Method and system for constructing broadband radio environment map based on compressed sensing

Abstract

The present invention provides a method and system for constructing a broadband radio environment map based on compressed sensing, comprising: step S1: establishing a system model according to the area where the broadband radio environment map is to be constructed; step S2: converting the system model into a compressed sensing model by jointly utilizing the sparsity of space and frequency domains; step S3: designing a spatial measurement matrix, and constructing a frequency domain measurement matrix, and forming a space-frequency measurement matrix in the compressed sensing model with the spatial measurement matrix and the frequency domain measurement matrix; step S4: solving the compressed sensing model, restoring the position of each transmitting source in the area and the power spectrum density on the broadband; step S5: constructing a broadband radio environment map according to the position of each transmitting source in the area and the power spectrum density on the broadband. The present invention can further reduce spatial sampling points and sampling data, and reduce the complexity of constructing a broadband radio environment map while ensuring high accuracy.

Description

Technical Field

[0001] The present invention relates to the technical fields of wireless communications, cognitive networks, and spectrum mapping, and in particular to a method and system for constructing a broadband radio environment map based on compressed sensing. Background Art

[0002] The rapid development of wireless communications has led to a surge in wireless devices, making the electromagnetic environment increasingly complex. In order to more effectively manage and utilize spectrum resources in space (including sub-band occupancy, sub-band power, signal modulation, etc.), radio environment maps have become a research hotspot after cognitive radio. Since radio environment maps include information in multiple dimensions such as space, frequency and time, they are considered to be an effective means to handle tasks such as spectrum monitoring, opportunistic access, network planning and routing in wireless communications.

[0003] Many existing radio environment map construction methods are designed for narrowband systems. The paper "Radio environment map construction with spatially distributed sensors" proposes a method to simulate the spectrum data generation process, which can infer the received signal strength of sensor-free spatial points to build a radio environment map. The paper "Constructing accurate radio environment maps with kriging interpolation in cognitive radio networks" proposes a method based on residual maximum likelihood to estimate relevant parameters, and then generates radio environment maps through kriging interpolation. The papers "3D compressed spectrum mapping with sampling locations optimization in spectrum-heterogeneous environment" and "Improved performance of spectrum cartography based on compressive sensing in cognitive radio networks" take advantage of the sparsity of sources in space and use CS to construct radio environment maps. However, these narrowband schemes cannot fully reflect the spectrum information in space, resulting in limited functionality of radio environment maps.

[0004] The opposite of the narrowband solution is the broadband radio environment map construction solution. The paper "Distributed spectrum sensing for cognitive radio networks by exploiting sparsity" uses the sparsity of space and frequency domains and proposes a model coefficient estimator based on the Lasso algorithm to obtain unoccupied frequency bands in space. However, this solution is highly complex and consumes more communication resources. The paper "Learning power spectrum maps from quantized power measurements" proposes a method to construct a broadband radio environment map through non-parametric and semi-parametric estimation, but it requires knowing the power spectrum density of the transmitting source. Summary of the invention

[0005] In view of the defects in the prior art, the present invention provides a method and system for constructing a broadband radio environment map based on compressed sensing.

[0006] According to a method and system for constructing a broadband radio environment map based on compressed sensing provided by the present invention, the scheme is as follows:

[0007] In a first aspect, a method for constructing a broadband radio environment map based on compressed sensing is provided, the method comprising:

[0008] Step S1: Establishing a system model according to the area where a broadband radio environment map is to be constructed;

[0009] Step S2: jointly utilizing the spatial and frequency domain sparsity to transform the system model into a compressed sensing model;

[0010] Step S3: designing a spatial measurement matrix and constructing a frequency domain measurement matrix, and combining the spatial measurement matrix and the frequency domain measurement matrix to form a space-frequency measurement matrix in a compressed sensing model;

[0011] Step S4: solving the compressed sensing model to restore the position of each emission source in the area and the power spectrum density on the broadband;

[0012] Step S5: construct a broadband radio environment map according to the location of each transmitting source in the area and the power spectrum density on the broadband.

[0013] Preferably, the system model includes:

[0014] The area for constructing the broadband radio environment map is divided into a total of N c grid points, and deploy sensor devices capable of performing spectrum sampling within a certain bandwidth at m1 spatial sampling points in the region; N mThe signals emitted by the signal sources are superimposed on each other to form a radio environment with a certain bandwidth W. W is divided into N b sub-band;

[0015] The broadband radio environment map in the target area is modeled as a 3D tensor consisting of a planar 2D and a frequency domain 1D Where N x and N y Respectively represent the number of grid points in the x and y directions, N b Represents the number of subbands divided within the bandwidth W in the f direction; for ease of representation, the tensor is assembled into a matrix Each column of P corresponds to a vector consisting of the power spectral density of the subband in W at a grid point;

[0016] The matrix P is the broadband radio environment map of the target area. To obtain the complete P matrix, all columns of P are assembled from top to bottom into column vectors. The system model is:

[0017]

[0018] in, is an empty-frequent sparse dictionary, represents the channel matrix, γ i,j represents the path loss between points i and j;

[0019] is the vector to be recovered with a quasi-block sparse structure, X j Corresponding to the jth grid point, the expression is:

[0020]

[0021] in, Represents the vector of power spectral density on all sub-bands in W of the mth transmitting source, s m is the grid point corresponding to the position of the mth emission source, is the set of grid points where the emission source exists, N is composed of 0 b ×1 vector; σ 2 is the power spectral density of Gaussian white noise, N is composed of 1 c N b dimensional vector.

[0022] Preferably, the compressed sensing model includes:

[0023] Relative to all grid points, the sparseness of the emission source is K1 = N m ;

[0024] The sparsity K of the subband occupied by the mth source relative to the number of all subbands in W is 2,m =||θ m ||0, where ||θ m ||0 is θ m 0-norm of ;

[0025] Both forms of sparsity are contained in X, and the number of non-zero elements of X does not exceed

[0026] The compressed sensing model constructed based on the above two sparsities is:

[0027]

[0028] in, is the space-frequency measurement matrix, and Represent the spatial measurement matrix and the frequency domain measurement matrix respectively; m1 and m2 represent the number of spatial sampling points and the number of subbands sampled in the frequency domain respectively; represents a set of spatial sampling points, represents the set of sampled subbands; Indicated by P l The elements in are the indices of the rows in the unit matrix of size N×N; Φ l The element 1 in each row represents the spatial sampling point, Φ f Element 1 in each row represents the sampled subband.

[0029] Preferably, the step S3 comprises:

[0030] make is the space-frequency perception matrix, and the compressed sensing model is further written as Corresponding to the quasi-block sparse structure of X, the space-frequency perception matrix Divide into N c perceptual sub-matrices, namely

[0031] To reduce The column correlation of X is improved to improve the recovery accuracy of X, and the spatial measurement matrix Φ is designed using the RCC-based spatial measurement matrix optimization algorithm. l include:

[0032] 1) Calculate Ψ l The eigenvalues ​​and corresponding eigenvectors of

[0033] 2) l The square of the eigenvalue of

[0034] 3) Find the m1 eigenvalues ​​and corresponding eigenvectors that are closest to 1 after the eigenvalue is squared;

[0035] 4) The m1 eigenvalues ​​closest to 1 form a diagonal matrix ∑′, and the corresponding eigenvectors are arranged in rows from top to bottom to form a matrix Φ l ′;

[0036] 5) Use Ψ′ l =Φ′ l T ∑′Φ′ l Approximate Ψ l ;

[0037] 6) Calculate R = Ψ l -Ψ′ l ;

[0038] 7) Take the index of the m1 row with the smallest 2-norm of R to form the set P l ;

[0039] 8) According to Get the spatial measurement matrix Φ l ;

[0040] Randomly select m2 frequency domain sampling subbands to form a set P f ,according to Get the frequency domain measurement matrix Φ f ;

[0041] according to The space-frequency measurement matrix Φ in the compressed sensing model is obtained.

[0042] Preferably, step S4 comprises: solving the compressed sensing model using a QBSBMP algorithm:

[0043] Step S4.1: Perform K1 cycles, select the i-th sensing submatrix corresponding to the position of the emission source in the i-th cycle, and find the positions of all emission sources in the area after the K1 cycles are completed;

[0044] Step S4.2: According to the perceptual sub-matrix, the quasi-block sparse vector X is restored to obtain the power spectrum density of each transmitting source on the broadband.

[0045] Preferably, the step S4.1 comprises:

[0046] 1) Initialize residual r =;

[0047] 2) For the i-th cycle, follow Update the j-th perception sub-matrix;

[0048] 3) Initialize the residual r of the perception submatrix b =;

[0049] 4) According to Select the jth perceptual submatrix that matches the current r b The best matching column;

[0050] 5) Follow Update b , where B is the matrix composed of all the selected columns in the i-1 selected sensing sub-matrices corresponding to the emission source positions, a b Indicates the selected Φ j The matrix composed of all the columns of Denote (B∪ b )’s pseudo-inverse matrix;

[0051] 6) When Φ j After the column selection is completed, the final r b The 2-norm of is saved to the set C N middle;

[0052] 7) After traversing all N c After the perceptual sub-matrices, select C N The index corresponding to the smallest element in is selected as the i-th perception submatrix corresponding to the position of the emission source, and the index is saved in the set Λ B middle;

[0053] 8) Follow Update the residual r, where A is the matrix composed of all the selected columns in the i selected perception sub-matrices, is the pseudo-inverse matrix of A;

[0054] 9) Loop K1 times to obtain all the perception sub-matrices corresponding to the emission source positions.

[0055] Preferably, the step S4.2 comprises:

[0056] 1) Select all the sensing sub-matrices corresponding to the emission source positions, according to Calculate the projection coefficient X0 of y on matrix A;

[0057] 2) The tth cycle obtains the value of [Λ B ] t The non-zero elements on the corresponding blocks, where [Λ B ] t Denotes the set Λ B The tth element in ;

[0058] 3) After K1 cycles, all non-zero elements of all non-zero blocks of X are obtained, thus obtaining X.

[0059] Preferably, step S5 comprises:

[0060] Constructing a broadband radio environment map is equivalent to obtaining the tensor T, Contains all the information of tensor T; after obtaining X, according to

[0061]

[0062] The tensor T is obtained to reconstruct the broadband radio environment map.

[0063] In a second aspect, a system for constructing a broadband radio environment map based on compressed sensing is provided, the system comprising:

[0064] Module M1: Establishing a system model based on the area where a broadband radio environment map is to be constructed;

[0065] Module M2: Jointly utilize spatial and frequency domain sparsity to transform the system model into a compressed sensing model;

[0066] Module M3: designing a spatial measurement matrix and constructing a frequency domain measurement matrix, and combining the spatial measurement matrix and the frequency domain measurement matrix to form a space-frequency measurement matrix in a compressed sensing model;

[0067] Module M4: solving the compressed sensing model to restore the position of each emission source in the area and the power spectrum density on the broadband;

[0068] Module M5: construct a broadband radio environment map according to the location of each emission source in the area and the power spectrum density on the broadband.

[0069] Preferably, the system model includes:

[0070] The area for constructing the broadband radio environment map is divided into a total of N c grid points, and deploy sensor devices capable of performing spectrum sampling within a certain bandwidth at m1 spatial sampling points in the region; N m The signals emitted by the signal sources are superimposed on each other to form a radio environment with a certain bandwidth W. W is divided into N b sub-band;

[0071] The broadband radio environment map in the target area is modeled as a 3D tensor consisting of a planar 2D and a frequency domain 1D Where N x and N y Respectively represent the number of grid points in the x and y directions, N b Represents the number of subbands divided within the bandwidth W in the f direction; for ease of representation, the tensor is assembled into a matrix Each column of P corresponds to a vector consisting of the power spectral density of the subband in W at a grid point;

[0072] The matrix P is the broadband radio environment map of the target area. To obtain the complete P matrix, all columns of P are assembled from top to bottom into column vectors. The system model is:

[0073]

[0074] in, is an empty-frequent sparse dictionary, represents the channel matrix, γ i,j represents the path loss between points i and j;

[0075] is the vector to be recovered with a quasi-block sparse structure, X j Corresponding to the jth grid point, the expression is:

[0076]

[0077] in, Represents the vector of power spectral density on all sub-bands in W of the mth transmitting source, s m is the grid point corresponding to the position of the mth emission source, is the set of grid points where the emission source exists, N is composed of 0 b ×1 vector; σ 2 is the power spectral density of Gaussian white noise, N is composed of 1 c N b dimensional vector;

[0078] The compressed sensing model includes:

[0079] Relative to all grid points, the sparseness of the emission source is K1 = N m ;

[0080] The sparsity K of the subband occupied by the mth source relative to the number of all subbands in W is 2,m =||θ m ||0, where ||θ m ||0 is θ m 0-norm of ;

[0081] Both forms of sparsity are contained in X, and the number of non-zero elements of X does not exceed

[0082] The compressed sensing model constructed based on the above two sparsities is:

[0083]

[0084] in, is the space-frequency measurement matrix, and Represent the spatial measurement matrix and the frequency domain measurement matrix respectively; m1 and m2 represent the number of spatial sampling points and the number of subbands sampled in the frequency domain respectively; represents a set of spatial sampling points, represents the set of sampled subbands; Indicated by P l The elements in are the indices of the rows in the unit matrix of size N×N; Φ l The element 1 in each row represents the spatial sampling point, Φ f The element 1 in each row represents the sampled subband;

[0085] The step S3 comprises:

[0086] make is the space-frequency perception matrix, and the compressed sensing model is further written as Corresponding to the quasi-block sparse structure of X, the space-frequency perception matrix Divide into N c perceptual sub-matrices, namely

[0087] To reduce The column correlation of X is improved to improve the recovery accuracy of X, and the spatial measurement matrix Φ is designed using the RCC-based spatial measurement matrix optimization algorithm. l include:

[0088] 1) Calculate Ψ l The eigenvalues ​​and corresponding eigenvectors of

[0089] 2) l The square of the eigenvalue of

[0090] 3) Find the m1 eigenvalues ​​and corresponding eigenvectors that are closest to 1 after the eigenvalue is squared;

[0091] 4) The m1 eigenvalues ​​closest to 1 form a diagonal matrix ∑′, and the corresponding eigenvectors are arranged in rows from top to bottom to form a matrix Φ′ l ;

[0092] 5) Use Ψ′ l =Φ′ l T ∑′Φ′ l Approximate Ψ l ;

[0093] 6) Calculate R = Ψ l -Ψ′ l ;

[0094] 7) Take the index of the m1 row with the smallest 2-norm of R to form the set Pl ;

[0095] 8) According to Get the spatial measurement matrix Φ l ;

[0096] Randomly select m2 frequency domain sampling subbands to form a set P f ,according to Get the frequency domain measurement matrix Φ f ;

[0097] according to Obtain the space-frequency measurement matrix Φ in the compressed sensing model;

[0098] The step S4 includes: solving the compressed sensing model using the QBSBMP algorithm:

[0099] Step S4.1: Perform K1 cycles, select the i-th sensing submatrix corresponding to the position of the emission source in the i-th cycle, and find the positions of all emission sources in the area after the K1 cycles are completed;

[0100] Step S4.2: According to the sensing sub-matrix, the quasi-block sparse vector X is restored to obtain the power spectrum density of each transmitting source on the broadband;

[0101] The step S4.1 comprises:

[0102] 1) Initialize residual r =;

[0103] 2) For the i-th cycle, follow Update the j-th perception sub-matrix;

[0104] 3) Initialize the residual r of the perception submatrix b =;

[0105] 4) According to Select the jth perceptual submatrix that matches the current r b The best matching column;

[0106] 5) Follow Update b , where B is the matrix composed of all the selected columns in the i-1 selected sensing sub-matrices corresponding to the emission source positions, A b Indicates the selected Φ j The matrix composed of all the columns of Denote (B∪A b )’s pseudo-inverse matrix;

[0107] 6) When Φ j After the column selection is completed, the final r b The 2-norm of is saved to the set C N middle;

[0108] 7) After traversing all N c After the perceptual sub-matrices, select C N The index corresponding to the smallest element in is selected as the i-th perception submatrix corresponding to the position of the emission source, and the index is saved in the set Λ B middle;

[0109] 8) Follow Update the residual r, where A is the matrix composed of all the selected columns in the i selected perception sub-matrices, is the pseudo-inverse matrix of A;

[0110] 9) Loop K1 times to obtain all the sensing sub-matrices corresponding to the emission source positions;

[0111] The step S4.2 comprises:

[0112] 1) Select all the sensing sub-matrices corresponding to the emission source positions, according to Calculate the projection coefficient X0 of y on matrix A;

[0113] 2) The tth cycle obtains the value of [Λ B ] t The non-zero elements on the corresponding blocks, where [Λ B ] t Denotes the set Λ B The tth element in ;

[0114] 3) After K1 cycles, all non-zero elements of all non-zero blocks of X are obtained, thus obtaining X;

[0115] The step S5 comprises:

[0116] Constructing a broadband radio environment map is equivalent to obtaining the tensor T, Contains all the information of tensor T; after obtaining X, according to

[0117]

[0118] The tensor T is obtained to reconstruct the broadband radio environment map.

[0119] Compared with the prior art, the present invention has the following beneficial effects:

[0120] 1. The present invention constructs a broadband radio environment map based on compressed sensing. Compared with a narrowband radio environment map, it can reflect the frequency band occupancy information and occupied power size on the broadband; compared with other broadband radio environment map construction methods, it can ensure that the spatial sampling points and sampling data are further reduced under the premise of high-precision construction, thereby reducing the construction complexity;

[0121] 2. The present invention proposes a spatial measurement matrix optimization algorithm based on RCC, which can further reduce the spatial sampling points and reduce the algorithm complexity compared with the spatial measurement matrix optimization algorithm based on QR-pivoting; and proposes a QBSBMP compressed sensing recovery algorithm. For the case where the recovered vector has a quasi-block sparse structure, compared with the OMP algorithm, it can significantly improve the recovery accuracy while reducing the algorithm time complexity. BRIEF DESCRIPTION OF THE DRAWINGS

[0122] Other features, objects and advantages of the present invention will become more apparent from the detailed description of non-limiting embodiments made with reference to the following drawings:

[0123] Figure 1 A flow chart of a method for constructing a wideband radio environment map based on compressed sensing;

[0124] Figure 2 Schematic diagram of normalized area for building broadband radio environment maps;

[0125] Figure 3 A tensor model diagram for a broadband radio environment map;

[0126] Figure 4 is a schematic diagram of the structure of the vector X to be recovered with a quasi-block sparse structure;

[0127] Figure 5 This is the recovery effect diagram of the quasi-block sparse vector X. DETAILED DESCRIPTION

[0128] The present invention is described in detail below in conjunction with specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, for those of ordinary skill in the art, several changes and improvements can also be made without departing from the concept of the present invention. These all belong to the protection scope of the present invention.

[0129] Embodiment 1:

[0130] The embodiment of the present invention provides a method for constructing a broadband radio environment map based on compressed sensing, referring to Figure 1 As shown, the method specifically includes:

[0131] Step S1: Establish a system model according to the area where a broadband radio environment map is to be constructed.

[0132] The system model in step S1 specifically includes:

[0133] The area for constructing the broadband radio environment map is divided into a total of N c grid points, such as Figure 2As shown, a sensor device capable of performing spectrum sampling within a certain bandwidth is deployed at m1 spatial sampling points in the region. m The signals emitted by the signal sources are superimposed on each other to form a radio environment with a certain bandwidth W. W is divided into N b The more grid points are divided in an area, the higher the accuracy of constructing the broadband radio environment map.

[0134] Corresponds to Figure 2 The broadband radio environment map is modeled as a 3D tensor consisting of plane (2D) and frequency domain (1D) Where N x and N y Respectively represent the number of grid points in the x and y directions, N b Indicates the number of subbands divided within the bandwidth W in the f direction, such as Figure 3 As shown. For ease of representation, the tensor is assembled into a matrix Each column of P corresponds to a vector consisting of the power spectral density of the subband within W at a grid point.

[0135] The matrix P also gives the broadband radio environment map of the target area. In order to obtain the complete P matrix, all columns of P are assembled from top to bottom into column vectors. The system model is:

[0136]

[0137] in, is an empty-frequent sparse dictionary, represents the channel matrix, γ i,j represents the path loss between points i and j;

[0138] is a vector to be recovered with a quasi-block sparse structure, and its structure is as follows Figure 4 As shown. j Corresponding to the jth grid point, the expression is:

[0139]

[0140] in, Represents the vector of power spectral density on all sub-bands in W of the mth transmitting source, s m is the grid point corresponding to the position of the mth emission source, is the set of grid points where the emission source exists, N is composed of 0 b ×1 vector; σ 2 is the power spectral density of Gaussian white noise, N is composed of 1 c Nb dimensional vector.

[0141] Step S2: Jointly utilize the spatial and frequency domain sparsity to transform the system model into a compressed sensing model.

[0142] Specifically, the compressed sensing model in step S2 includes:

[0143] There are two forms of sparsity in practical scenarios:

[0144] (1) Relative to all grid points, the number of emission sources in the region is sparse, and the sparseness of the emission sources is K1 = N m ;

[0145] (2) Relative to the number of all subbands in W, the subbands occupied at the same time are sparse. The sparsity of the subband occupied by the mth source is K 2,m =||θ m ||0, where ||θ m ||0 is θ m 0-norm of ;

[0146] Both forms of sparsity are contained in X, and the number of non-zero elements of X does not exceed The compressed sensing model constructed based on the above two sparsities is:

[0147]

[0148] in, is the space-frequency measurement matrix, and Represent the spatial measurement matrix and the frequency domain measurement matrix respectively; m1 and m2 represent the number of spatial sampling points and the number of subbands sampled in the frequency domain respectively; represents a set of spatial sampling points, represents the set of sampled subbands; Indicated by P l The elements in are the indices of the rows in the unit matrix of size N×N; Φ l The element 1 in each row represents the spatial sampling point, Φ f Element 1 in each row represents the sampled subband.

[0149] Step S3: Design the spatial measurement matrix using the RCC-based spatial measurement matrix optimization algorithm, and construct the space-frequency measurement matrix in the compressed sensing model together with the frequency domain measurement matrix.

[0150] Specifically, step S3 includes:

[0151] make is the space-frequency perception matrix, and the compressed sensing model is further written as Corresponding to the quasi-block sparse structure of X, the space-frequency perception matrix Divide into N c perceptual sub-matrices, namely

[0152] In order to reduce The column correlation of X is improved, and the recovery accuracy of X is improved. The present invention provides a spatial measurement matrix optimization algorithm based on RCC to optimize the spatial sampling points and design the spatial measurement matrix Φ l , the algorithm includes:

[0153] (1) Calculation of Ψ l The eigenvalues ​​and corresponding eigenvectors of

[0154] (2) l The square of the eigenvalue of

[0155] (3) Find the m1 eigenvalues ​​and corresponding eigenvectors that are closest to 1 after the eigenvalue is squared;

[0156] (4) The m1 eigenvalues ​​closest to 1 form a diagonal matrix ∑′, and the corresponding eigenvectors are arranged in rows from top to bottom to form a matrix Φ′ l ;

[0157] (5) Using Ψ′ l =Φ′ l T∑′Φ′ l Approximate Ψ l ;

[0158] (6) Calculate R = Ψ l -Ψ′ l ;

[0159] (7) Take the index of the m1 row with the smallest 2-norm of R to form the set P l ;

[0160] (8) According to Get the spatial measurement matrix Φ l ;

[0161] Randomly select m2 frequency domain sampling subbands to form a set P f ,according to Get the frequency domain measurement matrix Φ f ;

[0162] according to The space-frequency measurement matrix Φ in the compressed sensing model is obtained.

[0163] Step S4: Use the QBSBMP algorithm to solve the compressed sensing model and restore the position of each emission source in the area and the power spectrum density on the broadband.

[0164] In step S4, solving the compressed sensing model using the QBSBMP algorithm includes:

[0165] Step S4.1: Perform K1 cycles, select the i-th sensing sub-matrix corresponding to the position of the emission source in the i-th cycle, and after the K1 cycles are completed, the positions of all emission sources in the area can be found.

[0166] Specifically, step S4.1 includes:

[0167] (1) Initialize the residual r =;

[0168] (2) For the i-th cycle, according to Update the j-th perception sub-matrix;

[0169] (3) Initialize the perception submatrix residual r b =;

[0170] (4) Based on Select the jth perceptual submatrix that matches the current r b The best matching column;

[0171] (5) According to Update b , where B is the matrix composed of all the selected columns in the i-1 selected sensing sub-matrices corresponding to the emission source positions, A b Indicates the selected Φ j The matrix composed of all the columns of Denote (B∪A b )’s pseudo-inverse matrix;

[0172] (6) When Φ j After the column selection is completed, the final r b The 2-norm of is saved to the set C N middle;

[0173] (7) After traversing all N c After the perceptual sub-matrices, select C N The index corresponding to the smallest element in is selected as the i-th perception submatrix corresponding to the position of the emission source, and the index is saved in the set Λ B middle;

[0174] (8) According to Update the residual r, where A is the matrix composed of all the selected columns in the i selected perception sub-matrices, is the pseudo-inverse matrix of A;

[0175] (9) Loop K1 times to obtain all the perception sub-matrices corresponding to the emission source positions.

[0176] Step S4.2: Based on the perceptual submatrix corresponding to the emission source position obtained in the previous step, the quasi-block sparse vector X is restored to obtain the power spectrum density of each emission source on the broadband.

[0177] Specifically, step S4.2 includes:

[0178] (1) After selecting all the sensing sub-matrices corresponding to the emission source positions, Calculate the projection coefficient X0 of y on matrix A;

[0179] (2) The tth cycle obtains the value of [Λ B ] t The non-zero elements on the corresponding blocks, where [Λ B ] t Denotes the set Λ B The tth element in ;

[0180] (3) After K1 cycles, all non-zero elements of all non-zero blocks of X are obtained, thus obtaining X.

[0181] Step S5: Construct a broadband radio environment map based on the recovered information.

[0182] Specifically, step S5 includes:

[0183] Constructing a broadband radio environment map is equivalent to obtaining the tensor T, Contains all the information of tensor T; after obtaining X, according to

[0184]

[0185] The tensor T can be obtained to reconstruct the broadband radio environment map.

[0186] The present invention also provides a system for constructing a broadband radio environment map based on compressed sensing, comprising:

[0187] Module M1: Build a system model based on the area where a broadband radio environment map is to be constructed.

[0188] The system model in module M1 includes:

[0189] The area for constructing the broadband radio environment map is divided into a total of N c grid points, such as Figure 2 As shown, a sensor device capable of performing spectrum sampling within a certain bandwidth is deployed at m1 spatial sampling points in the region. m The signals emitted by the signal sources are superimposed on each other to form a radio environment with a certain bandwidth W. W is divided into N bThe more grid points are divided in an area, the higher the accuracy of constructing the broadband radio environment map.

[0190] Corresponds to Figure 2 The broadband radio environment map is modeled as a 3D tensor consisting of plane (2D) and frequency domain (1D) Where N x and N y Respectively represent the number of grid points in the x and y directions, N b Indicates the number of sub-bands divided within the bandwidth W, such as Figure 3 As shown. For ease of representation, the tensor is assembled into a matrix Each column of P corresponds to a vector consisting of the power spectral density of the subband within W at a grid point.

[0191] The matrix P also gives the broadband radio environment map of the target area. In order to obtain the complete P matrix, all columns of P are assembled from top to bottom into column vectors. The system model is:

[0192]

[0193] in, is an empty-frequent sparse dictionary, represents the channel matrix, γ i,j represents the path loss between points i and j, N b ×N b The unit array of

[0194] is a vector to be recovered with a quasi-block sparse structure, and its structure is as follows Figure 4 As shown; X j Corresponding to the jth grid point, the expression is:

[0195]

[0196] in Represents the vector of power spectral density on all sub-bands in W of the mth transmitting source, s m is the grid point corresponding to the position of the mth emission source, is the set of grid points corresponding to the location of the emission source, N is composed of 0 b ×1 vector; σ 2 is the power spectral density of Gaussian white noise, N is composed of 1 c N b dimensional vector.

[0197] Module M2: Jointly exploit spatial and frequency domain sparsity to transform the system model into a compressed sensing model.

[0198] Specifically, the compressed sensing model in module M2 includes:

[0199] There are two forms of sparsity in practical scenarios:

[0200] (1) Relative to all grid points, the number of emission sources in the region is sparse, and the sparseness of the emission sources K1 = m ;

[0201] (2) Relative to the number of all subbands in W, the subbands occupied at the same time are sparse. The sparsity of the subband occupied by the mth source is K 2,m =||θ m ||0, where ||θ m ||0 is θ m 0-norm of ;

[0202] Both forms of sparsity are contained in X, and the number of non-zero elements of X does not exceed The compressed sensing model constructed based on the above two sparsities is:

[0203]

[0204] in, is the space-frequency measurement matrix, and Represent the spatial measurement matrix and the frequency domain measurement matrix respectively; m1 and m2 represent the number of spatial sampling points and the number of subbands sampled in the frequency domain respectively; represents a set of spatial sampling points, represents the set of sampled subbands; Indicated by P l The elements in are the indices of the rows in the unit matrix of size N×N; Φ l The element 1 in each row represents the spatial sampling point, Φ f Element 1 in each row represents the sampled subband.

[0205] Module M3: Use the RCC-based spatial measurement matrix optimization algorithm to design the spatial measurement matrix, which together with the frequency domain measurement matrix constitutes the space-frequency measurement matrix in the compressed sensing model.

[0206] The module M3 specifically includes:

[0207] make is the space-frequency perception matrix, and the compressed sensing model is further written as Corresponding to the quasi-block sparse structure of X, the space-frequency perception matrix Divide into N cperceptual sub-matrices, namely

[0208] In order to reduce The column correlation of X is improved, and the recovery accuracy of X is improved. The present invention provides a spatial measurement matrix optimization algorithm based on RCC to optimize the spatial sampling points and design the spatial measurement matrix Φ l , the algorithm includes:

[0209] (1) Calculation of Ψ l The eigenvalues ​​and corresponding eigenvectors of

[0210] (2) l The square of the eigenvalue of

[0211] (3) Find the m1 eigenvalues ​​and corresponding eigenvectors that are closest to 1 after the eigenvalue is squared;

[0212] (4) The m1 eigenvalues ​​closest to 1 form a diagonal matrix ∑′, and the corresponding eigenvectors are arranged in rows from top to bottom to form a matrix Φ′ l ;

[0213] (5) Using Ψ′ l =Φ′ l T ∑′Φ′ l Approximate Ψ l ;

[0214] (6) Calculate R = Ψ l -Ψ′ l ;

[0215] (7) Take the index of the m1 row with the smallest 2-norm of R to form the set P l ;

[0216] (8) According to Get the spatial measurement matrix Φ l ;

[0217] Randomly select m2 frequency domain sampling subbands to form a set P f ,according to Get the frequency domain measurement matrix Φ f ;according to The space-frequency measurement matrix Φ in the compressed sensing model is obtained.

[0218] Module M4: Use the QBSBMP algorithm to solve the compressed sensing model and restore the position of each emission source in the area and the power spectrum density on the broadband.

[0219] The QBSBMP algorithm is used in module M4 to solve the compressed sensing model, including:

[0220] Module M4.1: Perform K1 cycles, select the i-th sensing sub-matrix corresponding to the location of the emission source in the i-th cycle, and after K1 cycles, the locations of all emission sources in the area can be found;

[0221] Module M4.2: Based on the perception submatrix corresponding to the emission source position obtained in the previous step, the quasi-block sparse vector X is restored to obtain the power spectrum density of each emission source on the broadband.

[0222] Specifically, module M4.1 includes:

[0223] (1) Initialize the residual r =;

[0224] (2) For the i-th cycle, according to Update the j-th perception sub-matrix;

[0225] (3) Initialize the perception submatrix residual r b =;

[0226] (4) Based on Select the jth perceptual submatrix that matches the current r b The best matching column;

[0227] (5) According to Update b , where B is the matrix composed of all the selected columns in the i-1 selected sensing sub-matrices corresponding to the emission source positions, A b Indicates the selected Φ j The matrix composed of all the columns of Denote (B∪A b )’s pseudo-inverse matrix;

[0228] (6) When Φ j After the column selection is completed, the final r b The 2-norm of is saved to the set C N middle;

[0229] (7) After traversing all N c After the perceptual sub-matrices, select C N The index corresponding to the smallest element in is selected as the i-th perception submatrix corresponding to the position of the emission source, and the index is saved in the set Λ B middle;

[0230] (8) According to Update the residual r, where A is the matrix composed of all the selected columns in the i selected perception sub-matrices, is the pseudo-inverse matrix of A;

[0231] (9) Loop K1 times to obtain all the perception sub-matrices corresponding to the emission source positions.

[0232] Specifically, the module M4.2 includes:

[0233] (1) After selecting all the sensing sub-matrices corresponding to the emission source positions, Calculate the projection coefficient X0 of y on matrix A;

[0234] (2) The tth cycle obtains the value of [Λ B ] t The non-zero elements on the corresponding blocks, where [Λ B ] t Denotes the set Λ B The tth element in ;

[0235] (3) After K1 cycles, all non-zero elements of all non-zero blocks of X are obtained, thus obtaining X.

[0236] Module M5: Construct a broadband radio environment map based on the recovered information.

[0237] Constructing a broadband radio environment map is equivalent to obtaining the tensor T, Contains all the information of tensor T; after obtaining X, according to

[0238]

[0239] The tensor T can be obtained to reconstruct the broadband radio environment map.

[0240] Embodiment 2:

[0241] Example 2 is a preferred example of Example 1.

[0242] According to the present invention, the spatial measurement matrix is ​​designed by using the RCC-based measurement matrix optimization algorithm and the compressed sensing model is solved by using the QBSBMP algorithm, and finally a broadband radio environment map is constructed, including:

[0243] Step M1: Establish system model according to region:

[0244] Step M1.1: Scene creation:

[0245] Divide the target area into a total of N c grid points, such as Figure 2 As shown. Set the monitoring bandwidth W and divide W into N b The more sub-bands are divided, the more accurate the power in W is. Sensor devices that can perform spectrum sampling within a certain bandwidth are deployed at m1 spatial sampling points in the area. The more grid points are divided in the area, the higher the accuracy of constructing the broadband radio environment map.

[0246] Corresponds to Figure 2The broadband radio environment map is modeled as a 3D tensor consisting of plane (2D) and frequency domain (1D) Where N x and N y Respectively represent the number of grid points in the x and y directions, N b Indicates the number of subbands divided within the bandwidth W in the f direction, such as Figure 3 As shown. For ease of representation, the tensor is assembled into a matrix Each column of P corresponds to a vector consisting of the power spectral density of the subband within W at a grid point.

[0247] Step M1.2: System Modeling:

[0248] The power spectral density of the mth emission source is modeled as:

[0249]

[0250] in, Represents a group in N b subbands, θ m,q Represents the coefficient of the mth transmitting source in the qth subband.

[0251] The jth (j=1,…,N c The PSD in W at ) grid points is expressed as:

[0252]

[0253] in, b(f)=[b1(f),b(f),…,b q (f)] T , Represents the column vector of coefficients on all subbands of the mth transmitting source, σ 2 represents the power spectral density of Gaussian white noise, s m (m=1,…,N m ) represents the grid point representing the position of the mth emission source, represents the path loss between the position of the mth transmitting source and the jth grid point applied to the PSD, and α is the path loss exponent. For convenience and without loss of generality, assume Independent of frequency.

[0254] d i,j Represents the distance between two places and is defined as:

[0255]

[0256] Among them, dist(a,b) represents the distance between points a and b.

[0257] Select a set of non-overlapping rectangles with a height of 1 covering W, and take a sample point for each sub-band. At this time, θ m It represents the vector of power spectrum density of all sub-bands in W of the mth transmitting source. At each sampling frequency, Φ j The value of (f) is:

[0258]

[0259] Among them, p j is the j-th column of the matrix P, Indicates size N b ×1 matrix of all 1s, is a vector to be recovered with a quasi-block sparse structure, and its structure is as follows Figure 4 As shown. j Corresponding to the jth grid point, the expression is:

[0260]

[0261] in, represents the set of grid points where there are emitting sources, N is composed of 0 b ×1 vector.

[0262] To obtain the complete P matrix, all columns of P are assembled from top to bottom into column vectors. The system model is:

[0263]

[0264] in, is an empty-frequent sparse dictionary, represents the channel matrix.

[0265] Step M2: Convert the system model into a compressed sensing model:

[0266] There are two forms of sparsity in the spatial and frequency domains:

[0267] (1) The sparsity of the emission source in space, whose sparsity K1 = N m ;

[0268] (2) The sparsity of the subbands occupied within W of the mth source, whose sparsity K 2,m =||θ m ||0;

[0269] So there is a spatial measurement matrix and the frequency domain measurement matrix The space-frequency measurement matrix of the joint space and frequency domain is The compressed sensing model of the system is:

[0270]

[0271] m1 and m2 represent the number of spatial sampling points and the number of subbands sampled in the frequency domain, respectively. represents a set of spatial sampling points, represents the set of sampled subbands, Indicates that according to P l The elements in are the rows of the N×N unit matrix, Φ l The element 1 in each row represents the spatial sampling point, Φ f Element 1 in each row represents the sampled subband.

[0272] Step M3: Use the RCC-based spatial measurement matrix optimization algorithm to design the spatial measurement matrix, which together with the frequency domain measurement matrix constitutes the space-frequency measurement matrix in the compressed sensing model:

[0273] make is the space-frequency perception matrix, and the compressed sensing model is further written as Corresponding to the quasi-block sparse structure of X, the space-frequency perception matrix Divide into N c perceptual sub-matrices, namely

[0274] In order to reduce The column correlation of X is improved, and the recovery accuracy of X is improved. The present invention provides a spatial measurement matrix optimization algorithm based on RCC to optimize the spatial sampling points and design the spatial measurement matrix Φ l In order to describe the algorithm more clearly, the following algorithm flow is given:

[0275]

[0276] Randomly select m2 frequency domain sampling subbands to form a set P f ,according to Get the frequency domain measurement matrix Φ f ;

[0277] according to The space-frequency measurement matrix Φ in the compressed sensing model is obtained.

[0278] Step M4: Use the QBSBMP algorithm to solve the compressed sensing model:

[0279] Step M4.1: Perform k i In the i-th cycle, the i-th sensing submatrix corresponding to the position of the emission source is selected. After K1 cycles, the positions of all emission sources in the area can be found.

[0280] Step M 4.2: According to the sensing submatrix corresponding to the emission source position obtained in the previous step, the quasi-block sparse vector X is restored to obtain the power spectrum density of each emission source in the broadband.

[0281] In order to describe the algorithm flow more clearly, the pseudo code of step M4 is given:

[0282]

[0283]

[0284] Where <,> represents the inner product of two vectors, C I U{Λ b} represents the set Λ b Add as an element to set C I In, C A ∪{A b} means that the matrix A b Add as an element to set C A middle, Indicates that the collection As an element added to the set Λ, Represents the set C I The b k elements, According to the set P f The elements in the vector X1 are indexed by the elements in |[Λ] t | represents the set [Λ] t len(0) represents the number of elements in vector X0.

[0285] The recovery effect of the quasi-block sparse vector X is as follows Figure 5As shown, the horizontal axis is the number of spatial sampling points m1, and the vertical axis is the recovery error of X. The figure shows the comparison results of six schemes, among which "RCC-QBSBMP" adopts the RCC-based algorithm provided by the present invention to design the spatial measurement matrix and use the QBSBMP algorithm to solve the compressed sensing model, "QR-QBSBMP" adopts the QR-pivoting-based algorithm to design the spatial measurement matrix and use the QBSBMP algorithm to solve the compressed sensing model, "Rand-QBSBMP" randomly selects spatial sampling points to design the spatial measurement matrix and uses the QBSBMP algorithm to solve the compressed sensing model, "RCC-OMP" adopts the RCC-based algorithm to design the spatial measurement matrix and uses the OMP algorithm to solve the compressed sensing model, "QR-OMP" adopts the QR-pivoting-based algorithm to design the spatial measurement matrix and uses the OMP algorithm to solve the compressed sensing model, and "Rand-OMP" randomly selects spatial sampling points to design the spatial measurement matrix and uses the OMP algorithm to solve the compressed sensing model. It can be concluded from the figure that “RCC-QBSBMP” can make the recovery error of X converge stably to 0 when the spatial sampling points are the least.

[0286] Step M5: Construct broadband radio environment map:

[0287] Constructing a broadband radio environment map is equivalent to obtaining the tensor T, Contains all the information of tensor T; after obtaining X, according to

[0288]

[0289] The tensor T can be obtained to reconstruct the broadband radio environment map.

[0290] The embodiment of the present invention provides a method and system for constructing a broadband radio environment map based on compressed sensing. The broadband radio environment map is constructed based on compressed sensing. Compared with the narrowband radio environment map, it can reflect the frequency band occupancy information and the occupied power size on the broadband; compared with other broadband radio environment map construction methods, it can ensure that the spatial sampling points and sampling data are further reduced under the premise of high-precision construction, thereby reducing the construction complexity. Compared with the spatial measurement matrix optimization algorithm based on RCC, the spatial measurement matrix optimization algorithm based on QR-pivoting can further reduce the spatial sampling points and reduce the algorithm complexity; the QBSBMP compressed sensing recovery algorithm is proposed. For the case where the recovered vector has a quasi-block sparse structure, compared with the OMP algorithm, it can significantly improve the recovery accuracy while reducing the algorithm time complexity.

[0291] Those skilled in the art know that, in addition to realizing the system and its various devices, modules, and units provided by the present invention in a purely computer-readable program code, it is entirely possible to realize the same functions in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers by logically programming the method steps. Therefore, the system and its various devices, modules, and units provided by the present invention can be considered as a hardware component, and the devices, modules, and units included therein for realizing various functions can also be regarded as structures within the hardware component; the devices, modules, and units for realizing various functions can also be regarded as both software modules for realizing the method and structures within the hardware component.

[0292] The above describes the specific embodiments of the present invention. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art can make various changes or modifications within the scope of the claims, which does not affect the essence of the present invention. In the absence of conflict, the embodiments of the present application and the features in the embodiments can be combined with each other arbitrarily.

Claims

1. A method for constructing a broadband radio environment map based on compressed sensing, characterized in that: include: Step S1: Establishing a system model according to the area where a broadband radio environment map is to be constructed; Step S2: jointly utilizing the spatial and frequency domain sparsity to transform the system model into a compressed sensing model; Step S3: designing a spatial measurement matrix and constructing a frequency domain measurement matrix, and combining the spatial measurement matrix and the frequency domain measurement matrix to form a space-frequency measurement matrix in a compressed sensing model; Step S4: solving the compressed sensing model to restore the position of each emission source in the area and the power spectrum density on the broadband; Step S5: constructing a broadband radio environment map according to the location of each transmitting source in the area and the power spectrum density on the broadband; The system model includes: The area for constructing the broadband radio environment map is divided into a total of N c grid points, and deploy sensor devices capable of performing spectrum sampling within a certain bandwidth at m1 spatial sampling points in the region; N m The signals emitted by the signal sources are superimposed on each other to form a radio environment with a certain bandwidth W. W is divided into N b sub-band; The broadband radio environment map in the target area is modeled as a 3D tensor consisting of a planar 2D and a frequency domain 1D Where N x and N y Represents the number of grid points in the x and y directions, N b Represents the number of subbands divided within the bandwidth W in the f direction; for ease of representation, the tensor is assembled into a matrix Each column of P corresponds to a vector consisting of the power spectral density of the subband in W at a grid point; The matrix P is the broadband radio environment map of the target area. To obtain the complete P matrix, all columns of P are assembled from top to bottom into column vectors. Then the system model is: in, is an empty-frequent sparse dictionary, represents the channel matrix, γ i，j represents the path loss between points i and j; is the vector to be recovered with a quasi-block sparse structure, X j Corresponding to the jth grid point, the expression is: in, Represents the vector of power spectral density on all sub-bands in W of the mth transmitting source, s m is the grid point corresponding to the position of the mth emission source, is the set of grid points where the emission source exists, N is composed of 0 b ×1 vector; σ 2 is the power spectral density of Gaussian white noise, N is composed of 1 c N b dimensional vector; The compressed sensing model includes: Relative to all grid points, the sparseness of the emission source is K1 = N m ; The sparsity K of the subband occupied by the mth source relative to the number of all subbands in W is 2，m =||θ m ||0, where ||θ m ||0 is θ m 0-norm of ; Both forms of sparsity are contained in X, and the number of non-zero elements of X does not exceed The compressed sensing model constructed based on the above two sparsities is: in, is the space-frequency measurement matrix, and Represent the spatial measurement matrix and the frequency domain measurement matrix respectively; m1 and m2 represent the number of spatial sampling points and the number of subbands sampled in the frequency domain respectively; represents a set of spatial sampling points, represents the set of sampled subbands; Indicated by P l The elements in are the indices of the rows in the unit matrix of size N×N; Φ l The element 1 in each row represents the spatial sampling point, Φ f The element 1 in each row represents the sampled subband; The step S3 comprises: make is the space-frequency perception matrix, and the compressed sensing model is further written as Corresponding to the quasi-block sparse structure of X, the space-frequency perception matrix Divide into N c perceptual sub-matrices, namely To reduce The column correlation of X is improved to improve the recovery accuracy of X, and the spatial measurement matrix Φ is designed using the RCC-based spatial measurement matrix optimization algorithm. l include: 1) Calculate Ψ l The eigenvalues ​​and corresponding eigenvectors of 2) l The square of the eigenvalue of 3) Find the m1 eigenvalues ​​and corresponding eigenvectors that are closest to 1 after the eigenvalue is squared; 4) The m1 eigenvalues ​​closest to 1 form a diagonal matrix ∑′, and the corresponding eigenvectors are arranged in rows from top to bottom to form a matrix Φ′ l ; 5) Use Approximate Ψ l ; 6) Calculate R = Ψ l -Ψ′ l ; 7) Take the index of the m1 row with the smallest 2-norm of R to form the set P l ; 8) According to Get the spatial measurement matrix Φ l ; Randomly select m2 frequency domain sampling subbands to form a set P f ,according to Get the frequency domain measurement matrix Φ f ; according to Obtain the space-frequency measurement matrix Φ in the compressed sensing model; The step S4 includes: solving the compressed sensing model using the QBSBMP algorithm: Step S4.1: perform K1 cycles, select the i-th sensing submatrix corresponding to the position of the emission source in the i-th cycle, and find the positions of all emission sources in the area after the K1 cycles are completed; Step S4.2: According to the sensing sub-matrix, the quasi-block sparse vector X is restored to obtain the power spectrum density of each transmitting source on the broadband; The step S4.1 comprises: 1) Initialize the residual r = y; 2) For the i-th cycle, follow Update the j-th perception sub-matrix; 3) Initialize the residual r of the perception submatrix b = r; 4) According to Select the jth perceptual submatrix that matches the current r b The best matching column; 5) Follow Update b , where B is the matrix composed of all the selected columns in the i-1 selected sensing sub-matrices corresponding to the emission source positions, A b Indicates the selected Φ j The matrix composed of all the columns of Denote (B∪A b )’s pseudo-inverse matrix; 6) When Φ j After the column selection is completed, the final r b The 2-norm of is saved to the set C N middle; 7) After traversing all N c After the perceptual sub-matrices, select C N The index corresponding to the smallest element in is selected as the i-th perception submatrix corresponding to the position of the emission source, and the index is saved in the set Λ B middle; 8) Follow Update the residual r, where A is the matrix composed of all the selected columns in the i selected perception sub-matrices, is the pseudo-inverse matrix of A; 9) Loop K1 times to obtain all the perception sub-matrices corresponding to the emission source positions; The step S4.2 comprises: 1) Select all the sensing sub-matrices corresponding to the emission source positions, according to Calculate the projection coefficient X0 of y on matrix A; 2) The tth cycle obtains the value of [Λ B ] t The non-zero elements on the corresponding blocks, where [Λ B ] t Denotes the set Λ B The tth element in ; 3) After K1 cycles, all non-zero elements of all non-zero blocks of X are obtained, thus obtaining X; The step S5 comprises: Constructing a broadband radio environment map is equivalent to obtaining the tensor T, Contains all the information of tensor T; after obtaining X, according to The tensor T is obtained to reconstruct the broadband radio environment map.

2. A broadband radio environment map construction system based on compressed sensing, characterized in that: include: Module M1: Establishing a system model based on the area where a broadband radio environment map is to be constructed; Module M2: Jointly utilize spatial and frequency domain sparsity to transform the system model into a compressed sensing model; Module M3: designing a spatial measurement matrix and constructing a frequency domain measurement matrix, and combining the spatial measurement matrix and the frequency domain measurement matrix to form a space-frequency measurement matrix in a compressed sensing model; Module M4: solving the compressed sensing model to restore the position of each emission source in the area and the power spectrum density on the broadband; Module M5: constructing a broadband radio environment map according to the location of each emission source in the area and the power spectrum density on the broadband; The system model includes: The area for constructing the broadband radio environment map is divided into a total of N c grid points, and deploy sensor devices capable of performing spectrum sampling within a certain bandwidth at m1 spatial sampling points in the region; N m The signals emitted by the signal sources are superimposed on each other to form a radio environment with a certain bandwidth W. W is divided into N b sub-band; The broadband radio environment map in the target area is modeled as a 3D tensor consisting of a planar 2D and a frequency domain 1D Where N x and N y Represents the number of grid points in the x and y directions, N b Represents the number of subbands divided within the bandwidth W in the f direction; for ease of representation, the tensor is assembled into a matrix Each column of P corresponds to a vector consisting of the power spectral density of the subband in W at a grid point; The matrix P is the broadband radio environment map of the target area. To obtain the complete P matrix, all columns of P are assembled from top to bottom into column vectors. Then the system model is: in, is an empty-frequent sparse dictionary, represents the channel matrix, γ i，j represents the path loss between points i and j; is the vector to be recovered with a quasi-block sparse structure, X j Corresponding to the jth grid point, the expression is: in, Represents the vector of power spectral density on all sub-bands in W of the mth transmitting source, s m is the grid point corresponding to the position of the mth emission source, is the set of grid points where the emission source exists, N is composed of 0 b ×1 vector; σ 2 is the power spectral density of Gaussian white noise, N is composed of 1 c N b dimensional vector; The compressed sensing model includes: Relative to all grid points, the sparseness of the emission source is K1 = N m ; The sparsity K of the subband occupied by the mth source relative to the number of all subbands in W is 2，m =||θ m ||0, where ||θ m ||0 is θ m 0-norm of ; Both forms of sparsity are contained in X, and the number of non-zero elements of X does not exceed The compressed sensing model constructed based on the above two sparsities is: in, is the space-frequency measurement matrix, and Represent the spatial measurement matrix and the frequency domain measurement matrix respectively; m1 and m2 represent the number of spatial sampling points and the number of subbands sampled in the frequency domain respectively; represents a set of spatial sampling points, represents the set of sampled subbands; Indicated by P l The elements in are the indices of the rows in the unit matrix of size N×N; Φ l The element 1 in each row represents the spatial sampling point, Φ f The element 1 in each row represents the sampled subband; The step S3 comprises: make is the space-frequency perception matrix, and the compressed sensing model is further written as Corresponding to the quasi-block sparse structure of X, the space-frequency perception matrix Divide into N c perceptual sub-matrices, namely To reduce The column correlation of X is improved to improve the recovery accuracy of X, and the spatial measurement matrix Φ is designed using the RCC-based spatial measurement matrix optimization algorithm. l include: 1) Calculate Ψ l The eigenvalues ​​and corresponding eigenvectors of 2) l The square of the eigenvalue of 3) Find the m1 eigenvalues ​​and corresponding eigenvectors that are closest to 1 after the eigenvalue is squared; 4) The m1 eigenvalues ​​closest to 1 form a diagonal matrix ∑′, and the corresponding eigenvectors are arranged in rows from top to bottom to form a matrix Φ′ l ; 5) Use Approximate l ; 6) Calculate R = Ψ l -Ψ′ l ; 7) Take the index of the m1 row with the smallest 2-norm of R to form the set P l ; 8) According to Get the spatial measurement matrix Φ l ; Randomly select m2 frequency domain sampling subbands to form a set P f ,according to Get the frequency domain measurement matrix Φ f ; according to Obtain the space-frequency measurement matrix Φ in the compressed sensing model; The step S4 includes: solving the compressed sensing model using the QBSBMP algorithm: Step S4.1: perform K1 cycles, select the i-th sensing submatrix corresponding to the position of the emission source in the i-th cycle, and find the positions of all emission sources in the area after the K1 cycles are completed; Step S4.2: According to the sensing sub-matrix, the quasi-block sparse vector X is restored to obtain the power spectrum density of each transmitting source on the broadband; The step S4.1 comprises: 1) Initialize the residual r = y; 2) For the i-th cycle, follow Update the j-th perception sub-matrix; 3) Initialize the residual r of the perception submatrix b = r; 4) According to Select the jth perceptual submatrix that matches the current r b The best matching column; 5) Follow Update b , where B is the matrix composed of all the selected columns in the i-1 selected sensing sub-matrices corresponding to the emission source positions, A b Indicates the selected Φ j The matrix composed of all the columns of Denote (B∪A b )’s pseudo-inverse matrix; 6) When Φ j After the column selection is completed, the final r b The 2-norm of is saved to the set C N middle; 7) After traversing all N c After the perceptual sub-matrices, select C N The index corresponding to the smallest element in is selected as the i-th perception submatrix corresponding to the position of the emission source, and the index is saved in the set Λ B middle; 8) Follow Update the residual r, where A is the matrix composed of all the selected columns in the i selected perception sub-matrices, is the pseudo-inverse matrix of A; 9) Loop K1 times to obtain all the perception sub-matrices corresponding to the emission source positions; The step S4.2 comprises: 1) Select all the sensing sub-matrices corresponding to the emission source positions, according to Calculate the projection coefficient X0 of y on matrix A; 2) The tth cycle obtains the value of [Λ B ] t The non-zero elements on the corresponding blocks, where [Λ B ] t Denotes the set Λ B The tth element in ; 3) After K1 cycles, all non-zero elements of all non-zero blocks of X are obtained, thus obtaining X; The step S5 comprises: Constructing a broadband radio environment map is equivalent to obtaining the tensor T, Contains all the information of tensor T; after obtaining X, according to The tensor T is obtained to reconstruct the broadband radio environment map.

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