Anti-interception and anti-sorting identification oriented multi-aircraft networking radar waveform dynamic design method and system

Abstract

The application discloses a kind of multi-aircraft networking radar waveform dynamic design methods and systems for anti-interception and anti-sorting identification, comprising: constructing multi-aircraft networking radar waveform dynamic design scene for anti-interception and anti-sorting identification;Construct multi-aircraft networking radar transmitting waveform signal model and echo model;Total mutual information between target echo and target scattering signal received by multi-aircraft networking radar is used to characterize target detection performance;KL distance is used as passive detection system interception and sorting identification comprehensive performance measurement index;Under the constraint of mutual information threshold, total radiant energy constraint and radar node constraint condition, with minimizing total KL distance as optimization target, construct multi-aircraft networking radar waveform dynamic design model for anti-interception and anti-sorting identification, and solve using greedy algorithm and Lagrange multiplier method;The application reduces the total KL distance between passive detection system intercepted signal and Gaussian white noise, improves radio frequency stealth performance.

Description

Technical Field

[0001] This invention belongs to the technical field of radar signal processing, specifically relating to a dynamic design method and system for multi-aircraft networked radar waveforms for anti-interception and anti-sorting identification. Background Technology

[0002] Currently, multi-vehicle networked radar collaborative detection has become an important means of enhancing regional awareness. Through the distributed configuration of multiple flight platforms, spatial diversity, complementary perspectives, and data fusion can be achieved, thereby significantly improving target detection and tracking performance. However, with the rapid development of electronic countermeasures technology, radar radiation signals are easily intercepted, sorted, and identified by passive detection systems, leading to the exposure of aircraft platforms, mission disruption, and even attacks, seriously threatening the system's operational effectiveness and battlefield survivability.

[0003] Anti-interception and anti-sorting waveform design is a core technological breakthrough in modern electronic warfare and radar system design. Its core advantage lies in the multi-dimensional collaborative optimization of the time-frequency-energy-modulation domain of radar transmitted signals, constructing dynamic and uncertain radiation characteristics in the signal dimension. While ensuring detection performance, the radiation characteristics are deeply "hidden" in environmental noise or non-threat signals, thereby significantly reducing the probability of being intercepted, sorted and identified by passive detection systems.

[0004] However, existing radar signal waveform designs suffer from problems such as failing to comprehensively consider anti-interception and anti-sorting performance, and failing to fully exploit and utilize target electromagnetic scattering characteristics. Therefore, research on dynamic waveform design methods for multi-aircraft networked radars aimed at anti-interception and anti-sorting is of great significance. Summary of the Invention

[0005] Purpose of the invention: The purpose of this invention is to provide a dynamic waveform design method and system for multi-vehicle networked radar to improve its anti-interception and anti-sorting performance.

[0006] Technical solution: The method described in this invention includes the following steps:

[0007] Construct a dynamic design scenario for multi-aircraft networked radar waveforms for anti-interception and anti-sorting identification purposes;

[0008] Construct a radar transmission waveform signal model and echo model for multi-aircraft networked radar;

[0009] The target detection performance is characterized by the total mutual information between the target echo and the target scattered signal received by a multi-vehicle networked radar.

[0010] The total KL distance between the intercepted signal of the passive detection system and the Gaussian white noise is used as the comprehensive performance evaluation index of the passive detection system in terms of interception and sorting identification.

[0011] Under the constraints of mutual information threshold, total radiated energy and radar node, a dynamic design model for multi-vehicle networked radar waveforms for anti-interception and anti-sorting identification is constructed with minimizing the total KL distance of the radio frequency stealth waveform of multi-vehicle networked radar as the optimization objective.

[0012] The dynamic design model is solved using a greedy algorithm and the Lagrange multiplier method. The solutions include: fixing the emission energy, optimizing node selection, and converting the dynamic design model into an integer programming problem, which is then solved using a greedy algorithm; and fixing the node selection, optimizing the emission energy, and converting the dynamic design model into a convex optimization problem, which is then solved using the Lagrange multiplier method.

[0013] Furthermore, the constructed scenario for dynamic design of multi-aircraft networked radar waveforms for anti-interception and anti-sorting identification is as follows:

[0014] Considering multi-aircraft networked radar systems, there are a total of The system consists of radars of different systems, each operating in monostatic mode and employing high-gain, low-sidelobe beams to detect different targets; assuming... The targets are widely distributed in the airspace. The number of targets has been obtained in advance through radar search mode, and the passive detection system is carried by each target.

[0015] Furthermore, methods for constructing multi-vehicle network radar transmitted waveform signal models and echo models include:

[0016] No. The transmitted waveform radiated by the radar transmitting antenna is The impulse response of the signal illuminating space is goal Above, after being scattered by the target, the first... The radar receiver received the first The echo signal of a target is represented as follows:

[0017] ;

[0018] in, Indicates the first The radar receiver received the first One target echo signal; Represents a time series; , and This represents the energy attenuation coefficient during signal propagation. This represents zero-mean Gaussian white noise; This represents the convolution operation.

[0019] Furthermore, the total mutual information is represented as:

[0020] ;

[0021] in, This represents the total mutual information between the target echo and the target scattered signal received by the multi-vehicle network radar; This indicates the radar signal bandwidth of multi-aircraft networking. The bandwidth is divided into multiple non-overlapping sub-bands; Indicates the first One goal, , Indicates the total number of targets; It is a node selection variable. Indicates the first Radar illumination target , Indicates the first Radar does not illuminate the target ; Indicates the first Radar targeting The duration of the transmitted signal; Indicates the number of sub-band divisions; Indicates the first The frequency of each frequency band; Indicates the first Radar transmitting antenna on the target Radiation gain in the direction; Indicates the first Radar receiving antenna gain; Indicates the first The wavelength of the radar's transmitted waveform; Indicates the first The spectrum of the radar's transmitted waveform; Indicate target The variance of the impulse response; Indicates the first Radar and Target The distance between them; Indicates the first One-sided power spectral density of Gaussian white noise in a radar receiver.

[0022] Furthermore, the total KL distance between each radar signal intercepted by the passive detection system and the Gaussian white noise is expressed as:

[0023] ;

[0024] in, This represents the total KL distance between the intercepted signal and the Gaussian white noise of the passive detection system. This indicates the radar signal bandwidth of multi-aircraft networking. The bandwidth is divided into multiple non-overlapping sub-bands; Indicates the first One goal, , Indicates the total number of targets; It is a node selection variable. Indicates the first Radar illumination target , Indicates the first Radar does not illuminate the target ; Indicates the first Radar targeting The duration of the transmitted signal; Indicates the number of sub-band divisions; Indicates the first The frequency of each frequency band; Indicates the first Radar transmitting antenna on the target Radiation gain in the direction; Indicates the first Radar receiving antenna gain; Indicates the first The wavelength of the radar's transmitted waveform; Indicates the first The spectrum of the radar's transmitted waveform; Indicates the first Radar and Target The distance between them; Indicates the first One-sided power spectral density of Gaussian white noise in a radar receiver.

[0025] Furthermore, the dynamic design model for multi-aircraft networked radar waveforms, oriented towards anti-interception and anti-sorting identification, is expressed as follows:

[0026] ;

[0027] in, This represents the total KL distance between the intercepted signal and the Gaussian white noise of the passive detection system. This represents the total mutual information between the target echo and the target scattered signal received by the multi-vehicle network radar; This refers to the pre-set mutual information threshold for multi-vehicle networked radar target detection based on mission requirements; It is a node selection variable. Indicates the first Radar illumination target , Indicates the first Radar does not illuminate the target ; Indicates simultaneous illumination of the target The upper limit of the number of radars; Indicates the first Radar illumination target The spectrum; Indicates the first Radar targeting The upper limit of the transmitted signal energy.

[0028] Furthermore, by fixing the launch energy and optimizing node selection, the dynamic design model is equivalent to an integer programming problem, including:

[0029] Assume that the energy distribution of the transmitted waveform spectrum of all radars for all targets is known. And it satisfies the energy constraint; at this point, the optimization model is equivalent to:

[0030] ;

[0031] in, It is a node selection variable. Indicates the first Radar illumination target , Indicates the first Radar does not illuminate the target ; This refers to the pre-set mutual information threshold for multi-vehicle networked radar target detection based on mission requirements; and These are intermediate variables, represented as follows:

[0032] ;

[0033] ;

[0034] in, and It is an intermediate variable; This indicates the radar signal bandwidth of multi-aircraft networking. The bandwidth is divided into multiple non-overlapping sub-bands; Indicates the first Radar targeting The duration of the transmitted signal; Indicates the first Radar transmitting antenna on the target Radiation gain in the direction; Indicates the first Radar receiving antenna gain; Indicates the first The wavelength of the radar's transmitted waveform; Indicates the first The spectrum of the radar's transmitted waveform; Indicates the first Radar and Target The distance between them; Indicates the first One-sided power spectral density of Gaussian white noise in a radar receiver. Indicate target The variance of the impulse response.

[0035] Furthermore, by fixing the node selection and optimizing the emission energy, the dynamic design model is equivalent to a convex optimization problem; including:

[0036] Known Fixed, valid sets are defined ;make , , The optimization problem is:

[0037] The optimization model is then equivalent to:

[0038] ;

[0039] in, Indicates radar Irradiation target Time and frequency points Energy; and As an intermediate variable; This indicates the radar signal bandwidth of multi-aircraft networking. The bandwidth is divided into multiple non-overlapping sub-bands; Indicates the first Radar targeting The duration of the transmitted signal; This refers to the pre-set mutual information threshold for multi-vehicle networked radar target detection based on mission requirements; Indicates the first Radar targeting The upper limit of the transmitted signal energy; This indicates a valid set of pairs.

[0040] The system corresponding to the method includes:

[0041] The scenario building unit is used to construct dynamic design scenarios for multi-aircraft networked radar waveforms for anti-interception and anti-sorting identification purposes.

[0042] The transmission and echo model building unit is used to build the transmission waveform signal model and echo model of a multi-vehicle network radar.

[0043] The index construction unit is used to characterize the target detection performance by using the total mutual information between the target echo and the target scattering signal received by the multi-aircraft networked radar; the total KL distance between the intercepted signal of the passive detection system and the Gaussian white noise is used as the comprehensive performance index of the passive detection system's interception and sorting identification.

[0044] The dynamic design model building unit is used to construct a dynamic design model for multi-vehicle networked radar waveforms with the optimization objective of minimizing the total KL distance of the radio frequency stealth waveform of the multi-vehicle networked radar under the constraints of mutual information threshold, total radiated energy and radar node, and anti-interception and anti-sorting identification.

[0045] The model solving unit is used to solve the dynamic design model using a greedy algorithm and the Lagrange multiplier method. It includes: fixing the emission energy, optimizing the node selection, and converting the dynamic design model into an integer programming problem, which is then solved using a greedy algorithm; and fixing the node selection, optimizing the emission energy, and converting the dynamic design model into a convex optimization problem, which is then solved using the Lagrange multiplier method.

[0046] The computer program product corresponding to the method includes a computer program / instruction that implements the method when executed by a processor.

[0047] Beneficial effects: Compared with the prior art, the significant technical effects of this invention are as follows: By jointly optimizing the node selection and frequency energy of multi-vehicle network radar, a transmission signal model and a reception signal model of multi-vehicle network radar are constructed. The mutual information between the target echo and the target scattering signal received by the radar receiver is used as a performance indicator for target detection of multi-vehicle network radar. The KL distance between the intercepted signal of the passive detection system and Gaussian white noise is used as a comprehensive performance indicator for the interception and sorting identification of the passive detection system. With minimizing the total KL distance as the optimization objective, a waveform dynamic design model for multi-vehicle network radar oriented towards anti-interception and anti-sorting identification is constructed to improve the radio frequency stealth performance of multi-vehicle network radar. Attached Figure Description

[0048] Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation

[0049] The structure and working process of the present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0050] Based on actual combat scenarios, this invention proposes a dynamic design method for the waveform of multi-vehicle networked radar for anti-interception and anti-sorting identification. Under the constraints of mutual information threshold, total radiated energy and radar node, the method minimizes the total KL distance of the radio frequency stealth waveform of multi-vehicle networked radar, thereby improving the anti-interception and anti-sorting identification performance of multi-vehicle networked radar.

[0051] The main task of the method described in this invention is to consider the cooperative detection of multiple targets by a multi-vehicle networked radar. Each radar operates in monostatic mode and uses high-gain, low-sidelobe beams for detection. Multiple targets are widely distributed in the airspace, and the number of targets is pre-determined through radar search modes. The passive detection system is carried by each target. First, a transmission signal model and a reception signal model for the multi-vehicle networked radar are constructed. Then, the mutual information between the target echo and the target scattered signal received by the radar receiver is used as a performance indicator for target detection by the multi-vehicle networked radar. Second, the Kullback-Leibler (KL) distance between the passive detection system's intercepted signal and Gaussian white noise is used as a comprehensive performance indicator for the passive detection system's interception and sorting / identification capabilities. Finally, with minimizing the total KL distance as the optimization objective, a dynamic waveform design model for the multi-vehicle networked radar, oriented towards anti-interception and anti-sorting / identification, is constructed and solved using a greedy algorithm and the Lagrange multiplier method, thereby improving the radio frequency stealth performance of the multi-vehicle networked radar.

[0052] like Figure 1 As shown, the method of the present invention includes the following steps:

[0053] 1. Construct a dynamic design scenario for multi-aircraft networked radar waveforms for anti-interception and anti-sorting identification purposes;

[0054] Considering multi-aircraft networked radar systems, there are a total of The system consists of radars of different systems, each operating in monostatic mode and employing high-gain, low-sidelobe beams to detect different targets. Assume... The targets are widely distributed in the airspace. The number of targets has been obtained in advance through radar search mode, and the passive detection system is carried by each target.

[0055] 2. Construct a multi-vehicle network radar transmit waveform signal model and echo model;

[0056] No. The transmitted waveform radiated by the radar transmitting antenna is The impulse response of the signal illuminating space is goal Above, after being scattered by the target, the first... The radar receiver received the first The echo signal of a target is represented as follows:

[0057] (1)

[0058] in, Indicates the first The radar receiver received the first One target echo signal; Represents a time series; , and This represents the energy attenuation coefficient during signal propagation. This represents zero-mean Gaussian white noise; This represents the convolution operation.

[0059] 3. Mutual information is used as a performance indicator for target detection in multi-aircraft networked radar systems;

[0060] The target detection performance is characterized by the total mutual information between the target echo and the target scattered signal received by a multi-vehicle networked radar, which can be expressed as:

[0061] (2)

[0062] in, This represents the total mutual information between the target echo and the target scattered signal received by the multi-vehicle network radar; This indicates the radar signal bandwidth of multi-aircraft networking. The bandwidth is divided into multiple non-overlapping sub-bands; Indicates the first One goal, , Indicates the total number of targets; It is a node selection variable. Indicates the first Radar illumination target , Indicates the first Radar does not illuminate the target ; Indicates the first Radar targeting The duration of the transmitted signal; Indicates the number of sub-band divisions; Indicates the first The frequency of each frequency band; Indicates the first Radar transmitting antenna on the target Radiation gain in the direction; Indicates the first Radar receiving antenna gain; Indicates the first The wavelength of the radar's transmitted waveform; Indicates the first The spectrum of the radar's transmitted waveform; Indicate target The variance of the impulse response; Indicates the first Radar and Target The distance between them; Indicates the first One-sided power spectral density of Gaussian white noise in a radar receiver.

[0063] 4. The total KL distance is used as the comprehensive performance indicator for the passive detection system in terms of interception, sorting, and identification.

[0064] In the On each sub-band, the first Signals intercepted by the passive detection system mounted on the target With Gaussian white noise The KL distance between them is expressed as:

[0065] (3)

[0066] in, Indicates the first Signal intercepted by the passive detection system With Gaussian white noise KL distance between them; Indicates the first Radar targeting The duration of the transmitted signal; This indicates the radar signal bandwidth of multi-aircraft networking. The bandwidth is divided into multiple non-overlapping sub-bands; Indicates the first Radar transmitting antenna on the target Radiation gain in the direction; Indicates the first Radar receiving antenna gain; Indicates the first The wavelength of the radar's transmitted waveform; Indicates the first The spectrum of the radar's transmitted waveform; Indicates the first Radar and Target The distance between them; Indicates the first One-sided power spectral density of Gaussian white noise in a radar receiver.

[0067] The KL distance between the intercepted signal and Gaussian white noise of the passive detection system is used to characterize the overall interception, sorting, and identification performance of the passive detection system. The total KL distance between each radar signal intercepted by the passive detection system and the Gaussian white noise is then expressed as:

[0068] (4)

[0069] in, This represents the total KL distance between the intercepted signal and the Gaussian white noise of the passive detection system. This indicates the radar signal bandwidth of multi-aircraft networking. The bandwidth is divided into multiple non-overlapping sub-bands; Indicates the first One goal, , Indicates the total number of targets; It is a node selection variable. Indicates the first Radar illumination target , Indicates the first Radar does not illuminate the target ; Indicates the first Radar targeting The duration of the transmitted signal; Indicates the number of sub-band divisions; Indicates the first The frequency of each frequency band; Indicates the first Radar transmitting antenna on the target Radiation gain in the direction; Indicates the first Radar receiving antenna gain; Indicates the first The wavelength of the radar's transmitted waveform; Indicates the first The spectrum of the radar's transmitted waveform is a discrete spectrum; Indicates the first Radar and Target The distance between them; Indicates the first One-sided power spectral density of Gaussian white noise in a radar receiver.

[0070] 5. Construct a dynamic design model for multi-aircraft networked radar waveforms for anti-interception and anti-sorting identification purposes;

[0071] Under the constraints of mutual information threshold, total radiated energy, and radar node, a dynamic design model for multi-vehicle networked radar waveforms, oriented towards anti-interception and anti-sorting identification, is constructed with the goal of minimizing the total KL distance of the multi-vehicle networked radar radio frequency stealth waveform, as shown in Equation (5):

[0072] (5)

[0073] in, This represents the total KL distance between the intercepted signal and the Gaussian white noise of the passive detection system. This represents the total mutual information between the target echo and the target scattered signal received by the multi-vehicle network radar; This refers to the pre-set mutual information threshold for multi-vehicle networked radar target detection based on mission requirements; It is a node selection variable. Indicates the first Radar illumination target , Indicates the first Radar does not illuminate the target ; Indicates simultaneous illumination of the target The upper limit of the number of radars; Indicates the first Radar illumination target The spectrum of is a continuous spectrum; Indicates the first Radar targeting The upper limit of the transmitted signal energy.

[0074] The first constraint in (5) indicates that the mutual information of the transmitted waveform of the multi-vehicle network radar needs to meet the threshold; the second constraint indicates the node selection constraint of the multi-vehicle network radar; and the third constraint indicates the total radiated energy constraint of the multi-vehicle network radar.

[0075] 6. Solve the optimization model (5) using a greedy algorithm and the Lagrange multiplier method;

[0076] The optimization model (5) contains various types of radio frequency resources and is a nonlinear, non-convex, multi-constraint optimization problem. The greedy algorithm and the Lagrange multiplier method are used to solve the optimization model (5).

[0077] 1) Fixed transmission energy, optimized node selection. Assume the energy distribution of the transmitted waveform spectrum of all radars for all targets is known. And it satisfies the energy constraint. The optimization model is then equivalent to:

[0078] (6)

[0079] in, It is a node selection variable. Indicates the first Radar illumination target , Indicates the first Radar does not illuminate the target ; This refers to the pre-set mutual information threshold for multi-vehicle networked radar target detection based on mission requirements; and These are intermediate variables, represented as follows:

[0080] (7)

[0081] (8)

[0082] in, and It is an intermediate variable; This indicates the radar signal bandwidth of multi-aircraft networking. The bandwidth is divided into multiple non-overlapping sub-bands; Indicates the first Radar targeting The duration of the transmitted signal; Indicates the first Radar transmitting antenna on the target Radiation gain in the direction; Indicates the first Radar receiving antenna gain; Indicates the first The wavelength of the radar's transmitted waveform; Indicates the first The spectrum of the radar's transmitted waveform is a discrete spectrum; Indicates the first Radar and Target The distance between them; Indicates the first One-sided power spectral density of Gaussian white noise in a radar receiver. Indicate target The variance of the impulse response.

[0083] Optimization problem (6) is a 0-1 integer programming problem, which can be solved using a greedy algorithm. The solution process is as follows:

[0084] (a) Define the benefit-cost ratio function as:

[0085] (9)

[0086] in, This represents the benefit-cost ratio function. and It's an intermediate variable. We want sufficient mutual information and a small KL distance, so we should prioritize choosing the variable that maximizes mutual information while minimizing the KL distance. Small radar nodes.

[0087] (b) Initialize radar parameters and calculate all feasible pairs. of , and ;

[0088] (c) according to Sort in ascending order to get feasible pairs:

[0089] (10)

[0090] in, It is feasible for the total number. Indicates the first One feasible pair, and .

[0091] (d) Let For the selected set, Initialize the current mutual information. , .

[0092] right :

[0093] i) Inspection Whether it can be included, including radar constraints. Not yet assigned to any target, target constraint Number of radars already allocated ;

[0094] ii) If If it can be added, then , ;

[0095] iii) If Then stop.

[0096] 2) Fixed node selection to optimize transmission energy. (Known) Fixed, valid sets are defined .make , , Then the optimized model is equivalent to:

[0097] (11)

[0098] in, Indicates radar Irradiation target Time and frequency points Energy; and As an intermediate variable; This indicates the radar signal bandwidth of multi-aircraft networking. The bandwidth is divided into multiple non-overlapping sub-bands; Indicates the first Radar targeting The duration of the transmitted signal; This refers to the pre-set mutual information threshold for multi-vehicle networked radar target detection based on mission requirements; Indicates the first Radar targeting The upper limit of the transmitted signal energy; This indicates a valid set of pairs.

[0099] The optimization problem (11) is a convex optimization problem, which can be solved using the Lagrange multiplier method.

[0100] (a) Construct the Lagrange function for:

[0101] (12)

[0102] in, Indicates radar Irradiation target Time and frequency points Energy; and As an intermediate variable; This indicates the radar signal bandwidth of multi-aircraft networking. The bandwidth is divided into multiple non-overlapping sub-bands; Indicates the first Radar targeting The duration of the transmitted signal; This refers to the pre-set mutual information threshold for multi-vehicle networked radar target detection based on mission requirements; Indicates the first Radar targeting The upper limit of the transmitted signal energy; and It represents the Lagrange multiplier.

[0103] (b) Fix the multipliers and solve for the original variables:

[0104] Lagrange function pairs Taking the derivative and setting it to zero, we get:

[0105] (13)

[0106] in, Indicates radar Irradiation target Time and frequency points Energy; and As an intermediate variable; This indicates the radar signal bandwidth of multi-aircraft networking. The bandwidth is divided into multiple non-overlapping sub-bands; Indicates the first Radar targeting The duration of the transmitted signal; and It represents the Lagrange multiplier.

[0107] because We can obtain:

[0108] (14)

[0109] in, Indicates radar Irradiation target Time and frequency points Energy; and As an intermediate variable; This indicates the radar signal bandwidth of multi-aircraft networking. The bandwidth is divided into multiple non-overlapping sub-bands; Indicates the first Radar targeting The duration of the transmitted signal; and It represents the Lagrange multiplier.

[0110] (c) Calculate the constraint violation amount;

[0111] The amount of mutual information constraint violation is:

[0112] (15)

[0113] in, This indicates the amount of mutual information constraint violation; Represents total mutual information; This refers to the mutual information threshold for multi-vehicle networked radar target detection, which is pre-set according to mission requirements.

[0114] Energy constraint violation is:

[0115] (16)

[0116] in, This indicates the amount of mutual information constraint violation; Indicates radar Irradiation target Time and frequency points Energy; Indicates the first Radar targeting The upper limit of the transmitted signal energy.

[0117] (d) Update the multipliers;

[0118] Update the Lagrange multipliers according to the following formula;

[0119] (17)

[0120] in, and It is the step size; and They are Lagrange multipliers; This indicates the amount of mutual information constraint violation; This indicates the amount of mutual information constraint violation.

[0121] (e) When both conditions are met , and If the threshold is indicated, the iteration stops; otherwise, steps (b) to (d) are repeated.

[0122] Working principle and process of this invention:

[0123] This invention considers the collaborative detection of multiple targets by a multi-vehicle networked radar. Each radar operates in monostatic mode and employs high-gain, low-sidelobe beams for detection. Multiple targets are widely distributed in the airspace, and the number of targets is pre-determined through radar search modes. Passive detection systems are carried by each target. First, a transmit signal model and a receive signal model for the multi-vehicle networked radar are constructed. Then, the mutual information between the target echo and the target scattered signal received by the radar receiver is used as a performance indicator for target detection. Second, the KL distance between the passive detection system's intercepted signal and Gaussian white noise is used as a comprehensive performance indicator for the passive detection system's interception and sorting / identification capabilities. Finally, with minimizing the total KL distance as the optimization objective, a dynamic waveform design model for the multi-vehicle networked radar, oriented towards anti-interception and anti-sorting / identification, is constructed. The constructed optimization model is a nonlinear, non-convex, multi-constraint optimization problem containing various types of radio frequency resources, solved using a greedy algorithm and the Lagrange multiplier method.

[0124] In another embodiment, a multi-aircraft network radar waveform dynamic design system for anti-interception and anti-sorting identification includes:

[0125] The scenario building unit is used to construct dynamic design scenarios for multi-aircraft networked radar waveforms for anti-interception and anti-sorting identification purposes.

[0126] The transmission and echo model building unit is used to build the transmission waveform signal model and echo model of a multi-vehicle network radar.

[0127] The index construction unit is used to characterize the target detection performance by using the total mutual information between the target echo and the target scattering signal received by the multi-aircraft networked radar; the total KL distance between the intercepted signal of the passive detection system and the Gaussian white noise is used as the comprehensive performance index of the passive detection system's interception and sorting identification.

[0128] The dynamic design model building unit is used to construct a dynamic design model for multi-vehicle networked radar waveforms with the optimization objective of minimizing the total KL distance of the radio frequency stealth waveform of the multi-vehicle networked radar under the constraints of mutual information threshold, total radiated energy and radar node, and anti-interception and anti-sorting identification.

[0129] The model solving unit is used to solve the dynamic design model using a greedy algorithm and the Lagrange multiplier method. It includes: fixing the emission energy, optimizing the node selection, and converting the dynamic design model into an integer programming problem, which is then solved using a greedy algorithm; and fixing the node selection, optimizing the emission energy, and converting the dynamic design model into a convex optimization problem, which is then solved using the Lagrange multiplier method.

[0130] In another embodiment, a computer program product includes a computer program / instructions that, when executed by a processor, implement the method described.

Claims

1. A dynamic waveform design method for multi-aircraft networked radar oriented towards anti-interception and anti-sorting identification, characterized in that, Includes the following steps: Construct a dynamic design scenario for multi-aircraft networked radar waveforms for anti-interception and anti-sorting identification purposes; Construct a radar transmission waveform signal model and echo model for multi-aircraft networked radar; The target detection performance is characterized by the total mutual information between the target echo and the target scattered signal received by a multi-vehicle networked radar. The total KL distance between the intercepted signal of the passive detection system and the Gaussian white noise is used as the comprehensive performance evaluation index of the passive detection system in terms of interception and sorting identification. Under the constraints of mutual information threshold, total radiated energy and radar node, a dynamic design model for multi-vehicle networked radar waveforms for anti-interception and anti-sorting identification is constructed with minimizing the total KL distance of the radio frequency stealth waveform of multi-vehicle networked radar as the optimization objective. The dynamic design model is solved using a greedy algorithm and the Lagrange multiplier method; including: fixing the launch energy, optimizing node selection, and converting the dynamic design model into an integer programming problem, which is then solved using a greedy algorithm; By fixing the node selection and optimizing the emission energy, the dynamic design model is equivalent to a convex optimization problem, which is solved using the Lagrange multiplier method.

2. The method according to claim 1, characterized in that, The constructed scenario for dynamic waveform design of multi-aircraft networked radar for anti-interception and anti-sorting identification is as follows: Considering multi-aircraft networked radar systems, there are a total of The system consists of radars of different systems, each operating in monostatic mode and employing high-gain, low-sidelobe beams to detect different targets; assuming... The targets are widely distributed in the airspace. The number of targets has been obtained in advance through radar search mode, and the passive detection system is carried by each target.

3. The method according to claim 1, characterized in that, Methods for constructing transmitted waveform signal models and echo models for multi-vehicle networked radars include: No. The transmitted waveform radiated by the radar transmitting antenna is The impulse response of the signal illuminating space is goal Above, after being scattered by the target, the first... The radar receiver received the first The echo signal of a target is represented as follows: ； in, Indicates the first The radar receiver received the first One target echo signal; Represents a time series; , and This represents the energy attenuation coefficient during signal propagation. This represents zero-mean Gaussian white noise; This represents the convolution operation.

4. The method according to claim 1, characterized in that, Total mutual information is represented as: ； in, This represents the total mutual information between the target echo and the target scattered signal received by the multi-vehicle network radar; This indicates the radar signal bandwidth of multi-aircraft networking. The bandwidth is divided into multiple non-overlapping sub-bands; Indicates the first One goal, , Indicates the total number of targets; It is a node selection variable. Indicates the first Radar illumination target , Indicates the first Radar does not illuminate the target ; Indicates the first Radar targeting The duration of the transmitted signal; Indicates the number of sub-band divisions; Indicates the first The frequency of each frequency band; Indicates the first Radar transmitting antenna on the target Radiation gain in the direction; Indicates the first Radar receiving antenna gain; Indicates the first The wavelength of the radar's transmitted waveform; Indicates the first The spectrum of the radar's transmitted waveform; Indicate target The variance of the impulse response; Indicates the first Radar and Target The distance between them; Indicates the first One-sided power spectral density of Gaussian white noise in a radar receiver.

5. The method according to claim 1, characterized in that, The total KL distance between each radar signal intercepted by the passive detection system and the Gaussian white noise is expressed as: ； in, This represents the total KL distance between the intercepted signal and the Gaussian white noise of the passive detection system. This indicates the radar signal bandwidth of multi-aircraft networking. The bandwidth is divided into multiple non-overlapping sub-bands; Indicates the first One goal, , Indicates the total number of targets; It is a node selection variable. Indicates the first Radar illumination target , Indicates the first Radar does not illuminate the target ; Indicates the first Radar targeting The duration of the transmitted signal; Indicates the number of sub-band divisions; Indicates the first The frequency of each frequency band; Indicates the first Radar transmitting antenna on the target Radiation gain in the direction; Indicates the first Radar receiving antenna gain; Indicates the first The wavelength of the radar's transmitted waveform; Indicates the first The spectrum of the radar's transmitted waveform; Indicates the first Radar and Target The distance between them; Indicates the first One-sided power spectral density of Gaussian white noise in a radar receiver.

6. The method according to claim 1, characterized in that, The dynamic design model for multi-aircraft networked radar waveforms, designed for anti-interception and anti-sorting identification, is expressed as follows: ； in, This represents the total KL distance between the intercepted signal and the Gaussian white noise of the passive detection system. This represents the total mutual information between the target echo and the target scattered signal received by the multi-vehicle network radar; This refers to the pre-set mutual information threshold for multi-vehicle networked radar target detection based on mission requirements; It is a node selection variable. Indicates the first Radar illumination target , Indicates the first Radar does not illuminate the target ; Indicates simultaneous illumination of the target The upper limit of the number of radars; Indicates the first Radar illumination target The spectrum; Indicates the first Radar targeting The upper limit of the transmitted signal energy.

7. The method according to claim 1, characterized in that, With a fixed launch energy and optimized node selection, the dynamic design model is equivalent to an integer programming problem, including: Assume that the energy distribution of the transmitted waveform spectrum of all radars for all targets is known. And it satisfies the energy constraint; at this point, the optimization model is equivalent to: ； in, It is a node selection variable. Indicates the first Radar illumination target , Indicates the first Radar does not illuminate the target ; This refers to the pre-set mutual information threshold for multi-vehicle networked radar target detection based on mission requirements; and These are intermediate variables, represented as follows: ； ； in, and It is an intermediate variable; This indicates the radar signal bandwidth of multi-aircraft networking. The bandwidth is divided into multiple non-overlapping sub-bands; Indicates the first Radar targeting The duration of the transmitted signal; Indicates the first Radar transmitting antenna on the target Radiation gain in the direction; Indicates the first Radar receiving antenna gain; Indicates the first The wavelength of the radar's transmitted waveform; Indicates the first The spectrum of the radar's transmitted waveform; Indicates the first Radar and Target The distance between them; Indicates the first One-sided power spectral density of Gaussian white noise in a radar receiver. Indicate target The variance of the impulse response.

8. The method according to claim 1, characterized in that, Fixed node selection optimizes emission energy, transforming the dynamic design model into a convex optimization problem; including: Known Fixed, valid sets are defined ;make , , The optimization problem is: The optimization model is then equivalent to: ； in, Indicates radar Irradiation target Time and frequency points Energy; and As an intermediate variable; This indicates the radar signal bandwidth of multi-aircraft networking. The bandwidth is divided into multiple non-overlapping sub-bands; Indicates the first Radar targeting The duration of the transmitted signal; This refers to the pre-set mutual information threshold for multi-vehicle networked radar target detection based on mission requirements; Indicates the first Radar targeting The upper limit of the transmitted signal energy; This indicates a valid set of pairs.

9. A dynamic waveform design system for multi-aircraft networked radar oriented towards anti-interception and anti-sorting identification, characterized in that, include: The scenario building unit is used to construct dynamic design scenarios for multi-aircraft networked radar waveforms for anti-interception and anti-sorting identification purposes. The transmission and echo model building unit is used to build the transmission waveform signal model and echo model of a multi-vehicle network radar. The index construction unit is used to characterize the target detection performance by using the total mutual information between the target echo and the target scattering signal received by the multi-aircraft networked radar; the total KL distance between the intercepted signal of the passive detection system and the Gaussian white noise is used as the comprehensive performance index of the passive detection system's interception and sorting identification. The dynamic design model building unit is used to construct a dynamic design model for multi-vehicle networked radar waveforms with the optimization objective of minimizing the total KL distance of the radio frequency stealth waveform of the multi-vehicle networked radar under the constraints of mutual information threshold, total radiated energy and radar node, and anti-interception and anti-sorting identification. The model solving unit is used to solve the dynamic design model using a greedy algorithm and the Lagrange multiplier method; it includes: fixing the launch energy, optimizing node selection, converting the dynamic design model into an integer programming problem, and solving it using a greedy algorithm; By fixing the node selection and optimizing the emission energy, the dynamic design model is equivalent to a convex optimization problem, which is solved using the Lagrange multiplier method.

10. A computer program product comprising a computer program / instructions, characterized in that, When the computer program / instructions are executed by the processor, they implement the method described in any one of claims 1-8.

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