Intermittent sampling forwarding interference suppression method

Abstract

The invention discloses an intermittent sampling and forwarding interference suppression method, which belongs to the technical field of radar anti-interference signal processing, and comprises the following steps of: after receiving an echo signal with interference, minimizing an interference suppression ratio and a generalized integral sidelobe ratio of a non-matched filter as a target, and taking signal-to-noise ratio loss as a constraint condition; constructing a non-matched filter optimization model; and constructing an augmented Lagrange function to solve the non-matched filter optimization model, and outputting an optimal non-matched filter. According to the non-matched filter optimization model, the signal-to-noise ratio loss is used as a direct constraint condition, the output result of the non-matched filter is more directly displayed, compared with other methods, multiple constraint terms are fused into the model, the constraint conditions are reduced, the optimal result is easier to achieve through a single constraint condition, and the optimization effect is better.

Description

Technical Field

[0001] The present invention relates to the technical field of radar anti-interference signal processing, and in particular to an intermittent sampling and forwarding interference suppression method. Background Art

[0002] Radar is widely used in ground observation and space exploration missions, and plays an important role in the civilian field. With the widespread application of digital radio frequency memory (DRFM) technology in electronic jamming systems, the types of active coherent interference are increasing, the electromagnetic environment faced by radar is becoming increasingly complex, and various electronic interferences seriously restrict the detection performance of radar. Interrupted Sampling Repeater Jamming (ISRJ) is a form of coherent interference. Through digital radio frequency memory technology, the jammer is allowed to quickly sample, process and forward the radar signal after receiving it, reducing the high isolation requirements between the transmitting and receiving antennas. The radar signal is sampled and repeated using periodic sampling pulses to generate dense false targets, causing dense interference effects on the radar. In addition, based on digital radio frequency memory technology, the jammer can quickly sample and forward the radar signal, thereby reducing the delay time of the jamming signal. Due to the technical advantages of intermittent sampling jamming, electronic countermeasures have become a difficult problem and hot topic that more and more researchers are concerned about.

[0003] Existing methods for suppressing intermittent sampling interference can be divided into the following categories:

[0004] (1) The first type of method is mainly based on the processing of received signals, including bandpass filter design, time-frequency analysis, etc. Among them, the bandpass filter method suppresses intermittent sampling interference by designing a bandpass filter for echo segments; the time-frequency analysis method uses short-time Fourier transform to extract the time-frequency characteristics of echo and interference signals, and filters the interference signal in the time-frequency transform domain.

[0005] (2) The second method is to design the waveform of the radar transmission signal to counter the radar. It mainly uses phase-coded waveform design to make the echo and interference signal orthogonal, reducing the difficulty of separating the interference and echo signals. It has high flexibility and strong optimizability, and is widely used to counter active deception interference.

[0006] The above method for suppressing intermittent sampling interference has the following problems:

[0007] (1) The bandpass filter method relies on parameters such as the center frequency, bandwidth, and filter order. When completely separating interference from the signal, it will destroy the complete spectrum of the linear frequency modulation signal, resulting in the appearance of grating lobes in the pulse compression result. The time-frequency analysis method will destroy the target information covered by the interference area in the time-frequency transform domain.

[0008] (2) The anti-interference effect of the countermeasure method based only on waveform design is worse than that of the method of jointly designing waveform and non-matching filter.

[0009] Regarding the design method of non-matching filter, the invention patent application with publication number CN117289217A and patent name "Method and device for joint transmission and reception to resist intermittent sampling forwarding interference" discloses: taking the integration level of interference signal and the integration sidelobe level of target signal as the goal, and considering the waveform constant modulus constraint, receiving filter energy constraint and non-matching filter peak loss constraint, a joint constraint optimization objective function for resisting intermittent sampling forwarding interference is established, and it is solved and updated iteratively to output the current radar transmission waveform and the non-matching filter used by the radar receiving end. The method model of non-matching filter to resist intermittent sampling forwarding interference in this patent application constrains the signal-to-noise ratio through multiple constraints. Compared with a single constraint, the optimization effect needs to be improved. Summary of the invention

[0010] The purpose of the present invention is to overcome the problems of the prior art and provide an intermittent sampling forwarding interference suppression method.

[0011] The object of the present invention is to achieve the following technical solution: a method for suppressing intermittent sampling and forwarding interference, the method comprising the following steps:

[0012] After receiving the echo signal with interference, the non-matched filter optimization model is constructed with the goal of minimizing the interference suppression ratio and generalized integrated sidelobe ratio of the non-matched filter and the signal-to-noise ratio loss as a constraint condition.

[0013] An augmented Lagrangian function is constructed to solve the non-matched filter optimization model and output the optimal non-matched filter.

[0014] In one example, the non-matched filter optimization model is:

[0015] ;

[0016] in, represents the optimization weight; represents the interference suppression ratio; represents the generalized integrated sidelobe ratio; Indicates signal-to-noise ratio loss; Indicates the lower limit of signal-to-noise ratio loss.

[0017] In one example, the interference suppression ratio The calculation expression is:

[0018] ;

[0019] in, and The length is A column vector composed of 0 and 1 (N is a preset value used to determine the vector length) is used to select the interference energy part and the main lobe part in the complete echo signal respectively; represents the Hadamard product; Indicates the target signal filtering result; Indicates the interference signal filtering result; Solve for the p-norm. When the p-norm approaches infinity, the interference suppression ratio In the calculation expression of, the numerator represents the interference energy and the denominator represents the signal main lobe energy.

[0020] In one example, the generalized integrated sidelobe ratio The calculation expression is:

[0021] ;

[0022] in, and Indicates the length is The column vectors of 0 and 1 are used to select the side lobe part and the main lobe part of the complete echo signal respectively; represents the Hadamard product; Indicates the target signal filtering result; Solve for the p-norm.

[0023] In one example, the signal-to-noise ratio loss The calculation expression is:

[0024] ;

[0025] in, represents conjugate transpose; represents an unmatched filter; Indicates complete echo signal; loss of signal-to-noise ratio In the calculation expression of , the numerator represents the signal energy after filtering, and the denominator represents the signal energy before filtering.

[0026] In one example, before the step of constructing the non-matched filter optimization model, the method further includes:

[0027] According to the sampling function of the intermittent sampling forwarding interference, the discrete form representation of the signal interference component and the signal non-interference component after zero padding is calculated;

[0028] Obtain the complete echo signal and the interference signal filtering results according to the discrete form representation after the signal interference component and the signal non-interference component are filled with zero;

[0029] Calculate the peak sidelobe ratio of the non-matched filter output result in the absence of interference and the peak sidelobe ratio of the interference signal filtering result;

[0030] According to the peak sidelobe ratio of the non-matched filter output result and the peak sidelobe ratio of the interference signal filtering result, the optimal phase coding transmission waveform optimization objective function for resisting intermittent sampling forwarding interference is established;

[0031] The optimal phase-coded transmit waveform optimization objective function is solved by the gradient iteration method, and the optimal phase-coded transmit waveform is output.

[0032] In one example, the discrete form of the signal interference component and the signal non-interference component after zero padding is expressed as:

[0033] ;

[0034] ;

[0035] in, and Represent the signal uninterfered component and signal interfered component respectively; is the discrete mathematical form of the sampling function, which is composed of 0 and 1 with a length of A column vector of , where 1 indicates sampling and 0 indicates no sampling; represents the Hadamard product; Represents an imaginary unit; transmits a signal , Indicates The phase of the sampling points, the signal exists sampling points; represents transpose; Indicates the length The unit value matrix of .

[0036] In one example, the complete echo signal And interference signal filtering results for:

[0037] ;

[0038] ;

[0039] in, represents the inverse Fourier transform matrix; Indicates the length is The Fourier transform matrix of represents Hadamard product; * represents conjugation; and They represent the signal uninterfered component and the signal interfered component respectively.

[0040] In one example, the peak sidelobe ratio of the non-matched filter output is , Peak sidelobe ratio of interference signal filtering result for:

[0041] ;

[0042] ;

[0043] in, and Indicates the length is 0 and 1 column vectors, which are used to select the complete echo signal The middle side lobe part and the main lobe part; The length is A column vector of 0s and 1s, used to select the complete echo signal The interference energy part; Indicates the interference signal filtering result; For the discrete p paradigm, when p approaches infinity, Approaching the maximum value of the vector; It is an output without modulation interference, and its result does not change with the sampling function.

[0044] In one example, the optimal phase-coded transmission waveform optimization objective function for resisting intermittent sampling forwarding interference is for:

[0045] ;

[0046] in, Represents optimization weight; Represents the peak sidelobe ratio of the non-matched filter output; Indicates the peak sidelobe ratio of the interference signal filtering result.

[0047] It should be further explained that the technical features corresponding to the above examples can be combined or replaced with each other to form a new technical solution.

[0048] Compared with the prior art, the technical solution provided by the present invention brings at least the following beneficial effects:

[0049] (1) In one example, the non-matching filter counteracting intermittent sampling forwarding suppression model (non-matching filter optimization model) takes the signal-to-noise ratio loss as a direct constraint condition, which more directly displays the output result of the non-matching filter. Compared with other methods, multiple constraints are integrated into the model, which reduces the constraints. A single constraint condition is easier to achieve the optimal result, and the optimization effect is better. At the same time, when considering the output result of the transmitted waveform after passing through the non-matching filter, the single peak sidelobe ratio is no longer used as the design indicator, and a generalized comprehensive sidelobe evaluation indicator is introduced, which has a better optimization effect on the waveform detection performance.

[0050] (2) In one example, before the radar transmits a signal, an optimal phase-coded transmit waveform suitable for suppressing intermittent sampling forwarding interference is designed based only on the interference sampling function. The transmit waveform can be optimized and designed independently without using an unmatched filter.

[0051] (3) In one example, after receiving an echo with interference, a non-matching filter counteracting intermittent sampling forwarding suppression model based on fast Fourier transform is constructed according to the intermittent sampling forwarding interference sampling function and the coded signal designed before transmission. The transmission signal and the non-matching filter can be optimized and designed independently, that is, there is no need to design the interference signal under the premise of a known non-matching filter, nor is there any need to design the non-matching filter signal under the premise of a known interference signal, which is convenient for practical application. At the same time, compared with the model based on convolution calculation, the non-matching filter counteracting intermittent sampling forwarding suppression model based on fast Fourier transform in this application has faster calculation efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0053] Figure 1 A method flow chart provided for an example of the present invention;

[0054] Figure 2 A method flow chart is provided for a preferred example of the present invention. DETAILED DESCRIPTION

[0055] To make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be described in detail and completely in conjunction with the drawings in the implementation of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings can be arranged and designed using different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the present application for protection, but merely represents selected embodiments of the present invention.

[0056] The technical solution of the present invention is described clearly and completely below in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0057] In addition, the technical features involved in the different embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0058] In one example, if Figure 1 As shown, a method for suppressing intermittent sampling forwarding interference, specifically a method for designing an unmatched filter to resist intermittent sampling interference, comprises the following steps:

[0059] S10: After the radar receives the echo signal with interference, the non-matching filter optimization model is constructed with the goal of minimizing the interference suppression ratio and generalized integrated sidelobe ratio of the non-matching filter and the signal-to-noise ratio loss as a constraint condition;

[0060] S20: Construct an augmented Lagrangian function to solve the non-matched filter optimization model and output the optimal non-matched filter.

[0061] Specifically, before the signal is transmitted, the most suitable phase-encoded waveform parameter configuration is predetermined according to the pulse width of the interference signal and the set sampling period. After receiving the echo signal carrying intermittent sampling forwarding interference, the non-matching filter will be flexibly set according to the sampling characteristics of these signals. In this process, the primary concern is how the non-matching filter affects the final output effect to ensure that its efficiency is maximized. In this example, after receiving the echo signal with interference, a non-matching filter design model that comprehensively optimizes the interference suppression ratio and the integral sidelobe ratio is established with the signal-to-noise ratio loss as a constraint. The optimization model suppresses interference to the maximum extent while ensuring the output signal performance. This model does not require the constraints of waveform constant modulus constraints and receiving filter energy constraints, which have been included in mathematical modeling. When constructing a non-matching filter sequence, the existing model uses a constant energy constraint, which reduces the optimization effect in this constraint, and the model of the present invention converts the constraint into a signal-to-noise ratio model without affecting the output result.

[0062] In one example, the non-matched filter optimization model is:

[0063] ;

[0064] in, represents the optimization weight; represents the interference suppression ratio; represents the generalized integrated sidelobe ratio; Indicates signal-to-noise ratio loss; Indicates the lower limit of signal-to-noise ratio loss.

[0065] In one example, the interference suppression ratio The calculation process is as follows:

[0066] Get the result after the target signal and interference signal pass through the non-matched filter:

[0067] ;

[0068] ;

[0069] in, Indicates that the signal has no interference component; represents the signal interference component; Is the length The Fourier transform matrix of It is the inverse Fourier transform matrix. Generally, the interference suppression effect of the non-matched filter is evaluated by comparing the interference energy after suppression with the signal energy. It can be expressed as

[0070] ;

[0071] in, and The length is The column vectors of 0 and 1 are used to select the interference energy part and the main lobe part of the complete echo signal respectively; represents the Hadamard product; Indicates the target signal filtering result; Indicates the interference signal filtering result; Solve for the p norm. When p approaches infinity, the interference suppression ratio In the calculation expression of, the numerator represents the interference energy and the denominator represents the signal main lobe energy.

[0072] This example uses Fourier transform for calculation, which is simpler and more efficient than using convolution for calculation.

[0073] In one example, the design of the non-matched filter needs to consider the output signal performance. In this example, the generalized integrated sidelobe ratio is used as the signal evaluation index. The calculation expression is:

[0074] ;

[0075] in, and Indicates the length is The column vectors of 0 and 1 are used to select the side lobe part and the main lobe part of the complete echo signal respectively; represents the Hadamard product; Indicates the target signal filtering result; Solve for the p-norm. When p=2, the generalized integral sidelobe ratio The calculation expression is expressed as the peak sidelobe ratio (PSLR) of the signal. When p approaches infinity, the generalized integrated sidelobe ratio The calculation expression represents the signal’s Integration Side Lobe Ratio (ISLR).

[0076] In this example, when considering the output result of the transmitted waveform after passing through the non-matched filter, a single peak sidelobe ratio is no longer used as a design indicator. Instead, a generalized comprehensive sidelobe evaluation indicator is introduced. When optimizing the waveform output result, two design indicators, peak sidelobe ratio or integral sidelobe ratio, are used, which has a better effect on optimizing the waveform detection performance.

[0077] In one example, a non-matching filter changes the spectrum of a signal, amplifying or suppressing signal components of a specific frequency, which usually affects the signal-to-noise ratio of the signal. Therefore, when using a non-matching filter to suppress interference, the signal-to-noise ratio loss of the signal must be considered. After the signal is processed by a non-matching filter, the signal-to-noise ratio loss It is expressed as:

[0078] ;

[0079] in, represents conjugate transpose; represents an unmatched filter; Indicates complete echo signal; loss of signal-to-noise ratio In the calculation expression of , the numerator represents the signal energy after filtering, and the denominator represents the signal energy before filtering.

[0080] In one example, in order to solve the non-matched filter optimization model, an augmented Lagrangian function is constructed and a penalty term is introduced into the objective function. It is expressed as:

[0081]

[0082] in, is the Lagrange multiplier; is the penalty factor used to adjust the impact of the penalty term; the gradient of the augmented Lagrangian function is expressed as:

[0083]

[0084] in, Represents the gradient; when using the augmented Lagrangian function for optimization, the gradient iteration optimization method is selected to minimize the augmented Lagrangian function value. When the function derivative is less than the gradient optimization accuracy Stop the iteration when , and determine whether the result meets the termination condition; if not, update the Lagrange multiplier under different constraints , and penalty factor Iterate again to ensure that interference suppression, signal-to-noise ratio loss and signal sidelobe limiting are all met in the final result.

[0085] The present invention also includes a method for suppressing intermittent sampling forwarding interference based on a radar transmission waveform and a non-matching filter joint design, including the above-mentioned anti-intermittent sampling interference non-matching filter design method, and before executing the anti-intermittent sampling interference non-matching filter design method, it also includes

[0086] In one example, a design method for a phase-coded waveform and a non-matched filter with known prior information is proposed, that is, before the step of constructing a non-matched filter optimization model, according to the signal sampling characteristics of intermittent sampling forwarding interference, the relationship between the interference component and the non-interference component of the signal is analyzed in the waveform design process, and a waveform design method with known prior information is proposed, including the following steps:

[0087] S010: According to the sampling function of intermittent sampling forwarding interference, the discrete form representation of the signal interference component and the signal non-interference component after zero padding is calculated. By analyzing the sampling function, it can be determined at which time points the signal will be sampled to form an interference signal, and the unsampled part constitutes the non-interference component of the signal.

[0088] S020: Obtain the complete echo signal and the interference signal filtering result according to the discrete form representation after zero padding of the signal interference component and the signal non-interference component. The discrete form representation after zero padding is conducive to accurately representing and processing the signal, thereby achieving effective separation and processing of the complete signal and the interference component, and then obtaining the complete echo signal and the interference signal filtering result.

[0089] S030: Calculate the peak sidelobe ratio of the non-matched filter output result in the absence of interference and the peak sidelobe ratio of the interference signal filtering result.

[0090] S040: Establish an optimal phase-coded transmission waveform optimization objective function for resisting intermittent sampling forwarding interference according to the peak sidelobe ratio of the non-matched filter output result and the peak sidelobe ratio of the interference signal filtering result.

[0091] S050: Solve the optimal phase-coded transmit waveform optimization objective function through the gradient iteration method, and output the optimal phase-coded transmit waveform.

[0092] In one example, it is assumed that before the radar transmits a signal, the sampling function of the intermittent sampling forwarding interference is known. At this time, the sampling function for:

[0093] ;

[0094] in, represents a rectangular pulse function; represents the time variable; Indicates the signal interception time; Indicates the pulse width of the interference; represents the g-th interference pulse; Indicates the number of interference pulses; represents the Dirac function; Indicates the pulse repetition interval of the interference.

[0095] Correspondingly, the discrete form of the signal interference component and the signal non-interference component after zero padding is expressed as:

[0096] ;

[0097] ;

[0098] in, is the discrete mathematical form of the sampling function, which is composed of 0 and 1 with a length of A column vector of , where 1 indicates sampling and 0 indicates no sampling; Represents an imaginary unit; transmits a signal , Indicates The phase of the sampling points, the signal exists sampling points; represents transpose; Indicates the length is The unit value matrix of .

[0099] When designing the waveform, it is necessary to enhance the signal without interference The autocorrelation performance of and interference component The cross-correlation performance is thus chosen As a non-matched filter; however, when using a non-matched filter, the filter input is the complete echo signal, so the uninterrupted component is promoted in the waveform design The autocorrelation performance should be to enhance the complete signal and the undisturbed component signal The cross-correlation results.

[0100] In one example, the complete echo signal And interference signal filtering results for:

[0101] ;

[0102] ;

[0103] in, represents the inverse Fourier transform matrix; Indicates the length is The Fourier transform matrix of ; * indicates conjugation.

[0104] In one example, the peak-to-sidelobe ratio is often used to evaluate waveform performance during waveform design. The discrete form of the peak-to-sidelobe ratio as a result of the unmatched filter output is:

[0105] ;

[0106] in, For the discrete p-normal form, when Approaching infinity, Approaching the maximum value of the vector;

[0107] For interference signal filtering results The energy suppression can also be evaluated by the above evaluation method. Then the interference signal filtering result is The peak sidelobe ratio is expressed in discrete form as:

[0108] ;

[0109] in, It is the output without modulation interference, and its result does not change with the sampling function. The calculation expression is:

[0110] ;

[0111] In this example, The calculation expression of is actually an expression for calculating the correlation between the interference component and the undisturbed component.

[0112] In one example, the optimal phase-coded transmission waveform optimization objective function for resisting intermittent sampling forwarding interference is for:

[0113] ;

[0114] in, Represents optimization weight.

[0115] In one example, the calculation process for solving the optimal phase-encoded transmit waveform optimization objective function is as follows:

[0116] calculate about and The gradient of is:

[0117] ;

[0118] Where: and Respectively expressed as:

[0119]

[0120]

[0121] in, represents the overall objective function of waveform optimization; operator Indicates the extraction of the real part of the parameter; operator Indicates the modulus of each element in the solution vector. The above problem is an unconstrained optimization problem with a known gradient. Through the gradient iteration method, the step size and gradient of each cycle are continuously updated to iteratively reduce the objective function to solve the optimization problem.

[0122] Combining the above examples, we can obtain a preferred example of the present invention, such as Figure 2 As shown, at this time, the method of the present invention comprises the following steps:

[0123] S100: Calculate the discrete form representation of the signal interference component and the signal non-interference component after zero padding according to the sampling function of the intermittent sampling forwarding interference;

[0124] S200: Obtaining a complete echo signal and an interference signal filtering result according to a discrete form representation of a signal interference component and a signal non-interference component after zero padding;

[0125] S300: Calculating the peak sidelobe ratio of the output result of the non-matched filter in the absence of interference and the peak sidelobe ratio of the interference signal filtering result;

[0126] S400: establishing an optimal phase-coded transmission waveform optimization objective function for resisting intermittent sampling forwarding interference according to the peak sidelobe ratio of the non-matched filter output result and the peak sidelobe ratio of the interference signal filtering result;

[0127] S500: solving the optimal phase-encoded transmission waveform optimization objective function by gradient iteration method, and outputting the optimal phase-encoded transmission waveform;

[0128] S600: After the radar receives the echo signal with interference, the non-matching filter optimization model is constructed with the goal of minimizing the interference suppression ratio and generalized integrated sidelobe ratio of the non-matching filter and the signal-to-noise ratio loss as a constraint condition;

[0129] S700: constructing an augmented Lagrangian function to solve the non-matched filter optimization model and outputting an optimal non-matched filter.

[0130] The present invention designs an optimal phase-coded transmission waveform according to an interference sampling function before the radar transmits a signal; after receiving an echo with interference, a non-matching filter for suppressing intermittent sampling forwarding interference is constructed according to the interference sampling function and the coding signal designed before transmission, thereby reducing interference energy and improving the detection accuracy of real targets.

[0131] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

[0132] The above are only some embodiments of the present invention. For those skilled in the art, several modifications and improvements can be made without departing from the creative concept of the present invention, which all belong to the protection scope of the present invention.

Claims

1. A method for suppressing intermittent sampling and forwarding interference, characterized in that: The following steps are involved: After receiving the echo signal with interference, the non-matched filter optimization model is constructed with the goal of minimizing the interference suppression ratio and generalized integrated sidelobe ratio of the non-matched filter and the signal-to-noise ratio loss as a constraint condition. An augmented Lagrangian function is constructed to solve the non-matched filter optimization model and output the optimal non-matched filter.

2. The intermittent sampling forwarding interference suppression method according to claim 1, characterized in that: The non-matched filter optimization model is: ； in, represents the optimization weight; represents the interference suppression ratio; represents the generalized integrated sidelobe ratio; Indicates signal-to-noise ratio loss; Indicates the lower limit of signal-to-noise ratio loss.

3. The intermittent sampling forwarding interference suppression method according to claim 1, characterized in that: The interference suppression ratio The calculation expression is: ； in, and The length is The column vectors of 0 and 1 are used to select the interference energy part and the main lobe part of the complete echo signal respectively; represents the Hadamard product; Indicates the target signal filtering result; Indicates the interference signal filtering result; Solve for the p-norm.

4. The intermittent sampling forwarding interference suppression method according to claim 1, characterized in that: The generalized integrated sidelobe ratio The calculation expression is: ； in, and Indicates the length The column vector composed of 0 and 1 is used to select the side lobe part and the main lobe part of the complete echo signal, where N is a preset value; represents the Hadamard product; Indicates the target signal filtering result; Solve for the p-norm.

5. The intermittent sampling forwarding interference suppression method according to claim 1, characterized in that: The signal-to-noise ratio loss The calculation expression is: ； in, represents conjugate transpose; represents an unmatched filter; Indicates complete echo signal; loss of signal-to-noise ratio In the calculation expression of , the numerator represents the signal energy after filtering, and the denominator represents the signal energy before filtering.

6. The intermittent sampling forwarding interference suppression method according to claim 1, characterized in that: Before the step of constructing the non-matched filter optimization model, the method further includes: According to the sampling function of the intermittent sampling forwarding interference, the discrete form representation of the signal interference component and the signal non-interference component after zero padding is calculated; Obtain the complete echo signal and the interference signal filtering results according to the discrete form representation after the signal interference component and the signal non-interference component are filled with zero; Calculate the peak sidelobe ratio of the non-matched filter output result in the absence of interference and the peak sidelobe ratio of the interference signal filtering result; According to the peak sidelobe ratio of the non-matched filter output result and the peak sidelobe ratio of the interference signal filtering result, the optimal phase coding transmission waveform optimization objective function for resisting intermittent sampling forwarding interference is established; The optimal phase-coded transmit waveform optimization objective function is solved by the gradient iteration method, and the optimal phase-coded transmit waveform is output.

7. The intermittent sampling forwarding interference suppression method according to claim 6, characterized in that: The discrete form of the signal interference component and the signal non-interference component after zero padding is expressed as: ； ； in, and Represent the signal uninterfered component and signal interfered component respectively; is the discrete mathematical form of the sampling function, which is composed of 0 and 1 with a length of A column vector of , where 1 indicates sampling and 0 indicates no sampling; represents the Hadamard product; Represents an imaginary unit; transmits a signal , Indicates The phase of the sampling points, the signal exists sampling points; represents transpose; Indicates the length The unit value matrix of .

8. The intermittent sampling forwarding interference suppression method according to claim 6, characterized in that: Complete echo signal And interference signal filtering results for: ； ； in, represents the inverse Fourier transform matrix; Indicates the length The Fourier transform matrix of represents Hadamard product; * represents conjugation; and They represent the signal uninterfered component and the signal interfered component respectively.

9. The intermittent sampling forwarding interference suppression method according to claim 6, characterized in that: Peak-to-sidelobe ratio of the unmatched filter output , Peak sidelobe ratio of interference signal filtering result for: ； ； in, Indicates the complete echo signal; and Indicates the length 0 and 1 column vectors, which are used to select the complete echo signal The middle side lobe part and the main lobe part; The length is A column vector of 0s and 1s; Indicates the interference signal filtering result; It is a discrete p paradigm; It is an output without modulation interference, and its result does not change with the sampling function.

10. The intermittent sampling forwarding interference suppression method according to claim 6, characterized in that: The optimal phase-coded transmission waveform optimization objective function for resisting intermittent sampling forwarding interference for: ； in, Represents optimization weight; Represents the peak sidelobe ratio of the non-matched filter output; Indicates the peak sidelobe ratio of the interference signal filtering result.

Images