A dense false target jamming waveform optimization method

Abstract

The application discloses a dense false target jamming waveform optimization method, comprising the following steps: constructing a dense false target jamming model with adjustable interval, amplitude and phase; constructing a mixed integer model with multiple parameters and multiple constraints; and performing jamming waveform optimization based on grid adaptive direct search (MADS). The application takes the average value of the CFAR detection threshold and the peak power as a target function and a constraint condition, and is aimed at the mixed integer model with multiple parameters and multiple constraints. The application proposes a dense false target jamming waveform optimization method based on the grid adaptive direct search (MADS), and the waveform optimization method has higher optimization efficiency and better jamming and deception effects compared with the same type of jamming.

Description

TECHNICAL FIELD

[0001] The present application relates to waveform optimization, in particular to a dense false target jamming waveform optimization method. BACKGROUND

[0002] Traditional noise suppression jamming technology is difficult to achieve good jamming effect when facing advanced radars and countermeasure equipment used in modern battlefield. The modern dense false target jamming has the characteristics of good correlation with radar transmitted signals and high utilization efficiency. Its lower transmission power requirement helps to miniaturize the jamming equipment, thereby generating a large number of jamming signals. Under appropriate parameter settings, the dense false target jamming has both deception and suppression properties, and is widely used in radar countermeasure field. The dense false target jamming generates a large number of false echoes similar to radar echo signals to affect the detection of real targets by radar. However, the distance between the false targets formed by the typical dense false target jamming is equal, and the arrangement is regular, which is easy to be identified. Under the existing radar jamming identification and various anti-jamming measures technology, it is difficult to form effective deception.

[0003] The optimization of radar jamming waveform is an important part of radar jamming system and an important way to improve the effect of radar jamming, which has important theoretical significance and practical value. The current research mainly focuses on overcoming the problems of fixed parameters, lack of flexibility, single suppression or deception jamming characteristics of the jamming waveform. The detection cost can be used as an evaluation index to evaluate the pros and cons of the jamming waveform. However, the detection cost is obviously affected by the distance between the false targets, and it is difficult to generate high-density equidistant false target signals under the premise of ensuring the transmission power and correlation.

[0004] Modern radars mostly use CFAR processing. The CFAR radar can adjust the radar detection threshold according to the size of the environmental clutter caused by clouds, rain, multipath and other disturbances, and various disturbances, to ensure the constant false alarm probability. The anti-jamming effect of CFAR radar under multi-false target jamming has a guiding value for the optimization of jamming waveform. The current research proposes a guided design method for dense false target jamming from the perspective of parameter optimization, such as the design method of dense false target jamming interval under blind CFAR parameters, radar CFAR detection threshold and different interval multi-false target jamming effect under multi-false target jamming. However, there is a lack of further improvement of jamming effect from the perspective of optimizing jamming waveform. The peak-to-average ratio of the dense false target jamming generated by the traditional multi-parameter jamming waveform optimization method is too large. At the same time, the convergence speed of the multi-parameter waveform optimization method is slow, the quality of the obtained optimized parameters is low, and the suppression jamming effect is not ideal when applied. SUMMARY

[0005] The present application aims to overcome the shortcomings of the prior art and provide a dense false target jamming waveform optimization method. The purpose of the present application is achieved by the following technical scheme: a dense false target jamming waveform optimization method, comprising:

[0006] S1: According to the interval, the sparse area-dense area-sparse area is divided into three areas, and the dense false target interference form with adjustable interval, amplitude and phase is provided.

[0007] S2: According to the form of dense false target, a multi-parameter and multi-constrained mixed integer model is constructed.

[0008] S3: Taking the average of CFAR detection threshold as the evaluation index, a jamming waveform optimization algorithm based on grid adaptive direct search (MADS) is proposed for the multi-parameter and multi-constrained mixed integer model.

[0009] S4: The jamming waveform optimization algorithm is solved by the grid adaptive direct search (MADS) algorithm, and the optimal solution of the jamming waveform parameter is obtained to guide the design of the jamming waveform.

[0010] Preferably, the specific form of the dense false target jamming signal is a linear frequency modulation signal.

[0011] Preferably, the dense false target jamming signal is processed by pulse compression.

[0012] Preferably, the step S1 comprises:

[0013] S11: A typical dense false target jamming signal j(t) is constructed:

[0014]

[0015] Where k is the frequency modulation slope of the linear frequency modulation signal, T is the pulse width of the linear frequency modulation signal, the jammer generates dense false target jamming with equal interval Δt, and the received signal has N segments.

[0016] S12: An interval, initial phase and amplitude optimization model of dense false target jamming is constructed.

[0017] Preferably, the step S12 comprises:

[0018] S121: An interval optimization dense false target (IO-DFT) model is constructed.

[0019] S122: An interval and initial phase joint optimization dense false target (IPO-DFT) model is constructed.

[0020] S123: An Interval-Phase-Amplitude Optimization Dense False Target (IPAO-DFT) model is constructed.

[0021] Preferably, the Interval Optimization Dense False Target (IO-DFT) model comprises:

[0022]

[0023] where i, j are the number of retransmissions, I+J=n, and n is the number of superimposed jamming signals. is the jamming signal in the dense area, Δt i is the jamming interval in the dense area; is the jamming signal in the sparse area, Δt j is the jamming interval in the sparse area.

[0024] Preferably, the Interval-Phase Optimization Dense False Target (IPO-DFT) model comprises:

[0025]

[0026] where is the initial phase of the jamming signal in the dense area, is the initial phase of the jamming signal in the sparse area.

[0027] Preferably, the Interval-Phase-Amplitude Optimization Dense False Target (IPAO-DFT) model comprises:

[0028]

[0029] where a is the amplitude of the jamming signal in the dense area, a j is the amplitude of the jamming signal in the sparse area.

[0030] Preferably, the output response r1(t) of the Interval Optimization Dense False Target (IO-DFT) after the matched filter is:

[0031]

[0032] where a is the jammer amplitude, T is the jammer pulse width, k is the chirp rate of the LFM signal, i, j are the number of retransmissions, I + J = n, i.e., there are n signals superimposed, Δt i is the jammer interval in dense region, Δt j is the jammer interval in sparse region.

[0033] Preferably, the interval and initial phase jointly optimize the dense false target jamming (Interval-Phase Optimization Dense False Target, IPO-DFT) and the output response r2(t) of the matched filter is:

[0034]

[0035] where a is the jammer amplitude, T is the jammer pulse width, k is the chirp rate of the LFM signal, i, j are the number of retransmissions, I + J = n, i.e., there are n signals superimposed, Δt i is the jammer interval in dense region, Δt j is the jammer interval in sparse region, is the initial phase of jammer in dense region, is the initial phase of jammer in sparse region.

[0036] Preferably, the interval, initial phase and amplitude jointly optimize the dense false target jamming (Interval-Phase-Amplitude Optimization Dense False Target, IPAO-DFT) and the output response r3(t) of the matched filter is:

[0037]

[0038] where a i is the jammer amplitude in dense region, a j is the jammer amplitude in sparse region, T is the jammer pulse width, k is the chirp rate of the LFM signal, i, j are the number of retransmissions, I + J = n, i.e., there are n signals superimposed, Δt i is the jammer interval in dense region, Δt j is the jammer interval in sparse region, is the initial phase of jammer in dense region, is the initial phase of jammer in sparse region.

[0039] Preferably, the dense false target jamming is processed by the cell average constant false alarm rate (CACFAR) and the detection threshold of the cell average constant false alarm rate is:

[0040]

[0041] where is the multiplicative factor of CACFAR detector, is the desired constant false alarm rate, M is the number of reference cells, and l represents the signal power in the distance cell.

[0042] Preferably, the power of the dense false target jamming after pulse compression is |r1(t)| 2 , |r2(t)| 2 , and |r3(t)| 2 is the power time function of the output response r(t) at time t, and its value is the square of the response modulus. The detection threshold in the range (l a , l b ) where the target is located is used to establish the target function. The amplitude of the jamming signal is set to 1.

[0043] Preferably, the IO-DFT jamming target function and the constraint condition are:

[0044]

[0045]

[0046] Δ1<|Δt i -Δt i-1 |<Δ2,i=1,2,…,I

[0047] Δ2<|Δt j -Δt j-1 |<Δ3,j=1,2,…,J

[0048] In the formula, Δ1 and Δ2 are the minimum and maximum intervals of the dense area respectively; Δ2 and Δ3 are the minimum and maximum intervals of the sparse area respectively. V1 is the average constant false alarm detection threshold of the cell, P fa is the constant false alarm rate, M is the number of reference cells, Δt i is the jamming interval of the dense area, Δt j is the jamming interval of the sparse area, is the jamming signal of the dense area, is the jamming signal of the sparse area, i and j are the number of times of retransmission, I+J=n, that is, there are n signal superpositions;

[0049] Preferably, the IPO-DFT jamming target function and the constraint condition are:

[0050]

[0051]

[0052] Δ1<|Δt i -Δt i-1 |<Δ2,i=1,2,…,I

[0053] Δ2 < |Δt j -Δt j-1 | < Δ3, j = 1, 2, …, J

[0054]

[0055] where Δ1, Δ2 are the minimum and maximum intervals of dense region respectively, Δ2, Δ3 are the minimum and maximum intervals of sparse region respectively, V2 is the average constant false alarm detection threshold of unit, P fa is the constant false alarm rate, M is the number of reference units, Δt i is the interference interval of dense region, Δt j is the interference interval of sparse region, is the initial phase of interference of dense region, is the initial phase of interference of sparse region, is the interference signal of dense region, is the interference signal of sparse region, i, j are the number of times of retransmission, I + J = n, that is, there are n signals superimposed;

[0056] Preferably, the IPAO-DFT interference target function and the constraint condition are:

[0057]

[0058]

[0059] Δ1 < |Δt i -Δt i-1 | < Δ2, i = 1, 2, …, I

[0060] s.t. Δ2 < |Δt j -Δt j-1 | < Δ3, j = 1, 2, …, J

[0061]

[0062] 0 < a ≤ 1

[0063] where Δ1, Δ2 are the minimum and maximum intervals of dense region respectively, Δ2, Δ3 are the minimum and maximum intervals of sparse region respectively, V3 is the average constant false alarm detection threshold of unit, a i is the interference amplitude of dense region, a j is the interference amplitude of sparse region, P fa is the constant false alarm rate, M is the number of reference units, Δt i is the interference interval of dense region, Δt j is the interference interval of sparse region, is the initial phase of interference of dense region, For sparse area interference initial phase, For dense area interference signal, For sparse area interference signal, i, j is the number of times of forwarding, I+J=n, that is, there are n signals superimposed;

[0064] Preferably, when optimizing the IO-DFT interference using the grid adaptive direct search algorithm (MADS), the IO-DFT interference objective function is redefined as:

[0065]

[0066] That is, search for the interval parameter Δ t to make the objective function value f Ω (Δt) minimum, at which time there is the maximum cell constant false alarm detection threshold value V1; wherein the interval Ω is the feasible region of Δt n , ψ Ω is the feasible region indicator function, if Let f Ω =∞, if Δt∈Ω d ,

[0067] Preferably, when optimizing the IPO-DFT interference using the grid adaptive direct search algorithm (MADS), the IPO-DFT interference objective function is redefined as:

[0068]

[0069] That is, search for the interval parameter Δ t , to make the objective function value minimum, at which time there is the maximum cell constant false alarm detection threshold value V2. Wherein Ω is the feasible region, Ω c is the feasible region of .

[0070] Preferably, when optimizing the IPO-DFT interference using the grid adaptive direct search algorithm (MADS), the IPO-DFT interference objective function is redefined as:

[0071]

[0072] That is, search for the interval parameter Δ t , x c to make the objective function value f Ω (x c , Δt) minimum, at which time there is the maximum cell constant false alarm detection threshold value V3; wherein Ω is the feasible region, continuous variable x c represents the initial phase with a set of amplitudes A, with n c denoting the dimension of x c , Ω c being the feasible region of x c .

[0073] Preferably, the initial iteration point method of the mesh adaptive direct search algorithm (MADS) is:

[0074] An initial iteration point x = (x c , x d ) is established, x c denoting the continuous variable, x d denoting the discrete variable, in the neighborhood of which there is:

[0075] f Ω (x) ≤ f Ω (v), v being in the feasible region:

[0076] where B ε (x c ) means: for any N(x) = {y e Ω: y c = x c , ||y d - x d ||1 < 1}, y d taking discrete values.

[0077] Preferably, the optimization process of the mesh adaptive direct search algorithm (MADS) is mainly divided into search steps and detection steps, the main goal of the search steps and the detection steps being to generate improved mesh points. The search steps select a finite number of trial points on the mesh, calculate the f Ω of these mesh points, and establish improved mesh points by comparing with the function value f Ω (x) of the initial point.

[0078] Preferably, the mesh adaptive direct search algorithm (MADS) adopts interval optimization and joint optimization methods for parameter iteration.

[0079] Preferably, if the mesh adaptive direct search algorithm (MADS) generates an improved mesh point x k+1 in the feasible region Ω in the kth search step or detection step, satisfying f Ω (x k+1 ) < f Ω (x k ), the iteration is successful, and the mesh parameter can remain unchanged or increase in the next iteration.

[0080] Preferably, the stopping condition for the Grid Adaptive Direct Search (MADS) algorithm to optimize the spacing, initial phase, and amplitude parameters of dense false target interference is: when the objective function value |f| in the (k+1)th iteration... Ω (x)-f Ω (x k+1 )|<1×10 -13 When the iteration stops, return the interval Δt and the initial phase. and the value of amplitude a This is the optimal solution for optimizing the spacing, initial phase, and amplitude of dense false target interference. This represents the optimal average detection threshold.

[0081] The beneficial effects of this invention are as follows: Compared with typical dense false target interference, this invention has a dense false target interference form with adjustable interval, amplitude and phase, which has both suppression and deception effects, the highest detection threshold and the best interference effect; Compared with genetic algorithm (GA), grid adaptive direct search algorithm (MADS) is a solution method for solving multi-constraint, nonlinear complex models. The MADS algorithm has a faster convergence speed and is better than the GA algorithm in terms of optimization results. Attached Figure Description

[0082] Figure 1 This is a typical dense false target interference waveform diagram described in the specific implementation method.

[0083] Figure 2 The image shows the result of pulse compression processing of a typical dense false target interference described in the specific implementation method.

[0084] Figure 3 The image shows the result of CFAR processing of a typical dense false target interference described in the specific implementation method.

[0085] Figure 4 This is a flowchart of the Grid Adaptive Direct Search (MADS) algorithm described in a specific implementation.

[0086] Figure 5 The waveform diagram is shown for the Interval Optimization Dense False Target (IO-DFT) interference described in the specific implementation.

[0087] Figure 6 The image shows the result of pulse compression processing of the Interval Optimization Dense False Target (IO-DFT) error described in the specific implementation.

[0088] Figure 7Waveform of interval optimization dense false target (IO-DFT) interference as described in the detailed description.

[0089] Figure 8 Waveform of interval-phase optimization dense false target (IPO-DFT) interference as described in the detailed description.

[0090] Figure 9 Processed result waveform of interval-phase optimization dense false target (IPO-DFT) interference after pulse compression as described in the detailed description.

[0091] Figure 10 Processed result waveform of interval-phase optimization dense false target (IPO-DFT) interference after CFAR as described in the detailed description.

[0092] Figure 11 Waveform of interval-phase-amplitude optimization dense false target (IPAO-DFT) interference as described in the detailed description.

[0093] Figure 12 Processed result waveform of interval-phase-amplitude optimization dense false target (IPAO-DFT) interference after pulse compression as described in the detailed description.

[0094] Figure 13 Processed result waveform of interval-phase-amplitude optimization dense false target (IPAO-DFT) interference after CFAR as described in the detailed description. DETAILED DESCRIPTION

[0095] The technical solutions of the present application will be described in further detail below with reference to the drawings, but the protection scope of the present application is not limited to the following description.

[0096] A dense false target jamming waveform optimization method, comprising: S1: constructing a typical dense false target jamming signal, and constructing a dense false target jamming signal model with adjustable interval, amplitude and phase.

[0097] S2: constructing a dense false target jamming function suitable for a grid adaptive direct search algorithm (MADS) from the dense false target jamming signal model after considering pulse compression and CFAR processing.

[0098] S3: using the grid adaptive direct search algorithm (MADS) to establish a grid for the dense false target jamming function parameters, and adaptively optimizing the optimal solution by searching and detecting, and comparing with the performance of the typical dense false target jamming signal and the dense false target jamming signal with adjustable interval, amplitude and phase optimized by using the genetic algorithm (GA).

[0099] In a more specific implementation, the typical false target jamming signal model in step S1 is constructed as follows:

[0100] The linear frequency modulation signal has a large time-bandwidth product, and the radar system after pulse compression processing has the advantages of long action distance and high range resolution. Let the expression of the received signal of the jammer be:

[0101]

[0102] In the formula, k is the frequency modulation slope of the linear frequency modulation signal, and T is the pulse width of the linear frequency modulation signal.

[0103] The jammer needs to generate dense false target jamming with equal intervals Δt, so the received signal is divided into N segments. The nth dense false target jamming j n (t) is expressed as:

[0104]

[0105] In the formula, a is the amplitude of the jamming signal, and n=0, 1, 2, …, N-1.

[0106] The expression of the typical dense false target jamming with time interval Δt is:

[0107]

[0108] In a specific implementation, the interval superposition method is used to generate dense false target jamming, the number of generated false targets is set to 60, the jamming amplitude is 1, the interval Δt=0.33 μs, and the initial phase is 0. The waveform is as shown in FIG. 2. Figure 1 ​

[0109] According to the matched filter theory, the echo signal enters the radar receiver and is pulse compressed in the matched filter. The output response of the dense false target after pulse compression is:

[0110]

[0111] where the pulse response function is

[0112] In a more specific implementation, the interval, amplitude and phase adjustable dense false target jamming signal model in step S1 is constructed as follows:

[0113] The expression of interval optimization dense false target jamming (IO-DFT) is:

[0114]

[0115] where i, j are the number of times of forwarding, I+J=n, that is, n jamming signals are superimposed. is the dense area jamming signal, Δt i is the dense area jamming interval; is the sparse area jamming signal, Δt j is the sparse area jamming interval.

[0116] The interval of dense false target jamming is optimized, the number of generated false targets is set to 60, the jamming amplitude is 1, the interval Δt=0.33 μs, and the initial phase is 0. This interval Δt is no longer a uniform value, but different values. In a specific implementation, the intervals Δ1, Δ2, Δ3 are set to 0.067 μs, 0.33 μs, and 0.67 μs, respectively. The jamming area is set to sparse-dense-sparse. The purpose of this setting is to raise the detection threshold and generate false targets exceeding the threshold.

[0117] The expression of interval-phase optimization dense false target jamming (IPO-DFT) is:

[0118]

[0119] where is the initial phase of the dense area jamming, is the initial phase of the sparse area jamming.

[0120] To further improve the jamming effect, the time interval and initial phase of the dense false target jamming are jointly optimized. The number of generated false targets is set to 60, the jamming amplitude is 1, the intervals Δ1, Δ2, and Δ3 are set to 0.067 μs, 0.33 μs, and 0.67 μs, respectively, and the initial phase range is 0-2π.

[0121] The expression of the interval-phase-amplitude optimization dense false target jamming (IPAO-DFT) is:

[0122]

[0123] where a is the dense area jamming amplitude, a j is the sparse area jamming amplitude.

[0124] The number of generated false targets is set to 60, the initial jamming amplitude is 1, the intervals Δ1, Δ2, and Δ3 are set to 0.067 μs, 0.33 μs, and 0.67 μs, respectively, and the initial phase range is 0-2π.

[0125] In a more specific implementation, the output response expression of the dense false target jamming after the pulse compression processing in step S2 is:

[0126] The output response r1(t) of the interval optimization dense false target jamming (IO-DFT) after pulse compression is:

[0127]

[0128] The output response r2(t) of the interval-phase optimization dense false target jamming (IPO-DFT) after pulse compression is:

[0129]

[0130] The output response r3(t) of the interval-phase-amplitude optimization dense false target jamming (IPAO-DFT) after pulse compression is:

[0131]

[0132] In a more specific implementation, the CFAR processing step of the dense false target jamming signal in step S2 and the interference target function and constraint condition after CFAR processing are as follows:

[0133] CFAR processing can form a suppressing jamming effect on the signal, so that the effect of the jamming signal is better. The main processing methods of CFAR include: cell average constant false alarm rate processing (CACFAR), cell average greatest constant false alarm rate processing (GOCACFAR), cell average smallest constant false alarm rate processing (SOCACFAR), ordered statistics constant false alarm rate processing (OSCFAR), etc. In a specific implementation of the present application, cell average constant false alarm rate processing (CACFAR) is adopted.

[0134] CFAR processing is based on the following assumption: assuming that the noise signal parameters in the reference cell and the to-be-detected cell are consistent. The CFAR processing window is mainly divided into three parts: the to-be-detected cell, the protection cell, and the reference cell. The to-be-detected cell is mainly used to judge whether there is a target; the protection cell is mainly used to prevent the error estimation of noise power when the target crosses multiple cells; the noise in the reference cell is consistent with that in the to-be-detected cell, so the power value thereof can be used to represent the noise power value of the to-be-detected cell. CFAR processing is to dynamically adjust the detection threshold through the estimation of the noise power of the to-be-detected cell, so as to maximize the target detection probability while keeping the false alarm rate unchanged. The detection threshold of cell average constant false alarm rate (CACFAR) is as follows:

[0135]

[0136] wherein is a multiplicative factor of the CACFAR detector, P fa is a constant false alarm rate, and M is the number of reference cells; x l represents the signal power in the distance cell.

[0137] Assuming that is the position of the real target, and the false targets are In the dense area, falls in the reference cell of , so that the background noise power level is estimated to be high and cannot detect ; by analogy, falls in the reference cell of , so that cannot be detected. Conversely, if does not fall in the reference cell of , , it can be detected.

[0138] The powers of the dense false targets with adjustable interval, amplitude, and phase after pulse compression are |r1(t)|2 r2(t) 2 r3(t) 2 The target function is established with the detection threshold mean value in the target range (l a l b ) of the target. The interference signal amplitude is set as 1 to ensure that the obtained interference signal power will not exceed the peak power output by the jammer.

[0139] The interval optimization dense false target (IO-DFT) target function and constraint conditions are as follows:

[0140]

[0141]

[0142] Δ1<|Δt i -Δt i-1 |<Δ2,i=1,2,…,I

[0143] Δ2<|Δt j -Δt j-1 |<Δ3,j=1,2,…,J

[0144] In the formula, Δ1 and Δ2 are the minimum interval and the maximum interval of the dense area respectively; and Δ2 and Δ3 are the minimum interval and the maximum interval of the sparse area respectively.

[0145] The interval-phase optimization dense false target (IPO-DFT) target function and constraint conditions are as follows:

[0146]

[0147]

[0148] Δ1<|Δt i -Δt i-1 |<Δ2,i=1,2,…,I

[0149] Δ2<|Δt j -Δt j-1 |<Δ3,j=1,2,…,J

[0150]

[0151] Interval-Phase-Amplitude Optimization Dense False Target (IPAO-DFT) objective function and constraint conditions:

[0152]

[0153]

[0154] Δ1<|Δt i -Δt i-1 |<Δ2,i=1,2,…,I

[0155] s.t.Δ2<|Δt j -Δt j-1 |<Δ3,j=1,2,…,J

[0156]

[0157] 0<a≤1

[0158] In a more specific implementation, the mesh adaptive direct search algorithm (MADS) and its parameter optimization process for interval, amplitude and phase adjustable dense false target jamming signals in step S3 are as follows:

[0159] The mesh adaptive direct search algorithm (MADS) is developed from the generalized pattern search algorithm, and is a derivative-free optimization algorithm for solving non-smooth constrained programming. By establishing a grid for the problem model parameters, the method of search and detection is used to adaptively optimize the optimal solution. The MADS algorithm provides a solution to solve multi-constrained, nonlinear complex models.

[0160] When using the MADS algorithm to optimize the dense false target jamming signal parameters, the interval optimization dense false target (IO-DFT) jamming objective function is redefined:

[0161]

[0162] Where the interval Ω is the feasible region of Δt n , and ψ Ω is the feasible region indicator function. If Let f Ω =∞, if Δt∈Ω d ,

[0163] The interval-phase optimization dense false target (IPO-DFT) objective function is redefined as:

[0164]

[0165] where is the feasible region, Ω c is the feasible region of .

[0166] The interval-phase-amplitude optimization dense false target (IPAO-DFT) objective function is redefined as:

[0167]

[0168] where is the feasible region, continuous variable x c represents the initial phase and the set of amplitudes A, with n c representing the dimension of x c , Ω c is the feasible region of x c .

[0169] The mesh adaptive direct search (MADS) algorithm first needs to be initialized to establish an initial iteration point x = (x c , x d ) of a local minimum, where x c represents continuous variables and x d represents discrete variables, and within its neighborhood there is:

[0170] f Ω (x) ≤ f Ω (v)

[0171] The feasible region of v is:

[0172]

[0173] where B ε (x c ) has the meaning that for any N(x) = {y e Ω: y c = x c , ||y d - x d ||1 < 1}, y d takes discrete values.

[0174] In a specific implementation, the parameters are set as:

[0175] ω + = 1.0, ω - = 1.0, τ = 4, D = [I - I], G = [I]

[0176] The process of MADS optimization mainly consists of a search step and a probe step.

[0177] The main goal of the search step and the probe step is to generate an improved grid point. The search step selects a finite number of trial points on the grid, and calculates the function values of these grid points. Ω By comparing with the initial point function value f Ω (x), the improved grid point is established.

[0178] The grid at the kth iteration when optimizing the jamming of the spaced-apart dense false targets is:

[0179]

[0180] where the grid parameters V k represent the trial points evaluated before the kth iteration (V0 is the initial trial point). For all possible values of the discrete variable Δt, i = 1, 2,..., i max , the positive generating set D i = G i Z i , where the nonsingular generating matrix

[0181] The grid at the kth iteration when optimizing the jamming of the joint dense false targets is:

[0182]

[0183] where,

[0184] When the improved grid point is generated, the MADS iteration will stop, otherwise, the probe step is entered. The probe step searches for an improved grid point on the framework, and performs a local search according to the probe direction.

[0185] The framework P k at the kth iteration when optimizing the jamming of the spaced-apart dense false targets is:

[0186]

[0187] where, D k (Δt)} is a positive generating set, and any d ∈ D k(Δt) can be represented by column vectors in D(Δt). The test point Δt k To the frame point The distance is bounded, that is In the formula For frame parameters, and

[0188] The framework P for the k-th iteration of joint optimization of dense false target interference k for:

[0189]

[0190] The parameter update condition for the optimization process of the Mesh Adaptive Direct Search (MADS) algorithm is: if an improved grid point x is generated in the feasible region Ω in the k-th search or probe step. k+1 , satisfying f Ω (x k+1 )<f Ω (x k The iteration was successful. The mesh parameters will be updated for the next iteration. It can remain unchanged or increase; conversely, Reduce. Mesh parameters. The update rules are as follows:

[0191]

[0192] in Given a fixed rational number τ>1 and two integers ω - ≤-1 and ω + ≥0.

[0193] The optimization flowchart of the Mesh Adaptive Direct Search (MADS) algorithm is attached. Figure 4 As shown.

[0194] In the specific implementation process, during the search step, in grid M k Select 10 grid points and calculate f for these grid points. Ω If f Ω ≤f Ω If (x) is found, an improved grid point is formed, and the probe step is skipped. If no improved grid point is found, the probe step is initiated. During the probe step, in frame P... k Find an improved grid point when its objective function value f Ω <f Ω (x) performs mesh parameter updates, updating the parameters. and Let k = k+1, then if the stopping condition is met: when the objective function value |f| in the (k+1)th iteration is... Ω (x)-f Ω (xk+1 )|<1×10 -13 When the interval of dense false target interference is optimized using the above algorithm, the interval Δt is returned. k+1 The value of Δt k+1 To find the optimal solution for interval optimization of dense false target interference, f Ω (Δt k+1 The optimal detection threshold mean is Δt. When using the above algorithm to jointly optimize the spacing, initial phase, and amplitude of dense false target interference, the returned values ​​are the spacing Δt and the initial phase. and the value of amplitude a This is the optimal solution for optimizing the spacing, initial phase, and amplitude of dense false target interference. This represents the optimal average detection threshold.

[0195] When the iteration stopping condition is not met, the calculated parameters need to be used as a basis to continue updating the parameters. At this time, the objective function has not yet reached the optimal solution. When the iteration stopping condition is met, the parameters at this time are the final optimized parameters. At this time, the optimal solution of the objective function can be obtained, and the interference signal has the best performance.

[0196] In the specific implementation process, the optimal interval parameter Δt can be obtained after MADS optimization for IO-DFT interference. k+1 So that the objective function f Ω (Δt k+1 When the interference signal waveform j1(t) is at its minimum, it has the best interference performance.

[0197] For IPO-DFT interference, the optimal spacing and phase parameter Δt can be obtained after MADS optimization. k+1 , Make the objective function The minimum value is reached. At this point, the interference signal waveform j2(t) exhibits optimal interference performance.

[0198] For IPAO-DFT jamming, the optimal solution for dense decoy jamming with optimized spacing, initial phase, and amplitude can be obtained after MADS optimization. Δt k+1 , so that the objective function At its minimum, the interference signal waveform j3(t) exhibits optimal interference performance.

[0199] The following simulation experiment was conducted based on the dense false target interference signal generation and optimization process described in the above specific implementation method:

[0200] To raise the detection threshold of typical dense false target interference after CFAR processing while maintaining deception effectiveness, three optimization methods were implemented: interval optimization, joint optimization of interval and initial phase, and joint optimization of interval, initial phase, and amplitude. These three optimization methods improved the interference effect, and comparative analysis revealed the optimal method. The mean detection threshold was used as an indicator for quantitative evaluation, measuring the advantages of the proposed optimization method compared to typical interference. Furthermore, a comparison with the Genetic Algorithm (GA) revealed the advantages of the MADS algorithm. The basic parameters of the linear frequency modulated signal and the basic parameters of CFAR processing are shown in Table 1.

[0201] Table 1 Radar linear frequency modulation and CFAR parameters

[0202]

[0203] For typical dense decoy jamming, after pulse compression, 60 decoys spaced Δt apart are formed, which are then attached to... Figure 3 As can be seen, the amplitude of the interference target remains below the detection threshold. If the target is within the set interference coverage area, it cannot be detected. The calculated average detection threshold is 35.7 dB.

[0204] The interference interval parameters for dense false targets are optimized, while other parameters remain consistent with those for typical dense false targets. In this case, the interval Δt is no longer a uniform value but rather varies. The interference region is set as a sparse region-dense region-sparse region; this setting aims to raise the detection threshold and generate false targets exceeding the threshold. Δ1, Δ2, and Δ3 are set to 0.067μs, 0.33μs, and 0.67μs respectively, and the MADS algorithm is used to optimize the interval. (See attached...) Figure 6 As can be seen, after pulse compression, the dense false target interference, after optimization, forms three parts: a sparse region, a dense region, and a sparse region. The arrangement of the false targets is no longer regular, and this setting can hinder existing interference identification techniques. (See attached...) Figure 7 As can be seen, the optimized dense false target interference raises the detection threshold and generates 40 false targets exceeding the threshold. Compared with typical interference, the optimized interval dense false targets overcome the technical limitation that the arrangement pattern of false targets is easily identifiable, achieving both deception and interference effects, raising the detection threshold, and improving the interference effect.

[0205] To further improve the jamming effect, the time interval and initial phase of the dense decoy jamming were jointly optimized. The initial phase range was set to 0–2π, and the interval parameters Δ1, Δ2, and Δ3 were set to 0.067 μs, 0.33 μs, and 0.67 μs, respectively. The remaining parameters were consistent with those of typical dense decoy jamming. The Grid Adaptive Direct Search (MADS) algorithm was used to optimize the parameters. (See attached...) Figure 9It can be seen that the dense false target jamming pulse pressure gain after optimization of interval and initial phase is close to 70, and compared with typical jamming, the dense false target after optimization of interval and initial phase has the jamming characteristics after optimization of interval, and the detection threshold is higher, and the jamming effect is better.

[0206] Finally, the time interval, initial phase and amplitude of the dense false target jamming are jointly optimized. Compared with the joint optimization of time interval and initial phase of the dense false target jamming, the joint optimization of time interval, initial phase and amplitude of the dense false target jamming optimizes the amplitude of each sub-jamming. Figure 12 It can be seen that the dense area pulse pressure gain is more than 90, but the sparse area pulse pressure gain is reduced, and this optimization method improves the detection threshold of the dense area by sacrificing the sparse area pulse pressure gain. By optimizing the jamming amplitude, the detection threshold of the dense false target after optimization of interval, initial phase and amplitude is higher than that of typical jamming and the other two optimization methods, and the dense false target after optimization of interval, initial phase and amplitude has both suppression jamming effect and deception jamming effect, the detection threshold is the highest, and the jamming effect is the best.

[0207] The detection threshold mean is used to quantitatively evaluate the jamming effect of the three simulation experiments, and the calculation results of the MADS algorithm and the genetic algorithm (GA) are compared in terms of detection threshold mean and CPU calculation time, and the evaluation results are shown in Table 2.

[0208] Table 2 Comparison of results of three dense false target jamming optimization models

[0209]

[0210] The CPU calculation time of the MADS algorithm is obtained by setting the value reaching the GA optimization result as the iteration stop condition. As shown in Table 2, the joint optimization method is better than the single parameter optimization method, and the joint optimization of interval, initial phase and amplitude has the best jamming effect; by comparing the calculation results of MADS and GA, the MADS algorithm is better than the GA algorithm in terms of result and speed.

[0211] The above embodiments are only preferred embodiments of the present application, and the protection scope of the present application is not limited to the above embodiments. Any technical scheme falling within the concept of the present application belongs to the protection scope of the present application. It should be pointed out that improvements and refinements made by ordinary skilled in the art without departing from the principles of the present application should also be considered as the protection scope of the present application.

Claims

1. A method for optimizing dense false target interference waveforms, characterized in that: Includes the following steps: S1: Construct a dense false target interference model with adjustable interval, amplitude, and phase; S2: Construct a mixed integer model with multiple parameters and constraints; S3: Interference waveform optimization based on mesh adaptive direct search; Step S1 includes: S11: Generation and processing of typical dense false target interference; S12: Construct an optimization model for the spacing, initial phase, and amplitude of dense false target interference, including: S121. Construct an interval-optimized dense false target interference model, i.e., an IO-DFT model, including: Where i and j are the number of forwardings, and I+J=n is the superposition of n interference signals; For interference signals in dense areas, Δt i Interference interval for densely populated areas; For interference signals in the sparse region, Δt j Interference interval for sparse regions; S122. Construct a joint optimization model for dense false target interference based on the interval and initial phase, i.e., the IPO-DFT model, including: in The initial phase of interference in dense areas. The initial phase of the interference in the sparse region; S123. Construct a dense false target interference model that jointly optimizes the interval, initial phase, and amplitude, i.e., the IPAO-DFT model, including: Where a i For the interference amplitude in the dense area, a j The amplitude of interference in the sparse region; Step S2 includes: S21: Input the dense false target interference j1(t), j2(t), j3(t) into the matched filter for pulse compression to obtain the output responses r1(t), r2(t), r3(t): The output response r1(t) is: Where a is the amplitude of the interference signal, T is the pulse width of the interference signal, k is the frequency modulation slope of the linear frequency modulated signal, i,j are the number of forwardings, I+J=n, that is, there are n signals superimposed, Δt i For the dense area interference interval, Δt j Interference interval for sparse regions; The output response r2(t) is: Where a is the amplitude of the interference signal, T is the pulse width of the interference signal, k is the frequency modulation slope of the linear frequency modulated signal, i,j are the number of forwardings, I+J=n, that is, there are n signals superimposed, Δt i For the dense area interference interval, Δt j Interference interval for sparse regions The initial phase of interference in dense areas. The initial phase of the interference in the sparse region; The output response r3(t) is: Where a i For the interference amplitude in the dense area, a j The amplitude of the interference in the sparse region is given by Δt, where T is the pulse width of the interference signal, k is the frequency modulation slope of the linear frequency modulated signal, i and j are the number of relays, and I + J = n, meaning there are n signals superimposed. i For the dense area interference interval, Δt j Interference interval for sparse regions The initial phase of interference in dense areas. The initial phase of the interference in the sparse region; S22. Obtain the power of the dense false target interference after pulse compression, which is |r1(t)| 2 |r2(t)| 2 |r3(t)| 2 Let r(t) be the power-time function of the output response r(t) at time t, and its value is the square of the response magnitude, within the range of the target (l a ,l b The objective function is established based on the average detection threshold within the range, and the amplitude of the interference signal is set to 1. S23. The mixed-integer model with multiple parameters and constraints is obtained in the following form: The objective function and constraints for the IO-DFT disturbance are as follows: Δ1<|Δt i -Δt i-1 |<Δ2,i=1,2,…,I Δ2<|Δt j -Δt j-1 |<Δ3,j=1,2,…,J In the formula, Δ1 and Δ2 are the minimum and maximum intervals in the dense region, respectively; Δ2 and Δ3 are the minimum and maximum intervals in the sparse region, respectively; V1 is the unit average constant false alarm detection target threshold; and P... fa The constant false alarm rate is M, where M is the number of reference units, and Δt is the constant false alarm rate. i For the dense area interference interval, Δt j Interference interval for sparse regions This is an interference signal in a densely populated area. For sparse region interference signals, i and j are the number of forwardings, and I+J=n, meaning there are a total of n superimposed signals; The objective function and constraints for IPO-DFT interference are as follows: Δ1<|Δt i -Δt i-1 |<Δ2,i=1,2,…,I Δ2<|Δt j -Δt j-1 |<Δ3,j=1,2,…,J In the formula, Δ1 and Δ2 are the minimum and maximum intervals in the dense region, respectively; Δ2 and Δ3 are the minimum and maximum intervals in the sparse region, respectively; V2 is the unit average constant false alarm threshold for target detection; and P... fa The constant false alarm rate is M, where M is the number of reference units, and Δt is the constant false alarm rate. i For the dense area interference interval, Δt j Interference interval for sparse regions The initial phase of interference in dense areas. The initial phase of the interference in the sparse region. This is an interference signal in a densely populated area. For sparse region interference signals, i and j are the number of forwardings, and I+J=n, meaning there are a total of n superimposed signals; The IPAO-DFT interference objective function and constraints are as follows: Δ1<|Δt i -Δt i-1 |<Δ2,i=1,2,…,I s.t.Δ2<|Δt j -Δt j-1 |<Δ3,j=1,2,…,J 0＜a≤1 In the formula, Δ1 and Δ2 are the minimum and maximum intervals in the dense region, respectively; Δ2 and Δ3 are the minimum and maximum intervals in the sparse region, respectively; V3 is the unit average constant false alarm detection target threshold; a i For the interference amplitude in the dense area, a j P represents the amplitude of interference in the sparse region. fa The constant false alarm rate is M, where M is the number of reference units, and Δt is the constant false alarm rate. i For the dense area interference interval, Δt j Interference interval for sparse regions The initial phase of interference in dense areas. The initial phase of the interference in the sparse region. This is an interference signal in a densely populated area. For sparse region interference signals, i and j are the number of forwardings, and I+J=n, meaning there are a total of n superimposed signals; Step S3 includes: S31. Define the disturbance objective function based on Mesh Adaptive Direct Search (MADS); S32. Initialize the relevant parameters for mesh adaptive direct search; S33. Generate improved grid points through search and probe steps; S34. Set parameter update rules and stop conditions.

2. The method for optimizing dense false target interference waveforms according to claim 1, characterized in that... Step S31 includes: Define the IO-DFT interference objective function under MADS: That is, the search interval parameter Δ t Make the objective function value f Ω (Δt) is at its minimum, at which point the maximum unit constant false alarm detection threshold value V1 is obtained; the interval is... Ω is Δt n The feasible region where ψ is located Ω For the feasible region indicator function, if Let f Ω =∞, if Δt∈Ω d , Define the IPO-DFT interference objective function under MADS: That is, the search interval parameter Δ t , Make the objective function value At its minimum, the maximum unit constant false alarm detection threshold value V2 is obtained; where For the feasible region, Ω c for The feasible domain; Define the IPAO-DFT interference objective function under MADS: That is, the search interval parameter Δ t x c Make the objective function value f Ω (x c When Δt) is minimized, the maximum unit constant false alarm detection threshold value V3 is obtained; where Let x be the feasible region, a continuous variable. c Indicates the initial phase The set of amplitudes a, denoted by n c x represents c The dimension, Ω c For x c The feasible domain.

3. The method for optimizing dense false target interference waveforms according to claim 1, characterized in that... Step S32 includes: Establish an initial iteration point x = (x) for a local minimum. c ,x d ), x c Let x represent a continuous variable. d Represents a discrete variable, in its neighborhood Contains: f Ω (x)≤f Ω (v), the feasible region containing v is: Among them B ε (x c The meaning of ) is: for any N(x) = {y∈Ω:y} c =x c ,||y d -x d ||1≤1},y d Take discrete values.

4. The method for optimizing dense false target interference waveforms according to claim 1, characterized in that... The search step in step S33 includes: Select a finite number of test points on the grid and calculate f for these grid points. Ω By comparing the function value f at the initial point Ω (x) Compare and establish improved grid points; when optimizing dense false target interference at intervals, the grid in the k-th iteration is: Among them, grid parameters V k V0 represents the test point evaluated up to the k-th iteration, where V0 is the initial test point; for all possible values ​​of the discrete variable Δt, i = 1, 2, ..., i max The positive generating set D i =G i Z i The non-singular generating matrix Select a finite number of test points on the grid and calculate f for these grid points. Ω By comparing the function value f at the initial point Ω (x) Compare and establish improved grid points; when jointly optimizing dense false target interference, the grid in the k-th iteration is: in, 5. The method for optimizing dense false target interference waveforms according to claim 1, characterized in that... The detection step in step S33 includes: Find improved grid points on the framework, perform a local search along the detection direction, and optimize the framework P in the k-th iteration when encountering dense false target interference. k for: Among them, D k (Δt) is a positively generating set, for any d∈D k (Δt) using D k The column vector in (Δt) represents the test point Δt. k To the frame point The distance is bounded, that is In the formula For frame parameters, and Find improved grid points on the framework and perform a local search along the detection direction; jointly optimize the framework P for the k-th iteration when dealing with dense false target interference. k for:

6. The method for optimizing dense false target interference waveforms according to claim 1, characterized in that... The parameter update rules include: If, in the k-th search or probe step, an improved grid point x is generated in the feasible region Ω... k+1 , satisfying f Ω (x k+1 )<f Ω (x k The iteration was successful. The mesh parameters will be updated for the next iteration. It can remain unchanged or increase; conversely, Reduce mesh parameters The update rules are as follows: in Given a fixed rational number τ>1 and two integers ω - ≤-1 and ω + ≥0.

7. The method for optimizing dense false target interference waveforms according to claim 1, characterized in that... The stopping conditions include: When the objective function value of the (k+1)th iteration is |f Ω (x)-f Ω (x k+1 )|<1×10 -13 When the iteration stops, f Ω (Δt k+1 The mean of the detection threshold is the optimal value.

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