MIMO channel estimation method under low-resolution quantized observation based on diffusion model and expectation propagation

Abstract

This invention relates to a MIMO channel estimation method based on a diffusion model and expectation propagation under low-resolution quantized observations. It involves acquiring a quantized observation matrix, a pilot matrix, and historical channel data. A denoising diffusion implicit model is employed, and the prior distribution of the MIMO channel matrix is ​​learned unsupervised through forward noise addition to obtain the channel prior score function. To address the nonlinear constraints introduced by the quantized observation matrix, a posterior distribution satisfying the quantization interval constraints is constructed, and the expectation propagation algorithm is used to iteratively approximate it as a Gaussian distribution, calculating the likelihood gradient. Combined with the prior score function, the likelihood gradient is integrated into the inverse sampling process of the denoising diffusion implicit model. Using the quantized observation matrix and pilot matrix as guiding conditions, the initial noise is gradually sampled to a channel estimation result consistent with the quantized observations through gradient guidance. Compared with existing technologies, this invention has advantages such as high accuracy, strong versatility, and good stability.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, and in particular to a method for MIMO channel estimation based on a diffusion model and desired propagation under low-resolution quantized observation. Background Technology

[0002] Multiple-input multiple-output (MIMO) technology is a core technology of modern wireless communication systems, widely used in 4G LTE, 5G, and future 6G networks, significantly improving spectral efficiency, link reliability, and system capacity. However, the realization of these performance gains is highly dependent on accurate channel state information (CSI). In practical deployments, especially in massive MIMO systems, the power consumption and cost of high-resolution analog-to-digital converters (ADCs) become major bottlenecks. ADC power consumption increases rapidly with sampling rate and resolution, prompting systems to adopt low-resolution quantization, such as 1-4 bits, to achieve energy-efficient receiver designs. Coarse-grained quantization introduces severe nonlinear distortion, posing a significant challenge to traditional channel estimation methods. Traditional least squares (LS) and linear minimum mean square error (LMMSE) estimators show significant performance degradation when processing quantized observations. While compressed sensing methods are effective in some scenarios, they require carefully designed sparse representations and have limited generalization capabilities across different propagation environments. Furthermore, existing methods typically require the measurement matrix to have a special structure, such as row orthogonality, to simplify the calculation of the likelihood function. This is constrained in practical systems by factors such as pilot design flexibility, peak-to-average power ratio, and compatibility with existing standards. Meanwhile, compressed sensing methods rely on the assumption of channel sparsity in a certain transform domain, such as the angle domain or the time-delay-Doppler domain, but this assumption often does not hold in rich scattering environments.

[0003] In recent years, generative models have offered new insights into this problem. Diffusion models, which have achieved breakthroughs in fields such as image generation, can model channel priors by learning complex high-dimensional data distributions. However, directly applying diffusion models faces the challenge of calculating the likelihood function due to quantization nonlinearity. Existing methods suffer from the assumption of a linear Gaussian measurement model and strict constraints on the measurement matrix structure, making them difficult to widely apply in practical MIMO systems. Furthermore, the numerical stability and generalizability of the algorithms at different quantization resolutions need improvement. Therefore, how to achieve high-precision, stable, and highly generalizable estimation of quantized MIMO channels under low-resolution ADC conditions, without relying on channel sparsity assumptions and pilot matrix structural constraints, is a key technical problem that needs to be solved. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the existing technology by providing a MIMO channel estimation method based on diffusion model and expectation propagation under low-resolution quantization observation. The likelihood gradient obtained by iterative approximation of expectation propagation algorithm is used as a guiding term and integrated into the inverse sampling process of denoising diffusion implicit model. This achieves the joint utilization of quantization constraints and learned priors. Under low-resolution ADC conditions, high-precision MIMO channel estimation can be achieved without channel sparsity assumptions and pilot matrix structural constraints.

[0005] The objective of this invention can be achieved through the following technical solutions: According to one aspect of the present invention, a method for MIMO channel estimation based on a diffusion model and desired propagation under low-resolution quantization observations is provided, the specific steps of which include: S1. Acquire the quantized observation matrix obtained by the receiver after quantization by a low-resolution analog-to-digital converter, the known pilot matrix and historical channel data at the transmitter; S2. Input the historical channel matrix data into the denoising diffusion implicit model, and perform unsupervised training through forward denoising and reverse denoising processes to obtain the prior score function that characterizes the distribution law of the channel matrix. S3. Using the channel distribution determined by the prior score function as the prior, and based on the noise statistical characteristics introduced by the diffusion process in the current diffusion step, establish a Gaussian prior for the residual variable of the received signal. Combine the quantization interval constraint imposed on the received signal by the quantization observation matrix to construct a truncated Gaussian posterior distribution formed by quantization interval truncation. Input the truncated Gaussian posterior distribution into the expectation propagation algorithm for iterative approximation and output the likelihood gradient in Gaussian distribution form. S4. Input the likelihood gradient into the inverse sampling process of the denoising diffusion implicit model, and work together with the prior score function. Using the quantized observation matrix and the pilot matrix as constraints, iteratively sample from the initial noise matrix to output the final channel estimation result.

[0006] Furthermore, the specific steps for unsupervised training in S2 include: The forward diffusion process is set to gradually add Gaussian noise to the real channel matrix until the channel matrix evolves into pure noise; the noise prediction network is trained with the goal of minimizing the difference between the predicted noise and the real noise, which represents the prior score function. The noise prediction network directly processes channel data in matrix form, with inputs being a noisy channel matrix and the current diffusion step index, and outputting an estimated noise matrix.

[0007] Furthermore, the specific steps of the expectation propagation algorithm in S3 for iterative approximation include: treating each quantized observation in the quantized observation matrix as a box constraint on the received signal; introducing a Gaussian likelihood station function to approximate each box constraint; iteratively updating the station parameters by using moment consistency among three equivalent representations: forced truncation of Gaussian distribution, complete prior plus likelihood station, and bi-station; and calculating the likelihood gradient based on the converged station parameters after convergence.

[0008] Furthermore, during the iterative update of the station parameters, the real and imaginary parts of the received signal are subjected to expectation propagation processing, and a damped update mechanism is adopted to perform a weighted average of the updated station parameters and the previous station parameters to enhance numerical stability.

[0009] Furthermore, the step of calculating the likelihood gradient based on the converged site parameters further includes: calculating the score function corresponding to each quantized observation based on the converged site parameters; using the measurement relationship between the received signal and the channel matrix, mapping the score function to the channel matrix space through the chain rule to obtain the likelihood gradient; projecting the likelihood gradient onto the channel state space of the current diffusion step, and applying gradient clipping to limit gradient values ​​exceeding a preset threshold to within the threshold range.

[0010] Furthermore, the specific steps in S4 that involve iterative sampling starting from the initial noise matrix include: Initialize a random noise matrix following a complex Gaussian distribution as the initial channel state. In each reverse diffusion step, firstly, use the noise prediction network trained in S2 to estimate the noise components in the current channel state and recover the clean channel estimate. Calculate the predicted received signal based on the clean channel estimate and the pilot matrix collected in S1. Perform the expectation propagation iteration in S3, and calculate the likelihood gradient using the diffusion prior variance and the quantization interval corresponding to the quantization observation matrix collected in S1. Generate a preliminary channel state based on the prior update direction. Superimpose the likelihood gradient, adjusted by adaptive step size, onto the preliminary channel state to form the final channel state of the current step. Iterate step by step until all reverse steps are completed, and output the final channel estimation result.

[0011] Furthermore, the adaptive step size is dynamically adjusted according to the current diffusion step index, and gradually decreases with the diffusion step size. The specific step size value is determined by the ratio of the current step index to the total number of steps.

[0012] Furthermore, the iterative convergence condition of the expectation propagation algorithm in S3 is that the difference between the mean of the truncated Gaussian distribution and the mean of the complete prior plus likelihood site distribution, as well as the difference between their variances, are both lower than a preset tolerance threshold.

[0013] According to a second aspect of the present invention, an electronic device is provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the program to implement the method described thereon.

[0014] According to a third aspect of the present invention, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the method described thereon.

[0015] Compared with the prior art, the present invention has the following beneficial effects: (1) This invention learns the prior distribution of the channel matrix from historical channel data in an unsupervised manner by using a denoising diffusion implicit model. It does not require assuming that the channel is sparse in the transformation domain such as the angle domain and the time delay-Doppler domain, nor does it require manually designing a sparse representation dictionary. This data-driven prior learning method can automatically adapt to the channel characteristics under different propagation environments, so that this method can still accurately model the channel distribution in non-sparse scenarios such as rich scattering environments. This significantly improves the generalization ability and robustness of channel estimation in different propagation environments, and provides reliable estimation performance for complex and ever-changing wireless propagation environments in actual deployment.

[0016] (2) In view of the nonlinear constraints introduced by quantization observation, the present invention uses the expectation propagation algorithm to iteratively approximate the truncated Gaussian posterior distribution to a Gaussian distribution, and processes the real and imaginary parts of the received signal separately during the iterative update process. At the same time, a damped update mechanism is introduced to perform a weighted average of the updated station parameters and the previous station parameters, so that the method can be applied to the design of any pilot matrix without requiring the pilot matrix to have orthogonality, unitarity or special sparse mode. Furthermore, it can maintain numerical stability under quantization conditions from 1 bit to very low resolution to medium resolution, avoiding the numerical instability problem caused by high signal-to-noise ratio and narrow quantization range. Thus, it provides greater flexibility for pilot design in practical systems constrained by factors such as peak-to-average power ratio and standard compatibility.

[0017] (3) This invention integrates the likelihood gradient calculated by the expectation propagation algorithm into the back sampling process of the denoising diffusion implicit model as a guiding term. In each back diffusion step, after generating the preliminary channel state based on the prior update direction, the likelihood gradient adjusted by the adaptive step size is superimposed to form the final channel state. This gradient guiding mechanism achieves a dynamic balance between channel prior and measurement consistency, so that the initial random noise matrix can be gradually guided to a high-quality channel estimate that simultaneously meets the learning prior and quantization observation. Therefore, this method can output high-precision channel estimation results under low-resolution ADC conditions, effectively overcoming the defect of the traditional method that has a serious performance degradation under quantization nonlinearity, and providing technical support for the practical deployment of low-power large-scale MIMO systems. Attached Figure Description

[0018] Figure 1 This is a flowchart of a MIMO channel estimation method based on a diffusion model and desired propagation of low-resolution quantized observations. Detailed Implementation

[0019] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0020] In existing technologies, traditional methods such as least squares and linear least mean square error estimators significantly degrade performance for MIMO channel estimation under low-resolution quantization conditions because they cannot effectively handle the severe nonlinear distortion introduced by quantization. While compressed sensing methods are effective in certain scenarios, they rely on the assumption of channel sparsity in specific transform domains, such as the angle domain and the time-delay-Doppler domain. This assumption often does not hold in rich scattering environments, and typically requires the measurement matrix to have special structures such as row orthogonality to simplify likelihood calculations. This is constrained in practical systems by factors such as pilot design flexibility, peak-to-average power ratio, and standard compatibility. In recent years, diffusion models have been attempted as generative models for modeling channel priors, but existing schemes face the problem of difficulty in calculating the likelihood function due to quantization nonlinearity, and most assume linear Gaussian measurement models or impose strict restrictions on the measurement matrix structure, making them difficult to widely apply in general MIMO systems. To address the aforementioned issues, this invention proposes a MIMO channel estimation method based on a diffusion model and expectation propagation under low-resolution quantization observations. A denoising diffusion implicit model is employed to learn the prior channel distribution from historical channel data in an unsupervised manner, without requiring sparsity assumptions. To address the nonlinear constraints of quantization observations, an expectation propagation algorithm is introduced to iteratively approximate the truncated Gaussian posterior distribution to a Gaussian distribution, yielding a computable likelihood gradient. This process is applicable to arbitrary pilot matrix designs, requires no row orthogonality assumptions, and maintains numerical stability from 1 bit to very low resolution to medium resolution through a damped update mechanism. The likelihood gradient is integrated as a guiding term into the inverse sampling process of the denoising diffusion implicit model. An adaptive step size adjustment dynamically balances prior and measurement consistency, ultimately sampling a high-precision channel estimate from the initial noise. Therefore, this invention achieves high-precision, stable, and highly generalizable MIMO channel estimation under low-resolution ADC conditions without requiring channel sparsity assumptions or pilot matrix structural constraints, providing crucial technical support for the practical deployment of low-power large-scale MIMO systems.

[0021] like Figure 1As shown in this embodiment, a MIMO channel estimation method based on a diffusion model and desired propagation under low-resolution quantization observations is provided. The specific steps include: S1. Acquire the quantized observation matrix obtained by the receiver after quantization by a low-resolution analog-to-digital converter, the known pilot matrix and historical channel data at the transmitter; S2. Input the historical channel matrix data into the denoising diffusion implicit model, and perform unsupervised training through forward denoising and reverse denoising processes to obtain the prior score function that characterizes the distribution law of the channel matrix. S3. Using the channel distribution determined by the prior score function as the prior, and based on the noise statistical characteristics introduced by the diffusion process in the current diffusion step, establish a Gaussian prior for the residual variable of the received signal. Combined with the quantization interval constraint imposed on the received signal by the quantization observation matrix, construct a truncated Gaussian posterior distribution formed by truncating the Gaussian prior through the quantization interval. Input the truncated Gaussian posterior distribution into the expectation propagation algorithm for iterative approximation and output the likelihood gradient in the form of a Gaussian distribution. S4. Input the likelihood gradient into the inverse sampling process of the denoising diffusion implicit model, and work together with the prior score function to quantize the observation matrix and pilot matrix as conditional constraints. Iterate sampling step by step from the initial noise matrix to output the final channel estimation result.

[0022] Specifically, this embodiment considers narrowband point-to-point MIMO links, and the base station is equipped with Root transmitting antenna, user equipment configuration Root receiving antenna. During the pilot transmission phase, the base station transmits... Known pilot symbols are used for channel estimation. Here is the MIMO channel matrix, where Indicates the first root transmitting antenna to the first Complex channel coefficients of the root receiving antenna. Base station transmit pilot matrix. The received signal before quantization is: , in, The additive white Gaussian noise matrix follows the rules of... , The mean is variance is The complex Gaussian distribution.

[0023] This embodiment directly processes the signal model in matrix form, eliminating the need for vectorization and preserving the natural structure of the MIMO channel matrix, thus facilitating the application of matrix variable diffusion models. It considers using a low-resolution analog-to-digital converter at the receiver to process the signal. Each element Bit quantization. Let... For having A uniform up-quantizer with quantization levels has the following decision threshold: , codebook is ,in: , Quantization step size is ( ), the code is usually taken as .

[0024] The quantized receiver observation matrix is ​​as follows: , in, and These represent element-wise application to the real and imaginary parts, respectively. : , This embodiment addresses the pilot matrix. No structural assumptions are imposed, in particular, no structural requirements are made. Orthogonal, unitary, or possessing special sparse modes. This versatility is crucial for practical systems because pilot design is often constrained by factors such as power, peak-to-average power ratio, and compatibility with existing standards.

[0025] The goal of this embodiment is to quantize the observation matrix. Estimating the channel matrix Its core is to calculate the posterior distribution. According to Bayes' theorem: , in, For channel priors, To quantify the measurement likelihood, the log-posterior gradient can be decomposed into: , This embodiment provides a prior score function through a denoising diffusion implicit model and a computable approximation of the likelihood gradient through an expectation propagation algorithm, thereby ultimately forming a posterior sampling algorithm for quantized channel estimation.

[0026] The specific steps for unsupervised training in S2 include: The forward diffusion process is set to gradually add Gaussian noise to the real channel matrix until the channel matrix evolves into pure noise; the noise prediction network is trained with the goal of minimizing the difference between the predicted noise and the real noise, so that its representation forms the prior score function; The noise prediction network directly processes channel data in matrix form. The input is a noisy channel matrix and the current diffusion step index, and the output is an estimated noise matrix.

[0027] This embodiment uses the Denoising Diffusion Implicit Model (DDIM) framework to represent the channel prior. The prior distribution of the channel matrix is ​​learned through a forward noise addition process and a reverse denoising process, resulting in the prior score function. Let the true channel matrix be... Follows the data distribution The forward process, expressed with added Gaussian noise, is: , in, Index for discrete diffusion steps, The elements are independent and identically distributed, and follow a complex Gaussian distribution. Noise scheduling coefficient satisfy That is, when When the channel becomes pure noise, It will then be restored to a clean channel.

[0028] This embodiment parameterizes a noise prediction network. Used to extract from a noisy channel matrix Estimating the noise matrix This noise prediction network directly processes channel data in matrix form, taking a noisy channel matrix and the current diffusion step index as inputs, and outputting an estimated noise matrix.

[0029] The training objective of the noise prediction network is to minimize the difference between the predicted noise and the actual noise, expressed as: , in For time-dependent weights, It is the Frobenius norm.

[0030] After training, samples are generated through a reverse diffusion process, given... Network prediction The expression is: , The clean channel matrix is ​​then estimated as follows: , The update rule for unconditional sampling is: , This deterministic mapping allows for efficient sampling, which takes 50-100 steps in this implementation, providing a basis for subsequent posterior sampling.

[0031] The specific steps of the expectation propagation algorithm in S3 for iterative approximation include: treating each quantized observation in the quantized observation matrix as a box constraint on the received signal; introducing a Gaussian likelihood station function to approximate each box constraint; iteratively updating the station parameters by using moment consistency among three equivalent representations: forced truncation of Gaussian distribution, complete prior plus likelihood station, and bi-station; and calculating the likelihood gradient based on the converged station parameters after convergence.

[0032] A key challenge in posterior sampling is calculating the likelihood gradient of the quantized observation matrix. In the diffusion step The noise prediction network provides an estimate of the clean channel matrix. Define predictive measurement and residual .

[0033] According to the forward diffusion process, the residual It has a zero-mean Gaussian prior, and its variance is determined by the level of diffused noise, expressed as: , in , Originating from noise scheduling.

[0034] Quantify the observation matrix for measurement Apply box constraints: , in For the corresponding elements of the quantized observation matrix The quantization interval is defined, with the real and imaginary parts processed separately. This is an indicator function.

[0035] The posterior, combining prior and constraint, is: , This distribution is difficult to handle due to the truncated Gaussian product.

[0036] This embodiment employs the expectation propagation algorithm to provide a systematic Gaussian approximation method, which approximates the above posterior by replacing each box constraint with a Gaussian site function.

[0037] The approximate form is: , in Gaussian in natural parametric form , and For natural parameters. Since the Gaussian product is still Gaussian, It is manageable.

[0038] When iteratively updating the station parameters, the real and imaginary parts of the received signal are subjected to expectation propagation processing, and a damped update mechanism is adopted to perform a weighted average of the updated station parameters and the previous station parameters to enhance numerical stability.

[0039] This embodiment iteratively determines site parameters by forcing moment consistency among three equivalent representations. For each measurement element, two sets of site parameters are maintained, including the likelihood site... Used for approximate quantization constraints, prior sites Used for intermediate calculations to ensure consistency.

[0040] The expectation propagation algorithm enforces moment consistency among three equivalent representations during its iteration process. The first representation is the truncated prior form, which combines box constraints with prior stations to obtain a truncated Gaussian distribution. This distribution is constrained by the quantization interval boundaries, and its mean and variance are given by the moment calculation formula of the truncated Gaussian. The second representation is the full prior plus likelihood station form, which multiplies the diffusion prior (i.e., the zero-mean Gaussian distribution) with the likelihood station to obtain a tractable Gaussian distribution. The third representation is the two-station form, which multiplies the prior station with the likelihood station, also yielding a Gaussian distribution. The expectation propagation algorithm iteratively requires that the means and variances of the three remain consistent: the moments of the truncated Gaussian distribution are equal to the Gaussian moments of the full prior plus likelihood station, and also equal to the Gaussian moments of the two-station distribution. Through this moment consistency constraint, the algorithm progressively updates the station parameters, ultimately making the Gaussian approximate the true truncated posterior distribution.

[0041] Specifically, the truncation prior is obtained by combining box constraints and prior sites: , in , The cutoff interval is The mean and variance of the truncated Gaussian are calculated using the standard Gaussian moments formula.

[0042] The moments of the truncated Gaussian are: , in , These are standard Gaussian PDF and CDF, respectively.

[0043] The complete prior plus likelihood site is: the diffusion prior. Similarity site Multiplication, the expression is: , Its variance is The mean is .

[0044] Two sites refer to: combining prior sites Similarity site The expression is: , Its variance is The mean is .

[0045] Expected communication through requirements and To enforce consistency, derive the update equation: , , The iterative steps involve performing moment matching sequentially between the truncated prior form and the bi-site form, and between the complete prior plus likelihood bi-site form and the bi-site form, repeating this iterative process, and employing a damped update mechanism. Typical damping coefficient ,until and Below the preset tolerance threshold, such as We obtain the expected propagation parameters for convergence.

[0046] Calculating the likelihood gradient based on the converged site parameters further includes: calculating the score function corresponding to each quantized observation based on the converged site parameters; mapping the score function to the channel matrix space using the chain rule based on the measurement relationship between the received signal and the channel matrix to obtain the likelihood gradient; projecting this likelihood gradient onto the channel state space of the current diffusion step and applying gradient clipping to limit gradient values ​​exceeding a preset threshold to within the threshold range. Gradient clipping is used to ensure the numerical stability of the sampling process. Specifically, the likelihood gradient is calculated... Then, the amplitude of each element is limited to a preset threshold range, typically 50. Gradient clipping can prevent sampling instability caused by gradient explosion, while ensuring the repeatability of the algorithm.

[0047] After the expected propagation converges, the likelihood gradient is calculated. For each measurement element, the real and imaginary parts are processed separately, and the score function is: , in , , To quantize the interval boundaries, Let be the complementary error function. The exact score of the truncated Gaussian under the approximate posterior of the expected propagation is given.

[0048] By measuring equations Applying the chain rule, we obtain the likelihood gradient: , in elements After calculating the real and imaginary parts separately from the above formula, we can combine them to form: .

[0049] To integrate into the diffusion step The reverse process projects the gradient onto... space: , Gradient clipping is employed to limit gradient values ​​exceeding a preset threshold, such as 50, to within the threshold range, ensuring numerical stability during the sampling process.

[0050] The specific steps for iterative sampling starting from the initial noise matrix in S4 include: Initialize a random noise matrix following a complex Gaussian distribution as the initial channel state. In each reverse diffusion step, firstly, use the noise prediction network trained in S2 to estimate the noise components in the current channel state and recover the clean channel estimate. Calculate the predicted received signal based on the clean channel estimate and the pilot matrix collected in S1. Perform the expectation propagation iteration in S3, and calculate the likelihood gradient using the diffusion prior variance and the quantization interval corresponding to the quantization observation matrix collected in S1. Generate a preliminary channel state based on the prior update direction. Superimpose the likelihood gradient, adjusted by adaptive step size, onto the preliminary channel state to form the final channel state of the current step. Iterate step by step until all reverse steps are completed, and output the final channel estimation result.

[0051] This algorithm combines the prior score function of the denoising-diffusion implicit model with the likelihood gradient provided by the expectation propagation algorithm to form a posterior sampling algorithm for quantized channel estimation. The algorithm modifies the update rule of the standard denoising-diffusion implicit model by injecting the likelihood gradient.

[0052] Specifically, a random noise matrix following a complex Gaussian distribution is initialized as the initial channel state. And extract the quantized observation matrix. Corresponding quantization interval In each reverse diffusion step Perform the following operations: First, the trained noise prediction network is used. Estimate the noise components in the current channel state: , And recover the clean channel estimate: .

[0053] Secondly, the predicted received signal is calculated based on the clean channel estimation and pilot matrix: , And determine the diffusion prior variance: ,in .

[0054] Then, perform the expectation propagation iteration, using the diffusion prior variance. Observation noise Quantization observation matrix For the corresponding quantization interval, expectation propagation is performed on the real and imaginary parts respectively to obtain converged station parameters and calculate the likelihood score. Thus, the likelihood gradient is obtained. Gradient clipping limits gradient values ​​exceeding a preset threshold of 50 to within the threshold range.

[0055] Finally, a preliminary channel state is generated based on the prior update direction: , The likelihood gradient, adjusted with an adaptive step size, is then superimposed on the initial channel state to form the final channel state for the current step. , in To guide weights, For adaptive step size.

[0056] Iterate step by step until all reverse steps are completed, and output the final channel estimation result. .

[0057] The adaptive step size is dynamically adjusted according to the current diffusion step index and gradually decreases with the diffusion step size. The specific step size value is determined by the ratio of the current step index to the total number of steps.

[0058] Adaptive step size The expression is: , in Index for the current diffusion step, This represents the total number of diffusion steps.

[0059] The initial step size is relatively large, and the step size of subsequent steps gradually decreases, so that the algorithm relies more on the likelihood gradient to guide the sampling direction in the early steps, and gradually converges to the posterior distribution that conforms to the quantized observation in the later steps.

[0060] The iterative convergence condition of the expectation propagation algorithm in S3 is that the difference between the mean of the truncated Gaussian distribution and the mean of the complete prior plus likelihood site distribution, as well as the difference between their variances, are both lower than a preset tolerance threshold.

[0061] Specifically, the iterative convergence condition of the expectation propagation algorithm is: the mean of the truncated Gaussian distribution. The mean of the complete prior plus likelihood site distribution The difference between them, and the variance of both. and The differences between them are all lower than the preset tolerance threshold, such as When the convergence condition is met, stop the expectation propagation iteration and output the converged station parameters for subsequent likelihood gradient calculation.

[0062] Therefore, the method provided in this embodiment does not require the assumption that the channel is sparse in the transform domain, nor does it require the pilot matrix to have special structures such as orthogonality or unitarity. It can adapt to different propagation environments and system configurations, and has a wide range of applications. The same pre-trained denoising diffusion implicit model can handle quantization observations with different bit resolutions by adjusting the quantization interval parameters without retraining. Moreover, the damping update mechanism of the expectation propagation algorithm ensures that numerical stability is maintained under quantization conditions ranging from extremely low resolution to medium resolution. By implicitly learning the prior distribution of the channel from historical channel data through the diffusion model, there is no need to manually design sparse dictionaries or statistical models, resulting in strong generalization ability. At the same time, this method is based on the Bayesian posterior sampling framework, and the expectation propagation approximation has theoretical guarantees, making the algorithm behavior interpretable and predictable. Therefore, this embodiment provides a technical solution for quantization MIMO channel estimation that is clear in principle, has excellent performance, and is flexible in application.

[0063] The method provided in this embodiment employs a denoising-diffusion implicit model framework. Through forward denoising and inverse denoising processes, it learns the prior distribution of the MIMO channel matrix in an unsupervised manner, obtaining the prior score function. This model directly processes channel data in matrix form, requiring no domain transformation or vectorization operations, thus preserving the natural structure of the channel matrix. The training process only requires historical channel data and is not dependent on specific quantization resolution or signal-to-noise ratio conditions.

[0064] Furthermore, to address the nonlinear constraints introduced by the quantization observation matrix, the quantization measurement is modeled as a truncated Gaussian posterior distribution under box constraints. This truncated Gaussian posterior distribution is iteratively approximated to a Gaussian distribution using the expectation propagation algorithm, achieving moment consistency matching among the three equivalent representations and outputting the likelihood gradient in Gaussian form. This method is applicable to arbitrary pilot matrix designs, requiring no assumptions of orthogonality or unitarity of the pilot matrix, and maintains numerical stability at different quantization resolutions through a damped update mechanism.

[0065] Meanwhile, this embodiment integrates the likelihood gradient obtained from the expected propagation calculation into the inverse sampling process of the denoising diffusion implicit model. Using the quantized observation matrix and pilot matrix as constraints, a balance is achieved between channel prior and measurement consistency through adaptive step size adjustment. A deterministic sampling strategy and gradient pruning technique are employed to ensure the stability and repeatability of the algorithm. In each inverse diffusion step, the prior score and likelihood gradient are combined to progressively guide the initial noise matrix to a high-quality channel estimation result consistent with the quantized observations.

[0066] Specifically, the method provided in this embodiment iteratively approximates the posterior distribution through the expectation propagation algorithm, enabling it to handle arbitrary pilot matrix designs, including non-orthogonal, non-unitary, and pilots with arbitrary power constraints. This provides greater flexibility for pilot design in practical systems constrained by factors such as peak-to-average power ratio and compatibility. Simultaneously, by learning the implicit prior of the channel directly from historical channel data through a diffusion model, it eliminates the need for manual sparse representation design and the assumption of channel sparsity in the angle domain, time-delay-Doppler domain, or other transform domains. This allows it to adapt to channel characteristics under different propagation environments and exhibits better generalization capabilities. Furthermore, through the iterative damped update mechanism of expectation propagation, this method maintains stable performance under quantization conditions ranging from extremely low to medium resolutions, avoiding numerical instability issues caused by high signal-to-noise ratios and narrow quantization intervals. Moreover, it eliminates the need to retrain the model for different quantization resolutions; only the quantization interval parameters need to be adjusted for adaptation. In addition, this method uses the deterministic sampling mechanism of the denoised diffusion implicit model to replace the random sampling of the standard diffusion model, which significantly reduces the number of diffusion steps required. Combined with the closed update rule of the expectation propagation algorithm, the overall inference efficiency is high, making it suitable for practical deployment scenarios where latency requirements are not extremely stringent.

[0067] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working process of the described module can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0068] The electronic device of this invention includes a central processing unit (CPU), which can perform various appropriate actions and processes according to computer program instructions stored in read-only memory (ROM) or loaded from a storage unit into random access memory (RAM). The RAM may also store various programs and data required for device operation. The CPU, ROM, and RAM are interconnected via a bus. Input / output (I / O) interfaces are also connected to the bus.

[0069] Multiple components in the device are connected to an I / O interface, including: input units such as a keyboard, mouse, etc.; output units such as various types of displays, speakers, etc.; storage units such as disks, optical disks, etc.; and communication units such as network interface cards, modems, wireless transceivers, etc. The communication unit allows the device to exchange information / data with other devices through computer networks such as the Internet and / or various telecommunications networks. The processing unit performs the various methods and processes described above, such as the method of the present invention. For example, in some embodiments, the method of the present invention may be implemented as a computer software program tangibly contained in a machine-readable medium, such as a storage unit. In some embodiments, part or all of the computer program may be loaded and / or installed on the device via ROM and / or the communication unit. When the computer program is loaded into RAM and executed by the CPU, one or more steps of the method of the present invention described above may be performed. Alternatively, in other embodiments, the CPU may be configured to execute the method of the present invention by any other suitable means (e.g., by means of firmware).

[0070] The functions described above in this document can be performed, at least in part, by one or more hardware logic components. For example, exemplary types of hardware logic components that can be used, without limitation, include: Field Programmable Gate Arrays (FPGAs), Application-Specific Integrated Circuits (ASICs), Application Standard Products (ASSPs), System-on-Chip (SoCs), Complex Programmable Logic Devices (CPLDs), and so on.

[0071] The program code used to implement the methods of the present invention can be written in any combination of one or more programming languages. This program code can be provided to a processor or controller of a general-purpose computer, special-purpose computer, or other programmable data processing device, such that when executed by the processor or controller, the program code causes the functions / operations specified in the flowcharts and / or block diagrams to be implemented. The program code can be executed entirely on the machine, partially on the machine, as a standalone software package partially on the machine and partially on a remote machine, or entirely on a remote machine or server.

[0072] In the context of this invention, a machine-readable medium can be a tangible medium that may contain or store a program for use by or in conjunction with an instruction execution system, apparatus, or device. A machine-readable medium can be a machine-readable signal medium or a machine-readable storage medium. Machine-readable media can include, but are not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatus, or devices, or any suitable combination of the foregoing. More specific examples of machine-readable storage media include electrical connections based on one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fibers, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination of the foregoing.

[0073] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in the present invention, and these modifications or substitutions should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for MIMO channel estimation based on a diffusion model and expected propagation under low-resolution quantized observations, characterized in that, The specific steps include: S1. Acquire the quantized observation matrix obtained by the receiver after quantization by a low-resolution analog-to-digital converter, the known pilot matrix and historical channel data at the transmitter; S2. Input the historical channel matrix data into the denoising diffusion implicit model, and perform unsupervised training through forward denoising and reverse denoising processes to obtain the prior score function that characterizes the distribution law of the channel matrix. S3. Using the channel distribution determined by the prior score function as the prior, and based on the noise statistical characteristics introduced by the diffusion process in the current diffusion step, establish a Gaussian prior for the residual variable of the received signal. Combine the quantization interval constraint imposed on the received signal by the quantization observation matrix to construct a truncated Gaussian posterior distribution formed by quantization interval truncation. Input the truncated Gaussian posterior distribution into the expectation propagation algorithm for iterative approximation and output the likelihood gradient in Gaussian distribution form. S4. Input the likelihood gradient into the inverse sampling process of the denoising diffusion implicit model, and work together with the prior score function. Using the quantized observation matrix and the pilot matrix as constraints, iteratively sample from the initial noise matrix to output the final channel estimation result.

2. The MIMO channel estimation method based on a diffusion model and expected propagation under low-resolution quantization observations according to claim 1, characterized in that, The specific steps for unsupervised training in S2 include: The forward diffusion process is set to gradually add Gaussian noise to the real channel matrix until the channel matrix evolves into pure noise; the noise prediction network is trained with the goal of minimizing the difference between the predicted noise and the real noise, so that it represents the prior score function; The noise prediction network directly processes channel data in matrix form, with inputs being a noisy channel matrix and the current diffusion step index, and outputting an estimated noise matrix.

3. The MIMO channel estimation method based on a diffusion model and expected propagation under low-resolution quantization observations according to claim 1, characterized in that, The specific steps of the expectation propagation algorithm in S3 for iterative approximation include: treating each quantized observation in the quantized observation matrix as a box constraint on the received signal; introducing a Gaussian likelihood station function to approximate each box constraint; iteratively updating the station parameters by using moment consistency among three equivalent representations: forced truncation of Gaussian distribution, complete prior plus likelihood station, and bi-station; and calculating the likelihood gradient based on the converged station parameters after convergence.

4. The MIMO channel estimation method based on a diffusion model and expected propagation under low-resolution quantization observations according to claim 3, characterized in that, When iteratively updating the station parameters, the real and imaginary parts of the received signal are subjected to expected propagation processing, and a damped update mechanism is adopted to perform a weighted average of the updated station parameters and the previous station parameters to enhance numerical stability.

5. The MIMO channel estimation method based on a diffusion model and expected propagation under low-resolution quantization observations according to claim 3, characterized in that, The step of calculating the likelihood gradient based on the converged site parameters further includes: calculating the score function corresponding to each quantized observation based on the converged site parameters; using the measurement relationship between the received signal and the channel matrix, mapping the score function to the channel matrix space through the chain rule to obtain the likelihood gradient; projecting the likelihood gradient onto the channel state space of the current diffusion step, and applying gradient clipping to limit gradient values ​​exceeding a preset threshold to within the threshold range.

6. The MIMO channel estimation method based on a diffusion model and expected propagation under low-resolution quantization observations according to claim 1, characterized in that, The specific steps in S4, which involve iterative sampling starting from the initial noise matrix, include: Initialize a random noise matrix following a complex Gaussian distribution as the initial channel state. In each reverse diffusion step, firstly, use the noise prediction network trained in S2 to estimate the noise components in the current channel state and recover the clean channel estimate. Calculate the predicted received signal based on the clean channel estimate and the pilot matrix collected in S1. Perform the expectation propagation iteration in S3, and calculate the likelihood gradient using the diffusion prior variance and the quantization interval corresponding to the quantization observation matrix collected in S1. Generate a preliminary channel state based on the prior update direction. Superimpose the likelihood gradient, adjusted by adaptive step size, onto the preliminary channel state to form the final channel state of the current step. Iterate step by step until all reverse steps are completed, and output the final channel estimation result.

7. The MIMO channel estimation method based on a diffusion model and expected propagation under low-resolution quantization observations according to claim 6, characterized in that, The adaptive step size is dynamically adjusted according to the current diffusion step index and gradually decreases with the diffusion step size. The specific step size value is determined by the ratio of the current step index to the total number of steps.

8. The MIMO channel estimation method based on a diffusion model and expected propagation under low-resolution quantization observations according to claim 1, characterized in that, The iterative convergence condition of the expectation propagation algorithm in S3 is that the difference between the mean of the truncated Gaussian distribution and the mean of the complete prior plus likelihood site distribution, as well as the difference between their variances, are both lower than a preset tolerance threshold.

9. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the program, it implements the method as described in any one of claims 1 to 8.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the method as described in any one of claims 1 to 8.

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