulus is 1, for all m, ρ m is the complex scaling factor of the symbol vector, X m,n =ρ m X 1,n Constraints that describe how the subsequent parts of X are constructed, where X m,n By ρ m Multiply by X 1,n Get, X m,N+l =0 constraint, ensuring that some elements in X are zero, Constraints ensure that the modulus of Y is Where M and N represent the sizes of the time and frequency dimensions respectively.

8. The method for optimizing the comprehensive mutual fuzzy function loop based on certain information according to claim 7, characterized in that: The computationally feasible particular model is: At this time, the index set is T=[-M,…,0,…,M], min means that the goal is to minimize the subsequent expression, 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 a complex exponential function, introducing a phase angle φ kp The phase shift, φ kp Indicates the phase angle, which is used to describe the phase shift of the signal. H represents the conjugate transpose of X, J kp represents the complex representation of the mutual ambiguity function template, Y represents the received signal processing vector in the optimization model, st represents the constraint condition, |X m |=1 represents the constraint condition, ensuring that the modulus of the mth row in X is 1, for all m, Represents a constraint condition, ensuring that the modulus of Y is φ kp ∈[0,2π) represents the constraint condition, limiting the phase angle φ kp The value range of .

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