A MIMO Channel Estimation Method Based on an Energy-Parameterized Diffusion Model

Abstract

This invention discloses a MIMO channel estimation method based on an energy parameterized diffusion model, belonging to the field of wireless communication technology. The method includes the following steps: S1, collecting a channel training dataset for a MIMO wireless communication system; S2, constructing a generative prior network for the energy parameterized diffusion model; S3, training the energy parameterized diffusion model using the collected channel training dataset; S4, during the deployment phase, generating channel priors using the trained energy parameterized diffusion model; and employing iterative sampling based on the acceptance-rejection criterion for posterior inference to gradually recover channel estimates from randomly initialized noise vectors, selecting the result of the last iteration as the final channel estimate. This invention uses an energy parameterized diffusion model to explicitly model the channel prior distribution, improving the accuracy of MIMO channel estimation under low pilot overhead conditions and reducing computational overhead and estimation delay.

Description

Technical Field

[0001] This invention relates to a MIMO channel estimation method based on an energy parameterized diffusion model, belonging to the field of wireless communication technology. Background Technology

[0002] In Multiple-Input Multiple-Output (MIMO) communication systems, channel estimation is a critical technology, and its accuracy largely determines the performance of the end-to-end system. With the development of sixth-generation mobile communication systems, the number of antennas has increased significantly. How to efficiently and accurately acquire channel state information with limited pilot overhead has become an important problem that urgently needs to be solved.

[0003] Traditional channel estimation methods, such as least squares, linear least mean square error, and compressed sensing-based estimators, rely on mathematical models and ideal assumptions, resulting in significant performance degradation in real-world, complex scenarios. Data-driven deep learning methods employ a supervised learning paradigm, which improves estimation performance to some extent, but suffers from sensitivity to system configuration and poor generalization ability.

[0004] In recent years, the rise of generative artificial intelligence has provided new solutions to the problem of high-dimensional channel estimation. Existing research has applied generative models such as generative adversarial networks (GANs) and variational autoencoders (VAEs) to channel estimation, but problems remain, including unstable GAN training and difficulty in representing complex channel structures. Diffusion models, as an emerging class of generative models, generate data through progressive denoising and have demonstrated strong capabilities in modeling complex data distributions and generating high-quality samples. Most existing studies on channel estimation based on diffusion models use fractional parameterization methods, where neural networks directly fit the logarithmic gradient of the channel probability distribution and achieve channel recovery through iterative sampling from the posterior distribution. However, the large number of inference steps and network parameters results in high storage overhead and high estimation latency. Furthermore, since the network only provides gradient estimates rather than explicit probability values, it cannot incorporate an acceptance-rejection step during sampling; all sampled data are retained, which can affect the accuracy of the estimation to some extent. Summary of the Invention

[0005] Technical Problem: To address the aforementioned shortcomings in existing technologies, this invention provides a MIMO channel estimation method based on an energy parameterized diffusion model. It explicitly models the channel distribution using an energy function and employs iterative sampling based on the acceptance-rejection criterion, achieving high-precision and low-complexity acquisition of channel state information with limited pilot overhead.

[0006] Technical Solution: The MIMO channel estimation method based on an energy parameterized diffusion model of the present invention specifically includes the following steps:

[0007] S1. Collect channel training datasets for MIMO wireless communication systems;

[0008] S2. Construct a generative prior network for an energy parameterized diffusion model, wherein the model explicitly models the channel prior distribution through an energy function;

[0009] S3. Use the collected channel training dataset to train the energy parameterized diffusion model;

[0010] S4. During the deployment phase, channel priors are generated using the trained energy parameterized diffusion model; posterior inference iterative sampling based on the acceptance-rejection criterion is adopted to gradually recover channel estimates from randomly initialized noise vectors, and the result of the last iteration is selected as the final channel estimate.

[0011] Preferably, the energy parameterized diffusion model employs a lightweight convolutional neural network structure, with inputs consisting of noisy channel samples and time step embeddings.

[0012] Preferably, the lightweight convolutional neural network includes the following steps:

[0013] S201. The input is initially processed using two stacked convolutional layers with a kernel size of 3×3. The first convolutional layer uses the rectified linear unit activation function.

[0014] S202 and the time step number t are mapped into embedding vectors through a sinusoidal position encoder and a fully connected neuron layer, and then further decomposed into scaling sub-vectors. and bias subvector The sinusoidal position encoder is a method that maps time step numbers into continuous vector representations and generates position embeddings through a sine function, making it easier for the model to perceive time step information.

[0015] S203, Scale the subvector Perform point-by-point multiplication with the output of step S201, and then multiply with the bias sub-vector. Perform point-by-point addition;

[0016] S204. The features processed in step S203 are transformed using three stacked convolutional layers, wherein the first two convolutional layers use rectified linear unit activation functions.

[0017] S205. The final output tensor of step S204 is used as the output of the energy parameterized diffusion model, and is used to construct the energy function together with the noisy channel data.

[0018] Preferably, step S3 specifically includes:

[0019] S301. Set the total number of diffusion time steps T and the noise intensity corresponding to different time step numbers in the energy parameterized diffusion model, and set the training round variable. and the maximum number of training rounds N;

[0020] S302. In each training round, the data loader is traversed to obtain batch training data. The time step number t is randomly selected, and a Gaussian white noise variable of the intensity corresponding to the time step number t is generated and added to the obtained batch training data to obtain noisy channel data.

[0021] S303. Input the noisy channel data and time step number t into the energy parameterized diffusion model of step S2, and calculate the total energy value using the model's output. The expression is:

[0022]

[0023] in, It is noisy channel data. It is the trainable parameter vector of the energy parameterized diffusion model. The norm of a vector It is the output of the energy parameterized diffusion model;

[0024] S304, Regarding the total energy value about Taking the derivative, we obtain the gradient vector. Calculate the cost function value between it and the Gaussian white noise variable, further calculate the gradient of the cost function value and backpropagate it to optimize the parameters of the energy parameterized diffusion model;

[0025] S305. Determine if the training early stop condition is met. If yes, end step S3; otherwise, set the training round variable. Then determine whether the training round variable n is greater than the maximum training round N. If yes, end step S3; otherwise, jump to step S302.

[0026] Preferably, step S4 specifically includes:

[0027] S401. Set the total diffusion time steps T, and the time step variable. Gaussian noise samples are randomly generated from a standard normal distribution;

[0028] S402. Calculate the logarithmic gradient of the prior probability. The expression is:

[0029]

[0030] in, It is a time step Noise disturbances channel variables. It is a pre-set noise intensity coefficient. It is the output of the trained energy parameterized diffusion model. The norm of a vector Represents the variable Find the gradient. This represents the prior probability distribution of the noise channel variables at time step t;

[0031] Calculate the logarithmic gradient of the likelihood term of the noise disturbance. The expression is:

[0032]

[0033] in, It is the received signal vector. It is the channel noise variance. It is the observation matrix. It is the identity matrix. This is the transpose of the matrix. The inverse of the matrix. This represents the likelihood probability distribution at time step t;

[0034] S403. Calculate the new proposed channel vector. The expression is:

[0035]

[0036] in, , It is a pre-set noise intensity coefficient. It is a pre-set gradient step size. It is Gaussian noise randomly generated from a standard normal distribution;

[0037] S404. Calculate the logarithm of the acceptance-rejection probability according to the Metropolis-Hastings criterion. The expression is:

[0038]

[0039] in, Indicates the channel vector proposed Shift to time step Noise perturbation channel variables The probability of; Indicates from time step Noise perturbation channel variables Transfer to proposed channel vector The probability of;

[0040] A random number is uniformly selected from the interval [0,1]. ,judge Greater than or equal to Is it true? If not, then set the time step. Channel variables If so, then let the time step... Channel variables ;

[0041] S405, Set Time Step Variable Check if the time step variable t is less than or equal to 0. If not, proceed to step S402; if yes, end step S4 and obtain the final channel estimate. ,in, It is a time step Channel variables.

[0042] Beneficial effects: Compared with the prior art, the technical solution provided by the present invention has the following beneficial effects:

[0043] 1. Because the energy parameterized diffusion model explicitly models the prior distribution of the channel, the Metropolis-Hastings acceptance-rejection criterion can be combined during the sampling process to effectively filter out low-quality intermediate samples and guide the sampling process to converge to the high posterior probability region, thereby significantly improving the accuracy of channel estimation under low pilot overhead conditions.

[0044] 2. High computational efficiency and good real-time performance: The energy parameterized diffusion model constructed in this invention adopts a lightweight convolutional neural network structure with few parameters and low computational complexity. Simultaneously, the combination of an explicit energy function and an efficient sampling step reduces the number of iterations required to achieve the same estimation performance, thereby reducing computational overhead and estimation delay, and better meeting the real-time channel estimation requirements of practical MIMO systems. Attached Figure Description

[0045] Figure 1 This is a flowchart of the MIMO channel estimation method based on the energy parameterized diffusion model according to an embodiment of the present invention;

[0046] Figure 2 This is a network structure diagram of the energy parameterized diffusion model according to an embodiment of the present invention;

[0047] Figure 3 The graph shows a comparison of the normalized mean square error performance of the embodiments of the present invention and the comparative method when the pilot density is equal to 0.6. Detailed Implementation

[0048] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0049] I. System Model of This Embodiment

[0050] Consider a having root transmitting antenna and In this embodiment, the number of antennas in a MIMO system with a single receiving antenna is [number missing]. , Both the transmitter and receiver use uniform linear arrays. A total of [number] arrays were allocated. Several symbols are used for pilot transmission and channel estimation, and it is assumed that the MIMO channel is in The pilot symbols remain quasi-static during transmission. The pilot symbols employ Quadrature Phase Shift Keying (QPSK) modulation, selected with equal probability from the constellation diagram. The real-valued transmission constellation is... And satisfy the unity power constraint. Pilot density In this embodiment In the k-th time slot, the received signal can be expressed as:

[0051]

[0052] Where H is The MIMO channel matrix to be estimated in dimension 1. It is the kth 3D pilot symbol vector, For the kth A Vaticaned white Gaussian noise vector whose elements have zero mean and variance. The complex Gaussian distribution. (The rest of the text appears to be incomplete and requires further context.) The pilot symbols are stacked in matrix form, and the received signal can be further represented as:

[0053]

[0054] in, for 3D pilot matrix, for A noise matrix. Transforming the spatial channel model to a angular domain representation and using vectorization, the received signal vector y can be represented as:

[0055]

[0056] Where A is A real-valued observation matrix of dimension h is A real-valued angular domain channel vector of dimension n, where each element has zero mean and variance. of A Gaussian noise vector. This embodiment addresses the channel estimation problem given a triplet. In this case, the channel vector h is estimated. This estimation problem can be modeled as a posterior inference problem, the core of which lies in how to effectively utilize the prior channel distribution and combine it with observation data to infer the posterior distribution. This invention utilizes an energy parameterized diffusion model to learn the prior information of the channel distribution, thereby achieving inference from the posterior distribution. Iterative sampling in the process.

[0057] II. Specific Steps of This Embodiment

[0058] like Figure 1 As shown in the figure, this embodiment of the invention provides a flowchart of a MIMO channel estimation method based on an energy parameterized diffusion model, including the following steps:

[0059] S1. Collect channel training datasets for MIMO wireless communication systems;

[0060] S2. Construct a generative prior network for an energy parameterized diffusion model;

[0061] S3. Using the channel training dataset collected in step S1, train the energy parameterized diffusion model constructed in step S2.

[0062] S4. During the deployment phase, channel priors are generated using the trained energy parameterized diffusion model; posterior inference iterative sampling based on the acceptance-rejection criterion is adopted to gradually recover channel estimates from randomly initialized noise vectors, and the result of the last iteration is selected as the final channel estimate.

[0063] Furthermore, in this embodiment, the training data set collected by S1 contains 10,000 training data points, each corresponding to a channel implementation in a specific scenario, covering typical wireless channel characteristics such as different signal-to-noise ratios, multipath delay spread, and angle spread, in order to enhance the generalization ability of the model.

[0064] Furthermore, Figure 2 The diagram illustrates the network structure of the energy parameterized diffusion model used in this example. This energy parameterized diffusion model employs a lightweight convolutional neural network structure, its core function being to parameterize the energy function, explicitly defining the channel prior distribution through its output and input. The input consists of noisy channel samples and time-step embeddings. The lightweight convolutional neural network includes the following steps:

[0065] S201. The input is initially processed using two stacked convolutional layers with a kernel size of 3×3. The first convolutional layer uses the rectified linear unit activation function.

[0066] S202 and the time step number t are mapped into embedding vectors through a sinusoidal position encoder and a fully connected neuron layer, and then further decomposed into scaling sub-vectors. and bias subvector ;

[0067] S203, Scale the subvector Perform point-by-point multiplication with the output of step S201, and then multiply with the bias sub-vector. Perform point-by-point addition; this operation aims to adaptively inject time-step information into the channel characteristics, enabling the network to distinguish processing stages with different noise levels;

[0068] S204. The features processed in step S203 are transformed using three stacked convolutional layers, wherein the first two convolutional layers use rectified linear unit activation functions; the final output tensor of step S204 is used as the output of the energy parameterized diffusion model; this output, together with the noisy channel data, constitutes the energy function, thereby explicitly defining the channel prior distribution.

[0069] Furthermore, S3 specifically includes:

[0070] S301. Set the total diffusion time steps T=100 for the energy parameterized diffusion model, the noise intensity corresponding to different time step numbers (set according to linear or cosine scheduling rules), and the training round variables. The maximum number of training rounds is N=500;

[0071] S302. In each training round, iterate through the data loader to obtain batch training data, and randomly select the time step number t ( ), generate Gaussian white noise variables of intensity corresponding to time step number t, and add them to the acquired batch training data to obtain noisy channel data;

[0072] S303. Input the noisy channel data and time step number t into the energy parameterized diffusion model of step S2, and calculate the total energy value using the model's output. The expression is:

[0073]

[0074] in, It is noisy channel data. It is the trainable parameter vector of the energy parameterized diffusion model. The norm of a vector It is the output of the energy parameterized diffusion model;

[0075] S304, Regarding the total energy value about Taking the derivative, we obtain the gradient vector. Calculate the cost function value between it and the Gaussian white noise variable. The expression is:

[0076]

[0077] in, This indicates the mathematical expectation of a small batch of training data.

[0078] The gradient of the cost function value is further calculated and backpropagated to optimize the parameters of the energy parameterized diffusion model. ;

[0079] S305. Determine if the training early stop condition is met. If yes, end step S3; otherwise, set the training round variable. Then determine whether the training round variable n is greater than the maximum training round N. If yes, end step S3; otherwise, jump to step S302.

[0080] Furthermore, in this embodiment, the 10,000 training data points are divided into 500 training epochs, with each epoch containing 128 mini-batches. This embodiment uses the Adam optimizer with an initial learning rate of 0.0001, and employs a cosine annealing strategy to adjust the learning rate, thereby optimizing the trainable parameters in the network through unsupervised learning. .

[0081] Furthermore, S4 specifically includes:

[0082] S401. Set the total diffusion time steps T=100, and the time step variable... Gaussian noise samples are randomly generated from a standard normal distribution as initial channel variables; this step initiates the backdiffusion (denoising) process.

[0083] S402. Calculate the logarithmic gradient of the prior probability. The expression is:

[0084]

[0085] in, It is a time step Noise disturbances channel variables. It is a pre-set noise intensity coefficient. It is the output of the trained energy parameterized diffusion model. The norm of a vector Represents the variable Find the gradient. This represents the prior probability distribution of the noise channel variables at time step t;

[0086] Calculate the logarithmic gradient of the likelihood term of the noise disturbance. The expression is:

[0087]

[0088] in, It is the received signal vector. It is the channel noise variance. It is the observation matrix. It is the identity matrix. This is the transpose of the matrix. The inverse of the matrix. This represents the likelihood probability distribution at time step t;

[0089] S403. Calculate the new proposed channel vector. The expression is:

[0090]

[0091] in, , It is a pre-set noise intensity coefficient (consistent with the scheduling rules during training). It is a pre-set gradient step size (e.g., 0.1). It is Gaussian noise randomly generated from a standard normal distribution; this step proposes a potentially better new channel sample based on gradient information;

[0092] S404. The ratio of the product of the target posterior distribution and the transition probability is used as the acceptance probability. In this embodiment, the calculation is based on the Metropolis-Hastings (MH) criterion, and can be expressed as follows:

[0093]

[0094] in, This indicates that at time step t, given the observed signal Under the condition of proposing channel vector The posterior probability, This indicates that at time step t, given the observed signal Under the condition of noise perturbation channel variables The posterior probability, Indicates the channel vector proposed Shift to time step Noise perturbation channel variables The probability of; Indicates from time step Noise perturbation channel variables Transfer to proposed channel vector The probability of;

[0095] Using Bayes' theorem, calculate the logarithm of the acceptance-rejection probability. The expression is:

[0096]

[0097] A random number is uniformly selected from the interval [0,1]. ,judge Greater than or equal to Is it true? If not, then set the time step. The channel variable is the channel variable of the previous time step t, that is... If so, then let the time step... The channel variable is the proposed channel vector, i.e. This acceptance-rejection step is key to improving estimation accuracy. It filters out low-quality proposals by using probability judgment, ensuring that the sampling process favors regions with high posterior probabilities.

[0098] S405, Set Time Step Variable Check if the time step variable t is less than or equal to 0. If not, proceed to step S402; if yes, end step S4 and obtain the final channel estimate. ,in, It is a time step The channel variables. When the time step is back to 0, the recovery process from pure noise to clean channel estimation is complete.

[0099] III. Implementation Results

[0100] A comparison is made between the MIMO channel estimation method of the energy parameterized diffusion model in this embodiment of the invention and similar techniques, and the results are as follows: Figure 3 As shown:

[0101] Figure 3 Pilot density is given The normalized mean square error (NMSE) of this invention was compared with that of the fractional parameterized diffusion model and the denoising diffusion model. It can be seen that across the entire signal-to-noise ratio (SNR) range, this invention shows a 2-3 dB performance improvement compared to the fractional parameterized diffusion model and a 0.5-2 dB performance improvement compared to the denoising diffusion model. This result verifies the effectiveness of the energy parameterization method and accept-reject sampling mechanism used in this invention in improving channel estimation accuracy.

[0102] The above description, in conjunction with the accompanying drawings, is merely a preferred embodiment of the present invention and should not be construed as limiting the scope of the claims. It should be understood that any equivalent changes made without departing from the spirit of the present invention are within the scope of protection covered by the claims.

Claims

1. A method for MIMO channel estimation based on energy parameterized diffusion model, characterized in that, The method comprises the following steps: S1, collecting a channel training data set of a MIMO wireless communication system; S2, constructing an energy parameterized diffusion model generative prior network, which explicitly models the channel prior distribution through an energy function; the energy parameterized diffusion model adopts a lightweight convolutional neural network structure, and the input is a noisy channel sample and a time step embedding; the output of the model and the noisy channel data jointly constitute an energy function; S3, training the energy parameterized diffusion model using the collected channel training data set; The S3 specifically comprises: S301, set the diffusion total time step number T of the energy parameterized diffusion model, the noise intensity corresponding to different time step sequence numbers, set the training round variable and the maximum training round N; S302, in each training round, traversing a data loader to obtain batch training data, randomly selecting a time step number t, generating a Gaussian white noise variable corresponding to the intensity of the time step number t, and adding it to the obtained batch training data to obtain noisy channel data; S303. Input the noisy channel data and time step number t into the energy parameterized diffusion model of step S2, and calculate the total energy value using the model's output. The expression is: ； wherein, is noisy channel data, is a trainable parameter vector of the energy parameterized diffusion model, denotes a norm of a vector, is an output of the energy parameterized diffusion model; S304、to the total energy value Regarding derivation, the gradient vector is obtained , the cost function value between the gradient vector and the Gaussian white noise variable is calculated, the gradient of the cost function value is further calculated and back propagated, and the parameters of the energy parameterized diffusion model are optimized; S305, judging whether the training early stop condition is met, if yes, ending step S3; if no, setting the training round variable and judging whether the training round variable n is greater than the maximum training round N, if yes, ending step S3; if no, jumping to step S302; S4, in the deployment stage, generating a channel prior using the trained energy parameterized diffusion model; using an acceptance-rejection criterion based posterior inference iterative sampling to gradually recover a channel estimation value from a randomly initialized noise vector, and selecting the result of the last iteration as the final channel estimation value.

2. The method of claim 1, wherein, The construction of the lightweight convolutional neural network comprises the following steps: S201, using two stacked convolutional layers to preliminarily process the input, and the convolution kernel size is 3×3, wherein the first convolutional layer adopts a rectified linear unit activation function; S202, the time step sequence number t is mapped to an embedding vector through the sinusoidal position encoder and the fully connected neuron layer in turn, and is further split into a scaled sub-vector and a bias sub-vector . ; S203、scaling the sub-vectors point-wise multiplication with the output of step S201, and point-wise addition with a bias sub-vector point-wise addition S204, using three stacked convolutional layers to convert the features processed in step S203, wherein the first two convolutional layers adopt a rectified linear unit activation function.

3. The method of claim 1, wherein, The step S4 specifically comprises: S401、Set the total diffusion time step number T, time step sequence number Gaussian noise samples are randomly generated from the standard normal distribution as initial channel variables; In S402, the log gradient value of the prior probability is calculated. The expression is: ； wherein, is a time step index is a noisy perturbed channel variable, is a pre-set noise intensity coefficient, is an output of the trained energy parameterized diffusion model, denotes a norm of a vector, denotes a gradient of a variable with respect to a variable denotes a prior probability distribution of the noisy channel variable at time step index t; Computing a log gradient value of a noise disturbance likelihood term , the expression is: ； wherein is the received signal vector, is the channel noise variance, is the observation matrix, is the identity matrix, is the transpose of a matrix, is the inverse of a matrix, denotes the likelihood probability distribution at time step number t; S403、Calculate a new proposed channel vector The expression is: ； wherein, , is a pre-set noise intensity coefficient, is a pre-set gradient step size, is a Gaussian noise randomly generated from a standard normal distribution; S404, Calculate the logarithm value of acceptance-rejection probability according to Metropolis-Hastings criterion , the expression is: ； wherein denotes the probability of transitioning from the proposed channel vector to the noise perturbed channel variable at time step index ; denotes the probability of transitioning from the noise perturbed channel variable at time step index to the proposed channel vector , denotes the acceptance probability, which is the ratio of the target posterior distribution to the product of the transition probabilities. A random number is uniformly selected from the interval [0,1]. ,judge Greater than or equal to Is it true? If not, then set the time step number. Channel variables If so, then set the time step number. Channel variables ; S405, set time step number ; determine whether the time step number t is less than or equal to 0, if not, jump to step S402, if yes, end step S4, and obtain the final channel estimation value , wherein, is the channel variable of the time step .

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