A method for electromagnetic wave rain attenuation completion measurement based on non-negative matrix decomposition

Abstract

The present invention relates to an electromagnetic wave rain attenuation completion measurement method based on non-negative matrix decomposition, which belongs to the field of wireless communication. The method first uses a linear regression model to preliminarily fill in the missing values ​​in the matrix, then uses the data of other known columns as features to fit the linear regression model, and uses the model to predict the missing values ​​to improve the accuracy of initialization, and finally performs non-negative matrix decomposition on the initialized matrix, and by traversing different potential dimensions, selects the dimension value that can maximize the correlation coefficient of non-missing values ​​between the reconstructed matrix and the measurement matrix as the final result. The method of the present invention does not rely on a specific rain attenuation model or parameter setting, has strong versatility, and can adapt to the needs of completing electromagnetic wave rain attenuation data in different regions and under different parameter conditions.

Description

Technical Field

[0001] The present invention relates to the field of wireless communications, and in particular to an electromagnetic wave rain attenuation completion measurement method based on non-negative matrix decomposition, which is used for completing and reconstructing electromagnetic wave rain attenuation trends with missing values. Background Art

[0002] In wireless communication systems, electromagnetic waves are affected by natural factors such as rain attenuation during propagation. Rain attenuation refers to the phenomenon that when electromagnetic waves pass through a rainy area, the signal is attenuated due to the absorption and scattering of electromagnetic wave energy by raindrops. Accurately estimating and completing electromagnetic wave rain attenuation data is of great significance for the design and optimization of wireless communication systems. However, due to the limitations of collection equipment or environment, rain attenuation data usually has missing values, which affects the integrity and accuracy of the data.

[0003] The national invention patent "Method, device, processor and computer-readable storage medium for implementing radio electromagnetic situation interpolation processing based on propagation model" applied by Li Ji and others from Shanghai Chuangyuan Instrument Technology Co., Ltd. and authorized with announcement number CN113959443B uses interpolation processing for situation fusion.

[0004] As traditional missing data completion methods, such as interpolation or statistical interpolation methods, they often fail to fully capture the complexity and potential patterns of the data, which can easily lead to unsatisfactory completion effects. In response to this problem, Chang Xin and others from the 54th Institute of China Electronics Technology Group Corporation applied for a national invention patent "An Intelligent Electromagnetic Spectrum Map Fusion Method Based on Dense Autoencoders" with an authorization announcement number of CN118070230B, which directly used a dense encoder based on deep learning for situation fusion. However, this method requires that the historical data set and the data of the application scenario are relevant.

[0005] In the article "Electromagnetic Spectrum Map Construction Method Based on Residual Autoencoder" published in the journal "Radio Communication Technology" by Zhang Han and others from the School of Information and Communication Engineering of Harbin Engineering University, the use of residual encoder to reconstruct the electromagnetic spectrum map also has the problems of large amount of training data and migration ability.

[0006] Therefore, there is an urgent need in the prior art for a method that can efficiently fill in missing values ​​and improve data accuracy. Summary of the invention

[0007] The purpose of the present invention is to provide an electromagnetic wave rain attenuation completion measurement method based on non-negative matrix decomposition, aiming to improve the completion accuracy of missing data and thus improve the quality of the entire situation characterization.

[0008] The technical solution adopted by the present invention is:

[0009] A method for measuring and complementing electromagnetic wave rain attenuation based on non - negative matrix factorization includes the following steps:

[0010] Step 1: Divide the target area into grids, randomly measure the electromagnetic wave rain attenuation data per unit distance in some of the grids, and obtain an electromagnetic wave rain attenuation measurement matrix with missing values;

[0011] Step 2: Use a linear regression model to predict the missing values in the electromagnetic wave rain attenuation measurement matrix, and obtain an initial complemented matrix without missing values;

[0012] Step 3: Use different decomposition dimensions, decompose the initial complemented matrix based on the non - negative matrix factorization method, and obtain a reconstructed matrix according to each decomposition result;

[0013] Step 4: Select the best reconstructed matrix as the final measurement matrix for complementing the electromagnetic wave rain attenuation situation, so as to obtain the electromagnetic wave rain attenuation data per unit distance of each grid.

[0014] Furthermore, the specific method of Step 1 is as follows:

[0015] Step 1 - 1: Divide the target area into grids with squares of side length , and the number of rows and columns after division are I and J respectively;

[0016] Step 1 - 2: Randomly select E grids, where E < IJ, set an electromagnetic wave rain attenuation measurement device in each grid, and measure the electromagnetic wave rain attenuation data per unit distance of the E grids at the specified rainfall rate R;

[0017] Step 1 - 3: Construct an electromagnetic wave rain attenuation measurement matrix A with I rows and J columns:

[0018] A = [ a 11 ⋯ a 1 J ⋮ a ij ⋯ a I 1 ⋯ a IJ ]

[0019] Among them, the matrix elements corresponding to the E grids are the electromagnetic wave rain attenuation data per unit distance of the corresponding grids, and other matrix elements are missing values NaN.

[0020] Furthermore, the specific method of Step 2 is as follows:

[0021] Step 2 - 1: For the th column of the electromagnetic wave rain attenuation situation measurement matrix A, identify the row positions of each missing value and the row positions of each non - missing value ;

[0022] Step 2 - 2: Use the row positions as eigenvalues to construct a feature set X; for the th column of the electromagnetic wave rain attenuation situation measurement matrix A, the The matrix elements of the rows are used as target values ​​to construct the target set Y;

[0023] Step 2-3: Use the linear regression model to train based on the feature set X and the target set Y to obtain a linear regression model ;

[0024] Step 2-4: Substitute the electromagnetic wave rain attenuation situation measurement matrix A into The row positions of all missing values ​​in the column are entered into the linear regression model , get the predicted value of each missing value ;

[0025] Step 2-5: Repeat steps 2-1 to 2-4 until all J values ​​are traversed and the initial completion matrix without missing values ​​is obtained. .

[0026] Furthermore, in step 3, for the decomposition dimension p, the way to obtain the reconstructed matrix is:

[0027] Step 3-1: Use non-negative matrix factorization to complete the initial matrix Decomposed into two non-negative matrices and , where the matrix The dimension is I×p, the matrix The dimension is p×J;

[0028] Step 3-2: Calculate the reconstructed matrix under the decomposition dimension p:

[0029] .

[0030] Furthermore, the specific method of step 4 is:

[0031] The correlation coefficient of the non-missing values ​​between each reconstruction matrix and the electromagnetic wave rain attenuation measurement matrix is ​​calculated, and the reconstruction matrix with the highest correlation coefficient is selected as the final electromagnetic wave rain attenuation situation completion measurement matrix, thereby obtaining the electromagnetic wave rain attenuation data per unit distance of each grid.

[0032] The beneficial effects of the present invention are:

[0033] 1. Efficient missing value processing: The present invention predicts the missing values ​​after preliminary filling through a regression model, which can effectively improve the initial estimation accuracy of the missing values ​​and provide better initial conditions for subsequent matrix decomposition.

[0034] 2. Accurate matrix reconstruction: The present invention adopts non-negative matrix decomposition technology to achieve high-precision reconstruction of the original matrix by selecting the optimal potential dimension. This method can better maintain the characteristics of the original data and make the completed data close to the real data in terms of statistical characteristics.

[0035] 3. Flexibility and adaptability: The method of the present invention does not rely on a specific rain attenuation model or parameter setting, has strong versatility, and can adapt to the needs of completing electromagnetic wave rain attenuation data in different regions and under different parameter conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 Flow chart of the method of the present invention.

[0037] Figure 2 Schematic diagram of electromagnetic wave rain attenuation situation measurement matrix.

[0038] Figure 3 This is a complete matrix diagram of the electromagnetic wave rain attenuation situation.

[0039] Figure 4 This is a schematic diagram of the relationship between rank value and correlation coefficient.

[0040] Figure 5 This is a schematic diagram of the electromagnetic wave rain attenuation situation completion matrix. DETAILED DESCRIPTION

[0041] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

[0042] An electromagnetic wave rain attenuation completion measurement method based on non-negative matrix decomposition is proposed. The method first uses a linear regression model to preliminarily fill in the missing values ​​in the matrix, then uses the data of other known columns as features to fit the linear regression model, and uses the model to predict the missing values ​​to improve the accuracy of initialization. Finally, the initialized matrix is ​​subjected to non-negative matrix decomposition. By traversing different potential dimensions, the dimension value that can maximize the correlation coefficient of non-missing values ​​between the reconstructed matrix and the measured matrix is ​​selected as the final result.

[0043] like Figure 1 As shown, the specific steps include:

[0044] Step 1: Divide the target area into grids and measure the electromagnetic wave rain attenuation at each grid unit distance;

[0045] Step 1-1: Mesh the target area:

[0046] The target area is =1 km square grid, the number of rows and columns are I and J respectively, both of which are 10.

[0047] Step 1-2: Measure the electromagnetic wave rain attenuation at each grid unit distance:

[0048] E electromagnetic wave rain attenuation measurement devices are placed in E grids, where E is 80, and the electromagnetic wave rain attenuation data per unit distance under the specified rainfall rate R is obtained by measurement. , where R is 10 mm / h, and a total of E grids of electromagnetic wave rain attenuation data per unit distance are obtained, where. According to the number of rows I, the number of columns J and the electromagnetic wave rain attenuation data per unit distance Construct the electromagnetic wave rain attenuation situation measurement matrix A, such as Figure 2 As shown in the figure, the electromagnetic wave rain attenuation data per unit distance of the grid that has not been measured is set to the missing value NaN.

[0049] A = [ a 11 ⋯ a 1 J ⋮ a ij ⋯ a I 1 ⋯ a IJ ]

[0050] In addition, in order to facilitate the verification of the algorithm, the electromagnetic wave rain attenuation data per unit distance in all grids are measured to obtain the complete electromagnetic wave rain attenuation situation B, such as Figure 3 shown.

[0051] Step 2: Initialize the electromagnetic wave rain attenuation grid data with missing values;

[0052] Step 2-1: Separate known values ​​from missing values:

[0053] For each column , identify and store the row locations of missing values and the row positions of the non-missing values , and store them separately and In space.

[0054] Step 2-2: Extract data with known values:

[0055] From the filled matrix Extract The corresponding row data is used as training data, and its row position As eigenvalues, in the filled matrix The corresponding As the target value, traverse the row positions of all non-missing values ​​in the column to form the feature set X and the target set Y.

[0056] Step 2-3: Train the regression model:

[0057] Use the linear regression model to train based on the feature matrix feature set X and the target set Y to obtain the linear regression model .

[0058] Step 2-4: Get data with missing values:

[0059] The row locations where missing values ​​are stored of Enter the linear regression model , get the predicted missing value data assigned .

[0060] Step 2-5: Obtain a situation matrix without missing values :

[0061] Repeat steps 2-1 to 2-4 until j has traversed all J values, and a situation matrix with no missing values ​​will be obtained. .

[0062] Step 3: Use non-negative matrix factorization technology to reconstruct the initialized data;

[0063] Step 3-1: Matrix decomposition:

[0064] The situation matrix is ​​transformed into Decomposed into two non-negative matrices and , where the matrix The dimension is I×p, the matrix The dimension of is p×J, where p is the selected rank value.

[0065] Step 3-2: Calculate the reconstruction matrix:

[0066] .

[0067] Step 4, selecting the best reconstruction matrix as the final electromagnetic wave rain attenuation situation completion measurement matrix;

[0068] Step 4-1: Calculate the correlation coefficient:

[0069] Calculate the correlation coefficient of non-missing values ​​between the reconstruction matrix and the measurement matrix .

[0070] Step 4-2: Traverse different p values, ranging from [1,10], repeat steps 3-1 to 3-3, select the reconstructed matrix with the highest correlation coefficient as the final completion result, and select the optimal rank value of 4. The relationship between rank value and correlation coefficient is shown in the figure Figure 4 As shown, the completed matrix is Figure 5 shown.

[0071] The correlation coefficient between the electromagnetic wave rain attenuation situation completion result and the complete electromagnetic wave rain attenuation situation B is 0.9259, indicating that this method can achieve the electromagnetic wave rain attenuation situation completion under the premise of ensuring high similarity.

Claims

1. A method for measuring electromagnetic wave rain attenuation complement based on non-negative matrix decomposition, characterized in that: It includes the following steps: Step 1: Divide the target area into grids, randomly measure the unit-distance electromagnetic wave rain attenuation data in some of the grids, and obtain an electromagnetic wave rain attenuation measurement matrix with missing values. The specific method is as follows: Step 1-1: Take the side length as The target area is divided into grids by squares, and the number of rows and columns after division are I and J respectively; Step 1-2: Randomly select E grids, where E < IJ. Set an electromagnetic wave rain attenuation measurement device in each grid, and measure the unit-distance electromagnetic wave rain attenuation data of the E grids at the specified rainfall rate R. Step 1-3: Construct an electromagnetic wave rain attenuation measurement matrix A with I rows and J columns: Among them, the matrix elements corresponding to the E grids are the unit-distance electromagnetic wave rain attenuation data of the corresponding grids, and the other matrix elements are missing values NaN. Step 2: Use a linear regression model to predict the missing values in the electromagnetic wave rain attenuation measurement matrix, and obtain an initial completion matrix without missing values. The specific method is as follows: Step 2-1: For the electromagnetic wave rain attenuation situation measurement matrix A Columns, identifying the row location of each missing value and the row position of each non-missing value ; Step 2-2: Change the row position As the eigenvalue, construct the feature set X; the electromagnetic wave rain attenuation situation measurement matrix A is Ledi The matrix elements of the rows are used as target values ​​to construct the target set Y; Step 2-3: Use the linear regression model to train based on the feature set X and the target set Y to obtain a linear regression model ; Step 2-4: Substitute the electromagnetic wave rain attenuation situation measurement matrix A into The row positions of all missing values ​​in the column are entered into the linear regression model , get the predicted value of each missing value ; Step 2-5: Repeat steps 2-1 to 2-4 until all J values ​​are traversed and the initial completion matrix without missing values ​​is obtained. ; Step 3: Use different decomposition dimensions to decompose the initial completion matrix based on the non-negative matrix factorization method, and obtain a reconstruction matrix according to each decomposition result. Among them, for the decomposition dimension p, the method to obtain the reconstruction matrix is: Step 3-1: Use non-negative matrix factorization to complete the initial matrix Decomposed into two non-negative matrices and , where the matrix The dimension is I×p, the matrix The dimension is p×J; Step 3-2: Calculate the reconstruction matrix under the decomposition dimension p: ； Step 4: Select the best reconstruction matrix as the final electromagnetic wave rain attenuation situation completion measurement matrix, so as to obtain the unit-distance electromagnetic wave rain attenuation data of each grid. The specific method is as follows: Calculate the correlation coefficient of the non-missing values between each reconstruction matrix and the electromagnetic wave rain attenuation measurement matrix, and select the reconstruction matrix with the highest correlation coefficient as the final electromagnetic wave rain attenuation situation completion measurement matrix, so as to obtain the unit-distance electromagnetic wave rain attenuation data of each grid.

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