Radio map estimation method and device based on minimization of truncation kernel norm

Abstract

The invention discloses a radio map estimation method and device based on a minimization truncation kernel norm, and the method comprises the steps: collecting radio map data, and building a radio map matrix based on the radio map data; sampling the radio map matrix to obtain a sampling matrix; based on the radio map matrix and the sampling matrix, constructing an optimization objective function for minimizing a truncation kernel norm of a radio map estimation matrix; and solving the optimized objective function to obtain an estimated value of the radio map matrix. In the embodiment of the invention, the radio estimation task is carried out by utilizing the advantages of the truncated kernel norm regularization technology in the matrix completion and low-rank matrix recovery problems, so that the estimation can be better realized in a low sampling rate and complex radio environment, and the performance is excellent.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technology, and in particular to a radio map estimation method and device based on minimizing a truncated nuclear norm. Background Art

[0002] With the rapid development of wireless communication technology and digital signal processing technology, the wireless communication environment has become more and more complex. Factors such as channel attenuation, electromagnetic interference, and receiving system diversity significantly affect the propagation of radio signals, resulting in a decrease in signal quality at the receiving end. In this context, it becomes particularly important to build an accurate radio map.

[0003] Traditional radio map estimation methods are mainly suitable for open spaces and high sampling rates, but perform poorly in low sampling rates and complex environments. These methods usually rely on propagation models and can provide relatively accurate predictions under ideal conditions. However, data sparsity and environmental complexity make these methods difficult to meet the needs, and obtaining high sampling rate data requires a lot of measurements and resources, which is unrealistic in many cases.

[0004] To address these issues, a variety of methods based on machine learning and optimization techniques have been proposed. These methods can intelligently process and optimize existing measurement data and build relatively accurate radio maps even when data is sparse. However, these machine learning-based methods still face the challenge of poor performance in complex building environments in practical applications. On the other hand, for complex building environments, low-rank matrix recovery and matrix completion techniques can effectively restore signal strength distribution in the case of low missing data by utilizing the inherent structural characteristics of the signal, but the effect is still not ideal in the case of high missing data. Summary of the invention

[0005] Based on this, it is necessary to provide a radio map estimation method, apparatus, computer device and storage medium based on minimizing the truncated nuclear norm to address the above technical issues, so as to solve at least one problem existing in the above prior art.

[0006] In a first aspect, an embodiment of the present application is implemented by providing a radio map estimation method based on minimizing a truncated nuclear norm, including:

[0007] collecting radio map data, and constructing a radio map matrix based on the radio map data;

[0008] Sampling the radio map matrix to obtain a sampling matrix;

[0009] constructing an optimization objective function for minimizing a truncated nuclear norm of a radio map estimation matrix based on the radio map matrix and the sampling matrix;

[0010] The optimization objective function is solved to obtain an estimated value of the radio map matrix.

[0011] In one embodiment, the radio map data is unobstructed radio map data, and collecting the radio map data includes:

[0012] Determine the spatial loss function of the emission source based on the emission source position, the path loss coefficient, and the log-normal shadow component sampled from the Gaussian distribution;

[0013] Determine the power spectral density of the transmitting source based on the center frequency, sidelobe width, and random intensity scaling;

[0014] A radio map signal strength is determined based on a spatial loss function of the transmission source and a power spectral density of the transmission source.

[0015] In one embodiment, the optimization objective function includes a first intermediate variable and a second intermediate variable, and solving the optimization objective function to obtain an estimated value of a radio map matrix includes:

[0016] Solving the first intermediate variable and the second intermediate variable of the optimization objective function by using a first solving algorithm;

[0017] Based on the first intermediate variable and the second intermediate variable, the optimization objective function is solved by a second solving algorithm to obtain an estimated value of the radio map matrix.

[0018] In one embodiment, solving the first intermediate variable and the second intermediate variable of the optimization objective function by using the first solving algorithm includes:

[0019] Initializing a radio map estimation matrix based on the radio map matrix and the sampling matrix;

[0020] Performing singular value decomposition on the initialized radio map estimation matrix to obtain a left singular vector matrix, a right singular vector matrix and a singular value matrix;

[0021] Determine a first intermediate variable based on the left singular vector matrix;

[0022] A second intermediate variable is determined based on the right singular vector matrix.

[0023] In one embodiment, the singular value decomposition of the initialized radio map matrix can be calculated by the following formula:

[0024] The singular value decomposition of the initialized radio map matrix can be calculated by the following formula:

[0025] [U l ,∑ l , V l ]=svd(X l ).

[0026] Among them, U l represents the left singular vector matrix, V l represents the right singular vector matrix, ∑ l represents the singular value matrix, X l represents the initialized radio map matrix, X l =M Ω , M represents the radio map matrix, Ω represents the sampling matrix, and svd represents the singular value operator.

[0027] In one embodiment, solving the optimization objective function by a second solving algorithm to obtain an estimated value of a radio map matrix includes:

[0028] Construct and solve the objective function;

[0029] Lagrange multipliers and penalty terms are introduced, and the objective function is solved by a polynomial alternating direction multiplier algorithm to obtain an estimated value of the radio map matrix.

[0030] In one embodiment, the introducing of Lagrange multipliers and penalty terms and solving the objective function by a polynomial alternating direction multiplier algorithm to obtain an estimated value of the radio map matrix includes:

[0031] Step a: Initialize X l =M Ω , W l =X l , Y l =X l , β = 1 and k = 1;

[0032] Step b: Fix W k , Y k ,calculate

[0033] Step c: Fix X k+1 , Y k ,calculate And make

[0034] Step d: Fix X k+1 , calculate Y k+1 =Y k +β(X k+1 -W k+1 );

[0035] Step e: Update k=k+1;

[0036] Step f: Determine whether the preset convergence condition is met at present;

[0037] If not, repeating steps bf until the preset convergence condition is met, outputting the estimated value of the radio map matrix;

[0038] Among them, A l represents the first intermediate variable, B l represents the second intermediate variable, M Ω represents the submatrix of the radio map matrix about the sampling point, Ω is the sampling matrix, M is the radio map matrix, ∈ represents the allowable error, β represents the penalty parameter, k represents the iteration counter, the initial k is 1, and k increases by 1 in each round, W k represents the relaxation matrix updated in the kth iteration, Y k represents the updated Lagrange multiplier matrix in the kth iteration, Y represents the Lagrange multiplier matrix, which reflects the degree of violation of the constraints in the optimization process, and X k+1 represents the estimate of the radio map matrix M at the k+1th iteration, D 1 / β represents the soft threshold operator, W k+1 represents the relaxation matrix updated in the k+1th iteration, T represents the transpose, represents an orthogonal map acting on complements, that is, for any matrix,

[0039] In one embodiment, the objective function is expressed as:

[0040] The objective function to be solved is expressed as:

[0041]

[0042] stX=W,

[0043] W Ω =M Ω

[0044] Among them, A l represents the first intermediate variable, B l represents the second intermediate variable, M Ω Indicates M Ω represents the submatrix of the radio map matrix about the sampling point, Ω is the sampling matrix, M is the radio map matrix, W Ω represents the sub-matrix of the relaxation matrix W with respect to the sampling points.

[0045] In a second aspect, a radio map estimation device based on minimizing a truncated nuclear norm is provided, comprising:

[0046] a radio map matrix acquisition unit, configured to collect radio map data and construct a radio map matrix based on the radio map data;

[0047] A sampling matrix acquisition unit, used for sampling the radio map matrix to obtain a sampling matrix;

[0048] an optimization objective function construction unit, configured to construct, based on the radio map matrix and the sampling matrix, an optimization objective function for minimizing a truncated nuclear norm of a radio map estimation matrix;

[0049] A solving unit is used to solve the optimization objective function to obtain an estimated value of the radio map matrix.

[0050] In a third aspect, a computer device is provided, comprising a memory, a processor, and computer-readable instructions stored in the memory and executable on the processor, wherein when the processor executes the computer-readable instructions, the above-mentioned radio map estimation method based on minimizing the truncated nuclear norm is implemented.

[0051] In a fourth aspect, a readable storage medium is provided, wherein when the computer-readable instructions are executed by one or more processors, the one or more processors execute the radio map estimation method based on minimizing the truncated nuclear norm as described above.

[0052] The above-mentioned radio map estimation method, device, computer equipment and storage medium based on minimizing the truncated nuclear norm, the method implementation includes: collecting radio map data, constructing a radio map matrix based on the radio map data; sampling the radio map matrix to obtain a sampling matrix; based on the radio map matrix and the sampling matrix, constructing an optimization objective function to minimize the truncated nuclear norm of the radio map estimation matrix; solving the optimization objective function to obtain an estimated value of the radio map matrix. In the embodiment of the present application, the advantages of the truncated nuclear norm regularization technology in matrix completion and low-rank matrix recovery problems are used to perform radio estimation tasks, so that estimation can be better achieved in low sampling rates and complex radio environments, and the performance is excellent. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for use in the description of the embodiments of the present invention will be briefly introduced below. Obviously, the accompanying drawings in the following description are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative labor.

[0054] Figure 1is a flow chart of a radio map estimation method based on minimizing the truncated nuclear norm in one embodiment of the present invention;

[0055] Figure 2 is an example of a radio map data set under an unobstructed condition in one embodiment of the present invention;

[0056] Figure 3 is an example of a radio map data set under occlusion in one embodiment of the present invention;

[0057] Figure 4 1 is a schematic diagram of the estimation effect of an estimation algorithm based on maximizing the truncated nuclear norm in an unobstructed environment according to an embodiment of the present invention;

[0058] Figure 5 It is a schematic diagram of the estimation effect of the existing algorithm in an environment with occlusion in one embodiment of the present invention;

[0059] Figure 6 1 is a schematic diagram of the estimation effect of an estimation algorithm based on maximizing the truncated nuclear norm in an obstructed environment according to an embodiment of the present invention;

[0060] Figure 7 It is a schematic diagram of the estimation effect of the existing algorithm in an environment with occlusion in one embodiment of the present invention;

[0061] Figure 8 is a structural schematic diagram of a radio map estimation method and device based on minimizing the truncated nuclear norm in one embodiment of the present invention;

[0062] Fig. 9 is a schematic diagram of a computer device according to an embodiment of the present invention. DETAILED DESCRIPTION

[0063] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0064] In one embodiment, if Figure 1 As shown, a radio map estimation method based on minimizing the truncated nuclear norm is provided, comprising the following steps:

[0065] In step S110, radio map data is collected, and a radio map matrix is ​​constructed based on the radio map data;

[0066] In the embodiment of the present application, the radio map data includes unobstructed radio map data and obstructed radio map data. Figure 2 , shows an example of a radio map data set under unobstructed conditions. Unobstructed radio map data specifically refers to radio data when there is no obstruction from buildings or other objects. Similarly, see Figure 3 , shows an example of a radio map data set under occlusion. The occluded radio map data is the radio data when there are objects such as buildings blocking it. By acquiring the radio map data in a certain area, the radio map matrix can be formed. It means that the radio map matrix M is a real matrix with m rows and n columns. represents a real matrix with m rows and n columns, where m and n represent the number of rows and columns of the radio map matrix respectively.

[0067] The radio map data may specifically include information such as geographic location and signal strength.

[0068] in, Figure 2 , Figure 3 In the example, the horizontal and vertical axis units represent the index values ​​in the matrix. For example, if X is 51*51, the horizontal axis is 1-51, and the vertical axis is the same.

[0069] In an embodiment of the present application, for unobstructed wireless map data, collecting radio map data includes:

[0070] Determine the spatial loss function of the emission source based on the emission source position, the path loss coefficient, and the log-normal shadow component sampled from the Gaussian distribution;

[0071] Determine the power spectral density of the transmitting source based on the center frequency, sidelobe width, and random intensity scaling;

[0072] A radio map signal strength is determined based on a spatial loss function of the transmission source and a power spectral density of the transmission source.

[0073] Specifically, for the spatial loss function SLF of the transmitting source, reference can be made to the transmitting source position, the path loss coefficient, and the log-normal shadow component sampled from the Gaussian distribution, the autocorrelation of which is related to the decorrelation distance. Specifically, it can be expressed as Among them, y = (i, j) represents the spatial coordinate, r r is the position of the rth source, γ r is the log-normal shadow component associated with the emission source r, which can be represents the autocorrelation between y and y′, where d corr is the decorrelation distance, v r Indicates from The value sampled in .

[0074] The power spectral density (PSD) of the transmitting source depends on the center frequency, sidelobe width and random intensity scaling, which are sampled from different distributions. Finally, the radio map signal strength is calculated by combining SLF, PSD and noise tensor. It can be expressed as in, is the center frequency of the M subbands of the transmitting source r, Controls the sidelobe width of the PSD of the transmitter r in its i-th subband, is the random intensity scaling of the PSD of the transmitting source r in its ith subband, sinc 2 represents the square of the sinc function, that is k represents the frequency index, for example, the final C r (k) represents the value of the PSD of transmitter r at the kth frequency, f i (r) Denotes the center frequency of the i-th subband of transmitter r.

[0075] In getting r and c r After that, the strength of the radio map signal can be calculated by the following formula: Where N represents the noise tensor.

[0076] In one embodiment of the present application, the obstructed radio map data can be obtained through existing data sets, for example, the RadioMapSeer data set contains 700 city maps, each of which has 80 transmitter locations and corresponding simulated radio maps. PL0: reference path loss; γ: path loss index; d: propagation distance; Additional losses due to factors such as reflection and diffraction] and generated by intelligent ray tracing (IRT2) based on secondary interaction with the geometry structure.

[0077] It should be noted that all simulations can be calculated using WinProp software. The size of each map is 256×256 square meters and is converted into a grayscale image of 256×256 pixels, where each pixel represents one square meter. The pixel value inside the building is 1, and the pixel value outside is 0. Each simulated radio map stores the path loss (in dB) from the pixel location to the transmitter location at each pixel. The path loss value P L is converted to grayscale pixel value f, where M1 is the maximum path loss value of all radio graphs in the dataset, and P L，tmc is the cutoff threshold. In this data set, P L，tmc =-147dB.

[0078] In step S120, the radio map matrix is ​​sampled to obtain a sampling matrix;

[0079] In one embodiment of the present application, a plurality of sampling points may be set for the radio map matrix, and each sampling point may be sampled, and the sampled radio map data may be recorded to generate the sampling matrix. It means that the sampling matrix Ω is a real matrix with m rows and n columns. Represents a real matrix with m rows and n columns.

[0080] In step S130, based on the radio map matrix and the sampling matrix, an optimization objective function is constructed to minimize the truncated nuclear norm of the radio map estimation matrix;

[0081] In the embodiment of the present application, the radio map matrix Sampling Matrix When the value at the sampling point (i, j) is sampled, Ω(i, j) = 1, otherwise Ω(i, j) = 0. Let the radio map estimation matrix be X. Then the optimization objective function of minimizing the truncated nuclear norm of the radio map estimation matrix can be specifically expressed as:

[0082]

[0083] xT Ω =M Ω .

[0084] Where A represents the first intermediate vector, B represents the second intermediate vector, and T represents transpose.

[0085] Tr(AXB T ) indicates that Tr represents the trace operation, which is expressed as a matrix (AXB T ) and the sum of the singular values ​​of X Ω Represents the submatrix of the estimation matrix about the sampling point, M Ω represents the submatrix of the radio map matrix about the sampling point, M Ω =M⊙Ω, ⊙ is the Hadamard product, ||X|| * It represents the estimated nuclear norm of the matrix X, which is the sum of all singular values ​​of the matrix X.

[0086] The constraint condition of the above optimization objective function is specifically to minimize the truncated nuclear norm of the estimation matrix X while making the position of the estimation matrix X at the sampling point equal to the value at the real radio map matrix M.

[0087] In step S140, the optimization objective function is solved to obtain an estimated value of the radio map matrix.

[0088] In the embodiment of the present application, when solving the optimization objective function, the above optimization objective function can be divided into two parts for solving, as shown below:

[0089] The optimization objective function includes a first intermediate variable and a second intermediate variable, and solving the optimization objective function to obtain an estimated value of a radio map matrix includes:

[0090] Solving the first intermediate variable and the second intermediate variable of the optimization objective function by using a first solving algorithm;

[0091] Based on the first intermediate variable and the second intermediate variable, the optimization objective function is solved by a second solving algorithm to obtain an estimated value of the radio map matrix.

[0092] The first solution algorithm is used to fix the radio map estimation matrix and solve the first intermediate variable A and the second intermediate variable B, and the second solution algorithm is used to fix the first intermediate variable A and the second intermediate variable B and solve the estimated value of the radio map matrix. The first solution algorithm can be a singular value decomposition algorithm, and the second solution algorithm can solve the optimization target by constructing a solution, and introducing Lagrange multipliers and penalty terms to solve the optimization target to obtain the estimated value of the radio map matrix.

[0093] Further, solving the first intermediate variable and the second intermediate variable of the optimization objective function by the first solving algorithm includes:

[0094] Step 1: Initializing a radio map estimation matrix based on the radio map matrix and the sampling matrix;

[0095] Step 2: performing singular value decomposition on the initialized radio map estimation matrix to obtain a left singular vector matrix, a right singular vector matrix and a singular value matrix;

[0096] Step 3: Determine a first intermediate variable based on the left singular vector matrix;

[0097] Step 4: Determine the second intermediate variable based on the right singular vector matrix.

[0098] Specifically, the wireless map matrix M can be input Ω , where Ω is the sampling matrix, truncation parameter r and tolerance ∈.

[0099] Initialization: X1 = M Ω , l=1

[0100] The singular value decomposition of the initialized radio map matrix can be calculated by the following formula:

[0101] [U l ,∑ l , V l ]=svd(X l );

[0102] in, U l represents the left singular vector matrix, V l represents the right singular vector matrix, ∑ l represents the singular value matrix, X l represents the initialized radio map matrix, X l =M Ω , M represents the radio map matrix, Ω represents the sampling matrix, and svd represents the singular value operator.

[0103] After decomposing the above singular values, we can get the left singular vector matrix U l , right singular vector matrix V l And the singular value matrix ∑ l , A can be calculated by the following formula l , B l , specifically expressed as:

[0104] A l =(u1, .., u r ) T , B l =(v1, .., v r ) T

[0105] Understandable, A. l Yes l The first r vectors of and take the transpose, B l Is to take V l Take the first r vectors of and take the transpose.

[0106] Step 5: Based on the calculated A l , B l , can be further solved by the second solution algorithm Among them, X Ω =M Ω ;

[0107] Step 6: Update l=l+1;

[0108] Step 7: Determine whether the current convergence condition is met ||X l -X l-1 || F ≤∈, (where X l With X l-1 is the estimated value of two consecutive times. When the estimated value changes very little, represents the Frobenius norm, m and n are the number of rows and columns of the matrix Z respectively, then X is considered to converge). If not, return to step 2 and execute steps 2-7 again until the convergence conditions are met, then the estimated value of the radio map matrix is ​​output.

[0109] In an embodiment of the present application, solving the optimization objective function by a second solving algorithm to obtain an estimated value of the radio map matrix includes:

[0110] Construct and solve the objective function;

[0111] Lagrange multipliers and penalty terms are introduced, and the objective function is solved by a polynomial alternating direction multiplier algorithm to obtain an estimated value of the radio map matrix.

[0112] The objective function can be specifically expressed as:

[0113]

[0114] stX=W,

[0115] W Ω =M Ω

[0116] Among them, W is an intermediate variable.

[0117] The augmented Lagrangian equation for solving the objective function can be expressed as:

[0118]

[0119] Where X is the estimate of the radio map, W is a relaxation matrix used to relax the constraints during the solution process, Y is the matrix corresponding to the penalty term, Tr is the trace of the calculation matrix, that is, the sum of the singular values, and β>0 represents the penalty parameter.

[0120] In one embodiment of the present application, specifically, ADMM (Alternating Direction Method of Multipliers) may be used to solve the goal.

[0121] The introducing of Lagrange multipliers and penalty terms and solving the objective function by a polynomial alternating direction multiplier algorithm to obtain an estimated value of the radio map matrix includes:

[0122] Step a: Initialize X1 = M Ω , W1=X l , Y l =X l , β = 1 and k = 1;

[0123] Step b: Fix W k , Y k ,calculate

[0124] Step c: Fix X k+1 , Y k ,calculate And make

[0125] Step d: Fix x k+1 , calculate Y k+1 =Y k +β(x k+1 -W k+1 );

[0126] Step e: Update k=k+1;

[0127] Step f: Determine whether the preset convergence condition is met at present;

[0128] If not, repeating steps bf until the preset convergence condition is met, outputting the estimated value of the radio map matrix;

[0129] Among them, Al represents the first intermediate variable, Bl represents the second intermediate variable, M Ω represents the submatrix of the radio map matrix about the sampling point, which is calculated as M Ω (i, j) = M(i, j) · Ω(i, j), Ω is the sampling matrix, M is the radio map matrix, ∈ represents the allowable error, β represents the penalty parameter, k represents the iteration counter, the initial k is 1, and k increases by 1 in each round, W k represents the relaxation matrix updated in the kth iteration (W is a relaxation matrix used to relax constraints during the solution process), Y k represents the updated Lagrange multiplier matrix in the kth iteration, Y represents the Lagrange multiplier matrix, which reflects the degree of violation of the constraints in the optimization process, and X k+1 represents the estimate of the radio map matrix M at the k+1th iteration, D 1 / β Denotes the soft thresholding operator, and the specific calculation formula is D 1 / β (Z)=sign(Z)·max(|Z|-1 / β, 0), W k+1 represents the relaxation matrix updated in the k+1th iteration, T represents the transpose, represents an orthogonal map acting on complements, that is, for any matrix,

[0130] In one embodiment of the present application, the objective function is expressed as:

[0131]

[0132] stX=W,

[0133] W Ω =M Ω .

[0134] Among them, Al represents the first intermediate variable, B l represents the second intermediate variable, M Ω Indicates M Ω represents the submatrix of the radio map matrix about the sampling point, Ω is the sampling matrix, M is the radio map matrix, W Ω Represents the submatrix of the relaxation matrix W about the sampling point. The specific calculation formula is W Ω (i,j)=W(i,j)·Ω(i,j).

[0135] Among them, the convergence condition can be ||X l -X l-1 || F ≤∈, where X l With X l-1 is the estimated value of two consecutive times. When the estimated value changes very little, that is, F represents, where ||X l -X l-1 || F Indicates (letter meaning), if not, iterate the above steps again until the convergence condition is met, then output the estimated value of the radio map matrix.

[0136] Where Dτ represents the soft threshold operator, which can be specifically expressed as:

[0137] D τ (Y): =UD τ (S)V T , D τ (S) = diag({(σ i -τ) +} l≤i≤r ).

[0138] Where r is the rank of Y, Y = USV T is the singular value decomposition (SVD) of Y, as well as is an orthogonal matrix, and t + =max{0, t} means taking the maximum value between t and 0, diag({(σ i -τ) +} 1≤i≤r ) represents a diagonal matrix, where each corresponding element on the diagonal is (σ i -τ) +, there are a total of r elements, i ranges from 1 to r.

[0139] In the embodiment of the present application, for the radio map data without occlusion, under the condition of 20% random sampling rate, the estimation effect obtained by minimizing the truncated nuclear norm method TNNR and solving it can be as follows: Figure 4 As shown, based on existing methods, such as Nuclear Norm Regularization (NNR), Figure 5 As shown, it can be seen that the estimation effect of the method of minimizing the truncated nuclear norm is significantly better than that of NNR.

[0140] For radio map data with occlusion, under the condition of 40% random sampling rate, the estimation effect obtained by minimizing the truncated nuclear norm method TNNR and solving it can be shown as follows Figure 6 As shown, based on existing methods, for example, NNR can be Figure 7 As shown, it can be seen that under the same sampling rate, compared with the real radio map, the outline of the occluder can be better estimated, while the estimation effect of the original algorithm is poor.

[0141] In the embodiments of the present application, the advantages of truncated nuclear norm regularization technology in matrix completion and low-rank matrix recovery problems are utilized to perform radio estimation tasks, so that estimation can be achieved better with excellent performance in low sampling rates and complex radio environments.

[0142] It should be understood that the order of execution of the steps in the above embodiment does not necessarily mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiment of the present invention.

[0143] In one embodiment, a radio map estimation apparatus based on minimizing the truncated nuclear norm is provided, and the radio map estimation apparatus based on minimizing the truncated nuclear norm corresponds one-to-one to the radio map estimation method based on minimizing the truncated nuclear norm in the above embodiment. Figure 8 As shown, the radio map estimation device based on minimizing the truncated nuclear norm includes a radio map matrix acquisition unit 10, a sampling matrix acquisition unit 20, an optimization objective function construction unit 30 and a solution unit 40. The functional modules are described in detail as follows:

[0144] A radio map matrix acquisition unit 10, configured to collect radio map data and construct a radio map matrix based on the radio map data;

[0145] A sampling matrix acquisition unit 20, configured to sample the radio map matrix to obtain a sampling matrix;

[0146] An optimization objective function construction unit 30 is used to construct an optimization objective function for minimizing a truncated nuclear norm of a radio map estimation matrix based on the radio map matrix and the sampling matrix;

[0147] The solving unit 40 is used to solve the optimization objective function to obtain an estimated value of the radio map matrix.

[0148] In an embodiment of the present application, the radio map data is unobstructed radio map data, and the radio map matrix acquisition unit 10 is further used to:

[0149] Determine the spatial loss function of the emission source based on the emission source position, the path loss coefficient, and the log-normal shadow component sampled from the Gaussian distribution;

[0150] Determine the power spectral density of the transmitting source based on the center frequency, sidelobe width, and random intensity scaling;

[0151] A radio map signal strength is determined based on a spatial loss function of the transmission source and a power spectral density of the transmission source.

[0152] In an embodiment of the present application, the optimization objective function includes a first intermediate variable and a second intermediate variable, and the solving unit 40 is further used to:

[0153] Solving the first intermediate variable and the second intermediate variable of the optimization objective function by using a first solving algorithm;

[0154] Based on the first intermediate variable and the second intermediate variable, the optimization objective function is solved by a second solving algorithm to obtain an estimated value of the radio map matrix.

[0155] In one embodiment of the present application, the solving unit 40 is further configured to:

[0156] Initializing a radio map estimation matrix based on the radio map matrix and the sampling matrix;

[0157] Performing singular value decomposition on the initialized radio map estimation matrix to obtain a left singular vector matrix, a right singular vector matrix and a singular value matrix;

[0158] Determine a first intermediate variable based on the left singular vector matrix;

[0159] A second intermediate variable is determined based on the right singular vector matrix.

[0160] In one embodiment of the present application, the solving unit 40 is further configured to:

[0161] [U l ,∑ l , Vl ]=svd(X l ).

[0162] Among them, U l represents the left singular vector matrix, V l represents the right singular vector matrix, ∑ l represents the singular value matrix, X l Initialized radio map matrix, X l =MΩ, M represents the radio map matrix, Ω represents the sampling matrix, and svd represents the singular value operator. In one embodiment of the present application, the solving unit 40 is further used to:

[0163] Construct and solve the objective function;

[0164] Lagrange multipliers and penalty terms are introduced, and the objective function is solved by a polynomial alternating direction multiplier algorithm to obtain an estimated value of the radio map matrix.

[0165] In one embodiment of the present application, the solving unit 40 is further configured to:

[0166] Step a: Initialize X l =M Ω , W l =X l , Y l =X l , β = 1 and k = 1;

[0167] Step b: Fix W k , Y k ,calculate

[0168] Step c: Fix X k+1 , Y k ,calculate And make

[0169] Step d: Fix x k+1 , calculate Y k+1 =Y k +β(X k+1 -W k+1 );

[0170] Step e: Update k=k+1;

[0171] Step f: Determine whether the preset convergence condition is met at present;

[0172] If not, repeating steps bf until the preset convergence condition is met, outputting the estimated value of the radio map matrix;

[0173] Among them, Al represents the first intermediate variable, Bl represents the second intermediate variable, M Ω represents the submatrix of the radio map matrix about the sampling point, Ω is the sampling matrix, M is the radio map matrix, ∈ represents the allowable error, β represents the penalty parameter, k represents the iteration counter, the initial k is 1, and k increases by 1 in each round, W k represents the relaxation matrix updated in the kth iteration, Y k represents the updated Lagrange multiplier matrix in the kth iteration, Y represents the Lagrange multiplier matrix, which reflects the degree of violation of the constraints in the optimization process, and X k+1 represents the estimate of the radio map matrix M at the k+1th iteration, D 1 / β represents the soft threshold operator, W k+1 represents the relaxation matrix updated in the k+1th iteration, T represents the transpose, represents an orthogonal map acting on complements, that is, for any matrix,

[0174] In one embodiment of the present application, the solving unit 40 is further configured to:

[0175]

[0176] stX=W,

[0177] W Ω =M Ω

[0178] Among them, A l represents the first intermediate variable, B l represents the second intermediate variable, M Ω Indicates M Ω represents the submatrix of the radio map matrix about the sampling point, Ω is the sampling matrix, M is the radio map matrix, W Ω represents the sub-matrix of the relaxation matrix W with respect to the sampling points.

[0179] In the embodiments of the present application, the advantages of truncated nuclear norm regularization technology in matrix completion and low-rank matrix recovery problems are utilized to perform radio estimation tasks, so that estimation can be achieved better with excellent performance in low sampling rates and complex radio environments.

[0180] For the specific definition of the radio map estimation device based on minimizing the truncated nuclear norm, please refer to the definition of the radio map estimation method based on minimizing the truncated nuclear norm in the above text, which will not be repeated here. Each module in the above-mentioned radio map estimation device based on minimizing the truncated nuclear norm can be implemented in whole or in part by software, hardware and a combination thereof. The above-mentioned modules can be embedded in or independent of the processor in the computer device in the form of hardware, or can be stored in the memory of the computer device in the form of software, so that the processor can call and execute the operations corresponding to the above modules.

[0181] In one embodiment, a computer device is provided. The computer device may be a terminal device, and its internal structure diagram may be as follows: Fig. 9 As shown. The computer device includes a processor, a memory, and a network interface connected through a system bus. Among them, the processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a readable storage medium. The readable storage medium stores computer-readable instructions. The network interface of the computer device is used to communicate with an external terminal through a network connection. When the computer-readable instructions are executed by the processor, a radio map estimation method based on minimizing the truncated nuclear norm is implemented. The readable storage medium provided in this embodiment includes a non-volatile readable storage medium and a volatile readable storage medium.

[0182] In an embodiment of the present application, a computer device is provided, including a memory, a processor, and computer-readable instructions stored in the memory and executable on the processor. When the processor executes the computer-readable instructions, the steps of the radio map estimation method based on minimizing the truncated nuclear norm as described above are implemented.

[0183] In an embodiment of the application, a readable storage medium is provided, wherein the readable storage medium stores computer-readable instructions, and when the computer-readable instructions are executed by a processor, the steps of the radio map estimation method based on minimizing the truncated nuclear norm as described above are implemented.

[0184] Those of ordinary skill in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be implemented by instructing related hardware through computer-readable instructions, and the computer-readable instructions can be stored in a non-volatile readable storage medium or a volatile readable storage medium. When the computer-readable instructions are executed, they may include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, storage, database or other media used in the embodiments provided in this application may include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM) or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in many forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link (Synchlink) DRAM (SLDRAM), memory bus (Rambus) direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0185] Those skilled in the art can clearly understand that for the convenience and simplicity of description, only the division of the above-mentioned functional units and modules is used as an example. In actual applications, the above-mentioned functions can be distributed and completed by different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above.

[0186] The embodiments described above are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. Such modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be included in the protection scope of the present invention.

Claims

1. A radio map estimation method based on minimizing the truncated nuclear norm, characterized in that: The method comprises: collecting radio map data, and constructing a radio map matrix based on the radio map data; Sampling the radio map matrix to obtain a sampling matrix; constructing an optimization objective function for minimizing a truncated nuclear norm of a radio map estimation matrix based on the radio map matrix and the sampling matrix; The optimization objective function is solved to obtain an estimated value of the radio map matrix.

2. The radio map estimation method for minimizing the truncated nuclear norm according to claim 1, characterized in that The radio map data is unobstructed radio map data, and collecting the radio map data includes: Determine the spatial loss function of the emission source based on the emission source position, the path loss coefficient, and the log-normal shadow component sampled from the Gaussian distribution; Determine the power spectral density of the transmitting source based on the center frequency, sidelobe width, and random intensity scaling; A radio map signal strength is determined based on a spatial loss function of the transmission source and a power spectral density of the transmission source.

3. The radio map estimation method based on minimizing the truncated nuclear norm according to claim 1, characterized in that: The optimization objective function includes a first intermediate variable and a second intermediate variable, and solving the optimization objective function to obtain an estimated value of a radio map matrix includes: Solving the first intermediate variable and the second intermediate variable of the optimization objective function by using a first solving algorithm; Based on the first intermediate variable and the second intermediate variable, the optimization objective function is solved by a second solving algorithm to obtain an estimated value of the radio map matrix.

4. The radio map estimation method based on minimizing the truncated nuclear norm according to claim 3, characterized in that: Solving the first intermediate variable and the second intermediate variable of the optimization objective function by using the first solving algorithm includes: Initializing a radio map estimation matrix based on the radio map matrix and the sampling matrix; Performing singular value decomposition on the initialized radio map estimation matrix to obtain a left singular vector matrix, a right singular vector matrix and a singular value matrix; Determine a first intermediate variable based on the left singular vector matrix; A second intermediate variable is determined based on the right singular vector matrix.

5. The radio map estimation method based on minimizing the truncated nuclear norm according to claim 3, characterized in that: The singular value decomposition of the initialized radio map matrix can be calculated by the following formula: [U l ,Σ l ,V l ]=svd(X l ); Among them, U l represents the left singular vector matrix, V l represents the right singular vector matrix, ∑ l represents the singular value matrix, X l represents the initialized radio map matrix, X1 = M Ω , M represents the radio map matrix, Ω represents the sampling matrix, and svd represents the singular value operator.

6. The radio map estimation method based on minimizing the truncated nuclear norm according to claim 3, characterized in that: Solving the optimization objective function by a second solving algorithm to obtain an estimated value of a radio map matrix includes: Construct and solve the objective function; Lagrange multipliers and penalty terms are introduced, and the objective function is solved by a polynomial alternating direction multiplier algorithm to obtain an estimated value of the radio map matrix.

7. The radio map estimation method based on minimizing the truncated kernel norm according to claim 6, characterized in that: The introducing of Lagrange multipliers and penalty terms and solving the objective function by a polynomial alternating direction multiplier algorithm to obtain an estimated value of the radio map matrix includes: Step a: Initialize X1 = M Ω , W1 = X1, Y1 = X1, β = 1 and k = 1; Step b: Fix W k , Y k ,calculate Step c: Fix X k+1 , Y k ,calculate And make Step d: Fix x k+1 , calculate Y k+1 =Y k +β(X k+1 -W k+1 ); Step e: Update k=k+1; Step f: Determine whether the preset convergence condition is met at present; If not, repeating steps bf until the preset convergence condition is met, outputting the estimated value of the radio map matrix; Among them, A k represents the first intermediate variable, B k represents the second intermediate variable, M Ω represents the submatrix of the radio map matrix about the sampling point, Ω is the sampling matrix, M is the radio map matrix, ∈ represents the allowable error, β represents the penalty parameter, k represents the iteration counter, the initial k is 1, and k increases by 1 in each round, W k represents the relaxation matrix updated in the kth iteration, Y k represents the updated Lagrange multiplier matrix in the kth iteration, Y represents the Lagrange multiplier matrix, which reflects the degree of violation of the constraints in the optimization process, and X k+1 represents the estimate of the radio map matrix M at the k+1th iteration, D 1 / β represents the soft threshold operator, W k+1 represents the relaxation matrix updated in the k+1th iteration, T represents the transpose, represents an orthogonal map acting on complements, that is, for any matrix, 8. The radio map estimation method based on minimizing the truncated kernel norm according to claim 6, characterized in that: The objective function to be solved is expressed as: stX=W, W Ω =M Ω ; Among them, A l represents the first intermediate variable, B l represents the second intermediate variable, M Ω Indicates M Ω represents the submatrix of the radio map matrix about the sampling point, Ω is the sampling matrix, M is the radio map matrix, and W Ω represents the sub-matrix of the relaxation matrix W with respect to the sampling points.

9. A radio map estimation device based on minimizing the truncated nuclear norm, characterized in that: The device comprises: a radio map matrix acquisition unit, configured to collect radio map data and construct a radio map matrix based on the radio map data; A sampling matrix acquisition unit, used for sampling the radio map matrix to obtain a sampling matrix; an optimization objective function construction unit, configured to construct, based on the radio map matrix and the sampling matrix, an optimization objective function for minimizing a truncated nuclear norm of a radio map estimation matrix; A solving unit is used to solve the optimization objective function to obtain an estimated value of the radio map matrix.

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