A method for designing an interference rejection filter based on a least mean square algorithm

Abstract

The application discloses a design method of an interference suppression mismatch filter based on a least mean square algorithm, and first, radar transmitting signals and intermittent sampling retransmission type interference signals are constructed, and mismatch filter coefficients are initialized; then, pulse compression output results are calculated, and the mismatch filter coefficients are optimized based on the least mean square algorithm; finally, the pulse compression results in which interference false targets are effectively suppressed are obtained by using the optimized mismatch filter; the application can effectively suppress the intermittent sampling retransmission type interference, reduce the amplitudes of the interference false targets, and thus the targets can be effectively detected.

Description

Technical Field

[0001] This invention relates to the field of radar electronic countermeasures technology, specifically to a design method for interference suppression mismatch filters based on the least mean square algorithm. Background Technology

[0002] The electromagnetic environment of modern battlefields is becoming increasingly complex, and electronic countermeasures and countermeasures technologies are rapidly developing. Electromagnetic interference has become a significant bottleneck restricting radar effectiveness. Among these, intermittent sampling-and-retransmitting jamming based on Digital Radio Frequency Memory (DRFM) technology is a novel type of active jamming. This jamming signal is coherent with the radar's transmitted signal, exhibiting high jamming efficiency and is widely used in radar countermeasures, posing a new threat to modern radar systems. Therefore, researching suppression techniques for intermittent sampling-and-retransmitting jamming is of great significance.

[0003] Traditional interference suppression methods mainly focus on the spatial, time, and frequency domains. Spatial domain anti-jamming primarily employs sidelobe concealment and cancellation methods, using adaptive beamforming to combat active interference. However, for intermittent sample-and-repeat interference, these spatial methods are ineffective when the jammer and the real target are at the same angle. In the time domain, interference suppression is typically achieved by designing complex waveforms, including intra-pulse orthogonal linear frequency modulation-phase coded waveforms, sparse Doppler-sensitive waveforms, and time-domain discontinuous waveforms. However, these waveform design methods are often computationally complex and cannot guarantee real-time performance. Frequency domain anti-jamming mainly utilizes frequency agility and frequency diversity techniques, but these methods have limited performance against coherent interference such as intermittent sample-and-repeat interference.

[0004] Therefore, based on pulse compression radar systems, a design method for interference suppression mismatch filters based on the least mean square algorithm is developed to effectively suppress intermittent sampling and relay interference, reduce the amplitude of interference false targets, and thus enable the target to be effectively detected. This has important practical significance and application value. Summary of the Invention

[0005] This invention proposes a design method for interference suppression mismatch filter based on the least mean square algorithm in pulse compression radar systems, starting from the signal processing level. This method can effectively suppress intermittent sampling and relay interference, reduce the amplitude of interference false targets, and thus enable the target to be effectively detected.

[0006] The technical solution for implementing the present invention is as follows:

[0007] A method for designing a mismatch filter for interference suppression based on the least mean square algorithm is proposed. First, a radar transmitted signal and an intermittently sampled and relayed jamming signal are constructed, and the coefficients of the mismatch filter are initialized. Then, the pulse compression output is calculated, and the coefficients of the mismatch filter are optimized based on the least mean square algorithm. Finally, the optimized mismatch filter is used to obtain the pulse compression result in which the jamming false targets are effectively suppressed.

[0008] The specific process of this invention is as follows:

[0009] Step S1: Construct the radar transmission signal and the intermittent sampling and relay jamming signal.

[0010] Let the radar transmitted signal be denoted as s[n], where n = 1, 2, ..., N, and N is the total signal length. The working principle of intermittent sampling and forwarding jamming is as follows: when the jammer detects the radar transmitted signal, it starts sampling. After a period of time, sampling stops to obtain the first jamming slice. According to the forwarding requirements in the controller, the jamming slice is forwarded with a delay. Then, the sampling and forwarding process is repeated until the radar transmitted pulse ends. Based on the working principle of intermittent sampling and forwarding jamming, the jamming signal j[n] is constructed to obtain the radar echo signal y[n] containing the transmitted signal and the jamming signal.

[0011] Step S2: Calculate the current signal mismatch filter output.

[0012] Let the coefficients of the mismatch filter be denoted as h[n], which can be represented in vector form as h. First, an initial mismatch filter is randomly generated, and then the output of the radar echo signal after passing through the mismatch filter is calculated. When the radar is subjected to intermittent sampling and repeating interference, i.e., when the j[n] signal exists, a series of realistic false targets will be formed. Generally, the first false target will be delayed by one sampling pulse width compared to the real target. If the interference energy radiated by the jammer is large, i.e., the jamming-to-signal ratio (JSR) is large, the amplitude of the false target in the output result may be greater than the amplitude of the target. The real target will be submerged in the interference of the false target, thus affecting the radar's detection of the real target.

[0013] Step S3: Optimize the mismatch filter based on the least mean square algorithm.

[0014] When intermittent sampling-forwarding interference is well suppressed, the desired mismatch filter output is a delta function, representing the presence of only the real target and zero at other time delays. The optimal mismatch filter for suppressing intermittent sampling-forwarding interference in this invention has an output closest to the ideal output. This invention uses a minimum mean square algorithm to optimize the filter coefficients, designing the mismatch filter by minimizing the mean square error between the ideal and actual outputs to achieve interference suppression. The coefficients of this optimal mismatch filter for suppressing interference are denoted as h. opt .

[0015] Step S4 yields the pulse pressure results for interference suppression.

[0016] The radar echo signal is compared with the optimal mismatch filter h from step S3. opt Perform convolution to obtain the pulse compression result of the mismatch filter for interference suppression, denoted as r. opt At this point, the pulse pressure result r opt In this system, the amplitude of false targets is significantly reduced, thereby exposing the real targets, which the radar can then use for target detection and ranging.

[0017] Step S1 includes the following steps:

[0018] Step S11, denote the intermittent sampling pulse sequence as p[n], and its expression is:

[0019]

[0020] Where u(n) is the unit step signal, τ n It is the sampling pulse width, that is, the number of sampling points corresponding to each interference slice of the interference signal, T s is the sampling pulse repetition interval, and M is the number of sampling pulses.

[0021] Step S12, the jammer's sampled signal is the product of the radar transmitted signal and the intermittent sampling pulses, denoted as s. s [n], that is

[0022]

[0023] Step S13, the intermittent sampling and forwarding interference signal is the delay of the sampled signal, denoted as j[n], i.e.

[0024] j[n]=s s [n-τ d (3)

[0025] Where τ d This is the delay forwarding factor for the interference signal.

[0026] According to the properties of the Fourier transform, the time-domain delay can be equivalent to multiplying the frequency-domain delay by the forwarding factor. Therefore, another expression for the intermittent sampling forwarding interference signal can be obtained, which is...

[0027] j[n]=AF -1 T d F[s[n]·p[n]] (4)

[0028] Where A is the amplitude of the jamming signal emitted by the jammer, and T d Forwarding delay factor τ d The corresponding matrix forms, F and F -1These are the Fourier transform and its inverse transform, respectively.

[0029] Step S14: The radar echo is the superposition of the radar transmitted signal and the jamming signal, which can be expressed by the following formula.

[0030] y[n]=s[n]+j[n] (5)

[0031] Construct a signal matrix Y from the echo signal; its expression is as follows:

[0032]

[0033] Step S2 includes the following steps:

[0034] Step S21: Initialize the mismatch filter coefficients to obtain h[n].

[0035] Step S22, the output of the pulse compression radar is denoted as r[k], and its vector form is r, which is the convolution of the radar echo signal and the mismatch filter, and can be expressed as:

[0036]

[0037] The radar pulse compression output is written in matrix form, i.e.

[0038] r = Y H h (8)

[0039] Use this result as the output of the current signal mismatch filtering.

[0040] Step S3 includes the following steps:

[0041] Step S31: Construct an ideal interference suppression output. This output contains only the real target, and all other time delays are zero. The ideal output can be represented by the following formula, which can be written in vector form as d.

[0042]

[0043] Step S32: Calculate the difference between the actual output and the ideal output to obtain the error vector e, which can be calculated using the following formula.

[0044] e = dr = dY H h (10)

[0045] Step S33, define the cost function as mean squared error, i.e.

[0046] f(h)=E[e[k] 2 ]=E[(d[k]-r[k]) 2 ]=E[(d[k]-Y k H h) 2(11)

[0047] Where Y k Let Y represent the column vector formed by the k-th column of matrix Y. The first term in the above equation is independent of the mismatch filter coefficients.

[0048] Therefore, the mismatch filtering optimization problem for resisting intermittent sampling and forwarding interference is obtained as follows:

[0049] min f(h) (12)

[0050] Step S34: Take the partial derivative of the objective function in the optimization problem with respect to the mismatch filter coefficients to obtain the following equation.

[0051]

[0052] To ensure the cost function gradually decreases, the mismatch filter coefficients should be updated in the direction of gradient descent. That is...

[0053]

[0054] Where μ is the step size factor.

[0055] Step S35, after substituting equation (13) into equation (14), the final formula for updating the mismatched filter coefficients is obtained as follows:

[0056] h new =h old +2μYe (15)

[0057] Step S36: Repeat steps S32 to S35 until the algorithm converges or meets the set maximum number of iterations. Use the mismatch filter coefficients from the last iteration as the optimized interference suppression filter coefficients, denoted as h. opt .

[0058] Step S4 includes the following steps:

[0059] The output r of the radar echo signal after passing through the optimal interference suppression mismatch filter opt For, that is

[0060] r opt =Y H h opt (16)

[0061] At this point, the peak value is the actual target signal, which can be used to carry out further operations such as target identification or tracking.

[0062] Beneficial effects:

[0063] (1) This invention targets intermittent sampling and forwarding interference and counters it from the signal processing level. It suppresses interference by designing a mismatch filter. Compared with spatial and frequency domain interference suppression methods, it does not require higher hardware costs.

[0064] (2) The present invention updates the coefficients of the mismatched filter based on the least mean square algorithm. In practical applications, only the radar echo signal and the ideal output signal need to be known. The method has low computational complexity and fast convergence speed.

[0065] (3) The present invention can effectively suppress intermittent sampling and forwarding interference. Simulation results show that the method described in the present invention can reduce the amplitude of false targets by 30-40dB, and has a good interference suppression effect. Attached Figure Description

[0066] Figure 1 A flowchart illustrating the design method for interference suppression filters based on the least mean square algorithm;

[0067] Figure 2 This is a schematic diagram of intermittent sampling and forwarding interference.

[0068] Figure 3 The following are time-domain waveforms of radar transmitted signals and intermittent sampling and repeating jamming signals: (a) is the time-domain waveform of the transmitted signal, and (b) is the time-domain waveform of the jamming signal.

[0069] Figure 4 The output diagram of the matched filter pulse compression at the initial stage;

[0070] Figure 5 This is a graph showing the mean square error as a function of the number of iterations.

[0071] Figure 6 The output diagram shows the results of the mismatched filter pulse compression. Detailed Implementation

[0072] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, a simulation example of applying the present invention will be given below, and the technical solutions of the present invention will be clearly and completely described in conjunction with the accompanying drawings.

[0073] Consider the following simulation scenario: The radar transmits an arbitrary random phase-coded signal, and the source waveform parameters and the operating parameters of the intermittent sampling repeater jammer are shown in the table below.

[0074]

[0075]

[0076] The specific steps of a design method for an interference suppression mismatch filter based on the least mean square algorithm are as follows: Figure 1 As shown:

[0077] Step S1: Construct the radar transmission signal and the intermittent sampling and relay jamming signal.

[0078] The schematic diagram of intermittent sampling and forwarding interference under these simulation parameters is as follows: Figure 2 As shown.

[0079] Step S11, the intermittent sampling pulse sequence p[n] is obtained from the intermittent sampling repeater interference parameters according to equation (1).

[0080]

[0081] Where L is the number of sampling points within the width of each intermittent sampling pulse.

[0082] Step S12, assuming the radar transmitted signal is a random phase-coded signal, the expression for s[n] is:

[0083] s[n]=exp(jφ n n = 1, 2, ..., N (18)

[0084] Where φ n ∈[0,2π], the sampling signal s of the jammer is obtained according to equation (2). s [n].

[0085] Step S13: Obtain the intermittent sampling and forwarding interference signal j[n] according to equation (3) or equation (4). The amplitude A of the interference signal transmitted by the jammer can be calculated from the interference-to-signal ratio, and the interference signal delay forwarding factor τ is... d It is 1us.

[0086] Step S14: The radar echo y[n] is the sum of the radar transmitted signal and the jamming signal, which can be calculated by equation (5). For ease of subsequent representation and calculation, the signal matrix Y is constructed using the echo signal y[n].

[0087] The time-domain waveforms of radar transmitted signals and intermittent sampling and repeating jamming signals are as follows: Figure 3 As shown in (a) and (b).

[0088] Step S2: Calculate the current signal mismatch filter output.

[0089] Step S21: First, initialize the coefficients h[n] of the mismatched filter. Here, the coefficients of the matched filter are used as the initial values, i.e., initialized using the following formula.

[0090] h[n]=s * [-n] (19)

[0091] Step S22: Calculate the output of the current signal mismatch filter for the pulse compression radar using equation (8).

[0092] The initial matched filter pulse compression output is as follows: Figure 4 As shown in the figure, the amplitude of the matched filter output from the real target is normalized. Figure 4 It can be seen that at this time, two high-amplitude interference false targets appeared in the pulse compression results, and the real target was completely blocked. The interference seriously affected the radar's detection performance.

[0093] Step S3: Optimize the mismatch filter based on the least mean square algorithm.

[0094] Step S31: Construct the ideal interference suppression output using equation (9);

[0095] Step S32: Subtract the actual mismatch filter output in equation (8) from the ideal output in step S31 to obtain the error vector e.

[0096] Step S33: Using equations (11) and (12), the mismatch filtering optimization problem against intermittent sampling forwarding interference is obtained.

[0097] Step S34: Solve the above optimization problem using equations (13) and (14).

[0098] Step S35: Update the mismatch filter coefficients using equation (15).

[0099] Step S36: Repeat steps S32 and S35 until the algorithm reaches the maximum number of iterations. In this simulation experiment, the maximum number of iterations is set to 3000. The mean squared error as a function of the number of iterations during the iteration process is shown in the curve below. Figure 5 As shown. The mismatch filter coefficients from the last iteration are used as the optimized interference suppression filter coefficients, i.e., h. opt .

[0100] Step S4 yields the pulse pressure results for interference suppression.

[0101] Using equation (16), the radar echo signal is convolved with the mismatch filter for interference suppression to obtain the pulse compression result r of the mismatch filter. opt ,like Figure 6 As shown, the dashed line represents the matched filtering result, and the solid line represents the mismatch filtering result for interference suppression. It can be seen that the mismatch filtering method effectively suppresses the amplitude of the interference false target, and the real target can be clearly seen in the pulse compression result.

[0102] The amplitudes of matched filtering and mismatch filtering for real and false targets were statistically analyzed, and the amplitude loss of real targets and the interference suppression effect of false targets were calculated. The results are shown in the table below (unit / dB).

[0103] Real target False Target 1 False Target 2 Matched filtering -0.63 9.33 9.81 Mismatch Filtering -3.58 -21.74 -32.42 Amplitude loss / interference suppression 2.95 31.07 42.23

[0104] Depend on Figure 6 As shown in the statistical results in the table above, the method of the present invention can reduce the amplitude of false targets by about 30 to 40 dB, effectively suppress intermittent sampling and relay interference, and ensure the working efficiency of the radar in the interference environment.

[0105] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for designing an interference suppression mismatch filter based on the least mean square algorithm, characterized in that... The steps of this method include: Step S1: Construct the radar transmission signal and the intermittent sampling and repeating jamming signal; The radar transmission signal is denoted as , , The total signal length is given. When the jammer detects the radar's transmitted signal, it begins sampling. After a certain period, sampling stops, resulting in the first jamming slice. The jamming slice is then forwarded with a delay according to the forwarding requirements in the controller. This sampling and forwarding process is repeated until the radar's transmitted pulse ends, thus constructing the jamming signal. The radar echo signal containing both the transmitted signal and the jamming signal is obtained. ; Step S2: Calculate the current signal mismatch filter output; The coefficients of the mismatched filter are denoted as... Represented in vector form as First, an initial mismatch filter is randomly generated. Then, the output of the radar echo signal after passing through the mismatch filter is calculated. When the radar is subjected to intermittent sampling and repeater interference, i.e. When the signal is present, a series of realistic false targets will be formed. The first false target will be delayed by one sampling pulse width compared with the real target. Step S3: Optimize the mismatch filter based on the least mean square algorithm; When intermittent sampling and forwarding interference is well suppressed, the desired mismatch filter output is The function represents a function where only the real target exists, and all other time delays are zero. The least mean square algorithm is used to optimize the filter coefficients. A mismatch filter is designed to suppress interference by minimizing the mean square error between the ideal and actual outputs. The optimal mismatch filter coefficients for this interference suppression are denoted as... ; Step S4: Obtain the pulse pressure result of interference suppression; The radar echo signal is compared with the optimal mismatch filter in step S3. Perform convolution to obtain the pulse compression result of the mismatch filter for interference suppression, denoted as... At this point, in the pulse pressure results In this process, the amplitude of the false targets is greatly reduced, thereby exposing the real targets, which the radar uses for target detection and ranging. Step S1 includes the following steps: Step S11, denoted as the intermittent sampling pulse sequence. Its expression is in For unit step signal, It is the sampling pulse width, which is the number of sampling points corresponding to each interference slice of the interference signal. It is the sampling pulse repetition interval. It is the number of sampling pulses; Step S12, the jammer's sampled signal is the product of the radar transmitted signal and the intermittent sampling pulses, denoted as... ,Right now Step S13, the intermittent sampling and relay interference signal is the delay of the sampled signal, denoted as... ,Right now in The delay forwarding factor for the interference signal; Another expression for the intermittent sampling and relay interference signal is obtained as follows: in The amplitude of the jamming signal emitted by the jammer. Forwarding Delay Factor The corresponding matrix form, and These are the Fourier transform and its inverse transform, respectively. Step S14, the radar echo is the superposition of the radar transmitted signal and the jamming signal, expressed by the following formula: Construct a signal matrix from the echo signal Its expression is Step S2 includes the following steps: Step S21: Initialize the mismatch filter coefficients to obtain... ; Step S22, record the output of the pulse compression radar as The vector form is It is the convolution of the radar echo signal and the mismatched filter, expressed as: The radar pulse compression output is written in matrix form, i.e. Use this result as the output of the current signal mismatch filtering; Step S3 includes the following steps: Step S31: Construct an ideal interference suppression output. This output contains only the real target, and all other time delays are zero. The ideal output is represented by the following formula, written in vector form as follows: : Step S32: Calculate the difference between the actual output and the ideal output to obtain the error vector. Calculate using the following formula: Step S33, define the cost function as mean squared error, i.e. in Represented by matrix The A column vector composed of columns; the first term in the above formula is independent of the mismatch filter coefficients; Therefore, the mismatch filtering optimization problem for resisting intermittent sampling and forwarding interference is obtained as follows: ; Step S34: Take the partial derivative of the objective function in the optimization problem with respect to the mismatch filter coefficients to obtain the following equation. To gradually reduce the cost function, the mismatch filter coefficients should be updated in the direction of gradient descent; that is... in, These represent the mismatch filter coefficients obtained in the current update and the previous iteration, respectively. Step size factor; Step S35 yields the final formula for updating the mismatched filter coefficients: Step S36: Repeat steps S32 to S35 until the algorithm converges or meets the set maximum number of iterations. Use the mismatch filter coefficients from the last iteration as the optimized interference suppression filter coefficients, denoted as... ; Step S4 includes the following steps: The output of the radar echo signal after passing through the optimal interference suppression mismatch filter For, that is At this point, the peak value is the actual target signal, which is used to identify or track the target.

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