Extended intermittent sampling forwarding interference method for resisting nonlinear frequency modulation waveform

Abstract

The invention relates to an extended intermittent sampling forwarding interference method for resisting a nonlinear frequency modulation waveform. The method comprises the following steps: defining an extended intermittent sampling function, determining the time-frequency modulation correspondence of an LFM waveform based on a stationary phase principle, and popularizing the time-frequency modulation correspondence of the LFM waveform to the time-frequency modulation correspondence of an NLFM waveform; designing the extended intermittent sampling function according to the time-frequency modulation correspondence of the NLFM waveform by taking the frequency domain period sampling result of the ISRJ on the LFM as a target to obtain a designed extended intermittent sampling function; the electromagnetic metamaterial modulates an incident radar signal according to the designed extended intermittent sampling function, and modulated echoes are subjected to pulse compression processing to obtain a plurality of false targets. Compared with the traditional intermittent sampling and forwarding interference, the method can realize a better deception interference effect aiming at the NLFM waveform.

Description

Technical Field

[0001] The present application relates to the field of radar electronic countermeasure technology, and in particular to a method for countering extended intermittent sampling and forwarding interference of nonlinear frequency modulation waveforms. Background Art

[0002] Interrupted Sampling Repeater Jamming (ISRJ), a typical coherent jamming technique, has become a hot topic in radar electronic countermeasures due to its low latency and time-sharing nature. In recent years, a large number of studies have emerged to further enhance ISRJ jamming effectiveness. These include employing aperiodic or non-uniform intermittent sampling schemes to generate suppressive jamming, employing joint modulation methods such as amplitude-frequency shifting or phase-frequency shifting to generate deceptive false targets while simultaneously overwriting the characteristics of real targets, and employing photon-assisted or electromagnetic metamaterial-based hardware architectures to further reduce system complexity, increase operating bandwidth, and minimize transmission latency. Numerous studies have demonstrated that the actual jamming effectiveness of ISRJ is closely related to radar waveform characteristics, with some high-degree-of-freedom waveforms even being custom-designed to suppress ISRJ-generated deceptive jamming. However, research on optimizing ISRJ effectiveness based on radar waveform characteristics, particularly in generating multiple false target effects, is relatively lacking.

[0003] The existing ISRJ theoretical framework is based on the spectral replication and shift caused by time-domain periodic modulation, and further incorporates the waveform's ambiguity function characteristics to analyze jamming effectiveness. However, with the exception of typical radar waveforms such as linear frequency modulation (LFM), providing a closed-form solution for the waveform's ambiguity function is extremely challenging. This further limits the analysis of ISRJ jamming effectiveness for non-linear frequency modulation (NLFM) waveforms to qualitative and simulation-based analysis. In practice, ISRJ jamming of NLFM waveforms often exhibits a pattern of a single false target and a range of clutter, which differs from the expected deceptive jamming effect of densely packed false targets similar to that of LFM waveforms. Summary of the Invention

[0004] Based on this, it is necessary to provide an extended intermittent sampling forwarding interference method for counteracting nonlinear frequency modulation waveforms with better deception interference effect to address the above technical problems.

[0005] A method for counteracting extended intermittent sampling and forwarding interference of a nonlinear frequency modulation waveform, the method comprising: An extended intermittent sampling function is defined, and the time-frequency modulation correspondence of the LFM waveform is determined based on the stationary phase principle, and the time-frequency modulation correspondence of the LFM waveform is extended to the time-frequency modulation correspondence of the NLFM waveform. Taking the frequency domain periodic sampling result of LFM by ISRJ as the target, an extended intermittent sampling function is designed according to the time-frequency modulation correspondence of NLFM waveform, and the designed extended intermittent sampling function is obtained. The electromagnetic metamaterial modulates the incident radar signal according to the designed extended intermittent sampling function, and the modulated echo is processed by pulse compression to obtain multiple false targets.

[0006] The aforementioned extended intermittent sampling and forwarding jamming method for countering nonlinear frequency modulation waveforms defines an extended intermittent sampling function. Based on the stationary phase principle, the time-frequency modulation correspondence of the waveform is determined. The extended intermittent sampling function is then designed based on the frequency modulation characteristics of the waveform to establish a frequency-domain periodic sampling pattern. The electromagnetic metamaterial modulates the incident radar signal according to the designed sampling function, and the modulated echo undergoes pulse compression processing to generate multiple false targets. Considering the false target generation problem from the new perspective of frequency-domain modulation, compared to traditional ISRJ, it has greater adaptability to radar waveforms and better deception jamming effects. BRIEF DESCRIPTION OF THE DRAWINGS

[0007] Figure 1 1 is a flow chart of a method for counteracting extended intermittent sampling and forwarding interference of a nonlinear frequency modulation waveform in one embodiment; Figure 2 FIG2 is a comparison of the interference effects of EISRJ and ISRJ on DLFM, PFM, and HFM waveforms when the frequency domain sampling periods are 0.03B, 0.06B, and 0.1B in one embodiment, as well as a schematic diagram of the corresponding designed non-periodic extended intermittent sampling function; wherein, Figure 2 (1a) is the extended intermittent sampling function designed for DLFM waveform when the frequency domain sampling period is 0.03B, 0.06B and 0.1B; Figure 2 (2a) is the extended intermittent sampling function designed for the polynomial frequency modulation PFM waveform when the frequency domain sampling period is 0.03B, 0.06B and 0.1B; Figure 2 (3a) is the extended intermittent sampling function designed for the hyperbolic frequency modulation (HFM) waveform when the frequency domain sampling period is 0.03B, 0.06B, and 0.1B; Figure 2 (1b) is a comparison of the interference effects of the traditional ISRJ and the proposed EISRJ under the DLFM waveform when the frequency domain sampling period is 0.03B; Figure 2 (2b) is a comparison diagram of the interference effects of the traditional ISRJ and the proposed EISRJ under the PFM waveform when the frequency domain sampling period is 0.03B; Figure 2(3b) is a comparison of the interference effects of the traditional ISRJ and the proposed EISRJ under the HFM waveform when the frequency domain sampling period is 0.03B; Figure 2 (1c) is a comparison of the interference effects of the traditional ISRJ and the proposed EISRJ under the DLFM waveform when the frequency domain sampling period is 0.06B; Figure 2 (2c) is a comparison diagram of the interference effects of the traditional ISRJ and the proposed EISRJ under the PFM waveform when the frequency domain sampling period is 0.06B; Figure 2 (3c) is a comparison of the interference effects of the traditional ISRJ and the proposed EISRJ under the HFM waveform when the frequency domain sampling period is 0.06B; Figure 2 (1d) is a comparison of the interference effects of the traditional ISRJ and the proposed EISRJ under the DLFM waveform when the frequency domain sampling period is 0.1B; Figure 2 (2d) is a comparison diagram of the interference effects of the traditional ISRJ and the proposed EISRJ under the PFM waveform when the frequency domain sampling period is 0.1B; Figure 2 (3d) is a comparison diagram of the interference effects of the traditional ISRJ and the proposed EISRJ under the HFM waveform when the frequency domain sampling period is 0.1B. DETAILED DESCRIPTION

[0008] In order to make the purpose, technical solutions and advantages of this application more clear, the following further describes this application in detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain this application and are not intended to limit this application.

[0009] In one embodiment, Figure 1 As shown, a method for counteracting extended intermittent sampling and forwarding interference of nonlinear frequency modulation waveform is provided, comprising the following steps: Step 102: define an extended intermittent sampling function, determine the time-frequency modulation correspondence of the LFM waveform based on the stationary phase principle, and generalize the time-frequency modulation correspondence of the LFM waveform to the time-frequency modulation correspondence of the NLFM waveform.

[0010] Define the extended intermittent sampling function as (1) in, Indicates time, It is a 01 alternating sequence, 1 represents the sampling process, Indicates the The length of time of each segment, , Taking into account the actual radar signal pulse width is a finite value, without loss of generality, it is assumed here .

[0011] The expression of LFM waveform is (2) in, , Indicates the modulation frequency of the LFM waveform, represents the signal bandwidth, is the pulse width, Indicates time.

[0012] The extended intermittent sampling signal under the LFM waveform can be expressed as (3) According to the stationary phase principle, we can get (4) in, Indicates the time length under LFM waveform The corresponding spectrum width, , , and Respectively and spectrum. The frequency range is limited to Comparing equations (3) and (4), we can see that for LFM signals, the product modulation in a given time slot can be approximately regarded as the product modulation of the frequency band corresponding to the time slot, which is the time-frequency modulation correspondence of the LFM waveform.

[0013] Considering that different types of continuous frequency modulation waveforms can be piecewise linearly approximated using LFM waveforms, we first consider a basic double-piecewise linear frequency modulation (DLFM) waveform, which is expressed as (5) in, and , and ,as well as and Represent the pulse width, signal bandwidth, and modulation frequency of the first and second linear frequency modulation intervals respectively. 、 、 、 All are positive numbers. , Here, Note that Equation (5) satisfies the continuity of instantaneous frequency and phase.

[0014] The extended intermittent sampling signal under the DLFM waveform can be expressed as (6) Without loss of generality, assume , , , and are all positive numbers. According to formula (3) and formula (4), The spectrum of can be approximately expressed as (7) in, (8) and Respectively and spectrum. and The frequency range is limited to and .because and and Therefore, the following relationship holds.

[0015] (9) Therefore, formula (7) can be further expressed as (10) in, for The spectrum, By comparing Equations (6) and (10), we can obtain the time-frequency modulation correspondence of the DLFM waveform. Condition (9) shows that only DLFM waveforms with non-overlapping instantaneous frequencies can be simplified as in Equation (10). Furthermore, based on the idea of piecewise linear approximation, the time-frequency modulation correspondence of other NLFM waveforms can be recursively derived from the derivation results of the DLFM waveform.

[0016] Step 104 , taking the frequency domain periodic sampling result of LFM by ISRJ as a target, an extended intermittent sampling function is designed according to the time-frequency modulation correspondence of the NLFM waveform to obtain a designed extended intermittent sampling function.

[0017] ISRJ performs periodic sampling in the time domain, that is, , , ,in, represents the sampling pulse duration, represents the pulse repetition period and the time domain sampling period. Therefore, , , ,in, , , which means that the constant modulation frequency of the LFM signal and the ISRJ time domain period product modulation together lead to the frequency domain periodic sampling effect, which is specifically expressed as (11) In order to facilitate the derivation, is assumed to be even, represents the frequency domain sampling period, is an impulse function. The fundamental properties of the Fourier transform indicate that periodic sampling in the frequency domain ultimately leads to periodic extension in the time domain. Therefore, the ISRJ's multi-target deception jamming effect against LFM fundamentally stems from the establishment of a periodic sampling pattern in the frequency domain.

[0018] The time-frequency modulation correspondence of the NLFM waveform makes it possible to produce a frequency domain periodic sampling effect by changing the sampling pulse time length. Consider a NLFM waveform with time-frequency modulation correspondence, and divide it into The general form of the frequency domain modulation effect can be expressed as (12) in, For the The spectrum width of each segment, , , By The average frequency modulation rate within each segment is determined. Comparing formula (12) and formula (11), we can see that mean , , Therefore, the extended intermittent sampling function is designed as (13) In step 106 , the electromagnetic metamaterial modulates the incident radar signal according to the designed extended intermittent sampling function, and the modulated echo is subjected to pulse compression processing to obtain multiple false targets.

[0019] The electromagnetic metamaterial modulates the incident radar signal according to the designed sampling function, and the modulated echo can generate multiple false targets through pulse compression processing. Specifically, for the NFLM waveform that meets the time-frequency modulation correspondence , the pulse compression result of the extended intermittent sampling signal can be finally expressed as (14) in, represents convolution, represents the inverse Fourier transform, for The corresponding matched filter, Based on the Fourier transform time-frequency correspondence, It can be further expressed as (15) in, , represents the frequency domain sampling period, It can be seen that the interference result of EISRJ will be expressed as a time interval , amplitude weighted A series of false targets.

[0020] The aforementioned extended intermittent sampling and forwarding jamming method for countering nonlinear frequency modulation waveforms defines an extended intermittent sampling function. Based on the stationary phase principle, the time-frequency modulation correspondence of the waveform is determined. The extended intermittent sampling function is then designed based on the frequency modulation characteristics of the waveform to establish a frequency-domain periodic sampling pattern. The electromagnetic metamaterial modulates the incident radar signal according to the designed sampling function, and the modulated echo undergoes pulse compression processing to generate multiple false targets. Considering the false target generation problem from the new perspective of frequency-domain modulation, compared to traditional ISRJ, it has greater adaptability to radar waveforms and better deception jamming effects.

[0021] In one embodiment, the extended intermittent sampling function is defined as:

[0022] in, Indicates time, It is a 01 alternating sequence, 1 represents the sampling process, Indicates the The length of time of each segment, , , Indicates the actual radar signal pulse width.

[0023] In one embodiment, determining the time-frequency modulation correspondence of the LFM waveform based on the stationary phase principle includes: The extended intermittent sampling signal under the LFM waveform is expressed as

[0024] in, represents the LFM waveform, is a 01 alternating sequence, N Indicates the number of segments, Indicates the The length of time of each segment, represents the extended intermittent sampling function; According to the stationary phase principle, the spectrum of the extended intermittent sampling signal is obtained as

[0025] in, Indicates the time length under LFM waveform The corresponding spectrum width, , , and Respectively and spectrum.

[0026] In one embodiment, the time-frequency modulation correspondence of the LFM waveform is such that the product modulation in a given time slot is approximately regarded as the product modulation of the frequency band corresponding to the time slot.

[0027] In one embodiment, the time-frequency modulation correspondence of the LFM waveform is extended to the time-frequency modulation correspondence of the NLFM waveform, including: Different types of continuous frequency modulation waveforms can be piecewise linearly approximated using LFM waveforms. Considering a basic dual piecewise linear frequency modulation DLFM waveform, the extended intermittent sampling signal under the DLFM waveform is expressed as

[0028] in, represents the LFM waveform, is a 01 alternating sequence, N Indicates the number of segments, Indicates the The length of time of each segment, represents the extended intermittent sampling function, 1 and 2 represent the first linear frequency modulation interval and the second linear frequency modulation interval, respectively.

[0029] In one embodiment, based on the stationary phase principle, the spectrum of the extended intermittent sampling signal under the DLFM waveform is obtained as follows:

[0030] in, for The spectrum, , Indicates the time length under LFM waveform The corresponding spectrum width, , , is a 01 alternating sequence, N Indicates the number of segments.

[0031] In one embodiment, the time-frequency modulation correspondence of the DLFM waveform is obtained according to the extended intermittent sampling signal under the DLFM waveform and the frequency spectrum of the extended intermittent sampling signal under the DLFM waveform.

[0032] In one embodiment, the frequency domain period sampling result of LFM by ISRJ is:

[0033] in, , , represents the sampling pulse duration, represents the pulse repetition period and the time domain sampling period, represents the frequency domain sampling period, is the impulse function, N Indicates the number of segments, Indicates the segments.

[0034] In one embodiment, an extended intermittent sampling function is designed based on the frequency domain periodic sampling result of the LFM by the ISRJ according to the time-frequency modulation correspondence of the NLFM waveform, and the designed extended intermittent sampling function includes: The NLFM waveform with time-frequency modulation correspondence is divided into The segment is linearly approximated, and the frequency domain modulation effect is expressed as

[0035] in, For the The spectrum width of each segment, , , By The average frequency modulation within each segment is determined. is a 01 alternating sequence, N Denotes the number of segments. mean , , , then the designed extended intermittent sampling function is .

[0036] In a specific embodiment, Figure 2The interference effects of EISRJ and ISRJ on DLFM, PFM, and HFM waveforms are compared for frequency domain sampling periods of 0.03B, 0.06B, and 0.1B, along with the corresponding designed aperiodic extended intermittent sampling functions. The signal pulse width is 40µs, the bandwidth is 300MHz, and the duty cycle is 1 / 4. The first linear segment of the DLMF signal accounts for 2 / 3 of its duration and 3 / 4 of its bandwidth. The PFM phase function is a cubic polynomial.

[0037] For DLFM waveform, since the modulation frequency of the first segment is greater than that of the second segment, the time domain interval is smaller than that of the second segment under the same bandwidth requirement. Figure 2 (1a) is consistent with the change of the pulse width of the modulation sequence. Figure 2 As can be seen from (1b)-(1d), due to the piecewise linearity of the DLFM waveform, ISRJ forms a false target. However, the overall nonlinearity results in a low amplitude of the false target, and the energy leaks to the surrounding area to form a cluttered interference area. In contrast, EISRJ forms a false target with a higher amplitude, and the shape is consistent with the 0th-order main false target. In addition, the amplitude and position distribution of the false target generated by EISRJ are close to the theoretical values (marked with yellow circles), reflecting the correctness of the EISRJ theoretical derivation. The slight error in amplitude mainly comes from the approximation of the POSP principle. Note that Figure 2 The mainlobe width of the false targets in (1b)-(1d) appears to be increasing, which is consistent with the unchanged signal bandwidth. This is because the increase in the frequency domain sampling period reduces the spacing between the false target positions in the time domain. When the first two false target peaks are presented with the same image width, the lateral display resolution increases, resulting in a relatively larger mainlobe width.

[0038] For PFM waveform, since the modulation frequency increases with time, the pulse time slot width decreases continuously under the same bandwidth length requirement. Figure 2 (2a) Match. Figure 2 It can be seen from (2b)-(2d) that due to the nonlinearity of the signal modulation frequency, the ISRJ pulse compression result does not generate any additional false targets except the 0th order main false target. In contrast, the EISRJ forms multiple regular false targets, and the main lobe shape is consistent with the 0th order main false target. The amplitude distribution and position distribution of the false targets generated by EISRJ are also consistent with the theory, reflecting the correctness of the EISRJ theory. The slight error in amplitude mainly comes from the approximation between the piecewise linear approximation and the POSP principle. Note that the pulse compression sidelobes of the EISRJ are higher, which is determined by the pulse compression characteristics of the PFM waveform itself. For the HFM waveform, since its modulation frequency decreases with time, the pulse time slot width continues to increase under the same bandwidth length requirement, which is consistent with the Figure 2(3a) also agrees. Note that Figure 2 The pulse compression sidelobes in (3b)-(3d) are not as high as those in the PFM waveform, reflecting the correlation between the EISRJ interference results and the waveform characteristics. The rest of the conditions are similar to those of the PFM waveform.

[0039] In summary, the proposed EISRJ has better deception jamming effects on multiple false targets with various NLFM waveforms than the traditional ISRJ under various frequency domain sampling periods, which reflects the superiority of the proposed method.

[0040] It should be understood that although Figure 1 The steps in the flowchart are shown in sequence as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified in this document, there is no strict order restriction for the execution of these steps, and these steps can be executed in other orders. In addition, Figure 1 At least part of the steps may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily executed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least part of the sub-steps or stages of other steps.

[0041] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0042] The above-described embodiments merely represent several implementation methods of the present application. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present application. It should be noted that a person of ordinary skill in the art may make various modifications and improvements without departing from the spirit of the present application, and these modifications and improvements fall within the scope of protection of the present application. Therefore, the scope of protection of the present application shall be determined by the appended claims.

Claims

1. A method for counteracting extended intermittent sampling and forwarding interference of nonlinear frequency modulation waveform, characterized in that: The method comprises: An extended intermittent sampling function is defined, and the time-frequency modulation correspondence of the LFM waveform is determined based on the stationary phase principle, and the time-frequency modulation correspondence of the LFM waveform is extended to the time-frequency modulation correspondence of the NLFM waveform. Taking the frequency domain periodic sampling result of LFM by ISRJ as the target, an extended intermittent sampling function is designed according to the time-frequency modulation correspondence of NLFM waveform, and the designed extended intermittent sampling function is obtained. The electromagnetic metamaterial modulates the incident radar signal according to the designed extended intermittent sampling function, and the modulated echo is processed by pulse compression to obtain multiple false targets.

2. The method according to claim 1, characterized in that The extended intermittent sampling function is defined as: in, Indicates time, It is a 01 alternating sequence, 1 represents the sampling process, Indicates the The length of time of each segment, , , Indicates the actual radar signal pulse width.

3. The method according to claim 1, wherein The time-frequency modulation correspondence of the LFM waveform is determined based on the stationary phase principle, including: The extended intermittent sampling signal under the LFM waveform is expressed as in, represents the LFM waveform, is a 01 alternating sequence, N Indicates the number of segments, Indicates the The length of time of each segment, represents the extended intermittent sampling function; According to the stationary phase principle, the spectrum of the extended intermittent sampling signal is obtained as in, Indicates the time length under LFM waveform The corresponding spectrum width, , , and Respectively and spectrum.

4. The method according to claim 3, characterized in that The time-frequency modulation correspondence of the LFM waveform is that the product modulation in a given time slot is approximately regarded as the product modulation of the frequency band corresponding to the time slot.

5. The method according to claim 1, wherein The time-frequency modulation correspondence of the LFM waveform is extended to the time-frequency modulation correspondence of the NLFM waveform, including: Different types of continuous frequency modulation waveforms can be piecewise linearly approximated using LFM waveforms. Considering a basic dual piecewise linear frequency modulation DLFM waveform, the extended intermittent sampling signal under the DLFM waveform is expressed as in, represents the LFM waveform, is a 01 alternating sequence, N Indicates the number of segments, Indicates the The length of time of each segment, represents the extended intermittent sampling function, 1 and 2 represent the first linear frequency modulation interval and the second linear frequency modulation interval, respectively.

6. The method according to claim 5, characterized in that Based on the stationary phase principle, the spectrum of the extended intermittent sampling signal under the DLFM waveform is obtained as follows: in, for The spectrum, , Indicates the time length under LFM waveform The corresponding spectrum width, , , is a 01 alternating sequence, N Indicates the number of segments.

7. The method according to claim 6, characterized in that The method further comprises: The time-frequency modulation correspondence of the DLFM waveform is obtained according to the extended intermittent sampling signal under the DLFM waveform and the frequency spectrum of the extended intermittent sampling signal under the DLFM waveform.

8. The method according to claim 1, characterized in that The frequency domain period sampling result of LFM by ISRJ is: in, , , represents the sampling pulse duration, represents the pulse repetition period and the time domain sampling period, represents the frequency domain sampling period, is the impulse function, N Indicates the number of segments, Indicates the segments.

9. The method according to claim 8, characterized in that Taking the frequency domain periodic sampling results of LFM by ISRJ as the target, an extended intermittent sampling function is designed according to the time-frequency modulation correspondence of NLFM waveform. The designed extended intermittent sampling function includes: The NLFM waveform with time-frequency modulation correspondence is divided into The frequency domain modulation effect is expressed as in, For the The spectrum width of each segment, , , By The average frequency modulation within each segment is determined. is a 01 alternating sequence, N Indicates the number of segments.

10. The method according to claim 9, wherein The method further comprises: make mean , , , then the designed extended intermittent sampling function is 。

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