Remote support interference waveform design method based on pursuit game

Abstract

The invention discloses a long-distance support interference waveform design method based on a pursuit game. The method comprises the following steps: step 1, designing long-distance support interference scenes of a radar, a target and a jammer; 2, sampling is carried out based on a pulse string general model, and pulse string code elements are generated; 3, the code element model of the pulse string is limited, and a modulation mode and a radar signal model are determined; step 4, establishing a game information mode among the radar, the target and the jammer; and 5, constructing a waveform design model, and generating an optimized waveform. Aiming at the problem that a traditional game solving algorithm is extremely difficult to solve in a large-scale network, the method can efficiently obtain the optimal transmitted waveform and the matched waveform through a reverse iteration method, thereby improving the anti-interference capability of a radar system, and effectively solving the problem of calculation efficiency of attack and defense strategy selection in the large-scale network.

Description

Technical Field

[0001] The present invention belongs to the technical field of radar waveform design, and in particular relates to a long-distance support jamming waveform design method based on pursuit-escape game. 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] Although modern radar waveform design methods have made significant progress, there are still some shortcomings. These shortcomings are mainly reflected in the following aspects: radar waveforms are not adaptable enough in dynamic environments (such as rapidly changing targets, terrain, and weather conditions). It is necessary to develop adaptive waveform design methods to adjust waveform parameters according to real-time environmental changes to improve the flexibility and robustness of the system; some advanced waveform design methods (such as compressed sensing and deep learning) have high computational complexity and high requirements for hardware resources. It is necessary to optimize algorithms, reduce computational complexity, and improve real-time processing capabilities. At the same time, it is necessary to develop dedicated hardware (such as FPGA and ASIC) to accelerate calculations. In particular, the current waveform design process often relies on the experience and manual adjustments of experts and lacks automation. It is necessary to develop an automated waveform design system based on machine learning and artificial intelligence 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 technology and mathematical modeling, 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.

[0005] 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.

[0006] 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. Summary of the invention

[0007] In view of this, the present invention discloses a long-distance support interference waveform design method based on pursuit-escape game. 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 through the following technical solution, a comprehensive mutual fuzzy function loop optimization method based on determined information, the method comprising the following steps:

[0009] Step 1: Design the long-range support jamming scenario of radar, target, and jammer;

[0010] Step 2, sampling based on the general model of the pulse train to generate pulse train symbols;

[0011] Step 3, limiting the code element model of the pulse train, determining the modulation mode and the radar signal model;

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

[0013] Step 5: construct a waveform design model to generate an optimized waveform.

[0014] Furthermore, the long-distance support interference scenario is:

[0015] The radar is located at the origin of the coordinate system, forming a spherical envelope and a burn-through envelope B(0,R max ),B(0,R min ), R max is the maximum range of radar and anti-missile system, R min is the burn-through distance of the radar, in the burn-through envelope B(0,R max ), it is impossible to effectively detect and threaten the target and jammer. min ) can accurately detect the target; the distance between the jammer and the radar is R1. The meaning of long-distance support interference is that the jammer does not enter the spherical envelope to avoid risks, but interferes near the spherical envelope, so R1>Rmax ,R1=R max +δ,δ is the relative safety distance; the jammer is located in envelope B(0,R max +δ) and B(0,R max ); the current target is located in the envelope B(0,R max ) and B(0,R min )between.

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

[0017] The signal within a CPI is a pulse train formed by M pulses;

[0018] Pulse duration: The duration of the mth pulse of the signal is T s,m , m∈[1,…,M], referred to as pulse width;

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

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

[0021] So the function u m The support set of (t) is [0,T s,m ], and the value in the rest is 0;

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

[0023] Amplitude modulation mode: The amplitude modulation mode of the mth pulse of the signal is a m (t), m∈[1,…,M], where t is time, indicating the amount of amplitude change over time, where function a m The support set of (t) is [0,T s,m ], the value is 1 on it and 0 on the rest;

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

[0025] Frequency modulation mode: The frequency modulation mode of the mth pulse of the signal is f m (t), m∈[1,…,M], where t is time, indicating the amount of frequency change over 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;

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

[0027] Phase modulation mode: The phase modulation mode of the mth pulse of the signal is θ m (t), m∈[1,…,M], where t is time, indicating the amount of phase change over 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;

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

[0029]

[0030] T r,i is the period of the ith pulse of the signal;

[0031] The general model of a pulse train with a modulation pattern is expressed as

[0032]

[0033] Furthermore, according to the general model of pulse train with modulation mode, for a fixed pulse duration T s,m , pulse repetition period T r,m and two of the amplitude, frequency, and phase, to modulate the other to obtain a special modulation signal model;

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

[0035]

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

[0037]

[0038] In the special modulation signal model, the phase modulation model is:

[0039]

[0040] Furthermore, for the general model of the pulse train, the initial frequency and phase are eliminated by local demodulation:

[0041] For a general model of a pulse train with a modulation pattern

[0042]

[0043] Define the local demodulator as:

[0044]

[0045] According to complex conjugate multiplication, we get:

[0046]

[0047] Furthermore, the zero-sum game model between the radar party and the jammer is:

[0048] The template spaces of radar self-ambiguity function and mutual ambiguity function are

[0049] M radar,auto ,M radar,cross

[0050] The jammer’s interference pattern space is

[0051] M jammer ,j∈M jammer

[0052] The first level of game between radar and jammer is in M auto ,M cross ,M jammer The real target and interference energy distribution area are 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:

[0053] For the jammer:

[0054]

[0055] std∈M auto oeLh cross ,j∈M jammer

[0056] For radar:

[0057]

[0058] std∈M auto oeLh cross ,j∈M jammer

[0059] 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:

[0060] For the jammer:

[0061]

[0062] std∈M auto oeLh cross ,j∈M jammer

[0063] For radar:

[0064]

[0065] std∈M auto oeLh cross ,j∈M jammer

[0066] 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:

[0067] Radar control function: (S radar (t),W match∨mis (t)) is the amplitude, frequency, and phase modulation function, denoted as

[0068] u radar (t)=(S radar (t),W match∧mis (t); a m,n (t),f m,n (t),θ m,n (t))

[0069] 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;

[0070] Jammer control function: The parameters in the deception forwarding jamming mode are controlled by delay and Doppler shift modulation, denoted as

[0071] v jammer (t)=(t jammer ,f d,jammer )

[0072] t jammer is the delay, f d,jammer is Doppler shift modulation, d is the template;

[0073] 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;

[0074] Target function: The difference between the template set by the fuzzy function and the true fuzzy function of the transmitted waveform

[0075] Construct a conceptual model of differential game with parameter modulation under deterministic information mode and uncertain information mode.

[0076] Furthermore, the differential game model under the deterministic information mode is constructed as follows:

[0077] For radar:

[0078]

[0079] For the jammer:

[0080]

[0081] 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.

[0082] 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:

[0083] For radar:

[0084]

[0085] For the jammer:

[0086]

[0087] Therefore, a two-layer game model of the game between radar, target and jammer is constructed; the first layer is a coarse-grained fuzzy function template and jammer interference mode selection game model based on extended game. Through the game, the template type and interference mode are determined, and according to the different information modes, two types of deterministic and uncertain types are constructed; the second layer is based on the first layer, and is a fine-grained parameter modulation game model based on differential game. Through the game, the radar's transmission waveform and matching and mismatch filter waveforms are determined.

[0088] Furthermore, for the model

[0089]

[0090] 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;

[0091] First derive the objective function

[0092]

[0093] in

[0094]

[0095] Observe the last term of the objective function expansion

[0096] Re(X H AX)

[0097] To use the loop iteration technique, we follow

[0098]

[0099] Iteration produces two sequences

[0100]

[0101] The iterative method is:

[0102] Step 1: Generate random initialization according to the constraints of vector $X$ and X (0) .

[0103] Step 2: For fixed and X (.) , calculated

[0104]

[0105] And update A (.)

[0106] Step 3: For a fixed phase offset and sequence X (.) , calculated

[0107]

[0108] Step 4: For fixed and Calculated

[0109]

[0110] 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;

[0111] Step 5: Repeat steps 2, 3, and 4 until the convergence threshold is met;

[0112] Output: Final X (.) .

[0113] Compared with the existing methods, the present invention aims at the problem that traditional game solving algorithms are extremely difficult to solve in large-scale networks. Through the reverse iteration method, the optimal transmission waveform and matching waveform can be efficiently obtained, thereby improving the anti-interference ability of the radar system and effectively solving the computational efficiency problem of attack and defense strategy selection in large-scale networks. BRIEF DESCRIPTION OF THE DRAWINGS

[0114] Figure 1 A schematic diagram of a process flow of an embodiment of the present invention is shown;

[0115] Figure 2 The range Doppler diagram of the target echo and the interference before optimization in the embodiment of the present invention is shown;

[0116] Figure 3 A 2D mutual ambiguity function diagram of a transmission waveform before optimization according to an embodiment of the present invention is shown;

[0117] 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

[0118] 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.

[0119] 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.

[0120] like Figure 1 As shown, a comprehensive mutual fuzzy function loop optimization method based on determined information includes expressing

[0121] Step 1: Design the long-range support jamming scenario of radar, target, and jammer;

[0122] Step 2, sampling based on the general model of the pulse train to generate pulse train symbols;

[0123] Step 3, limiting the code element model of the pulse train, determining the modulation mode and the radar signal model;

[0124] Step 4, establish the game information model among radar, target and jammer;

[0125] Step 5, constructing a waveform design model to generate an optimized waveform;

[0126] Specifically, the long-distance support interference scenario is:

[0127] Radar, target, and jammer constitute the three players in the long-range support jamming scenario. The radar stands at the origin of the coordinate system, and its maximum range of action in coordination with the anti-missile system is R max , with the radar as the center, R max The radius forms the spherical envelope B(0,R max ), any enemy aircraft entering this envelope is extremely risky. If a certain enemy aircraft, that is, a target, wants to penetrate into the envelope space, the target's own interference stealth capability is relatively weak, and at this time another jammer is needed to provide long-distance cover for it. The distance between the jammer and the radar is R1. The meaning of long-distance support jamming is that the jammer does not enter the spherical envelope to avoid risks, but performs jamming near the spherical envelope, so R1>R max ,R1=R max +δ,δ is a relatively small safe distance. The jammer’s cover for the target is not absolute. When the distance between the target and the radar is close enough, the jammer loses its interference significance, and the radar can definitely detect the target clearly. This distance is called the radar’s burn-through distance, recorded as R min , which constitutes the burn-through envelope of the radar system, denoted as B(0,Rmin ). So the jammer's cover for the target occurs at B(0,R max ), B(0,R min ) this area.

[0128] In summary, in the long-distance support jamming scenario, the radar is located at the origin of the coordinate system, forming two envelopes B(0,R max ),B(0,R min ), in the envelope B(0,R max ), it is impossible to effectively detect and threaten the target and jammer. min ), occupying an absolute advantage and being able to accurately detect the target; the jammer is located in envelope B(0,R max +δ) and B(0,R max ); the current target is located in the envelope B(0,R max ) and B(0,R min )between.

[0129] Specifically, the general model of the pulse train is:

[0130] Pulse train: The signal within a CPI is a pulse train formed by M pulses.

[0131] Pulse duration: The duration of the mth pulse of the signal is T s,m , m∈[1,…,M], referred to as pulse width.

[0132] Pulse repetition period: The period of the mth pulse of the signal is T r,m , m∈[1,…,M].

[0133] Constant modulus complex envelope: The constant modulus complex envelope of the mth pulse of the signal is u m (t), m∈[1,…,M]

[0134] So the function u m The support set of (t) is [0,T s,m ], and the values ​​in the rest are 0.

[0135] Initial amplitude: The initial amplitude of the mth pulse of the signal is a m (0), m∈[1,…,M].

[0136] Amplitude modulation mode: The amplitude modulation mode of the mth pulse of the signal is a m (t), m∈[1,…,M], where t is time, indicating the amount of amplitude change over time, where function a m The support set of (t) is [0,T s,m ], on which the value is 1, and the value is 0 in the rest.

[0137] Initial frequency: The initial frequency of the mth pulse of the signal is f m (0), m∈[1,…,M].

[0138] Frequency modulation mode: The frequency modulation mode of the mth pulse of the signal is f m (t), m∈[1,…,M], where t is time, indicating the amount of frequency change over time, where the function f m The support set of (t) is [0,T s,m ], on which the value is 1, and the value is 0 in the rest.

[0139] Initial phase: The initial phase of the mth pulse of the signal is θ m (0), m∈[1,…,M].

[0140] Phase modulation mode: The phase modulation mode of the mth pulse of the signal is θ m (t), m∈[1,…,M], where t is time, indicating the amount of phase change over time, where the function θ m The domain of (t) is [0,T s,m ], on which the value is 1, and the value is 0 in the rest.

[0141] In summary, the general model of a pulse train without modulation mode is expressed as

[0142]

[0143] Such a signal model is too simple. In addition to the pulse duration T s,m and the pulse repetition period T r,m Apart from simple modulation, it cannot modulate the amplitude, frequency, and phase, and naturally cannot meet the needs of complex games.

[0144] The general model of a pulse train with a modulation pattern is expressed as

[0145]

[0146] Such a signal model is relatively complex, and the pulse duration T can be s,m , pulse repetition period T r,m , amplitude, frequency, and phase modulation can theoretically meet the needs of complex games. However, because the radar system is a hardware system, it is constrained by the physical performance of the device and it is difficult to modulate the pulse train from multiple dimensions at the same time. Instead, the pulse train is modulated in one or a few dimensions. For example, a fixed pulse duration T s,m , pulse repetition period T r,m And by modulating two of the amplitude, frequency, and phase on the other one, a special modulation signal model can be obtained.

[0147] Amplitude modulation model:

[0148]

[0149] Frequency modulation model:

[0150]

[0151] Phase modulation model:

[0152]

[0153] When we study the general model of pulse train, we usually eliminate the initial frequency and phase by local demodulation.

[0154]

[0155] Define the local demodulator as

[0156]

[0157] So complex conjugate multiplication gives

[0158]

[0159] Furthermore, the zero-sum game model between the radar party and the jammer is:

[0160] We denote the template space of radar self-ambiguity function and mutual ambiguity function as

[0161] M radar,auto ,M radar,cross

[0162] The jammer’s interference pattern space is

[0163] M jammer ,j∈M jammer

[0164] represents a certain interference pattern. So the first level of game between radar and jammer is the game on Mauto, Mcross, and Mjammer. 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.

[0165] For the jammer:

[0166]

[0167] std∈Mauto oeLh cross ,j∈M jammer

[0168] For radar:

[0169]

[0170] std∈M auto oeLh cross ,j∈M jammer

[0171] 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.

[0172] For the jammer:

[0173]

[0174] std∈M auto oeLh cross ,j∈M jammer

[0175] For radar:

[0176]

[0177] std∈M auto oeLh cross ,j∈M jammer

[0178] 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.

[0179] 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.

[0180] Radar control function: (S radar (t),W match∨mis (t)) is the amplitude, frequency, and phase modulation function, denoted as

[0181] u radar (t)=(S radar (t),W match∨mis (t); a m,n (t),f m,n (t),θ m,n (t))

[0182] Jammer control function: parameter control under a certain jamming mode. This topic mainly focuses on deception forwarding jamming, mainly delay and Doppler shift modulation, recorded as

[0183] v jammer (t)=(t jammer ,f d,jammer )

[0184] 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.

[0185] Target function: The difference between the template set by the fuzzy function and the true fuzzy function of the transmitted waveform (filter).

[0186] Therefore, we can construct a conceptual model of differential game with parameter modulation under deterministic information mode and uncertain information mode.

[0187] First, the differential game model under the deterministic information mode is constructed as follows.

[0188] For radar:

[0189]

[0190] For the jammer:

[0191]

[0192] 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.

[0193] For radar:

[0194]

[0195] For the jammer:

[0196]

[0197] 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.

[0198] Furthermore, the derivation is:

[0199] For the model

[0200]

[0201] First derive the objective function

[0202]

[0203] in

[0204]

[0205] Observe the last term of the objective function expansion

[0206] Re(X H AX)

[0207] To use the loop iteration technique, we follow

[0208]

[0209] Iteration produces two sequences

[0210]

[0211] The iterative method is:

[0212] Step 1: Generate random initialization according to the constraints of vector $X$ and X (0) .

[0213] Step 2: For fixed and X (.) , calculated

[0214]

[0215] And update A (.)

[0216] Step 3: For fixed and X (.) , calculated

[0217]

[0218] Step 4: For fixed and Calculated

[0219]

[0220] Step 5: Repeat steps 2, 3, and 4 until the convergence threshold is met.

[0221] Output: Final X (.)

[0222] 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. 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.

[0223] The present invention aims at the problem that traditional game solving algorithms are extremely difficult to solve in large-scale networks. Through the reverse iteration method, the optimal transmission waveform and matching waveform can be efficiently obtained, thereby improving the anti-interference ability of the radar system and effectively solving the computational efficiency problem of attack and defense strategy selection in large-scale networks.

[0224] 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.

[0225] 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".

[0226] 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.

[0227] 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 long-distance support jamming waveform design method based on pursuit-escape game, characterized in that: The following steps are involved: Step 1: Design the long-range support jamming scenario of radar, target, and jammer; Step 2, sampling based on the general model of the pulse train to generate pulse train symbols; Step 3, limiting the code element model of the pulse train, determining the modulation mode and the radar signal model; Step 4, establish the game information model among radar, target and jammer; Step 5: construct a waveform design model to generate an optimized waveform.

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

3. The long-distance support jamming waveform design method based on the pursuit-escape game according to claim 1 is characterized in that: The general model of the pulse train is: The signal within a CPI is a pulse train formed by M pulses; Pulse duration: The duration of the mth pulse of the signal is T s,m , m∈[1,…,M], referred to as pulse width; Pulse repetition period: The period of the mth pulse of the signal is T r,m , m∈[1,…,M]; Constant modulus complex envelope: The constant modulus complex envelope of the mth pulse of the signal is u m (t), m∈[1,…,M] So the function u m The support set of (t) is [0,T s,m ], and the value in the rest is 0; Initial amplitude: The initial amplitude of the mth pulse of the signal is a m (0), m∈[1,…,M]; Amplitude modulation mode: The amplitude modulation mode of the mth pulse of the signal is a m (t), m∈[1,…,M], where t is time, indicating the amount of amplitude change over time, where function a m The support set of (t) is [0,T s,m ], the value is 1 on it and 0 on the rest; Initial frequency: The initial frequency of the mth pulse of the signal is f m (0), m∈[1,…,M]; Frequency modulation mode: The frequency modulation mode of the mth pulse of the signal is f m (t), m∈[1,…,M], where t is time, indicating the amount of frequency change over 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; Initial phase: The initial phase of the mth pulse of the signal is θ m (0), m∈[1,…,M]; Phase modulation mode: The phase modulation mode of the mth pulse of the signal is θ m (t), m∈[1,…,M], where t is time, indicating the amount of phase change over 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; In summary, the general model of a pulse train without modulation mode is expressed as T r,i is the period of the ith pulse of the signal; The general model of a pulse train with a modulation pattern is expressed as 4. The long-distance support jamming waveform design method based on the pursuit-escape game according to claim 3 is characterized in that: According to the general model of pulse train with modulation pattern, for a fixed pulse duration T s,m , pulse repetition period T r,m and two of the amplitude, frequency, and phase, to modulate the other to obtain a special modulation signal model; In the special modulation signal model, the amplitude modulation model is: In the special modulation signal model, the frequency modulation model is: In the special modulation signal model, the phase modulation model is:

5. The long-distance support jamming waveform design method based on the pursuit-escape game according to claim 4 is characterized in that: For the general model of pulse train, the initial frequency and phase are eliminated by local demodulation: For a general model of a pulse train with a modulation pattern Define the local demodulator as: According to complex conjugate multiplication, we get:

6. The long-distance support jamming waveform design method based on the pursuit-escape game according to claim 1 is characterized in that: The zero-sum game model between the radar party and the jammer is: The template spaces of radar self-ambiguity function and mutual ambiguity function are M radar,auto ,M radar,cross The jammer’s interference pattern space is M jammer ,j∈M jammer The first level of game between radar and jammer is in M auto ,M cross ,M jammer The real target and interference energy distribution area are The target and interference energy areas designed by template d are The distance or coverage measure between regions is dist, so the conceptual model of the first-level game is as follows: For the jammer: For radar: 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: For radar: If the choice of the first-level game has been determined, that is, the template d of the fuzzy function and the interference pattern j of the jammer have been determined, then the second-level parameter fine-tuning differential game stage is entered: Radar control function: (S radar (t),W match∨mis (t)) is the amplitude, frequency, and phase modulation function, denoted as u radar (t)=(S radar (t),W match∨mis (t);a m,n (t),f m,n (t),θ m,n (t)) a m,n (t) is the amplitude function, f m,n (t) is the frequency function, θ m,n (t) is the phase modulation function, S radar (t) is the time domain waveform of the radar signal, W march∨mis (t) is the output of the matched filter; Jammer control function: The parameters in the deception forwarding jamming mode are controlled by delay and Doppler shift modulation, denoted as v jammer (t)=(t jammer ,f d,jammer ) t jammer is the delay, f d,jammer is Doppler shift modulation, d is the template; State space: The state space of the game is the real-time evolution of the local signal-to-noise ratio on the range-Doppler plane; Objective function: The difference between the template set by the fuzzy function and the true fuzzy function of the transmitted waveform constructs a differential game conceptual model of parameter modulation under deterministic information mode and uncertain information mode.

7. The long-distance support jamming waveform design method based on the pursuit-escape game according to claim 6 is characterized in that: The differential game model under the deterministic information mode is constructed as follows: For radar: For the jammer: Among them, Q target and Q jammer Represents the characteristic set of target and interference source respectively, g k,p is a discrete template of the mutual ambiguity function, which is used to describe the characteristics of the signal in the radar system, where k and p are the discretized time delay and frequency offset indices, and d auto∨cross (τ,f) is the error between the discrete template of the mutual fuzzy function and its expected value, χ auto∨cross,S,W (τ, f) are the self-ambiguity and mutual-ambiguity functions used to describe the correlation between signals S and W under time delay τ and frequency offset f. and They represent the local signal-to-noise ratio and interference-to-noise ratio respectively, and their dynamic changes are determined by the internal state of the system and the external control input u radar (t) and v jammer (t) determined by and It is a function that describes the dynamic evolution and is used to calculate the rate of change of the local signal-to-noise ratio and interference-to-noise ratio.

8. The long-distance support jamming waveform design method based on the pursuit-escape game according to claim 6 is characterized in that: The differential game model under the uncertain information mode is constructed as follows. Here, the uncertain information mode is uncertain about the distance area and Doppler frequency shift area of ​​the target, so the expectation in the following model is to find the expectation of the area with probability distribution: For radar: For the jammer: Thus, a two-layer game model among radar, target and jammer is constructed. The first layer is a coarse-grained fuzzy function template and jammer interference mode selection game model based on extended game. Through the game, the template type and interference mode are determined. According to the different information modes, two types of deterministic and uncertain types are constructed. The second layer is based on the first layer 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 long-distance support jamming waveform design method based on the pursuit-escape game according to claim 1 is characterized in that: For the model 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 Observe the last term of the objective function expansion Re(X H AX) To use the loop iteration technique, we follow Iteration produces two sequences The iterative method is: Step 1: Generate random initialization according to the constraints of vector $X$ and X (0) . Step 2: For fixed and X (.) , calculated And update A (.) Step 3: For a fixed phase offset and sequence X (.) , calculated Step 4: For fixed and 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 5: Repeat steps 2, 3, and 4 until the convergence threshold is met; Output: Final X (.) .

Images