Digital signal processing method based on automatic shielding of interference signals of 5G repeater

Abstract

The application discloses a digital signal processing method based on automatic shielding of 5G repeater interference signals, and relates to the technical field of digital signal processing.The application solves the technical problems of insufficient utilization of interference space characteristics and poor interference cooperative suppression effect.The application combines a time domain power integration and a scene threshold model, dynamically calculates a threshold according to historical data of a repeater area and base station load, adapts to different scenes such as urban core areas and suburban areas, reduces interference misjudgment and omission rates, breaks through single time domain power threshold judgment, extracts space characteristics such as DOA, polarization angle and inclination angle of interference, uses a DBSCAN clustering algorithm, clusters "interference groups" based on space characteristic dimensions, distinguishes multipath interference, coherent interference and isolated interference, constructs an interference group space correlation graph, a cooperative beam forming and a real-time updating suppression system, divides a strong correlation interference subgraph by using a graph segmentation algorithm, designs unified shielding parameters for the subgraph, and the suppression strategy is more targeted.

Description

Technical Field

[0001] This invention relates to the field of digital signal processing technology, specifically a digital signal processing method based on automatic shielding of interference signals from 5G repeaters. Background Technology

[0002] In wireless communication, especially 5G communication scenarios, while repeaters and other equipment enhance signal coverage, they are also prone to introducing various interference signals, such as drone interference and co-channel interference from neighboring cells. These interferences can affect communication quality, leading to problems such as signal misinterpretation and abnormal base station load.

[0003] According to patent application CN107357169B, an automated control model for shielding interference signals is disclosed, including a temperature preprocessing block, an alarm block, a comparison block, and a 5-second on-delay timer. The temperature preprocessing block is sequentially connected to the alarm block and the on-delay timer, and is also connected to the comparison block. The temperature preprocessing block preprocesses the temperature signal to obtain a temperature signal value. The comparison block compares the preprocessed temperature signal value with a set value, and then executes the control according to different program control models. This invention ensures accurate and reliable signals, timely and effective interlocking, and identifies and shields signal abrupt changes caused by interference. In actual field applications, the shielding rate reaches 100%.

[0004] However, while existing technologies can perform simple signal power threshold judgment and interference classification, they have the following shortcomings when facing complex scenarios:

[0005] Classifying interference solely based on time-domain power thresholds makes it difficult to accurately identify interference signals in complex scenarios and can easily lead to misjudgments.

[0006] The lack of fine-grained clustering of the spatial features of the classified interference makes it impossible to distinguish the "interference group", resulting in insufficient targeting of the suppression strategy;

[0007] Interference suppression often employs simple shielding or fixed beamforming, without combining spatial correlation characteristics of interference groups for collaborative optimization. This results in poor suppression effectiveness, insufficient real-time performance, and difficulty in adapting to the dynamic needs of 5G scenarios. Summary of the Invention

[0008] To address the shortcomings of existing technologies, this invention provides a digital signal processing method for automatic shielding of interference signals from 5G repeaters, which solves the problems of insufficient utilization of interference spatial characteristics and poor interference collaborative suppression effect.

[0009] To achieve the above objectives, the present invention provides the following technical solution: a digital signal processing method for automatic shielding of interference signals from 5G repeaters, which specifically includes the following steps:

[0010] The power integral of the data signal is calculated, and a preset threshold is determined based on historical communication data. The two are then compared to filter out interference signals and normal signals.

[0011] The interference signals are shielded, the direction of arrival of the interference signals is calculated using a subspace algorithm, and their polarization characteristics are obtained. The correlation between the interference signals is analyzed based on the spatial coherence coefficient, and the correlated interference signals and uncorrelated interference signals are classified.

[0012] The DBSCAN clustering algorithm is used to construct a dataset with DOA and polarization features as coordinates. The number of other points in the neighborhood of each point in the dataset is calculated according to the Euclidean formula, and the same disturbance group is classified according to the number.

[0013] To achieve coordinated suppression of the same interference group, an optimized objective function is constructed, and a beamforming weight vector is calculated. This weight vector is then used as a standard for suppression, and a comprehensive shielding is achieved by combining it with the interference correlation diagram.

[0014] As a further aspect of the present invention, the specific method for filtering interference signals and normal signals is as follows:

[0015] Digital signals are labeled as r, where r = 1, 2, ..., f, and f represents the type of digital signal. According to the formula... The power integral E corresponding to the digital signal r is calculated. r Where t1 and t2 are time windows, Calculate the instantaneous power of signal r(t);

[0016] Collect historical communication data from the area where the repeater is located and construct a threshold calculation model. The preset threshold E is calculated. y Where L is the current load rate of the base station, and E avg The integral of the average power of a historical normal signal. The scene coefficient is used to compare the two and filter out interference signals and normal signals.

[0017] As a further aspect of the present invention, the specific method for comparing and filtering interference signals and normal signals is as follows:

[0018] If the power integral E r Greater than the preset threshold E y If the corresponding digital signal is classified as an interference signal, it is labeled as i, where i = 1, 2, ..., j, and j represents the type of interference signal. Conversely, if the power integral E r Less than the preset threshold E y If so, the corresponding numerical signal will be classified as a normal signal.

[0019] As a further aspect of the present invention, the specific method for shielding the interference signal is as follows:

[0020] Multi-channel signals are simultaneously acquired using a 5G base station MIMO antenna array to form a spatiotemporal domain dataset. Where N is the number of antennas and T is the number of sampling points, the direction of arrival of the interference signal is calculated using the subspace algorithm, and the polarization characteristics of the signal are calculated, including the polarization angle and tilt angle.

[0021] Calculate the sample covariance matrix for the spatiotemporal domain data X: , where X H Let X be the conjugate transpose, and T be the number of snapshots. This is achieved through eigenvalue decomposition. Separate signal subspace U s With noise subspace U n Next, construct the spatial spectral function: ,in For array guide vector, The direction of arrival of the interference signal is obtained by spectral peak search. , where j is the number of interfering signals;

[0022] polarization angle E x and E y These represent the horizontal and vertical polarization components, and the tilt angle. .

[0023] As a further aspect of the present invention, the specific method for classifying related interference signals and unrelated interference signals is as follows:

[0024] According to the formula Calculate the spatial coherence coefficient between interfering signals, where a i Let i be the steering vector of the i-th interference signal. For a i The conjugate transpose of the obtained spatial coherence coefficient is simultaneously used to obtain the spatial coherence coefficient. Compare with the judgment threshold;

[0025] If the spatial coherence coefficient If a threshold is determined, two corresponding interference signals are marked as correlated interference signals; otherwise, if the spatial coherence coefficient is not determined, the two signals are marked as correlated interference signals. If the threshold is less than the threshold, it indicates that the two interference signals are spatially uncorrelated and are recorded as uncorrelated interference signals.

[0026] As a further aspect of the present invention, the specific method for classifying the same interference group based on quantity is as follows:

[0027] The DOA and polarization angle of each interference signal and tilt angle The features of the i-th interference signal are combined into a feature vector, and the feature vector of the i-th interference signal is represented as x. i =[DOA i , ], where i = 1, 2, ..., j, further obtaining the dataset X = [x1, x2, ..., xj]. j ];

[0028] For each point x in the dataset i Calculate its radius Other points within the neighborhood are calculated based on Euclidean distance, with point x... i [DOA i , ] and x j [DOA j , Substitute into the formula to calculate the Euclidean distance d(x). i x j ), and d(x) i x j )= And the obtained Euclidean distance d(x) i x j ) and radius The number is determined by comparing neighboring regions.

[0029] As a further aspect of the present invention, the specific method for determining the quantity by comparing the obtained Euclidean distance with the neighborhood is as follows:

[0030] If d(x) i x j )≤ Then we consider point x i and x j Within the neighborhood, simultaneously obtain the radius. The minimum number of points MinPts corresponding to the neighborhood is then calculated for each point x. i Perform classification and identification;

[0031] If point x i of If the number of points in the neighborhood is greater than or equal to the minimum number of points MinPts, then that point is designated as the core point. i It's not the core point, but it falls on a certain core point. Within the neighborhood, this point is designated as the boundary point. If point x i If a point is neither a core point nor a boundary point, it is recorded as a noise point.

[0032] As a further aspect of the present invention, the specific method for collaboratively suppressing the same interference group is as follows:

[0033] Construct the optimization objective function Where w is the beamforming weight vector and R is the signal covariance matrix. w is the desired signal steering vector. H Rw is the beam output power, w H =1 is a constraint condition;

[0034] Based on the above objective function, construct the Lagrange function. ,in Let w be the carrier wavelength. Taking the derivative with respect to w and setting the derivative to 0, we get... Combined with the constraint w H =1, solving the system of equations gives... And suppressive processing is performed based on the obtained beamforming weight vector w;

[0035] Meanwhile, the interference source is regarded as a graph node, and the spatial correlation is used as the edge weight. An interference correlation graph is constructed, and a graph segmentation algorithm is used to divide the strongly correlated interference into subgraphs. A uniform shielding parameter is designed for each subgraph.

[0036] This invention provides a digital signal processing method for automatic shielding of interference signals from 5G repeaters. Compared with existing technologies, it has the following advantages:

[0037] This invention combines "time-domain power integration + scenario-based threshold model" to dynamically calculate thresholds based on historical data of repeater areas and base station load. It adapts to different scenarios such as urban core areas and suburbs, reducing the error rate and missed detection rate of interference. It breaks through the single time-domain power threshold judgment, extracts spatial features of interference such as DOA, polarization angle, and tilt angle, and uses the DBSCAN clustering algorithm to cluster "interference groups" based on spatial feature dimensions, distinguishing between multipath interference, coherent interference, and isolated interference.

[0038] This invention constructs a suppression system of "interference group spatial correlation graph + cooperative beamforming + real-time update". It uses graph segmentation algorithm to divide strongly correlated interference subgraphs, designs unified shielding parameters for subgraphs, and makes the suppression strategy more targeted. It adopts recursive least squares to update the covariance matrix in real time, adapts to 5G dynamic scenarios, and ensures that the suppression effect is continuously effective. Attached Figure Description

[0039] Figure 1 This is a diagram illustrating the steps and methods of the present invention. Detailed Implementation

[0040] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0041] Please see Figure 1 This application provides a digital signal processing method for automatic shielding of interference signals from 5G repeaters, which specifically includes the following steps:

[0042] Step S1: Obtain the digital signal corresponding to the repeater and label the digital signal as r, where r = 1, 2, ..., f, and f represents the type of digital signal. Simultaneously, calculate the power integral of the digital signal r in the time domain according to the formula... The power integral E corresponding to the digital signal r is calculated. r Where t1 and t2 are time windows, The instantaneous power of signal r(t) is calculated, and the resulting power integral E is also calculated. r With preset threshold E y Comparison, and a preset threshold E y The specific calculation method is as follows:

[0043] By collecting historical communication data from the area where the repeater is located, statistically analyzing the normal signal power integral range, and combining this with the current base station load, a threshold calculation model is constructed. The preset threshold E is calculated. y Where L is the current load rate of the base station, and E avg The integral of the average power of a historical normal signal. and For example, the scene coefficient, such as the urban core area. =0.8, =0.2, suburbs =0.9, =0.1;

[0044] If the power integral E r Greater than the preset threshold E y If the corresponding digital signal is classified as an interference signal, it is labeled as i, where i = 1, 2, ..., j, and j represents the type of interference signal. Conversely, if the power integral E r Less than the preset threshold E y If so, the corresponding numerical signal will be classified as a normal signal.

[0045] Taking a 5G repeater station of an operator in the core urban area as an example: During the evening peak on weekdays (18:00-20:00), the repeater station covers an area with dense office buildings, and the base station load rate reaches 75%. A time window [t1, t2] = 10ms is set, digital signals are collected and labeled to calculate the power integral, and the historical average power integral E of normal signals is calculated. avg =5, according to the formula The preset threshold E is calculated. y =4.15;

[0046] A digital signal power integral E r The value is 6. Since 6 > 4.15, this digital signal is an interference signal.

[0047] Step S2: The interference signals obtained from the classification are shielded, and multi-channel signals are simultaneously acquired using a 5G base station MIMO antenna array (such as 64T64R) to form a spatiotemporal domain dataset. Where N is the number of antennas and T is the number of sampling points. For example, in a drone interference scenario, a uniform linear array (ULA) is used to collect signals. Spatial angle information is extracted using the phase difference between each antenna. Subspace algorithms (such as MUSIC and ESPRIT) are used to calculate the direction of arrival (DOA) of the interference signal, and the signal polarization characteristics are calculated. The polarization characteristics include polarization angle and tilt angle. The specific processing method is as follows:

[0048] Taking drone interference as an example, the ULA array is preferred, taking advantage of its high resolution in the horizontal dimension. Array parameter settings:

[0049] Array element spacing d= / 2, For example, 3.5 GHz corresponds to d ≈ 4.3 cm;

[0050] Array length L = (N-1)d;

[0051] Calculate the sample covariance matrix for the spatiotemporal domain data X: , where X H Let X be the conjugate transpose of X, and T be the number of quicks, satisfying T≥2N;

[0052] Through eigenvalue decomposition Separate signal subspace U s With noise subspace U n Next, construct the spatial spectral function: ,in This is the array guide vector, specifically in the ULA (Uniform Linear Array) scenario. The direction of arrival of the interference signal is obtained by spectral peak search. , where j is the number of interfering signals;

[0053] Using dual-polarized array elements (such as Polarization), analyzing the polarization state of the interference signal:

[0054] polarization angle : Describes the direction of rotation of the polarization ellipse, E x and E y These are the horizontal and vertical polarization components, respectively;

[0055] inclination : Describes the axial ratio of the polarization ellipse, ;

[0056] For the received signal of the dual-polarized array element, the polarization correlation coefficient matrix is ​​calculated, and the polarization ellipse parameters are fitted using maximum likelihood estimation (MLE) to achieve the polarization angle. and tilt angle The estimate;

[0057] The spatial correlation between interference signals is quantified by the inner product operation of the steering vectors, according to the formula. Calculate the spatial coherence coefficient between interfering signals, where a i Let i be the steering vector of the i-th interference signal. For a i The conjugate transpose of the obtained spatial coherence coefficient is simultaneously used to obtain the spatial coherence coefficient. Compared with the judgment threshold, if the spatial coherence coefficient If a threshold is determined, two corresponding interference signals are marked as correlated interference signals; otherwise, if the spatial coherence coefficient is not determined, the two signals are marked as correlated interference signals. If the threshold is exceeded, it indicates that the two interference signals are spatially uncorrelated and are recorded as uncorrelated interference signals.

[0058] Step S3: Using the DBSCAN clustering algorithm, with DOA and polarization features as coordinates, related interference signals are divided into the same "interference group", and the specific processing method is as follows:

[0059] The DOA and polarization angle of each interference signal and tilt angle The features of the i-th interference signal are combined into a feature vector, and the feature vector of the i-th interference signal is represented as x. i =[DOA i , ], where i = 1, 2, ..., j, further obtaining the dataset X = [x1, x2, ..., xj]. j ];

[0060] For each point x in the dataset i Calculate its radius Other points within the neighborhood are calculated based on Euclidean distance, with point x...i [DOA i , ] and x j [DOA j , Substitute into the formula to calculate the Euclidean distance d(x). i x j ), and d(x) i x j )= And the obtained Euclidean distance d(x) i x j ) and radius Neighborhood comparison;

[0061] If d(x) i x j )≤ Then we consider point x i and x j Within the neighborhood, simultaneously obtain the radius. The minimum number of points in the neighborhood, MinPts, specifically represents the number of points in a given neighborhood. A point must contain at least a certain number of points within its neighborhood to be considered a core point. Then, for each point x... i Perform classification and identification;

[0062] If point x i of If the number of points in the neighborhood is greater than or equal to (≥) the minimum number of points MinPts, then that point is designated as the core point. i It's not the core point, but it falls on a certain core point. Within the neighborhood, this point is designated as the boundary point. If point x i If a point is neither a core point nor a boundary point, it is recorded as a noise point, and so on, to obtain all the same "interference group".

[0063] Based on practical analysis, for example, 5G millimeter-wave base stations (25GHz), =10.7mm), using a 64-element ULA (Uniform Linear Array), covering three-dimensional spatial interference, including UAV interference (multipath scenario), generating 3 main interference paths, as shown in the table below:

[0064] ;

[0065] For each interference path, calculate the normalized features:

[0066] Path 1: x1 = [0.667, 0.5, 0.333] T Path 2: x2 = [0.678, 0.522, 0.356] TPath 3: x3 = [0.833, 0.667, 0.5] T ;

[0067] Calculate the normalized distance between path 1 and path 2, d(x1, x2) = (Small distance, highly similar features), the normalized distance d(x1, x3) between path 1 and path 3 = (Large distance, significant differences in characteristics);

[0068] Path 1 Neighborhood: Contains path 2 (distance 0.031≤0.05), and the number of points in the neighborhood is 2, which is less than the minimum number of points 3, so it is not determined as a core point for the time being;

[0069] Path 2 Neighborhood: Contains path 1 (distance 0.031≤0.05), and the number of points in the neighborhood is 2, which is less than the minimum number of points 3, so it is not determined as a core point for the time being;

[0070] Path 3 Neighborhood: No other interfering points (distance 1 / 2 of the path > 0.05), the number of points in the neighborhood = 0, and it is determined to be a noise point.

[0071] Since multipath interference from drones typically exhibits a continuous density distribution, after collecting more snapshot data, the number of points in the neighborhood of path 1 / 2 reaches the minimum number of points, MinPts=3. Therefore, the number of points in the neighborhood of path 1 / 2... If there are ≥3 points in the neighborhood, it is upgraded to a core point; if path 3 is still isolated, it is determined to be a noise point.

[0072] Step S4: Perform cooperative suppression on the obtained "interference group" and construct an optimization objective function: , where w is the beamforming weight vector (N×1) and R is the signal covariance matrix (N×N). Let w be the desired signal steering vector (N×1). H Rw represents the beam output power (scalar), w H =1 is a constraint condition;

[0073] Based on the above objective function, construct the Lagrange function. ,in Let w be the carrier wavelength. Taking the derivative with respect to w and setting the reciprocal to 0, we get... Combined with the constraint w H =1, solving the system of equations gives... The interference is suppressed based on the obtained beamforming weight vector w. Simultaneously, the interference source is treated as a graph node, and spatial correlation is used as the edge weight to construct an interference correlation graph. A graph segmentation algorithm (such as spectral clustering) is used to divide strongly correlated interference into subgraphs, and uniform shielding parameters (such as filter coefficients and beam null directions) are designed for each subgraph.

[0074] Next, recursive least squares (RLS) is used to update the covariance matrix R with a period of 10ms. Specifically... ,in It is a forgetting factor, and The value is 0.98.

[0075] The data in the above formulas are all calculated using numerical values, without substituting the units of the parameters. In addition, the contents not described in detail in this specification are all prior art known to those skilled in the art.

[0076] The above embodiments are only used to illustrate the technical methods of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical methods of the present invention without departing from the spirit and scope of the technical methods of the present invention.

Claims

1. A digital signal processing method based on automatic shielding of interference signals from 5G repeaters, characterized in that, The method specifically includes the following steps: The power integral of the data signal is calculated, and a preset threshold is determined based on historical communication data. The two are then compared to filter out interference signals and normal signals. The specific processing method is as follows: By collecting historical communication data from the area where the repeater is located, statistically analyzing the normal signal power integral range, and combining this with the current base station load, a threshold calculation model is constructed. The preset threshold E is calculated. y Where L is the current load rate of the base station, and E avg The integral of the average power of a historical normal signal. For scene coefficients; The interference signals are shielded, the direction of arrival of the interference signals is calculated using a subspace algorithm, and their polarization characteristics are obtained. The correlation between the interference signals is analyzed based on the spatial coherence coefficient, and the correlated interference signals and uncorrelated interference signals are classified. The DBSCAN clustering algorithm is used to construct a dataset with DOA and polarization features as coordinates. The number of other points in the neighborhood of each point in the dataset is calculated according to the Euclidean formula, and the same disturbance group is classified according to the number. To collaboratively suppress the same interference group, an optimized objective function is constructed, and beamforming weight vectors are calculated. These weight vectors are used as the standard for suppression, and comprehensive shielding is achieved by combining the interference correlation diagram. The specific processing method is as follows: Construct the optimization objective function Where w is the beamforming weight vector and R is the signal covariance matrix. w is the desired signal steering vector. H Rw is the beam output power, w H =1 is a constraint condition; Based on the above objective function, construct the Lagrange function. ,in Let w be the carrier wavelength. Taking the derivative with respect to w and setting the derivative to 0, we get... Combined with the constraint w H =1, solving the system of equations gives... And suppressive processing is performed based on the obtained beamforming weight vector w; Meanwhile, the interference source is regarded as a graph node, and the spatial correlation is used as the edge weight. An interference correlation graph is constructed, and the strongly correlated interference is divided into subgraphs using a graph segmentation algorithm. A uniform shielding parameter is designed for each subgraph.

2. The digital signal processing method based on automatic shielding of interference signals from 5G repeaters according to claim 1, characterized in that, The specific method for filtering interference signals and normal signals is as follows: Digital signals are labeled as r, where r = 1, 2, ..., f, and f represents the type of digital signal, according to the formula... The power integral E corresponding to the digital signal r is calculated. r Where t1 and t2 are time windows, Calculate the instantaneous power of signal r(t).

3. The digital signal processing method based on automatic shielding of interference signals from 5G repeaters according to claim 1, characterized in that, The specific method for simultaneously comparing the two and filtering out interference signals and normal signals is as follows: If the power integral E r Greater than the preset threshold E y If the corresponding digital signal is classified as an interference signal, it is labeled as i, where i = 1, 2, ..., j, and j represents the type of interference signal. Conversely, if the power integral E r Less than the preset threshold E y If so, the corresponding numerical signal will be classified as a normal signal.

4. The digital signal processing method for automatic shielding of interference signals from 5G repeaters according to claim 1, characterized in that, The specific method for shielding interference signals is as follows: Multi-channel signals are simultaneously acquired using a 5G base station MIMO antenna array to form a spatiotemporal domain dataset. Where N is the number of antennas and T is the number of sampling points, the direction of arrival of the interference signal is calculated using the subspace algorithm, and the polarization characteristics of the signal are calculated, including the polarization angle and tilt angle. Calculate the sample covariance matrix for the spatiotemporal domain data X: , where X H Let X be the conjugate transpose, and T be the number of snapshots. This is achieved through eigenvalue decomposition. Separate signal subspace U s With noise subspace U n Next, construct the spatial spectral function: ,in For array guide vector, The direction of arrival of the interference signal is obtained by spectral peak search. , where j is the number of interfering signals; polarization angle E x and E y These represent the horizontal and vertical polarization components, and the tilt angle. .

5. The digital signal processing method based on automatic shielding of interference signals from 5G repeaters according to claim 1, characterized in that, The specific method for classifying relevant and unrelated interference signals is as follows: According to the formula Calculate the spatial coherence coefficient between interfering signals, where a i Let i be the steering vector of the i-th interference signal. For a i The conjugate transpose of the obtained spatial coherence coefficient is simultaneously used to obtain the spatial coherence coefficient. Compare with the judgment threshold; If the spatial coherence coefficient If a threshold is determined, two corresponding interference signals are marked as correlated interference signals; otherwise, if the spatial coherence coefficient is not determined, the two signals are marked as correlated interference signals. If the threshold is less than the threshold, it indicates that the two interference signals are spatially uncorrelated and are recorded as uncorrelated interference signals.

6. The digital signal processing method based on automatic shielding of interference signals from 5G repeaters according to claim 1, characterized in that, The specific method for classifying the same interference group based on quantity is as follows: The DOA and polarization angle of each interference signal and tilt angle The features of the i-th interference signal are combined into a feature vector, and the feature vector of the i-th interference signal is represented as x. i =[DOA i , ], where i = 1, 2, ..., j, further obtaining the dataset X = [x1, x2, ..., xj]. j ]; For each point x in the dataset i Calculate its radius Other points within the neighborhood are calculated based on Euclidean distance, with point x... i [DOA i , ] and x j [DOA j , Substitute into the formula to calculate the Euclidean distance d(x). i x j ), and d(x) i x j )= And the obtained Euclidean distance d(x) i x j ) and radius The number is determined by comparing neighboring regions.

7. The digital signal processing method based on automatic shielding of interference signals from 5G repeaters according to claim 6, characterized in that, The specific method for determining the quantity by comparing the obtained Euclidean distance with the neighborhood is as follows: If d(x) i x j )≤ Then we consider point x i and x j Within the neighborhood, simultaneously obtain the radius. The minimum number of points MinPts corresponding to the neighborhood is then calculated for each point x. i Perform classification and identification; If point x i of If the number of points in the neighborhood is greater than or equal to the minimum number of points MinPts, then that point is designated as the core point. i It's not the core point, but it falls on a certain core point. Within the neighborhood, this point is designated as the boundary point. If point x i If a point is neither a core point nor a boundary point, it is recorded as a noise point.

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