Dynamic spectrum mapping method based on non-negative matrix factorization and deep learning

Abstract

The invention belongs to the technical field of information and communication, and relates to a dynamic spectrum mapping method based on non-negative matrix factorization and deep learning. The invention provides a frequency spectrum charting method suitable for a dynamic electromagnetic environment, which combines non-negative matrix factorization and deep learning, models a dynamic frequency spectrum situation based on dynamic radiation source separation and space-time data representation, decomposes the dynamic frequency spectrum situation into space-time-frequency related low-dimensional feature factors and estimates the space-time-frequency related low-dimensional feature factors respectively, and further recovers a complete RM based on a representation model. According to the method, the problem that the accuracy of a traditional frequency spectrum mapping method is reduced in a dynamic electromagnetic environment is solved by mining the time domain characteristics of the radiation source, and compared with an existing frequency spectrum mapping method, the method has obvious estimation performance advantages in the scene of space sparse sampling and dense frequency spectrum occupied by the radiation source.

Description

Technical Field

[0001] The present invention belongs to the field of information and communication technologies, and relates to a dynamic spectrum cartography method based on non-negative matrix factorization and deep learning. Background Art

[0002] In recent years, with the rapid development of mobile Internet, industrial Internet and Internet of Things, the demand for electromagnetic spectrum has been increasing day by day, and the spectrum resources have become increasingly tense. In the face of the increasingly complex electromagnetic spectrum environment and the continuous growth of spectrum usage demands, in order to maintain the order and security of the electromagnetic spectrum and improve the overall utilization efficiency of spectrum resources, it is urgent to utilize the spectrum state data sensed by limited nodes to mine the spectrum situation information in the wide-area space.

[0003] Generally, the spectrum situation in a certain fixed area can be characterized by spatio-temporal-frequency gridded data. This multi-dimensional grid data is collectively called a radio map (RM), also known as a spectrum situation, and can be regarded as the superposition of the product of the power spectral density (PSD) and the spatial loss field (SLF) of each radiation source in the area. Spectrum cartography (SC) aims to recover the complete RM from sparse sensor samples in the airspace, and is an effective means to obtain the global spectrum situation using limited observation resources. Existing methods mainly consider spectrum cartography in static scenarios. In practical applications, in the scenario where the electromagnetic spectrum situation changes dynamically, the accuracy of static spectrum cartography methods is limited, and it is difficult to effectively track the changes in the situation. Summary of the Invention

[0004] Aiming at the problem that the accuracy of the existing spectrum cartography methods for estimating the dynamic electromagnetic spectrum situation is limited, the present invention proposes a dynamic spectrum cartography method based on non-negative matrix factorization and deep learning.

[0005] The technical solution of the present invention is as follows:

[0006] A dynamic spectrum cartography method based on non-negative matrix factorization and deep learning. It is assumed that there are multiple radiation sources in the observation area. The space of the observation area is divided into I×J equally spaced grids, the frequency band of the signals emitted by the radiation sources is divided into K frequency points, and the observation time domain contains T frames. Then the spectrum situation is expressed as where the value at the spatial position (i, j) at the k-th frequency point in the t-th frame is:

[0007]

[0008] where, and Denote the power spectral density (PSD) and the spatial fading field (SLF) of the \(R\) radiation sources in the observation domain at the \(t\)-th frame as \(t = 1, 2, \cdots, T\). Then the spectral situation tensor at the \(t\)-th frame is denoted as

[0009]

[0010] where “\(\omicron\)” represents the outer product operation;

[0011] The dynamic spectrum mapping method includes:

[0012] S1. On each frame of the observation period, deploy sensors sparsely in the observation area space. Each sensor acquires the situation data of the entire observation frequency band at its location. Define that at the \(t\)-th frame, all the sampled grid situation data constitutes a sampled situation matrix:

[0013]

[0014] where \(\Omega\) (t) \(=\{l|\text{vec}(W (t) )(l) = 1\}\) represents the one-dimensional index set of the sampling positions. \(l\) is a dummy variable representing the one-dimensional index of the spatial grid, and \(\text{vec}(\cdot)\) represents the vectorization operator. \(W (t) represents the sampling mask. The definition of the sampling mask is that \(W (t) (i, j)=1\) when the grid \((i, j)\) belongs to the set of grid positions sampled by the sensor at the \(t\)-th frame, otherwise \(W (t) (i, j)=0\), and \(|\Omega (t) | = M (t) \), where \(M (t) represents the number of grids sampled by the sensor. X (t) \((:, i, j)\) represents the situation tensor fiber of the sampling grid \((i, j)\) that acquires the complete \(K\) frequency points. X (1) represents the mode-1 expansion form of the tensor X ; combined with the expression of X (t) \), is expressed as:

[0015]

[0016] where the factor matrices are the PSD matrix of the radiation source and the sampled SLF matrix at the \(t\)-th frame respectively:

[0017]

[0018] where is the set of positions formed by the sensor sampling grid positions;

[0019] S2. During a period of stable PSD of the radiation source PS for T W frame long time window τ = t - T W +1,...,t, combined with the expression of, construct a characterization model for mining the time-domain characteristics of the radiation source based on non-negative matrix factorization and deep learning:

[0020]

[0021] where is the known sampling situation matrix within the time window, is the unknown radiation source PSD matrix within the time window, is the unknown radiation source sampling SLF matrix within the time window; g θ (·) is the radiation source SLF generation module composed of a trained neural network, z r is the SLF low-dimensional spatio-temporal characterization vector in the radiation source SLF generation module; define the spatio-temporal sampling mask within the window as satisfies Ω W ={l|vec(W W )(l)=1} is the spatio-temporal sampling index set;

[0022] The spatio-temporal characterization generation method of is as follows: z r generates the SLF sequence through g θ (·) and then samples according to the index set Ω W to obtain

[0023] S3. Convert the characterization model into an optimization problem to solve:

[0024]

[0025] where Z = [z1,...,z R T , G θ (·) represents the vectorized operation function corresponding to g θ (·), satisfying G θ (Z)(r,:,:,:) = g θ (z r );

[0026] Solve the optimization problem based on the block coordinate descent framework, and obtain the estimates of the radiation source PSD matrix and SLF tensor within the window according to the solution. Finally, synthesize the situation to obtain the situation tensor estimate on the complete observation domain.​

[0027] Further, the trained neural network in S2 refers to a radiation source SLF generation network based on deep learning. The input of the generation network is the sampled radiation source SLF sequence and the sampling mask. After passing through the spatial encoder and the spatio-temporal encoder, a low-dimensional spatio-temporal representation vector z is obtained. r The process of obtaining z r is defined as data spatio-temporal compression, denoted as f θ (·); z r After passing through the spatio-temporal decoder and the spatial decoder, the generated SLF sequence is obtained. The process of obtaining the generated SLF sequence from z r is defined as expansion recovery, denoted as g θ (·). The generated SLF sequence is the complete SLF sequence on each frame within the window, that is, the recovered SLF sequence. The training method of the generation network is as follows:

[0028] Construct a data set from the existing radiation source SLF sequence database or the SLF sequence generated by simulation. The SLF sequence generated by simulation is generated according to the following model:

[0029]

[0030] where x = (i, j) is the coordinate at any position in space, is the position coordinate of the radiation source r at the t-th frame. Let the initial coordinate of the radiation source be randomly generated and perform Brownian motion within the observation area, η r is the path loss factor of the radiation source r, is the shadow fading component of the radiation source r at the position x at the t-th frame, following a normal distribution;

[0031] On the SLF sequence, intercept a subsequence with a length of T W frames to form to constitute the SLF training set During training, randomly generate sampling masks to form W W (t, :, :) = W (t) to constitute the sampling mask set Through the training module, on the training set, from the sampled SLF sequence, based on data spatio-temporal compression - expansion recovery of the complete SLF sequence, the neural network learns to z r the mapping f θ (·) and from z r to the mapping g θ(·); The training objective is to minimize the mean square loss error between the recovered SLF sequence and the labeled SLF sequence by optimizing the neural network parameters θ on the training set:

[0032]

[0033] Among them, represents the expectation operator, and the neural network parameters are updated by the adaptive dynamic gradient descent algorithm until the objective converges.

[0034] Furthermore, the specific method for solving the optimization problem based on the block coordinate descent framework, obtaining the estimates of the PSD matrix of the radiation sources in the window and the SLF tensor according to the solution, and finally synthesizing the situation to obtain the situation tensor estimate on the complete observation domain is as follows:

[0035] Obtain the initial estimate of the optimization problem through the NMF solution algorithm of hierarchical alternating least squares, including:

[0036] Select r = 1,..., R, and alternately update the following parameters:

[0037]

[0038] Denote the error The parameter estimate after convergence is Let From obtain the initial estimate of the spatio-temporal low-dimensional representation of SLF, where F θ (·) represents the vectorization processing function of f θ (·), and obtain the initial estimate of the optimization problem

[0039] Alternately solve the sub-problems of C W and Z in the optimization problem. At the nth iteration, the parameter estimate The update criterion is as follows:

[0040]

[0041] Solve them respectively through the non-negative least squares algorithm and the gradient descent algorithm, and obtain the estimates of the PSD matrix of the radiation sources in the window and the SLF tensor according to the solution when the optimization problem converges: In the t-th frame, the PSD and SLF estimates of each radiation source are

[0042] Synthesize the situation according to the expression of X (t) Combine the estimates over the time stream t = 1,..., T, so as to obtain the situation tensor estimate on the complete observation domain:

[0043] ​

[0044] The effective effect of the present invention is that the present invention proposes a spectrum mapping method applicable to a dynamic electromagnetic environment. By exploring the time-domain characteristics of radiation sources, the problem of reduced accuracy of traditional spectrum mapping methods in a dynamic electromagnetic environment is solved. Compared with existing spectrum mapping methods, the present invention has obvious estimation performance advantages in scenarios with sparse spatial sampling and dense spectra occupied by radiation sources. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 is a system block diagram of the present invention.

[0046] Figure 2 is a schematic diagram of the overall architecture of the SLF parametric spatio-temporal characterization learning module.

[0047] Figure 3 is a schematic diagram of NMSE of the method proposed in the present invention and existing spectrum mapping methods for estimating dynamic situations on each frame at a 1% spatial sampling rate.

[0048] Figure 4 is a schematic diagram of a situation slice estimated at a certain frequency point on a certain frame by the method proposed in the present invention and existing spectrum mapping methods at a 1% spatial sampling rate. DETAILED DESCRIPTION OF THE INVENTION

[0049] Non-negative Matrix Factorization (NMF) can effectively characterize the superposition characteristics of radiation sources in the spectrum situation and the physical non-negative characteristics of the PSD and SLF of radiation sources. A Deep Neural Network (DNN) can effectively characterize the spatial characteristics and time dynamics of the SLF of radiation sources. Therefore, the present invention combines non-negative matrix factorization and deep learning, models the dynamic spectrum situation based on dynamic radiation source separation and spatio-temporal data characterization, decomposes it into low-dimensional feature factors related to space-time-frequency and estimates them separately, and then restores the complete RM based on the characterization model.

[0050] The present invention considers a spatio-temporal-frequency observation domain where multiple radiation sources coexist. The spatial region is divided into I×J equally spaced grids, the frequency bands of the signals emitted by the radiation sources are divided into K frequency points, and the observation time domain contains T frames. The spectrum situation is represented by a fourth-order tensor which can be regarded as the superposition of the PSD and SLF of each radiation source in the observation domain. Under narrowband conditions, the SLF of a radiation source at different frequency points can be approximately regarded as the same. Thus, X At the t-th frame, at the spatial position (i,j), the value at frequency point k satisfies:

[0051]

[0052] where, and respectively represent the PSD and SLF of R radiation sources in the observation domain at the t-th frame. Correspondingly, the spectral situation tensor at the t-th frame is denoted as According to the relationship in Equation (1), it satisfies:

[0053]

[0054] where represents the outer product operation.

[0055] The present invention aims to estimate the radio map on the complete observation domain from the spatial sparse sampling of the dynamic radio map that satisfies the relationships in Equations (1) and (2) X , and the involved method includes the following steps:

[0056] Step 1: Sensor deployment and situation data collection.

[0057] The following sensor deployment paradigm is adopted in the present invention: On each frame of the observation period, sensors are sparsely deployed in space, and each sensor acquires the situation data of the entire observation frequency band at its location. Specifically, at the t-th frame, there are M (t) grids sampled by sensors, and their positions constitute the position set Define the sampling mask

[0058]

[0059] Define the one-dimensional index set of its sampling positions as Ω (t) ={l|vec(W (t) )(l)=1}, where vec(·) represents the vectorization operator, and |Ω (t) | = M (t) . The sampling grid (i, j) acquires the situation tensor fiber of the complete K frequency points X (t) (:, i, j). At the t-th frame, the situation data of all sampling grids constitute the sampling situation matrix: where A (n) represents the mode-n expansion form of the tensor A . Using the relationship in Equation (2), the sampling situation matrix satisfies:

[0060]

[0061] where the factor matrices are respectively the radiation source PSD matrix and the sampling SLF matrix at the t-th frame, and have the following structure:

[0062]

[0063] Among them Step 2: Mine the dynamic situation characterization modeling of the time-domain characteristics of the radiation source.

[0064] Within a certain period of time when the operating mode of the radiation source is stable, its PSD can be regarded as stable. At the t-th frame, take a time window τ of length T W frames, τ = t0 - T W +1,..., t, and the PSD matrix of the radiation source within the window is denoted as Then according to Equation (5), the sampling situation within the window satisfies:

[0065]

[0066] Among them are respectively the situation matrix and the radiation source SLF matrix connected in series along the space-time domain within the window, At the same time, define the SLF sequence within the window Satisfy Define the set of sampling positions within the window

[0067] Considering that the PSD and SLF of the radiation source are non-negative in physical meaning; at the same time, the SLF of the radiation source has specific space-time characteristics. For example, the value of the radiation source SLF decays radially from the radiation source position to the surrounding in space, and the SLF of the radiation source changes dynamically according to a certain law in the time domain (such as continuous change of the radiation source position, and correlation of the electromagnetic environment between adjacent frames). Establish the following characterization model for mining the time-domain characteristics of the radiation source for the sampling situation within the window:

[0068]

[0069] In Equation (7), g θ (·) is a radiation source SLF generation module composed of a neural network, which learns the low-dimensional parametric space-time characterization of the SLF by mining the time-domain characteristics of the radiation source, and generates the SLF sequence of the radiation source r within the window from the vector z r in the low-dimensional internal parameter space: Among them Define the space-time sampling mask within the window as Satisfy Space-time sampling index set Ω W ={l|vec(W W )(l)=1}, there is

[0070] The first two rows in Equation (7) constitute the NMF model, ensuring the parameter (i.e., the radiation source parameter ) It has unique decoupling under certain conditions; the constraint of the last line can be regarded as the spatio-temporal constraint of the sampled SLF of the radiation source based on the neural network, assisting in the separation of the above radiation source parameters and by setting to complete the values of the missing samples of SLF in the spatio-temporal domain.

[0071] To learn the low-dimensional parametric spatio-temporal representation of SLF, a Convolutional-Long Short-Term Memory (Conv-LSTM) network under the Spatial-Temporal Auto-Encoder architecture is trained, and its overall architecture is as Figure 2 shown. The input of the module is the sequence of sampled maps obtained by sampling the SLF sequence of the radiation source r within the window. The sampled maps on each frame are compressed into low-dimensional spatial representation vectors by the spatial encoder respectively, and then the low-dimensional spatial representation vectors within the entire window are input into the spatio-temporal encoder to be compressed into a low-dimensional spatio-temporal representation vector z r ; then it is expanded by the mirror structure, and finally the complete SLF on each frame within the window is generated.

[0072] Table 2 and Table 2 respectively give the structures of each sub-module in the network and the specific structures of the sub-structural layers:

[0073] Table 1 Structures of Each Sub-module in the Network

[0074]

[0075] Table 2 Specific Structures of the Sub-structural Layers in the Network

[0076]

[0077]

[0078] By training the module on the SLF dataset to recover the complete SLF sequence based on data spatio-temporal compression-expansion from the sampled SLF sequence, the neural network learns the mapping f r from to z θ (·) and the mapping g r from z to θ (·). During the training process, the sampling mask is randomly generated, and the loss function is the root mean square error (Mean Square Error, MSE) between the SLF sequence generated by the network and the label .

[0079] Step 3: Model parameter estimation and situation generation.

[0080] According to the situation representation model in Equation (7), the model solution is transformed into solving an optimization problem:

[0081]

[0082] where \(Z = [z_1,...,z R T , \(G θ (·)\) represents the vectorized operation function corresponding to \(g θ (·)\), and satisfies: G θ (Z)(r,:,:,:) = g θ (z r ).

[0083] Solve this problem based on the Block Coordinate Descent (BCD) framework.

[0084] First, obtain a preliminary estimate of the problem through the NMF solution algorithm of Hierarchical Alternating Least Squares (HALS) as follows:

[0085] In each iteration, select \(r = 1,...,R\) and alternately update the parameters according to equations (9) and (10):

[0086]

[0087] Denote the error The parameter estimate after convergence is Let From obtain the initial estimate of the SLF spatio-temporal low-dimensional representation, where \(F θ (·)\) is defined similarly to \(G θ (·)\) and represents the vectorized processing function of \(f θ (·)\). Take as the initialization of the problem in equation (8).

[0088] Then, iteratively and alternately solve the sub-problems of equation (8) with respect to \(C W and \(Z\) respectively. In the \(n\)th iteration, the parameter estimate is updated according to the following criteria:

[0089]

[0090] Among them, the problem in equation (11) is solved by the Non-negative Least Squares (NNLS) algorithm; the problem in equation (12) is solved by the Gradient Descent (GD) algorithm. ​

[0091] When the problem (8) converges (denoted as the N - th iteration), the estimates of the PSD matrix of the radiation sources within the window and the SLF tensor are obtained according to the solution: At the t - th frame, the PSD and SLF estimates of each radiation source are Synthesize the situation according to Equation (2) Combining the estimates over the time flow t = 1,..., T, the situation tensor estimate over the complete observation domain can be obtained:

[0092]

[0093] The following gives an example and conducts a simulation to visually describe the method of the present invention.

[0094] In this example, the geospatial range is 100×100m 2 , which is divided into I×J = 50×50 uniform grids; the signal transmission frequency band is divided into K = 64 equally - spaced frequency points; at the t - th frame, the SLF of the radiation source r consists of a path - loss component and a shadow - fading component:

[0095]

[0096] where x=(i, j) is the coordinate at any spatial position, is the position coordinate of the radiation source r at the t - th frame, and it is assumed that the radiation source moves uniformly within the observation area at a certain speed. η r is the path - loss factor of the radiation source r, is the shadow - fading component (in dB) of the radiation source r at position x at the t - th frame, which follows a normal distribution. In the test scenario, η r is taken from a uniform distribution on [2, 2.5], and the moving speed of the radiation source is about 1m per frame.

[0097] The PSD of the radiation source r follows the following model:

[0098]

[0099] This model indicates that the PSD of the radiation source r is composed of the superposition of B frequency - domain basis functions, controlling the amplitude, center frequency, and bandwidth of the b - th basis function respectively. The test scenario is the case where the radiation sources densely occupy the spectrum: each radiation source has B = 10 frequency - domain bases, is taken from a uniform distribution on [0.5, 2], is taken from a uniform distribution on [3, 4], and are randomly distributed within 10 corresponding sub - frequency bands evenly divided in the observation frequency band. It is assumed that the PSD of the radiation source mutates every 50 frames and remains stable until the next mutation.

[0100] To highlight the advantages of the present invention in terms of performance, it is compared with the following existing methods, including: the static spectrum mapping method combining LL1 tensor block decomposition (Block-Term Decomposition, BTD) and thin plate splines (TPS) interpolation (denoted as LL1-TPS); the static spectrum mapping method combining NMF and neural network (Deepgenerative priOr With Joint OptimizatioN for Spectrum cartography, DowJons). Both the neural network module in DowJons and the present invention are in η r Obtained from the uniform distribution in [2, 3], and the radiation source makes a Brownian motion with a variance of 1 m per frame in the SLF dataset. The time window length in the present invention is taken as T W = 8. The specific measurement index for situation estimation is the normalized mean square error (NMSE) of situation estimation on each frame:

[0101]

[0102] The performance of the spectrum mapping method for mining the time-domain characteristics of radiation sources in the present invention example and the existing methods is as Figure 3 , Figure 4 shown. Figure 3 Shows the NMSE of the situation estimation error of each algorithm on each frame at a spatial grid sampling rate of ρ = 1% X . Among them, LL1+TPS and DowJons do not utilize the time-domain characteristics of the radiation source, so their accuracy and stability are worse than the method proposed in the present invention.

[0103] The slices of the estimated situation at a certain frequency point on a certain frame of the method proposed in the present invention and the existing methods are visually displayed. Since the method proposed in the present invention utilizes the time-domain information of the radiation source for situation characterization and estimation, the accuracy of the restored situation is better than that of other methods, and the situation information around the radiation source can be restored more clearly.

Claims

1. A dynamic spectrum mapping method based on non-negative matrix decomposition and deep learning. It is assumed that there are multiple radiation sources in the observation area, the observation area space is divided into I×J equally spaced grids, the frequency band of the radiation source emission signal is divided into K frequency points, and the observation time domain is defined to contain T frames. The spectrum situation is expressed as The value of the spatial position (i, j) at the kth frequency point in the tth frame is: in, and They represent the power spectral density PSD and spatial fading field SLF of the R radiation sources in the observation domain at the tth frame, t=1,2,...,T, then the spectrum situation tensor at the tth frame is recorded as in represents the outer product operation; Characterized in that the dynamic spectrum mapping method comprises: S1. In each frame of the observation period, sensors are sparsely deployed in the observation area space. Each sensor obtains the situation data of the entire observation frequency band at its location. It is defined that in the tth frame, all sampling grid situation data constitute the sampling situation matrix: Among them, Ω (t) = {lvec(W (t) )(l)=1} represents the one-dimensional index set of sampling positions, l is a dummy variable, representing the one-dimensional index of the spatial grid, vec(·) represents the vectorization operator, W (t) represents the sampling mask, which is defined as the grid (i, j) belonging to the set of grid positions sampled by the sensor in the tth frame. (t) (i,j)=1, otherwise W (t) (i,j)=0,|Ω (t) |=M (t) , M (t) represents the number of grids sampled by the sensor, X (t) (:,i,j) indicates that the sampling grid (i,j) obtains the situation tensor fiber of the complete K frequency points, X (1) Representing a tensor X mode-1 expansion form; combined with X (t) The expression of It is expressed as: Among them, the factor matrix They are the radiation source PSD matrix and sampling SLF matrix of the tth frame respectively: in is the set of locations consisting of the grid locations sampled by the sensor; S2, in a period of T where the radiation source PSD is stable W Frame long time window τ = tT W +1,...,t, combined Based on non-negative matrix factorization and deep learning, a characterization model for mining the time domain characteristics of radiation sources is constructed: in, is the known sampling situation matrix in the time window, is the PSD matrix of the unknown radiation source in the time window, is the unknown radiation source sampling SLF matrix within the time window; g θ (·) is the radiation source SLF generation module composed of the trained neural network, z r is the SLF low-dimensional space-time representation vector in the radiation source SLF generation module; the space-time sampling mask in the window is defined as satisfy Ω W = {l|vec(W W )(l)=1} is a set of space-time sampling indices; The space-time representation of z is generated as follows: r By g θ (·) Generate SLF sequence Then according to the index set Ω W Sampling S3. Convert the representation model into an optimization problem: Where Z = [z1,...,z R ] T , G θ (·) indicates g θ (·) The corresponding vectorized operation function satisfies G θ (Z)(r,:,:,:)=g θ (z r ); The optimization problem is solved based on the block coordinate descent framework, and the PSD matrix and SLF tensor of the radiation source in the window are estimated according to the solution. Finally, the situation is synthesized to obtain the situation tensor estimation on the complete observation domain.

2. The method for dynamic spectrum mapping based on non-negative matrix decomposition and deep learning according to claim 1, characterized in that: The trained neural network in S2 refers to the radiation source SLF generation network based on deep learning. The input of the generation network is the sampled radiation source SLF sequence and the sampling mask. After the spatial encoder and the space-time encoder, the low-dimensional space-time representation vector z is obtained. r , we will get z r The process is defined as data space-time compression, denoted as f θ (·); z r After the space-time decoder and the spatial decoder, the generated SLF sequence is obtained and will be represented by z r The process of obtaining the generated SLF sequence is defined as dilation recovery, denoted as g θ (·), the generated SLF sequence is the complete SLF sequence on each frame in the window, that is, the restored SLF sequence; the training method of the generated network is as follows: The data set is constructed from the existing radiation source SLF sequence database or the SLF sequence generated by simulation. The SLF sequence generated by simulation is generated according to the following model: Where x = (i, j) is the coordinate of any position in space, is the position coordinate of the radiation source r in the tth frame, the initial coordinates of the radiation source are randomly generated, and it performs Brownian motion in the observation area, η r is the path loss factor of the radiation source r, is the shadow fading component of the radiation source r at position x in the tth frame, which obeys the normal distribution; On the SLF sequence, the truncation length is T W Subsequence of frames composition Constructing the SLF training set During training, randomly generate sampling masks composition Composing the sampling mask set Through the training module, the complete SLF sequence is restored from the sampled SLF sequence based on the data space-time compression-expansion on the training set, so that the neural network can learn to z r The mapping f θ (·) and z r arrive The mapping g θ (·); The training goal is to minimize the mean squared loss error between the recovered SLF sequence and the label SLF sequence by optimizing the neural network parameters θ on the training set: in, Represents the expected operator, and the neural network parameters are updated through the adaptive dynamic gradient descent algorithm until the target converges.

3. The method for dynamic spectrum mapping based on non-negative matrix decomposition and deep learning according to claim 1, characterized in that: The specific method of solving the optimization problem based on the block coordinate descent framework, obtaining the estimation of the PSD matrix and SLF tensor of the radiation source in the window according to the solution, and finally synthesizing the situation to obtain the situation tensor estimation on the complete observation domain is: The NMF solution algorithm of hierarchical alternating least squares is used to obtain a preliminary estimate of the optimization problem, including: Select r=1,...,R and update the following parameters alternately: Error The parameter estimates after convergence are make Depend on Get an initial estimate of the SLF space-time low-dimensional representation, where F θ (·) indicates f θ (·) to obtain a preliminary estimate of the optimization problem Alternating solution optimization problem about C W and Z subproblems, at the nth iteration, the parameter estimation The update guidelines are as follows: The non-negative least squares algorithm and the gradient descent algorithm are used to solve the problem. When the optimization problem converges, the PSD matrix and SLF tensor of the radiation source in the window are estimated according to the solution: In the tth frame, the PSD and SLF of each radiation source are estimated as follows: According to X (t) The expression synthesis situation Combining the estimates on the time stream t=1,...,T, we get the situation tensor estimate over the complete observation domain:

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