Space-time cellular network flow prediction method based on frequency domain MLP

Abstract

The invention discloses a time-space cellular network traffic prediction method based on frequency domain MLP. The method comprises the following steps: S1, obtaining cellular network traffic historical data from a server; and S2, inputting the historical data of the cellular network traffic into the constructed network traffic prediction model so as to output cellular network traffic prediction data. The network traffic prediction model comprises a time decomposition embedding module used for decomposing cellular network traffic historical data into seasonal data and trend data to obtain seasonal characteristics and trend characteristics; the frequency domain feature extraction module is used for performing frequency domain conversion on the seasonal features and the trend features so as to extract spatial-temporal features; the multi-scale space-time attention module is used for capturing multi-scale information from the space-time features through pooling and convolution operations of different scales to obtain trend component output and seasonal component output; and the deep convolution feedforward prediction module is used for outputting cellular network flow prediction data according to the obtained trend component output and the seasonal component output.

Description

Technical Field

[0001] The present invention relates to the technical field of network data processing, and in particular to a method for predicting spatiotemporal cellular network traffic based on frequency domain MLP. Background Art

[0002] With the rapid development of 5G networks, the surge in user data demand has brought major challenges to network operators. The continuous upgrading of base station hardware facilities and the increase in energy consumption requirements have made network management more complicated. At the same time, emerging applications such as autonomous driving and digital twins have put forward strict requirements on quality of service (QoS). Dynamically adjusting the transmission power of base stations according to network traffic conditions is crucial for telecom operators to improve service quality while optimizing operating costs. However, predicting cellular network traffic is a challenging spatiotemporal data prediction task for the following reasons:

[0003] First, with the widespread use of smart devices and the continuous development of mobile communication technology, cellular network traffic has shown increasingly diverse and complex patterns. The network traffic patterns in each region are significantly different in the time dimension, showing unique dynamic behaviors with obvious periodicity and trend changes.

[0004] Secondly, in the spatial dimension, the cellular network traffic in the city is unevenly distributed, mainly concentrated in local areas, while it is more dispersed in the global scope. This shows that there is local spatial dependence between adjacent areas, and long-distance spatial dependence between distant areas. In addition, the cellular network traffic in each area is not only affected by its historical data, but also constrained by various external factors.

[0005] In recent years, many studies have been devoted to solving the difficult problems in cellular network traffic prediction. Traditional statistical methods and machine learning techniques have been widely used in cellular network traffic prediction, but these methods are often inefficient in dealing with complex spatiotemporal relationships in traffic data. With the development of artificial intelligence, deep learning methods such as recurrent neural networks (RNNs), long short-term memory networks (LSTMs), convolutional neural networks (CNNs), and graph neural networks (GNNs) have gradually been adopted to reveal the complex dependencies in cellular network traffic and thus improve prediction accuracy. However, these techniques still face challenges in extracting periodic changes, frequency features, and high dynamic range data, resulting in low prediction accuracy for cellular network traffic. Summary of the invention

[0006] In view of the technical problem in the prior art that the cellular network traffic prediction model is complex and leads to low cellular network traffic prediction accuracy, the present invention proposes a spatiotemporal cellular network traffic prediction method based on frequency domain MLP.

[0007] In order to achieve the above object, the present invention provides the following technical solutions:

[0008] The spatiotemporal cellular network traffic prediction method based on frequency domain MLP includes the following steps:

[0009] S1: Obtain cellular network traffic history data from the server;

[0010] S2: Input the cellular network traffic history data into the constructed network traffic prediction model to output the cellular network traffic prediction data.

[0011] Preferably, in S1, the cellular network traffic prediction task is regarded as a spatiotemporal prediction problem;

[0012] For each time step t, the tensor X t ∈R C×V×H , represents the network traffic of all grids in the entire area at the time step t, specifically:

[0013]

[0014] In formula (1), X t ∈R C represents the vector containing C types of traffic type values ​​in the grid cell located at coordinates (V, H) at time t; V represents the number of rows of the grid division; H represents the number of columns of the grid division;

[0015] Using the observed flow sequence of the first p time steps Predicting Cellular Network Traffic X t :

[0016] X t =f(X t-p ,X t-p+1 ,...,X t-1 ) (2)

[0017] In formula (2), X t represents the cellular network traffic at time t; f represents the network traffic prediction model; X t-p represents the cellular network traffic at time tp; X t-p+1 Represents the cellular network traffic at time t-p+1.

[0018] Preferably, S2 includes:

[0019] S2-1: Build a network traffic prediction model;

[0020] S2-2: Decompose the historical data of cellular network traffic into seasonal data and trend data, and embed the seasonal data and trend data to obtain corresponding seasonal characteristics and trend characteristics;

[0021] S2-3: Perform frequency domain conversion on the trend feature to extract first spatial data and first temporal data; perform frequency domain conversion on the seasonal feature to extract second spatial data and second temporal data;

[0022] S2-4: Capturing multi-scale information from the first spatial data, the first temporal data, and the second spatial data, and the second temporal data to obtain a trend component output and a seasonal component output;

[0023] S2-5: Output cellular network traffic forecast data based on the trend component output and the seasonal component output.

[0024] Preferably, in S2-1, the network traffic prediction model includes a time decomposition embedding module, a frequency domain feature extraction module, a multi-scale spatiotemporal attention module and a deep convolution feedforward prediction module; wherein,

[0025] A time decomposition and embedding module is used to decompose the historical data of cellular network traffic into seasonal data and trend data, and embed the seasonal data and trend data to obtain seasonal characteristics and trend characteristics;

[0026] A frequency domain feature extraction module, used for performing frequency domain conversion on seasonal features and trend features, thereby extracting spatiotemporal features, including first spatial data, first temporal data, second spatial data, and second temporal data;

[0027] Multi-scale spatiotemporal attention module, which is used to capture multi-scale information from spatiotemporal features through pooling and convolution operations at different scales to obtain trend component output and seasonal component output;

[0028] The deep convolution feedforward prediction module is used to output cellular network traffic prediction data based on the trend component output and the seasonal component output.

[0029] Preferably, the S2-2 includes:

[0030] S2-2-1: Decompose the historical data of cellular network traffic into seasonal data and trend data:

[0031] X Trend =AvgPool(Padding(X flatten )), X Seasonal =X flatten -X Trend (3)

[0032] In formula (3), X Trend Indicates trend data; X Seasonal represents seasonal data; AvgPool represents moving average operation; Padding represents data padding; X flatten Represents cellular network traffic history data;

[0033] S2-2-2: For the decomposed trend data X Trend and seasonal data X Seasonal Apply embedding operations respectively to obtain trend features and seasonal features;

[0034] H Trend =X' Trend ×θ d ∈R N×T×D (4)

[0035] In formula (4), H Trend Represents trend characteristics, N represents the flow of N city grids, N = V*H, V represents the number of rows of grid division; H represents the number of columns of grid division; T represents the length of the time dimension, the number of time steps of the sequence, that is, the data of the past T time moments; D represents the dimension of the feature space after data embedding;

[0036] Similarly, the seasonal characteristic H Seasonal for:

[0037] H Seasonal =X' Seasonal ×θ d ∈R N×T×D (5)

[0038] In formula (5), H Seasonal Indicates seasonal characteristics; X' Seasonal Represents seasonal data X Seasonal The transpose of θ d represents a learnable vector.

[0039] Preferably, the S2-3 includes:

[0040] S2-3-1: Perform frequency domain conversion on trend characteristics to extract first spatial data; perform frequency domain conversion on seasonal characteristics to extract second spatial data;

[0041] S2-3-2: Perform frequency domain conversion on trend characteristics to extract first time data; perform frequency domain conversion on seasonal characteristics to extract second time data.

[0042] Preferably, the S2-3-1 includes:

[0043] First, the trend feature H Trend ∈R N×T×D Transpose to H' Trend ∈R T×N×D ;

[0044] Secondly, for each time step k∈(1,T), the trend feature is independently applied with a fast Fourier transform in the spatial dimension to obtain a spatial complex number:

[0045]

[0046] In formula (6), Represents the spatial complex number corresponding to the trend feature; F spatial represents fast Fourier transform; H' Trend represents the transposition of trend characteristics; D represents dimension; N represents the number of grids; C represents complex space;

[0047] Next, use the MLP operation to process the spatial complex number corresponding to the trend feature to obtain the complex frequency domain signal of the trend feature:

[0048]

[0049] In formula (7), The first frequency domain signal representing the trend characteristics; MLP frequency-domain represents the MLP operation; W spatial represents the complex weight matrix, W spatial Real part of the complex matrix, dimension R D×D ; W spatial The imaginary part of the complex matrix, dimension R D×D ; j represents a complex unit; B spatial represents the complex bias, Represents the complex bias B spatial The real part of the dimension is R D ; Represents the complex bias B spatial The imaginary part of

[0050] Then, the inverse fast Fourier transform is applied to convert the trend feature first frequency domain signal Convert back to the first time domain And the first time domain of T time steps Combined into the first time domain overall feature Z t ∈R T×N×D :

[0051]

[0052] In formula (8), Represents the first time domain signal of trend characteristics; represents inverse fast Fourier transform;

[0053] Transpose the trend characteristics H' Trend Aggregate with the overall time domain features processed by the frequency domain feature extraction module:

[0054] Z' t =Z t +H' Trend ∈R T×N×D (9)

[0055] In formula (9), Z' t The first aggregated data representing trend characteristics; Z t The first time domain overall characteristic representing the trend characteristic; H' Trend Indicates trend feature transposition;

[0056] Finally, the aggregated data Z' of the trend characteristics is t The dimension is converted to get Z" t ∈R N×T×D , Z” t The first spatial data representing trend characteristics.

[0057] Preferably, the S2-5 includes:

[0058] S2-5-1: Aggregate the trend component output and seasonal component to obtain the aggregate output;

[0059] S2-5-2: The aggregated output is input into the final layer of the deep convolutional feedforward prediction module to generate cellular network traffic prediction data.

[0060] Preferably, in S2-5-1, the aggregate output is:

[0061] S ot =α×S st +(1-α)×S Tt ∈R N×T×D (10)

[0062] In formula (10), S ot represents the aggregate output, S st ∈R N×T×D represents the seasonal component output after the multi-scale spatiotemporal attention module; S Tt ∈R N×T×D represents the output of the trend component; α represents the weighting parameter.

[0063] Preferably, in S2-5-2, the method for calculating the cellular network traffic prediction data is:

[0064] Y t =σ((S t Φ 1 +b 1 )Φ 2 +b 2 )Φ 3 +b 3 ,

[0065]

[0066] In formula (15), Y t Indicates output; Y t represents the output; σ represents the activation function; S t represents the reshaping of the aggregation output; Φ 1 , Φ 2 , Φ 3 Both represent weights; b 1 、b 2 、b 3 Both represent bias; Indicates output Y t The final output after rearranging and reshaping the dimensions; Reshape indicates the activation function; Permute indicates the dimension exchange operation; dims = (0, 2, 1) indicates the dimension conversion; X out represents cellular network traffic prediction data; MSD-FFN represents multi-scale feed-forward layer.

[0067] In summary, due to the adoption of the above technical solution, compared with the prior art, the present invention has at least the following beneficial effects:

[0068] By combining MLP with a multi-scale spatiotemporal attention mechanism and a deep residual feed-forward layer for the first time, the time domain, frequency domain, multi-scale global and local spatial domains, and spatiotemporal correlations are comprehensively considered, thus achieving more accurate and comprehensive predictions.

[0069] In order to enhance the ability to capture complex data relationships, an innovative frequency-domain spatiotemporal MLP block is designed to improve feature propagation and learning capabilities through residual connections; in addition, a multi-scale spatiotemporal attention (MSTA) module is introduced to effectively capture multi-scale spatiotemporal dependencies; at the same time, a deep convolutional feedforward network module is developed to further enhance the expressive power of local spatial features.

[0070] A seasonal-trend decomposition method was also used for individual forecasts, and the results were evaluated through weighted fusion to improve the forecast accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Figure 1 4 is a flow chart of a method for spatiotemporal cellular network traffic prediction based on frequency domain MLP according to an exemplary embodiment of the present invention.

[0072] Figure 2 Schematic diagram of a network traffic prediction model according to an exemplary embodiment of the present invention.

[0073] Figure 3 Schematic diagram of cellular traffic prediction results and error analysis according to an exemplary embodiment of the present invention. DETAILED DESCRIPTION

[0074] The present invention is further described in detail below in conjunction with the examples and specific implementation methods. However, this should not be understood as the scope of the above subject matter of the present invention being limited to the following examples, and all technologies realized based on the content of the present invention belong to the scope of the present invention.

[0075] In the description of the present invention, it is necessary to understand that the terms "longitudinal", "lateral", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", etc., indicating the orientation or position relationship, are based on the orientation or position relationship shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present invention.

[0076] Cellular network traffic prediction is essentially a spatiotemporal regression problem. Cellular network traffic data shows obvious periodicity and complexity, and is also affected by holiday effects and emergencies. In addition, in geographic space, there is local correlation between adjacent locations, and there is also a certain correlation between distant locations, showing significant spatial characteristics. Current research on cellular network traffic prediction can be roughly divided into three categories of methods: traditional statistical methods, machine learning-based methods, and deep learning-based methods.

[0077] (1) For example, traditional statistical methods:

[0078] Traditional linear models are statistical methods based on probability distribution. These models are relatively simple to simulate and fast to execute, but require multiple parameters to be manually set to fit the data. Such models include autoregressive (AR) models, moving average (MA) models, autoregressive moving average (ARMA) models, and autoregressive integrated moving average (ARIMA) models. In early studies, forecasting models were mainly applied to stationary data. If the data does not meet the stationarity assumption, the model may not be able to accurately fit the data.

[0079] Xu et al. used an autoregressive model to predict network traffic, which is able to capture the autoregressive relationship in time series data. However, the model has limitations in predicting non-stationary data and is prone to lag problems. Tian et al. used the ARMA model to model network traffic, but the training process of the model is highly dependent on parameter selection, and different parameter selections can lead to significant differences in prediction results.

[0080] The ARIMA model processes stationary data through differential operations and has wide applicability. It can effectively extract trend and seasonal characteristics in data without a lot of training. In the literature, researchers used the ARIMA model to analyze network traffic peaks, and the results showed that the average error of the model was relatively low. However, the model has high requirements on data quality, is sensitive to outliers, and has poor robustness, so its scope of application is limited to a certain extent.

[0081] (2) Machine learning-based methods

[0082] Machine learning methods mainly include support vector machines (SVM), random forests (RF) and Prophet models. According to relevant research, these models are superior to traditional statistical methods in feature extraction and prediction performance, and can effectively capture complex time series characteristics. However, as network complexity increases and the spatial distribution characteristics of cellular traffic no longer conform to the traditional Poisson or Markov distribution, these machine learning methods still have certain limitations.

[0083] Xu et al. used a method combining Prophet with Gaussian process regression (GPR) for traffic forecasting. Rizwan et al. used a support vector regression (SVR) model to analyze call detail record (CDR) data of mobile networks with high spatiotemporal resolution, and the results showed that this method performed well in Internet traffic forecasting. Although this hybrid model improves the prediction performance, its high computational complexity limits its application in large-scale datasets.

[0084] (3) Methods based on deep learning

[0085] With the continuous development of deep learning, especially in the context of the continuous growth of computing power and data size, more and more researchers have begun to design and propose innovative frameworks to cope with the spatiotemporal complexity of cellular network traffic data. These data are usually highly nonlinear and have significant spatiotemporal dependencies, making traditional statistical and machine learning methods face great challenges in processing such data. To solve this problem, deep learning methods have gradually become the mainstream choice for processing cellular traffic data, showing its unique advantages in capturing complex spatiotemporal patterns.

[0086] For example, recurrent neural networks (RNNs) and long short-term memory networks (LSTMs), as classic methods for modeling time series data, can effectively capture temporal dependencies in data. RNNs transfer information between time steps through recurrent connections, thereby retaining historical information in time series. However, RNNs often encounter the problem of gradient vanishing or exploding when dealing with long-term dependencies. LSTM effectively alleviates this problem by introducing a gating mechanism, enabling it to handle longer time series. However, some studies that apply these two methods have failed to fully address the problem of spatiotemporal cellular traffic prediction, resulting in less than ideal prediction performance.

[0087] At the same time, convolutional neural networks (CNNs), which are well-known for their powerful image processing capabilities, have also been applied to spatiotemporal data analysis. The convolutional layers of CNNs can effectively capture local spatial features, enabling them to learn spatial patterns in spatiotemporal data (such as cellular network traffic data). For example, some studies have adopted 2D or 3D CNNs and ResNet architectures for cellular spatiotemporal prediction. However, since CNNs are not designed for spatiotemporal prediction, their receptive field is limited and they perform poorly in capturing global spatiotemporal dependencies. To address this problem, Lin et al. proposed a temporal convolutional network (TCN) for outdoor cellular traffic spatiotemporal prediction, which enhances the time series prediction capability by introducing causal convolution and dilated convolution.

[0088] In recent years, models based on attention mechanisms have attracted widespread attention. By assigning greater weights to key parts of the input data, the attention mechanism is able to capture key features more accurately. For example, the Transformer architecture uses the self-attention mechanism to efficiently capture global spatiotemporal dependencies and significantly improves training efficiency through parallel computing, becoming the preferred architecture in fields such as traffic prediction and natural language processing. In addition, the concepts of multi-view learning and multi-scale learning have gradually been introduced into spatiotemporal data modeling. Multi-view learning extracts features from multiple perspectives, while multi-scale learning extracts spatiotemporal information at different scales. Recent studies combining these concepts (such as the Transformer-based model GLSTTN and the multi-view global attention network MVSTGN) have made important progress in cellular spatiotemporal traffic prediction.

[0089] (4) Multilayer Perceptron (MLP) method for time series prediction

[0090] In recent years, multilayer perceptrons (MLPs) have attracted widespread attention in the field of time series forecasting due to their simple structure, high computational efficiency, and ability to model nonlinear relationships. Unlike traditional statistical models or deep learning architectures such as RNN, CNN, or Transformer, MLPs learn feature representations through fully connected layers, making them well suited for processing high-dimensional time series data. The DLinear model shows that simple linear layers can achieve excellent forecasting performance by directly learning time series mappings, challenging the reliance on complex deep learning architectures. This insight has inspired the development of lightweight MLP models that employ strategies such as block processing, frequency domain modeling, and feature-time dimension fusion.

[0091] For example, PatchTST and TSMixer split time series data into small blocks and apply MLP modules for intra-block and inter-block learning to capture local and global dependencies, balancing efficiency and accuracy. FreTS uses discrete Fourier transform (DFT) to model in the frequency domain and applies MLP to the real and imaginary parts to capture global patterns and suppress noise, thereby effectively learning the dependencies between time and features in short-term and long-term predictions. Similarly, FTMLP (Feature-Temporal MLP) introduces a dual-module architecture that integrates feature and time dimensions. Its feature module models variable interactions through a gating mechanism, while the time module extracts time series patterns through frequency domain filtering.

[0092] These works have achieved spatiotemporal feature fusion to a certain extent, but processes such as block processing may lead to information loss. In addition, the extracted features may not be sufficient and fail to fully utilize the frequency domain characteristics and local multi-scale information. Therefore, enhancing the feature extraction mechanism by integrating multi-scale and frequency domain modeling becomes the key to improving the model's ability to capture complex spatiotemporal dependencies.

[0093] like Figure 1 As shown, the present invention provides a spatiotemporal cellular network traffic prediction method based on frequency domain MLP, which specifically includes the following steps:

[0094] S1: Obtain cellular network traffic history data from the server.

[0095] In this embodiment, the cellular network traffic prediction task is considered as a spatiotemporal prediction problem, because time and space factors have a significant impact on cellular traffic. From a spatial perspective, the urban area is divided into a grid of V rows and H columns, and each grid corresponds to a position in the vertical and horizontal directions. In the time dimension, the cellular network traffic can be expressed as represents the spatiotemporal traffic sequence, which refers to the traffic data within the time period T, capturing the cellular traffic value X of each grid at time t in the urban area t ,Multiple types of traffic records are made at equal time intervals.

[0096] For each time step t, the tensor X t ∈R C×V×H , represents the network traffic of all grids in the entire area at the time step t, specifically:

[0097]

[0098] In formula (1), X t ∈R C represents the vector containing C types of traffic type values ​​in the grid cell located at coordinates (V, H) at time t; V represents the number of rows of the grid division; H represents the number of columns of the grid division;

[0099] In this embodiment, the goal of the present invention is to use the observed flow sequence of the first p time steps Predicting Cellular Network Traffic X t , this process can be expressed as:

[0100] X t =f(X t-p ,X t-p+1 ,...,X t-1 ) (2)

[0101] In formula (2), X t represents the cellular network traffic at time t; f represents the network traffic prediction model, which is used to capture the potential complex patterns in cellular network traffic data; X t-p represents the cellular network traffic at time tp; X t-p+1 Represents the cellular network traffic at time t-p+1.

[0102] S2: Input the cellular network traffic history data into the constructed network traffic prediction model to output the cellular network traffic prediction data.

[0103] S2-1: Build a network traffic prediction model.

[0104] In this embodiment, Figure 2 As shown, the network traffic prediction model includes a time decomposition embedding module, a frequency domain feature extraction module, a multi-scale spatiotemporal attention module and a deep convolution feedforward prediction module; the output end of the time decomposition embedding module is connected to the input end of the frequency domain feature extraction module, the output end of the frequency domain feature extraction module is connected to the input end of the multi-scale spatiotemporal attention module, and the output end of the multi-scale spatiotemporal attention module is connected to the input end of the deep convolution feedforward prediction module.

[0105] Among them, the time decomposition embedding module is used to decompose the historical data of cellular network traffic into seasonal data and trend data, and embed the seasonal data and trend data to extract short-term and long-term features;

[0106] The frequency domain feature extraction module is used to convert seasonal data and trend data from time domain to frequency domain to time domain, thereby extracting spatiotemporal features;

[0107] A multi-scale spatiotemporal attention module for capturing multi-scale information from spatiotemporal features through pooling and convolution operations at different scales;

[0108] The deep convolutional feedforward prediction module is used to output high-precision cellular network traffic prediction data based on multi-scale information.

[0109] S2-2: Input the historical data of cellular network traffic into the time decomposition embedding module, decompose it into seasonal data and trend data, and embed the seasonal data and trend data to obtain the corresponding seasonal characteristics (short-term characteristics) and trend characteristics (long-term characteristics).

[0110] In this embodiment, the cellular network traffic history data at the past t time points is used. As input data, X t-T Represents the historical data of cellular network traffic at time tT.

[0111] S2-2-1: In this embodiment, the input data is a historical flow observation tensor X input ∈R T×V×H , represents the network traffic data in T time steps (time dimension), V rows and H columns (spatial grid); T represents the period, V represents the number of rows of grid division; H represents the number of columns of grid division; for the convenience of calculation, the historical traffic observation tensor X input Adjust to list format, represented by X flatten ∈R T×N , N = V × H; X input ∈R T×V×H Convert to X flatten ∈R T×N , X flatten It is a matrix after a "flatten" operation, where N = V × H, which means that the spatial dimension of V × H is flattened into a one-dimensional vector. The flattening process compresses the flow data of each spatial location into a one-dimensional format so that it can be input into the subsequent time series decomposition.

[0112] Then X flatten Decompose into seasonal and trend data for independent forecasting:

[0113] X Trend=AvgPool(Padding(X flatten )), X Seasonal =X flatten -X Trend (3)

[0114] In formula (3), X Trend Indicates trend data, used to represent the long-term changes or overall direction of data; X Seasonal Represents seasonal data, which is used to capture patterns or periodic changes in the data that occur repeatedly at specific time intervals (such as daily, weekly, or monthly); AvgPool represents a moving average operation, which ensures that the sequence length remains unchanged through padding; Padding represents data padding, that is, padding the flattened data to adjust its shape. Padding ensures that the dimension of the output remains unchanged after the pooling operation.

[0115] S2-2-2: Then, for the decomposed trend data X Trend and seasonal data X Seasonal Embedding operations are applied separately to obtain trend features and seasonal features.

[0116] In this embodiment, the embedding operation is described by taking trend data as an example:

[0117] First, the trend data X Trend ∈R T×N Transpose to X' Trend ∈R N×T×1 , and then with a learnable vector θ d ∈R 1×d Multiply and transform the dimension to get the trend feature H Trend :

[0118] H Trend =X' Trend ×θ d ∈R N×T×D (4)

[0119] In formula (4), N represents the traffic of N city grids, N = V*H, V represents the number of rows of grid division; H represents the number of columns of grid division; T represents the length of the time dimension, the number of time steps of the sequence, that is, the data of the past T time moments; D represents the dimension of the feature space after data embedding.

[0120] Similarly, the seasonal characteristic H Seasonal for:

[0121] H Seasonal =X' Seasonal ×θ d ∈R N×T×D (5)

[0122] In formula (5), H Seasonal Indicates seasonal characteristics; X' Seasonal Represents seasonal data X Seasonal The transpose of θ d represents a learnable vector.

[0123] S2-3: Perform frequency domain conversion on the trend characteristics to extract first spatial data and first temporal data; perform frequency domain conversion on the seasonal characteristics to extract second spatial data and second temporal data.

[0124] Recent models typically use Transformer or GCN for spatiotemporal prediction, but these techniques are inefficient in capturing spatiotemporal complexity and perform poorly in extracting global and local periodic features of cellular traffic. Cellular traffic typically exhibits regular patterns due to daily usage cycles, peak and off-peak hours, and seasonal fluctuations. By applying Fourier transforms, these periodic features can be revealed more clearly, helping to identify trends, anomalies, and correlations hidden in the time domain.

[0125] Therefore, it is proposed to use a frequency domain feature extraction module (MLP model) in the frequency domain to capture spatiotemporal features more efficiently. In addition, the same model architecture is used to predict seasonal data and trend data, so that trends and cyclical fluctuations can be fully modeled.

[0126] S2-3-1: Perform frequency domain conversion on trend characteristics to extract first spatial data; perform frequency domain conversion on seasonal characteristics to extract second spatial data.

[0127] In cellular network traffic prediction, traffic at different spatial locations is interdependent and affects each other. The frequency domain feature extraction module captures the relationship and characteristics between different spatial locations. Specifically, the frequency domain feature extraction module uses the output trend feature H of the time decomposition embedding layer Trend and seasonal characteristics H Seasonal as input.

[0128] In this embodiment, the trend feature H Trend and seasonal characteristics H Seasonal The extraction method is the same, so the trend feature H Trend Take this as an example to illustrate.

[0129] In this embodiment, the frequency domain feature extraction module includes a spatial extraction unit and a temporal extraction unit; the spatial extraction unit is used to extract first spatial data from trend features and second spatial data from seasonal features; the temporal extraction unit is used to extract first temporal data from trend features and second temporal data from seasonal features.

[0130] In order to perform Fourier transform in the spatial domain, we first transform H Trend =X' Trend ×θ d ∈R N×T×D Transpose to H' Trend ∈R T×N×D .

[0131] Second, for each time step k∈(1,T), a fast Fourier transform (F spatial (·)) obtains a spatial complex number, that is, converts the trend feature from the time domain to the first frequency domain to perform spatial domain feature learning:

[0132]

[0133] In formula (6), Represents the spatial complex number corresponding to the trend feature; F spatial represents fast Fourier transform; H' Trend represents the transpose of trend characteristics; D represents dimension; N represents the number of grids; C represents complex space. In Fourier transform, data is usually converted from real space to complex space to process data containing frequency components.

[0134] Next, use the MLP operation to process the spatial complex number corresponding to the trend feature to obtain the complex frequency domain signal of the trend feature:

[0135]

[0136] In formula (7), The first frequency domain signal representing the trend characteristics; MLP frequency-domain represents the MLP operation; W spatial represents the complex weight matrix, W spatial Real part of the complex matrix, dimension R D×D ; W spatial The imaginary part of the complex matrix, dimension R D×D ; j represents a complex unit; B spatial represents the complex bias, Represents the complex bias B spatial The real part of the dimension is R D ; Represents the complex bias B spatial The imaginary part of .

[0137] These weight matrices W spatial With bias B spatial Used for calculation of real and imaginary parts respectively.

[0138] Then, the inverse fast Fourier transform (IFFT) is applied to convert the trend feature first frequency domain signal Convert back to the first time domain And the first time domain of T time steps Combined into the first time domain overall feature Z t ∈R T×N×D .

[0139]

[0140] In formula (8), Represents the first time domain signal of trend characteristics; Represents Inverse Fast Fourier Transform (IFFT).

[0141] Add a residual connection to transpose the trend feature H' Trend Aggregate with the overall time domain features processed by the frequency domain feature extraction module to further enhance the feature representation capability:

[0142] Z' t =Z t +H' Trend ∈R T×N×D (9)

[0143] In formula (9), Z' t The first aggregated data representing trend characteristics; Z t The first time domain overall characteristic representing the trend characteristic; H' Trend Indicates trend feature transposition.

[0144] Finally, the aggregated data Z' of the trend characteristics is t The dimension is converted to get Z" t ∈R N×T×D , Z” t The first spatial data representing trend characteristics.

[0145] Similarly, the second spatial data of seasonal characteristics can be obtained.

[0146] S2-3-2: Perform frequency domain conversion on trend characteristics to extract first time data; perform frequency domain conversion on seasonal characteristics to extract second time data.

[0147] In this embodiment, the trend feature H Trend and seasonal characteristics H Seasonal The extraction method is the same, so the trend feature H Trend Take this as an example to illustrate.

[0148] The temporal extraction unit is designed to capture the frequency domain features of the temporal channel. Specifically, the output Z" learned from the spatial extraction unit module t ∈R N×T×D As the input of the time extraction unit, for each spatial channel n∈(1,N), a fast Fourier transform (FFT) is independently performed in the time dimension to obtain a time complex number, that is, the trend feature is converted from the time domain to the second frequency domain to perform time domain feature learning:

[0149]

[0150] In formula (10), Represents the time complex corresponding to the trend feature, Z” t The first spatial data representing the trend characteristics; F temporal represents fast Fourier transform (FFT); D represents dimension; T represents the length of time dimension.

[0151] Secondly, use the MLP operation to process the time complex number corresponding to the trend feature to obtain the second frequency domain signal of the trend feature:

[0152]

[0153] In formula (11), The second frequency domain signal representing trend characteristics; MLP frequency-domain represents the MLP operation; W temporal represents the complex weight matrix, represents the complex weight matrix W temporal The real part of represents the complex weight matrix W temporal The imaginary part of B temporal represents the complex bias, represents the real part of the complex bias; Represents the imaginary part of the complex bias.

[0154] These weight matrices W temporal With bias B temporal Used for calculation of real and imaginary parts respectively.

[0155] Then, the inverse fast Fourier transform (IFFT) is applied to convert the trend feature into the second frequency domain signal Convert back to the second time domain And the second time domain of N spatial channels Combined into the second time domain overall feature S t ∈R N×T×D .

[0156]

[0157] In formula (12), The second time domain signal representing the trend characteristics; Represents Inverse Fast Fourier Transform (IFFT).

[0158] Add a residual connection to connect the first spatial data of the trend feature with the second time domain overall feature S t Aggregation is performed to further enhance the feature representation capability:

[0159] S' t =S t +Z” t ∈R T×N×D (13)

[0160] In formula (13), S' t The second aggregate data representing trend characteristics; Z" t Represents the first spatial data; S t Represents the overall characteristics of the second time domain.

[0161] Finally, the second aggregated data S with trend characteristics is t The dimension is converted to obtain S" t ∈R N×T×D , S” t The first-time data showing trend characteristics.

[0162] Similarly, second time data with seasonal characteristics can be obtained.

[0163] S2-4: The first spatial data and the first temporal data extracted from the trend feature and the second spatial data and the second temporal data extracted from the seasonal feature are input into the multi-scale spatiotemporal attention (MSTA) module to capture multi-scale information (i.e., considering multiple levels in the time domain and the spatial domain, capturing local spatial features and cross-spatial features as well as time domain features) to obtain trend component output and seasonal component output.

[0164] Previous studies on extracting local information for cellular traffic prediction mainly rely on CNN-based models, which use dense convolutional network frameworks but are limited to capturing local information and dependencies. These methods fail to fully exploit spatiotemporal dependencies and multi-scale cross-spatial features, which are critical for accurate feature extraction. To address these limitations and enhance the model's ability to capture spatiotemporal dependencies and multi-scale cross-spatial features, this scheme proposes a multi-scale spatiotemporal attention (MSTA) module, which adopts an efficient attention mechanism and multi-scale feature aggregation strategy to effectively model complex spatiotemporal relationships.

[0165] The multi-scale spatiotemporal attention (MSTA) module first divides the input features (including first spatial data, second spatial data, first temporal data, and second temporal data) into K subspace groups along the channel dimension. For each subspace group, global average pooling is applied in the temporal and embedding dimensions to extract global context information and obtain context feature vectors. The context feature vectors are concatenated and feature fused and compressed through 1×1 convolutions. The nonlinear representation capability is then enhanced through activation functions. The attention weights across channels are aggregated through element-wise multiplication to dynamically model cross-channel and spatiotemporal dependencies. At the same time, a 3×3 convolution operation is introduced to capture local spatial features and supplement the modeling of spatial details. Through cross-spatial feature aggregation, the MSTA module integrates the spatial information in the 1×1 and 3×3 branches to generate two spatial attention maps. On this basis, the module uses hybrid pooling (AMP) to combine the advantages of maximum pooling and average pooling, which not only retains finer local details but also extracts global semantic information. By effectively integrating the attention mechanism in the parallel network, the MSTA module significantly enhances the network's spatiotemporal perception ability in the cellular traffic prediction task, thereby providing more efficient and accurate feature representation, and then outputting trend component output and seasonal component output.

[0166] S2-5: Input the trend component output and seasonal component output information into the deep convolution feedforward prediction module for prediction, and output the cellular network traffic prediction data.

[0167] S2-5-1: In this embodiment, a simple weighted aggregation method is used to aggregate the trend component output and the seasonal component output. The formula is as follows:

[0168] S ot =α×S st +(1-α)×S Tt ∈R N×T×D (14)

[0169] In formula (14), S ot represents the aggregate output, S st ∈R N×T×D represents the seasonal component output after the multi-scale spatiotemporal attention module; S Tt ∈R N×T×D represents the output of the trend component; α represents the weighting parameter, which is set to 0.8.

[0170] S2-5-2: Output the aggregated data S ot ∈R N×T×D Reshape into S t ∈R N×(T*D) , and input into the final layer of the deep convolutional feedforward prediction module to generate cellular network traffic prediction data, as shown below:

[0171] Y t =σ((S t Φ 1 +b 1 )Φ 2 +b 2 )Φ 3 +b 3 ,

[0172]

[0173] In formula (15), Y t represents the output; σ represents the activation function, usually ReLU or Sigmoid, etc., which is used to increase the nonlinearity of the model; S t represents the reshaping of the aggregation output; Φ 1 , Φ 2 , Φ 3 Both represent weights; b 1 、b 2 、b 3 Both represent bias; Indicates output Y t The final output after rearranging and reshaping the dimensions is further input into a multi-scale deep feedforward network to model these spatial features; Reshape represents an activation function; Permute represents a dimension exchange operation, which exchanges the dimensions of the data to meet the subsequent operation requirements; dims = (0, 2, 1) means changing the order of the dimensions from (0, 1, 2) to (0, 2, 1), which is usually used to process spatiotemporal data shape represents dimension conversion; X out represents cellular network traffic prediction data; MSD-FFN represents multi-scale feed-forward layer.

[0174] The specific mathematical representation of MSD-FFN is as follows:

[0175]

[0176] X' 1 =RELU(Conv k×k (X 1 ))

[0177] X' 2 =Upsample(RELU(Conv k×k (Downsample(X 1 ))))

[0178] X' 3 = Downsample(RELU(Conv k×k (Upsample(X 1 ))))

[0179] XResDWC =X 1 +X' 1 +X' 2 +X' 3

[0180] X out = Dropout(Conv 1×1 (X ResDWC )) (16)

[0181] That is, firstly, the input is convolved (Conv) Perform convolution operation, then apply Relu activation function, and finally apply Dropout operation for regularization to prevent overfitting, and get X 1 ;

[0182] Then for X 1 Perform a convolution operation and then apply the Relu activation function to get X' 1 ;

[0183] At the same time, for X 1 After downsampling, convolution is performed, and then the Relu activation function is applied, and then the result is upsampled to obtain X' 2 ;

[0184] At the same time, for X 1 After upsampling, convolution is performed, and then the Relu activation function is applied, and then the result is downsampled to obtain X' 3 ;

[0185] Then, multiple results X 1 , X' 1 , X' 2 , X' 3 Perform addition operations, and residual connections are usually used in deep learning to help the model train better.

[0186] In formula (16), Conv 1×1 represents 1×1 convolution; RELU represents activation function; Dropout represents average pooling; Conv k×k represents k×k convolution; Upsample represents upsampling; Downsample represents downsampling; X 1 , X' 1 , X' 2 , X' 3 , X ResDWC represents the intermediate variable; X out Represents cellular network traffic forecast data.

[0187] In this embodiment, in order to verify the technical effect of the present invention, an experimental verification is carried out.

[0188] (1) Dataset

[0189] The dataset used in this study comes from the real-world public telecommunication dataset "Telecom Italia BigData Challenge". This cellular dataset records traffic data for three activities (SMS, calls, and Internet) in the Milan area over a two-month period (from November 1, 2013 to December 31, 2013). This dataset has been widely used by numerous influential studies, demonstrating its continued importance and applicability in this research field.

[0190] The Milan area is divided into square grids, each covering an area of ​​approximately 235 x 235 m. The data for each service is aggregated in each grid cell at ten-minute intervals.

[0191] (2) Experimental setup and evaluation

[0192] Comparison Methods: To comprehensively evaluate the performance of our proposed cellular spatiotemporal traffic forecasting model, we compare it with the state-of-the-art cellular traffic forecasting methods, as well as classical and recent time series forecasting methods.

[0193] Experimental Design: To ensure a fair comparison, our experiments follow the same preprocessing steps as in previous studies, focusing on forecasting 20x20 grid cells in the central area of ​​Milan. In addition, the 10-minute time scale is converted to an hourly scale to facilitate resource planning for network operators. The first seven weeks of data are used to build the training set, and the last week of data is used for testing. The lookback window is set to 25 to be consistent with the latest open source model GLSTTN in order to compare the prediction of cellular traffic in the next hour.

[0194] In our experiments, the lookback window is kept fixed and the optimization is performed using the Adam optimizer with an initial learning rate of 0.001. The models are trained for 300 training epochs with a batch size of 32. The learning rate is halved at 50% and 75% of the total training epochs. All models are trained on two NVIDIA RTX 4090 GPUs and trained using data parallelism.

[0195] Evaluation Method: To evaluate the performance of the proposed model, we used three standard metrics: The first one is the Root Mean Square Error (RMSE), which represents the square root of the average of the squared differences between the predicted and actual values. This metric measures the accuracy of the model in terms of error margin, and smaller values ​​indicate better performance.

[0196]

[0197] The second metric is the Mean Absolute Error (MAE), which measures the average of the absolute differences between the predicted value and the actual value. Compared with RMSE, MAE is less sensitive to outliers, and the smaller the MAE value, the higher the prediction accuracy.

[0198]

[0199] The third indicator is the coefficient of determination (R 2 ), which measures the ability of the model to explain the variability in the data. 2 The value ranges from 0 to 1. The closer the value is to 1, the better the model fit is and the stronger the model's ability to explain the relationship between the independent variable and the dependent variable is.

[0200]

[0201] (3) Experimental results and analysis

[0202] Quantitative Analysis: To achieve a fair comparison, the baseline model is evaluated using the same experimental settings and datasets, and the results are shown in Table 1.

[0203] Table 1. Comparison of the present invention and the baseline method in three cellular traffic predictions.

[0204]

[0205] Experimental results show that the proposed method significantly outperforms all baseline models in terms of RMSE, MAE, and R2 values ​​on three different cellular services (SMS, calls, and Internet). Specifically, compared with the state-of-the-art GLSTTN model, STMLP reduces the error in MAE by 7.65% to 15.14% and the error in RMSE by 3.64% to 10.57%. In addition, the R2 indicator shows an improvement in prediction accuracy ranging from 0.65% to 1.15%.

[0206] It can be observed that the models that only focus on time prediction (ARIMA, LSTM) perform relatively poorly, with higher RMSE, MAE and R2. This shows that relying only on the time dimension for prediction is not enough to solve the complexity of spatiotemporal cellular traffic prediction, and spatial dependency features also need to be highly valued.

[0207] In contrast, spatiotemporal models such as STC-NET, MVSTGN, and GLSTTN demonstrate the advantages of incorporating spatial features. However, our model outperforms these baseline models, highlighting the effectiveness of our approach.

[0208] At the same time, although the FRTS model with good generalization ability for time series prediction performs relatively well, there is still a certain gap compared with the model that extracts both temporal and spatial features. This shows that spatial feature extraction plays a vital role in cellular traffic prediction and cannot be ignored.

[0209] Overall, by better extracting spatiotemporal features and capturing local and global features at different scales, our model more effectively completes the task of cellular traffic prediction. In addition, despite adopting a simpler MLP architecture, our model still outperforms the latest Transformer and GCN-based models. At the same time, it also shows relative advantages in parameter efficiency and training speed.

[0210] Prediction effect: The weekly cellular traffic prediction results and error analysis for the (50,58) area are visualized to demonstrate the performance of the STMLP model.

[0211] like Figure 3 As shown in the figure, the three sub-figures on the left show the comparison between the predicted values ​​and the actual values ​​of SMS, Calls and Internet traffic. From these figures, it can be seen that STMLP can effectively predict these three types of traffic and fit their periodicity and trend changes well.

[0212] The three middle subplots show the distribution of relative errors. For SMS and call traffic, the errors are mainly concentrated during peak traffic hours, while for Internet traffic, which fluctuates more, the errors are more evenly distributed on both sides. The cumulative distribution function (CDF) subplot on the right shows the overall distribution of prediction errors. The curve rises rapidly on the left, indicating that most prediction errors are small and have high accuracy. As the error increases, the curve gradually flattens, reflecting the low frequency of large errors, showing the overall accuracy of the STMLP model.

[0213] The present application also provides a computer-readable medium, on which is stored the method for predicting spatiotemporal cellular network traffic based on frequency domain MLP described in the embodiment.

[0214] The computer-readable medium may be a computer-readable signal medium or a computer-readable storage medium or any combination of the two. The computer-readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, device or device, or any combination of the above. More specific examples of computer-readable storage media may include, but are not limited to, an electrical connection with one or more wires, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above. In the present disclosure, a computer-readable storage medium may be any tangible medium containing or storing a program that may be used by or in conjunction with an instruction execution system, device or device. In the present disclosure, a computer-readable signal medium may include a data signal propagated in a baseband or as part of a carrier wave, in which a computer-readable program code is carried. This propagated data signal may take a variety of forms, including but not limited to an electromagnetic signal, an optical signal, or any suitable combination of the above. Computer-readable signal media may also be any computer-readable medium other than computer-readable storage media, which may send, propagate or transmit a program for use by or in conjunction with an instruction execution system, apparatus or device. The program code contained on the computer-readable medium may be transmitted using any appropriate medium, including but not limited to: wireless, wire, optical cable, RF, etc., or any suitable combination of the above.

[0215] The computer readable medium may be included in the system described in the above embodiment; or it may exist independently without being assembled into the system. The above computer readable medium carries one or more programs. When the above one or more programs are executed by a system, the system implements the spatiotemporal cellular network traffic prediction method based on frequency domain MLP as described in the embodiment.

[0216] Those skilled in the art will appreciate that the above-mentioned embodiments are specific examples for implementing the present invention, and in actual applications, various changes may be made thereto in form and detail without departing from the spirit and scope of the present invention.

Claims

1. A spatiotemporal cellular network traffic prediction method based on frequency domain MLP, characterized in that: The following steps are involved: S1: Obtain cellular network traffic history data from the server; S2: Input the cellular network traffic history data into the constructed network traffic prediction model to output the cellular network traffic prediction data.

2. The method for predicting spatiotemporal cellular network traffic based on frequency domain MLP as claimed in claim 1, characterized in that: In S1, the cellular network traffic prediction task is considered as a spatiotemporal prediction problem; For each time step t, the tensor X t ∈R C×V×H , represents the network traffic of all grids in the entire area at the time step t, specifically: In formula (1), X t ∈R C represents the vector containing C types of traffic type values ​​in the grid cell located at coordinates (V, H) at time t; V represents the number of rows of the grid division; H represents the number of columns of the grid division; Using the observed flow sequence of the first p time steps Predicting Cellular Network Traffic X t : X t =f(X t-p ,X t-p+1 ,...,X t-1 ) (2) In formula (2), X t represents the cellular network traffic at time t; f represents the network traffic prediction model; X t-p represents the cellular network traffic at time tp; X t-p+1 Represents the cellular network traffic at time t-p+1.

3. The method for predicting spatiotemporal cellular network traffic based on frequency domain MLP as claimed in claim 1, characterized in that: The S2 includes: S2-1: Build a network traffic prediction model; S2-2: Decompose the historical data of cellular network traffic into seasonal data and trend data, and embed the seasonal data and trend data to obtain corresponding seasonal characteristics and trend characteristics; S2-3: Perform frequency domain conversion on the trend feature to extract first spatial data and first temporal data; perform frequency domain conversion on the seasonal feature to extract second spatial data and second temporal data; S2-4: Capturing multi-scale information from the first spatial data, the first temporal data, and the second spatial data, and the second temporal data to obtain a trend component output and a seasonal component output; S2-5: Output cellular network traffic forecast data based on the trend component output and the seasonal component output.

4. The method for predicting spatiotemporal cellular network traffic based on frequency domain MLP as claimed in claim 3, characterized in that: In S2-1, the network traffic prediction model includes a time decomposition embedding module, a frequency domain feature extraction module, a multi-scale spatiotemporal attention module and a deep convolution feedforward prediction module; wherein, A time decomposition and embedding module is used to decompose the historical data of cellular network traffic into seasonal data and trend data, and embed the seasonal data and trend data to obtain seasonal characteristics and trend characteristics; A frequency domain feature extraction module, used for performing frequency domain conversion on seasonal features and trend features, thereby extracting spatiotemporal features, including first spatial data, first temporal data, second spatial data, and second temporal data; The multi-scale spatiotemporal attention module is used to capture multi-scale information from spatiotemporal features through pooling and convolution operations at different scales to obtain trend component output and seasonal component output; The deep convolution feedforward prediction module is used to output cellular network traffic prediction data based on the trend component output and the seasonal component output.

5. The method for predicting spatiotemporal cellular network traffic based on frequency domain MLP as claimed in claim 3, characterized in that: The S2-2 includes: S2-2-1: Decompose the historical data of cellular network traffic into seasonal data and trend data: X Trend =AvgPool(Padding(X flatten )),X Seasonal =X flatten -X Trend (3) In formula (3), X Trend Indicates trend data; X Seasonal represents seasonal data; AvgPool represents moving average operation; Padding represents data padding; X flatten Represents cellular network traffic history data; S2-2-2: For the decomposed trend data X Trend and seasonal data X Seasonal Apply embedding operations respectively to obtain trend features and seasonal features; H Trend =X’ Trend ×θ d ∈R N×T×D (4) In formula (4), H Trend Represents trend characteristics, N represents the flow of N city grids, N = V*H, V represents the number of rows of grid division; H represents the number of columns of grid division; T represents the length of the time dimension, the number of time steps of the sequence, that is, the data of the past T time moments; D represents the dimension of the feature space after data embedding; Similarly, the seasonal characteristic H Seasonal for: H Seasonal =X’ Seasonal ×θ d ∈R N×T×D (5) In formula (5), H Seasonal Indicates seasonal characteristics; X' Seasonal Represents seasonal data X Seasonal The transpose of θ d represents a learnable vector.

6. The method for predicting spatiotemporal cellular network traffic based on frequency domain MLP as claimed in claim 3, characterized in that: The S2-3 includes: S2-3-1: Perform frequency domain conversion on trend characteristics to extract first spatial data; perform frequency domain conversion on seasonal characteristics to extract second spatial data; S2-3-2: Perform frequency domain conversion on trend characteristics to extract first time data; perform frequency domain conversion on seasonal characteristics to extract second time data.

7. The method for predicting spatiotemporal cellular network traffic based on frequency domain MLP as claimed in claim 6, characterized in that: The S2-3-1 includes: First, the trend feature H Trend ∈R N×T×D Transpose to H' Trend ∈R T×N×D ; Second, for each time step k∈ ( 1,T ) , applying fast Fourier transform to the trend features independently in the spatial dimension to obtain a spatial complex number: In formula (6), Represents the spatial complex number corresponding to the trend feature; F spatial represents fast Fourier transform; H' Trend represents the transposition of trend characteristics; D represents dimension; N represents the number of grids; C represents complex space; Next, use the MLP operation to process the spatial complex number corresponding to the trend feature to obtain the complex frequency domain signal of the trend feature: In formula (7), The first frequency domain signal representing the trend characteristics; MLP frequency-domain represents the MLP operation; W spatial represents the complex weight matrix, W spatial Real part of the complex matrix, dimension R D×D ; W spatial The imaginary part of the complex matrix, dimension R D×D ; j represents a complex unit; B spatial represents the complex bias, Represents the complex bias B spatial The real part of the dimension is R D ; Represents the complex bias B spatial The imaginary part of Then, the inverse fast Fourier transform is applied to convert the trend feature first frequency domain signal Convert back to the first time domain And the first time domain of T time steps Combined into the first time domain overall feature Z t ∈R T×N×D : In formula (8), Represents the first time domain signal of trend characteristics; represents inverse fast Fourier transform; Transpose the trend characteristics H' Trend Aggregate with the overall time domain features processed by the frequency domain feature extraction module: Z’ t =Z t +H’ Trend ∈R T×N×D (9) In formula (9), Z' t The first aggregated data representing trend characteristics; Z t The first time domain overall characteristic representing the trend characteristic; H' Trend Indicates trend feature transposition; Finally, the aggregated data Z' of the trend characteristics is t The dimension is converted to get Z" t ∈R N×T×D , Z” t The first spatial data representing trend characteristics.

8. The method for predicting spatiotemporal cellular network traffic based on frequency domain MLP as claimed in claim 3, characterized in that: The S2-5 includes: S2-5-1: Aggregate the trend component output and seasonal component to obtain the aggregate output; S2-5-2: The aggregated output is input into the final layer of the deep convolutional feedforward prediction module to generate cellular network traffic prediction data.

9. The method for predicting spatiotemporal cellular network traffic based on frequency domain MLP as claimed in claim 8, characterized in that: In S2-5-1, the aggregate output is: S ot =α×S st +(1-a)×S Tt ∈R N×T×D (10) In formula (10), S ot represents the aggregate output, S st ∈R N×T×D represents the seasonal component output after the multi-scale spatiotemporal attention module; S Tt ∈R N×T×D represents the output of the trend component; α represents the weighting parameter.

10. The method for predicting spatiotemporal cellular network traffic based on frequency domain MLP as claimed in claim 8, characterized in that: In S2-5-2, the method for calculating the cellular network traffic prediction data is: Y t =σ((S t Φ1+b1)Φ2+b2)Φ3+b3, In formula (15), Y t Indicates output; Y t represents the output; σ represents the activation function; S t represents the reshaping of the aggregation output; Φ1, Φ2, Φ3 all represent weights; b1, b2, b3 all represent biases; Indicates output Y t The final output after rearranging and reshaping the dimensions; Reshape indicates the activation function; Permute indicates the dimension exchange operation; dims = ( 0,2,1 ) Indicates the dimension conversion; X out represents cellular network traffic prediction data; MSD-FFN represents multi-scale feed-forward layer.

Images