Intermittent sampling noise convolution interference suppression method based on K-means clustering algorithm

Abstract

The invention relates to an intermittent sampling noise convolution interference suppression method based on a K-means clustering algorithm. The method comprises the following steps: receiving a baseband echo signal; performing short-time Fourier transform on the baseband echo signal to generate a time-frequency domain matrix; iteratively clustering the standard normal distribution matrix by adopting a K-means algorithm, dividing data points in the standard normal distribution matrix into a target signal cluster and an interference signal cluster, and generating a binary mask matrix; eliminating an interference block corresponding to the intermittent sampling noise convolution interference from the time-frequency domain matrix by using the optimized binary mask matrix to obtain a time-frequency domain matrix after the interference is eliminated; the optimized binary mask matrix is obtained by performing multi-scale morphological filtering processing on an area marked as 1 in the binary mask matrix; and performing short-time inverse Fourier transform on the time-frequency domain matrix after interference elimination to obtain an echo signal for suppressing intermittent sampling noise convolution interference. The method can effectively suppress the intermittent sampling noise convolution interference.

Description

Technical Field

[0001] This invention belongs to the field of radar electronic countermeasures technology, specifically relating to a method for suppressing intermittent sampling noise convolution interference based on the K-means clustering algorithm. Background Technology

[0002] Modern radar systems face increasingly complex and intelligent electromagnetic interference environments. Jamming techniques have evolved from traditional blocking and suppression jamming to coherent deception jamming based on Digital Radio Frequency Memory (DRFM), with continuously improving countermeasure capabilities. Intermittent Sample-and-Forward Jamming (ISRJ), in particular, poses a serious challenge to radar detection and identification due to its ability to generate realistic false targets by utilizing the coherent characteristics of radar signals. However, technological evolution has given rise to a more complex jamming style—Intermittent Sampling Noise Convolution Jamming (ISNCJ). This jamming style marks a significant transformation in jamming mechanisms: it is no longer limited to simple deception or suppression, but rather integrates intermittent sampling and forwarding techniques with broadband noise through convolution operations, deeply fusing the two mechanisms of "deception" and "suppression." ISNCJ retains some coherence with the radar signal to gain processing gain, while achieving wide-spectrum coverage and energy dissipation through noise convolution, resulting in complex and hybrid characteristics in both the time and frequency domains, posing a new and more severe threat to existing radar anti-jamming methods.

[0003] Currently, countermeasures against radar jamming can be mainly divided into two directions: one is from the transmitting end, designing radar waveforms with anti-jamming capabilities, such as using intra-pulse orthogonal coding, frequency agility, or random frequency modulation, aiming to increase the difficulty for jammers to accurately replicate or predict signals; the other is from the receiving end, processing the received mixed signals to filter out or suppress jamming components. The former often relies on prior assumptions about jamming parameters and has complex waveform design, placing high demands on radar hardware systems; the latter focuses more on post-processing of signals.

[0004] Specifically, existing technologies still have significant shortcomings in countering intermittent sampling interference (ISNCJ). At the transmitting end, while some studies have proposed using specifically coded linear frequency modulated signals or random frequency-hopping waveforms, these methods are mostly designed for traditional intermittent sampling direct forwarding interference, their core idea being to disrupt the continuity or correlation of the interference signal. However, ISNCJ, through noise convolution, has already partially disrupted the signal's regularity, significantly reducing the effectiveness of transmitting-end anti-interference methods that rely on specific signal structures (such as discontinuities). At the receiving end, existing research has attempted to suppress interference in the time-frequency domain, for example, by constructing bandpass filters, extracting signal differential features, or using short-time Fourier transform to identify interference energy blocks. These methods can handle interference with relatively concentrated energy distribution to some extent, but their intelligence is limited, usually relying on manually set thresholds or preset interference models, making it difficult to adaptively address the complex characteristics of ISNCJ in the time-frequency domain, which features scattered and irregular energy distribution. More importantly, existing technologies have not yet formed a closed-loop, systematic countermeasure system for ISNCJ, from "interference characteristic identification" to "interference strategy formulation" to "interference suppression." Summary of the Invention

[0005] To address the aforementioned problems in the existing technology, this invention provides a method for suppressing intermittent sampling noise convolution interference based on the K-means clustering algorithm. The technical problem to be solved by this invention is achieved through the following technical solution: This invention provides a method for suppressing intermittent sampling noise convolution interference based on the K-means clustering algorithm, comprising: Receive baseband echo signals that are mixed with intermittent sampling noise convolution interference and target echoes; A short-time Fourier transform is performed on the baseband echo signal to generate a time-frequency domain matrix, which is used to reflect the distribution characteristics of the baseband echo signal in the time-frequency domain. The K-means algorithm is used to iteratively cluster the standard normal distribution matrix. Based on the energy clustering characteristics of the intermittent sampling noise convolution interference in the time-frequency domain, the data points in the standard normal distribution matrix are divided into target signal clusters and interference signal clusters. The interference signal clusters are marked as 1, and the target signal clusters are marked as 0, generating a binary mask matrix. The standard normal distribution matrix is ​​obtained by normalizing the time-frequency domain matrix. Using the optimized binary mask matrix, interference blocks corresponding to the intermittent sampling noise convolution interference are removed from the time-frequency domain matrix to obtain the interference-free time-frequency domain matrix; the optimized binary mask matrix is ​​obtained by performing multi-scale morphological filtering on the regions marked as 1 in the binary mask matrix; A short-time Fourier inverse transform is performed on the time-frequency domain matrix after interference removal to obtain the echo signal with suppressed intermittent sampling noise convolution interference.

[0006] Compared with the prior art, the beneficial effects of the present invention are as follows: (1) Constructing a closed-loop countermeasure system for novel interference: For the first time, this invention proposes a complete technical solution for intermittent sampling noise convolution interference that has both deception and suppression characteristics, from "time-frequency characteristic analysis" to "intelligent interference identification" and then to "precise interference removal", filling the gap in systematic countermeasure methods in this field and forming an effective technical closed loop.

[0007] (2) Achieving adaptive and intelligent interference suppression: By introducing an unsupervised K-means clustering algorithm, this invention can automatically and adaptively complete the division and labeling of interference and target signal clusters based on the inherent differences in the energy distribution of intermittent sampling noise convolution interference and target echo in the time and frequency domain (interference energy is high and scattered, while the target is linearly distributed). It does not require prior knowledge of interference parameters or manual setting of complex thresholds, which significantly improves the intelligence level and environmental adaptability of the method.

[0008] (3) Improve the accuracy and robustness of interference suppression: Based on cluster extraction, a post-processing step of multi-scale morphological filtering is innovatively combined. This step can effectively eliminate isolated noise points caused by energy fluctuations and fill holes in the interference area, thereby obtaining a complete and continuous interference mask. This design greatly optimizes the extraction quality of the interference area, making the subsequent interference removal operation more accurate, effectively suppressing interference while minimizing damage to the real target signal.

[0009] (4) Promising engineering applications: The main processing flow of this invention is completed at the signal processing level. Starting from the baseband signal at the receiving end, interference suppression is achieved through algorithms such as time-frequency transformation, cluster analysis, image filtering, and inverse transformation. It places no special requirements on the radar transmitter hardware system and is easy to integrate and apply on existing radar platforms, providing a practical technical approach to dealing with new and complex interference. Simulation results show that this method can successfully recover the target signal from echoes overwhelmed by strong interference, significantly improving the radar's target detection and survivability in complex electromagnetic environments. Attached Figure Description

[0010] Figure 1 This is a flowchart illustrating a method for suppressing intermittent sampling noise convolution interference based on the K-means clustering algorithm provided in an embodiment of the present invention. Figure 2 This is a time-frequency diagram of the target signal whose transmitted signal is a linear frequency modulated signal, provided in an embodiment of the present invention. Figure 3This is a time-frequency diagram of intermittent sampling direct forwarding interference provided in an embodiment of the present invention; Figure 4a This is a time-domain waveform diagram of intermittent sampling noise convolution interference provided in an embodiment of the present invention; Figure 4b This is a spectrum diagram of intermittent sampling noise convolution interference provided in an embodiment of the present invention; Figure 4c This is a time-frequency diagram of intermittent sampling noise convolution interference after short-time Fourier transform, provided in an embodiment of the present invention. Figure 5 This is a schematic diagram illustrating the preliminary extraction of interference regions in the time-frequency domain using the K-means clustering algorithm provided in this embodiment of the invention. Figure 6 This is a schematic diagram illustrating how the echo signal, provided in an embodiment of the present invention, uses multi-scale morphological filtering in the time-frequency domain to further eliminate redundant noise points in the time-frequency graph; Figure 7a This is a time-frequency diagram of intermittent sampling noise convolution interference after being removed in the time-frequency domain, as provided in the embodiments of the present invention. Figure 7b This is the time domain and spectrum diagram of the recovered signal after the intermittent sampling noise convolution interference is removed in the time-frequency domain, as provided in the embodiments of the present invention. Figure 8a This is a schematic diagram of the target signal pulse compression output result provided in an embodiment of the present invention; Figure 8b This is a schematic diagram of the total echo pulse compression output result under intermittent sampling noise convolution interference provided by an embodiment of the present invention; Figure 8c This is a schematic diagram of the recovered signal pulse compression output result after interference suppression under intermittent sampling noise convolution interference, provided by an embodiment of the present invention. Detailed Implementation

[0011] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0012] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. In addition, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.

[0013] Although the invention has been described herein in conjunction with various embodiments, those skilled in the art will understand and implement other variations of the disclosed embodiments by reviewing the accompanying drawings, disclosure, and appended claims in carrying out the claimed invention. In the claims, the word "comprising" does not exclude other components or steps, and "a" or "an" does not exclude a plurality. A single processor or other unit can implement several functions listed in the claims. While different dependent claims may recite certain measures, this does not mean that these measures cannot be combined to produce good results.

[0014] The following is a detailed description of the intermittent sampling noise convolution interference suppression method based on the K-means clustering algorithm proposed in this invention, with reference to the accompanying drawings.

[0015] Figure 1 This is a flowchart illustrating a method for suppressing intermittent sampling noise convolution interference based on the K-means clustering algorithm, provided in an embodiment of the present invention. Figure 1 As shown, the method includes steps 110-150, specifically: Step 110: Receive the baseband echo signal that is mixed with intermittent sampling noise convolution interference and target echo.

[0016] First, we introduce intermittent sampling noise convolution interference. Here, intermittent sampling noise convolution interference = intermittent sampling + forwarding interference + noise convolution. It precisely describes the complete process of "acquiring radar signal segments through intermittent sampling, then convolving these segments with noise, and finally forwarding them." This terminology is very common in professional fields and is used to define emerging and more complex technical phenomena. This term, or its core idea (Intermittent Sampling followed by Noise Convolution), has been proposed and discussed in recent research in the field of radar countermeasures to describe a new type of composite interference that combines "deceptiveness" (because it samples real radar signals and has coherence) and "suppression" (because it has broadband blocking characteristics after convolution with noise).

[0017] Specifically, the intermittent sampling noise convolution interference can be expressed as: ; in It is complex Gaussian white noise.

[0018] Furthermore, intermittent sampling noise convolution interference It can be represented as: ; in, For the first The amplitude of the interference. For carrier frequency, For frequency modulation slope, For the number of slices of the interference machine, To interfere with slice width, The delay introduced by the radial distance between the radar and the jammer.

[0019] Before receiving the baseband echo signal, the method further includes: transmitting a linear frequency modulated signal and receiving the radio frequency echo signal after being superimposed by target reflection and environmental interference within a coherent processing time; performing down-conversion processing and low-pass filtering processing on the radio frequency echo signal in sequence to obtain the baseband echo signal.

[0020] Specifically, linear frequency modulated signal It can be represented as: ; in, Indicates the pulse width of the transmitted signal. For frequency modulation slope, For signal bandwidth, Indicates the carrier frequency. It indicates a fast time, or a distance in time. Indicates slow time. Indicates the pulse repetition time. Indicates the number of pulses. Represents a rectangular window function.

[0021] Specifically, the jammed echo signal received by the radar includes the target echo signal and the jamming signal, among which the baseband target echo signal... It can be represented as: ; in, The delay introduced by the radial distance between the radar and the target. It is the speed of light.

[0022] Based on this, the baseband echo signal is obtained by down-converting and low-pass filtering the RF echo signal after the superposition of target reflection and environmental interference (i.e., including target echo and intermittent sampling noise convolution interference). The baseband echo signal It can be represented as: ; in The variance is Complex Gaussian white noise.

[0023] Step 120: Perform a short-time Fourier transform on the baseband echo signal to generate a time-frequency domain matrix. The time-frequency domain matrix is ​​used to reflect the distribution characteristics of the baseband echo signal in the time-frequency domain.

[0024] In the time-frequency domain, the energy of a linear frequency modulated (LFM) signal is strictly distributed along a diagonal line on the time-frequency plot (e.g., obtained through STFT). The slope of this line is determined by the signal's modulation rate (bandwidth / duration). The energy is highly localized on the time-frequency plane, exhibiting a clear "knife-edge" characteristic. In contrast, intermittent sampling noise convolution interference has dispersed, chaotic, and blocky energy distribution on the time-frequency plot. Due to the randomness of the noise and the discontinuity of sampling, its energy is widely and scattered across the time-frequency plane, forming patches of "energy clouds" or "spot clusters." It lacks a global linear structure; its energy distribution is two-dimensionally diffuse.

[0025] To better distinguish between the target echo and the intermittent sampling noise convolution interference signal, the baseband echo signal is analyzed here. Performing a short-time Fourier transform, the signal can be represented in the time-frequency domain as follows: ; in, It is the selected window function. It is the original signal. It is a sliding time window function. It is an integral variable. It is time. The signal frequency.

[0026] Step 130: The K-means algorithm is used to iteratively cluster the standard normal distribution matrix. Based on the energy clustering characteristics of intermittent sampling noise convolution interference in the time-frequency domain, the data points in the standard normal distribution matrix are divided into target signal clusters and interference signal clusters. The interference signal cluster is marked as 1 and the target signal cluster is marked as 0, generating a binary mask matrix. The standard normal distribution matrix is ​​obtained by normalizing the time-frequency domain matrix.

[0027] Here, the standard normal distribution matrix is ​​obtained by normalizing the time-frequency domain matrix, including: calculating the mean and standard deviation of all elements in the time-frequency domain matrix; subtracting the mean from each element in the time-frequency domain matrix and dividing by the standard deviation to obtain the standard normal distribution matrix with a mean of 0 and a standard deviation of 1.

[0028] Specifically, Z-score standardization is used to transform the original data into a standard normal distribution with a mean of 0 and a standard deviation of 1. This can be represented as: ; in, For the entire time-frequency graph matrix The average of all elements in the set. For the entire time-frequency graph matrix The standard deviation of all elements in the matrix. and They can be represented as: ; ; in, For matrix The total number of elements in the text.

[0029] Here, step 130 includes: calculating the energy amplitude of each data point in the standard normal distribution matrix as its feature vector; randomly selecting two data points as initial cluster centers; calculating the Euclidean distance of each data point to each cluster center, and assigning it to the first or second cluster center according to the shortest distance corresponding to each data point; randomly selecting two data points again as updated cluster centers based on the clustering results; continuing the next round of clustering and cluster center updates until the change in cluster centers is less than a preset threshold or the maximum number of iterations is reached, stopping the iteration, and obtaining the final first and second clusters; based on the characteristics of intermittent sampling noise convolution interference exhibiting concentrated energy and scattered distribution in the time-frequency domain, selecting the clusters with an energy mean greater than or equal to a preset threshold from the two clusters, initially marking them as interference signal clusters, and initially marking the other cluster as the target signal cluster, generating a binary mask matrix with the same dimension as the standard normal distribution matrix.

[0030] For example, assuming that after Z-score normalization, a simplified 4×4 standard normal distribution matrix is ​​obtained, the values ​​of which represent the energy amplitude of each time-frequency unit: ; In this matrix, the row index represents time, and the column index represents frequency.

[0031] First, each element in the matrix represents the energy amplitude, with a total of 16 data points. The feature vector set is: [0.1, 0.1, 2.5, 2.3, 0.2, 0.2, 2.6, 2.4, 0.3, 0.3, 2.4, 2.2, 0.4, 0.4, 2.3, 2.1]. Two data points are randomly selected, for example: center 1 = 0.1, center 2 = 2.5; the Euclidean distance (one-dimensional feature, i.e., the absolute difference) from each data point to the two centers is calculated and assigned: The data points closer to center 1 (0.1) include: 0.1, 0.1, 0.2, 0.2, 0.3, 0.3, 0.4, 0.4, forming cluster A; the data points closer to center 2 (2.5) include: 2.5, 2.3, 2.6, 2.4, 2.4, 2.2, 2.3, 2.1, forming cluster B. Calculate the mean of each cluster as the new center, where the mean of cluster A is 0.25 and the mean of cluster B is 2.35. Repeat the assignment and update steps until the center change is less than a threshold (e.g., 0.01). Assume the calculated energy mean of the two clusters is: cluster A has a mean of 0.25, and cluster B has a mean of 2.35. The preset threshold is assumed to be 1.0. Since the energy mean of cluster B is ≥1.0, it is initially labeled as an interfering signal cluster, and the energy mean of cluster A is <1.0, it is initially labeled as the target signal cluster.

[0032] Step 140: Using the optimized binary mask matrix, remove the interference blocks corresponding to the intermittent sampling noise convolution interference from the time-frequency domain matrix to obtain the time-frequency domain matrix after interference removal; the optimized binary mask matrix is ​​obtained by performing multi-scale morphological filtering on the regions marked as 1 in the binary mask matrix.

[0033] Specifically, the optimized binary mask matrix is ​​obtained by performing multi-scale morphological filtering on the regions marked as 1 in the binary mask matrix. This includes: performing morphological filtering on the binary mask matrix using multiple structuring elements of different scales. For each structuring element, morphological closing and opening operations are performed sequentially to eliminate isolated noise points caused by energy fluctuations due to intermittent sampling noise convolution interference in the binary mask matrix, and to fill the holes caused by cluster boundary effects in the intermittent sampling noise convolution interference region. The binary mask matrices processed by each structuring element are then fused, and the optimized binary mask matrix is ​​generated by taking the maximum pixel value at the corresponding position in each binary mask matrix.

[0034] Here, morphological opening is a classic image processing operation used to process binary images (such as binary mask matrices). It is essentially a sequential combination of two more fundamental operations: opening = erosion + dilation. Erosion can be understood as sliding a small structuring element (imagine a miniature template, such as a 3x3 pixel square) across the image. The center point outputs a "1" only when the area completely covered by the structuring element is all "1"s (foreground); otherwise, it outputs a "0". This causes the white foreground area (your obfuscated area) to shrink overall, with the edges being "eroded," and particularly small isolated points disappearing entirely. Dilation can be understood as sliding the same structuring element. The center point outputs a "1" as long as the area covered by the structuring element contains at least one "1". This causes the shrunken foreground area to expand again, restoring its approximate size, but isolated points completely eliminated by erosion cannot be recovered.

[0035] Here, morphological closing is another classic image processing operation used to process binary images (such as binary mask matrices). It complements opening and operates in the reverse order. Essentially, it is a sequential combination of two basic operations: closing = dilation followed by erosion.

[0036] In the interference suppression process, K-means clustering may produce sporadic holes (points that should be 1 are mistakenly labeled as 0) in interference regions marked as "1" due to local fluctuations in interference energy or boundary effects, or cause small breaks in interference regions that should be connected. Closing operations are mainly used to solve the "holes" and "breaks" in the binary mask matrix after clustering. Through a combination of "dilation followed by erosion," these holes and breaks, smaller than the size of the structuring element, are specifically filled. Dilation temporarily fills and connects them, while subsequent erosion ensures that the interference region does not over-expand, roughly maintaining the original boundaries, while permanently preserving the filled areas. This, combined with opening operations (eliminating isolated points), improves the robustness and usability of the binary mask.

[0037] Specifically, using the optimized binary mask matrix, interference blocks corresponding to the intermittent sampling noise convolution interference are removed from the time-frequency domain matrix to obtain the interference-free time-frequency domain matrix. This includes: performing a logical NOT operation on the optimized binary mask matrix to obtain an inverse mask matrix; and multiplying the inverse mask matrix element-wise with the time-frequency domain matrix to set the regions marked as 1 in the time-frequency domain matrix to zero, thereby obtaining the interference-free time-frequency domain matrix.

[0038] Step 150: Perform a short-time inverse Fourier transform on the time-frequency domain matrix after removing interference to obtain the echo signal that suppresses intermittent sampling noise convolution interference.

[0039] Specifically, the expression for the echo signal that suppresses intermittent sampling noise convolution interference is: ; ; in, It is time. For signal frequency, It is a time-frequency domain matrix. It is an echo signal that suppresses intermittent sampling noise convolution interference. It is the time-frequency domain matrix after removing interference. It is a reverse mask matrix. It is the optimized binary mask matrix.

[0040] To address the shortcomings of existing technologies, such as the lack of systematic countermeasures, difficulty in effectively suppressing intermittent sampling noise convolutional interference which possesses both deceptive and suppressive characteristics, and the reliance on prior knowledge, low intelligence, and insufficient suppression accuracy of existing methods, this invention provides an intermittent sampling noise convolutional interference suppression method based on the K-means clustering algorithm. This method achieves adaptive, high-precision identification and separation of interference signals through the coordinated processing of time-frequency analysis, unsupervised clustering, and morphological filtering. It effectively eliminates complex interference while preserving the true target, forming a complete "identification-strategy-suppression" closed-loop countermeasure system, significantly improving the radar's anti-interference capability and target detection performance in complex electromagnetic environments.

[0041] To demonstrate the effectiveness of this invention, the following simulation experiments are conducted for further illustration.

[0042] (1) Simulation conditions: The target signal transmitted by the radar is a linear frequency modulated signal, with an initial carrier frequency of Pulse duration pulse bandwidth Pulse repetition period The receiver noise follows a variance of The complex Gaussian distribution, signal-to-noise ratio Noise-to-interference ratio .

[0043] Radial distance of the target relative to the radar Intermittent sampling directly forwards the interference slice width Number of reposts Number of slices .

[0044] (2) Simulation content and results: Simulation 1: The simulation shows the time-frequency diagram of the target signal after short-time Fourier transform when the transmitted signal is a linear frequency modulated signal. The result is as follows: Figure 2 As shown, the target signal appears as a "sloping line" in the time-frequency domain due to its linear frequency modulation characteristics.

[0045] Simulation 2 simulates the time-frequency diagram of intermittent sampling direct forwarding interference when the transmitted signal is a linear frequency modulated signal. The results are as follows: Figure 3 As shown in the figure, the jammer samples the target signal and then forwards it directly, resulting in a discontinuous time-frequency diagram.

[0046] Simulation 3 simulates the time domain, spectrum, and time-frequency plot of intermittent sampling noise convolutional interference. The results are as follows: Figure 4a , 4b As shown in 4c. Intermittent sampling direct forwarding interference is formed by convolution with complex Gaussian noise, and is generated by... Figure 4a and Figure 4cIt can be seen that the intermittent sampling noise convolution interference exhibits a suppressive effect, directly overwhelming the target signal. From Figure 4b It can be seen that intermittent sampling noise convolution interference has similar characteristics to intermittent sampling interference in the frequency domain.

[0047] Simulation 4: The simulated transmitted signal is a linear frequency modulated signal, and the interference pattern is intermittent sampling noise convolution interference. The noise is complex Gaussian white noise. The total echo is subjected to short-time Fourier transform, and the K-means clustering algorithm is used in the time-frequency domain to initially extract the interference region. The results are as follows: Figure 5 As shown, the K-means clustering algorithm can extract most of the noise data.

[0048] Simulation 5: The echo signal of the intermittent sampling noise convolution interference pattern was extracted using the K-means clustering algorithm. Multi-scale morphological filtering was then used to further eliminate redundant noise points in the time-frequency graph to obtain more complete interference region data. The results are as follows: Figure 6 As shown, although K-means clustering can extract the main interference regions from a macroscopic perspective, it can produce some isolated noise points or holes due to occasional energy fluctuations in time-frequency data points or boundary effects of the clustering algorithm. Morphological filtering, on the other hand, uses opening and closing operations to form more regular and continuous interference regions, making it easier to filter out interference more completely.

[0049] Simulation 6: The echo signal with intermittent sampling noise convolution interference was processed using multi-scale morphological methods. The time-frequency diagram after removing the interference region from the original time-frequency diagram is shown in Figure 7a. The time-frequency diagram was then subjected to inverse short-time Fourier transform to obtain the time-domain and spectrum of the interference-suppressed echo, as shown in Figure 7a. Figure 7b As shown, the intermittent sampling noise convolution interference is suppressed.

[0050] Simulation 7: The simulated transmitted signal is a linear frequency modulated signal, and the interference pattern is intermittent sampling noise convolution interference. The pulse compression results of the echo signal before and after anti-interference are shown. The result of pulse compression of the target signal is as follows: Figure 8a As shown, the target is at a distance of 3000 meters. The pulse compression results of the total echo signal before and after anti-jamming are as follows: Figure 8b , 8c As shown, before anti-jamming, pulse compression of the total echo signal completely submerges the signal because the intermittent sampling noise convolution interference is obtained by convolving intermittent sampling interference with complex Gaussian white noise. Therefore, it is coherent with the radar's matched filter and will also acquire radar processing gain. After anti-jamming, pulse compression makes the signal stand out, and the interference is successfully suppressed.

[0051] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A method for suppressing intermittent sampling noise convolution interference based on K-means clustering algorithm, characterized in that, include: Receive baseband echo signals that are mixed with intermittent sampling noise convolution interference and target echoes; A short-time Fourier transform is performed on the baseband echo signal to generate a time-frequency domain matrix, which is used to reflect the distribution characteristics of the baseband echo signal in the time-frequency domain. The K-means algorithm is used to iteratively cluster the standard normal distribution matrix. Based on the energy clustering characteristics of the intermittent sampling noise convolution interference in the time-frequency domain, the data points in the standard normal distribution matrix are divided into target signal clusters and interference signal clusters. The interference signal clusters are marked as 1, and the target signal clusters are marked as 0, generating a binary mask matrix. The standard normal distribution matrix is ​​obtained by normalizing the time-frequency domain matrix. Using the optimized binary mask matrix, interference blocks corresponding to the intermittent sampling noise convolution interference are removed from the time-frequency domain matrix to obtain the interference-free time-frequency domain matrix; the optimized binary mask matrix is ​​obtained by performing multi-scale morphological filtering on the regions marked as 1 in the binary mask matrix; A short-time Fourier inverse transform is performed on the time-frequency domain matrix after interference removal to obtain the echo signal with suppressed intermittent sampling noise convolution interference.

2. The intermittent sampling noise convolution interference suppression method based on K-means clustering algorithm according to claim 1, characterized in that, The K-means algorithm is used to iteratively cluster the standard normal distribution matrix. Based on the energy clustering characteristics of the intermittent sampling noise convolution interference in the time-frequency domain, the data points in the standard normal distribution matrix are divided into target signal clusters and interference signal clusters. The interference signal clusters are marked as 1, and the target signal clusters are marked as 0, generating a binary mask matrix, including: Calculate the energy amplitude of each data point in the standard normal distribution matrix to use as its eigenvector; Two data points are randomly selected as the initial cluster centers; Calculate the Euclidean distance of each data point to each cluster center, and assign it to the first or second cluster center based on the shortest distance corresponding to each data point. Based on the clustering results, two data points were randomly selected again as the updated cluster centers; Continue with the next round of clustering and cluster center updates until the change in cluster centers is less than a preset threshold or the maximum number of iterations is reached, then stop iterating and obtain the final first and second clusters; Based on the characteristics of intermittent sampling noise convolution interference in the time-frequency domain, which exhibits concentrated energy and scattered distribution, clusters with an average energy value greater than or equal to a preset threshold are selected from two clusters and initially labeled as the interference signal clusters. The other cluster is initially labeled as the target signal cluster, and a binary mask matrix with the same dimension as the standard normal distribution matrix is ​​generated.

3. The intermittent sampling noise convolution interference suppression method based on K-means clustering algorithm according to claim 2, characterized in that, Before receiving the baseband echo signal, the method further includes: Within one coherent processing time, a linear frequency modulated signal is transmitted and a radio frequency echo signal after being superimposed by target reflection and environmental interference is received; The radio frequency echo signal is sequentially down-converted and low-pass filtered to obtain the baseband echo signal.

4. The intermittent sampling noise convolution interference suppression method based on K-means clustering algorithm according to claim 1, characterized in that, The optimized binary mask matrix is ​​obtained by performing multi-scale morphological filtering on the regions marked as 1 in the binary mask matrix, including: The binary mask matrix is ​​subjected to morphological filtering using structuring elements of multiple different scales. For each structuring element, morphological closing and morphological opening operations are performed sequentially to eliminate isolated noise points in the binary mask matrix caused by energy fluctuations due to intermittent sampling noise convolution interference, and to fill the holes caused by cluster boundary effects in the intermittent sampling noise convolution interference region. The binary mask matrices processed by each scale structuring element are fused together, and the optimized binary mask matrix is ​​generated by taking the maximum pixel value at the corresponding position in each binary mask matrix.

5. The intermittent sampling noise convolution interference suppression method based on K-means clustering algorithm according to claim 1, characterized in that, The step of using the optimized binary mask matrix to remove interference blocks corresponding to the intermittent sampling noise convolution interference from the time-frequency domain matrix to obtain the interference-removed time-frequency domain matrix includes: Perform a logical NOT operation on the optimized binary mask matrix to obtain the inverse mask matrix; The inverse mask matrix is ​​multiplied element-wise with the time-frequency domain matrix to set the regions marked as 1 in the time-frequency domain matrix to zero, thereby obtaining the time-frequency domain matrix after interference removal.

6. The intermittent sampling noise convolution interference suppression method based on K-means clustering algorithm according to claim 1, characterized in that, The standard normal distribution matrix is ​​obtained by normalizing the time-frequency domain matrix, including: Calculate the mean and standard deviation of all elements in the time-frequency domain matrix; Subtracting the mean from each element in the time-frequency domain matrix and dividing by the standard deviation yields the standard normal distribution matrix with a mean of 0 and a standard deviation of 1.

7. The intermittent sampling noise convolution interference suppression method based on K-means clustering algorithm according to claim 5, characterized in that, The expression for the echo signal that suppresses intermittent sampling noise convolution interference is: ； ； in, It is time. For signal frequency, It is the time-frequency domain matrix, It is the echo signal that suppresses intermittent sampling noise convolution interference. It is the time-frequency domain matrix after removing interference. It is the inverse mask matrix, It is the optimized binary mask matrix.

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