Wireless spectrum map data completion method
By introducing adaptive thresholding and semi-quadratic optimization techniques into the spectrum tensor model, the problem of low spectrum map quality under complex noise environments is solved, and high-precision spectrum map completion is achieved under both Gaussian and non-Gaussian noise environments, thereby improving the robustness of spectrum management and network stability.
Patent Information
- Application Number
- CN202510901689.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-07-01
- Publication Date
- 2025-12-19
AI Technical Summary
In complex noise environments, existing technologies struggle to generate high-precision spectrum maps, especially when prior knowledge of noise distribution is lacking, resulting in low-quality spectrum maps.
A robust spectrum map completion method based on adaptive threshold is adopted. By integrating the dynamic threshold mechanism into the spectrum tensor model, the threshold parameters are dynamically adjusted and the threshold function is automatically shrunk to distinguish between signal components and noise components. The non-convex optimization problem is transformed into a convex optimization problem using semi-quadratic theory, and iterative optimization is performed using the projection gradient method.
In both Gaussian and non-Gaussian noise environments, it significantly improves the robustness and completion accuracy of the spectrum map, enhances spectrum utilization and management, alleviates spectrum conflicts, and ensures network reliability and stability.
Smart Images
Figure CN121174205A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application belongs to the field of wireless communication, and particularly relates to a robust completion method of spectrum data based on adaptive threshold in a complex noise environment. BACKGROUND
[0002] Electromagnetic spectrum is a kind of scarce resource. With the rapid development of emerging technologies such as mobile Internet, Internet of Things, big data and artificial intelligence, the number of user equipment and electronic systems has increased rapidly, and the demand for spectrum resources has shown an explosive growth trend. In the face of increasingly complex electromagnetic environment, how to efficiently monitor and manage electromagnetic spectrum has become a problem to be solved.
[0003] Spectrum map is one of the effective forms of expression of electromagnetic environment in a specific geographic area, which quantitatively describes the complex electromagnetic environment from multiple dimensions such as geographic location, time domain and frequency domain, and visualizes the information of electromagnetic energy distribution and spectrum resource distribution combined with geographic information, thereby providing comprehensive and accurate electromagnetic environment information. Spectrum map has wide application in spectrum monitoring and management, spectrum sharing and access, dynamic network planning, etc., and can improve spectrum utilization and management level, effectively alleviate spectrum conflict and ensure network reliability and stability. It has important research significance and application value to complete high-precision spectrum map.
[0004] Due to the influence of complex noise in actual scene, there is a problem of insufficient ability in depicting the spatial distribution of low-intensity electromagnetic signals, and the quality of generated spectrum map is low. And due to the lack of prior knowledge of noise distribution in the target area in practice, it is particularly important to design a spectrum map completion method suitable for various noise scenes. SUMMARY
[0005] The present application breaks the limitation of Gaussian noise assumption, and provides a robust completion method of wireless spectrum map based on adaptive threshold in complex environment of Gaussian and non-Gaussian noise (impulse noise). The method integrates a dynamic threshold mechanism into the spectrum tensor model, dynamically adjusts the threshold parameter and realizes the automatic shrinkage of the threshold function, so as to effectively distinguish the signal component and the noise component, and further obtain stronger robustness in complex noise environment.
[0006] In the first aspect, the present application provides a robust completion method of wireless spectrum map based on adaptive threshold, which comprises the following steps:
[0007] S1: according to the frequency spectrum situation superposition model, the spectrum data containing missing data and mixed noise are modeled as a three-dimensional block tensor decomposition model in three dimensions of two-dimensional plane space and frequency.
[0008] S2: In order to limit the influence of abnormal data such as pulse noise, a non-convex optimization function based on adaptive threshold is proposed to construct a spectral data repair model based on low-rank tensor completion.
[0009] S3: The above non-convex optimization problem is converted into a convex function optimization problem by using semi-quadratic theory.
[0010] S4: The optimization function is matrixed so as to be processed under the block successive upper bound minimization algorithm framework subsequently.
[0011] S5: For each single-variable optimization problem, the projection gradient method is used to iteratively optimize each factor until the convergence condition is met.
[0012] In one possible implementation manner, the step S1 is specifically:
[0013] Assuming that a target geographic area is divided into an I×J grid, the number of observed frequency bands is K, and there are R unknown spatial radiation sources in the area. According to the spectral posture superposition model, the spectral posture in the space-frequency domain can be represented as the sum of the spectral postures contributed by each radiation source. Under this model, the spectral posture of a single radiation source can be expressed as the product of the PSD of the radiation source along each frequency band and the SLF. Specifically, the signal PSD caused by the rth radiation source at the (i,j) spatial position at the kth frequency point satisfies:
[0014]
[0015] where S r is the SLF of the radiation source r, which can generally be decomposed into a path loss and a shadow fading component; c r represents the PSD function of the radiation source r.
[0016] Further, two assumptions are made to simplify the model: (1) the transmitter uses the frequency band in a sparse manner, that is, c r has sparsity. (2) The signal bandwidth is relatively small compared to its carrier frequency, and at this time the channel experiences flat fading, that is, the change of the SLF is independent of the frequency, that is, for any frequency k within the signal bandwidth, S r (i,j,k)≈S r (i,j). Based on the above assumptions, the PSD of the actual signal is modeled as a tensor The SLF and PSD of the radiation source r are represented as a matrix S r ∈R I×J and a vector c r ∈R K ×1 , and considering the influence of noise , formula (1) can be written as:
[0017]
[0018] The above model is called the two-factor BTD model, the symbol ○ represents the outer product operation, and each factor in the above formula has a specific physical meaning, so the model has interpretability.
[0019] Further, define Ω as a set of deployed sensor positions, the spatial sampling rate p = |Ω| / IJ, and the corresponding sampling tensor satisfies
[0020] Due to the non-negativity of SLF and PSD and the low rank of SLF in practice, based on the BTD model, the spectral map completion can be described as the following optimization problem:
[0021]
[0022] where the symbol * represents the Hadamard product, is the spectral data tensor, and the regular term characterizes the sparsity of it, and λ is the penalty parameter thereof, and the rank L << min(I, J).
[0023] In a possible implementation manner, the step S2 is specifically:
[0024] By setting a threshold in the data fidelity term and adaptively adjusting the threshold by a robust measure method, the normal elements and abnormal contaminated elements can be flexibly distinguished. Specifically, the first term of formula (3) is rewritten in the form of elements as:
[0025]
[0026] where the threshold θ > 0, and the set z ijk = w i,j,k (x ijk -p ijk ), p ijk is obtained from formula (1).
[0027] In a possible implementation manner, the step S3 is specifically:
[0028] Formula (4) is a non-convex optimization problem, and is also non-convex for a single variable. A semi-quadratic optimization scheme is adopted to convert the problem into a convex optimization problem of a single variable. According to the semi-quadratic theory, formula (4) can be rewritten as:
[0029]
[0030] where,
[0031] define Problem (5) can be rewritten as:
[0032]
[0033] s.t.rank(S r )≤L,S r ≥0,c r ≥0 (6)
[0034] In a possible implementation manner, the step S4 specifically includes:
[0035] Let the observed tensor unfold:R I×J×K →R IJ×K , then Specifically, the operator changes the tensor as follows:
[0036]
[0037] Further, define the row selection set Ω r of M, and let N = |Ω r |, then the observation matrix:
[0038] Y = M (Ω r , : ) = PM∈R N×K (8)
[0039] where P∈R N×IJ is the row selection matrix corresponding to the set Ω r .
[0040] Similarly, there is and it is noted that the following equation is established:
[0041] M = SC T (9)
[0042] where S = (vec (S1),..., vec (S R ))∈R IJ×R , C = (c1,..., c r )∈R K×R .
[0043] Further, according to (8), (9), (6) is converted into the following matrix optimization problem:
[0044]
[0045] In a possible implementation manner, the step S5 specifically includes:
[0046] For the factor matrix A, the updating process is as follows:
[0047]
[0048] Firstly, (11) is converted into vector form:
[0049]
[0050] where e (k) = vec(Y - PS (k) C (k)T ) is the fitting error of the kth iteration, and a (k) is the outlier vector of the kth iteration. The optimal solution of (12) is a (k+1) = T θ (e (k) ), which is defined as follows:
[0051]
[0052] Further, from (13), the optimal solution is affected by the threshold parameter θ, and a fixed θ may not guarantee the convergence of the algorithm, so θ needs to be iteratively updated in a non-decreasing robust metric way:
[0053]
[0054] where is a robust metric index. The median absolute deviation metric method is used to determine
[0055]
[0056] where Med(·) is the median operator. After obtaining the optimal solution a (k+1) , it is matrixed to obtain A k+1 .
[0057] Further, for the factor matrix C, the solution process of the subproblem is as follows:
[0058]
[0059] According to the projection gradient algorithm, the update method is:
[0060]
[0061] where [·] + is a non-negative projection operator that projects negative values to 0.
[0062] Further, for the factor matrix S, let the non-negative constraint set and the low-rank constraint set The solution process of the subproblem is as follows:
[0063]
[0064] According to the projection gradient algorithm and Eckart-Young-Mirsky theorem, the update method is:
[0065] S (k+1) = [U (k) (:,1:L)∑ (k) (1:L,1:L)V (k) (1:L,:) T ] + (19)。 BRIEF DESCRIPTION OF DRAWINGS
[0066] Figure 1 Flowchart of the spectrum map completion based on adaptive threshold.
[0067] Figure 2 Schematic diagram of spectral tensor matrixing and decomposition.
[0068] Figure 3 Estimation effect of the spectrum map under Gaussian noise scenario with SNR = 0 (first row) and SNR = 10 (second row).
[0069] Figure 4 Estimation effect of the spectrum map under non-Gaussian noise scenario with SNR = 0 (first row) and SNR = 10 (second row). DETAILED DESCRIPTION
[0070] The present application is further explained in the following examples, which are intended to illustrate the application and should not be construed to limit the scope of the application. Other advantages and benefits of the present application will be apparent from this disclosure. The present application can be implemented or applied in other different embodiments, and the details in the present specification can be modified or changed based on different views and applications without departing from the spirit of the present application. It should be noted that the figures provided in the following examples only schematically illustrate the basic concept of the present application, and the following examples and features in the examples can be combined with each other without conflict.
[0071] The accompanying drawings are only used for exemplary illustration, and the representation is only a schematic diagram, not a physical drawing, and should not be understood as a limitation on the present application. In order to better illustrate the embodiments of the present application, some components in the drawings can be omitted, enlarged or reduced, and do not represent the actual size of the product. It is understandable to those skilled in the art that some well-known structures and their descriptions in the drawings can be omitted.
[0072] The same or similar reference numerals in the drawings of the embodiments of the present application correspond to the same or similar components; in the description of the present application, it is understood that if the orientations or positional relationships indicated by the terms "upper", "lower", "left", "right", "front", "back" and the like are based on the orientations or positional relationships shown in the drawings, they are only for the convenience of describing the present application and simplifying the description, and do not indicate or imply that the devices or elements referred to must have a particular orientation, be constructed and operated in a particular orientation, therefore the terms describing the positional relationship in the drawings are only used for exemplary illustration, and cannot be understood as a limitation on the present application, for those skilled in the art, the specific meanings of the above terms can be understood according to the specific circumstances.
[0073] It should be noted that, as shown in Figure 1 , the completion process of the spectrum map under complex noise includes:
[0074] S1: According to the frequency spectrum situation superposition model, the spectrum data containing missing data and mixed noise are modeled as a three-dimensional block item tensor decomposition model in a two-dimensional plane space and three dimensions of frequency.
[0075] Assuming that the target geographical area is divided into a grid of IxJ, the number of observed frequency bands is K, and there are R unknown spatial radiation sources in the area. According to the spectrum situation superposition model, the spectrum situation in the space-frequency domain can be represented as the sum of the spectrum situations contributed by each radiation source in space. Under this model, the spectrum situation of a single radiation source can be expressed as the product of the PSD of the radiation source along each frequency band and the SLF. Specifically, the signal PSD caused by the rth radiation source at the (i, j) spatial position and the kth frequency point satisfies:
[0076]
[0077] where S r is the SLF of the radiation source r, which can usually be decomposed into path loss and shadow fading components; c r represents the PSD function of the radiation source r.
[0078] Further, two assumptions are made to simplify the model: (1) the transmitter uses the frequency band in a sparse manner, i.e. c r has sparsity. (2) The signal bandwidth is relatively small compared to its carrier frequency, at which time the channel experiences flat fading, i.e. the change of SLF is independent of frequency, i.e. for any frequency k within the signal bandwidth, S r (i, j, k) ≈ S r (i, j). Based on the above assumptions, the PSD of the actual signal is modeled as a tensor The SLF and PSD of the radiation source r are represented as matrix S r ∈ R I×J and vector c r ∈ RK×1 , and considering the effect of noise , formula (20) can be written as:
[0079]
[0080] The above model is called the two-factor BTD model, and the symbol represents the outer product operation, and each factor in the above formula has a specific physical meaning, so the model has interpretability.
[0081] Further, define Ω as the set of deployed sensor positions, the spatial sampling rate p = |Ω| / IJ, and the corresponding sampling tensor satisfies
[0082] Because of the non-negativity of SLF and PSD and the low rank of SLF in practice, based on the BTD model, the spectral map completion can be described as the following optimization problem:
[0083]
[0084] s.t.rank(S r )≤L, S r ≥0, c r ≥0. (22)
[0085] wherein the symbol * represents the Hadamard product, is the spectral data tensor, and the regular term characterizes its sparsity, and λ is its penalty parameter, and the rank L << min(I, J).
[0086] S2: To limit the influence of abnormal data such as impulse noise, a non-convex optimization function based on adaptive threshold is proposed to construct a spectral data repair model based on low-rank tensor completion.
[0087] By setting a threshold in the data fidelity term and adaptively adjusting the threshold by a robust measure method, normal elements and abnormal contaminated elements can be flexibly distinguished. Specifically, the first term of formula (22) is rewritten in the form of elements as:
[0088]
[0089] wherein the threshold θ > 0, and the set z ijk = w i，j，k (x ijk -p ijk ), p ijk is obtained from formula (20).
[0090] S3: The above non-convex optimization problem is transformed into a convex function optimization problem using semi-quadratic theory.
[0091] Equation (23) is a non-convex optimization problem, and it is also non-convex for a single variable. A semi-quadratic optimization scheme is used to transform the problem into a single-variable convex optimization problem. According to semi-quadratic theory, equation (23) can be rewritten as:
[0092]
[0093] in,
[0094] definition Rewrite problem (24) as follows:
[0095]
[0096] strank(S r )≤L,S r ≥0,c r ≥0 (25)
[0097] S4: Matrix the optimization function so that it can be processed later within the framework of the block continuous upper bound minimization algorithm.
[0098] It should be noted that, as Figure 2 As shown, let the observation tensor Define the expansion operator unfold: R I ×J×K →R IJ×K ,but Specifically, the operator makes the following changes to the tensor:
[0099]
[0100] Furthermore, define the row selection set of M. And let N = |Ω r |, then the observation matrix:
[0101] Y = M(Ω) r ,:)=PM∈R N×K (27)
[0102] Where P∈R N×IJ For set Ω r The corresponding row selection matrix.
[0103] Similarly, there are And note that the following equation holds true:
[0104] M = SC T (28)
[0105] in
[0106] Further, according to (27), (28), (25) is converted to the following matrix optimization problem:
[0107]
[0108] S5: For each single-variable optimization problem, and use the projection gradient method to iteratively optimize each factor until the convergence condition is met.
[0109] For factor matrix A, the update process is as follows:
[0110]
[0111] First, (30) is converted to vector form:
[0112]
[0113] where e (k) = vec(Y-PS (k) C (k)T ) is the fitting error of the kth iteration, and a (k) is the outlier vector of the kth iteration. The optimal solution of (31) is a (k+1) = T θ (e (k) ), which is defined as follows:
[0114]
[0115] Further, from (32), the optimal solution is affected by the threshold parameter θ, and a fixed θ may not guarantee the convergence of the algorithm, so θ needs to be updated in a non-decreasing robust measure:
[0116]
[0117] where is a robust measure index. The median absolute deviation measure method is used to determine
[0118]
[0119] where Med(·) is the median operator. After obtaining the optimal solution a (k+1) , it is matrixed to obtain A k+1 .
[0120] Further, for factor matrix C, the solution process of the subproblem is as follows:
[0121]
[0122] According to the projection gradient algorithm, the updating manner is:
[0123]
[0124] wherein, [·] + is a non-negative projection operator, projecting negative values to 0.
[0125] Further, for the factor matrix S, let the non-negative constraint set the low-rank constraint set The sub-problem solving process is as follows:
[0126]
[0127] According to the projection gradient algorithm and Eckart-Young-Mirsky theorem, the updating manner is:
[0128]
[0129] It should be noted that, Figure 3 and Figure 4 respectively show the estimation effect diagram of the spectrum map of the 8th frequency band under the condition of the spatial sampling rate of 0.2, SNR=0dB and SNR=10dB in the environment of Gaussian noise and non-Gaussian noise, the adaptive threshold block-term tensor decomposition spectrum map completion method (Adaptive Threshold Block-Term Tensor Decomposition, ATBTD) of the present application and the BCD, CBTD, NMF, LRTC four methods. Under the condition of Gaussian noise with SNR=10dB, the present application (ATBTD) obtains good estimation effect, and BCD and CBTD are slightly inferior to the present application under high signal-to-noise ratio. NMF destroys the spatial correlation and frequency domain correlation between high-dimensional spectral data, resulting in a decrease in the completion performance. LRTC uses tensor global low-rankness for completion, which may not be true in some scenarios, and also cannot capture the potential local low-rankness S r of the tensor, thereby resulting in poor performance. Under the condition of SNR=0dB, the present application has good noise robustness. BCD and CBTD have a decrease in performance in a low signal-to-noise ratio environment. In the non-Gaussian noise scenario, the present application can obtain a more accurate spectrum map. Finally, it is to be understood that the above-described embodiments are merely exemplary of the application and that a person skilled in the art can make modifications or equivalent substitutions to the technical solutions of the application without departing from the spirit and scope of the application, and all such modifications or equivalent substitutions should be encompassed in the scope of the claims of the application.
Claims
1. A method of wireless spectrum map data completion, the method comprising: The spectrum data completion method comprises the following steps: S1: according to a spectrum situation superposition model, the spectrum data containing missing data and mixed noise are modeled into a three-dimensional block item tensor decomposition model in three dimensions of two-dimensional space and frequency. S2: in order to limit the influence of abnormal data such as pulse noise, a non-convex optimization function based on an adaptive threshold is proposed to construct a spectrum data repair model based on low-rank tensor completion. S3: the non-convex optimization problem is converted into a convex function optimization problem by using semi-quadratic theory. S4: the optimization function is matrixed for subsequent processing under the block continuous upper bound minimization algorithm framework. S5: for each single variable optimization problem, the projection gradient method is used to iteratively optimize each factor until the convergence condition is met.
2. The method of claim 1, wherein, The step S1 is specifically: Assuming that a target geographical area is divided into an I*J grid, the number of observed frequency bands is K, and there are R unknown spatial radiation sources in the area. According to the spectrum situation superposition model, the spectrum situation in the space-frequency domain can be represented as the sum of the spectrum situations contributed by each radiation source in space. Under this model, the spectrum situation of a single radiation source can be expressed as the product of the emission power spectrum density (PSD) of the radiation source along each frequency band and the spatial loss function (SLF). Specifically, the signal PSD caused by the rth radiation source at the (i,j) spatial position at the kth frequency point satisfies: where S r is the SLF for the radiation source r, which can generally be decomposed into a path loss and a shadow fading component; c r denotes the PSD function for the radiation source r.
3. The method of claim 2, wherein, The above model is simplified by two assumptions: (1) the transmitter uses the frequency band in a sparse way, i.e. c r is sparse. (2) the signal bandwidth is relatively small compared to its carrier frequency, in which case the channel experiences flat fading, i.e. the variation of SLF is independent of frequency, i.e. S r (i,j,k) ~ S r (i,j) for any frequency k within the signal bandwidth. Based on the above assumptions, the PSD of the actual signal is modeled as a tensor The SLF and PSD of the radiation source r are represented as a matrix S r ∈ R I×J and a vector c r ∈ R K×1 , respectively, and considering the effect of noise , equation (1) can be written as: The above model is called the two-factor BTD model, and the symbol represents the outer product operation, and each factor in the above equation has a specific physical meaning, so the model has interpretability.
4. The method of claim 3, wherein, Let Ω be the set of deployed sensor locations, the spatial sampling rate p = |Ω| / IJ, and the corresponding sampling tensor satisfying Note that in practice the non-negativity of SLF and PSD and the low-rank property of SLF, based on the BTD model, the spectral map completion can be described as the following optimization problem: where the symbol * denotes the Hadamard product, is the spectral data tensor, the regularizer characterizing its sparsity, λ is its penalty parameter, and the rank L « min(I, J).
5. The method of claim 1, wherein, The step S2 is specifically: By setting a threshold in the data fidelity term and adaptively adjusting the threshold by a robust measurement method, normal elements and abnormal contaminated elements can be flexibly distinguished. Specifically, the first term of formula (3) is rewritten in the form of elements as follows: where the threshold value θ > 0, the set z ijk = w i，j，k (x ijk - p ijk ), p ijk is obtained from equation (1).
6. The method of claim 1, wherein, The step S3 is specifically: Formula (4) is a non-convex optimization problem, and for a single variable, it is also non-convex. In this paper, a semi-quadratic optimization scheme is used to convert the problem into a single variable convex optimization problem. According to the semi-quadratic theory, formula (4) can be rewritten as: wherein Definitions Rewrite problem (5) as:
7. The method of claim 1, wherein, The step S3 is specifically: Let the observed tensor be defined as unfold: R I×J×K → R IJ×K , then In particular, this operator changes the tensor as follows: Definition of the row selection set M Let N = |Ω r |, then the observation matrix: Y = M(Ω r , : ) = PM e R N×K (8) where P e R N×IJ is the set Ω r corresponding row selection matrix. Similarly, there are and note that the following equation holds: M = SC T (9) where S = (vec(S1),...,vec(S R )) e R IJ×R ,C = (c1,...,c r ) e R K×R . According to (8) and (9), (6) is converted into the following matrix optimization problem:
8. The method of claim 1, wherein, The step S4 is specifically: For the factor matrix A, the update process is as follows: First, (11) is converted into a vector form: Where e (k) =vec(Y-PS) (k) C (k)T Let α be the fitting error of the k-th iteration. (k) Let be the outlier vector of the k-th iteration. The optimal solution of equation (12) is a. (k+1) =T θ (e (k) ), which is defined as follows: As can be seen from (13), the optimal solution is affected by the threshold parameter θ, and fixed θ may not guarantee the convergence of the algorithm, so θ needs to be iteratively updated in a non-decreasing robust measurement manner: wherein is a robust measure of the degree of agreement. The measure method of median absolute deviation is used to determine where Med(·) is the median operator. The optimal solution a (k+1) After that, it is matrixed to get A k+1 . For the factor matrix C, the solution process of the subproblem is as follows: According to the projection gradient algorithm, the update method is as follows: wherein [·] + is a non-negative projection operator that projects negative values to 0. For the factor matrix S, let the low-rank constraint set The non-negativity constraint set The subproblem solution procedure is as follows: According to the projection gradient algorithm and the Eckart-Young-Mirsky theorem, the update method is as follows: S (k+1) = [U (k) (1:L, 1:L)∑ (k) (1:L, 1:L)V (k) (1:L, :) T ] + (19).