A method for suppressing intermittent sampling forwarding interference based on variational mode decomposition

Abstract

The present invention relates to a method for suppressing intermittent sampling forwarding interference based on variational modal decomposition, comprising: obtaining a target echo signal according to a transmitted signal; directly forwarding the interference signal and the target echo signal according to intermittent sampling to obtain a received signal of a radar; multiplying the received signal of the radar with the conjugate of a reference signal to obtain a de-skewing signal; decomposing the de-skewing signal by a variational modal decomposition method, obtaining multiple modal components after multiple iterations, and separating interference from the signal; based on the decomposed modal components, using a threshold segmentation method to eliminate interference, and then reconstructing the de-skewing signal from which interference is eliminated according to the modal components from which interference is eliminated, and then implementing pulse compression. The method of the present invention directly separates interference from the signal, eliminates interference more cleanly, does not have too much pulse pressure gain loss, and has low grating lobes.

Description

Technical Field

[0001] The present invention belongs to the technical field of radars and relates to a method for suppressing intermittent sampling forwarding interference based on variational mode decomposition. Background Art

[0002] Digital Radio Frequency Memory (DRFM), with its large-capacity digital storage and high-speed output forwarding capabilities, has become the primary implementation method and hardware foundation for generating coherent interference. Interrupted-Sampling Repeater Jamming (ISRJ) utilizes DRFM to intercept, delay, and forward radar transmission signals. It then leverages the matched filtering characteristics of pulse compression radar to achieve gain during signal processing, generating a highly coherent string of false targets. Traditional signal processing methods are unable to effectively identify and suppress ISRJ, significantly impacting radar target detection and parameter estimation.

[0003] Intrinsic Mode Functions (IMFs) can be generally understood as sub-signals decomposed from the original signal, representing amplitude-frequency modulated (AM) signals. VMD (Variational Mode Decomposition) assumes that all components are narrowband signals concentrated around their respective center frequencies. Therefore, VMD formulates a constrained optimization problem based on the component narrowband condition to estimate the center frequencies of signal components and reconstruct the corresponding components.

[0004] Currently, a method for countering intermittent sampling and forwarding interference based on segmented pulse compression of linear frequency modulation signals can be used to counter intermittent sampling and forwarding interference. Since intermittent sampling and forwarding interference involves partially sampling the signal before forwarding it, its time domain portion is discontinuous. To address this discontinuous nature of time domain sampling, the radar signal's matched filter is divided into uniform subsegments. Leveraging the orthogonality between subsegments and incorporating the concept of masking waveforms, a narrowband filter bank is used to separate the interference and target, then remove the interference. Finally, the signal is accumulated within and between pulses. However, when the jammer's interference parameters (sampling duration and forwarding duration) are unknown, segmented pulse compression requires continuous adjustment of the number of matched filter segments and the duration of each segment to achieve optimal segmentation. Furthermore, when the duration of each subsegment is too short, orthogonality between subsegments is difficult to achieve, resulting in residual interference. Summary of the Invention

[0005] In order to solve the above problems existing in the prior art, the present invention provides a method for suppressing intermittent sampling forwarding interference based on variational mode decomposition. The technical problem to be solved by the present invention is achieved through the following technical solutions:

[0006] An embodiment of the present invention provides a method for suppressing intermittent sampling forwarding interference based on variational mode decomposition, the method comprising:

[0007] Step 1: Based on the distance R between the target and the radar receiver and the delay time, the target echo signal is obtained according to the transmitted signal;

[0008] Step 2: directly forwarding the interference signal and the target echo signal according to intermittent sampling to obtain a radar receiving signal;

[0009] Step 3: multiplying the received signal of the radar by the conjugate of the reference signal to obtain a de-skewed signal, wherein the de-skewed signal includes a target echo de-skewed signal and an interference de-skewed signal;

[0010] Step 4: Decompose the de-skewed signal using the variational mode decomposition method. After multiple iterations, multiple modal components are obtained to separate the interference from the signal.

[0011] Step 5: Based on the decomposed modal components, the interference is eliminated using the threshold segmentation method, and then the interference-eliminated de-skewed signal is reconstructed according to the modal components of the interference, and then pulse compression is achieved.

[0012] In one embodiment of the invention, the transmission signal is represented by:

[0013]

[0014] Among them, S(t) is the transmitted signal, t is the time, T p is the pulse width of the signal, μ is the frequency modulation slope of the signal;

[0015] The target echo signal is expressed as:

[0016]

[0017] Among them, S r (t) is the target echo signal, A r is the target echo amplitude, τ is the delay time, τ=2R / c, c is the speed of light.

[0018] In one embodiment of the invention, the intermittent sampling and direct forwarding of the interference signal is expressed as:

[0019]

[0020] Among them, Sj (t) is the intermittent sampling and direct forwarding of interference signals, A j is the interference signal amplitude, N is the number of interference slices, 0≤n≤N, T j is the slice width of interference;

[0021] The received signal of the radar is expressed as:

[0022] S recv (t) = S r (t)+S J (t)

[0023] Among them, S recv (t) is the radar receiving signal.

[0024] In one embodiment of the invention, the reference signal is represented by:

[0025]

[0026] Among them, S ref (t) is the reference signal, t is time, T ref is the reference signal pulse width, τ ref is the reference signal delay, μ is the frequency modulation slope of the signal;

[0027] The de-skewing signal is expressed as:

[0028] S if (t) = S r_if (t)+S j_if (t)

[0029] Among them, S if (t) is the signal after de-skewing, S r_if (t) is the target echo de-slant signal, S j_if To interfere with the de-skew signal;

[0030] The target echo de-slant signal is expressed as:

[0031]

[0032] Among them, * is conjugated, T p is the pulse width of the signal, A r is the target echo amplitude, τ is the delay time;

[0033] The interference de-skew signal is expressed as:

[0034]

[0035] Among them, A j is the interference signal amplitude, N is the number of interference slices, 0≤n≤N, Tj is the slice width of the interference.

[0036] In one embodiment of the invention, step 4 includes:

[0037] Step 4.1: Obtain constraints that are satisfied based on the modal components and the de-skewed signal. The constraints that are satisfied are:

[0038]

[0039]

[0040] Among them, u k (t) is the kth modal component of the signal, ω k is the center frequency corresponding to the kth modal component, Indicates the {u k (t)}, {ω k}, represents the two-norm, st represents that the corresponding formula is satisfied, Indicates that the formula in the brackets is partial derivative with respect to time t, S if (t) is the signal after de-skewing;

[0041] Step 4.2: By augmenting the Lagrangian function, the constraints satisfied by the modal components and the de-skewed signal are equivalent to an unconstrained problem. The equivalent unconstrained problem is expressed as:

[0042]

[0043]

[0044] Where L represents the augmented Lagrangian function, λ(t) is the Lagrangian multiplier, and α is the second-order penalty factor. Denotes λ(t) and The inner product of

[0045] Step 4.3: Perform Fourier transform on the augmented Lagrangian function to obtain the transformed augmented Lagrangian function, which is expressed as:

[0046]

[0047] Among them, L({u k (ω)},{ω k},λ(ω)) is the transformed augmented Lagrangian function, S if (ω),u k (ω) and λ(ω) represent the de-skewed signal after Fourier transformation, the kth modal component, and the Lagrange multiplier, respectively, and ω is the frequency;

[0048] Step 4.4: Obtain the modal components and the center frequencies of the modal components after Fourier transformation according to the transformed augmented Lagrangian function, wherein the kth modal component u k (ω) is expressed as:

[0049]

[0050] Among them, u i (ω) is the i-th modal component after Fourier transform;

[0051] The center frequency ω of the kth modal component k Expressed as:

[0052]

[0053] Step 4.5: Based on the alternating multiplier method, the final mode is obtained according to the modal components after Fourier transformation and the center frequencies of the modal components obtained in step 4.4.

[0054] In one embodiment of the invention, step 4.5 includes:

[0055] Step 4.5.1. Determine the total number of modes K to be decomposed, set m = 0, and initialize λ 1 (ω), m is the number of iterations, where is the kth modal component after Fourier transform at the first iteration, is the center frequency of the kth modal component after the first iteration, λ 1 (ω) Lagrange multiplier after Fourier transformation at the first iteration;

[0056] Step 4.5.2: When the number of iterations m = m+1, update the modal component after Fourier transformation at the m+1th iteration, the kth modal component Expressed as:

[0057]

[0058] in, is the i-th modal component after Fourier transform at the m+1-th iteration, is the i-th modal component after Fourier transform at the m-th iteration, λ m (ω) is the Lagrange multiplier after Fourier transformation at the mth iteration, is the center frequency of the kth modal component at the mth iteration;

[0059] Update the center frequency of the m+1th modal component and the center frequency of the kth modal component Expressed as:

[0060]

[0061] Update the Lagrange multiplier after Fourier transformation at the m+1th iteration, which is expressed as:

[0062]

[0063] Among them, λ m (ω) is the Lagrange multiplier after Fourier transformation at the mth iteration, and β is the step size;

[0064] Step 4.5.3: Determine whether If not, continue to repeat steps 4.5.2 to 4.5.3. If satisfied, the decomposed mode is obtained, and the modal components after Fourier transformation at the m+1th iteration are inversely Fourier transformed to obtain the final modal components, where ∈ is the judgment condition for termination of iteration.

[0065] In one embodiment of the invention, step 5 includes:

[0066] Step 5.1: Accumulate the envelopes of the de-skewed signal corresponding to the S pulses to obtain an envelope mean, which is expressed as:

[0067]

[0068] Among them, E mean is the envelope mean, E s is the envelope of the de-skewed signal corresponding to the s-th pulse, 0≤s≤S;

[0069] Step 5.2: Obtain a threshold value according to the envelope average value. The threshold value is expressed as:

[0070] v=max(E mean ) / 4

[0071] Among them, v is the threshold, and max means taking the maximum value;

[0072] Step 5.3: Obtain the signal modal component after interference removal based on the relationship between the threshold and the final modal component. The kth modal component after interference removal is expressed as:

[0073]

[0074] Among them, u' k (t) is the kth modal component after removing interference, u kl (t) is the final k-th modal component;

[0075] Step 5.4: Obtain a de-skewed signal after removing interference according to the modal component after removing interference. The de-skewed signal after removing interference is expressed as:

[0076]

[0077] Among them, S if_dejam (t) is the de-skewed signal after removing interference;

[0078] Step 5.5: Perform Fourier transform on the de-skewed signal after removing interference to obtain the de-skewed signal S after Fourier transform. if_dejam (ω), S if_dejam (-ω) as a result of pulse compression.

[0079] Compared with the prior art, the present invention has the following beneficial effects:

[0080] The present invention deskews the linear frequency modulation signal and then decomposes it using variational mode decomposition. After variational mode decomposition, the signal is separated from the interference. Because the interference signal amplitude is much larger than the target echo, a threshold is used to remove the interference. Therefore, the method of the present invention directly separates the interference from the signal, resulting in relatively clean interference removal without significant pulse compression gain loss and low grating lobes.

[0081] Other aspects and features of the present invention will become apparent from the following detailed description, which proceeds with reference to the accompanying drawings. It should be understood, however, that the drawings are designed for illustrative purposes only and are not intended to limit the scope of the present invention, as reference should be made to the appended claims. It should also be understood that, unless otherwise indicated, the drawings are not necessarily drawn to scale and are intended merely to conceptually illustrate the structures and processes described herein. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] Figure 1 This is a flow chart of a method for suppressing intermittent sampling forwarding interference based on variational mode decomposition provided by an embodiment of the present invention;

[0083] Figure 2 This is a flow chart of an interference suppression algorithm provided by an embodiment of the present invention;

[0084] Figure 3 This is a schematic diagram of intermittent sampling direct forwarding interference provided by an embodiment of the present invention;

[0085] Figure 4 This is a time-frequency diagram of a received baseband signal provided by an embodiment of the present invention;

[0086] Figure 5 This is a time-frequency diagram of a signal after de-skewing provided by an embodiment of the present invention;

[0087] Figure 6 This is a time domain diagram of a VMD decomposition signal provided by an embodiment of the present invention;

[0088] Figure 7 This is a frequency domain diagram of a VMD decomposition signal provided by an embodiment of the present invention;

[0089] Figure 8 is a pulse pressure result before interference suppression provided by an embodiment of the present invention;

[0090] Figure 9 This is a pulse pressure result after interference suppression provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0091] The present invention will be further described in detail below with reference to specific examples, but the embodiments of the present invention are not limited thereto.

[0092] Example 1

[0093] See Figure 1 and Figure 2 , Figure 1 1 is a flow chart of a method for suppressing intermittent sampling forwarding interference based on variational mode decomposition provided by an embodiment of the present invention. Figure 2 This is a flow chart of an interference suppression algorithm provided by an embodiment of the present invention. Figure 2 The block diagrams of the received baseband signal and the de-skewing signal are both time-frequency diagrams, with the horizontal axis being time and the vertical axis being frequency. After de-skewing, the received signal is converted from a linear frequency modulation signal to a single carrier frequency signal. After VMD decomposition, the signal is separated from the interference, and the decomposition result block diagram shows a schematic diagram of the amplitude of the signal and the interference. An embodiment of the present invention provides a method for suppressing intermittent sampling forwarding interference based on variational mode decomposition. The method for suppressing intermittent sampling forwarding interference can specifically include steps 1 to 5, wherein:

[0094] Step 1: Based on the distance R between the target and the radar receiver and the delay time, the target echo signal is obtained according to the transmitted signal.

[0095] Specifically, a linear frequency modulation (LFM) signal is used as a pulse transmission baseband signal (ie, a transmission signal), and the transmission signal expression is as follows:

[0096]

[0097] Among them, S(t) is the transmitted signal, t is the time, T p is the pulse width of the signal, μ is the frequency modulation slope of the signal, then the bandwidth of the signal B=μT pAssuming the target is at a distance R from the radar receiver, the delay time of the echo signal relative to the transmitted signal is τ = 2R / c. Ignoring the influence of speed, the target echo signal can be obtained:

[0098]

[0099] Among them, S r (t) is the target echo signal, A r is the target echo amplitude, τ is the delay time, and c is the speed of light.

[0100] Step 2: Directly forward the interference signal and target echo signal according to intermittent sampling to obtain the radar receiving signal.

[0101] Specifically, intermittent sampling and forwarding interference samples the radar signal and then forwards it. The schematic diagram of intermittent sampling and direct forwarding interference is as follows: Figure 3 As shown in Figure 1, intermittent sampling repeated forwarding is similar to direct forwarding, but intermittent sampling repeated forwarding interference will repeatedly forward the signal multiple times after sampling the signal. Assuming the interference is self-defense interference, that is, the jammer is located at the same position as the target, so the distance between the jammer and the radar receiver is also R, and the corresponding delay time is also τ, the expression of the intermittent sampling direct forwarding interference signal can be obtained:

[0102]

[0103] Among them, S j (t) is the intermittent sampling and direct forwarding interference signal, A j is the interference signal amplitude, N is the number of interference slices, 0≤n≤N, T j is the slice width of the interference.

[0104] Therefore, the received signal expression of the radar is:

[0105] S recv (t) = S r (t)+S J (t) (4)

[0106] Among them, S recv (t) is the radar receiving signal.

[0107] Step 3: Multiply the radar received signal by the conjugate of the reference signal to obtain a de-skewed signal, wherein the de-skewed signal includes a target echo de-skewed signal and an interference de-skewed signal.

[0108] Specifically, the de-skew reference signal expression is as follows:

[0109]

[0110] Among them, S ref(t) is the reference signal, T ref is the reference signal pulse width, which is greater than the signal pulse width T p To be big, τ ref =2R ref / c is the reference signal delay, R ref is the distance corresponding to the reference signal.

[0111] The de-skewing signal can be obtained by multiplying the radar received signal with the conjugate of the reference signal. if (t) = S r_if (t)+S j_if (t), where S if (t) is the signal after de-skewing, S r_if is the target echo de-slant signal (i.e. the de-slant result of the target echo), S j_if is the interference de-skewed signal (ie, the de-skewed result of the interference signal).

[0112] The expression of the target echo de-slant signal is as follows:

[0113]

[0114] Among them, * is conjugated;

[0115] From the formula, we can see that the phase φ1(t)=2πμ(t ref -τ)t+jπ(τ 2 -τ ref 2 ), the instantaneous frequency is the derivative of the phase with respect to time, then the instantaneous frequency It can be seen that after de-skewing the signal, it becomes a single carrier frequency signal, and the signal frequency is related to the target distance.

[0116] The expression of interference de-skew signal is as follows:

[0117]

[0118] It can also be seen from the formula that after the interference signal is de-skewed, a single carrier frequency signal is obtained, and its instantaneous frequency can be expressed as f j_if =μ(τ ref -τ-T j ), and f r_if With μT j The frequency difference is large, so after de-skewing, the interference signal and the target echo signal become two signals with different single carrier frequencies, and this feature is used for subsequent interference separation processing.

[0119] Step 4: Decompose the de-skewed signal using the variational mode decomposition method. After multiple iterations, multiple modal components are obtained to separate the interference from the signal.

[0120] Step 4.1: Obtain the constraints satisfied based on the modal components and the de-skewed signal.

[0121] Specifically, K is the number of decomposed modes, {u k (t)}={u1(t),……,u K (t)},u k (t) is the kth modal component of the signal, 1≤k≤K, {ω k}={ω1,……,ω K},ω k is the center frequency corresponding to the kth modal component. We need to solve the modal components of the signal, that is, solve the following constraints:

[0122]

[0123] Among them, u k (t) is the kth modal component of the signal, ω k is the center frequency corresponding to the kth modal component, Indicates the {u k (t)}, {ω k}, represents the two-norm, st represents that the corresponding formula is satisfied, It means to find the partial derivative of the formula in the brackets with respect to time t.

[0124] Step 4.2: Equivalent the constraints satisfied by the modal components and the de-skewed signal to an unconstrained problem through augmented Lagrangian function.

[0125] Specifically, the Lagrangian multiplier λ(t) and the second-order penalty factor α are introduced, and the constrained inequality in step 4.1 is equivalent to an unconstrained problem through the augmented Lagrangian function. The equivalent unconstrained problem is expressed as:

[0126]

[0127] Where L represents the augmented Lagrangian function, Denotes λ(t) and The inner product of .

[0128] Step 4.3: Perform Fourier transform on the augmented Lagrangian function to obtain the transformed augmented Lagrangian function. The transformed augmented Lagrangian function is expressed as:

[0129]

[0130] Among them, L({u k (ω)},{ω k},λ(ω)) is the transformed augmented Lagrangian function, Sif (ω),u k (ω) and λ(ω) represent the de-skewing signal S if (t), kth modal component u k (t) and the Lagrange multiplier λ(t) after Fourier transformation, the de-skewed signal, the kth modal component and the Lagrange multiplier, ω is the frequency.

[0131] Step 4.4: Obtain the modal components and center frequencies of the modal components after Fourier transformation based on the transformed augmented Lagrangian function.

[0132] Specifically, first, k (ω) is updated, u k (ω)=argmin(L), transform the first term of the transformed augmented Lagrangian function from ω→ω-ω k ,get:

[0133]

[0134] The first term in the right side of formula (11) has only one relationship with u k (ω) corresponds to the integral at the minimum value of the two-norm, so we can get:

[0135]

[0136] The right side of formula (12) is k (ω) is the smallest when the first-order partial derivative is 0, that is:

[0137]

[0138] So we can get u k The update formula of (ω) is:

[0139]

[0140] Among them, u i (ω) is the i-th modal component after Fourier transform.

[0141] Then update ω k , The right side of the equation is ω k The minimum is achieved when the first-order partial derivative is 0, so the update formula can be obtained:

[0142]

[0143] Step 4.5: Based on the alternating substitution multiplier method (ADMM), the final mode is obtained according to the modal components after Fourier transformation and the center frequencies of the modal components obtained in step 4.4.

[0144] Step 4.5.1. Determine the total number of modes K to be decomposed, set m = 0, and initialize λ 1 (ω), m is the number of iterations, where is the kth modal component after Fourier transform at the first iteration, is the center frequency of the kth modal component after the first iteration, λ 1 (ω) Lagrange multiplier after Fourier transformation at the first iteration.

[0145] Because the self-defense intermittent sampling direct forwarding interference only produces a single frequency signal after de-skewing, the total number of decomposed modes is set to 3. This can effectively separate the interference while reducing the frequency impact caused by sudden changes in signal amplitude. For repeated forwarding interference, if it is forwarded q times, the interference will have q frequency components after de-skewing, so the total number of decomposed modes is set to q + 2.

[0146] Step 4.5.2: When the number of iterations m = m + 1, update The kth modal component after Fourier transformation at the m+1th iteration Expressed as:

[0147]

[0148] in, is the i-th modal component after Fourier transform at the m+1-th iteration, is the i-th modal component after Fourier transform at the m-th iteration, λ m (ω) is the Lagrange multiplier after Fourier transformation at the mth iteration, is the center frequency of the kth modal component at the mth iteration;

[0149] renew The center frequency of the kth modal component of the m+1th order Expressed as:

[0150]

[0151] λ(ω) utilizes {u k (ω)} and S if (ω) is updated, and the Lagrange multiplier λ after Fourier transformation at the m+1th iteration is updated. m+1 (ω), expressed as:

[0152]

[0153] Among them, λ m(ω) is the Lagrange multiplier after Fourier transformation at the mth iteration, and β is the step size of the iterative update.

[0154] Step 4.5.3: Determine whether If it is not satisfied, continue to repeat steps 4.5.2 to 4.5.3. If it is satisfied, the decomposed mode is obtained, and the kth modal component after Fourier transform at the m+1th iteration is Perform inverse Fourier transform to obtain the final kth modal component u kl (t), thus, we can obtain Perform inverse Fourier transform to obtain the final mode {u kl (t)}, where ∈ is the judgment condition for the termination of iteration, and ∈ can be set according to actual needs.

[0155] Step 5: Based on the decomposed modal components, the interference is eliminated using the threshold segmentation method, and then the interference-eliminated de-skewed signal is reconstructed according to the modal components of the interference, and then pulse compression is achieved.

[0156] Since the interference power is much higher than the target echo power at the radar receiver, the interference and signal can be judged by the amplitude of the signal based on the obtained modal decomposition results.

[0157] Step 5.1: Accumulate the envelopes of the de-skewed signals corresponding to the S pulses to obtain the envelope mean, which is expressed as:

[0158]

[0159] Among them, E mean is the envelope mean, E s is the envelope of the de-skewed signal corresponding to the s-th pulse, 0≤s≤S.

[0160] Step 5.2: Get the threshold value based on the envelope average value. The threshold value is expressed as:

[0161] v=max(E mean ) / 4

[0162] Among them, v is the threshold and max means taking the maximum value.

[0163] Step 5.3: Obtain the signal modal component after interference removal based on the relationship between the threshold and the final modal component.

[0164] Specifically, the interference is removed based on the threshold v to obtain the signal modal component after the interference is removed. The kth modal component after the interference is removed is expressed as:

[0165]

[0166] Among them, u' k (t) is the kth modal component after removing interference.

[0167] Step 5.4: Obtain the interference-removed de-skewed signal based on the modal components after interference removal. The interference-removed de-skewed signal is expressed as:

[0168]

[0169] Among them, S if_dejam (t) is the de-skewed signal after removing interference.

[0170] Step 5.5: Perform Fourier transform on the de-skewed signal after removing interference to obtain the de-skewed signal S after Fourier transform. if_dejam (ω), from formula (6), we can know that the de-skew signal S if_dejam The frequency of (ω) is negatively correlated with the target distance, so S if_dejam (-ω) as a result of pulse compression.

[0171] In order to demonstrate the method provided by the present invention, the following simulation experiment is used for illustration:

[0172] Set the parameters for transmitting LFM signal: bandwidth 40MHz, pulse width 20us, sampling rate 160MHz; intermittent sampling and forwarding interference parameters: sampling time 2us, forwarding once, interference-to-signal ratio 20dB; set the signal-to-noise ratio to 10dB. The time-frequency diagram of the signal before and after de-skewing is as follows Figure 4 and Figure 5 As shown, from Figure 4 and Figure 5 It can be seen from the figure that after de-skewing, both the signal and the interference become single-frequency signals.

[0173] After obtaining the de-skewed signal, perform VMD decomposition on the signal. Set the total number of VMD decomposition modes K = 3, the iteration termination judgment condition ∈ = 1e-6, and the decomposed signal time domain and frequency domain results are as follows: Figure 6 、 Figure 7 As shown in the figure, it can be seen that modal component 2 is the interference signal and modal component 3 is the target echo signal, successfully separating the interference from the signal. Then the interference is removed and we get Figure 9 The pulse pressure results after interference suppression are shown in the figure. Figure 8 It can be seen that the interference is successfully suppressed.

[0174] Since the segmented pulse compression is performed by combining the sampled matched filter sub-segments with the received signal for pulse compression and then accumulating, and the interference is sampled at intervals, the matched filters used at the end will be much less than the complete matched filters, which will inevitably result in a loss of more pulse compression gain; at the same time, the intermittent matched filters will make the pulse compression result grating lobe relatively high; there will be spectrum leakage between adjacent matched filter sub-segments, which will cause some interfering pulse compression results to remain. The present invention de-skews the linear frequency modulation signal and then decomposes the signal using variational mode decomposition. After variational mode decomposition, the signal and interference are separated. Since the amplitude of the interference signal is much larger than the target echo, a threshold is used to remove the interference. Therefore, the method of the present invention directly separates the interference from the signal, removes the interference more cleanly, does not cause too much pulse compression gain loss, and has a lower grating lobe.

[0175] In the description of an invention, the terms "first" and "second" are used for descriptive purposes only and should not be understood to indicate or imply relative importance or implicitly specify the number of the technical features indicated. Thus, a feature specified as "first" or "second" may explicitly or implicitly include one or more of such features. In the description of the invention, "plurality" means two or more, unless otherwise specifically defined.

[0176] In the description of this specification, the reference terms "one embodiment," "some embodiments," "example," "specific example," or "some examples" mean that the specific features, structures, materials, or characteristic data points described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristic data points described can be combined in any appropriate manner in any one or more embodiments or examples. In addition, those skilled in the art can combine and combine different embodiments or examples described in this specification.

[0177] The above is a further detailed description of the present invention in conjunction with specific preferred embodiments, and the specific implementation of the present invention should not be considered to be limited to these descriptions. For those skilled in the art of the present invention, without departing from the concept of the present invention, several simple deductions or substitutions can be made, which should be considered to fall within the scope of protection of the present invention.

Claims

1. A method for suppressing intermittent sampling forwarding interference based on variational mode decomposition, characterized in that: The inhibition method comprises: Step 1: Based on the distance R between the target and the radar receiver and the delay time, the target echo signal is obtained according to the transmitted signal; Step 2: directly forwarding the interference signal and the target echo signal according to intermittent sampling to obtain a radar receiving signal; Step 3: multiplying the received signal of the radar by the conjugate of the reference signal to obtain a de-skewed signal, wherein the de-skewed signal includes a target echo de-skewed signal and an interference de-skewed signal; Step 4: Decompose the de-skewed signal using the variational mode decomposition method. After multiple iterations, multiple modal components are obtained to separate the interference from the signal. Step 5: Based on the decomposed modal components, the interference is eliminated using the threshold segmentation method, and then the interference-eliminated de-skewed signal is reconstructed according to the modal components of the interference, and then pulse compression is achieved.

2. The method for suppressing intermittent sampling forwarding interference based on variational mode decomposition according to claim 1 is characterized in that: The transmission signal is expressed as: Among them, S(t) is the transmitted signal, t is the time, T p is the pulse width of the signal, μ is the frequency modulation slope of the signal; The target echo signal is expressed as: Among them, S r (t) is the target echo signal, A r is the target echo amplitude, τ is the delay time, τ=2R / c, c is the speed of light.

3. The method for suppressing intermittent sampling forwarding interference based on variational mode decomposition according to claim 2, characterized in that: The intermittent sampling and direct forwarding interference signal is expressed as: Among them, S j (t) is the intermittent sampling and direct forwarding interference signal, A j is the interference signal amplitude, N is the number of interference slices, 0≤n≤N, T j is the slice width of interference; The received signal of the radar is expressed as: S recv (t)=S r (t)+S J (t) Among them, S recv (t) is the radar receiving signal.

4. The method for suppressing intermittent sampling forwarding interference based on variational mode decomposition according to claim 1, characterized in that: The reference signal is expressed as: Among them, S ref (t) is the reference signal, t is time, T ref is the reference signal pulse width, τ ref is the reference signal delay, μ is the frequency modulation slope of the signal; The de-skewing signal is expressed as: S if (t)=S r_if (t)+S j_if (t) Among them, S if (t) is the signal after de-skewing, S r_if (t) is the target echo de-slant signal, S j_if To interfere with the de-skew signal; The target echo de-slant signal is expressed as: Among them, * is conjugated, T p is the pulse width of the signal, A r is the target echo amplitude, τ is the delay time; The interference de-skew signal is expressed as: Among them, A j is the interference signal amplitude, N is the number of interference slices, 0≤n≤N, T j is the slice width of the interference.

5. The method for suppressing intermittent sampling forwarding interference based on variational mode decomposition according to claim 1, characterized in that: The step 4 comprises: Step 4.1: Obtain constraints that are satisfied based on the modal components and the de-skewed signal. The constraints that are satisfied are: Among them, u k (t) is the kth modal component of the signal, ω k is the center frequency corresponding to the kth modal component, Indicates the {u k (t)}, {ω k }, represents the two-norm, st represents that the corresponding formula is satisfied, Indicates that the formula in the brackets is partial derivative with respect to time t, S if (t) is the signal after de-skewing; Step 4.2: By augmenting the Lagrangian function, the constraints satisfied by the modal components and the de-skewed signal are equivalent to an unconstrained problem. The equivalent unconstrained problem is expressed as: Where L represents the augmented Lagrangian function, λ(t) is the Lagrangian multiplier, and α is the second-order penalty factor. Denotes λ(t) and The inner product of Step 4.3: Perform Fourier transform on the augmented Lagrangian function to obtain the transformed augmented Lagrangian function, which is expressed as: Among them, L({u k (ω)},{ω k },λ(ω)) is the transformed augmented Lagrangian function, S if (ω),u k (ω) and λ(ω) represent the de-skewed signal after Fourier transformation, the kth modal component, and the Lagrange multiplier, respectively, and ω is the frequency; Step 4.4: Obtain the modal components and the center frequencies of the modal components after Fourier transformation according to the transformed augmented Lagrangian function, wherein the kth modal component u k (ω) is expressed as: Among them, u i (ω) is the i-th modal component after Fourier transform; The center frequency ω of the kth modal component k Expressed as: Step 4.5: Based on the alternating multiplier method, the final mode is obtained according to the modal components after Fourier transformation and the center frequencies of the modal components obtained in step 4.

4.

6. The method for suppressing intermittent sampling forwarding interference based on variational mode decomposition according to claim 5, characterized in that: The step 4.5 includes: Step 4.5.

1. Determine the total number of modes K to be decomposed, set m = 0, and initialize m is the number of iterations, where is the kth modal component after Fourier transform at the first iteration, is the center frequency of the kth modal component after the first iteration, λ 1 (ω) Lagrange multiplier after Fourier transformation at the first iteration; Step 4.5.2: When the number of iterations m = m+1, update the modal component after Fourier transformation at the m+1th iteration, the kth modal component Expressed as: in, is the i-th modal component after Fourier transform at the m+1-th iteration, is the i-th modal component after Fourier transform at the m-th iteration, λ m (ω) is the Lagrange multiplier after Fourier transformation at the mth iteration, is the center frequency of the kth modal component at the mth iteration; Update the center frequency of the m+1th modal component and the center frequency of the kth modal component Expressed as: Update the Lagrange multiplier after Fourier transformation at the m+1th iteration, which is expressed as: Among them, λ m (ω) is the Lagrange multiplier after Fourier transformation at the mth iteration, and β is the step size; Step 4.5.3: Determine whether If not, continue to repeat steps 4.5.2 to 4.5.

3. If satisfied, the decomposed mode is obtained, and the modal components after Fourier transformation at the m+1th iteration are inversely Fourier transformed to obtain the final modal components, where ∈ is the judgment condition for termination of iteration.

7. The method for suppressing intermittent sampling forwarding interference based on variational mode decomposition according to claim 1, characterized in that: The step 5 comprises: Step 5.1: Accumulate the envelopes of the de-skewed signal corresponding to the S pulses to obtain an envelope mean, which is expressed as: Among them, E mean is the envelope mean, E s is the envelope of the de-skewed signal corresponding to the s-th pulse, 0≤s≤S; Step 5.2: Obtain a threshold value according to the envelope average value. The threshold value is expressed as: v=max(E mean ) / 4 Among them, v is the threshold, and max means taking the maximum value; Step 5.3: Obtain the signal modal component after interference removal based on the relationship between the threshold and the final modal component. The kth modal component after interference removal is expressed as: Among them, u' k (t) is the kth modal component after removing interference, u kl (t) is the final k-th modal component; Step 5.4: Obtain a de-skewed signal after removing interference according to the modal component after removing interference. The de-skewed signal after removing interference is expressed as: Among them, S if_dejam (t) is the de-skewed signal after removing interference; Step 5.5: Perform Fourier transform on the de-skewed signal after removing interference to obtain the de-skewed signal S after Fourier transform. if_dejam (ω), S if_dejam (-ω) as a result of pulse compression.

Images