Frequency sequence estimation method based on FARIMA-LSTM model

Abstract

The invention discloses a frequency sequence estimation method based on a FARIMA-LSTM model, and the method comprises the steps: collecting a frequency band signal in a target environment, carrying out the preprocessing of the frequency band signal, mapping the preprocessed frequency band signal to a (0, 1) interval, obtaining a frequency sequence, inputting training set data into a constructed FARIMA model, estimating model parameters, generating a residual sequence according to the model parameters, and carrying out the estimation of the frequency sequence through the residual sequence. And training the constructed LSTM model by using the residual sequence, combining the FARIMA model with the trained LSTM model, inputting test set data into the FARIMA-LSTM model for single-step prediction, evaluating model performance and adjusting parameters, generating a frequency sequence from a signal to be estimated, inputting the frequency sequence into the trained FARIMA-LSTM model for single-step or multi-step frequency sequence prediction, and finally, performing frequency sequence prediction on the signal to be estimated. And outputting a single-step or multi-step estimation result. Fractional difference processing is carried out on a frequency time sequence through an FARIMA model, interference of periodic components on trend prediction is eliminated, meanwhile, deep mining is carried out on randomness, burstiness and nonlinear dynamic characteristics in FARIMA residual errors through an LSTM network, and step-by-step estimation of the frequency sequence is achieved.

Description

Technical Field

[0001] The present application relates to the field of wireless communication technology, and in particular to a frequency sequence prediction method based on a FARIMA-LSTM model. Background Art

[0002] In existing wireless communication systems, frequency hopping technology improves interference resistance by dynamically switching between preset frequency sequences. A typical application is the adaptive frequency hopping mechanism employed by the Bluetooth protocol, which dynamically maintains a set of available channels through real-time spectrum analysis, effectively adapting to changes in network channel quality. This technology has been further extended to cognitive communication systems, where it periodically detects "spectrum holes" to enable dynamic spectrum sharing, significantly improving spectrum utilization. However, when multiple communication systems coexist using similar adaptive mechanisms, spectrum resource contention and mutual interference can occur, leading to a sharp drop in communication efficiency.

[0003] Existing solutions mainly face two types of technical bottlenecks: First, traditional coordination mechanisms have problems such as delayed coordination response and a single channel quality assessment dimension in dense deployment scenarios; second, time series prediction methods based on machine learning have limited performance in complex electromagnetic environments, and their prediction accuracy is difficult to exceed the relative error threshold of 20%. This is mainly due to the fact that spectrum occupancy data has complex characteristics such as periodicity, burstiness, long-term and short-term dependencies, and Gaussian / non-Gaussian mixed noise. A single model cannot fully capture the multi-dimensional spatiotemporal correlation characteristics.

[0004] Current research trends indicate that model fusion technology offers a new path to improving prediction accuracy. Existing combination methods primarily include rudimentary fusion strategies such as static weight allocation based on the inverse error method and parallel integration based on bagging. However, these methods have yet to effectively address three core issues: first, the heterogeneity of multi-model feature spaces makes fusion decision-making difficult; second, the lack of a real-time mechanism for evaluating model contributions in dynamic electromagnetic environments; and third, the interference of negative transfer effects between models on prediction results. These issues result in reduced improvements in prediction accuracy in dense interference scenarios, making existing combination methods incapable of meeting the requirements of highly reliable communications. Summary of the Invention

[0005] The purpose of this application is to provide a frequency series prediction method based on the FARIMA-LSTM model in order to overcome the existing technical defects. The FARIMA model is used to perform fractional difference processing on the frequency time series to eliminate the interference of periodic components on trend prediction. At the same time, the LSTM network is used to deeply explore the randomness, burstiness and nonlinear dynamic characteristics in the FARIMA residuals to achieve gradual prediction of the frequency series.

[0006] The purpose of this application is achieved through the following technical solutions:

[0007] In the first aspect, the present application proposes a frequency sequence prediction method based on the FARIMA-LSTM model, the method comprising:

[0008] Collect the frequency band signals in the target environment and preprocess them, then map the preprocessed frequency band signals to the (0,1) interval to obtain a frequency sequence;

[0009] Divide the frequency series into training set data and test set data;

[0010] Input the training set data into the constructed FARIMA model to estimate the model parameters and generate the residual sequence according to the model parameters;

[0011] The constructed LSTM model is trained using the residual sequence to obtain the trained LSTM model;

[0012] The FARIMA model and the trained LSTM model are combined to form a FARIMA-LSTM model. The test set data is input into the FARIMA-LSTM model for single-step prediction. The model performance is evaluated and the parameters are adjusted to obtain the trained FARIMA-LSTM model.

[0013] The frequency sequence generated by the signal to be estimated is input into the trained FARIMA-LSTM model for single-step or multi-step frequency sequence prediction, and the single-step or multi-step estimation results are output.

[0014] In one possible implementation, the steps of collecting and preprocessing frequency band signals in a target environment, and mapping the preprocessed frequency band signals to a (0, 1) interval to obtain a frequency sequence include:

[0015] The frequency band signal in the target environment is collected for denoising and filtering, and then sliced ​​according to time accuracy to obtain the sliced ​​signal, and the frequency points are divided and numbered according to the preset bandwidth or frequency accuracy;

[0016] Map the slice signal into a frequency point number sequence and perform normalization;

[0017] The time slices that do not reach the preset power threshold are discarded, and the frequency point number sequence is evenly mapped to the (0,1) interval to form a frequency sequence.

[0018] In one possible implementation, the FARIMA model is expressed as: Among them F t represents the frequency sequence, B represents the time delay operator, Φ(B) is the p-order autoregressive term, Θ(B) is the q-order sliding average term, x t represents the residual sequence, is the fractional difference operator, and d represents the fractional difference order.

[0019] In one possible implementation, the step of inputting the training set data into the constructed FARIMA model to estimate model parameters and generating a residual sequence according to the model parameters includes:

[0020] The Abry-Veitch wavelet method is used to estimate the Hurst exponent based on the training data, and the fractional difference order d is determined by the Hurst exponent;

[0021] The fractional difference operator is obtained according to the fractional difference order d, and the frequency series is subjected to fractal filtering using the fractional difference operator to generate a filtered series that meets the characteristics of the ARMA model.

[0022] Based on the AIC criterion, the ARMA model order is determined for the filtered sequence to determine the optimal combination of autoregressive order p and moving average order q;

[0023] The parameter set of the ARMA model is obtained by approximate maximum likelihood estimation method;

[0024] Based on the optimal combination and parameter group, the training set data is input into the trained FARIMA model for step-by-step recursive prediction to generate a single-step prediction sequence;

[0025] Calculate the difference between the frequency sequence and the one-step prediction sequence to obtain the residual sequence.

[0026] In one possible implementation, the LSTM model includes multiple input layers, multiple hidden layers, and an output layer. The hidden layer uses an LSTM memory unit. The LSTM memory unit includes an input gate, a forget gate, and an output gate connected in sequence. The steps of training the constructed LSTM model using a residual sequence to obtain a trained LSTM model include:

[0027] Build an LSTM model and initialize it. Initialization includes setting the input layer, number of hidden layers, initial learning rate, and maximum number of iterations

[0028] Input the residual sequence as a training sample into the LSTM model to calculate the activation value of the input gate and the state candidate value;

[0029] Calculate the updated state value based on the activation value of the input gate and the state candidate value;

[0030] Calculate the activation value and output value of the output gate at time t based on the updated state value;

[0031] Combined with the actual value of the residual sequence, the loss function of the LSTM model is calculated based on the output value;

[0032] When the number of iterations does not reach the maximum number of iterations, the network weights and biases are updated until the iteration termination condition is met to obtain the trained LSTM model.

[0033] In one possible implementation, the activation value i t for i t =σ(X t W xt +h t-1 W hi +b i ), state candidate value for: Among them, X t represents the input of the LSTM memory unit at time t, h t-1 represents the input value of the input gate at time t-1, σ represents the sigmoid activation function, tanh represents the hyperbolic tangent activation function formula, W xt and W hi Represent the weights of the input gate activation function, b i Represents the bias of the input gate activation function, W xc and W hc Represent the weights of the candidate functions of the input gate state, b c Represents the bias of the candidate function for the input gate state.

[0034] In a possible implementation, the updated state value c t The calculation formula is: in Indicates element-wise multiplication, f t represents the activation value of the forget gate, c t-1 Indicates the state value at the previous moment.

[0035] In one possible implementation, the activation value o t The calculation formula is: t =σ(X t W xo +h t-1 W ho +b o ), output value h t The calculation formula is W xo and W ho Represent the control weights of the output gate activation function, b o Represents the bias of the output gate activation function.

[0036] In one possible implementation, the loss function uses the root mean square error, which is: Where RMSE (t) is the loss function value at time t, nn is the current sequence length, is the actual value of the residual sequence at time t, is the output value of the LSTM model at the i-th position at time t.

[0037] In one possible implementation, the steps of combining a FARIMA model and a trained LSTM model to form a FARIMA-LSTM model, inputting test set data into the FARIMA-LSTM model for single-step prediction, evaluating model performance, and adjusting parameters to obtain the trained FARIMA-LSTM model include:

[0038] Use the fractional difference operator to perform fractal filtering on the test set data to generate the test set ARMA sequence;

[0039] Recursively calculate the historical residual sequence based on the test set ARMA sequence and FARIMA parameter group;

[0040] Input the historical residual sequence into the LSTM model to obtain the residual single-step forecast value;

[0041] Calculate the single-step forecast value of the frequency series by combining the ARMA sequence, FARIMA parameter group and residual forecast value;

[0042] Compare the performance of the frequency series predictions with the actual values ​​of the test set;

[0043] When the performance does not reach the threshold, at least one parameter among the training sample length, the number of hidden units, the maximum number of iterations, and the ARMA model order is adjusted, and the FARIMA model and the LSTM model are retrained to obtain a trained FARIMA-LSTM model.

[0044] The above-mentioned main scheme of this application and its further options can be freely combined to form multiple schemes, all of which are schemes that can be adopted and protected by this application; and in this application, (non-conflicting options) can also be freely combined with each other and with other options. After understanding the scheme of this application, those skilled in the art will understand that there are many combinations based on existing technology and common knowledge, all of which are technical solutions to be protected by this application, and they are not exhaustive here.

[0045] The present application discloses a frequency sequence prediction method based on the FARIMA-LSTM model. The method first collects the frequency band signal in the target environment and preprocesses it. The preprocessed frequency band signal is mapped to the (0,1) interval to obtain a frequency sequence. The training set data is input into the constructed FARIMA model to estimate the model parameters. The residual sequence is generated according to the model parameters. The constructed LSTM model is trained using the residual sequence. The FARIMA model and the trained LSTM model are combined. The test set data is input into the FARIMA-LSTM model for single-step prediction. The model performance is evaluated and the parameters are adjusted. After the frequency sequence is generated by the signal to be estimated, it is input into the trained FARIMA-LSTM model for single-step or multi-step frequency sequence prediction, and the single-step or multi-step prediction results are output. The frequency time series is fractionally differencing processed by the FARIMA model to eliminate the interference of the periodic component on the trend prediction. At the same time, the LSTM network is used to deeply mine the randomness, burstiness and nonlinear dynamic characteristics in the FARIMA residual to achieve step-by-step prediction of the frequency series. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following is a brief introduction to the drawings required for use in the embodiments. It should be understood that the following drawings only show certain embodiments of the present application and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other relevant drawings can be obtained based on these drawings without creative work.

[0047] Figure 1 A flow chart of a frequency sequence prediction method based on the FARIMA-LSTM model proposed in an embodiment of the present application is shown.

[0048] Figure 2 A schematic diagram of the structure of the LSTM memory unit proposed in an embodiment of the present application is shown. DETAILED DESCRIPTION

[0049] The following describes the embodiments of the present application through specific examples. Those skilled in the art can easily understand the other advantages and effects of the present application from the content disclosed in this specification. The present application can also be implemented or applied through other different specific embodiments. The details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present application. It should be noted that the following embodiments and features in the embodiments can be combined with each other unless they conflict.

[0050] Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making any creative work shall fall within the scope of protection of this application.

[0051] In existing technologies, methods such as exponential backoff and power control are commonly used to address the problem of significant decreases in communication efficiency caused by mutual interference. However, in complex electromagnetic environments with a large number of shared users, the effectiveness needs to be further improved. In addition, the development of artificial intelligence and deep neural networks has made the prediction of future data based on historical data a research hotspot. The use of time series prediction methods can avoid frequency points or frequency bands where spectrum conflicts may occur in advance, thereby improving communication performance. These methods mainly include ARIMA, RBF networks, hidden Markov networks, RNNs, LSTMs, support vector machines, etc. However, the research objects of most prediction methods have their own specific constraints. Especially in complex electromagnetic environments, where there are both periodic frequency usage patterns and long-term and short-term dependent noisy time series, the learning and prediction capabilities of a single model are limited, and the accuracy cannot be significantly improved.

[0052] In order to solve the problem of frequency sequence estimation in a complex electromagnetic environment with multiple users, the embodiment of the present application proposes a frequency sequence estimation method based on the FARIMA-LSTM model. By collecting the time series of surrounding frequency usage, the FARIMA model is used to eliminate the periodic influence in the time series, reduce the impact of the period on the model fitting effect, and improve the trend prediction accuracy. At the same time, LSTM captures the randomness of the sequence, realizes the gradual estimation of the frequency sequence, and provides support for efficient spectrum sharing.

[0053] Please refer to Figure 1 , Figure 1 A flow chart of a frequency sequence prediction method based on a FARIMA-LSTM model proposed in an embodiment of the present application is shown, and the method includes the following steps:

[0054] Step S1: collect frequency band signals in the target environment and preprocess them, and map the preprocessed frequency band signals to the (0, 1) interval to obtain a frequency sequence.

[0055] After collecting the frequency band signal in the target environment, pre-processing operations such as denoising and filtering are first performed to improve the signal quality; then the signal is sliced ​​according to the preset time accuracy, and the slices that do not reach the power threshold are discarded; then the frequency band is divided and numbered according to the preset bandwidth or frequency accuracy, and the sliced ​​signal is mapped into a frequency point number sequence; finally, the sequence is evenly mapped to the (0,1) interval to obtain the frequency sequence F t .

[0056] Step S1 includes:

[0057] The frequency band signal in the target environment is collected for denoising and filtering, and then sliced ​​according to time accuracy to obtain the sliced ​​signal, and the frequency points are divided and numbered according to the preset bandwidth or frequency accuracy;

[0058] Map the slice signal into a frequency point number sequence and perform normalization;

[0059] The time slices that do not reach the preset power threshold are discarded, and the frequency point number sequence is evenly mapped to the (0,1) interval to form a frequency sequence.

[0060] First, the signal in the frequency band of interest is acquired in the target environment. Parameters such as the intermediate frequency (IF) and sampling frequency must be set during the acquisition process to ensure accurate signal capture. The acquired raw signal is stored on disk and then preprocessed, including but not limited to denoising and filtering, to remove noise and interference. The processed signal is then sliced ​​according to a preset time resolution. This divides the signal into time slices, each representing the signal state within a specific time interval. During the slicing process, time slices that do not meet the preset power threshold are discarded to preserve meaningful portions of the signal and reduce the data volume.

[0061] The frequency band is divided and numbered according to the preset bandwidth or frequency accuracy. Based on the frequency characteristics of the signal, the frequency band is divided into multiple frequency points, and each frequency point is assigned a unique number. The sliced ​​time signal is calculated to determine the frequency point to which it belongs. The signal of each time slice is subjected to frequency domain analysis to determine its corresponding frequency point number. The frequency point numbers of all time slices are arranged into a sequence in chronological order to form a preliminary frequency sequence. The frequency sequence is normalized to make the frequency sequence value range more uniform and evenly mapped to the (0, 1) interval. The resulting frequency sequence will be used for subsequent model construction and predictive analysis.

[0062] Step S2: Divide the frequency sequence into training set data and test set data;

[0063] The frequency sequence F obtained before processing t , divided into two parts according to a preset ratio: the first part is used as training set data to build the model, and the second part is used as test set data to verify the model performance.

[0064] Step S3: Input the training set data into the constructed FARIMA model to estimate the model parameters, and generate a residual sequence based on the model parameters.

[0065] The training data is fed into the constructed FARIMA model. The model automatically adjusts and calculates the values ​​of its parameters based on this data. This process is called model parameter estimation. Simply put, the model learns patterns from the training data and determines its internal parameters. Next, using the estimated model parameters, a residual sequence is generated. This residual sequence is a sequence of differences between the actual observations and the model's predictions, reflecting how well the model fits the data.

[0066] The expression of the FARIMA model is: Among them F t represents the frequency sequence, B represents the time delay operator, Φ(B) is the p-order autoregressive term, Θ(B) is the q-order sliding average term, x t represents the residual sequence, is the fractional difference operator, and d represents the fractional difference order.

[0067] In the FARIMA model (i.e., fractional autoregressive moving average model), the delay operator B satisfies BF t =F t-1 , the p-order autoregressive term Φ(B) and the q-order sliding average term Θ(B) are expressed as: Fractional difference order d∈(-0.5,0.5), fractional difference operator The binomial expansion of can be expressed as: The iterative calculation method of g(k) is:

[0068] Step S3 includes:

[0069] The Abry-Veitch wavelet method is used to estimate the Hurst exponent based on the training set data, and the fractional difference order d is determined by the Hurst exponent.

[0070] The fractional difference operator is obtained according to the fractional difference order d, and the frequency series is subjected to fractal filtering using the fractional difference operator to generate a filtered series that meets the characteristics of the ARMA model.

[0071] Based on the AIC criterion, the ARMA model order is determined for the filtered sequence to determine the optimal combination of autoregressive order p and moving average order q;

[0072] The parameter set of the ARMA model is obtained by approximate maximum likelihood estimation method;

[0073] Based on the optimal combination and parameter group, the training set data is input into the trained FARIMA model for step-by-step recursive prediction to generate a single-step prediction sequence;

[0074] Calculate the difference between the frequency sequence and the one-step prediction sequence to obtain the residual sequence.

[0075] The Abry-Veitch wavelet method was used to analyze the training data and estimate the Hurst exponent (H). The Hurst exponent is a measure of the long-term dependence of a time series, with a value between 0 and 1. Based on the estimated Hurst exponent, the fractional differencing order d = H - 0.5 was calculated. The fractional differencing order d describes the fractional differencing characteristics of a time series. When d = 0, the series has no long-term memory; when d > 0, the series exhibits long-term positive correlation; and when d < 0, the series exhibits long-term negative correlation.

[0076] Construct the fractional difference operator according to the fractional difference order d Perform fractal filtering on the original frequency sequence to remove the periodic components and noise in the sequence, extract the trend and long-term dependency parts in the sequence, and generate a new sequence W t , the series can be described by the autoregressive moving average model ARMA(p,q):

[0077] The Akaike Information Criterion (AIC) is used to determine the model order of the filtered sequence based on the preset maximum order. The AIC criterion determines the optimal combination of autoregressive order p and moving average order q for the sequence, allowing the model to fit the data while avoiding overfitting.

[0078] After determining the best combination of p and q, the approximate maximum likelihood estimation method is used to obtain the parameter group φ1, φ2, ..., φ of the ARMA model. p ,θ1,θ2,...,θ q , Approximate Maximum Likelihood Estimation is an approximation of traditional Maximum Likelihood Estimation, which is suitable for complex models or large data sets to improve computational efficiency.

[0079] Based on the determined optimal combination of p and q and the estimated parameter group, a complete FARIMA (p, d, q) model is constructed. t Input into the trained FARIMA model, perform step-by-step recursive prediction, and generate a single-step prediction sequence Specifically, at time point t, the model is used to predict the frequency value at time point t+1. This predicted value is based on the model's fitting of historical data and parameter estimation, where W t One-step forecast value after time point t for:

[0080]

[0081] So F t One-step forecast value after time point t

[0082] Finally, the generated single-step prediction sequence is used to calculate the residual sequence {x t The residual sequence is the difference between the original frequency sequence and the predicted sequence, that is, residual = actual value - predicted value The residual series reflects the difference between the model prediction and the actual observation, and can be used to further analyze the model's fitting effect and prediction accuracy, as well as whether there are patterns or noise that are not captured by the model.

[0083] Step S4: Use the residual sequence to train the constructed LSTM model to obtain a trained LSTM model.

[0084] To train the LSTM model, the residual sequence is first input into the LSTM network as a training example. The output is calculated through forward propagation, and the difference between the output and the actual value of the residual sequence is evaluated using a loss function. Next, in each iteration, if the number of iterations does not reach the preset maximum, the model updates its weights and biases through a backpropagation algorithm to minimize the loss function. This process is repeated until the maximum number of iterations is reached. Ultimately, the fully trained and optimized LSTM model effectively captures patterns and regularities in the residual sequence, thereby improving overall forecasting accuracy.

[0085] The LSTM model includes multiple input layers, multiple hidden layers and an output layer. The hidden layer uses an LSTM memory unit, and the LSTM memory unit includes an input gate, a forget gate and an output gate connected in sequence.

[0086] The LSTM model consists of an input layer, several hidden layers, and an output layer. The input layer is responsible for receiving input data, and the output layer outputs the predicted results. The hidden layer is the core of the LSTM network and contains multiple LSTM memory units.

[0087] Figure 2 The schematic diagram of the structure of the LSTM memory unit proposed in the embodiment of the present application is shown. The current input X t and the hidden state h at the previous moment t-1 As input, through the calculation of input gate, forget gate and output gate, it controls the flow and update of information and updates the memory unit state C t , and generate the output value h at the current moment t Each cell has an input gate, a forget gate, and an output gate. The input gate controls the entry of new information into the cell's state, the forget gate determines which information in the cell's state is discarded, and the output gate determines how to update the cell's output value. This structure enables LSTM to effectively handle long-term dependencies in time series.

[0088] Step S4 includes:

[0089] Build an LSTM model and initialize it. Initialization includes setting the input layer, number of hidden layers, initial learning rate, and maximum number of iterations

[0090] Input the residual sequence as a training sample into the LSTM model to calculate the activation value of the input gate and the state candidate value;

[0091] Calculate the candidate state value based on the activation value of the input gate and the state candidate value;

[0092] Calculate the activation value and output value of the output gate at time t based on the candidate state value;

[0093] Combined with the actual value of the residual sequence, the loss function of the LSTM model is calculated based on the output value;

[0094] When the number of iterations does not reach the maximum number of iterations, the network weights and biases are updated until the iteration termination condition is met to obtain the trained LSTM model.

[0095] When using an LSTM network, you must first initialize the network parameters. This includes setting the number of neurons in the input, hidden, and output layers, as well as hyperparameters such as the initial learning rate and maximum number of iterations. For example, in a given problem, the number of input layer neurons can be set to the number of input data features, the number of hidden layer neurons can be set to 100, the number of output layer neurons can be set to 1, the initial learning rate can be set to 0.01, and the maximum number of iterations can be set to 100. These parameters can be adjusted based on the specific task and dataset to optimize network performance.

[0096] According to the training samples, an iteration is performed to input a set of training samples into the input gate of the LSTM network, and the activation value i of the input gate is calculated. t And the candidate state value of the memory unit at time t Activation value i t for i t =σ(X t W xt +h t-1 W hi +b i ), state candidate value for: Among them, X t represents the input of the LSTM memory unit at time t, h t-1 represents the input value of the input gate at time t-1, σ represents the sigmoid activation function, tanh represents the hyperbolic tangent activation function formula, W xt and W hi Represent the weights of the input gate activation function, b i Represents the bias of the input gate activation function, W xc and Whc Represent the weights of the candidate functions of the input gate state, b c Represents the bias of the candidate function of the input gate state. The calculation formula of the sigmoid activation function σ is: The formula for the hyperbolic tangent activation function tanh is:

[0097] The LSTM memory unit needs to discard or save information, and the forget gate is based on the activation value i of the input gate. t And the candidate state value of the LSTM memory unit at time t Calculate the updated state value c t , and its calculation formula is: in Indicates element-wise multiplication, f t represents the activation value of the forget gate, c t-1 Represents the state value at the previous moment. The activation value f of the forget gate t is: f t =σ(X t W xf +h t-1 W hf +b f ), W xf and W hf Represent the weights of the forget gate activation function, b f Represents the bias of the forget gate activation function.

[0098] According to the updated state value c t Calculate the activation value o of the output gate at time t t And the output value h t , activation value o t The calculation formula is: t =σ(X t W xo +h t-1 W ho +b o ), output value h t The calculation formula is W xo and W ho Represent the control weights of the output gate activation function, b o Represents the bias of the output gate activation function.

[0099] When training the LSTM model, the actual value of the residual sequence is first used as a training sample. The model calculates the output value through forward propagation, and then uses the loss function to compare the difference between the output value and the actual value. The loss function uses RMSE (root mean square error), that is: Where RMSE (t)is the loss function value at time t, n is the current sequence length, is the actual value of the residual sequence at time t, is the output value of the LSTM model at position i at time t. If the current number of iterations has not reached the preset maximum number of iterations, the model will update the weights and biases through backpropagation to minimize the loss function. After each update, the number of iterations is increased by 1, and step S4 is repeated until the number of iterations reaches the maximum, resulting in a trained LSTM model.

[0100] Step S5: Combine the FARIMA model and the trained LSTM model to form a FARIMA-LSTM model, input the test set data into the FARIMA-LSTM model for single-step prediction, evaluate the model performance, and adjust the parameters to obtain the trained FARIMA-LSTM model.

[0101] The FARIMA model is designed to capture long-term trends and cyclical characteristics in time series data, while the LSTM model excels at capturing randomness and short-term fluctuations within the series. By using the output of the FARIMA model (the single-step forecast sequence) as input to the LSTM model, a FARIMA-LSTM model is constructed that can simultaneously process both long-term and short-term characteristics of the time series. The test data set is fed into the FARIMA-LSTM model. First, fractional differencing and ARMA modeling are performed on the data using the FARIMA component to generate a series of forecast values ​​and residuals. The LSTM model then performs a single-step forecast on the residual series to obtain the predicted residual values. The FARIMA model's forecast values ​​are combined with the LSTM model's residual values ​​to obtain the final single-step forecast result. Model performance is evaluated using metrics such as RMSE and MAE. If model performance is poor, optimization can be achieved by adjusting parameters such as the training sample length, the number of hidden units, the maximum number of iterations, the maximum order of the FARIMA model, the optimal combination of p and q, and the length of the residual training sample. Repeat the training steps of the FARIMA model and the LSTM model, and retrain the FARIMA-LSTM model until the model performance is satisfactory. Finally, a trained and performance-optimized FARIMA-LSTM model is obtained for frequency series prediction.

[0102] Step S5 includes:

[0103] Step S5-1, using the fractional difference operator to perform fractal filtering on the test set data to generate the test set ARMA sequence;

[0104] Step S5-2, recursively calculate the historical residual sequence based on the test set ARMA sequence and the FARIMA parameter group;

[0105] Step S5-3: Input the historical residual sequence into the LSTM model to obtain the residual single-step prediction value;

[0106] Step S5-4, calculating the single-step prediction value of the frequency series by combining the ARMA sequence, the FARIMA parameter group and the residual prediction value;

[0107] Step S5-5, comparing the performance of the frequency sequence prediction value with the actual value of the test set;

[0108] Step S5-6: When the performance does not reach the threshold, adjust at least one parameter among the training sample length, the number of hidden units, the maximum number of iterations, and the ARMA model order, and retrain the FARIMA model and the LSTM model to obtain a trained FARIMA-LSTM model.

[0109] Input the test set data into the FARIMA-LSTM model, perform single-step predictions step by step, and compare the predicted values ​​with the test values. If the performance is poor, you can adjust the parameters (training sample length, number of hidden units, maximum number of iterations, maximum order, optimal combination p and q, length of residual training samples, etc.) to train the FARIMA-LSTM network.

[0110] First, let the test set data be T t , using the aforementioned fractional difference operator T t Perform fractal filtering to obtain the ARMA sequence of the test set: Then, let the time to be predicted be t+1, that is, predict the time t+1 at time point t. Using A t sequence and the aforementioned parameter set φ1, φ2, ..., φ p ,θ1,θ2,...,θ q Recursively obtain the residual sequence {x t-q+1 ,...,x t-1 ,x t}, put {x t-q+1 ,...,x t-1 ,x t} Input the aforementioned LSTM network and obtain the output, which is the single-step prediction value of the residual Using A t sequence and the aforementioned parameter set φ1, φ2, ..., φ p ,θ1,θ2,...,θ q , calculated to obtain A t One-step forecast value after time point t for:

[0111]

[0112] So T t One-step forecast value after time point t for: Finally, repeat steps S5-2 to S5-4 to obtain the step-by-step prediction value of the test set data. At this time, the prediction value and the test value can be compared to evaluate the model performance.

[0113] Step S6: Generate a frequency sequence for the signal to be estimated and input it into the trained FARIMA-LSTM model to perform single-step or multi-step frequency sequence prediction, and output the single-step or multi-step prediction results.

[0114] After generating a frequency sequence from the frequency band signal to be estimated according to the processing method detailed in step S1 above, it is input into the established FARIMA-LSTM model. This model combines the FARIMA model's ability to model time series trends with the LSTM model's ability to capture short-term fluctuations in the sequence, thereby achieving single-step estimation of the frequency series. If multi-step estimation is required, this step is repeated, and estimation is performed step by step using a sliding window. That is, after each estimation, the newly obtained estimate is added to the existing sequence, and the earliest data point is removed to form a new input sequence. This is then input into the model again for the next single-step estimation, and so on, to achieve multi-step estimation of the frequency series.

[0115] In a possible embodiment, a plurality of communication radio stations are used for high-speed communication. The working frequency band of the communication radio stations is 900-930 MHz, the communication rate is 345 Kbps, and the variable frequency hopping rate is about 1000 hop / s.

[0116] Step S1: Use the communication receiving equipment to collect the space electromagnetic signal near the communication radio station. The collection time is 10 minutes. The intermediate frequency point is set to 900MHz and the sampling frequency is 245.76MHz. The collected data is stored in the disk as an unsigned integer of 16-bit quantization of IQ two channels; the collected data is filtered and then energy detection is performed. When a signal with a signal-to-noise ratio exceeding 13dB is detected, time slicing is completed according to a duration of 1ms and stored in the disk; the frequency band is divided into 200KHz frequency points, and after analyzing the sliced ​​time signal, it is found that only 63 frequency points are occupied, so the frequency points are numbered 0 to 63; then the frequency point numbers of all the sliced ​​time segment signals are calculated, and they are arranged into a frequency sequence in chronological order. Finally, the frequency sequence is evenly mapped to the (0,1) interval to form a sequence F t ;

[0117] Step S2: For the frequency sequence formed in step S1, the first part is used as the training set data for model construction, and the second part is used as the test set data according to the ratio of 9:1;

[0118] Step S3: Build a FARIMA model and use the training set data to estimate the model parameters:

[0119] Step S3.1, using the Abry-Veitch wavelet method to estimate the Hurst exponent of the training set data. Specifically, in this embodiment, the Hurst exponent estimated from the training set is 0.71, and the parameter d=0.21 is obtained;

[0120] Step S3.2, using the aforementioned fractional difference operator F t Perform fractal filtering to obtain the sequence W described by the autoregressive moving average model ARMA(p,q) t , Fractional difference operator The binomial expansion of is: The iterative calculation method of g(k) is:

[0121] Step S3.3, determine the maximum order P of the model according to the preset value, and then use the AIC (Akaike Information Criterion, minimum information criterion) criterion to determine the model order and determine the sequence W t The best combination of p and q; in this embodiment, the maximum order P is set to 100, and the sequence W is determined t The best combination of p and q is (45, 31);

[0122] Step S3.4, use approximate maximum likelihood estimation to get the sequence W t The parameter set φ1, φ2, ..., φ p ,θ1,θ2,...,θ q ;

[0123] Step S3.5, the training set data F t Input the trained FARIMA (p, d, q) model and recursively obtain F t One-step prediction sequence

[0124] Step S3.6, using the above single-step prediction sequence Get the residual sequence {x t},in

[0125] Step S4: Build an LSTM model and complete the training using the residual sequence obtained from the aforementioned training set data.

[0126] Initializing the LSTM network includes setting the initial learning rate to 0.01, the input layer to 1, the output layer to 1, the number of hidden layer units to 400, and the maximum number of iterations to 100 rounds;

[0127] According to the aforementioned residual sequence {x t}, train the LSTM network to obtain the weight of the LSTM model;

[0128] When using the residual sequence for training, the residual sequence can be divided into several residual training samples according to the length of p+q+1, and randomly shuffled to reduce overfitting; in this embodiment, the length of the residual training sample is 77;

[0129] Step S5: Combine the trained FARIMA and LSTM models to form a FARIMA-LSTM model. Input the test set data in step 2 into the FARIMA-LSTM model to test the performance of the FARIMA-LSTM model.

[0130] In step S5, the test set data is input into the FARIMA-LSTM model, and single-step predictions are performed step by step. The predicted values ​​are compared with the test values. If the performance is poor, the parameters (training sample length, number of hidden units, maximum number of iterations, maximum order, optimal combination p and q, length of residual training samples, etc.) can be adjusted, and steps S3-S4 are repeated to train the FARIMA-LSTM network.

[0131] Step S6: Generate a frequency sequence for the frequency band signal to be estimated using the method in step S1 and input it into the FARIMA-LSTM model to achieve single-step estimation of the frequency sequence. If multi-step estimation is required, repeat this step to achieve sliding step-by-step estimation.

[0132] Compared with the prior art, the embodiments of the present application have the following beneficial effects:

[0133] First, by combining the strengths of the FARIMA and LSTM models, frequency series can be more accurately estimated. The FARIMA model eliminates periodic effects in time series, improving trend forecast accuracy, while the LSTM model captures randomness and long-term dependencies within the series. This combination of the two results in more accurate forecasts, particularly in complex electromagnetic environments.

[0134] Second, in complex electromagnetic environments with multiple users, the proposed method can effectively address the difficulty of frequency sequence estimation. Compared with traditional methods, it demonstrates greater adaptability and robustness when processing noisy time series with periodicity and long- and short-term dependencies.

[0135] Third, by accurately estimating frequency sequences, the communication system can proactively avoid frequency points or bands where spectrum conflicts may occur. This helps improve spectrum utilization, reduce interference, and enhance the communication system's anti-interference capabilities and signal quality.

[0136] Fourth, it can complete frequency sequence estimation in a relatively short time. This is particularly important for communication systems with high real-time requirements, as it can quickly respond to frequency changes and adjust communication strategies in a timely manner.

[0137] Fifth, this method is not only applicable to the current communication scenario, but can also be extended to other similar spectrum management scenarios. In addition, the model parameters can be adjusted according to the specific scenario, enhancing the flexibility and applicability of the method.

[0138] In summary, this application discloses a frequency series prediction method based on the FARIMA-LSTM model. The FARIMA model is used to perform fractional difference processing on the frequency time series to eliminate the interference of periodic components on trend prediction. At the same time, the LSTM network is used to deeply explore the randomness, burstiness and nonlinear dynamic characteristics in the FARIMA residuals to achieve gradual prediction of the frequency series.

[0139] The above description is only a preferred embodiment of the present application and is not intended to limit the present application. Any modifications, equivalent replacements and improvements made within the spirit and principles of the present application should be included in the scope of protection of the present application.

Claims

1. A frequency series prediction method based on the FARIMA-LSTM model, characterized in that: The method comprises: Collect the frequency band signals in the target environment and preprocess them, then map the preprocessed frequency band signals to the (0,1) interval to obtain a frequency sequence; Divide the frequency series into training set data and test set data; Input the training set data into the constructed FARIMA model to estimate the model parameters and generate the residual sequence according to the model parameters; The constructed LSTM model is trained using the residual sequence to obtain the trained LSTM model; The FARIMA model and the trained LSTM model are combined to form a FARIMA-LSTM model. The test set data is input into the FARIMA-LSTM model for single-step prediction. The model performance is evaluated and the parameters are adjusted to obtain the trained FARIMA-LSTM model. The frequency sequence generated by the signal to be estimated is input into the trained FARIMA-LSTM model for single-step or multi-step frequency sequence prediction, and the single-step or multi-step estimation results are output.

2. The frequency sequence estimation method according to claim 1, wherein: The steps of collecting and preprocessing frequency band signals in the target environment, and mapping the preprocessed frequency band signals to the (0, 1) interval to obtain a frequency sequence include: The frequency band signal in the target environment is collected for denoising and filtering, and then sliced ​​according to time accuracy to obtain the sliced ​​signal, and the frequency points are divided and numbered according to the preset bandwidth or frequency accuracy; Map the slice signal into a frequency point number sequence and perform normalization; The time slices that do not reach the preset power threshold are discarded, and the frequency point number sequence is evenly mapped to the (0,1) interval to form a frequency sequence.

3. The frequency sequence estimation method according to claim 1, wherein: The expression of the FARIMA model is: Among them F t represents the frequency sequence, B represents the time delay operator, Φ(B) is the p-order autoregressive term, Θ(B) is the q-order sliding average term, x t represents the residual sequence, is the fractional difference operator, and d represents the fractional difference order.

4. The frequency sequence estimation method according to claim 3, wherein: The steps of inputting the training set data into the constructed FARIMA model to estimate the model parameters and generating the residual sequence according to the model parameters include: The Abry-Veitch wavelet method is used to estimate the Hurst exponent based on the training data, and the fractional difference order d is determined by the Hurst exponent; The fractional difference operator is obtained according to the fractional difference order d, and the frequency series is subjected to fractal filtering using the fractional difference operator to generate a filtered series that meets the characteristics of the ARMA model. Based on the AIC criterion, the ARMA model order is determined for the filtered sequence to determine the optimal combination of autoregressive order p and moving average order q; The parameter set of the ARMA model is obtained by approximate maximum likelihood estimation method; Based on the optimal combination and parameter group, the training set data is input into the trained FARIMA model for step-by-step recursive prediction to generate a single-step prediction sequence; Calculate the difference between the frequency sequence and the one-step prediction sequence to obtain the residual sequence.

5. The frequency sequence estimation method according to claim 1, wherein: The LSTM model includes multiple input layers, multiple hidden layers, and an output layer. The hidden layer uses an LSTM memory unit. The LSTM memory unit includes an input gate, a forget gate, and an output gate connected in sequence. The steps of training the constructed LSTM model using the residual sequence to obtain the trained LSTM model include: Build an LSTM model and initialize it. Initialization includes setting the input layer, number of hidden layers, initial learning rate, and maximum number of iterations. Input the residual sequence as a training sample into the LSTM model to calculate the activation value of the input gate and the state candidate value; Calculate the updated state value based on the activation value of the input gate and the state candidate value; Calculate the activation value and output value of the output gate at time t based on the updated state value; Combined with the actual value of the residual sequence, the loss function of the LSTM model is calculated based on the output value; When the number of iterations does not reach the maximum number of iterations, the network weights and biases are updated until the iteration termination condition is met to obtain the trained LSTM model.

6. The frequency sequence estimation method according to claim 5, wherein: Activation value i t for i t =σ(X t W xt +h t-1 W hi +b i ), state candidate value for: Among them, X t represents the input of the LSTM memory unit at time t, h t-1 represents the input value of the input gate at time t-1, σ represents the sigmoid activation function, tanh represents the hyperbolic tangent activation function formula, W xt and W hi Represent the weights of the input gate activation function, b i represents the bias of the input gate activation function, W xc and W hc Represent the weights of the candidate functions of the input gate state, b c Represents the bias of the candidate function for the input gate state.

7. The frequency sequence estimation method according to claim 6, wherein: Updated state value c t The calculation formula is: in Indicates element-wise multiplication, f t represents the activation value of the forget gate, c t-1 Indicates the state value at the previous moment.

8. The frequency sequence estimation method according to claim 7, wherein: Activation value o t The calculation formula is: t =σ(X t W xo +h t-1 W ho +b o ), output value h t The calculation formula is W xo and W ho Represent the control weights of the output gate activation function, b o Represents the bias of the output gate activation function.

9. The frequency sequence estimation method according to claim 5, wherein: The loss function uses the root mean square error, which is: Where RMSE (t) is the loss function value at time t, nn is the current sequence length, is the actual value of the residual sequence at time t, is the output value of the LSTM model at point i at time t.

10. The frequency sequence estimation method according to claim 1, wherein: The steps of combining the FARIMA model and the trained LSTM model to form a FARIMA-LSTM model, inputting the test set data into the FARIMA-LSTM model for single-step prediction, evaluating the model performance, and adjusting the parameters to obtain the trained FARIMA-LSTM model include: Use the fractional difference operator to perform fractal filtering on the test set data to generate the test set ARMA sequence; Recursively calculate the historical residual sequence based on the test set ARMA sequence and FARIMA parameter group; Input the historical residual sequence into the LSTM model to obtain the residual single-step forecast value; Calculate the single-step forecast value of the frequency series by combining the ARMA sequence, FARIMA parameter group and residual forecast value; Compare the performance of the frequency series predictions with the actual values ​​of the test set; When the performance does not reach the threshold, at least one parameter among the training sample length, the number of hidden units, the maximum number of iterations, and the ARMA model order is adjusted, and the FARIMA model and the LSTM model are retrained to obtain a trained FARIMA-LSTM model.

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