A coarsely predicted guided conditional residual diffusion model channel prediction method

Abstract

This invention proposes a coarse prediction-guided conditional residual diffusion model channel prediction method. The method first obtains a coarse prediction of the future CSI based on historical Channel State Information (CSI) sequences. Then, using this coarse prediction as the prior mean of the reverse refinement process, a conditional residual diffusion forward process is constructed, transitioning from the true future CSI value to the noisy state in the coarse prediction neighborhood. Subsequently, a conditional reverse refinement network is trained to estimate residual correction terms and noise removal terms based on the diffusion state, diffusion step index, and relevant conditional information. Finally, a denoising diffusion implicit model (DDIM) is used for a few steps of reverse update to obtain the future CSI prediction result. This invention can recover fine-grained random variation information missed in the coarse prediction result while maintaining the overall evolution trend of the future channel, improving the prediction accuracy of complex time-varying channels. Furthermore, by constraining the reverse process within the coarse prediction neighborhood, it enhances generation stability, reduces the number of reverse sampling steps, and lowers inference latency.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication technology, and in particular relates to a coarse prediction-guided channel prediction method for MIMO-OFDM systems with conditional residual diffusion model. Background Technology

[0002] As massively multi-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) wireless communication systems develop towards high-speed mobility, massive MIMO antennas, and broadband transmission, channel state information (CSI) changes rapidly with time, frequency, and spatial dimensions. Accurate prediction of CSI in the future will be of great significance for beamforming, precoding, resource scheduling, and link adaptation.

[0003] Existing neural network-based channel prediction methods typically model the prediction process from historical CSI to future CSI as a deterministic mapping. For example, they employ structures such as Recurrent Neural Networks (RNNs), Long Short-Term Memory (LSTM) networks, Convolutional Neural Networks (CNNs), or Transformers to extract channel sequence correlations. These methods offer advantages such as fast inference speed and stable output, but they usually only provide deterministic point predictions, making it difficult to characterize the randomness and multimodal features of wireless channel evolution. They are also prone to oversmoothing predictions in complex time-varying scenarios. Generative methods such as Diffusion Models (DMs) can model the future CSI distribution through a reverse denoising process. However, existing diffusion-based channel prediction methods all start from purely random states such as standard Gaussian noise and generate the predictions backwards. This makes them highly dependent on the cleanliness and stability of historical CSI or other conditional information, and they typically require a large number of backward sampling steps, resulting in high inference complexity and latency.

[0004] Therefore, how to maintain the stability of the generation process while simultaneously considering prediction performance and inference speed is a critical technical problem that needs to be solved in time-varying MIMO-OFDM channel prediction. This invention proposes a coarse prediction-guided conditional residual diffusion channel prediction method, which is not limited to a specific coarse prediction network. It can use any coarse prediction result as the initial prior for the reverse refinement process and combine it with historical CSI or other relevant conditional information for residual correction, thereby achieving a better balance between generation stability, prediction accuracy, and inference efficiency. Summary of the Invention

[0005] This invention provides a coarse-prediction-guided Conditional Residual Diffusion Model (CoRDM) channel prediction method. The method first obtains the coarse prediction result corresponding to the future channel to be predicted, along with conditional information related to the channel. Then, using the coarse prediction result as the initial prior or initial center for the reverse refinement process, an initial refined state with controlled perturbations is constructed. Next, guided by the conditional information, the CoRDM model performs at least one reverse update on the initial refined state to gradually correct the residual error in the coarse prediction result. Finally, the future channel prediction result is output. Unlike diffusion-based methods that generate the future channel from a purely random noise state, this invention directly uses the coarse prediction result to determine the starting point of the reverse refinement process, enabling the model to primarily perform local residual correction rather than generating a complete future channel from a random initial state. This reduces the number of reverse sampling steps and inference complexity while maintaining generation stability.

[0006] In one implementation, the coarse prediction result can be generated by any coarse prediction module, including but not limited to traditional extrapolation predictors, filters, low-rank approximation models, physical parameter tracking models, neural network predictors, autoencoder (AE) feature predictors, Transformer predictors, long short-term memory networks (LSTM), recurrent neural network (RNN) predictors, convolutional neural network (CNN) predictors, or combinations thereof. The coarse prediction result can be a channel prediction result for a future time period or a channel sequence prediction result composed of multiple future time periods. It should be understood that the specific structure of the coarse prediction module does not constitute a limitation on the scope of protection; as long as it can generate initial prediction results related to the future channel to be predicted, it can be used as the coarse prediction module in this patent.

[0007] In one implementation, the conditional information includes one or more of the following: historical channel state information (CSI), historical channel estimation results, pilot observation signals, channel feature representation, terminal speed, terminal location, motion trajectory, carrier frequency, subcarrier index, antenna array structure, scene category, propagation environment information, uplink measurement information, and interference statistics. The conditional information can be directly input into the conditional residual diffusion model, or it can be mapped to a latent space representation via a feature extraction module before being input into the conditional residual diffusion model. The source, dimension, and fusion method of the conditional information do not constitute a limitation on the scope of protection.

[0008] The technical solution adopted in this invention is as follows:

[0009] A coarse prediction-guided conditional residual diffusion model channel prediction method includes the following steps:

[0010] S1. Construct training samples, specifically: Define Indicates an instant in time The Channel State Information (CSI) matrix is ​​used to obtain the continuously acquired CSI sequence, in instantaneous time. For reference, the continuous Stacking the CSI matrices of historical moments along the time dimension yields the historical CSI sequence:

[0011] ,

[0012] in, Indicates the length of historical observations. Indicates the historical CSI sampling interval. This indicates that multiple CSI matrices are stacked along the time dimension. This represents a CSI sequence formed by CSI matrices from multiple historical moments;

[0013] Reference time After Stacking the CSI matrices at future moments along the time dimension yields a sequence of true future CSI values:

[0014] ,

[0015] in, Indicates the predicted length of the future. Indicates the future forecast interval;

[0016] Construct conditional information related to the future CSI to be predicted, denoted as ;

[0017] Thus, training samples are obtained. ,in, This represents the sample index; multiple training samples constitute the dataset. ,in, Indicates the total number of samples;

[0018] S2. Perform a coarse prediction of future CSI using the coarse prediction module, specifically: based on the historical CSI sequence constructed in S1. The coarse prediction results of the future CSI sequence are obtained, and this coarse prediction module is denoted as... ,in This represents its trainable parameters, and the future coarse prediction sequence of CSI is denoted as . ,in, Compared with the future CSI true value sequence obtained in S1 They have the same time dimension and channel dimension;

[0019] The coarse prediction module employs supervised training, with the goal of making the coarse prediction results directly approximate the future CSI true value sequence. Normalized mean squared error is used as the coarse prediction loss.

[0020] ;

[0021] S3, the future CSI truth sequence constructed based on S1 And the coarse prediction sequence of future CSI obtained from S2 The forward diffusion process of constructing the Conditional Residual Diffusion Model (CoRDM) is as follows:

[0022] Let the clean diffusion target be the future CSI truth value sequence, i.e.:

[0023] ,

[0024] in, Indicates the diffusion step as The clean state at time is a sequence of future CSI ground truth values ​​formed by stacking multiple future CSI matrices; the residual between the coarse prediction sequence and the future CSI ground truth sequence is defined as:

[0025] ,

[0026] in, This indicates the deviation of the coarse prediction result from the true value of the future CSI, and is used to characterize the direction and magnitude of correction needed in the subsequent refinement process;

[0027] Define the total number of forward diffusion steps as The diffusion step index is ,make and Let represent the residual scheduling coefficient and the noise scheduling coefficient, respectively, and define the cumulative residual intensity and the cumulative noise intensity as follows:

[0028] ,

[0029] in, The extent to which the diffusion state shifts from the future CSI true value sequence to the coarse prediction sequence. Control the intensity of random disturbances in the diffusion state; set This allows the forward diffusion terminal state to use the coarse prediction sequence as the initial mean;

[0030] The joint distribution of forward diffusion in CoRDM is defined as:

[0031] ,

[0032] in, This indicates a pre-defined forward diffusion process. Indicates the first The future CSI sequence state for each diffusion step corresponds to the single-step transition distribution as follows:

[0033] ,

[0034] This indicates that in each forward diffusion step, the state is... First, along the residual direction move Meanwhile, variance is added. , where for It is composed of stacked identity matrices. ;

[0035] The first step can be obtained by recursion through single-step transitions. Edge reparameterization form for each diffusion step:

[0036] ,

[0037] The corresponding edge distribution is:

[0038] ;

[0039] In any diffusion step Below, the diffusion state changes from the Clean Future CSI state. Residual injection items Noise disturbance item It consists of three parts;

[0040] when and At that time, the final future CSI diffusion state is obtained as follows:

[0041] ;

[0042] in, For noise;

[0043] S4. Design and train the CoRDM network, specifically:

[0044] Based on the forward diffusion process in S3, the CoRDM network is made to adjust according to the current diffusion state. diffusion step and condition information Estimate the residual terms introduced during the forward diffusion process. and noise terms ; Let CoRDM network be denoted as ,in, Indicate its trainable parameters, then the CoRDM network learns the mapping:

[0045] ,

[0046] in, For S3 The future CSI sequence state of each diffusion step For conditional information related to future CSI forecasts, For the diffusion step index, and These represent the residual estimate and noise estimate of the network output, respectively. During training, for each training sample, the coarse prediction sequence of future CSI obtained from S2 is first used. The future CSI truth sequence obtained from S1 Calculate residual monitoring objectives:

[0047] ,

[0048] Subsequently, from the diffusion step set In the random sampling diffusion step And sample noise:

[0049] ,

[0050] Construct the network input state based on the forward diffusion relationship in S3:

[0051] ,

[0052] Therefore, the network input corresponding to the current training sample is The target of network supervision is The CoRDM network is trained by minimizing the residual supervision loss and the noise supervision loss. The training loss function is defined as:

[0053] ,

[0054] in, and These represent the weight coefficients of the residual monitoring term and the noise monitoring term, respectively;

[0055] S5. After training the CoRDM network in S4, use the trained network parameters to perform backward inference for future CSIs. Employ a few-step backward update method based on a noise-reducing diffusion implicit model, updating only when... Reverse refinement is performed on the sparse subsequence composed of diffusion steps, where Suppose the diffusion step sequence used in CoRDM-DDIM reverse inference is as follows:

[0056] ,

[0057] in, Indicates the first The diffusion step index corresponding to each reverse refinement step. This indicates the actual number of inference steps set; the diffusion step sequence is selected from the complete diffusion step set through uniform sampling, non-uniform sampling, segmented sampling, or other methods set according to application requirements;

[0058] Based on S2, a coarse prediction sequence for future CSI is obtained. And the forward diffusion terminal state in S3:

[0059] ,

[0060] During inference, the reverse initial state is set within the neighborhood of the coarse prediction sequence, i.e.:

[0061] ,

[0062] in, This represents the initial reverse state during the reasoning phase;

[0063] For any reverse refinement step , the current state Diffusion step index and condition information Input the trained CoRDM network to obtain the residual estimate and noise estimate for the current step:

[0064] ,

[0065] in, This represents the network parameters after CoRDM training. This represents the residual estimate under the current backward step. This represents the noise estimate under the current backward step;

[0066] Based on the edge reparameterization relation in S3, the clean future CSI estimate corresponding to the current state is obtained by the following equation:

[0067] ;

[0068] In the random reverse update form, from Jump to The single-step reverse state transition is written as:

[0069] ,

[0070] in, , Used to control randomness in reverse updates;

[0071] Repeat the reverse update process until it reaches... The final output of the future CSI prediction is:

[0072] ,

[0073] in, This represents the final future CSI prediction sequence output by CoRDM.

[0074] Furthermore, in S2, the coarse prediction module adopts an encoder-type Transformer structure based on a channel attention mechanism. The coarse prediction process is as follows:

[0075] S21. Construct features from historical CSI sequences, Matrix transformation into:

[0076] ,

[0077] in, This indicates an operation that expands the historical CSI sequence into a matrix along the channel dimension. This indicates the number of channels after expansion; Each row corresponds to a channel "token", which is used in... The values ​​at each historical moment represent the temporal evolution characteristics of that channel position;

[0078] S22. A linear layer is used to map the historical time features of each channel "token" to the hidden dimension. At the same time, channel position embedding is added to distinguish different channel positions. The initial hidden representation is obtained as follows:

[0079] ,

[0080] in, For the input projection matrix, The bias matrix, This represents the hidden dimension, therefore ;

[0081] S23, Regarding the first Layer channel attention module, input is The query matrix, key matrix, and value matrix are obtained through linear projection:

[0082] ,

[0083] in, , The feature dimension of a single attention head is represented; the channel attention matrix and its output are:

[0084] ,

[0085] In the case of multi-head attention, the outputs of different attention heads are concatenated and obtained by output projection:

[0086] ,

[0087] in, Indicates the number of heads of attention. This indicates concatenation along the feature dimension. Indicates the output projection matrix;

[0088] Subsequently, residual connections, normalization, and a feedforward network are used to obtain the output of this layer:

[0089] ,

[0090] in, Representation layer normalization, Indicates the first Layered feedforward network; stacking channel attention modules After the layer, the hidden representation with enhanced channel correlation is obtained. Finally, the hidden dimensions are mapped to the future time dimension using the prediction output head, resulting in the expanded form of the coarse prediction matrix for future CSI:

[0091] ,

[0092] in, , ,therefore ;

[0093] S24. Restore the coarse CSI prediction matrix to the form of future CSI sequences through inverse matrix transformation. , This is a future CSI coarse prediction sequence formed by stacking coarse prediction CSI matrices from multiple future moments along the time dimension.

[0094] Furthermore, in S3, the CoRDM network is a two-dimensional UNet network. The UNet network takes the spliced ​​diffusion state and condition information as input, and provides the current diffusion step information to each layer of the network through diffusion step embedding. The specific processing procedure is as follows:

[0095] 1) Input feature extraction and diffusion step embedding: embed the current diffusion state With conditional information The network input is obtained by concatenating the data along the channel dimension. Subsequently, convolutional layers were used to... Initial feature extraction is performed to obtain an initial feature map. At the same time, the diffusion step index will be used. The input sinusoidal position encoding module is mapped to a diffusion time step embedding via a multilayer perceptron:

[0096] ,

[0097] This diffusion time step embedding is used to modulate intermediate features in subsequent residual blocks, enabling the network to distinguish residual and noise distributions at different diffusion steps;

[0098] 2) Encoder Feature Extraction: Assume the encoder includes... Layer downsampling module, the first The input of the layer encoder is denoted as ,in Each encoder layer includes, in sequence: A residual block, a linear attention module, and a downsampling operation; for the _th _ ... The first layer There are n residual blocks, and the input features are denoted as... ,in The processing flow is as follows:

[0099] ,

[0100] in, express convolution, Indicates group normalization, Indicates the activation function of the SigmoidLinear Unit; diffusion time step embedding. The scale modulation term and bias modulation term are generated by the multilayer perceptron (MLP), and the processing flow is shown in the following equation:

[0101] ,

[0102] in, This represents element-wise multiplication. This represents a multilayer perceptron; subsequently, the second convolutional sub-block further extracts features, and the processing flow is shown in the following equation:

[0103] ;

[0104] Add the output of the second convolutional sub-block to the residual jump branch to obtain the output of the residual block:

[0105] ,

[0106] in, This represents a residual jump mapping; when the number of input channels is the same as the number of output channels... It is an identity mapping; when the two are inconsistent, Depend on Convolution achieves channel matching; after After obtaining a residual block, we get ;

[0107] right Perform linear attention operations, let ,make The number of "tokens" in the representation space is first obtained through... Convolution yields the features of the query matrix, key matrix, and value matrix:

[0108] ,

[0109] After multiple rearrangements, the following is obtained: ,in Indicates the number of heads of attention. This represents the channel dimension of each attention head; in the linear attention module, the query matrix is ​​normalized along the channel dimension, the key matrix is ​​normalized along the spatial "token" dimension, and the value matrix is ​​scale-normalized, resulting in:

[0110] ;

[0111] Calculate the feature attention matrix between the key matrix and the value matrix:

[0112] ,

[0113] Then, the attention output is obtained based on the features of the context attention matrix and the query matrix:

[0114] ,

[0115] Finally, the multi-head outputs are rearranged into two-dimensional feature maps and then processed... Output projection and normalization yield linear attention output:

[0116] ;

[0117] No. The layer encoder obtains the input for the next layer through a downsampling operation:

[0118] ,

[0119] in, From step size The convolutional implementation is used to reduce spatial resolution and improve channel expressiveness. The intermediate features generated by each residual block or attention module in the layer are saved as skip connection features for use by the corresponding decoding layer;

[0120] 3) Intermediate layer global feature interaction: Completed After processing by the layer encoder, the encoded features at the lowest resolution are obtained. The intermediate layer consists of a residual block, a standard attention module, and another residual block, and the processing flow is shown in the following formula:

[0121] ,

[0122] The internal processing of the intermediate residual blocks is consistent with that of the residual blocks in the encoder, namely, feature updating is completed through two convolutional sub-blocks, group normalization, SiLU activation, diffusion time-step modulation, and residual skip branches; the standard attention module of the intermediate layer is used to model global dependencies at the lowest spatial resolution. ,make First through Convolution yields the features of the query matrix, key matrix, and value matrix, which are then rearranged using a multi-head algorithm. The standard attention weights and outputs are as follows:

[0123] ,

[0124] Will Rearranged back into a two-dimensional feature map, and then... The output projection yields the standard attention output;

[0125] 4) Decoder Feature Recovery: Assume the decoder includes... Layer upsampling module, number The input to the layer decoder is denoted as ,in , Each decoder layer sequentially performs skip connection splicing, A residual block, a linear attention module, and an upsampling operation; for the _th The first layer For each residual block, the current decoded feature is first concatenated with the skip connection feature saved by the corresponding encoder:

[0126] ,

[0127] in, , This represents the encoder skip connection features corresponding to the current decoding layer; then the features are updated through residual blocks:

[0128] ,

[0129] The decoder residual block also includes two convolutional sub-blocks, group normalization, SiLU activation, diffusion time-step modulation, and residual jump branches. After each residual block, a linear attention module is used to model the spatial correlation at the current resolution:

[0130] ,

[0131] The input to the next decoding layer is obtained through upsampling:

[0132] ,

[0133] in, It consists of nearest neighbor upsampling and convolution, and is used to progressively restore the spatial resolution of the feature map;

[0134] 5) Output head and single / dual network settings: After After layer decoding, the final decoded features are compared with the initial features retained at the input. The parts are assembled, and then passed through a residual block, and finally through a... Convolution yields the network output, and the processing flow is shown in the following formula:

[0135] ;

[0136] When using a single UNet network, the network output is as follows. The output channel is divided into residual estimation terms and noise estimation terms:

[0137] ;

[0138] When using two UNet networks, set up the residual prediction network. and noise prediction network At this time, the output of a single network That is, the two UNet outputs are respectively obtained as follows:

[0139] .

[0140] Furthermore, in S5, Set to:

[0141] ,

[0142] in, For randomness control parameters; when When, the reverse update contains random perturbations; when At that time, reverse update degenerates into deterministic update; in the form of deterministic reasoning, let ,but At this point, the update expression simplifies to:

[0143] ,

[0144] Support from arrive The skip-step update, without needing to traverse the entire... One diffusion step, therefore, when Even with a smaller value, it is still possible to achieve rapid refinement from the neighborhood of the coarse prediction sequence to the final future CSI prediction result.

[0145] The beneficial effects of this invention are as follows:

[0146] 1) Improve the accuracy of future CSI prediction in complex time-varying scenarios. This invention introduces a Conditional Residual Diffusion Model (CoRDM) to refine the prediction based on the coarse prediction results. This method overcomes the limitations of traditional deterministic prediction models in characterizing the random variations and multimodal uncertainties in complex time-varying channels. It enables the network not only to learn the overall evolution trend of the future channel, but also to further recover the fine-grained random variation information missed in the coarse prediction results. This improves the ability to characterize the multimodal and random variations in complex time-varying wireless channels, thereby improving the accuracy of future CSI prediction in high-speed mobile, massive MIMO, and broadband transmission scenarios.

[0147] 2) Enhancing the generation stability of diffused channel prediction. Existing diffused channel prediction methods typically start from a purely random state such as standard Gaussian noise and generate in reverse. This method is highly dependent on the cleanliness and stability of historical CSI or other conditional information, and is prone to unstable generation trajectories when conditions are affected by noise, estimation errors, or time delay mismatches. This invention uses the coarse prediction result of future CSI as the prior mean of the backward diffusion process of the Conditional Residual Diffusion Model (CoRDM). This allows the backward process to start from a coarse prediction neighborhood close to the target future CSI, and to perform residual correction and noise removal around this neighborhood. This reduces the generation uncertainty caused by pure noise initialization and improves the prediction robustness under low-quality input conditions.

[0148] 3) Reduce backsampling steps and inference latency in diffusion models. Existing diffusion models typically require a large number of backsampling steps to gradually recover the target CSI from random noise, resulting in high inference complexity and latency. This invention transforms the complete future CSI generation problem into a local residual refinement problem within the coarse prediction neighborhood, allowing the backsampling network to primarily learn residual correction terms and noise removal terms. Combined with DDIM-style skip-step backsampling inference, future CSI prediction results can be obtained with fewer backsampling update steps, thereby reducing computational complexity and inference latency, making it suitable for MIMO-OFDM wireless communication systems with high real-time requirements.

[0149] 4) It possesses strong versatility and scalability. This invention does not limit the specific structure of the coarse prediction module; the coarse prediction result can be obtained from a neural network predictor, a traditional extrapolation model, a filtering model, a low-rank prediction model, a physical parameter tracking model, or other prediction methods. Conditional information can also include historical CSI, perturbed historical CSI, channel estimation results, terminal motion information, or other relevant auxiliary information. Therefore, this invention can adapt to different channel representations, different prediction network structures, and different communication scenarios. Attached Figure Description

[0150] Figure 1 A schematic diagram of the coarse prediction-guided conditional residual diffusion model (CoRDM) channel prediction framework provided in an embodiment of the present invention.

[0151] Figure 2 This is a simulation result diagram showing the variation of the channel prediction normalized mean square error (NMSE) with future prediction time slots under different user terminal mobility scenarios according to an embodiment of the present invention. Figure 2 (a) Scenario corresponding to a user terminal moving at a speed of 30 km / h, Figure 2 (b) Scenario corresponding to a user terminal moving speed of 90 km / h, Figure 2 (c) The scenario where the user terminal moves at a speed of 120 km / h.

[0152] Figure 3 This figure shows the simulation results of the channel prediction normalized mean square error (NMSE) as a function of future prediction time slots under different historical conditions and channel signal-to-noise ratio (SNR) scenarios when the user terminal moves at a speed of 30 km / h, according to an embodiment of the present invention. Figure 3 (a) Scenarios corresponding to historical conditional channel SNR=0 dB Figure 3 (b) Scenario corresponding to historical conditional channel SNR=10 dB, Figure 3 (c) Scenarios corresponding to historical condition channel SNR=20 dB.

[0153] Figure 4 The Coarse Prediction Guided Conditional Residual Diffusion Model (CoRDM-DDIM) proposed in this embodiment of the invention is used at different backsampling steps. The simulation results show the variation of the channel prediction normalized mean square error (NMSE) with future prediction slots under the given conditions. Detailed Implementation

[0154] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments.

[0155] This invention includes the following steps:

[0156] S1. Constructing training samples for the coarse prediction module and the CoRDM network: Let... Indicates an instant in time The CSI matrix. For example, It can be the spatial frequency domain CSI, the angular delay domain CSI, the equivalent real-valued CSI after separating the real and imaginary parts, or a CSI matrix obtained from other channel representation methods. If in complex form, it is represented as... ,in Indicates the antenna-related dimensions. This represents the subcarrier or frequency dimension. If a real / imaginary separation method is used, then... The equivalent representation is a real-valued matrix or tensor, and its specific representation does not constitute a limitation on the scope of protection.

[0157] Given a continuously acquired CSI sequence, in terms of instantaneous time... For reference, the continuous Stacking the CSI matrices of historical moments along the time dimension yields the historical CSI sequence:

[0158] ,

[0159] in, Indicates the length of historical observations. Indicates the historical CSI sampling interval. This indicates that multiple CSI matrices are stacked along the time dimension. Therefore, This represents a CSI sequence formed by CSI matrices at multiple historical moments, rather than a CSI matrix at a single moment.

[0160] Correspondingly, the reference time After Stacking the CSI matrices at future moments along the time dimension yields a sequence of true future CSI values:

[0161] ,

[0162] in, Indicates the predicted length of the future. This indicates the future prediction interval. On the one hand, it can be used as the supervised ground truth during the training of the coarse prediction module, and on the other hand, it can also be used as the target future CSI sequence during the subsequent CoRDM training.

[0163] In one implementation, if the CSI at a single moment is represented using a real-to-virtual partitioning method, then... Then the historical CSI sequence and the future CSI truth sequence can be represented as follows:

[0164] ,

[0165] If we consider batch samples, the corresponding dimension can be represented as:

[0166] ,

[0167] in, Indicates the batch size.

[0168] To enhance the model's robustness to observation errors, estimation errors, or conditional perturbations, in one alternative implementation, perturbations can be introduced into the historical CSI sequence or other conditional information. For example, a perturbed historical CSI sequence is constructed:

[0169] ,

[0170] in, The historical CSI perturbation term can be additive Gaussian noise, channel estimation error, quantization error, feedback error, interpolation error, or other forms of observation perturbation. The perturbation strength can be randomly sampled based on a preset signal-to-noise ratio range or determined based on the actual system measurement error. During training, the coarse prediction module and the CoRDM network can use... or As input to improve prediction stability under low-quality conditions, as described later. and No distinction is made.

[0171] Furthermore, conditional information related to the future CSI to be predicted can be constructed, denoted as... The condition information may include historical CSI sequences. CSI sequences with perturbations The conditional information includes one or more of the following: channel estimation results, channel feature representation, terminal speed, terminal location, motion trajectory, carrier frequency, subcarrier index, antenna array structure, scene category, propagation environment information, uplink measurement information, and interference statistics. The conditional information can be obtained directly by concatenating the above information, or it can be obtained by a feature extraction network, encoder, mapping function, or other processing modules. The specific source, dimension, concatenation method, and feature extraction method of the conditional information do not constitute a limitation on the scope of protection.

[0172] Thus, a training sample can be obtained. .in, This represents the sample index. A dataset consists of multiple training samples. .in, This represents the total number of samples. The dataset can be further divided into training, validation, and test sets for coarse prediction module training, CoRDM network training, hyperparameter selection, and performance evaluation.

[0173] S2. Coarse Prediction of Future CSI: In an optional implementation, the present invention provides a coarse prediction module for predicting future CSI based on the historical CSI sequence constructed in S1. This yields a coarse prediction of the future CSI sequence. Let this coarse prediction module be denoted as... ,in This represents its trainable parameters. The input to the coarse prediction module can be a historical CSI sequence. It can also be an input consisting of historical CSI sequences and other relevant conditional information. Its output is a coarse prediction sequence of future CSI. ,in, Compared with the future CSI true value sequence obtained in S1 It has the same time and channel dimensions. This coarse prediction is used as the initial mean for the subsequent forward diffusion and backward inference processes in the CoRDM network.

[0174] The coarse prediction module provided by this invention employs supervised training, with the training objective of making the coarse prediction result directly approximate the future CSI true value sequence. Normalized mean square error is used as the coarse prediction loss.

[0175] .

[0176] Therefore, the coarse prediction module learns a deterministic coarse prediction mapping from historical CSI sequences to future CSI sequences, and its role is to provide the subsequent CoRDM network with an initial prediction result that is close to the target future CSI.

[0177] The coarse prediction module employs an encoder-based Transformer structure with a channel attention mechanism. This structure models the channel correlations in historical CSI sequences through an encoder-based attention module and directly obtains the coarse prediction results for future CSIs through output mapping. Specifically:

[0178] S21. Construct features from historical CSI sequences, Matrix transformation into:

[0179] ,

[0180] in, This represents a matrix operation that unfolds the real and imaginary components, antenna dimension, and frequency dimension in the historical CSI sequence into a channel dimension. This represents the number of channels after expansion. For example, when the CSI at a single moment uses a real-virtual partitioning, and the antenna correlation dimension is... Frequency dimension hour, .at this time, Each row corresponds to a channel "token", which is used in... The values ​​at each historical moment represent the temporal evolution characteristics of that channel position.

[0181] S22. A linear layer is used to map the historical time features of each channel "token" to the hidden dimension. At the same time, channel position embedding is added to distinguish different channel positions. The initial hidden representation is obtained as follows:

[0182] ,

[0183] in, For the input projection matrix, The bias matrix, This represents the hidden dimension, therefore .

[0184] S23, Regarding the first Layer channel attention module, input is The query matrix, key matrix, and value matrix are obtained through linear projection:

[0185] ,

[0186] in, , This represents the feature dimension of a single attention head. The channel attention matrix and its output are:

[0187] ,

[0188] in, This is used to characterize the correlation between channel "tokens" corresponding to different real and imaginary components, antenna positions, and frequency positions. In the case of multi-head attention, the outputs of different attention heads are concatenated and projected to obtain:

[0189] ,

[0190] in, Indicates the number of heads of attention. This indicates concatenation along the feature dimension. This indicates the output projection matrix.

[0191] Subsequently, residual connections, normalization, and a feedforward network are used to obtain the output of this layer:

[0192] ,

[0193] in, Representation layer normalization, Indicates the first Layered feedforward network. Stack the above channel attention modules. After the layer, the hidden representation with enhanced channel correlation is obtained. Finally, the hidden dimensions are mapped to the future time dimension using the prediction output head, resulting in the expanded form of the coarse prediction matrix for future CSI:

[0194] ,

[0195] in, , ,therefore .

[0196] S24. Then, through the inverse matrix transformation operation, it is restored to the form of a future CSI sequence. The aforementioned That is, a future CSI coarse prediction sequence formed by stacking coarse prediction CSI matrices from multiple future moments along the time dimension;

[0197] S3. Coarse Prediction-Guided Conditional Residual Diffusion Forward Process: Future CSI True Value Sequence Constructed Based on S1 And the coarse prediction sequence of future CSI obtained from S2 The forward diffusion process of CoRDM is constructed. This forward diffusion process is used to describe how the future CSI ground truth sequence gradually transitions to a noisy state centered on the coarse prediction sequence, thereby providing the diffusion state, residual supervision target, and noise supervision target for the subsequent reverse refinement network.

[0198] Let the clean diffusion target be the future CSI truth value sequence, i.e.:

[0199] ,

[0200] in, Indicates the diffusion step as The clean state at time t is a sequence of future CSI ground truth values ​​formed by stacking multiple future CSI matrices. Further, the residual between the coarse prediction sequence and the future CSI ground truth sequence is defined as:

[0201] ,

[0202] in, This indicates the deviation of the coarse prediction result from the true value of the future CSI, and is used to characterize the direction and magnitude of correction needed in the subsequent refinement process.

[0203] Let the total number of forward diffusion steps be The diffusion step index is .make and Let represent the residual scheduling coefficient and the noise scheduling coefficient, respectively, and define the cumulative residual intensity and the cumulative noise intensity as follows:

[0204] ,

[0205] in, The extent to which the diffusion state shifts from the future CSI true value sequence to the coarse prediction sequence. Control the intensity of random perturbations in the diffusion state. (Settings) This allows the forward diffusion terminal state to use the coarse prediction sequence as its initial mean.

[0206] The joint distribution of forward diffusion in CoRDM is defined as:

[0207] ,

[0208] in, This indicates a pre-defined forward diffusion process. Indicates the first The future CSI sequence states of each diffusion step. The corresponding single-step transition distribution is:

[0209] ,

[0210] This formula indicates that, in each forward diffusion step, the state... First, along the residual direction move Meanwhile, variance is added. , where for It is composed of stacked identity matrices. .

[0211] From the above single-step transfer recursion, we can obtain the first... Edge reparameterization form for each diffusion step:

[0212] ,

[0213] The corresponding edge distribution is:

[0214] .

[0215] Therefore, in any diffusion step Below, the diffusion state changes from the Clean Future CSI state. Residual injection items Noise disturbance item It consists of three parts.

[0216] when and At that time, the future CSI diffusion state at the endpoint can be obtained as follows:

[0217] .

[0218] The forward diffusion terminal distribution of CoRDM does not use pure Gaussian noise as the initial mean, but rather uses the future coarse prediction sequence of CSI as the initial mean, superimposed with... Controlled random perturbations. This design allows the subsequent reverse process to refine the conditional residual diffusion around the coarse prediction, thereby avoiding the over-reliance on historical CSI and conditional information by traditional diffusion models that generate complete future CSI sequences from purely random initial states.

[0219] Based on the aforementioned forward process, during the training phase, it is possible to... Arbitrary diffusion step in mid-sampling Resampling and through Construct the diffused input states for the reverse network. Meanwhile, and These serve as the residual and noise supervision targets for the subsequent CoRDM network, respectively. During the training of the subsequent CoRDM network, the inverse network can be based on the current diffusion state. diffusion step Condition information and coarse prediction sequence Learn to predict the residual at each diffusion step ,noise ;

[0220] S4. Design and train the CoRDM network, specifically:

[0221] Based on the forward diffusion process described in S3, the CoRDM network adjusts according to the current diffusion state. diffusion step and condition information Estimate the residual terms introduced during the forward diffusion process. and noise terms Let CoRDM network be... ,in, This represents its trainable parameters. The CoRDM network then learns the following mapping:

[0222] ,

[0223] in, For S3 The future CSI sequence state of each diffusion step For conditional information related to future CSI forecasts, For the diffusion step index, and These represent the residual estimate and noise estimate of the network output, respectively. During training, for each training sample, the coarse prediction sequence of future CSI is first obtained based on S2. The future CSI truth sequence obtained from S1 Calculate residual monitoring objectives:

[0224] ,

[0225] Subsequently, from the diffusion step set In the random sampling diffusion step And sample noise:

[0226] ,

[0227] Construct the network input state based on the forward diffusion relationship in S3:

[0228] ,

[0229] Therefore, the network input corresponding to the current training sample is The target of network supervision is The CoRDM network is trained by minimizing residual supervision loss and noise supervision loss. The training loss function is defined as:

[0230] ,

[0231] in, and These represent the weight coefficients of the residual supervision term and the noise supervision term, respectively. Through this loss function, the network simultaneously learns the directional residual correction corresponding to the coarse prediction error, as well as the random noise perturbation introduced during the forward diffusion process. In one embodiment, this invention provides a two-dimensional UNet network as a CoRDM network. The UNet network takes the spliced ​​diffusion state and condition information as input, and provides the current diffusion step information to each layer of the network through diffusion step embedding. The specific steps are as follows:

[0232] 1) Input feature extraction and diffusion step embedding: embed the current diffusion state With conditional information The network input is obtained by concatenating the data along the channel dimension. Subsequently, convolutional layers were used to... Initial feature extraction is performed to obtain an initial feature map. At the same time, the diffusion step index will be... The input sinusoidal position encoding module is mapped to a diffusion time step embedding via a multilayer perceptron:

[0233] ,

[0234] This diffusion time step embedding is used to modulate intermediate features in subsequent residual blocks, enabling the network to distinguish residual and noise distributions at different diffusion steps.

[0235] 2) Encoder Feature Extraction: Assume the encoder includes... Layer downsampling module. The input of the layer encoder is denoted as ,in Each encoder layer includes, in sequence: One residual block, one linear attention module, and one downsampling operation. For the first... The first layer There are n residual blocks, and the input features are denoted as... ,in The processing flow is shown in the following formula:

[0236]

[0237] in, express convolution, Indicates group normalization, This represents the activation function of the SigmoidLinear Unit. Diffusion time-step embedding. The scale modulation term and bias modulation term are generated by a multi-layer perceptron (MLP), and the processing flow is shown in the following equation:

[0238]

[0239] in, This represents element-wise multiplication, where This represents a multilayer perceptron. Subsequently, the second convolutional block further extracts features, and the processing flow is shown in the following equation:

[0240]

[0241] Add the output of the second convolutional sub-block to the residual jump branch to obtain the output of the residual block:

[0242] .

[0243] in, This represents the residual jump mapping. When the number of input channels matches the number of output channels... It is an identity mapping; when the two are inconsistent, Depend on Convolution achieves channel matching. After... After obtaining a residual block, we get .

[0244] right Perform linear attention operations. Let... ,make The number of "tokens" in the representation space. First, through... Convolution yields the features of the query matrix, key matrix, and value matrix:

[0245] ,

[0246] After multiple rearrangements, the following is obtained: ,in Indicates the number of heads of attention. This represents the channel dimension of each attention head. In the linear attention module, the query matrix is ​​normalized along the channel dimension, the key matrix is ​​normalized along the spatial "token" dimension, and the value matrix is ​​scale-normalized, resulting in:

[0247]

[0248] Calculate the feature attention matrix between the key matrix and the value matrix:

[0249] ,

[0250] Then, the attention output is obtained based on the features of the context attention matrix and the query matrix:

[0251] ,

[0252] Finally, the multi-head outputs are rearranged into two-dimensional feature maps and then processed... Output projection and normalization yield linear attention output:

[0253] .

[0254] The above linear attention is first constructed The characteristic matrix, without explicitly constructing The spatial attention matrix is ​​therefore suitable for modeling high-resolution feature maps in the encoder. Its main complexity can be derived from standard attention... Reduced to It has a greater inference speed advantage in higher-dimensional frequency-space domain CSI scenarios. The layer encoder obtains the input for the next layer through a downsampling operation:

[0255] ,

[0256] in, It can be determined by the step size. The convolutional implementation is used to reduce spatial resolution and improve channel expressiveness. The intermediate features generated by each residual block or attention module in the layer are saved as skip connection features for use by the corresponding decoding layer.

[0257] 3) Intermediate layer global feature interaction: Completed After processing by the layer encoder, the encoded features at the lowest resolution are obtained. The intermediate layer consists of a residual block, a standard attention module, and another residual block. The processing flow is shown in the following equation:

[0258]

[0259] The internal processing of the intermediate residual blocks is consistent with that of the residual blocks in the encoder, namely, feature updating is achieved through two convolutional sub-blocks, group normalization, SiLU activation, diffusion time-step modulation, and residual skip branches. The standard attention module in the intermediate layers is used to model global dependencies at the lowest spatial resolution. Let... ,make First through Convolution yields the features of the query matrix, key matrix, and value matrix, which are then rearranged using a multi-head algorithm. The standard attention weights and outputs are as follows:

[0260]

[0261] Will Rearranged back into a two-dimensional feature map, and then... The output projection yields the standard attention output. Due to the low resolution of the intermediate layers, standard attention can capture global spatial correlations with an acceptable computational cost.

[0262] 4) Decoder Feature Recovery: Assume the decoder includes... Layer-level sampling module. The input to the layer decoder is denoted as ,in , Each decoder layer sequentially performs skip connection splicing. One residual block (here) (Similar to the encoder), a linear attention module and an upsampling operation. For the first... The first layer For each residual block, the current decoded feature is first concatenated with the skip connection feature saved by the corresponding encoder:

[0263] ,

[0264] in, , This represents the encoder skip connection features corresponding to the current decoding layer. Then, the features are updated using residual blocks (here, residual blocks...). (Same as described in the encoder)

[0265] ,

[0266] The decoder residual block also includes two convolutional sub-blocks, group normalization, SiLU activation, diffusion time-step modulation, and residual jump branches. After each residual block, a linear attention module is used (here, the linear attention mechanism module). (Same as described in the encoder) Further model the spatial correlation at the current resolution:

[0267] ,

[0268] The input to the next decoding layer is obtained through upsampling:

[0269] ,

[0270] in, It can consist of nearest-neighbor upsampling and convolution to progressively restore the spatial resolution of the feature map. Through the above skip connections and upsampling process, the decoder can fuse the detailed information in the encoder with the global semantic information in the intermediate layers, thereby improving the estimation accuracy of the residual and noise terms.

[0271] 5) Output head and single / dual network settings: After After layer decoding, the final decoded features are compared with the initial features retained at the input. Perform splicing, and pass through a residual block (here, the residual block) (Same as described in the encoder), finally through a Convolution yields the network output, and the processing flow is shown in the following formula:

[0272]

[0273] When using a single UNet network, the network output is as follows. The output channel is divided into residual estimation terms and noise estimation terms:

[0274] .

[0275] When using two UNet networks, set up the residual prediction network. and noise prediction network At this time, the output of a single network That is, the two UNet outputs are respectively obtained as follows:

[0276]

[0277] This approach models residual estimation and noise estimation separately, enabling the two networks to learn directional residual correction and random perturbation removal respectively, thereby reducing mutual interference between different supervision targets. Alternatively, a multi-branch network with partially shared parameters can be used to output residual and noise terms. Linear attention modules are used at each stage of the encoder and decoder to reduce the computational complexity of attention on high-resolution feature maps; standard attention modules are used in the intermediate layers to capture global correlations at lower spatial resolution. It should be noted that the above UNet structure is only one implementation of the CoRDM network. Any neural network structure capable of outputting residual terms, noise terms, or a combination of both based on diffusion state, diffusion step index, and conditional information can be considered an implementation of the CoRDM network and falls within the scope of this invention.

[0278] S5, CoRDM-DDIM few-step backward inference process: After completing the training of the CoRDM network in S4, backward inference for future CSIs is performed using the trained network parameters. This is consistent with the training phase within the complete spread-step set. Unlike the random sampling diffusion step, the inference stage employs a few-step backward update method based on Denoising Diffusion Implicit Models (DDIM), updating only when the random sampling diffusion step is completed. Reverse refinement is performed on the sparse subsequence composed of diffusion steps, where This approach reduces the number of backward iterations, lowering inference complexity and latency. It should be understood that while the CoRDM-DDIM backsampling method here shares the same underlying idea as the general diffusion model DDIM backsampling, the specific implementation differs. Here, CoRDM-DDIM is a modified DDIM form that matches the CoRDM forward process constructed in S3.

[0279] Suppose the diffusion step sequence used in CoRDM-DDIM backward inference is:

[0280] ,

[0281] in, Indicates the first The diffusion step index corresponding to each reverse refinement step. This indicates the actual number of inference steps set. This subsequence can be selected from the complete set of diffusion steps using uniform sampling, non-uniform sampling, segmented sampling, or other methods specified according to application requirements.

[0282] First, a coarse prediction sequence of future CSI is obtained based on S2. And the forward diffusion terminal state in S3:

[0283] ,

[0284] During inference, the reverse initial state is set within the neighborhood of the coarse prediction sequence, i.e.:

[0285]

[0286] in, This represents the initial reverse state during the inference phase. Unlike the diffusion generation method that initializes from pure Gaussian noise (0 mean), this initialization method uses the coarse prediction sequence of future CSI as the initial mean, so that the reverse process starts from an initial position close to the target future CSI.

[0287] For any reverse refinement step , the current state Diffusion step index and condition information Input the trained CoRDM network to obtain the residual estimate and noise estimate for the current step:

[0288] ,

[0289] in, This represents the network parameters after CoRDM training. This represents the residual estimate under the current backward step. This represents the noise estimate under the current backward step.

[0290] Based on the edge reparameterization relation in S3, the clean future CSI estimate corresponding to the current state can be obtained by the following formula:

[0291] ,

[0292] This formula represents the recovery of the corresponding clean future CSI estimate from the current diffusion state using the complete residual direction and noise source predicted by the network.

[0293] In the general form of random reverse update, from Jump to The single-step reverse state transition can be written as:

[0294] ,

[0295] in, , Used to control randomness in reverse updates. In one implementation, Set to:

[0296] ,

[0297] in, This is a random control parameter. When When, the reverse update contains random perturbations; when At this point, the reverse update degenerates into a deterministic update. In the deterministic reasoning form, let... ,but At this point, the above update formula simplifies to:

[0298] ,

[0299] This formula supports from arrive The skip-step update, without needing to traverse the entire... One diffusion step. Therefore, when Even with a smaller value, rapid refinement from the coarse prediction sequence neighborhood to the final future CSI prediction result can still be achieved. Repeat the above reverse update process until... The final output is the future CSI prediction:

[0300] ,

[0301] in, This represents the final future CSI prediction sequence output by CoRDM.

[0302] In summary, the CoRDM-DDIM short-step backward inference process described in S5 uses the noisy state near the coarse prediction sequence as the initial state, and gradually removes noise disturbances and corrects residual errors through the trained CoRDM network, which can maintain high prediction accuracy while reducing the number of backward sampling steps.

[0303] Example

[0304] This embodiment considers the downlink CSI prediction scenario in a large-scale MIMO-OFDM system. The overall system processing flow is attached. Figure 1 As shown, firstly, a historical CSI sequence is constructed based on the historical downlink CSI obtained from continuous observations; then, a coarse prediction module is used to generate a future CSI coarse prediction sequence based on the historical CSI sequence; subsequently, the future CSI coarse prediction sequence is used as the prior mean of the coarse prediction guided residual diffusion model (CoRDM), and conditional residual diffusion is refined by combining historical CSI or other relevant conditional information; finally, the final future downlink CSI prediction result is obtained through a few-step back reasoning.

[0305] In this embodiment, the system uses a frequency-domain downlink CSI dataset generated from a standardized wireless propagation scenario for training and testing. Base station configuration. One transmit antenna port, user terminal configuration The system includes one receive antenna port. There are subcarriers, and the carrier frequency is . GHz, subcarrier spacing is kHz. Using Historical CSI slot predictions The downlink radio channel is modeled using a time-varying multipath fading channel that conforms to the statistical characteristics of mobile communication scenarios. Frequency-domain downlink CSI samples for 3GPP UMa NLOS scenarios are generated using the QuaDRiGa platform. The generated channels evolve over time and exhibit significant time-varying and random characteristics, reflecting the trend changes and random disturbances in future downlink CSI predictions under mobile terminal conditions. To improve the statistical stability of training and testing results, multiple independent channel samples are generated at the sample level using the Monte Carlo method.

[0306] During the dataset construction phase, historical CSI sequences and future CSI ground truth sequences are first constructed based on the continuous time-varying downlink frequency domain CSI, as defined in S1. For each sample, samples are extracted at preset time intervals within the historical observation interval, using a certain reference time as the boundary. The CSI matrix at each historical moment is stacked along the time dimension to form a historical CSI sequence. Extraction within the future observation interval after this reference time The CSI matrices at future moments are stacked along the time dimension to form a sequence of future CSI truth values. The resulting historical-future paired samples are used to describe the trend changes and random perturbation characteristics of the channel over time under different moving speeds or propagation conditions. The number of data samples is set to... One, of which As a training set As a verification set As a test set, it was used for network parameter learning, model selection and convergence determination, and generalization performance evaluation.

[0307] In the coarse prediction stage, the coarse prediction module employs an encoder-based Transformer network based on the channel attention mechanism described in S2. (Setting up the coarse prediction module...) Used to generate a coarse prediction sequence of future CSI based on historical CSI sequences. The coarse prediction module is trained using supervised learning, and its supervised ground truth is the sequence of future CSI ground truth values. In this embodiment, the AdamW optimizer is used for training, and the training learning rate is set to... .

[0308] In the refinement stage of Conditional Residual Diffusion Model Prediction (CoRDM), the network model adopts the UNet network structure described in S4, and the UNet encoder is configured with... decoder A four-level encoder-decoder structure with a basic number of channels. The multiplier for each channel is set to The network output uses two UNets to output the predicted residuals separately. and noise terms Conditional information Historical CSI sequence information ,exist Figure 2 The middle section contains clean historical CSI sequence information. Figure 3 The middle section contains historical CSI sequence information with different SNR Gaussian noise perturbations. During training, the L1 loss function is used to fit the predicted residuals. and noise terms At the same time, set and All are set to 1. Regarding training parameter settings, this embodiment uses the AdamW optimizer for training, and the CoRDM network training learning rate is set to... Batch size set to The number of training rounds is determined based on the convergence of the validation set. The total number of forward diffusion steps is set to... , Figure 2 , Figure 3 The CoRDM-DDIM inference step count is set to The diffusion endpoint noise scale parameter is set to To verify the performance of the method of the present invention, the following benchmark methods are compared with the method of the present invention: Appendix Figure 3 The paper presents a comparison of the NMSE of each method in future time slots under different historical CSI Gaussian noise SNR scenarios, assuming a terminal moving speed of . Figure 3 (a) Corresponding historical conditional channel SNR is The scene, Figure 3 (b) Corresponding historical conditional channel SNR is The scene, Figure 3 (c) Corresponding historical conditional channel SNR is This experiment simulates the scenario where historical CSI is affected by channel estimation errors, observation noise, or other conditional disturbances, examining the adaptability of various methods to changes in conditional information quality. As the historical CSI conditional SNR decreases from... Raise to The overall prediction performance of each method is improved, indicating that higher-quality historical conditions provide more reliable time-related information. Conversely, under low SNR conditions, historical CSIs contain strong perturbations, significantly increasing the difficulty of future channel prediction. The diffusion-based prediction method with a pure noise starting point is susceptible to condition mismatch in this case because it relies on perturbed historical conditions to guide the reverse generation path and recover the complete future CSI from a random initial state. The CoRDM method of this invention maintains superior NMSE performance under different historical CSI noise SNR conditions, demonstrating good prediction robustness under low-quality input conditions, reducing generation uncertainty caused by pure noise initialization, and enhancing generation stability under perturbed scenarios.

[0309] Appendix Figure 4 The paper presents the NMSE ablation results for future time slots under different CoRDM-DDIM backsampling step counts, assuming a terminal moving speed. This experiment verifies the impact of the number of backsampling steps on prediction performance and inference complexity. When the number of CoRDM-DDIM backsampling steps is small, CoRDM already achieves good future CSI prediction performance. As the number of backsampling steps increases from 1 to several smaller steps, the prediction error further decreases, indicating that a small number of backsampling updates can complete the main residual correction and noise removal. As the number of backsampling steps continues to increase, the improvement in prediction performance gradually saturates, and in some cases, even slightly decreases. This shows that when the coarse prediction results already provide effective structural priors, excessive backsampling updates do not necessarily bring additional benefits; instead, they may introduce approximation errors or error accumulation due to multiple discrete updates. The above results verify the effectiveness of this invention in reducing the number of backsampling steps by transforming the complete future CSI generation problem into a local residual refinement problem within the coarse prediction neighborhood. When CoRDM-DDIM skip-step inference is performed, CoRDM can achieve effective prediction with fewer reverse sampling steps, thereby reducing sampling complexity and inference latency, and meeting the low latency requirements of real-time MIMO-OFDM channel prediction tasks.

[0310] In summary, results under different moving speed scenarios demonstrate that CoRDM can improve the prediction accuracy of future CSI in complex time-varying channels. Results under different historical CSI noise SNR conditions show that CoRDM maintains good generation stability and robustness even when the quality of conditional information deteriorates. Results under different CoRDM-DDIM backsampling steps show that CoRDM can complete the refined recovery of future CSI with fewer backsampling steps, improving inference speed and adapting to low-latency requirements. Furthermore, since this invention only requires obtaining the coarse prediction result of future CSI and related conditional information, without limiting the specific structure of the coarse prediction module, it can be combined with different predictors, different conditional information, and different network backbones, exhibiting strong versatility and scalability.

Claims

1. A coarse prediction-guided channel prediction method using a conditional residual diffusion model, characterized in that, Includes the following steps: S1. Construct training samples, specifically: Define Indicates an instant in time The Channel State Information (CSI) matrix is ​​used to obtain the continuously acquired CSI sequence, in instantaneous time. For reference, the continuous Stacking the CSI matrices of historical moments along the time dimension yields the historical CSI sequence: ， in, Indicates the length of historical observations. Indicates the historical CSI sampling interval. This indicates that multiple CSI matrices are stacked along the time dimension. This represents a CSI sequence formed by CSI matrices from multiple historical moments; Reference time After Stacking the CSI matrices at future moments along the time dimension yields a sequence of true future CSI values: ， in, Indicates the predicted length of the future. Indicates the future forecast interval; Construct conditional information related to the future CSI to be predicted, denoted as ; Thus, training samples are obtained. ,in, This represents the sample index; multiple training samples constitute the dataset. ,in, Indicates the total number of samples; S2. Perform a coarse prediction of future CSI using the coarse prediction module, specifically: based on the historical CSI sequence constructed in S1. The coarse prediction results of the future CSI sequence are obtained, and this coarse prediction module is denoted as... ,in This represents its trainable parameters, and the future coarse prediction sequence of CSI is denoted as . ,in, Compared with the future CSI true value sequence obtained in S1 They have the same time dimension and channel dimension; The coarse prediction module employs supervised training, with the goal of making the coarse prediction results directly approximate the future CSI true value sequence. Normalized mean squared error is used as the coarse prediction loss. ； S3, the future CSI truth sequence constructed based on S1 And the coarse prediction sequence of future CSI obtained from S2 The forward diffusion process of constructing the Conditional Residual Diffusion Model (CoRDM) is as follows: Let the clean diffusion target be the future CSI truth value sequence, i.e.: ， in, Indicates the diffusion step as The clean state at time is a sequence of future CSI ground truth values ​​formed by stacking multiple future CSI matrices; the residual between the coarse prediction sequence and the future CSI ground truth sequence is defined as: ， in, This indicates the deviation of the coarse prediction result from the true value of the future CSI, and is used to characterize the direction and magnitude of correction needed in the subsequent refinement process; Define the total number of forward diffusion steps as The diffusion step index is ,make and Let represent the residual scheduling coefficient and the noise scheduling coefficient, respectively, and define the cumulative residual intensity and the cumulative noise intensity as follows: ， in, The extent to which the diffusion state shifts from the future CSI true value sequence to the coarse prediction sequence. Control the intensity of random disturbances in the diffusion state; set This allows the forward diffusion terminal state to use the coarse prediction sequence as the initial mean; The joint distribution of forward diffusion in CoRDM is defined as: ， in, This indicates a pre-defined forward diffusion process. Indicates the first The future CSI sequence state for each diffusion step corresponds to the single-step transition distribution as follows: ， This indicates that in each forward diffusion step, the state is... First, along the residual direction move Meanwhile, variance is added. , where for It is composed of stacked identity matrices. ; The first step can be obtained by recursion through single-step transitions. Edge reparameterization form for each diffusion step: ， The corresponding edge distribution is: ； In any diffusion step Below, the diffusion state changes from the Clean Future CSI state. Residual injection items Noise disturbance item It consists of three parts; when and At that time, the final future CSI diffusion state is obtained as follows: ； in, For noise; S4. Design and train the CoRDM network, specifically: Based on the forward diffusion process in S3, the CoRDM network is made to adjust according to the current diffusion state. diffusion step and condition information Estimate the residual terms introduced during the forward diffusion process. and noise terms ; Let CoRDM network be denoted as ,in, Indicate its trainable parameters, then the CoRDM network learns the mapping: ， in, For S3 The future CSI sequence state of each diffusion step For conditional information related to future CSI forecasts, For the diffusion step index, and These represent the residual estimate and noise estimate of the network output, respectively. During training, for each training sample, the coarse prediction sequence of future CSI obtained from S2 is first used. The future CSI truth sequence obtained from S1 Calculate residual monitoring objectives: ， Subsequently, from the diffusion step set In the random sampling diffusion step And sample noise: ， Construct the network input state based on the forward diffusion relationship in S3: ， Therefore, the network input corresponding to the current training sample is The target of network supervision is The CoRDM network is trained by minimizing the residual supervision loss and the noise supervision loss. The training loss function is defined as: ,in, and These represent the weight coefficients of the residual monitoring term and the noise monitoring term, respectively; S5. After training the CoRDM network in S4, use the trained network parameters to perform backward inference for future CSIs. Employ a few-step backward update method based on a noise-reducing diffusion implicit model, updating only when... Reverse refinement is performed on the sparse subsequence composed of diffusion steps, where Suppose the diffusion step sequence used in CoRDM-DDIM reverse inference is as follows: ， in, Indicates the first The diffusion step index corresponding to each reverse refinement step. This indicates the actual number of inference steps set; the diffusion step sequence is selected from the complete diffusion step set through uniform sampling, non-uniform sampling, segmented sampling, or other methods set according to application requirements; Based on S2, a coarse prediction sequence for future CSI is obtained. And the forward diffusion terminal state in S3: ， During inference, the reverse initial state is set within the neighborhood of the coarse prediction sequence, i.e.: ， in, This represents the initial reverse state during the reasoning phase; For any reverse refinement step , the current state Diffusion step index and condition information Input the trained CoRDM network to obtain the residual estimate and noise estimate for the current step: ， in, This represents the network parameters after CoRDM training. This represents the residual estimate under the current backward step. This represents the noise estimate under the current backward step; Based on the edge reparameterization relation in S3, the clean future CSI estimate corresponding to the current state is obtained by the following equation: ； In the random reverse update form, from Jump to The single-step reverse state transition is written as: ， in, , Used to control randomness in reverse updates; Repeat the reverse update process until it reaches... The final output of the future CSI prediction is: ， in, This represents the final future CSI prediction sequence output by CoRDM.

2. The coarse prediction-guided conditional residual diffusion model channel prediction method according to claim 1, characterized in that, In S2, the coarse prediction module adopts an encoder-based Transformer structure based on channel attention mechanism. The coarse prediction process is as follows: S21. Construct features from historical CSI sequences, Matrix transformation into: ， in, This indicates an operation that expands the historical CSI sequence into a matrix along the channel dimension. This indicates the number of channels after expansion; Each row corresponds to a channel "token", which is used in... The values ​​at each historical moment represent the temporal evolution characteristics of that channel position; S22. Use a linear layer to map the historical time features of each channel "token" to the hidden dimension. At the same time, in order to distinguish different channel positions, add channel position embedding. The initial hidden representation is obtained as follows: ， in, For the input projection matrix, The bias matrix, This represents the hidden dimension, therefore ; S23, Regarding the first Layer channel attention module, input is The query matrix, key matrix, and value matrix are obtained through linear projection: ， in, , The feature dimension of a single attention head is represented; the channel attention matrix and its output are: ， In the case of multi-head attention, the outputs of different attention heads are concatenated and obtained by output projection: ， in, Indicates the number of heads of attention. This indicates concatenation along the feature dimension. Indicates the output projection matrix; Subsequently, residual connections, normalization, and a feedforward network are used to obtain the output of this layer: ， in, Representation layer normalization, Indicates the first Layered feedforward network; stacking channel attention modules After the layer, the hidden representation with enhanced channel correlation is obtained. Finally, the hidden dimensions are mapped to the future time dimension using the prediction output head, resulting in the expanded form of the coarse prediction matrix for future CSI: ， in, , ,therefore ; S24. Restore the coarse CSI prediction matrix to the form of future CSI sequences through inverse matrix transformation. , This is a future CSI coarse prediction sequence formed by stacking coarse prediction CSI matrices from multiple future moments along the time dimension.

3. The coarse prediction-guided conditional residual diffusion model channel prediction method according to claim 1, characterized in that, In S3, the CoRDM network is a two-dimensional UNet network. The UNet network takes the spliced ​​diffusion state and condition information as input, and provides the current diffusion step information to each layer of the network through diffusion step embedding. The specific processing is as follows: 1) Input feature extraction and diffusion step embedding: embed the current diffusion state With conditional information The network input is obtained by concatenating the data along the channel dimension. ; Subsequently, convolutional layers were used to... Initial feature extraction is performed to obtain an initial feature map. At the same time, the diffusion step index will be used. The input sinusoidal position encoding module is mapped to a diffusion time step embedding via a multilayer perceptron: ， This diffusion time step embedding is used to modulate intermediate features in subsequent residual blocks, enabling the network to distinguish residual and noise distributions at different diffusion steps; 2) Encoder Feature Extraction: Assume the encoder includes... Layer downsampling module, the first The input of the layer encoder is denoted as ,in Each encoder layer includes, in sequence: A residual block, a linear attention module, and a downsampling operation; for the _th _ ... The first layer There are n residual blocks, and the input features are denoted as... ,in The processing flow is as follows: ， in, express convolution, Indicates group normalization, This represents the Sigmoid LinearUnit activation function; diffusion time step embedding. The scale modulation term and bias modulation term are generated by the multilayer perceptron (MLP), and the processing flow is shown in the following equation: ， in, This represents element-wise multiplication. This represents a multilayer perceptron; subsequently, the second convolutional sub-block further extracts features, and the processing flow is shown in the following equation: ； Add the output of the second convolutional sub-block to the residual jump branch to obtain the output of the residual block: ， in, This represents a residual jump mapping; when the number of input channels is the same as the number of output channels... It is an identity mapping; when the two are inconsistent, Depend on Convolution achieves channel matching; after After obtaining a residual block, we get ; right Perform linear attention operations, let ,make The number of "tokens" in the representation space is first obtained through... Convolution yields the features of the query matrix, key matrix, and value matrix: ， After multiple rearrangements, the following is obtained: ,in Indicates the number of heads of attention. This represents the channel dimension of each attention head; in the linear attention module, the query matrix is ​​normalized along the channel dimension, the key matrix is ​​normalized along the spatial "token" dimension, and the value matrix is ​​scale-normalized, resulting in: ； Calculate the feature attention matrix between the key matrix and the value matrix: ， Then, the attention output is obtained based on the features of the context attention matrix and the query matrix: ， Finally, the multi-head outputs are rearranged into two-dimensional feature maps and then processed... Output projection and normalization yield linear attention output: ； No. The layer encoder obtains the input for the next layer through a downsampling operation: ， in, From step size The convolutional implementation is used to reduce spatial resolution and improve channel expressiveness. The intermediate features generated by each residual block or attention module in the layer are saved as skip connection features for use by the corresponding decoding layer; 3) Intermediate layer global feature interaction: Completed After processing by the layer encoder, the encoded features at the lowest resolution are obtained. The intermediate layer consists of a residual block, a standard attention module, and another residual block, and the processing flow is shown in the following formula: ， The internal processing of the intermediate residual blocks is consistent with that of the residual blocks in the encoder, namely, feature updating is completed through two convolutional sub-blocks, group normalization, SiLU activation, diffusion time-step modulation, and residual skip branches; the standard attention module of the intermediate layer is used to model global dependencies at the lowest spatial resolution. ,make First through Convolution yields the features of the query matrix, key matrix, and value matrix, which are then rearranged using a multi-head algorithm. The standard attention weights and outputs are as follows: ， Will Rearranged back into a two-dimensional feature map, and then... The output projection yields the standard attention output; 4) Decoder Feature Recovery: Assume the decoder includes... Layer upsampling module, number The input to the layer decoder is denoted as ,in , Each decoder layer sequentially performs skip connection splicing, A residual block, a linear attention module, and an upsampling operation; for the _th The first layer For each residual block, the current decoded feature is first concatenated with the skip connection feature saved by the corresponding encoder: ， in, , This represents the encoder skip connection features corresponding to the current decoding layer; then the features are updated through residual blocks: ， The decoder residual block also includes two convolutional sub-blocks, group normalization, SiLU activation, diffusion time-step modulation, and residual jump branches. After each residual block, a linear attention module is used to model the spatial correlation at the current resolution: ， The input to the next decoding layer is obtained through upsampling: ， in, It consists of nearest neighbor upsampling and convolution, and is used to progressively restore the spatial resolution of the feature map; 5) Output head and single / dual network settings: After After layer decoding, the final decoded features are compared with the initial features retained at the input. The parts are assembled, and then passed through a residual block, and finally through a... Convolution yields the network output, and the processing flow is shown in the following formula: ； When using a single UNet network, the network output is as follows. The output channel is divided into residual estimation terms and noise estimation terms: ； When using two UNet networks, set up the residual prediction network. and noise prediction network At this time, the output of a single network That is, the two UNet outputs are respectively obtained as follows: 。 4. The coarse prediction-guided conditional residual diffusion model channel prediction method according to claim 1, characterized in that, In S5, Set to: ， in, For randomness control parameters; when When, the reverse update contains random perturbations; when At that time, reverse update degenerates into deterministic update; in the form of deterministic reasoning, let ,but At this point, the update expression simplifies to: ， Support from arrive The skip-step update, without needing to traverse the entire... One diffusion step, therefore, when Even with a smaller value, it is still possible to achieve rapid refinement from the neighborhood of the coarse prediction sequence to the final future CSI prediction result.

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