A Wireless Spectrum Prediction Method under Conditions of Data Missing and Noise Interference

Abstract

The present invention relates to a wireless spectrum prediction method under the conditions of missing data and noise interference. The method includes: Step 1, inputting spectrum data; Step 2, establishing a third-order tensor model of the spectrum data; Step 3, performing standardization processing on the data; Step 4, establishing a wireless spectrum prediction model; Step 5, solving the established wireless spectrum prediction model. The advantages and effects of the present invention are as follows: A new tensor adaptive nuclear norm is defined, which can avoid over-punishing the larger singular values in the spectrum tensor, better approximate the rank of the spectrum tensor, and effectively improve the prediction performance; universal modeling of noise can separate any type of noise with the same distribution condition and make accurate predictions during the spectrum prediction process, effectively coping with the spectrum data acquisition application scenarios with both missing data and noise interference, and proposing a brand-new wireless spectrum prediction method.

Description

Technical Field

[0001] The present invention relates to the field of signal processing, and particularly to a wireless spectrum prediction method under the conditions of data loss and noise interference. Background Art

[0002] As a non-renewable and limited resource, radio spectrum plays an indispensable role in maintaining social and economic stability and the security of various fields of the country. However, with the rapid development of various wireless access networks, the number of users of wireless services and the corresponding bandwidth requirements have increased explosively, and the scarcity problem of the spectrum has become particularly serious. In order to make full use of spectrum resources, various spectrum management schemes have emerged continuously. As a key technology in spectrum analysis, wireless spectrum prediction can infer the spectrum development trend from historical spectrum data and is the basis for managing and allocating spectrum resources.

[0003] Previous spectrum prediction work usually refers to prediction on a slot-by-slot basis, generally realizing the prediction of a single slot from a single domain, such as spectrum prediction technology based on the time domain. On this basis, some scholars have started from a two-dimensional perspective, jointly using the time domain and the frequency domain to utilize the correlation of spectrum data to realize the prediction of the spectrum states of all frequency points in a single slot. However, these works can only predict the spectrum states slot by slot and cannot effectively meet the demand for predicting the spectrum states in any time period.

[0004] In existing spectrum prediction research, the literature "Sun J, Wang J, Ding G, et al. Long-Term Spectrum State Prediction: An Image Inference Perspective[J]. IEEE Access, 2018, PP: 1-1." and the literature "Ge C, Wang Z, Zhang X, et al. Robust Long-Term Spectrum Prediction with Missing Values and Sparse Anomalies[J]. IEEE Access, 2019, PP(99): 1-1". respectively solve the cases where there are data missing and sparse anomalies in historical data, and propose a spectrum prediction method based on tensor completion. However, this method is limited to predicting on a monitoring day basis and cannot solve the prediction for any time period. More importantly, these technologies are all proposed under ideal conditions and do not consider the situation of noise interference in the received spectrum data. Since the existence of noise interference will destroy the low rank property of the tensor and does not meet the theoretical low rank condition for constructing the spectrum tensor model, the existing methods cannot make accurate predictions under the conditions of simultaneous data loss and noise interference.

[0005] Meanwhile, most of the current methods for denoising using tensor recovery represent the optimization objective as minimizing the sum of the tensor nuclear norm and the reconstruction error, that is

[0006]

[0007] where: represents the spectral tensor to be completed, represents the noise tensor. To recover the low-rank tensor from the observed data with noise, it should be noted that this optimization objective is only for the case without missing data, and there are some deficiencies in both terms of this problem. When solving the first term, it will involve a soft-thresholding shrinkage operation, which will cause an equal decrease in each singular value, making the variance of the estimated tensor smaller than that of the original tensor. And the second reconstruction error term assumes that the noise is zero-mean, and it cannot effectively separate non-zero-mean noise.

[0008] In the existing publicly available patent literature, for example, Chinese Invention Patent Application No. 202211281750.1 discloses a shortwave spectrum prediction method based on federated learning, which establishes a wireless network with a global user and multiple local users inside. The method is characterized by the following steps:

[0009] Step 1: Collect, analyze, and complete the spectrum data at multiple locations over a past period of time;

[0010] Step 2: Divide, standardize, and reconstruct the data set processed in Step 1;

[0011] Step 3: Construct a neural network model for local training to train the data set processed in Step 2;

[0012] Step 4: Construct a federated algorithm for fusing the local training models, and send the updated model to each local user to update the local model and make predictions.

[0013] For another example, Chinese Patent Application No. CN202111169587.5 discloses a spectrum prediction method driven by a radio frequency machine learning model, including: S1, collecting spectrum data and preprocessing the collected spectrum data; S2, determining the order of the autoregressive model according to the Akaike information criterion and determining the step size M of the input data; S3, expanding the linear combination process of the autoregressive model into an M-layer network structure, and introducing new trainable parameters in the M-layer network structure to construct an M-layer spectrum prediction network model driven by a radio frequency machine learning model; S4, training the spectrum prediction network model using the training set data; S5, determining whether the training is completed. If so, input the test set data into the trained spectrum prediction network model, output the prediction result, and end the process; if not, after adding one to the training iteration count, return to step S4 until the maximum iteration count is reached. The present invention not only endows the network with interpretability, improves the prediction performance, but also speeds up the convergence rate of the network.

[0014] None of the above-mentioned patent applications consider wireless spectrum prediction under conditions of data loss and noise interference.

[0015] Based on the above problems existing in the prior art, the present invention aims to re-establish a tensor reconstruction optimization objective for the collected spectrum data under the conditions of both data loss and noise interference, and proposes a wireless spectrum prediction method that can eliminate the noise interference of historical data and accurately predict the future spectrum conditions. Summary of the Invention

[0016] The object of the present invention is to overcome the deficiencies of the prior art, and in view of the situation where the collected spectrum data simultaneously has data loss and noise interference, a wireless spectrum prediction method under the conditions of data loss and noise interference is proposed. The method includes:

[0017] Step 1, inputting spectrum data:

[0018] Step 2, establishing a third-order tensor model of the spectrum data;

[0019] Step 3, performing standardization processing on the data;

[0020] Step 4, establishing a wireless spectrum prediction model;

[0021] Step 5, solving the established wireless spectrum prediction model.

[0022] Further, in step 1, the inputting spectrum data specifically includes: taking out the collected spectrum data from the spectrum database, mainly referring to the power spectral density value of the observed signal, and converting it into a spectrum data matrix in a conventional manner. The spectrum data matrix has time slots as the horizontal axis and frequency points as the vertical axis, denoted as X ∈ R A×B, at this time, the matrix elements are composed of two parts of data. One part is missing data, represented by 0; the other part is normally received data, which consists of the true value and noise interference.

[0023] Further, in step 2, the establishment of the third-order tensor model of the spectrum data specifically includes: according to different time periods of spectrum observation, different time units are selected as the Z-axis to establish a tensor To achieve the prediction function, a full-zero matrix is used to represent the part of the spectrum data to be predicted and added to the tensor to establish a spectrum tensor model:

[0024] Further, in step 3, the normalization processing of the spectrum data specifically includes: after the spectrum tensor model is established, the data needs to be normalized first. In order not to destroy the correlation of the data sequence of the same frequency point and the same time slot on different time units, the tensor is normalized in the third dimension. By fixing the x-axis and y-axis of the tensor, different tube fibers are taken out, and normalization is performed on each tube fiber so as to process the spectrum tensor in the following steps and effectively improve the convergence speed of the prediction algorithm. Since it is impossible to directly fill the full-zero matrix in the tensor, an appropriate tube fiber is selected to take the average value as the initial value of the prediction and filled into the (C + 1)-th frontal slice of the spectrum tensor. At this time:

[0025]

[0026] Among them: the first dimension represents the time slot in a day, the second dimension represents the frequency point, and the third dimension represents the date. Each element of this tensor represents the power spectral density of the j-th frequency point at the i-th time slot on the k-th day.

[0027] Further, in step 4: establish a wireless spectrum prediction model:

[0028] In view of the inherent correlation of each dimension of the real spectrum data, it is considered that the spectrum data in the case of no noise has low rank. Utilize the low rank of the spectrum tensor to recover the low rank spectrum tensor from the spectrum observation data containing noise, and establish a wireless spectrum prediction model;

[0029] The optimization objective of the conventional recovery of the low rank tensor from the noisy observation is:

[0030]

[0031] For the first item, the adaptive shrinkage of singular values is achieved by assigning different weights to the singular values of the spectral tensor. It is known that the main information of the spectral data is contained in the large singular values, while the small singular values are more caused by noise interference. Assigning weights is to slightly shrink the large singular values containing spectral features to retain the main information of the spectrum and better approximate the rank of the spectral tensor. The tensor adaptive nuclear norm is defined as the weighted sum of singular values. At this time, the optimization objective is the following formula (2):

[0032]

[0033] Where: represents the predicted spectral tensor, is the diagonal tensor after performing tensor singular value decomposition on , and α i represents the i-th adaptive coefficient, which is some negative powers of singular values, that is:

[0034]

[0035] In the above formula, the larger the singular value, the larger the denominator, and the smaller α i , the smaller the corresponding shrinkage operation, and the better the recovery performance of the spectral data;

[0036] For the second item of the conventional optimization objective, considering the case of non-zero mean noise, assume that the actual average value and variance of the noise are both unknown. Introduce u to represent the mean distribution of the noise, is a tensor with the same size as the noise tensor and all terms being u. The variance of the tensor is represented by the norm , as shown in the following formula (3),

[0037] It can be simply proved that this term takes the minimum value only when u is equal to the actual mean:

[0038]

[0039] In the above formula (3), when is the smallest, it is considered that u is equal to the true noise mean at this time, and the general case of noise can be recovered. When u = 0, it corresponds to the special case of zero mean noise, and the case of zero mean additive Gaussian noise is also included here;

[0040] By optimizing the two terms in the optimization objective of formula (1) respectively, the optimization problem of spectral prediction from noisy historical spectral data is reformulated as follows:

[0041]

[0042] Among them, the relaxation of the rank is represented by the newly proposed tensor adaptive nuclear norm in this method, which is specifically manifested as the weighted sum of tensor singular values. The second term is a general term model for noise. represents the observed spectral measurement values. represents the predicted spectral tensor. represents the separated noise tensor. λ is the penalty term parameter and is a positive number. u represents the noise mean. represents the sum of and has the same dimension size as, and all elements are tensors of u. Ω is the observation set. The elements in Ω are known values while other elements are missing. Therefore, the elements not belonging to Ω in are set to 0, and the remaining terms remain unchanged. The constraint condition ensures that the sum of the recovered spectral true value and the noise tensor is consistent with the original observed value on the elements of the observation set Ω.

[0043] Furthermore, in step 5: Solve the established wireless spectrum prediction model:

[0044] For equation (4) in step 4, substitute the tensor after data preprocessing in step 2 into the observed values, and perform tensor singular value decomposition on Take out the first positive slice of the singular values, that is, The elements on the diagonal of this positive slice are the singular values of the established third-order spectral tensor Select appropriate values to initialize the parameters. By iteratively updating the variables, make gradually approach the noise-free true spectrum data value, gradually separate the noise interference in the observed values; then, when the tensor adaptive nuclear norm defined by the sum of weighted singular values and the sum of noise variances are minimized, the predicted value of the spectrum and the separated additive noise are obtained, and at the same time, reliable filling of the missing data is completed. The above process is to use the alternating direction multiplier method, that is, the ADMM method to solve for the low-rank spectral tensor and the noise tensor The closed-form solution overview. Finally, the (C + 1)th positive slice of the output low-rank spectral tensor is the obtained spectrum prediction value.

[0045] The superior technical effects of the present invention are as follows:

[0046] 1. The wireless spectrum prediction method under the conditions of data missing and noise interference described in the present invention defines a new tensor adaptive nuclear norm, which can avoid over-punishing the larger singular values in the spectral tensor, better approximate the rank of the spectral tensor, and effectively improve the prediction performance.

[0047] 2. The wireless spectrum prediction method under the conditions of data missing and noise interference according to the present invention conducts a general modeling of noise, can separate any kind of noise with the same distribution condition during the spectrum prediction process and make accurate predictions, effectively cope with the spectrum data acquisition application scenarios with both data missing and noise interference, and proposes a brand-new wireless spectrum prediction method. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 Schematic flowchart of the wireless spectrum prediction method under the conditions of data missing and noise interference;

[0049] Figure 2 Schematic diagram showing the third-order spectrum tensor model;

[0050] Figure 3 Stereo visualization diagram showing the spectrum prediction data on the 5th day. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0051] In order to more clearly understand the above objects, features and advantages of the present invention, the following further describes the specific embodiments of the present invention in detail in conjunction with the accompanying drawings of the specification. Figures 1-3 The specific embodiments of the present invention will be further described in detail.

[0052] The open-source measured spectrum data set used in this example was collected from January 23, 2018 to January 26, 2018 for a total of 4 days of spectrum data, with a frequency band range of 30 - 130 MHz, and the purpose is to predict the spectrum state on the 5th day.

[0053] The wireless spectrum prediction method under the conditions of data missing and noise interference according to the present invention includes the following steps:

[0054] Step 1, establish a third-order tensor model. It is known that within the frequency band of 30 - 130 MHz, the time resolution is 10 s and the frequency resolution is 39.0625 KHz. Taking the time slot as the horizontal axis and the frequency point as the vertical axis, the spectrum data of each day can be modeled as a matrix of size 8640×2560. Due to the limitation of the spectrum sensor, the number of time slots collected each day cannot be completely accurate. Therefore, the data of the first 23 hours is intercepted for processing. In order to reduce the matrix scale and speed up the calculation, the data is further sampled so that two minutes is taken as a period and every 4 frequency points are sampled once. At this time, the spectrum data of each day can be modeled as D∈R 690×640 , and arranging the spectrum data matrices of these four days by day, a third-order spectrum tensor model can be established. The present invention can also use the historical data of the first 23 hours to predict the spectrum of the 24th hour. At this time, there are 30 time slots per hour and it can be modeled as Here, according to different prediction requirements, the corresponding modeling method needs to be selected. In this example, a third-order spectral tensor constructed with days as the Z-axis is adopted. To achieve the purpose of predicting the spectral state on the 5th day, a zero matrix is used as the spectral data matrix for the 5th day and added to the tensor, obtaining a third-order spectral tensor with a size of 690×640×5. The tensor data for the first 5 time slots and frequency points are shown in Table 1;

[0055] Table 1

[0056]

[0057] Step 2: Preprocess the data:

[0058] First, obtain the observation set Ω, save the position indexes of the missing data and the valid data. In this example, the missing data accounts for 10% of the total data. Then, by fixing the first two dimensions, different tube fibers are taken out. Each tube fiber is actually the spectral data of the same frequency point and the same time slot on different days. Along this direction, standardization operations are performed to map the data to the range of [0,1]; meanwhile, appropriate tube fibers are selected to fill the elements of the 5th day with the mean value of the data of the first 4 days. Here, the data sequence with no historical missing data and a smaller standard deviation is selected; the tensor after filling is used as the input of the prediction algorithm. There is a certain deviation between the initial value of this 5th day and the true value. In the prediction algorithm, every time a pair of variables is updated, the mean value needs to be recalculated to update the elements of the 5th day. Table 2 shows some of the spectral tensor data after data preprocessing;

[0059] Table 2

[0060]

[0061] Step 3: Establish a wireless spectrum prediction model, that is, model the problem of predicting from noisy historical spectrum data as shown in Equation (5):

[0062]

[0063] Among them, Ω is the observation set obtained in Step 2. The elements of this set are 1 where there is data in the observed value and 0 where there is missing data, which can represent the position of the valid data. In this embodiment, the missing data part accounts for 10% of the total data. Substitute the tensor with a size of 690×640×5 into the observed value, and perform tensor singular value decomposition on it to obtain the singular values of the spectral tensor

[0064] Step 4: Solve the established wireless spectrum prediction model to obtain prediction data. The specific steps can be divided into:

[0065] (1) Algorithm initialization: For each parameter in the algorithm, according to experience, the hyperparameter has better performance in practical applications. In this example, take λ = 0.017. The adaptive coefficient is determined by the parameter r. When r = 0, it is transformed into the standard nuclear norm, and the same shrinkage is applied to all singular values. Here, in this example, the grid search method is used to find the optimal value. Let r = 2, and the parameter ρ = 1.1 is used as the update step size to affect the convergence speed. Set the maximum number of iterations to 1000, and define the soft-thresholding shrinkage operator required in the solution process

[0066]

[0067] where that is is the diagonal tensor after performing tensor singular value decomposition on ; denotes performing the Fourier transform on along the third dimension, that is, performing the Fourier transform on all tube fibers of ;

[0068] (2) Reformulate the optimization problem using the augmented Lagrangian function. The ADMM algorithm provides a framework for solving some convex or non-convex optimization problems. In this embodiment, the original optimization problem is decomposed into several relatively easy sub-optimization problems for iterative solution. The closed-form solution of each optimization process guarantees the final recovery performance. To solve the optimization problem in Equation (5), it is reformulated using the augmented Lagrangian function as Equation (7):

[0069]

[0070] where is the Lagrange multiplier tensor, with the same size as . The parameter β is the introduced penalty parameter, which is initialized to 10 -3 , and set the maximum value β max = 10 5 ;

[0071] (3) Each variable is updated in the following order during iteration:

[0072]

[0073]

[0074]

[0075]

[0076]

[0077] β k+1 = min(ρβ k , β max )......(13),

[0078] Further solving the above formula to obtain the closed-form solutions of each variable, and in the specific operation, the variables are iteratively updated according to the following sequence of formulas:

[0079] Solving equation (8) to obtain the closed-form solution of the low-rank tensor :

[0080]

[0081] Re-update the data of the 5th day. In view of the fact that the spectral data continuously approaches the true value in each iterative update, the mean value of the first 4 days of updated data is used to re-update the data of the 5th day for the values in the pre-filled set, so that the influence of noise gradually becomes smaller;

[0082] Solving equation (9) to obtain the closed-form solution of the noise tensor :

[0083]

[0084] Solving equation (10) to update the noise mean μ:

[0085]

[0086] Solving equation (11) to obtain the closed-form solution of the observation tensor , ensuring that the sum of the recovered true spectral data value and the additive noise value is consistent with the original observation tensor on the sampling set:

[0087]

[0088] Using equations (12)-(13) to update the Lagrange multiplier and the penalty parameter β:

[0089] When the number of iterative updates reaches the pre-set maximum number of iterations 1000, or when the convergence condition is reached, the final result is output. At this time, the output is the recovered low-rank spectral tensor, which is noise-free and fills in the missing positions with data close to the true value, and the in it is the spectral prediction data of the 5th day, is the separated noise tensor. Thus, under the conditions of data missing and noise interference, the prediction of future spectra and the separation of noise are completed using incomplete historical data.

[0090] The present invention is not limited to the above-described embodiments. Without departing from the essence of the present invention, any variations, improvements, or substitutions that can be conceived by those skilled in the art fall within the protection scope of the present invention.

Claims

1. A method for predicting wireless spectrum under conditions of data loss and noise interference, characterized in that: include: Step 1, input spectrum data: Take the collected spectrum data from the spectrum database, mainly the power spectrum density value of the observed signal, and convert it into a spectrum data matrix in a conventional way. The spectrum data matrix takes the time slot as the horizontal axis and the frequency point as the vertical axis. X∈R A×B , the matrix elements at this time are composed of two parts of data, one part is missing data, represented by 0; the other part is normal received data, which is composed of true values ​​and noise interference Step 2: Establish a third-order tensor model for spectrum data: According to the different time periods of spectrum observation, select different time units as the Z axis to establish the tensor In order to realize the prediction function, a matrix of all zeros is used to represent the spectrum data to be predicted and added to the tensor In this paper, the spectrum tensor model is established Step 3, standardize the spectrum data: After the spectrum tensor model is established, the data must be standardized first. In order not to destroy the correlation of the data sequence of the same frequency point and the same time slot in different time units, the tensor is normalized in the third dimension. Different tube fibers are taken out by fixing the x-axis and y-axis of the tensor, and normalization is performed on each tube fiber, so that the spectrum tensor can be processed in the next step and the convergence speed of the prediction algorithm can be effectively improved. Since the all-zero matrix cannot be directly filled in the tensor, the appropriate tube fiber is selected to take the average value as the initial value of the prediction and fill it into the (C+1)th positive slice of the spectrum tensor. At this time: Among them: the first dimension represents the time slot of the day, the second dimension represents the frequency, and the third dimension represents the date. Each element of the tensor represents the power spectrum density of the jth frequency point in the i-th time slot on the k-th day; Step 4: Establish a wireless spectrum prediction model, including: In view of the inherent correlation of each dimension of the real spectrum data, the spectrum data in the noise-free case is considered to have low rank. The low rank of the spectrum tensor is used to recover the low rank spectrum tensor from the spectrum observation data containing noise, and a wireless spectrum prediction model is established. The conventional optimization goal for recovering low-rank tensors from noisy observations is: For the first item, adaptive shrinkage of singular values ​​is achieved by assigning different weights to the singular values ​​of the spectrum tensor. It is known that large singular values ​​contain the main information of the spectrum data, while small singular values ​​are more caused by noise interference. The weight assignment is to shrink the large singular values ​​containing the spectrum characteristics by a small amplitude to retain the main information of the spectrum and better approximate the rank of the spectrum tensor. The tensor adaptive nuclear norm is defined as the weighted sum of the singular values. At this time, the optimization objective is the following formula (2): in: represents the predicted spectrum tensor, For The diagonal tensor after the tensor singular value decomposition, α i represents the i-th adaptive coefficient, which is some negative power of the singular value, that is: In the above formula, the larger the singular value, the larger the denominator, α i The smaller it is, the smaller the corresponding shrinkage operation is, and the better the recovery performance of the spectrum data is; For the second term of the conventional optimization objective, we consider the case of non-zero mean noise and assume that the actual mean value of the noise is and variance are all unknown numbers, and u is introduced to represent the mean distribution of noise. is a tensor of the same size as the noise tensor with all entries u, and the variance of the tensor is expressed in terms of the norm It is shown in the following formula (3). It can be easily proved that this term reaches its minimum value only when u is equal to the actual mean: In the above formula (3), when When u is the smallest, it is considered that u is equal to the real noise mean at this time, and the noise in general can be restored; when u = 0, it corresponds to the special case of zero mean noise, and the case of zero mean additive Gaussian noise is also included here; By optimizing the two terms in the optimization objective of equation (1) respectively, the optimization problem of spectrum prediction from noisy historical spectrum data can be restated as follows: Among them, the rank relaxation is represented by the tensor adaptive nuclear norm newly proposed in this method, which is specifically expressed as the weighted sum of the tensor singular values. The second term is to model the general term of noise. represents the observed spectral measurement, represents the predicted spectrum tensor, represents the separated noise tensor, λ is the penalty parameter and is a positive number, u represents the noise mean, Representation and Tensors with the same dimension size and all elements are u, Ω is the observation set, The elements in Ω are known, but the other elements are missing, so The elements that do not belong to Ω are set to 0, and the other items remain unchanged. The constraint condition ensures that the elements of the sum of the true value of the restored spectrum and the noise tensor on the observation set Ω are consistent with the original observation values; Step 5, solving the established wireless spectrum prediction model: including: For formula (4) in step 4, the tensor after data preprocessing in step 2 is Substituting the observed values, Perform a tensor singular value decomposition and take out the first positive slice of the singular value, that is, The elements on the diagonal of this front slice are the third-order spectral tensor established The singular value of , select the appropriate value to initialize each parameter, and update the variables iteratively. Gradually approaching the true spectrum data value without noise, The noise interference in the observations is gradually separated; then, when the sum of the tensor adaptive nuclear norm defined by the sum of weighted singular values ​​and the noise variance is minimized, the predicted value of the spectrum and the separated additive noise are obtained, and the reliable filling of the missing data is completed at the same time. The above process is to use the alternating direction multiplier method, i.e., ADMM method, to solve and obtain the low-rank spectrum tensor and the noise tensor Overview of the closed-form solution, the final output is the low-rank spectral tensor The (C+1)th frontal slice is the spectrum prediction value obtained.

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