A Long-Range Support Jamming Waveform Design Method Based on Pursuit Game Theory

Abstract

This invention discloses a long-range support jamming waveform design method based on a pursuit-escape game theory approach, comprising the following steps: Step 1, designing a long-range support jamming scenario involving radar, target, and jammer; Step 2, sampling based on a general pulse train model to generate pulse train symbols; Step 3, defining the symbol model of the pulse train to determine the modulation mode and radar signal model; Step 4, establishing a game information pattern among the radar, target, and jammer; Step 5, constructing a waveform design model to generate the optimized waveform. This invention addresses the problem of the extreme difficulty of solving traditional game theory algorithms in large-scale networks. Through a reverse iterative method, it can efficiently obtain the optimal transmitted waveform and the matching waveform, thereby improving the anti-jamming capability of the radar system and effectively solving the computational efficiency problem of attack and defense strategy selection in large-scale networks.

Description

Technical Field

[0001] This invention belongs to the field of radar waveform design technology, and in particular relates to a long-range support jamming waveform design method based on pursuit and escape game theory. Background Technology

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

[0003] Despite significant progress in modern radar waveform design methods, several shortcomings remain. These shortcomings primarily manifest in the following aspects: Radar waveforms lack adaptability to dynamic environments (such as rapidly changing targets, terrain, and weather conditions), necessitating the development of adaptive waveform design methods to adjust waveform parameters based on real-time environmental changes, thereby improving system flexibility and robustness. Some advanced waveform design methods (such as compressed sensing and deep learning) have high computational complexity and demanding hardware resources, requiring algorithm optimization to reduce computational complexity and improve real-time processing capabilities. Simultaneously, the development of dedicated hardware (such as FPGAs and ASICs) is needed to accelerate computation. In particular, current waveform design processes often rely on expert experience and manual adjustments, lacking automation. Therefore, the development of automated waveform design systems based on machine learning and artificial intelligence is needed to improve design efficiency and accuracy.

[0004] The development of modern radar technology has driven the continuous evolution and optimization of waveform design methods. Based on advanced signal processing techniques and mathematical modeling methods, the new generation of radar waveform design aims to improve the performance of radar systems in target detection, tracking, and anti-jamming capabilities by optimizing the energy distribution, spectral characteristics, and spatiotemporal characteristics of the waveform.

[0005] The background technology of waveform design encompasses several aspects: First, it requires a comprehensive understanding and analysis of the radar's operating environment and usage scenarios. Different mission requirements may pose different challenges to the waveform design of radar systems, such as the identification of high-resolution targets, the realization of low-probability interception, and effective signal transmission in complex electromagnetic environments. Second, waveform design also needs to consider the actual characteristics and limitations of radar hardware, such as the frequency response, power output capability, and signal processing speed of the transmitter and receiver.

[0006] In traditional waveform design, researchers typically rely on mathematical models and simulation tools to evaluate the performance of different waveform schemes. These models involve radar signal propagation characteristics, target feature extraction methods, and interference suppression techniques. With advancements in computing power and algorithm optimization, modern waveform design increasingly employs methods based on statistical learning and optimization theory, leveraging big data analysis and adaptive algorithms to maximize signal processing efficiency in dynamic scenarios. Summary of the Invention

[0007] In view of this, the present invention discloses a long-range support jamming waveform design method based on pursuit and escape game theory. Based on existing target and jamming signal models, a series of waveform templates or optimized parameters are designed so that the radar system can extract target features to the maximum extent when receiving target signals, and suppress jamming to the maximum extent when facing jamming signals, thereby ensuring the stability and performance of the system.

[0008] The objective of this invention is achieved through the following technical solution: a comprehensive mutual fuzzy function cyclic optimization method based on deterministic information, the method comprising the following steps:

[0009] Step 1: Design long-range support jamming scenarios for radar, targets, and jammers;

[0010] Step 2: Sampling is performed based on the general model of the pulse train to generate pulse train symbols;

[0011] Step 3: Define the symbol model of the pulse train and determine the modulation mode and radar signal model;

[0012] Step 4: Establish a game information model among the radar, target, and jammer;

[0013] Step 5: Construct a waveform design model and generate the optimized waveform.

[0014] Furthermore, the aforementioned long-range support jamming scenario is as follows:

[0015] The radar is located at the origin, forming a spherical envelope and a burn-through envelope B(0,R). max ),B(0,R min ), R max R represents the maximum effective range of the radar and anti-missile system working together. min The radar's burn-through range is defined within the burn-through envelope B(0,R). max Beyond this, it cannot effectively detect or threaten targets and jammers within the envelope B(0,R). min Within a certain range, it can accurately detect targets; the distance between the jammer and the radar is R1. Long-range jamming support means that the jammer does not enter the spherical envelope to avoid risks, but performs jamming near the spherical envelope. Therefore, R1 > Rmax R1=R max +δ, where δ represents the relative safe distance; the jammer is located within the envelope B(0,R). max +δ) and B(0,R) max The current target is located within the envelope B(0,R). max ) and B(0,R min )between.

[0016] Furthermore, the general model of the aforementioned pulse train is as follows:

[0017] A signal within a CPI is a pulse train composed of M pulses;

[0018] Pulse duration: The duration of the m-th pulse of the signal is T. s,m , m∈[1,…,M], abbreviated as pulse width;

[0019] Pulse repetition period: The period of the m-th pulse of the signal is T. r,m , m∈[1,…,M];

[0020] Constant-modulus complex envelope: The constant-modulus complex envelope of the m-th pulse of the signal is u m (t), m∈[1,…,M]

[0021] Therefore, the function u m The support set of (t) is [0,T s,m The value in the remaining parts is 0;

[0022] Initial amplitude: The initial amplitude of the m-th pulse of the signal is a. m (0), m∈[1,…,M];

[0023] Amplitude modulation mode: The amplitude modulation mode of the m-th pulse of the signal is a m (t), m∈[1,…,M], where t is time, representing a quantity whose amplitude changes with time, where the function a m The support set of (t) is [0,T s,m The value of ] is 1 on it and 0 in the rest;

[0024] Initial frequency: The initial frequency of the m-th pulse of the signal is f. m (0), m∈[1,…,M];

[0025] Frequency modulation mode: The frequency modulation mode of the m-th pulse of the signal is f m (t), m∈[1,…,M], where t is time, and represents the quantity whose frequency changes with time, where the function f m The support set of (t) is [0,T s,m The value of ] is 1 on it and 0 in the rest;

[0026] Initial phase: The initial phase of the m-th pulse of the signal is θ. m (0), m∈[1,…,M];

[0027] Phase modulation mode: The phase modulation mode of the m-th pulse of the signal is θ m (t), m∈[1,…,M], where t is time, and represents the quantity of phase change with time, where the function θ m The domain of (t) is [0,T]. s,m The value of ] is 1 on it and 0 in the rest;

[0028] In summary, the general model of a pulse train without modulation mode is expressed as follows:

[0029]

[0030] T r,i It is the period of the i-th pulse of the signal;

[0031] A pulse train with modulation mode is generally expressed as a model of pulse train with modulation mode.

[0032]

[0033] Furthermore, based on the general model of a pulse train with modulation modes, for a fixed pulse duration T... s,m Pulse repetition period T r,m In addition, two of the amplitude, frequency, and phase parameters are used to modulate the other, resulting in a special modulation signal model;

[0034] In special modulation signal models, the amplitude modulation model is:

[0035]

[0036] In special modulation signal models, the frequency modulation model is:

[0037] In special modulation signal models, the phase modulation model is:

[0038]

[0039] Furthermore, for the general model of a pulse train, the initial frequency and phase are eliminated through local demodulation:

[0040] For the general model of a pulse train with modulation mode

[0041]

[0042] Define the local demodulator as:

[0043]

[0044] According to complex conjugate multiplication, we get:

[0045]

[0046] Furthermore, the zero-sum game model between the radar side and the jamming side is as follows:

[0047] The template spaces for radar self-ambiguity functions and mutual ambiguity functions are respectively

[0048] M auto M cross

[0049] The jamming mode space of the jammer is

[0050] M jammer ,j∈M jammer

[0051] The first layer of the game between radar and jammer is in M auto M cross M jammer In the game above, the actual target and the distribution area of ​​interference energy are The target and interference energy regions of template d are as follows: If the distance or coverage metric between regions is dist, then the conceptual model of the first-level game is as follows:

[0052] For jammers:

[0053]

[0054] For radar:

[0055]

[0056] If the region defined by template d has a probability distribution, then the above model is a stochastic model, and the expectation in the model below is the expectation of the region with the probability distribution:

[0057] For jammers:

[0058]

[0059] For radar:

[0060]

[0061] If the choices in the first layer of the game are already determined, that is, the template d of the fuzzy function and the interference pattern j of the interference machine are already determined, then we enter the second layer of parameter fine-tuning differential game stage:

[0062] Radar control function: (S radar (t),W match∨mis The amplitude, frequency, and phase modulation function of (t) is denoted as

[0063] u radar (t)=(S radar (t),W match∨mis (t); a m,n (t),f m,n (t),θ m,n (t))

[0064] 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;

[0065] The control function of the jammer: In the deception-forwarding jamming mode, the parameter control is time delay and Doppler shift modulation, denoted as...

[0066] v jammer (t)=(t jammer ,f d,jammer )

[0067] t jammer It's a time delay, f d,jammer It is Doppler translation modulation, where d is the template;

[0068] State space: The state space of a game is the real-time evolution of the local signal-to-noise ratio on the distance-Doppler plane;

[0069] Objective function: The difference between the template set by the ambiguity function and the actual ambiguity function of the transmitted waveform.

[0070] Construct a differential game concept model of parameter modulation under deterministic and uncertain information modes.

[0071] Furthermore, the differential game model under the deterministic information model is constructed as follows:

[0072] For radar:

[0073]

[0074] For jammers:

[0075]

[0076] Among them, Q target and Q jammerG represents the sets of characteristics of the target and the interference source, respectively. k,p It is a discrete template of the mutual ambiguity function, used to describe the characteristics of signals in a radar system, where k and p are the discretized time delay and frequency offset indices, and d auto∨cross (τ,f) is the error between the discrete template of the mutually ambiguous function and its expected value, χ auto∨cross,S,W (τ,f) are self-ambiguity and mutual ambiguity functions used to describe the correlation between signals S and W under time delay τ and frequency offset f. and These represent the local signal-to-noise ratio and the interference noise ratio, respectively, and their dynamic changes are determined by the system's internal state and the external control input u. radar (t) and v jammer Determined by (t), and It is a function that describes dynamic evolution and is used to calculate the rate of change of local signal-to-noise ratio and interference-to-noise ratio.

[0077] Furthermore, the differential game model under the uncertain information mode is constructed as follows. Here, the uncertain information mode has uncertainty in the distance region and Doppler shift region of the target. Therefore, the expectation in the following model is the expectation of the region with a probability distribution:

[0078] For radar:

[0079]

[0080] For jammers:

[0081]

[0082] Therefore, a two-layer game model is constructed to explore the interaction between the radar, the target, and the jammer. The first layer is a coarse-grained fuzzy function template and jammer jamming mode selection game model based on extended game theory. Through the game, the template type and jamming mode are determined, and two types, deterministic and uncertain, are constructed according to different information modes. The second layer is a fine-grained parameter modulation game model based on differential game theory, which is built on the first layer. Through the game, the radar's transmitted waveform and matched / mismatched filtering waveforms are determined.

[0083] Furthermore, regarding the model

[0084]

[0085] min X,Y This indicates a minimization operation on variables X and Y. This represents the summation of the index set T×F over time delay and frequency offset, g kp The discrete template representing the mutual ambiguity function describes the characteristics of the signal under time delay k and frequency offset p. X represents the modulus of the expected value of the mutual fuzzy function template. H J represents the conjugate transpose of X. kp The complex representation of the mutual ambiguity function template is given by Y, which represents the received signal processing vector in the optimization model.

[0086] First, derive the objective function.

[0087]

[0088] in

[0089]

[0090] Observe the last term of the objective function expansion

[0091] Re(X H AX)

[0092] In order to use the loop iteration technique, we based on

[0093]

[0094] Iteration produces two sequences

[0095]

[0096] The iterative method is as follows:

[0097] Step 1: Randomly initialize and generate vectors according to the constraints of vector $X$. and X (0) .

[0098] Step 2: For fixed... and X (.) Calculations yielded

[0099]

[0100] And update A (.)

[0101] Step 3: For a fixed phase shift and sequence X (.) Calculations yielded

[0102]

[0103] Step 4: For fixed and Calculated

[0104]

[0105] m and n are the row and column indices of matrix X, respectively. Representation matrix In the first iteration, the value of the element at position m, n It is the value of the element at position m, N+l during the first iteration;

[0106] Step 5: Repeat steps 2, 3, and 4 until the convergence threshold is met;

[0107] Output: The final X (.) .

[0108] Compared with existing methods, this invention addresses the problem that traditional game-theoretic algorithms are extremely difficult to solve in large-scale networks. By using a reverse iteration method, the optimal transmission waveform and matching waveform can be obtained efficiently, thereby improving the anti-jamming capability of the radar system and effectively solving the computational efficiency problem of attack and defense strategy selection in large-scale networks. Attached Figure Description

[0109] Figure 1 A flowchart illustrating an embodiment of the present invention is shown;

[0110] Figure 2 The image shows the range Doppler plots of the target echo and interference before optimization according to an embodiment of the present invention;

[0111] Figure 3 The diagram shows a 2D mutual ambiguity function plot of the transmitted waveform before optimization according to an embodiment of the present invention;

[0112] Figure 4 The optimized range Doppler plots of the target echo and interference according to an embodiment of the present invention are shown. Detailed Implementation

[0113] The present invention will be further described below with reference to the accompanying drawings, but this is not intended to limit the present invention in any way. Any modifications or substitutions made based on the teachings of the present invention shall fall within the protection scope of the present invention.

[0114] In this embodiment, linear frequency modulation is used to add noise and interference to the waveform. The effectiveness of the method is verified by comparing the signal-to-interference-plus-noise ratio before and after optimization.

[0115] like Figure 1 As shown, a comprehensive mutual fuzzy function iterative optimization method based on deterministic information includes a representation of...

[0116] Step 1: Design long-range support jamming scenarios for radar, targets, and jammers;

[0117] Step 2: Sampling is performed based on the general model of the pulse train to generate pulse train symbols;

[0118] Step 3: Define the symbol model of the pulse train and determine the modulation mode and radar signal model;

[0119] Step 4: Establish a game information model among the radar, target, and jammer;

[0120] Step 5: Construct a waveform design model and generate the optimized waveform;

[0121] Specifically, the long-range support jamming scenario is as follows:

[0122] Radar, target, and jamming equipment become the three players in a long-range jamming support scenario. The radar is positioned at the origin, and its maximum effective range in conjunction with the anti-missile system is R. max With the radar as the center, R max The sphere envelope B(0,R) is formed by the radius. max Any enemy aircraft entering this envelope faces significant risks. Given an enemy aircraft (the target) attempting to penetrate the envelope, given its relatively weak jamming and stealth capabilities, a separate jamming aircraft is needed to provide long-range cover. The distance between the jamming aircraft and the radar is R1. Long-range jamming support means the jamming aircraft does not enter the spherical envelope to avoid risk, but rather performs jamming near the envelope. Therefore, R1 > R. max R1=R max +δ, where δ represents a smaller relative safe distance. The jammer's protection of the target is not absolute. When the target is close enough to the radar, the jammer loses its jamming effect, and the radar can clearly detect the target. This distance is called the radar's burn-through distance, denoted as R. min This constitutes the burn-through envelope of the radar system, denoted as B(0,R). min Therefore, the jammer's cover for the target occurs at B(0,R). max B(0,R) min This area.

[0123] In summary, in long-range support jamming scenarios, the radar is located at the origin, forming two envelopes B(0,R). max ),B(0,R min ), in the envelope B(0,R) max Beyond this, it cannot effectively detect or threaten targets and jammers within the envelope B(0,R). min Within the envelope B(0,R), it holds an absolute advantage and can accurately detect targets; the jammer is located within the envelope B(0,R). max +δ) and B(0,R) max The current target is located within the envelope B(0,R). max ) and B(0,R min )between.

[0124] Specifically, the general model of the pulse train is as follows:

[0125] Pulse train: A signal within one CPI is a pulse train formed by M pulses.

[0126] Pulse duration: The duration of the m-th pulse of the signal is T. s,m , m∈[1,…,M], is abbreviated as pulse width.

[0127] Pulse repetition period: The period of the m-th pulse of the signal is T. r,m , m∈[1,…,M].

[0128] Constant-modulus complex envelope: The constant-modulus complex envelope of the m-th pulse of the signal is u m (t), m∈[1,…,M]

[0129] Therefore, the function u m The support set of (t) is [0,T s,m The value of ] in the rest is 0.

[0130] Initial amplitude: The initial amplitude of the m-th pulse of the signal is a. m (0), m∈[1,…,M].

[0131] Amplitude modulation mode: The amplitude modulation mode of the m-th pulse of the signal is a m (t), m∈[1,…,M], where t is time, representing a quantity whose amplitude changes with time, where the function a m The support set of (t) is [0,T s,m The value is 1 on it and 0 on the rest.

[0132] Initial frequency: The initial frequency of the m-th pulse of the signal is f. m (0), m∈[1,…,M].

[0133] Frequency modulation mode: The frequency modulation mode of the m-th pulse of the signal is f m (t), m∈[1,…,M], where t is time, and represents the quantity whose frequency changes with time, where the function f m The support set of (t) is [0,T s,m The value is 1 on it and 0 on the rest.

[0134] Initial phase: The initial phase of the m-th pulse of the signal is θ. m (0), m∈[1,…,M].

[0135] Phase modulation mode: The phase modulation mode of the m-th pulse of the signal is θ m(t), m∈[1,…,M], where t is time, and represents the quantity of phase change with time, where the function θ m The domain of (t) is [0,T]. s,m The value is 1 on it and 0 on the rest.

[0136] In summary, the general model of a pulse train without modulation mode is expressed as follows:

[0137]

[0138] Such a signal model is too simplistic, except for its ability to handle pulse duration T. s,m and pulse repetition period T r,m While it can perform simple modulation, it cannot modulate amplitude, frequency, or phase, and therefore cannot meet the needs of complex game theory.

[0139] A pulse train with modulation mode is generally expressed as a model of pulse train with modulation mode.

[0140]

[0141] Such a signal model is relatively complex, and it can be used to determine the pulse duration T. s,m Pulse repetition period T r,m Modulation can theoretically be achieved by controlling amplitude, frequency, and phase, which can meet the needs of complex games. However, because radar systems are hardware systems, they are constrained by the physical performance of their components, making it difficult to modulate pulse trains simultaneously from multiple dimensions. Instead, modulation is achieved in one or a few dimensions. For example, a fixed pulse duration T... s,m Pulse repetition period T r,m In addition to amplitude, frequency, and phase, two of these can be used to modulate the other, resulting in a special modulation signal model.

[0142] Amplitude modulation model:

[0143]

[0144] Frequency modulation model:

[0145]

[0146] Phase modulation model:

[0147]

[0148] When studying general pulse train models, we typically eliminate the initial frequency and phase through local demodulation. For general pulse train models with modulation modes...

[0149]

[0150] Define the local demodulator as

[0151]

[0152] Therefore, the complex conjugate multiplication can be obtained.

[0153]

[0154] Furthermore, the zero-sum game model between the radar side and the jamming side is as follows:

[0155] Let the template spaces of the radar self-ambiguity function and the mutual ambiguity function be respectively...

[0156] M auto M cross

[0157] The jamming mode space of the jammer is

[0158] M jammer ,j∈M jammer

[0159] This indicates a certain jamming mode. Therefore, the first layer of the game between radar and jammer is...

[0160] M auto M cross M jammer In the game above, assuming the actual target and interference energy distribution areas are... However, the target and interference energy region of template d design are... If the distance or coverage metric between regions is dist, then the conceptual model of the first-level game is as follows.

[0161] For jammers:

[0162]

[0163] For radar:

[0164]

[0165] If the region defined by template d has a probability distribution, then the above model can be constructed as a stochastic model, and the expectation in the model below is the expectation of the region with a probability distribution.

[0166] For jammers:

[0167]

[0168]

[0169] For radar:

[0170]

[0171] For first-level games, we should first study the extended game problem of template selection and interference mode selection under the condition of complete information, and then study the Bayesian extended game problem of template selection and interference mode selection without complete information.

[0172] If the choices in the first layer of the game have been determined, that is, the template d of the fuzzy function and the interference pattern j of the interference machine have been determined, then we enter the second layer of parameter fine-tuning differential game stage.

[0173] Radar control function: (S radar (t),W match∨mis The amplitude, frequency, and phase modulation function of (t) is denoted as

[0174] u radar (t)=(S radar (t),W match∨mis (t); a m,n (t),f m,n (t),θ m,n (t))

[0175] The control function of the jammer: parameter control under a certain jamming mode. This project mainly focuses on deception and forwarding jamming, primarily time delay and Doppler shift modulation, denoted as...

[0176] v jammer (t)=(t jammer ,f d,jammer )

[0177] State space: The state space of a game is the real-time evolution of the local signal-to-noise ratio on the distance-Doppler plane.

[0178] Objective function: The difference between the template set by the fuzzy function and the actual fuzzy function of the transmitted waveform (filtered).

[0179] Therefore, we can construct a conceptual model of differential game with parameter modulation under deterministic and uncertain information modes.

[0180] First, the differential game model under deterministic information mode is constructed as follows.

[0181] For radar:

[0182]

[0183] For jammers:

[0184]

[0185] Secondly, the differential game model under the uncertain information mode is constructed as follows. Here, the uncertain information mode mainly involves uncertainty about the distance region and Doppler shift region of the target. Therefore, the expectation in the model below is the expectation of the region with a probability distribution.

[0186] For radar:

[0187]

[0188] For jammers:

[0189]

[0190] Therefore, we constructed a two-layer game theory model involving the radar, target, and jammer. The first layer is a coarse-grained fuzzy function template and jammer jamming mode selection game model based on extended game theory. This model primarily determines the template type and jamming mode through game theory, and can construct deterministic and uncertain types depending on the information mode. The second layer, based on the first layer, is a fine-grained parameter modulation game model based on differential game theory. This model primarily determines the radar's transmitted waveform and matched / mismatched filtering waveforms through game theory. The above model is a conceptual model and a continuous model. Modern radar systems are primarily digital systems, which have discretized characteristics; therefore, the model is a discretized model based on the conceptual model.

[0191] Furthermore, the derivation is as follows:

[0192] For the model

[0193]

[0194] First, derive the objective function.

[0195]

[0196] in

[0197]

[0198] Observe the last term of the objective function expansion

[0199] Re(X H AX)

[0200] In order to use the loop iteration technique, we based on

[0201]

[0202] Iteration produces two sequences

[0203]

[0204] The iterative method is as follows:

[0205] Step 1: Randomly initialize and generate vectors according to the constraints of vector $X$. and X (0) .

[0206] Step 2: For fixed... and X (.) Calculations yielded

[0207]

[0208] And update A (.)

[0209] Step 3: For fixed... and X (.) Calculations yielded

[0210]

[0211] Step 4: For fixed and Calculated

[0212]

[0213] Step 5: Repeat steps 2, 3, and 4 until the convergence threshold is met.

[0214] Output: The final X (.)

[0215] Based on the above, the distance Doppler image before optimization in this embodiment is as follows: Figure 2 As shown, the mutual fuzziness function graph before optimization is as follows: Figure 3 As shown. To optimize this waveform, firstly, given the initial radar waveform, filtering, and other necessary parameters, calculate the two-dimensional color map and three-dimensional function map of the ambiguity function for the initial waveform and the filter. Based on the target and interference models, form a range Doppler image and calculate the local signal-to-interference-plus-noise ratio (SNR) of the target element. Modulate the initial radar waveform and filter using the ambiguity function-based model and algorithm described above, outputting the waveform and filter. Calculate the two-dimensional color map and three-dimensional function map of the ambiguity function for the modulated waveform and the filter. Again, based on the target and interference signal models, form a range Doppler image and calculate the local SNR of the target element. Compare the shapes of the ambiguity functions before and after, compare the clarity of the target element and the local SNR before and after, and the optimized range Doppler image is shown below. Figure 4 As shown.

[0216] This invention addresses the problem that traditional game theory algorithms struggle to solve problems in large-scale networks. By employing a reverse iteration method, it can efficiently obtain the optimal transmission waveform and matching waveform, thereby improving the anti-jamming capability of radar systems and effectively solving the computational efficiency problem of selecting attack and defense strategies in large-scale networks.

[0217] As used herein, the term "preferred" is meant as an example, illustration, or illustration. Any aspect or design described herein as "preferred" need not be construed as being more advantageous than other aspects or designs. Rather, the use of the term "preferred" is intended to present the concept in a specific manner. As used in this application, the term "or" is intended to mean an inclusive "or" rather than an exclusionary "or." That is, unless otherwise specified or clear from the context, "X uses A or B" naturally includes either of the permutations. That is, if X uses A; X uses B; or X uses both A and B, then "X uses A or B" is satisfied in any of the foregoing examples.

[0218] Furthermore, although this disclosure has been shown and described with respect to one or more implementations, equivalent variations and modifications will occur to those skilled in the art based on a reading and understanding of this specification and the accompanying drawings. This disclosure includes all such modifications and variations and is limited only by the scope of the appended claims. In particular, with respect to the various functions performed by the aforementioned components (e.g., elements, etc.), the terminology used to describe such components is intended to correspond to any component (unless otherwise indicated) that performs the specified function of said component (e.g., is functionally equivalent to it), even if structurally not equivalent to the disclosed structure performing the functions in the exemplary implementations of this disclosure shown herein. Moreover, although specific features of this disclosure have been disclosed with respect to only one of several implementations, such features may be combined with one or more features of other implementations that may be desirable and advantageous for a given or particular application. Furthermore, with regard to the use of the terms “comprising,” “having,” “containing,” or variations thereof in the Detailed Description or claims, such terms are intended to be included in a manner similar to the term “including.”

[0219] The functional units in this invention embodiment can be integrated into a processing module, or each unit can exist physically separately, or multiple units can be integrated into a module. The integrated module can be implemented in hardware or as a software functional module. If the integrated module is implemented as a software functional module and sold or used as an independent product, it can also be stored in a computer-readable storage medium. The storage medium mentioned above can be a read-only memory, a disk, or an optical disk, etc. The aforementioned devices or systems can execute the storage methods in the corresponding method embodiments.

[0220] In summary, the above embodiments are one implementation of the present invention, but the implementation of the present invention is not limited to the embodiments described above. Any changes, modifications, substitutions, combinations, or simplifications made that deviate from the spirit and principle of the present invention should be considered equivalent substitutions and are included within the protection scope of the present invention.

Claims

1. A method for designing long-range support interference waveforms based on a pursuit-escape game, characterized in that, Includes the following steps: Step 1: Design long-range support jamming scenarios for radar, targets, and jammers; Step 2: Sampling is performed based on the general model of the pulse train to generate pulse train symbols; Step 3: Define the symbol model of the pulse train and determine the modulation mode and radar signal model; Step 4: Establish a game information model among the radar, target, and jammer; Step 5: Construct a waveform design model and generate the optimized waveform; The long-range support jamming scenario is as follows: The radar is located at the origin, forming a spherical envelope and a burn-through envelope B(0,R). max ),B(0,R min ), R max R represents the maximum effective range of the radar and anti-missile system working together. min The radar's burn-through range is defined within the burn-through envelope B(0,R). max Beyond this, it cannot effectively detect or threaten targets and jammers within the envelope B(0,R). min Within a certain range, it can accurately detect targets; the distance between the jammer and the radar is R1. Long-range jamming support means that the jammer does not enter the spherical envelope to avoid risks, but performs jamming near the spherical envelope. Therefore, R1 > R max R1=R max +δ, where δ represents the relative safe distance; the jammer is located within the envelope B(0,R). max +δ) and B(0,R) max The current target is located within the envelope B(0,R). max ) and B(0,R min )between; The general model of the pulse train is as follows: A signal within a CPI is a pulse train consisting of M pulses; Pulse duration: The duration of the m-th pulse of the signal is T. s,m , m∈[1,…,M], abbreviated as pulse width; Pulse repetition period: The period of the m-th pulse of the signal is T. r,m , m∈[1,…,M]; Constant-modulus complex envelope: The constant-modulus complex envelope of the m-th pulse of the signal is u m (t), m∈[1,…,M] Therefore, the function u m The support set of (t) is [0,T s,m The value in the remaining parts is 0; Initial amplitude: The initial amplitude of the m-th pulse of the signal is a. m (0), m∈[1,…,M]; Amplitude modulation mode: The amplitude modulation mode of the m-th pulse of the signal is a m (t), m∈[1,…,M], where t is time, representing a quantity whose amplitude changes with time, where the function a m The support set of (t) is [0,T s,m The value of ] is 1 on it and 0 in the rest; Initial frequency: The initial frequency of the m-th pulse of the signal is f. m (0), m∈[1,…,M]; Frequency modulation mode: The frequency modulation mode of the m-th pulse of the signal is f m (t), m∈[1,…,M], where t is time, and f represents the frequency that changes with time, where the function f m The support set of (t) is [0,T s,m The value of ] is 1 on it and 0 in the rest; Initial phase: The initial phase of the m-th pulse of the signal is θ. m (0), m∈[1,…,M]; Phase modulation mode: The phase modulation mode of the m-th pulse of the signal is θ m (t), m∈[1,…,M], where t is time, and represents the quantity of phase change with time, where the function θ m The domain of (t) is [0,T]. s,m The value of ] is 1 on it and 0 in the rest; In summary, the general model of a pulse train without modulation mode is expressed as follows: T r,i It is the period of the i-th pulse of the signal; A pulse train with modulation mode is generally expressed as a model of pulse train with modulation mode.

2. The long-range support interference waveform design method based on pursuit and escape game theory as described in claim 1, characterized in that, Based on the general model of a pulse train with modulation mode, for a fixed pulse duration T s,m Pulse repetition period T r,m In addition, two of the amplitude, frequency, and phase parameters are used to modulate the other, resulting in a special modulation signal model; In special modulation signal models, the amplitude modulation model is: In special modulation signal models, the frequency modulation model is: In special modulation signal models, the phase modulation model is:

3. The long-range support interference waveform design method based on pursuit and escape game theory according to claim 2, characterized in that, For the general model of a pulse train, the initial frequency and phase are eliminated through local demodulation: For the general model of a pulse train with modulation mode Define the local demodulator as: According to complex conjugate multiplication, we get:

4. The long-range support interference waveform design method based on pursuit and escape game theory according to claim 1, characterized in that, The zero-sum game model of radar and jamming is as follows: The template spaces for radar self-ambiguity functions and mutual ambiguity functions are respectively M auto ,M cross The jamming mode space of the jammer is M jammer ,j∈M jammer The first layer of the game between radar and jammer is in M auto M cross M jammer In the game above, the actual target and the distribution area of ​​interference energy are The target and interference energy regions of template d are as follows: If the distance or coverage metric between regions is dist, then the conceptual model of the first-level game is as follows: For jammers: s.t.d∈M auto or M cross ,j∈M jammer For radar: s.t.d∈M auto or M cross ,j∈M jammer If the region defined by template d has a probability distribution, then the above model is a stochastic model, and the expectation in the model below is the expectation of the region with the probability distribution: For jammers: s.t.d∈M auto or M cross ,j∈M jammer For radar: s.t.d∈M auto or M cross ,j∈M jammer If the choices in the first layer of the game are already determined, that is, the template d of the fuzzy function and the interference pattern j of the interference machine are already determined, then we enter the second layer of parameter fine-tuning differential game stage: Radar control function: (S radar (t),W match∨mis The amplitude, frequency, and phase modulation function of (t) is denoted as u radar (t)=(S radar (t),W match∨mis (t);a m,n (t),f m,n (t),θ m,n (t)) a m,n (t) is the amplitude function, f m,n (t) is the frequency function, θ m,n (t) is the phase modulation function, S radar (t) is the time-domain waveform of the radar signal, W march∨mis (t) is the output of the matched filter; The control function of the jammer: In the deception-forwarding jamming mode, the parameter control is time delay and Doppler shift modulation, denoted as... v jammer (t)=(t jammer ,f d,jammer ) t jammer It's a time delay, f d,jammer It is Doppler translation modulation, where d is the template; State space: The state space of a game is the real-time evolution of the local signal-to-noise ratio on the distance-Doppler plane; Objective function: The difference between the template set by the fuzzy function and the real fuzzy function of the transmitted waveform is used to construct a differential game concept model of parameter modulation under deterministic information mode and uncertain information mode.

5. The long-range support jamming waveform design method based on pursuit and escape game theory according to claim 4, characterized in that, The differential game model under deterministic information is constructed as follows: For radar: For jammers: Among them, Q target and Q jammer G represents the sets of characteristics of the target and the interference source, respectively. k,p It is a discrete template of the mutual ambiguity function, used to describe the characteristics of signals in a radar system, where k and p are the discretized time delay and frequency offset indices, and d auto∨cross (τ,f) is the error between the discrete template of the mutually ambiguous function and its expected value, χ auto∨cross,S,W (τ,f) are self-ambiguity and mutual ambiguity functions used to describe the correlation between signals S and W under time delay τ and frequency offset f. and These represent the local signal-to-noise ratio and the interference noise ratio, respectively, and their dynamic changes are determined by the system's internal state and the external control input u. radar (t) and v jammer Determined by (t), and It is a function that describes dynamic evolution and is used to calculate the rate of change of local signal-to-noise ratio and interference-to-noise ratio.

6. The long-range support jamming waveform design method based on pursuit and escape game theory according to claim 4, characterized in that, The differential game model under the uncertain information mode is constructed as follows. Here, the uncertain information mode has uncertainty in the distance region and the Doppler shift region of the target. Therefore, the expectation in the model below is the expectation of the region with a probability distribution: For radar: For jammers: Therefore, a two-layer game model is constructed for the interaction between radar, target, and jammer. The first layer is a coarse-grained fuzzy function template and jammer jamming mode selection game model based on extended game theory. Through the game, the template type and jamming mode are determined, and two types, deterministic and uncertain, are constructed according to different information modes. The second layer builds upon the first layer by using a fine-grained parameter modulation game model based on differential game theory. Through game theory, it determines the radar's transmitted waveform and the matching and mismatch filtering waveforms.

7. The long-range support interference waveform design method based on pursuit and escape game theory according to claim 1, characterized in that, For the model min indicates that the variable is minimized. This represents the summation of the index set T×F over time delay and frequency offset, g kp The discrete template representing the mutual ambiguity function describes the characteristics of the signal under time delay k and frequency offset p. X represents the modulus of the expected value of the mutual fuzzy function template. H J represents the conjugate transpose of X. kp The complex representation of the mutual ambiguity function template is given by X, where X represents the received signal processing vector in the optimization model. First, derive the objective function. in Observe the last term of the objective function expansion Re(X H AX) In order to use the loop iteration technique, according to Iteration produces two sequences The iterative method is as follows: Step 1: Randomly initialize and generate vectors according to the constraints of vector $X$. and X (0) ; Step 2: For fixed... and X (.) Calculations yielded And update A (.) ; Step 3: For a fixed phase shift and sequence X (.) Calculations yielded Step 4: For fixed and Calculated m and n are the row and column indices of matrix X, respectively. Representation matrix In the first iteration, the value of the element at position m, n It is the value of the element at position m, N+l during the first iteration; Step 5: Repeat steps 2, 3, and 4 until the convergence threshold is met; Output: The final X (.) .

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