An OFDM channel estimation method combining super-resolution and denoising joint model

Abstract

The application relates to the technical field of wireless communication, and particularly provides an OFDM channel estimation method combining a super-resolution and denoising joint model. The method comprises the following steps: generating a data set through a constructed multipath Rayleigh fading channel model; converting a channel estimation problem in an OFDM system into an image super-resolution problem; constructing an improved super-resolution module SRCNN; adopting a residual learning mode to construct a denoising module DnCNN to predict noise between an output of the SRCNN module and an actual channel; adopting a feature fusion layer to connect the super-resolution module and the denoising module to share information and construct a joint model; adopting an end-to-end training strategy to optimize parameters of the super-resolution module and the denoising module; and simulating and verifying, evaluating an algorithm performance through a mean square error, setting multiple groups of signal-to-noise ratio parameters, and verifying performances of different models under different signal-to-noise ratios. The method realizes high-precision and low-overhead channel estimation, and improves applicability and engineering practice value.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, and in particular to an OFDM channel estimation method that combines a super-resolution and denoising joint model. Background Technology

[0002] With the widespread application of Orthogonal Frequency Division Multiplexing (OFDM) technology in 5G-Advanced and 6G communication systems, high-precision channel estimation has become a key challenge in improving system spectral efficiency and reliability. OFDM systems effectively combat frequency-selective fading through frequency-domain multi-carrier transmission, but in high-mobility scenarios and low signal-to-noise ratio environments, traditional channel estimation methods struggle to balance accuracy and real-time performance requirements. Especially in large-scale MIMO-OFDM systems, the channel matrix dimension increases significantly, and existing methods face problems of high computational complexity and accumulated estimation errors.

[0003] In existing technologies, the traditional least squares estimation (LS) combined with linear interpolation method is simple and easy to implement, but it is sensitive to noise and ignores the channel structure characteristics, resulting in a sharp deterioration in performance at low signal-to-noise ratios. While the method based on cascaded deep learning can improve the estimation accuracy, it suffers from error propagation problems caused by two-stage training, and the lack of coordinated optimization between super-resolution reconstruction and denoising modules limits the overall performance improvement.

[0004] Currently, the publicly available patent document CN119996119A, a channel estimation method based on super-resolution networks, utilizes a constructed convolutional neural network to extract target LR image features and performs super-resolution reconstruction of the channel image into HR image to achieve channel estimation. While the structure is simple, its channel estimation processing capability is weak, and its performance needs further improvement; the model can also be further refined. The publicly available patent document CN114363129A, a wireless fading channel estimation method based on deep dense residual networks, uses dense networks (DenseNets) and residual networks (ResNets) to improve deep neural networks (DNNs), constructing deep dense networks (DeDNN) and deep residual networks (ReDNN), respectively. These are then concatenated to form DeReNet, suppressing gradient explosion and vanishing problems during network training. However, the fully connected network structure suffers from numerous hyperparameters and is prone to losing spatial information. The international conference paper, *Deep Residual Learning Meets OFDM Channel*, further addresses this issue. Estimation employs cascaded deep learning methods (such as SRCNN and DnCNN in series), which can improve estimation accuracy. However, it suffers from error propagation problems caused by two-stage training, and the lack of coordinated optimization between super-resolution reconstruction and denoising modules limits the overall performance improvement. Summary of the Invention

[0005] In view of this, the present invention provides an OFDM channel estimation method that combines super-resolution and denoising joint model to achieve high-precision, low-overhead channel estimation, thereby improving applicability and engineering practice value.

[0006] In a first aspect, the present invention provides an OFDM channel estimation method combining a super-resolution and denoising joint model, the method comprising:

[0007] Step 1: Generate a dataset using the constructed multipath Rayleigh fading channel model;

[0008] Step 2: Based on Step 1, the channel estimation problem in the Orthogonal Frequency Division Multiplexing (OFDM) system is transformed into an image super-resolution problem;

[0009] Step 3: Based on Step 2, construct an improved super-resolution module SRCNN for reconstructing high-resolution images from low-resolution images;

[0010] Step 4: Construct a denoising module DnCNN using residual learning to predict the noise difference between the output of the SRCNN module and the real channel;

[0011] Step 5: Use a feature fusion layer to connect the super-resolution module and the denoising module to share information and build a joint model;

[0012] Step 6: Use an end-to-end training strategy to optimize the parameters of the super-resolution module and the denoising module;

[0013] Step 7: Simulation verification. The algorithm performance is evaluated by mean square error (MSE). Multiple signal-to-noise ratio (SNR) parameters are set to verify the performance of different models under different SNRs.

[0014] Optionally, step 1 includes: a multipath Rayleigh fading channel model whose path gain follows a complex Gaussian distribution, and introduces exponentially decaying time delay and random Doppler frequency shift to simulate frequency-selective and time-selective fading;

[0015] Step 11: Set system parameters: Set the number of subcarriers in the OFDM system to 72 and the number of symbols to 14; the pilot pattern adopts uniform distribution, with 24 pilot subcarriers and 14 pilot symbols;

[0016] Step 12: Generate multipath channels: The number of paths P is randomly generated. For each channel sample, 3 to 10 propagation paths are randomly generated, where the delay values ​​of each path follow an exponential distribution, and its probability density function is:

[0017] ;

[0018] in, τ is the attenuation coefficient; τ is the time delay;

[0019] The delay τ of each path follows an exponential distribution with a mean of 0.2. The generated delay values ​​are sorted and normalized to ensure that the maximum delay value is 1. The expression is as follows:

[0020] ;

[0021] The complex gain g of the path follows a standard complex Gaussian distribution, where both the real and imaginary parts follow independent Gaussian distributions with mean 0 and variance 1, and are multiplied by an exponential decay factor. To simulate path loss and demonstrate the relationship between path loss and time delay; the Doppler frequency shift ν of each path is uniformly and randomly generated within the range of [0, 0.1] to simulate the time variation of the channel;

[0022] Step 13, Calculate the channel response: For each subcarrier f and each symbol t, calculate the channel frequency response H[f,t], which is expressed as:

[0023] H ;

[0024] Where P is the number of paths. This represents the number of subcarriers, with a value of 72. This represents the number of symbols, with a value of 14.

[0025] Step 14: Add noise: Multiply the generated ideal channel response h with a random QPSK pilot symbol x to obtain a noiseless received signal; calculate the noise power according to the set signal-to-noise ratio, and add complex Gaussian white noise N to obtain the final received signal Y.

[0026] Step 15: Dataset partitioning: Repeat the above process to generate a total of 2800 samples; randomly partition them into training set, validation set and test set in a ratio of 2000:400:400.

[0027] Optionally, step 2 includes:

[0028] The time-frequency channel response matrix of an orthogonal frequency division multiplexing (OFDM) system is defined as a two-dimensional image, the initial channel estimate obtained through pilot symbols is defined as a low-resolution image, and the actual channel response is defined as a high-resolution image.

[0029] Step 21: At the pilot location, use least squares estimation (LS) to obtain the initial channel response: by ignoring the noise term. The effect of this is expressed by dividing the received signal by the known transmitted pilot symbols:

[0030] ;

[0031] in, Pilot position index set; The pilot signal for the transmitting end. The pilot signal received by the receiving end. This is the initial channel response at the pilot location obtained through LS estimation, i.e., the initial channel estimate.

[0032] Step 22: Two-dimensional interpolation, using bicubic interpolation, to obtain the initial channel response at the pilot position. Interpolate onto the entire time-frequency grid to obtain the initial channel estimation matrix H;

[0033] Step 23: Construct the input image by separating the real and imaginary parts of the complex-valued initial channel estimation matrix H as two channels, which together form a low-resolution image X with a size of 72×14×2.

[0034] The LS estimates of the pilot positions are extended to the entire time-frequency grid by interpolation. A bicubic interpolation method is used to interpolate the real and imaginary parts of the channel response, respectively. After interpolation, the complex channel matrix is ​​converted into a two-channel image format so that the channel estimation problem is transformed into an image super-resolution problem.

[0035] Optionally, step 3 includes:

[0036] The improved super-resolution module SRCNN consists of three core operational stages:

[0037] Step 31, Feature extraction layer: This layer processes the input low-resolution image through a 9×9 convolution, 256 filters, batch normalization (BN), and ReLU activation, extracting overlapping image patches and representing each patch as a high-dimensional feature vector. The expression is as follows:

[0038] ;

[0039] in, The convolution weights are 9×9×256; BN is the batch normalization operation; ReLU is the activation function.

[0040] Step 32, Non-linear mapping layer: This layer non-linearly maps the high-dimensional feature vector output from the first layer to another high-dimensional feature vector to learn non-linear combinations between different features. To deepen the intermediate mapping process and enhance the learning mapping ability, two convolutional layers are used, expressed as follows:

[0041] ;

[0042] ;

[0043] in, The convolution weights are 5×5×128; The convolution weights are 5×5×64;

[0044] One of the two convolutional layers has a structure of 5×5 convolution, 128 filters, batch normalized BN and ReLU activation; the other has a structure of 5×5 convolution, 64 filters, batch normalized BN and ReLU activation.

[0045] Step 33, Reconstruction Layer: A 5×5 convolution with 2 filters and linear activation is used to output 2 channels, corresponding to the channel responses of the real and imaginary parts after reconstruction, to reconstruct the information in the feature domain back to the image domain; the reconstruction layer aggregates the high-dimensional features from the previous steps to generate the final high-resolution image, i.e., the noisy image.

[0046] Optionally, the structure of the denoising module DnCNN in step 4 includes:

[0047] Step 41: The first layer is the input layer, and its structure consists of 3×3 convolution, 128 filters, batch normalized (BN) and ReLU activation.

[0048] Step 42: The middle 15 layers are deep feature extraction layers, whose structure consists of 3×3 convolution, 128 filters, batch normalization (BN), and ReLU activation.

[0049] Step 43: The last layer is the output layer, which has a structure of 3×3 convolution, 2 filters, linear activation, and 2 output channels. The real and imaginary parts of the noise residual are used to obtain the final denoising result through residual subtraction.

[0050] The noisy image output by the super-resolution module SRCNN is used as the input to the denoising module DnCNN. A 17-layer deep network is used to increase the network depth. All hidden layers use 128 filters. L2 regularization is used to constrain the weights in the convolutional layers to improve the model's generalization ability. The output layer produces a residual image, which is the predicted noise. Through residual learning, the predicted noise of the output is subtracted from the input to obtain the denoised image.

[0051] Optionally, step 5 includes:

[0052] Step 51, Input Layer: Receives low-resolution images;

[0053] Step 52, Feature extraction branch of SRCNN model: Output the final reconstruction result and retain the feature maps of the intermediate layers for subsequent fusion; shallow features contain detailed information, and deep features contain semantic information;

[0054] Step 53, Feature Fusion Layer: a. Multi-level Feature Extraction: Extract feature maps from different depths of the SRCNN module, including shallow features and deep features;

[0055] b. Cross-module feature transfer: Features from the SRCNN module are directly transferred to the corresponding layers of the DnCNN module through skip connections;

[0056] c. Feature fusion operation: Features from different sources are fused using a channel splicing method;

[0057] d. Adaptive weight learning: Automatically learns the importance weights of different feature sources to achieve adaptive fusion;

[0058] Step 54, Denoising branch of the DnCNN model: using the fused features as input.

[0059] Optionally, step 6 includes:

[0060] An end-to-end joint training mechanism is adopted, and end-to-end optimization is performed using a single loss function, the expression of which is:

[0061] ;

[0062] in, Let N represent the loss function, and let N represent the number of training samples in a batch. This represents the true channel matrix corresponding to the i samples. Let represent the estimated channel matrix for the i-th sample. This represents the square of the Frobenius norm of a matrix, which is the sum of the squares of all its elements; These represent the sets of parameter values ​​for the SRCNN module and the DnCNN module, respectively.

[0063] Employing a gradient cooperative propagation mechanism, during backpropagation, the gradient flows through both the SRCNN and DnCNN modules simultaneously, expressed as:

[0064] ;

[0065] ;

[0066] Where L represents the loss function, This represents the gradient of the loss function with respect to the joint output. This represents the final output of the joint model. This represents the output of the SRCNN module. This represents the noise predicted by the DnCNN module.

[0067] In a second aspect, embodiments of the present invention provide a computer-readable storage medium comprising a stored program, wherein, when the program is executed, it controls the device where the computer-readable storage medium is located to execute the OFDM channel estimation method combining a super-resolution and denoising joint model in the first aspect or any possible implementation thereof.

[0068] Thirdly, embodiments of the present invention provide an electronic device, including: one or more processors; a memory; and one or more computer programs, wherein the one or more computer programs are stored in the memory, and the one or more computer programs include instructions that, when executed by the device, cause the device to perform an OFDM channel estimation method combining a super-resolution and denoising joint model in the first aspect or any possible implementation of the first aspect.

[0069] The technical solution provided by this invention includes the following steps: generating a dataset by constructing a multipath Rayleigh fading channel model; transforming the channel estimation problem in an orthogonal frequency division multiplexing (OFDM) system into an image super-resolution problem; constructing an improved super-resolution module SRCNN for reconstructing high-resolution images from low-resolution images; constructing a denoising module DnCNN using residual learning to predict the noise between the output of the SRCNN module and the real channel; connecting the super-resolution module and the denoising module using a feature fusion layer to share information and construct a joint model; optimizing the parameters of the super-resolution module and the denoising module using an end-to-end training strategy; and verifying the algorithm's performance through simulation, evaluating the algorithm's performance using mean square error (MSE), and setting multiple sets of signal-to-noise ratio (SNR) parameters to verify the performance of different models under different SNRs. This method achieves high-precision, low-overhead channel estimation, improving its applicability and engineering practice value. Attached Figure Description

[0070] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0071] Figure 1 A flowchart of the OFDM channel estimation method combining super-resolution and denoising joint model provided in an embodiment of the present invention;

[0072] Figure 2 A schematic diagram of the architecture of the super-resolution module SRCNN provided in an embodiment of the present invention;

[0073] Figure 3 A schematic diagram of the architecture of the DnCNN denoising module provided in an embodiment of the present invention;

[0074] Figure 4 A schematic diagram of the architecture of the SRCNN+DnCNN joint model provided in an embodiment of the present invention;

[0075] Figure 5 A graph showing the relationship between signal-to-noise ratio and phase error provided in an embodiment of the present invention;

[0076] Figure 6 This is a performance curve showing the relationship between signal-to-noise ratio and mean square error provided in an embodiment of the present invention;

[0077] Figure 7 This is a schematic diagram of an electronic device provided in an embodiment of the present invention. Detailed Implementation

[0078] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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 embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0079] The terminology used in the embodiments of this invention is for the purpose of describing particular embodiments only and is not intended to limit the invention. The singular forms “a,” “the,” and “the” used in the embodiments of this invention are also intended to include the plural forms unless the context clearly indicates otherwise.

[0080] It should be understood that the term "and / or" used in this article is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, or B existing alone. Additionally, the character " / " in this article generally indicates that the preceding and following related objects have an "or" relationship.

[0081] Depending on the context, the word "if" as used here can be interpreted as "when," "when," "in response to determination," or "in response to detection." Similarly, depending on the context, the phrase "if determination" or "if detection (of the stated condition or event)" can be interpreted as "when determination," "in response to determination," "when detection (of the stated condition or event)," or "in response to detection (of the stated condition or event)."

[0082] Figure 1 The flowchart of the OFDM channel estimation method combining super-resolution and denoising joint model provided in the embodiments of the present invention is as follows: Figure 1 As shown, the method includes:

[0083] Step 1: Generate a dataset by constructing a multipath Rayleigh fading channel model.

[0084] In this embodiment of the invention, step 1 includes: a multipath Rayleigh fading channel model whose path gain follows a complex Gaussian distribution, and introduces exponentially decaying time delay and random Doppler frequency shift to simulate frequency-selective and time-selective fading;

[0085] In this embodiment of the invention, training data is generated through a multipath Rayleigh fading channel model, which includes: generating a large-scale, realistic channel dataset through software simulation for model training and testing.

[0086] Step 11: Set system parameters: Set the number of subcarriers in the OFDM system to 72 and the number of symbols to 14; the pilot pattern adopts uniform distribution, with 24 pilot subcarriers and 14 pilot symbols;

[0087] Step 12: Generate multipath channels: The number of paths P is randomly generated. For each channel sample, 3 to 10 propagation paths are randomly generated. This randomness simulates the uncertainty of the number of multipaths in the real environment. The time delay value of each path follows an exponential distribution, and its probability density function is:

[0088] ;

[0089] in, τ is the attenuation coefficient; τ is the time delay;

[0090] The delay τ of each path follows an exponential distribution with a mean of 0.2. The generated delay values ​​are sorted and normalized to ensure that the maximum delay value is 1. The expression is as follows:

[0091] ;

[0092] The complex gain g of the path follows a standard complex Gaussian distribution, where both the real and imaginary parts follow independent Gaussian distributions with mean 0 and variance 1, and are multiplied by an exponential decay factor. The path loss is simulated to demonstrate the relationship between path loss and time delay; the Doppler frequency shift ν of each path is uniformly and randomly generated within the range of [0, 0.1] to simulate the time variation of the channel;

[0093] Step 13, Calculate the channel response: For each subcarrier f and each symbol t, calculate the channel frequency response H[f,t], which is expressed as:

[0094] H ;

[0095] Where P is the number of paths. This represents the number of subcarriers, with a value of 72. This represents the number of symbols, with a value of 14.

[0096] Step 14: Add noise: Multiply the generated ideal channel response h with a random QPSK pilot symbol x to obtain a noiseless received signal; calculate the noise power according to the set signal-to-noise ratio (SNR, for example, 0 to 30 dB), and add complex Gaussian white noise N to obtain the final received signal Y.

[0097] Step 15: Dataset partitioning: Repeat the above process to generate a total of 2800 samples; randomly partition them into training set, validation set and test set in a ratio of 2000:400:400.

[0098] Step 2: Based on Step 1, the channel estimation problem in the Orthogonal Frequency Division Multiplexing (OFDM) system is transformed into an image super-resolution problem.

[0099] In this embodiment of the invention, step 2 includes:

[0100] The time-frequency channel response matrix of an orthogonal frequency division multiplexing (OFDM) system is defined as a two-dimensional image, the initial channel estimate obtained through pilot symbols is defined as a low-resolution image, and the actual channel response is defined as a high-resolution image.

[0101] Step 21: At the pilot location, use least squares estimation (LS) to obtain the initial channel response: by ignoring the noise term. The effect of this is expressed by dividing the received signal by the known transmitted pilot symbols:

[0102] ;

[0103] in, Pilot position index set; The pilot signal for the transmitting end. The pilot signal received by the receiving end. This is the initial channel response at the pilot location obtained through LS estimation, i.e., the initial channel estimate.

[0104] Step 22: Two-dimensional interpolation, using bicubic interpolation, to obtain the initial channel response at the pilot position. Interpolate onto the entire time-frequency grid to obtain the initial channel estimation matrix H;

[0105] Step 23: Construct the input image by separating the real and imaginary parts of the complex-valued initial channel estimation matrix H as two channels, which together form a low-resolution image X with a size of 72×14×2.

[0106] The LS estimates of the pilot positions are extended to the entire time-frequency grid (72×14) by interpolation. A bicubic interpolation method is used to interpolate the real and imaginary parts of the channel response respectively. After interpolation, the complex channel matrix is ​​converted into a two-channel image format so that the channel estimation problem is transformed into an image super-resolution problem.

[0107] Step 3: Based on Step 2, construct an improved super-resolution module SRCNN for reconstructing high-resolution images from low-resolution images.

[0108] In embodiments of the present invention, such as Figure 2 As shown, step 3 includes:

[0109] This invention makes several key improvements to the traditional SRCNN module, reconstructing a high-resolution channel image from a low-resolution input. The innovations are increased depth, optimized width, more stable training, and regularization mechanism to adapt to the special needs of channel estimation.

[0110] The improved super-resolution module SRCNN consists of three core operational stages:

[0111] Step 31, Feature extraction layer: This layer processes the input low-resolution image through a 9×9 convolution, 256 filters, batch normalization (BN), and ReLU activation, extracting overlapping image patches and representing each patch as a high-dimensional feature vector. The expression is as follows:

[0112] ;

[0113] in, The convolution weights are 9×9×256, where 256 represents 256 filters; BN is the batch normalization operation; ReLU is the activation function.

[0114] Step 32, Non-linear mapping layer: This layer non-linearly maps the high-dimensional feature vector output from the first layer to another high-dimensional feature vector to learn non-linear combinations between different features, thus enhancing the network's expressive power. To deepen the intermediate mapping process and enhance the learning mapping ability, two convolutional layers are used, expressed as follows:

[0115] ;

[0116] ;

[0117] in, The convolution weights are 5×5×128; The convolution weights are 5×5×64;

[0118] One of the two convolutional layers has a structure of 5×5 convolution, 128 filters, batch normalized BN and ReLU activation; the other has a structure of 5×5 convolution, 64 filters, batch normalized BN and ReLU activation.

[0119] In this embodiment of the invention, by adding an additional nonlinear mapping layer, the network can learn more complex feature combinations, effectively improving the model's ability to fit channel characteristics. The decreasing number of filters (256-128-64) conforms to the concept of feature compression, gradually focusing on the most relevant feature representations.

[0120] Step 33, Reconstruction Layer: A 5×5 convolution with 2 filters and linear activation is used to output 2 channels, corresponding to the channel responses of the real and imaginary parts after reconstruction, to reconstruct the information in the feature domain back to the image domain; the reconstruction layer aggregates the high-dimensional features from the previous steps to generate the final high-resolution image, i.e., the noisy image.

[0121] The improved SRCNN is not a simple replication of the traditional model, but rather involves multiple optimizations. The intermediate convolutional layers are increased from two to three, thereby enhancing the network's non-linear fitting ability and better learning of mapping relationships. More filters are used, increasing their width and strengthening the feature extraction capability of each layer. Batch normalization layers are added after each layer to accelerate training and stabilize gradients. L2 weight regularization is also used in the convolutional layers to prevent overfitting. This improved SRCNN module, as the front end of the joint model, provides high-quality feature input to the subsequent denoising module and is a key technical component for achieving high-precision channel estimation.

[0122] Step 4: Construct a denoising module DnCNN using residual learning to predict the noise between the output of the SRCNN module and the real channel.

[0123] In this embodiment of the invention, a residual learning strategy is employed to redefine the denoising task as learning the residual between a noisy image and a clean image, such as... Figure 3 As shown, the structure of the denoising module DnCNN in step 4 includes:

[0124] Step 41: The first layer is the input layer, and its structure consists of 3×3 convolution, 128 filters, batch normalized (BN) and ReLU activation.

[0125] Step 42: The middle 15 layers are deep feature extraction layers, whose structure consists of 3×3 convolution, 128 filters, batch normalization (BN), and ReLU activation.

[0126] Step 43: The last layer is the output layer, which has a structure of 3×3 convolution, 2 filters, linear activation, and 2 output channels. The real and imaginary parts of the noise residual are used to obtain the final denoising result through residual subtraction.

[0127] The noisy image output from the super-resolution module SRCNN is used as the input to the denoising module DnCNN. A 17-layer deep network is adopted to increase the network depth, giving it a larger receptive field and enabling it to capture a wider range of noise patterns and related features in the image. All hidden layers use 128 filters, which reduces the complexity caused by changes in network width and improves training stability. L2 regularization is used to constrain the weights in the convolutional layers to improve the model's generalization ability. Because it is a residual learning network, the output layer produces a residual image (predicted noise). Through residual learning, the predicted noise of the output is subtracted from the input to obtain the denoised image (final estimate). This completes the improved cascaded network.

[0128] Step 5: Use a feature fusion layer to connect the super-resolution module and the denoising module to share information and build a joint model.

[0129] In embodiments of the present invention, such as Figure 4 As shown, its core innovation lies in constructing an end-to-end unified network architecture, deeply integrating the super-resolution reconstruction and denoising processes into an end-to-end network. This allows the super-resolution module and the denoising module to be collaboratively optimized, rather than simply connected sequentially. Step 5 includes:

[0130] Step 51, Input Layer: Receives low-resolution images;

[0131] Step 52, Feature extraction branch of SRCNN model: Output the final reconstruction result and retain the feature maps of the intermediate layers for subsequent fusion; shallow features contain detailed information, and deep features contain semantic information;

[0132] Step 53, Feature Fusion Layer: This is the core innovation of this invention, and its specific implementation includes:

[0133] a. Multi-level feature extraction: Feature maps are extracted from different depths of the SRCNN module, including shallow edge features and deep semantic features;

[0134] b. Cross-module feature transfer: Features from the SRCNN module are directly transferred to the corresponding layers of the DnCNN module through skip connections;

[0135] c. Feature fusion operation: Features from different sources are fused using a channel splicing method;

[0136] d. Adaptive weight learning: Automatically learns the importance weights of different feature sources to achieve adaptive fusion;

[0137] Step 54, Denoising branch of DnCNN model: Use the fused features as input instead of just using the final output of SRCNN.

[0138] The joint model employs a multi-level feature fusion strategy, allowing feature maps of different depths from the SRCNN module to interact with the DnCNN module. Feature fusion achieves information complementarity through channel concatenation. The front-end SRCNN module maintains its original structure, and its output is no longer used as the final result but as an intermediate feature provided to the back-end. A feature transfer mechanism is designed to directly pass the intermediate layer output of the SRCNN module to the DnCNN module. Shallow features (edge ​​and contour information) are directly passed, while deep features (semantic and texture information) are fused across modules. High-frequency detail information is preserved through skip connections.

[0139] Step 6: Use an end-to-end training strategy to optimize the parameters of the super-resolution module and the denoising module.

[0140] In this embodiment of the invention, the network can learn intermediate representations that are both clear and easy to denoise. Step 6 includes:

[0141] An end-to-end joint training mechanism is adopted, and end-to-end optimization is performed using a single loss function, the expression of which is:

[0142] ;

[0143] in, Let N represent the loss function, and let N represent the number of training samples in a batch. This represents the true channel matrix corresponding to the i samples. Let represent the estimated channel matrix for the i-th sample. The squared Frobenius norm of a matrix, i.e., the sum of the squares of all its elements, is equivalent to the generalization of the squared L2 norm on matrices. These represent the sets of parameter values ​​for the SRCNN module and the DnCNN module, respectively.

[0144] Employing a gradient cooperative propagation mechanism, during backpropagation, the gradient flows through both the SRCNN and DnCNN modules simultaneously, expressed as:

[0145] ;

[0146] ;

[0147] Where L represents the loss function, This represents the gradient of the loss function with respect to the joint output. This represents the final output of the joint model. This represents the output of the SRCNN module. This represents the noise predicted by the DnCNN module.

[0148] Compared with traditional cascaded models, joint training produces a collaborative optimization effect. The SRCNN module learns to generate feature representations that are more conducive to the denoising of the DnCNN module. The DnCNN module adjusts the denoising strategy according to the final goal, and the two modules jointly optimize the global optimum towards the goal.

[0149] Step 7: Simulation verification. The algorithm performance is evaluated by mean square error (MSE). Multiple signal-to-noise ratio (SNR) parameters are set to verify the performance of different models under different SNRs.

[0150] In this embodiment of the invention, the effectiveness and advantages of the simulation results verification scheme are as follows:

[0151] To verify the effectiveness and advantages of the channel estimation scheme proposed in this invention, the performance of different channel estimation algorithms is compared and analyzed through simulation results. Specifically, four channel estimation algorithms were selected in the simulation: Least Squares + Interpolation (LS+Interpolation), Improved Super-Resolution Network Channel Estimation (SRNN), Cascade Model (SRCNN+DnCNN), and Joint Model (SRCNN+DnCNN). The performance was evaluated by mean square error (NMSE).

[0152] In this embodiment of the invention, the performance comparison is carried out below from different signal-to-noise ratios: channel estimation performance under different signal-to-noise ratios, such as... Figure 5 As shown, Figure 5 The table shows a comparison of the phase error as the signal-to-noise ratio changes among different algorithms, with detailed model training parameters shown in Table 1.

[0153] Table 1 Model training parameters

[0154] ;

[0155] As the signal-to-noise ratio (SNR) increases, the phase estimation accuracy of all methods shows an improving trend, but the joint model exhibits the best phase estimation performance under all SNR conditions. In the low SNR region (0-10dB), the phase error of the joint model is significantly lower than other methods, reducing the error by about 40% compared to the traditional LS+ interpolation method, demonstrating the advantage of deep learning models in noise suppression. As the SNR increases to 20-30dB, although the gap between methods narrows, the joint model still maintains its leading position, with its phase error consistently remaining at the lowest level. Notably, the joint model also shows a significant advantage over individual SRCNNs and cascaded models (SRCNN+DnCNN), indicating that end-to-end joint training can better optimize the extraction and reconstruction process of phase features, achieving more accurate phase information recovery. This superior phase estimation capability is of great significance for coherent detection and signal demodulation in communication systems, verifying the comprehensive superiority of the joint model in channel estimation tasks.

[0156] Channel estimation performance under different signal-to-noise ratios, such as Figure 6 As shown, Figure 6 The paper demonstrates the performance comparison of different algorithms in terms of mean squared error (MSE) as a function of signal-to-noise ratio (SNR). The proposed method (SRCNN+DnCNN joint model) shows significantly improved MSE compared to traditional algorithms (LS / SRCNN / SRCNN+DnCNN cascaded model) in the 0-30dB range. Furthermore, when the SNR exceeds 5dB, the joint model consistently and stably outperforms the cascaded model. This performance gap is particularly pronounced in the mid-to-high SNR range (15-25dB).

[0157] In this embodiment of the invention, a clear conclusion can be drawn: under all SNR conditions, the deep learning-based method significantly outperforms the traditional LS+ interpolation method. Traditional methods perform particularly poorly in low SNR environments (e.g., MSE of 0.131827 at 0 dB), highlighting their susceptibility to noise and the inherent limitations of simple interpolation methods. The proposed joint model achieves the lowest MSE in the vast majority of scenarios (specifically, from 5 dB to 30 dB). This sustained superiority demonstrates the effectiveness of the end-to-end training strategy in integrating super-resolution and denoising tasks into a unified framework.

[0158] Therefore, based on these simulation results, it can be concluded that the optimization scheme proposed in this invention is significantly superior to traditional channel estimation algorithms in terms of accuracy, computational efficiency, phase error, and performance.

[0159] This invention utilizes deep learning algorithms to solve the estimation problem of Orthogonal Frequency Division Multiplexing (OFDM) systems. The method defines the time-frequency response of a fast-fading communication channel as a two-dimensional image and uses known values ​​at pilot locations to determine the unknown values ​​of the channel response. The method defines the pilot values ​​as a low-resolution image. First, an improved SR network and a denoising IR network are cascaded to estimate the channel. Second, a joint network trained on both networks is used to estimate the channel. Simultaneously, considering that different signal-to-noise ratio samples have different confidence levels, confidence-based loss weights are assigned to data with different signal-to-noise ratios during network training to further improve the network's estimation performance. Experimental results show that the joint model outperforms the cascaded model, which in turn outperforms a single SRCNN network and the traditional LS+ interpolation method. The results confirm that the joint model can be efficiently used for OFDM channel estimation.

[0160] The present invention has the following beneficial effects:

[0161] I. Deep fusion of super-resolution and noise reduction;

[0162] Traditional cascaded models (SRCNN+DnCNN cascade) can perform channel interpolation and denoising tasks separately, but the two modules are trained independently and executed in series, leading to error propagation and module mismatch issues. This invention proposes an end-to-end joint deep learning model that deeply integrates super-resolution reconstruction and noise suppression into a unified network. Through shared feature representations and collaborative optimization mechanisms, it significantly reduces information loss in intermediate stages and improves the overall accuracy of channel estimation. Experimental results show that, over a wide signal-to-noise ratio range of 5 dB to 30 dB, the joint model outperforms traditional LS+ interpolation, independent SRCNN models, and cascaded models in terms of mean squared error (MSE).

[0163] II. End-to-end training mechanism achieves global optimization;

[0164] In traditional two-stage training strategies, the super-resolution module and the denoising module optimize separately with the goal of achieving local optima, making it difficult to achieve optimal overall performance. This invention employs a unified loss function, using the mean square error between the final output and the real channel as the optimization objective. During backpropagation, the gradient simultaneously applies to both the front-end super-resolution module and the back-end denoising module. This mechanism enables the front-end module to learn and generate intermediate features that are more beneficial for subsequent denoising processing, thereby achieving collaborative optimization between the two modules and effectively avoiding the error accumulation problem in cascaded models.

[0165] III. Network structure optimization and computational efficiency improvement;

[0166] This invention increases the network depth and width in the SRCNN part, introducing multi-level convolutions and batch normalization operations to improve nonlinear mapping capabilities; in the DnCNN part, a deep residual learning structure is adopted to enhance noise modeling capabilities. The joint model only requires one forward propagation to complete channel estimation during the inference phase, reducing intermediate result storage and transmission overhead compared to the cascaded model, significantly improving computational efficiency and real-time performance, and making it more suitable for deployment in practical communication systems.

[0167] The method of this invention defines the OFDM channel response as a two-dimensional image and constructs a channel estimation model based on a joint deep learning framework. It uses an improved SRCNN structure for feature extraction and preliminary reconstruction, performs residual learning and noise suppression through a DnCNN module, designs an end-to-end training strategy to achieve synergistic optimization of super-resolution and denoising processes, and conducts simulation verification under different signal-to-noise ratios. The results show that the method can improve the accuracy of channel estimation while having high robustness and low computational complexity, and has good prospects for engineering applications.

[0168] The technical solution provided by this invention includes the following steps: generating a dataset by constructing a multipath Rayleigh fading channel model; transforming the channel estimation problem in an orthogonal frequency division multiplexing (OFDM) system into an image super-resolution problem; constructing an improved super-resolution module SRCNN for reconstructing high-resolution images from low-resolution images; constructing a denoising module DnCNN using residual learning to predict the noise between the output of the SRCNN module and the real channel; connecting the super-resolution module and the denoising module using a feature fusion layer to share information and construct a joint model; optimizing the parameters of the super-resolution module and the denoising module using an end-to-end training strategy; and verifying the algorithm's performance through simulation, evaluating the algorithm's performance using mean square error (MSE), and setting multiple sets of signal-to-noise ratio (SNR) parameters to verify the performance of different models under different SNRs. This method achieves high-precision, low-overhead channel estimation, improving its applicability and engineering practice value.

[0169] The various steps in the embodiments of the present invention can be performed by an electronic device. This electronic device includes, but is not limited to, tablet computers, portable PCs, and desktop computers.

[0170] This invention provides a computer-readable storage medium including a stored program, wherein, when the program is running, it controls the electronic device containing the computer-readable storage medium to execute the above-described embodiment of the OFDM channel estimation method combining a super-resolution and denoising joint model.

[0171] Figure 7 A schematic diagram of an electronic device provided in an embodiment of the present invention, such as... Figure 7As shown, the electronic device 21 includes a processor 211, a memory 212, and a computer program 213 stored in the memory 212 and executable on the processor 211. When the computer program 213 is executed by the processor 211, it implements the OFDM channel estimation method combining super-resolution and denoising joint model in the embodiment. To avoid repetition, it will not be described in detail here.

[0172] Electronic device 21 includes, but is not limited to, processor 211 and memory 212. Those skilled in the art will understand that... Figure 7 This is merely an example of electronic device 21 and does not constitute a limitation on electronic device 21. It may include more or fewer components than shown, or combine certain components, or different components. For example, electronic device may also include input / output devices, network access devices, buses, etc.

[0173] The processor 211 may be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor or any conventional processor.

[0174] The memory 212 can be an internal storage unit of the electronic device 21, such as a hard disk or RAM of the electronic device 21. The memory 212 can also be an external storage device of the electronic device 21, such as a plug-in hard disk, Smart Media Card (SMC), Secure Digital (SD) card, or FlashCard equipped on the electronic device 21. Furthermore, the memory 212 can include both internal and external storage units of the electronic device 21. The memory 212 is used to store computer programs and other programs and data required by network devices. The memory 212 can also be used to temporarily store data that has been output or will be output.

[0175] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems, devices, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0176] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. An OFDM channel estimation method combining super-resolution and denoising joint model, characterized in that, The method includes: Step 1: Generate a dataset using the constructed multipath Rayleigh fading channel model; Step 2: Based on Step 1, the channel estimation problem in the Orthogonal Frequency Division Multiplexing (OFDM) system is transformed into an image super-resolution problem; Step 3: Based on Step 2, construct an improved super-resolution module SRCNN for reconstructing high-resolution images from low-resolution images; Step 4: Construct a denoising module DnCNN using residual learning to predict the noise difference between the output of the SRCNN module and the real channel; Step 5: Use a feature fusion layer to connect the super-resolution module and the denoising module to share information and build a joint model; Step 6: Use an end-to-end training strategy to optimize the parameters of the super-resolution module and the denoising module; Step 7: Simulation verification. The algorithm performance is evaluated by mean square error (MSE). Multiple signal-to-noise ratio (SNR) parameters are set to verify the performance of different models under different SNRs. Step 3 includes: The improved super-resolution module SRCNN consists of three core operational stages: Step 31, Feature extraction layer: This layer processes the input low-resolution image through a 9×9 convolution, 256 filters, batch normalization (BN), and ReLU activation, extracting overlapping image patches and representing each patch as a high-dimensional feature vector. The expression is as follows: ； in, The convolution weights are 9×9×256; BN is the batch normalization operation; ReLU is the activation function. Step 32, Non-linear mapping layer: This layer non-linearly maps the high-dimensional feature vector output from the first layer to another high-dimensional feature vector to learn non-linear combinations between different features. To deepen the intermediate mapping process and enhance the learning mapping ability, two convolutional layers are used, expressed as follows: ； ； in, The convolution weights are 5×5×128; The convolution weights are 5×5×64; One of the two convolutional layers has a structure of 5×5 convolution, 128 filters, batch normalized BN and ReLU activation; the other has a structure of 5×5 convolution, 64 filters, batch normalized BN and ReLU activation. Step 33, Reconstruction Layer: A 5×5 convolution with 2 filters and linear activation is used to output 2 channels, corresponding to the channel responses of the real and imaginary parts after reconstruction, to reconstruct the information in the feature domain back to the image domain; the reconstruction layer aggregates the high-dimensional features from the previous steps to generate the final high-resolution image, i.e., the noisy image.

2. The method according to claim 1, characterized in that, Step 1 includes: a multipath Rayleigh fading channel model whose path gain follows a complex Gaussian distribution, and introduces exponentially decaying time delay and random Doppler frequency shift to simulate frequency-selective and time-selective fading; Step 11: Set system parameters: Set the number of subcarriers in the OFDM system to 72 and the number of symbols to 14; the pilot pattern adopts uniform distribution, with 24 pilot subcarriers and 14 pilot symbols; Step 12: Generate multipath channels: The number of paths P is randomly generated. For each channel sample, 3 to 10 propagation paths are randomly generated, where the delay values ​​of each path follow an exponential distribution, and its probability density function is: ； in, τ is the attenuation coefficient; τ is the time delay; The delay τ of each path follows an exponential distribution with a mean of 0.

2. The generated delay values ​​are sorted and normalized to ensure that the maximum delay value is 1. The expression is as follows: ； The complex gain g of the path follows a standard complex Gaussian distribution, where both the real and imaginary parts follow independent Gaussian distributions with mean 0 and variance 1, and are multiplied by an exponential decay factor. To simulate path loss and demonstrate the relationship between path loss and time delay; the Doppler frequency shift ν of each path is uniformly and randomly generated within the range of [0, 0.1] to simulate the time variation of the channel; Step 13: Calculate the channel response: For each subcarrier f and each symbol t, calculate the channel frequency response H[f, t], which is expressed as: H ； Where P is the number of paths. This represents the number of subcarriers, with a value of 72. This represents the number of symbols, with a value of 14. Step 14: Add noise: Multiply the generated ideal channel response h with a random QPSK pilot symbol x to obtain a noiseless received signal; calculate the noise power according to the set signal-to-noise ratio, and add complex Gaussian white noise N to obtain the final received signal Y. Step 15: Dataset partitioning: Repeat the above process to generate a total of 2800 samples; randomly partition them into training set, validation set and test set in a ratio of 2000:400:

400.

3. The method according to claim 1, characterized in that, Step 2 includes: The time-frequency channel response matrix of an orthogonal frequency division multiplexing (OFDM) system is defined as a two-dimensional image, the initial channel estimate obtained through pilot symbols is defined as a low-resolution image, and the actual channel response is defined as a high-resolution image. Step 21: At the pilot location, use least squares estimation (LS) to obtain the initial channel response: by ignoring the noise term. The effect of this is expressed by dividing the received signal by the known transmitted pilot symbols: ； in, Pilot position index set; The pilot signal for the transmitting end. The pilot signal received by the receiving end. This is the initial channel response at the pilot location obtained through LS estimation, i.e., the initial channel estimate. Step 22: Two-dimensional interpolation, using bicubic interpolation, to obtain the initial channel response at the pilot position. Interpolate onto the entire time-frequency grid to obtain the initial channel estimation matrix H; Step 23: Construct the input image by separating the real and imaginary parts of the complex-valued initial channel estimation matrix H as two channels, which together form a low-resolution image X with a size of 72×14×2. The LS estimates of the pilot positions are extended to the entire time-frequency grid by interpolation. A bicubic interpolation method is used to interpolate the real and imaginary parts of the channel response, respectively. After interpolation, the complex channel matrix is ​​converted into a two-channel image format so that the channel estimation problem is transformed into an image super-resolution problem.

4. The method according to claim 1, characterized in that, The structure of the denoising module DnCNN in step 4 includes: Step 41: The first layer is the input layer, and its structure consists of 3×3 convolution, 128 filters, batch normalized (BN) and ReLU activation. Step 42: The middle 15 layers are deep feature extraction layers, whose structure consists of 3×3 convolution, 128 filters, batch normalization (BN), and ReLU activation. Step 43: The last layer is the output layer, which has a structure of 3×3 convolution, 2 filters, linear activation, and 2 output channels. The real and imaginary parts of the noise residual are used to obtain the final denoising result through residual subtraction. The noisy image output by the super-resolution module SRCNN is used as the input to the denoising module DnCNN. A 17-layer deep network is used to increase the network depth. All hidden layers use 128 filters. L2 regularization is used to constrain the weights in the convolutional layers to improve the model's generalization ability. The output layer produces a residual image, which is the predicted noise. Through residual learning, the predicted noise of the output is subtracted from the input to obtain the denoised image.

5. The method according to claim 1, characterized in that, Step 5 includes: Step 51, Input Layer: Receives low-resolution images; Step 52, Feature extraction branch of SRCNN model: Output the final reconstruction result and retain the feature maps of the intermediate layers for subsequent fusion; shallow features contain detailed information, and deep features contain semantic information; Step 53, Feature Fusion Layer: a. Multi-level Feature Extraction: Extract feature maps from different depths of the SRCNN module, including shallow features and deep features; b. Cross-module feature transfer: Features from the SRCNN module are directly transferred to the corresponding layers of the DnCNN module through skip connections; c. Feature fusion operation: Features from different sources are fused using a channel splicing method; d. Adaptive weight learning: Automatically learns the importance weights of different feature sources to achieve adaptive fusion; Step 54, Denoising branch of the DnCNN model: using the fused features as input.

6. The method according to claim 1, characterized in that, Step 6 includes: An end-to-end joint training mechanism is adopted, and end-to-end optimization is performed using a single loss function, the expression of which is: ； in, Let N represent the loss function, and let N represent the number of training samples in a batch. This represents the true channel matrix corresponding to the i samples. Let i represent the estimated channel matrix of the i-th sample. This represents the square of the Frobenius norm of a matrix, which is the sum of the squares of all its elements; These represent the sets of parameter values ​​for the SRCNN module and the DnCNN module, respectively. Employing a gradient cooperative propagation mechanism, during backpropagation, the gradient flows through both the SRCNN and DnCNN modules simultaneously, expressed as: ； ； Where L represents the loss function, This represents the gradient of the loss function with respect to the joint output. This represents the final output of the joint model. This represents the output of the SRCNN module. This represents the noise predicted by the DnCNN module.

7. A computer-readable storage medium, characterized in that, The computer-readable storage medium includes a stored program, wherein, when the program is executed, it controls the device containing the computer-readable storage medium to perform the OFDM channel estimation method combining a super-resolution and denoising joint model as described in any one of claims 1 to 6.

8. An electronic device, characterized in that, include: One or more processors; Memory; And one or more computer programs, wherein the one or more computer programs are stored in the memory, the one or more computer programs including instructions that, when executed by the device, cause the device to perform the OFDM channel estimation method combining super-resolution and denoising joint model as described in any one of claims 1 to 6.

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