A broadband multi-target multi-style jamming waveform optimization method and system

Abstract

The application provides a wideband multi-target multi-style jamming waveform optimization method and system, and belongs to the technical field of radar transmitting waveform design. The method is used for determining an optimized jamming waveform transmitted by a multi-target multi-style jamming device, the multi-target multi-style jamming device adopts a plurality of transmitting antennas, and the plurality of transmitting antennas are uniformly arranged. The method specifically comprises the following steps: S1, constructing an expected jamming signal in a frequency domain, wherein the expected jamming signal comprises a wideband noise jamming signal, a comb spectrum jamming signal and a deception jamming signal; S2, constructing a composite signal in the frequency domain based on a baseband signal, and further constructing a discrete composite signal in the frequency domain based on a discrete baseband signal; S3, constructing an optimization problem by using the expected jamming signal and the discrete composite signal in the frequency domain, and solving the optimization problem by using a Lawson algorithm to obtain the optimized jamming waveform.

Description

Technical Field

[0001] This invention belongs to the field of radar transmission waveform design technology, and in particular relates to a broadband multi-target multi-style interference waveform optimization method and system. Background Technology

[0002] Electronic warfare, as a crucial component of new-type and new-domain combat capabilities, has a significant impact on operational operations. Radar countermeasures, as an important part of electronic warfare, can effectively weaken or disrupt the operational effectiveness of the enemy's radar system, playing a vital role. Networked radar countermeasures are a key technology urgently needing breakthroughs in the field of radar countermeasures. To simultaneously counter threats from multiple radar targets in a networked radar system originating from different directions, with different systems and operating frequency bands, multi-target jamming technology has emerged. Multi-target jamming refers to using a single jammer to simultaneously interfere with multiple radars. Research has shown that using multi-target jamming methods to suppress multiple nodes of an enemy's networked radar system can effectively limit the system's target detection capabilities and increase the probability of successful operations. Therefore, multi-target jamming technology is an important development direction in the field of radar countermeasures.

[0003] Compared to traditional jamming equipment, broadband digital array jammers offer advantages such as high reconnaissance sensitivity, high jamming power, the ability to suppress multiple targets, and strong adaptability to complex electromagnetic environments, making them an important technological approach for achieving multi-target jamming. However, current typical implementations of broadband digital array multi-target jamming reveal several shortcomings, including the need for resource allocation and scheduling, a limited number of jamming nodes, short jamming duration, low antenna aperture utilization, and limited jamming patterns.

[0004] Currently, there are no publicly reported foreign reports on multi-target, multi-pattern jamming techniques. The techniques developed by domestic experts in this field suffer from limitations such as the inability to simultaneously achieve multi-target jamming, limited jamming patterns, and significant waveform fluctuations. The literature "Research on Robust Waveform Design Algorithm for Integrated RF Systems Based on MIMO Arrays [J]. Journal of Electronics and Information Technology. doi:10.11999 / JEIT220969." proposes using the Alternating Direction Method of Multipliers (ADMM) to solve the robust waveform design problem of integrated RF systems in narrowband far-field environments. However, the ADMM method proposed in the literature requires precise setting of the penalty factor.

[0005] Existing methods primarily target narrowband multi-functional radio frequency systems, with the main approach as follows: Using a Min-Max framework and the matching error between the synthesized and desired signals in the time domain as the objective function, a robust narrowband transmit waveform is designed under peak-to-average power ratio (PAPR) constraints. In implementation, the ADMM method is used to solve a non-convex optimization problem. However, existing methods are only applicable to narrowband multi-functional systems, and the resulting waveforms cannot cover a wide bandwidth, making it difficult to effectively interfere with networked radar systems. Furthermore, existing methods require precise setting of the penalty factor, increasing the time cost of waveform design. Moreover, existing methods cannot theoretically guarantee algorithm convergence. Summary of the Invention

[0006] This invention proposes a broadband multi-target, multi-pattern interference waveform optimization scheme. The technical problems this scheme aims to solve are: extending narrowband waveform design to broadband waveform design, enabling the designed waveform to cover a larger bandwidth, synthesizing interference signals with different center frequencies and patterns in different directions, and effectively suppressing networked radar systems; avoiding parameter selection, improving system waveform design time, and enhancing platform response speed; and improving the performance of existing algorithms while ensuring their convergence.

[0007] The first aspect of this invention proposes a broadband multi-target, multi-pattern jamming waveform optimization method. The method is used to determine an optimized jamming waveform emitted by a multi-target, multi-pattern jamming device, wherein the multi-target, multi-pattern jamming device employs multiple transmitting antennas arranged in a uniform array; the method specifically includes: Step S1: Construct the desired interference signal in the frequency domain, wherein the desired interference signal includes broadband noise interference signal, comb spectrum interference signal and deception interference signal; Step S2: Construct a synthesized signal in the frequency domain based on the baseband signal, and further construct a discrete synthesized signal in the frequency domain based on the discrete baseband signal; Step S3: Construct an optimization problem using the desired interference signal and the discrete synthesized signal in the frequency domain, and solve the optimization problem using the Lawson algorithm to obtain the optimized interference waveform.

[0008] According to the method of the first aspect of the present invention, in step S1: The broadband noise interference signal is ,0< t < t , t For signal duration, It is a white noise signal. The mean is 0 and the variance is 0. , Characterizing a Gaussian distribution, Represents convolution. h(t) The impulse response, the impulse response h(t) The frequency domain expression is , B 1 This indicates the interference frequency band of the broadband noise interference signal; The comb-spectrum interference signal is ,Include J The first single-carrier frequency signal, the first j The amplitude and frequency of each single carrier signal are respectively a j and f j ; The deception interference signal is , m For frequency modulation slope, B 2 This indicates the interference frequency band of the deceptive interference signal.

[0009] According to the method of the first aspect of the present invention, in step S1, the desired interference signal in the frequency domain is constructed. d f,k subscript f Represents the frequency domain. k Indicates the first k One desired interference signal, k = 1, 2, , K , K =3; specifically including: Discretize the broadband noise interference signal, the comb-spectrum interference signal, and the deception interference signal respectively to obtain the discretized broadband noise interference signal, comb-spectrum interference signal, and deception interference signal: in, l Indicates the first l Second sampling, l =0,1, , L -1, T s The sampling period is denoted as follows: The discretized broadband noise interference signal, comb spectrum interference signal, and spoofing interference signal are respectively denoted as... d 1 , d 2 and d 3 ; To each d 1 , d2 and d 3 conduct L The point discrete Fourier transform, then the th p Each frequency component is , f p = [1,e j2πp / L , , ,e j2π(L-1)p / L ] T The desired interference signal in the frequency domain is then... d f,k = [D k (-L / 2), ., D k (0), , D k (L / 2-1)] T .

[0010] According to the method of the first aspect of the present invention, in step S2, constructing the synthesized signal in the frequency domain based on the baseband signal specifically includes: The multi-target, multi-mode interference device includes N T A uniform array of transmitting antennas, with an element spacing of [missing information]. d T Then the first n The transmitted signals from each transmitting antenna are , x n ( t () represents the time-domain baseband signal. f c If it is the carrier frequency for transmitting signals, then i k The time-domain synthesized signal in the direction is , c Represents the speed of light. d T sin i k / c indicates the time delay between adjacent array elements; To each x n ( t )and Performing a Fourier transform, we obtain: in, B This refers to the baseband signal bandwidth. Further definition: but The Fourier transform is: This refers to the synthesized signal in the frequency domain.

[0011] According to the method of the first aspect of the present invention, in step S2, constructing the discrete synthesized signal in the frequency domain based on the discrete baseband signal specifically includes: Time-domain baseband signal x n ( t Discretize the data to obtain... , T s For the duration of the discretized symbol, the discrete baseband signal exist p The expression for each frequency point is: , x n = [ x n (0), x n (1), , x n ( L -1)] T ; definition ,but , X = [ x 1, x 2, , ],definition Then the discrete synthesized signal in the frequency domain is ; Further characterization yielded... , As an intermediate variable, x = vec( X ), where vec represents the vector straightening operation.

[0012] According to the method of the first aspect of the present invention, in step S3, constructing the optimization problem specifically includes: In the frequency domain Y k,p and The matching error between them is: in, B k = [ b k,-L / 2 , , b k,0 , , b k,L / 2-1 If ] is an intermediate variable, then the problem of minimizing the matching error is characterized as: in, and As a weighted variable, Represents a set of waveforms; Apply a peak-to-average power ratio (PAPR) constraint to the matching error minimization problem: in, e T For the emitted energy, 1 ≤ r ≤ L If the maximum peak-to-average ratio is given, then the problem of minimizing the matching error is further characterized as: Among them, i k In the presence of errors, i k ∈Θ k = [ i k,l , i k,u ], Θ k For the angle error range, i k,l and i k,u Let Θ be the upper and lower limits of the angle interval, respectively. k Divided into M k discrete points, Ω k = { i k,l , i k,2 , , },definition , , D = [ D 1, D 2, ,D K ] = [ , , , The optimization problem is: .

[0013] A second aspect of this invention provides a broadband multi-target, multi-pattern jamming waveform optimization system. The system is used to determine the optimized jamming waveform emitted by a multi-target, multi-pattern jamming device, wherein the multi-target, multi-pattern jamming device employs multiple transmitting antennas arranged in a uniform array; the system specifically includes: The first processing unit is configured to: construct a desired interference signal in the frequency domain, the desired interference signal including a broadband noise interference signal, a comb spectrum interference signal and a deception interference signal; The second processing unit is configured to: construct a synthesized signal in the frequency domain based on the baseband signal, and further construct a discrete synthesized signal in the frequency domain based on the discrete baseband signal; The third processing unit is configured to: construct an optimization problem using the desired interference signal and the discrete synthesized signal in the frequency domain, and solve the optimization problem using the Lawson algorithm to obtain the optimized interference waveform.

[0014] The system according to the second aspect of the present invention: The broadband noise interference signal is ,0< t < t , t For signal duration, It is a white noise signal. The mean is 0 and the variance is 0. , Characterizing a Gaussian distribution, Represents convolution. h(t) The impulse response, the impulse response h(t) The frequency domain expression is , B 1 This indicates the interference frequency band of the broadband noise interference signal; The comb-spectrum interference signal is ,Include J The first single-carrier frequency signal, the first j The amplitude and frequency of each single carrier signal are respectively a j and f j ; The deception interference signal is , m For frequency modulation slope,B 2 This indicates the interference frequency band of the deceptive interference signal.

[0015] According to a system of a second aspect of the present invention, the first processing unit is specifically configured to construct the desired interference signal in the frequency domain. d f,k subscript f Represents the frequency domain. k Indicates the first k One desired interference signal, k = 1, 2, , K , K =3; specifically including: Discretize the broadband noise interference signal, the comb-spectrum interference signal, and the deception interference signal respectively to obtain the discretized broadband noise interference signal, comb-spectrum interference signal, and deception interference signal: in, l Indicates the first l Second sampling, l =0,1, , L -1, T s The sampling period is denoted as follows: The discretized broadband noise interference signal, comb spectrum interference signal, and spoofing interference signal are respectively denoted as... d 1 , d 2 and d 3 ; To each d 1 , d 2 and d 3 conduct L The point discrete Fourier transform, then the th p Each frequency component is , f p = [1,e j2πp / L , , ,e j2π(L-1)p / L ] T The desired interference signal in the frequency domain is then... d f,k= [D k (-L / 2), ., D k (0), , D k (L / 2-1)] T .

[0016] According to a system of a second aspect of the present invention, the second processing unit is specifically configured to construct the synthesized signal in the frequency domain based on the baseband signal; specifically including: The multi-target, multi-mode interference device includes N T A uniform array of transmitting antennas, with an element spacing of [missing information]. d T Then the first n The transmitted signals from each transmitting antenna are , x n ( t () represents the time-domain baseband signal. f c If it is the carrier frequency for transmitting signals, then i k The time-domain synthesized signal in the direction is , c Represents the speed of light. d T sin i k / c indicates the time delay between adjacent array elements; To each x n ( t )and Performing a Fourier transform, we obtain: in, B This refers to the baseband signal bandwidth. Further definition: but The Fourier transform is: This refers to the synthesized signal in the frequency domain.

[0017] According to a system of a second aspect of the present invention, the second processing unit is specifically configured to construct a discrete synthesized signal in the frequency domain based on the discrete baseband signal; specifically including: Time-domain baseband signal x n ( t Discretize the data to obtain... , T s For the duration of the discretized symbol, the discrete baseband signal exist p The expression for each frequency point is: , x n = [ x n (0), x n (1), , x n ( L -1)] T ; definition ,but , X = [ x 1, x 2, , ],definition Then the discrete synthesized signal in the frequency domain is ; Further characterization yielded... , As an intermediate variable, x = vec( X ), where vec represents the vector straightening operation.

[0018] According to the system of the second aspect of the present invention, the third processing unit is specifically configured to construct the optimization problem; specifically including: In the frequency domain Y k,p and The matching error between them is: in, B k = [ b k,-L / 2 , , b k,0 , , b k,L / 2-1 If ] is an intermediate variable, then the problem of minimizing the matching error is characterized as: in, and As a weighted variable, Represents a set of waveforms; Apply a peak-to-average power ratio (PAPR) constraint to the matching error minimization problem: in, e T For the emitted energy, 1 ≤ r ≤ L If the maximum peak-to-average ratio is given, then the problem of minimizing the matching error is further characterized as: Among them, i k In the presence of errors, i k ∈Θ k = [ i k,l , i k,u ], Θ k For the angle error range, i k,l and i k,u Let Θ be the upper and lower limits of the angle interval, respectively. k Divided into M k discrete points, Ω k = { i k,l , i k,2 , , },definition , , D = [ D 1, D 2, , D K ] = [ , , , The optimization problem is: .

[0019] A third aspect of this invention discloses an electronic device. The electronic device includes a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it implements a broadband multi-target multi-pattern interference waveform optimization method according to the first aspect of this disclosure.

[0020] A fourth aspect of this invention discloses a computer-readable storage medium. The computer-readable storage medium stores a computer program, which, when executed by a processor, implements a broadband multi-target, multi-pattern interference waveform optimization method according to the first aspect of this disclosure.

[0021] As can be seen, based on the fundamental theory of array signals, the synthesized signal of electromagnetic waves emitted by a digital array at a certain location in space can be regarded as a linear combination of all transmitted waveforms, with the combination coefficients determined by factors such as the signal frequency, antenna array manifold, and interference azimuth. This invention focuses on the design of multi-target, multi-pattern interference waveforms based on a broadband digital array to fully utilize waveform diversity and spatial diversity capabilities. In waveform design, the potential errors in the prior angle information required for engineering implementation are considered, effectively reducing the synthesis error of the interference signal, avoiding the use of the ADMM method to solve non-convex optimization problems, and ensuring convergence. Attached Figure Description

[0022] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0023] Figure 1 This is a schematic diagram of a multi-target, multi-style interference device according to an embodiment of the present invention.

[0024] Figure 2 This is a flowchart of a broadband multi-target multi-style interference waveform optimization method according to an embodiment of the present invention.

[0025] Figure 3 This is a beam pattern according to an embodiment of the present invention.

[0026] Figure 4 This is a structural diagram of an electronic device according to an embodiment of the present invention. Detailed Implementation

[0027] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0028] PAPR: Peak-to-Average-Power-Ratio, which is the ratio of the square of the maximum value of the transmitted signal (voltage or current) to the average value of the square of the signal.

[0029] LFM: Linear Frequency Modulation, is a spread spectrum modulation technique that does not require pseudo-random coding sequences.

[0030] DFT: Discrete Fourier Transform, transforms a signal from the time domain to the frequency domain, and is a fundamental method for signal analysis.

[0031] WLS: Weighted Least Squares, which weights the original least squares problem to make it a new least squares problem.

[0032] ADMM: Alternating Direction Method of Multipliers, is a method for solving constrained optimization problems.

[0033] The first aspect of this invention proposes a broadband multi-target, multi-pattern interference waveform optimization method. The method is used to determine the waveform optimization of multi-target, multi-pattern interference devices (such as…). Figure 1 The method specifically includes (as shown) the optimized interference waveform emitted, wherein the multi-target multi-pattern jamming device employs multiple transmitting antennas in a uniform array; the method specifically includes (e.g.) Figure 2 (as shown) Step S1: Construct the desired interference signal in the frequency domain, wherein the desired interference signal includes broadband noise interference signal, comb spectrum interference signal and deception interference signal; Step S2: Construct a synthesized signal in the frequency domain based on the baseband signal, and further construct a discrete synthesized signal in the frequency domain based on the discrete baseband signal; Step S3: Construct an optimization problem using the desired interference signal and the discrete synthesized signal in the frequency domain, and solve the optimization problem using the Lawson algorithm to obtain the optimized interference waveform.

[0034] According to the method of the first aspect of the present invention, in step S1: The broadband noise interference signal is ,0< t < t , t For signal duration, It is a white noise signal. The mean is 0 and the variance is 0. , Characterizing a Gaussian distribution, Represents convolution. h(t) The impulse response, the impulse response h(t) The frequency domain expression is , B 1 This indicates the interference frequency band of the broadband noise interference signal; The comb-spectrum interference signal is ,Include J The first single-carrier frequency signal, the first j The amplitude and frequency of each single carrier signal are respectively a j and f j ; The deception interference signal is , m For frequency modulation slope, B 2 This indicates the interference frequency band of the deceptive interference signal.

[0035] According to the method of the first aspect of the present invention, in step S1, the desired interference signal in the frequency domain is constructed. d f,k subscript f Represents the frequency domain. k Indicates the first k One desired interference signal, k = 1, 2, , K , K =3; specifically including: Discretize the broadband noise interference signal, the comb-spectrum interference signal, and the deception interference signal respectively to obtain the discretized broadband noise interference signal, comb-spectrum interference signal, and deception interference signal: in, l Indicates the first l Second sampling, l=0,1, , L -1, T s The sampling period is denoted as follows: The discretized broadband noise interference signal, comb spectrum interference signal, and spoofing interference signal are respectively denoted as... d 1 , d 2 and d 3 ; To each d 1 , d 2 and d 3 conduct L The point discrete Fourier transform, then the th p Each frequency component is , f p = [1,e j2πp / L , , ,e j2π(L-1)p / L ] T The desired interference signal in the frequency domain is then... d f,k = [D k (-L / 2), ., D k (0), , D k (L / 2-1)] T .

[0036] According to the method of the first aspect of the present invention, in step S2, constructing the synthesized signal in the frequency domain based on the baseband signal specifically includes: The multi-target, multi-mode interference device includes N T A uniform array of transmitting antennas, with an element spacing of [missing information]. d T Then the first n The transmitted signals from each transmitting antenna are , x n ( t () represents the time-domain baseband signal. f c If it is the carrier frequency for transmitting signals, then i k The time-domain synthesized signal in the direction is , c Represents the speed of light. d T sin i k / c indicates the time delay between adjacent array elements; To each x n ( t )and Performing a Fourier transform, we obtain: in, B This refers to the baseband signal bandwidth. Further definition: but The Fourier transform is: This refers to the synthesized signal in the frequency domain.

[0037] According to the method of the first aspect of the present invention, in step S2, constructing the discrete synthesized signal in the frequency domain based on the discrete baseband signal specifically includes: Time-domain baseband signal x n ( t Discretize the data to obtain... , T s For the duration of the discretized symbol, the discrete baseband signal exist p The expression for each frequency point is: , x n = [ x n (0), x n (1), , x n ( L -1)] T ; definition ,but , X = [ x 1, x 2, , ],definition Then the discrete synthesized signal in the frequency domain is ; Further characterization yielded... , As an intermediate variable, x = vec( X ), where vec represents the vector straightening operation.

[0038] According to the method of the first aspect of the present invention, in step S3, constructing the optimization problem specifically includes: In the frequency domain Y k,p and The matching error between them is: in, B k = [ b k,-L / 2 , , b k,0 , , b k,L / 2-1 If ] is an intermediate variable, then the problem of minimizing the matching error is characterized as: in, and As a weighted variable, Represents a set of waveforms; Apply a peak-to-average power ratio (PAPR) constraint to the matching error minimization problem: in, e T For the emitted energy, 1 ≤ r ≤ L If the maximum peak-to-average ratio is given, then the problem of minimizing the matching error is further characterized as: Among them, i k In the presence of errors, i k ∈Θ k = [ i k,l , i k,u ], Θ k For the angle error range, i k,l and i k,uLet Θ be the upper and lower limits of the angle interval, respectively. k Divided into M k discrete points, Ω k = { i k,l , i k,2 , , },definition , , D = [ D 1, D 2, , D K ] = [ , , , The optimization problem is: .

[0039] Specific Example 1 Step 1: Construct the desired interference signal in the frequency domain d f,k The subscript f indicates the frequency domain. k Indicates the first k ( k = 1, 2, , K ( ) desired interference signals.

[0040] The specific sub-steps are as follows: 1) Determine the type and quantity of the interference signal (e.g., it is desired to synthesize three different types of interference signals). K = 3, broadband noise interference signal, comb spectrum interference signal, deception interference signal), the duration of each interference signal is the same, denoted as t .

[0041] White noise signal: That is, the mean is 0 and the variance is s 2 The Gaussian white noise signal. Then the broadband noise interference signal is... Where, 0 < t < t , Represents convolution. h ( t The frequency domain expression of ) is in, B 1 indicates the interference frequency band of the noise interference signal.

[0042] Comb-like interference signal: The comb-like interference signal is caused by J It is composed of superimposed single carrier frequency signals, and the first j The amplitude and frequency of each signal are denoted as follows: a j and f j .

[0043] Deceptive interference signals: This signal can be a linear frequency modulated (LFM) signal, where m For frequency modulation slope, m = B 2 / t , B 2 indicates the interference frequency band of the deception jamming signal.

[0044] 2) Discretize the desired signal in, l Indicates the first l Second sampling ( l = 0, 1, , L -1), T s The sampling period, i.e., the number of snapshots. L = t / T s The desired signals after analog-to-digital conversion are denoted as follows: d 1. d 2 and d 3.

[0045] 3) Perform processing on the desired signal L The point-discrete fourier transform (DFT) is the first... p Each frequency component can be represented as... in, f p = [1,ej2πp / L , , ,e j2π(L-1)p / L ] T The Fourier transform vector, p = - L / 2, , 0, , L / 2-1. The desired interference signal in the frequency domain can then be expressed as: d f,k = [ D k (- L / 2), , D k (0), , D k ( L / 2-1)] T Step 2: Constructing the synthesized signal in the frequency domain y k ( f ) ( k = 1, 2, , K The specific sub-steps are as follows: 1) Constructing a time-domain synthesized signal y k ( t Assuming a multi-target, multi-pattern interference system employs... N T There are 1 transmitting antenna, arranged in a uniform array, with an element spacing of . d T , will the n The transmitted signal of each antenna is denoted as in, x n ( t () is a time-domain baseband signal with a duration of t , f c As the carrier frequency for the transmitted signal, under the far-field assumption, i k The time-domain synthesized signal in the direction can be represented as Where c represents the speed of light. d T sin i k / c indicates the time delay between two adjacent array elements.

[0046] 2) For time-domain baseband signals x n ( t Perform a Fourier transform: in, B This refers to the baseband signal bandwidth.

[0047] 3) For the synthesized signal y k ( t Perform a Fourier transform: make Then the synthesized signal y k ( t The Fourier transform of ) can be expressed as: Step 3: Constructing a discrete synthesized signal in the frequency domain y f,k ( k = 1, 2, , K The specific sub-steps are as follows: 1) Discretize the time-domain baseband signal in, l Indicates the first l Each code element ( l = 0, 1, , L -1), T s The duration of the symbol.

[0048] 2) Discrete baseband signals in p The expression for each frequency point is: in, x n = [ x n (0), x n (1), , x n ( L -1)] T .

[0049] 3) Construct a more compact expression for the synthesized signal in the frequency domain. Let but in, X = [ x 1, x 2, , ] indicates the baseband signal transmitted by the array.

[0050] make The expression for the synthesized signal in the frequency domain is: 4) To Y k,p By deformation, we can obtain: in, As an intermediate variable, x = vec( X ), vec( This indicates that the vector will be straightened.

[0051] Step 4: Construct the optimization problem. The specific sub-steps are as follows: 1) In the frequency domain, the first k The matching error between the synthesized signal and the desired signal is in, B k = [ b k,-L / 2 , , b k,0 , , b k,L / 2-1 ] is an intermediate variable.

[0052] 2) In certain special cases, a lower fault tolerance rate needs to be considered. Therefore, the following matching error minimization problem should be considered: in, and As a weighted variable, Represents a set of waveforms.

[0053] 3) To make the designed waveform more suitable for engineering implementation, a peak-to-average ratio (PAPR) constraint is applied to the designed waveform. The specific expression for this constraint is as follows: in, e T For the emitted energy, 1 ≤ r ≤ L To allow the maximum peak-to-means ratio, and taking this constraint into account, the problem of minimizing the matching error can be characterized as: 4) Construct a robust waveform design problem. If prior information... i k ( k = 1, 2, , K There is an error, that is... i k ∈Θ k = [ i k,l , i k,u ], Θ k For the angle error range, i k,l and i k,u These are the upper and lower limits of the angle interval, respectively. For ease of calculation, Θ is... k Divided into M k discrete points, Ω k = { i k,l , i k,2 , , }.make , , D = [ D 1, D 2, , D K ] = [ , , , Therefore, within the angle interval, the problem of minimizing the matching error can be expressed as: The baseband signal is optimized by solving the above problem of minimizing the matching error.

[0054] Step 5: Use Lawson's algorithm to solve the problem of minimizing the matching error. This is a minimax problem, which can be solved using a series of weighted least squares (WLS) problems. The specific sub-steps are as follows: 1) Initialize, let q Indicates the number of iterations. q = 0, weighting coefficient β m,q = 1 / M ( m = 1, 2, , M Randomly generate baseband signals. x q In this iteration, the frequency domain error between the synthesized signal and the desired signal at each angle is... e m,q It can be represented as: 2) No. q In the +1 iteration, the update expression for the weight coefficients is as follows: in, d For a very small value (e.g., 10) -10 ) to avoid when β m,q When = 0, the weighting coefficient β m,q+1 The issue of not updating.

[0055] 3) Solve the following weighted least squares problem to update the baseband signal. x q+1 : make and Then the weighted least squares problem can be rewritten as This is a non-convex quadratic constraint quadratic optimization problem, which is solved using the upper bound function minimization method.

[0056] 4) Steps for minimizing the upper bound function: 4-1) Calculation T q+1 Maximum eigenvalue l max ( T q+1 ) 4-2) Order p = 0, calculateT q+1,neg = T q+1 - l max ( T q+1 ), we can get ( x - x q,p ) H T q+1,neg ( x - x q,p ) ≤ 0 Among them, subscript p This represents the first iteration of the upper bound function minimization method (inner loop). p The next iteration.

[0057] 4-3) Calculation x H T q+1 x upper bound function x H T q+1 x ≤ 2Re( x H T q+1,neg x q,p ) + 2 l max ( T q+1 ) e T - T q+1 x q,p If the constant term is ignored, then x H T q+1 x The problem of minimizing an upper bound function can be expressed as: in, u q+1,p = t q+1 - T q+1,neg x q,p It is an intermediate variable.

[0058] 4-4) Rewrite the aforementioned optimization problem as follows: when r = L When the optimal solution is: when r When = 1, the optimal solution is: Where, arg( ) represents the phase of the complex signal.

[0059] 4-5) If convergence or the maximum number of iterations is reached, then... x q,p+1 The value assigned x q+1 Convergence condition; otherwise, let p = p +1, repeat steps 4-2) to 4-4). The convergence condition is: || x q,p+1 - x q,p ||2≤ u I in, u I For example, the stopping iteration condition of the inner loop. u I = 10 -3 .

[0060] 5) If convergence or the maximum number of iterations is reached, stop iterating and obtain the result. x q+1 Otherwise, let q = q +1, repeat steps 2) to 4). The convergence condition is: in, u O For example, the stopping iteration condition of the inner loop. u O = 10 -3 .

[0061] 6) To x q+1 Reconstruction is performed to obtain the baseband signal transmitted by the system. X .

[0062] Specific Example 2 The number of broadband digital array transmit antennas used in the multi-target, multi-pattern jamming system is:N T = 16, the carrier frequency of the transmitted signal is f c = 2.9 GHz, bandwidth is B = 200 MHz, sampling frequency is f s = 400 MHz array elements are evenly spaced, and the spacing is d T =c / (2 f c + B c = 3×10 8 m / s. The code length of the signal transmitted by each antenna is... L = 256, the total emission energy is e T = 16. It is desired to generate 3 sets of interference signals, each with a duration of 0.6375 μs. i The energy generated near 40° is 1. e A Gaussian white noise signal with a bandwidth of 1 = 5 dB has an interference bandwidth of 1. B 1 = 40 MHz, the center frequency of the interference is f 1 = 2.98 GHz; in i The energy generated near 0° is 2. e The comb-spectrum interference signal with a density of 2 = 10 dB has seven interfering frequency points: 2.92, 2.93, 2.94, 2.95, 2.96, 2.97, and 2.98 GHz. i The energy generated near -50° is 3. e A deceptive interference signal (linear frequency modulation signal) of 3 = 10 dB, with an interference bandwidth of [missing information]. B 2 = 100 MHz, the interference center frequency is f 2 = 2.85 GHz, frequency modulation slope is m = 1.5686×10 14 Considering the angle estimation error, the error ranges are set as Θ1 = [38°, 42°], Θ2 = [-2°, 2°], and Θ3 = [-52°, -48°]. To facilitate waveform design, the angle error range of the desired signal is discretized in 0.4° intervals. N 1= N 2= N 3=11. Set the deception interference direction weighting coefficient to 3. w 3 = 5, the weighting coefficients for all other directions are 1, and the peak-to-average ratio is 5. r = 1. Set the maximum number of iterations for both the inner and outer loops to 100, and define the stopping condition for iteration. u I = u O = 10 -3 .

[0063] During baseband signal design, the maximum matching error between the synthesized signal and the desired signal continuously decreases and tends to converge. The synthesized beam pattern of the designed waveform is shown below. Figure 3 As shown, within the angular error range, a groove with an average depth of less than -35 dB is generated on the undesired spectrum, and the gain is highest on the desired spectrum.

[0064] A second aspect of this invention provides a broadband multi-target, multi-pattern jamming waveform optimization system. The system is used to determine the optimized jamming waveform emitted by a multi-target, multi-pattern jamming device, wherein the multi-target, multi-pattern jamming device employs multiple transmitting antennas arranged in a uniform array; the system specifically includes: The first processing unit is configured to: construct a desired interference signal in the frequency domain, the desired interference signal including a broadband noise interference signal, a comb spectrum interference signal and a deception interference signal; The second processing unit is configured to: construct a synthesized signal in the frequency domain based on the baseband signal, and further construct a discrete synthesized signal in the frequency domain based on the discrete baseband signal; The third processing unit is configured to: construct an optimization problem using the desired interference signal and the discrete synthesized signal in the frequency domain, and solve the optimization problem using the Lawson algorithm to obtain the optimized interference waveform.

[0065] The system according to the second aspect of the present invention: The broadband noise interference signal is ,0< t < t , t For signal duration, It is a white noise signal. The mean is 0 and the variance is 0. , Characterizing a Gaussian distribution, Represents convolution. h(t) The impulse response, the impulse response h(t) The frequency domain expression is , B 1 This indicates the interference frequency band of the broadband noise interference signal; The comb-spectrum interference signal is ,Include J The first single-carrier frequency signal, the first j The amplitude and frequency of each single carrier signal are respectively a j and fj ; The deception interference signal is , m For frequency modulation slope, B 2 This indicates the interference frequency band of the deceptive interference signal.

[0066] According to a system of a second aspect of the present invention, the first processing unit is specifically configured to construct the desired interference signal in the frequency domain. d f,k subscript f Represents the frequency domain. k Indicates the first k One desired interference signal, k = 1, 2, , K , K =3; specifically including: Discretize the broadband noise interference signal, the comb-spectrum interference signal, and the deception interference signal respectively to obtain the discretized broadband noise interference signal, comb-spectrum interference signal, and deception interference signal: in, l Indicates the first l Second sampling, l =0,1, , L -1, T s The sampling period is denoted as follows: The discretized broadband noise interference signal, comb spectrum interference signal, and spoofing interference signal are respectively denoted as... d 1 , d 2 and d 3 ; To each d 1 , d 2 and d 3 conduct L The point discrete Fourier transform, then the th p Each frequency component is , f p = [1,e j2πp / L , , ,e j2π(L-1)p / L] T The desired interference signal in the frequency domain is then... d f,k = [D k (-L / 2), ., D k (0), , D k (L / 2-1)] T .

[0067] According to a system of a second aspect of the present invention, the second processing unit is specifically configured to construct the synthesized signal in the frequency domain based on the baseband signal; specifically including: The multi-target, multi-mode interference device includes N T A uniform array of transmitting antennas, with an element spacing of [missing information]. d T Then the first n The transmitted signals from each transmitting antenna are , x n ( t () represents the time-domain baseband signal. f c If it is the carrier frequency for transmitting signals, then i k The time-domain synthesized signal in the direction is , c Represents the speed of light. d T sin i k / c indicates the time delay between adjacent array elements; To each x n ( t )and Performing a Fourier transform, we get: in, B This refers to the baseband signal bandwidth. Further definition: but The Fourier transform is: This refers to the synthesized signal in the frequency domain.

[0068] According to a system of a second aspect of the present invention, the second processing unit is specifically configured to construct a discrete synthesized signal in the frequency domain based on the discrete baseband signal; specifically including: Time-domain baseband signal x n ( t Discretize the data to obtain... , T s For the duration of the discretized symbol, the discrete baseband signal exist p The expression for each frequency point is: , x n = [ x n (0), x n (1), , x n ( L -1)] T ; definition ,but , X = [ x 1, x 2, , ],definition Then the discrete synthesized signal in the frequency domain is ; Further characterization yielded... , As an intermediate variable, x = vec( X ), where vec represents the vector straightening operation.

[0069] According to the system of the second aspect of the present invention, the third processing unit is specifically configured to construct the optimization problem; specifically including: In the frequency domain Y k,p and The matching error between them is: in, B k = [ b k,-L / 2 , , b k,0 , , bk,L / 2-1 If ] is an intermediate variable, then the problem of minimizing the matching error is characterized as: in, and As a weighted variable, Represents a set of waveforms; Apply a peak-to-average power ratio (PAPR) constraint to the matching error minimization problem: in, e T For the emitted energy, 1 ≤ r ≤ L If the maximum peak-to-average ratio is given, then the problem of minimizing the matching error is further characterized as: Among them, i k In the presence of errors, i k ∈Θ k = [ i k,l , i k,u ], Θ k For the angle error range, i k,l and i k,u Let Θ be the upper and lower limits of the angle interval, respectively. k Divided into M k discrete points, Ω k = { i k,l , i k,2 , , },definition , , D = [ D 1, D 2, , D K ] = [ , , , The optimization problem is: .

[0070] A third aspect of this invention discloses an electronic device. The electronic device includes a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it implements a broadband multi-target multi-pattern interference waveform optimization method according to the first aspect of this disclosure.

[0071] Figure 4 This is a structural diagram of an electronic device according to an embodiment of the present invention, such as... Figure 4 As shown, the electronic device includes a processor, memory, communication interface, display screen, and input device connected via a system bus. The processor provides computing and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The communication interface is used for wired or wireless communication with external terminals; wireless communication can be achieved through Wi-Fi, carrier networks, Near Field Communication (NFC), or other technologies. The display screen can be an LCD screen or an e-ink screen. The input device can be a touch layer covering the display screen, buttons, a trackball, or a touchpad mounted on the device's casing, or an external keyboard, touchpad, or mouse.

[0072] Those skilled in the art will understand that Figure 4 The structure shown is merely a structural diagram of the part related to the technical solution of this disclosure and does not constitute a limitation on the electronic device to which the solution of this application is applied. The specific electronic device may include more or fewer components than shown in the figure, or combine certain components, or have different component arrangements.

[0073] A fourth aspect of this invention discloses a computer-readable storage medium. The computer-readable storage medium stores a computer program, which, when executed by a processor, implements a broadband multi-target, multi-pattern interference waveform optimization method according to the first aspect of this disclosure.

[0074] As can be seen, based on the fundamental theory of array signals, the synthesized signal of electromagnetic waves emitted by a digital array at a certain location in space can be regarded as a linear combination of all transmitted waveforms, with the combination coefficients determined by factors such as the signal frequency, antenna array manifold, and interference azimuth. This invention focuses on the design of multi-target, multi-pattern interference waveforms based on a broadband digital array to fully utilize waveform diversity and spatial diversity capabilities. In waveform design, the potential errors in the prior angle information required for engineering implementation are considered, effectively reducing the synthesis error of the interference signal, avoiding the use of the ADMM method to solve non-convex optimization problems, and ensuring convergence.

[0075] The beneficial effects of this invention include: It overcomes the shortcomings of domestic multi-target jamming technology, fully utilizes the spatial and waveform degrees of freedom of broadband digital arrays, and can implement multi-target, multi-style jamming against networked radar systems, effectively limiting the performance of enemy detection systems. Even with errors in prior information such as angles, the waveform designed in this invention exhibits a very small synthesis error between the synthesized waveform and the desired waveform, improving system robustness and enhancing the platform's adaptability in complex environments, thus showing broad application prospects in modern warfare. This invention uses the Lawson method instead of the ADMM method to solve the Min-Max problem, effectively avoiding parameter selection and convergence issues, and improving system performance. The baseband waveform designed in this invention satisfies the peak-to-average power ratio constraint, avoiding the use of expensive linear methods and facilitating engineering implementation.

[0076] Please note that the technical features of the above embodiments can be combined arbitrarily. For the sake of brevity, not all possible combinations of the technical features in the above embodiments have been described. However, as long as the combination of these technical features does not contradict each other, it should be considered within the scope of this specification. The above embodiments only illustrate several implementation methods of this application, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the invention patent. It should be pointed out that for those skilled in the art, several modifications and improvements can be made without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A method for optimizing broadband multi-target, multi-pattern interference waveforms, characterized in that, The method is used to determine an optimized jamming waveform emitted by a multi-target, multi-pattern jamming device, wherein the multi-target, multi-pattern jamming device employs multiple transmitting antennas in a uniform array. The method specifically includes: Step S1: Construct the desired interference signal in the frequency domain, wherein the desired interference signal includes broadband noise interference signal, comb spectrum interference signal and deception interference signal; Step S2: Construct a synthesized signal in the frequency domain based on the baseband signal, and further construct a discrete synthesized signal in the frequency domain based on the discrete baseband signal; Step S3: Construct an optimization problem using the desired interference signal and the discrete synthesized signal in the frequency domain, and solve the optimization problem using the Lawson algorithm to obtain the optimized interference waveform; In step S1: The broadband noise interference signal is ,0< t < τ , τ For signal duration, It is a white noise signal. The mean is 0 and the variance is 0. , Characterizing a Gaussian distribution, Represents convolution. h(t) The impulse response, the impulse response h(t) The frequency domain expression is , B 1 This indicates the interference frequency band of the broadband noise interference signal; The comb-spectrum interference signal is ,Include J The first single-carrier frequency signal, the first j The amplitude and frequency of each single carrier signal are respectively a j and f j ; The deception interference signal is , μ For frequency modulation slope, B 2 This indicates the interference frequency band of the deceptive interference signal; In step S1, the desired interference signal in the frequency domain is constructed. d f,k subscript f Represents the frequency domain. k Indicates the first k One desired interference signal, k = 1, 2, , K , K =3; specifically including: Discretize the broadband noise interference signal, the comb spectrum interference signal, and the deception interference signal respectively to obtain the discretized broadband noise interference signal, comb spectrum interference signal, and deception interference signal: in, l Indicates the first l Second sampling, l =0,1, , L -1, T s The sampling period is denoted as follows: The discretized broadband noise interference signal, comb spectrum interference signal, and spoofing interference signal are respectively denoted as... d 1 , d 2 and d 3 ; To each d 1 , d 2 and d 3 conduct L Point discrete Fourier transform, then the th p Each frequency component is , f p = [1,e j2πp / L , , ,e j2π(L-1)p / L ] T The desired interference signal in the frequency domain is then... d f,k = [D k (-L / 2), ., D k (0), , D k (L / 2-1)] T .

2. The broadband multi-target multi-style interference waveform optimization method according to claim 1, characterized in that, In step S2, constructing the synthesized signal in the frequency domain based on the baseband signal specifically includes: The multi-target, multi-mode interference device includes N T A uniform array of transmitting antennas, with an element spacing of [missing information]. d T Then the first n The transmitted signals from each transmitting antenna are , x n ( t () represents the time-domain baseband signal. f c If it is the carrier frequency for transmitting signals, then θ k The time-domain synthesized signal in the direction is , c Represents the speed of light. d T sin θ k / c indicates the time delay between adjacent array elements; To each x n ( t )and Performing a Fourier transform, we get: in, B This refers to the baseband signal bandwidth. Further definition: but The Fourier transform is: This refers to the synthesized signal in the frequency domain.

3. The broadband multi-target multi-style interference waveform optimization method according to claim 2, characterized in that, In step S2, constructing the discrete synthesized signal in the frequency domain based on the discrete baseband signal specifically includes: Time-domain baseband signal x n ( t Discretize the data to obtain... , T s For the duration of the discretized symbol, the discrete baseband signal exist p The expression for each frequency point is: , x n = [ x n (0), x n (1), , x n ( L -1)] T ; definition ,but , X = [ x 1, x 2, , ],definition Then the discrete synthesized signal in the frequency domain is ; Further characterization yielded... , As an intermediate variable, x = vec( X ), where vec represents the vector straightening operation.

4. The broadband multi-target multi-style interference waveform optimization method according to claim 3, characterized in that, In step S3, constructing the optimization problem specifically includes: In the frequency domain Y k,p and The matching error between them is: in, B k = [ b k,-L / 2 , , b k,0 , , b k,L / 2-1 If ] is an intermediate variable, then the problem of minimizing the matching error is characterized as: in, and As a weighted variable, Represents a set of waveforms; Apply a peak-to-average power ratio (PAPR) constraint to the matching error minimization problem: in, e T For the emitted energy, 1 ≤ ρ ≤ L If the maximum peak-to-average ratio is given, then the problem of minimizing the matching error is further characterized as: Among them, θ k In the presence of errors, θ k ∈Θ k = [ θ k,l , θ k,u ], Θ k For the angle error range, θ k,l and θ k,u Let Θ be the upper and lower limits of the angle interval, respectively. k Divided into M k discrete points, Ω k = { θ k,l , θ k,2 , , },definition , , D = [ D 1, D 2, , D K ] = [ , , , The optimization problem is: 。 5. A broadband multi-target, multi-pattern interference waveform optimization system, characterized in that, The system is used to determine an optimized jamming waveform emitted by a multi-target, multi-pattern jamming device, which employs multiple transmitting antennas in a uniform array. The system specifically includes: The first processing unit is configured to: construct a desired interference signal in the frequency domain, the desired interference signal including a broadband noise interference signal, a comb spectrum interference signal and a deception interference signal; The second processing unit is configured to: construct a synthesized signal in the frequency domain based on the baseband signal, and further construct a discrete synthesized signal in the frequency domain based on the discrete baseband signal; The third processing unit is configured to: construct an optimization problem using the desired interference signal and the discrete synthesized signal in the frequency domain, and solve the optimization problem using the Lawson algorithm to obtain the optimized interference waveform; Wherein, the broadband noise interference signal is ,0< t < τ , τ For signal duration, It is a white noise signal. The mean is 0 and the variance is 0. , Characterizing a Gaussian distribution, Represents convolution. h(t) The impulse response, the impulse response h(t) The frequency domain expression is , B 1 This indicates the interference frequency band of the broadband noise interference signal; Wherein, the comb-like interference signal is ,Include J The first single-carrier frequency signal, the first j The amplitude and frequency of each single carrier signal are respectively a j and f j ; The deception interference signal is , μ For frequency modulation slope, B 2 This indicates the interference frequency band of the deceptive interference signal; Specifically, the first processing unit is configured to construct the desired interference signal in the frequency domain. d f,k subscript f Represents the frequency domain. k Indicates the first k One desired interference signal, k = 1, 2, , K , K =3; including: Discretize the broadband noise interference signal, the comb spectrum interference signal, and the deception interference signal respectively to obtain the discretized broadband noise interference signal, comb spectrum interference signal, and deception interference signal: in, l Indicates the first l Second sampling, l =0,1, , L -1, T s The sampling period is denoted as follows: The discretized broadband noise interference signal, comb spectrum interference signal, and spoofing interference signal are respectively denoted as... d 1 , d 2 and d 3 ; To each d 1 , d 2 and d 3 conduct L Point discrete Fourier transform, then the th p Each frequency component is , f p = [1,e j2πp / L , , ,e j2π(L-1)p / L ] T The desired interference signal in the frequency domain is then... d f,k = [D k (-L / 2), ., D k (0), , D k (L / 2-1)] T .

6. An electronic device, characterized in that, The electronic device includes a memory and a processor. The memory stores a computer program. When the processor executes the computer program, it implements the broadband multi-target multi-style interference waveform optimization method according to any one of claims 1-4.

7. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program, which, when executed by a processor, implements the broadband multi-target multi-style interference waveform optimization method according to any one of claims 1-4.

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