Wireless channel error distribution modeling method based on fusion of empirical formula and conditional generative adversarial network

Abstract

According to the wireless channel error distribution modeling method based on empirical formula and conditional generative adversarial network fusion, topographic features, physical error constraints and a conditional generative adversarial mechanism are introduced, environmental features such as terrains and buildings are used as conditional input of a conditional generative adversarial network (cGAN), adversarial training is carried out in combination with real propagation error data, and the accuracy of confrontation is improved. The model can learn a nonlinear mapping relation between geographic features and propagation errors, and a channel modeling result with physical consistency and terrain correlation is obtained, so that a traditional path loss model or a deep learning prediction model can be effectively assisted to be optimized; and reliable data support is provided for wireless propagation modeling and related model research in a scene with data scarcity or complex environment.

Description

Technical Field

[0001] This invention relates to the fields of wireless communication and artificial intelligence, and in particular to a method for modeling wireless channel error distribution based on the fusion of empirical formulas and conditional generative adversarial networks. Background Technology

[0002] Currently, in research on AI-based wireless channel prediction technology, existing modeling methods for extracting environmental elements are typically based on convolutional neural network (CNN) structures and their variants. [1] This method inputs terrain or feature information images into the model, effectively extracting environmental features in wireless signal propagation during neural network training, and outputting predicted path loss or received power. Although such methods can achieve high accuracy in specific scenarios, their performance and generalization ability are highly dependent on sufficient and high-quality training data. When encountering new scenarios or complex terrains, systematic biases can easily arise due to insufficient training samples or different statistical characteristics, leading to a decline in model performance.

[0003] In traditional methods, empirical formula models such as the COST 231-Hata model and the ITU-R P.1546 model are still widely used in wireless channel modeling and network planning. These models are based on statistical regression and physical propagation law derivation from a large amount of measured data, and have the advantages of low computational complexity, strong interpretability, and high implementation efficiency. However, in complex urban scenarios, mountainous terrain, or high-frequency propagation conditions, their prediction errors increase significantly, and the error distribution is often closely related to geographical environmental characteristics.

[0004] The existing technologies mainly include:

[0005] Wireless Channel Modeling Method and Apparatus [3] The technique involves: inputting noisy data into a generator, progressively refining noise features through linear mapping, convolutional upsampling, feature normalization, and channel attention mechanisms to ultimately generate wireless channel data. The generated wireless channel data and real channel data are then input into the discriminator of the target model. Based on the discrimination result, the generator's weight parameters are updated, training the generator to generate wireless channel data similar to the real channel data.

[0006] A Wireless Channel Modeling Implementation Method Based on Generative Adversarial Networks [4] The technique involves alternately training the discriminator and generator of an adversarial network using real channel data and generator-generated channel data until the discriminator can no longer distinguish between real and generated channel data. This allows the generator to learn the channel data and generate channel data with the same statistical properties.

[0007] A method and apparatus for predicting road loss [5]The method includes: acquiring sample data, wherein the sample data includes characteristic parameters affecting wireless propagation between transmitters and cells, parameter values ​​of the characteristic parameters, and measured path loss between each receiver and transmitter in the cell; rasterizing the characteristic parameters to generate a feature image; constructing a deep learning model based on the feature image and the measured path loss, wherein the input variable of the deep learning model is the feature image, and the output variable of the deep learning model is used to represent the path loss between each receiver and transmitter in the cell; and predicting the path loss using the constructed deep learning model.

[0008] A Channel Simulation Implementation Method Based on Conditional Generative Adversarial Networks [6] The original dataset is generated from actual transmitted and received signal pairs, and then represented as a two-dimensional time-frequency domain signal with two channels. This original dataset is used to train the conditional generative adversarial network (GAN) model. When the discriminator in the GAN cannot distinguish between the received signal in the real channel and the received signal generated by the GAN, the trained GAN model can accurately simulate the channel, and the network is equivalent to a model of the channel.

[0009] Existing related technologies all have their shortcomings. For example, wireless channel modeling methods and devices. [3] and a wireless channel modeling implementation method based on generative adversarial networks [4] These methods directly generate channel data without incorporating terrain features and relevant scene parameters. The generators independently generate data in the sample space, failing to establish continuous conditional relationships between positions or coordinates, making it difficult to generate and visualize a full-space error distribution map. (Example: A method and apparatus for predicting road loss.) [5] Relying entirely on measured data for training makes it prone to distortion when data is scarce or the scenario changes, and it cannot model the error distribution. For example, a channel simulation implementation method based on conditional generative adversarial networks... [6] The constraints mainly come from the statistical characteristics of the signal, and lack physical consistency constraints.

[0010] Reference documents:

[0011] [1] Chen Y, Xiang T, Zhang X. An Efficient Wireless Propagation LossPrediction Model based on 3D Terrain Features Extracted by Deep Learning[J]. IEEE Antennas and Wireless Propagation Letters, 2022, 22(5): 1055-1058.

[0012] [2] A. Marey, M. Bal, HF Ates and BK Gunturk, "PL-GAN: PathLoss Prediction Using Generative Adversarial Networks," IEEE Access, vol. 10, pp. 90474–90480, 2022.

[0013] [3] Xu Nan, He Yawen, Cheng Li, et al. Wireless channel modeling method and device [P]. Wuhan: CN119363254A, 2025-01-24.

[0014] [4] Sun Yanzan, Zhu Wenxing, Zhang Shunqing. Implementation method of wireless channel modeling based on generative adversarial network [P]. Shanghai: CN110875790A, 2020-03-10.

[0015] [5] Su Huiqiao, He Feng, Xu Zhijie, et al. A method and device for predicting road loss [P]. Beijing: CN109874146A, 2019-06-11.

[0016] [6] Sun Yanzan, Zhu Wenxing, Zhang Shunqing, et al. A channel simulation implementation method based on conditional generative adversarial networks [P]. Shanghai: CN110289927A, 2020-09-27. Summary of the Invention

[0017] This invention proposes a wireless channel error distribution modeling method based on the fusion of empirical formulas and conditional generative adversarial networks (GANs). Specifically, this method, based on traditional empirical channel models, combines GAN technology with terrain information as a conditional input to the generative model. This enables the model to automatically learn complex terrain errors that are difficult to consider in empirical formulas, achieving a channel error modeling method that combines physical propagation laws with deep generative learning capabilities. This effectively assists in optimizing traditional path loss models or deep learning prediction models and provides reliable data support in scenarios with scarce data or complex environments.

[0018] A wireless channel error distribution modeling method based on the fusion of empirical formulas and conditional generative adversarial networks includes the following steps:

[0019] Step 1: Collect sample data and build a dataset.

[0020] The sample data includes two-dimensional images containing terrain features, a set of electromagnetic parameters, and measured path loss from the transmitter to each receiver location.

[0021] The specific process of constructing the dataset is as follows:

[0022] Two-dimensional images containing terrain data are rasterized at a fixed resolution, with each raster representing a spatial coordinate point. Each raster cell is considered a pixel, and its pixel value represents the terrain height or occlusion feature of the center point, thus forming a complete terrain feature image. .

[0023] By substituting the electromagnetic parameters into the selected empirical formula model, the theoretical path loss at each measuring point is calculated, and the propagation error term is constructed by subtracting the measured results from the theoretical path loss.

[0024] The propagation error term is mapped to the pixel coordinate system of the rasterized terrain image according to its corresponding measurement point coordinates, thus obtaining the result corresponding to the terrain feature image. One-to-one correspondence of the true error distribution map This constitutes the dataset. .

[0025] Step 2: Construct a feature extraction module based on a convolutional neural network (CNN) to extract features from the constructed dataset and obtain a high-dimensional environmental feature map and a true error map;

[0026] The feature extraction process is as follows:

[0027] First, the terrain feature image Corresponding error distribution plot Perform geometric matching and projection unification. Project all data onto the same reference coordinate system and ensure that the terrain image and the error image are spatially aligned at the pixel level.

[0028] Then, the matched images are segmented and sliced ​​to cut the large image into several small blocks of fixed size;

[0029] Finally, the terrain feature image Converted to single-channel grayscale image, the resulting grayscale terrain feature image Error distribution plot All are represented in two-dimensional matrix form. ,in , and These represent the pixel values ​​for the image height and width, respectively. This is for the grayscale topographic feature image. Error distribution plot After removing extreme outliers, normalization is performed to obtain a high-dimensional environmental feature map and a true error map, specifically:

[0030] = , =

[0031] in and It is the global extremum calculated over all samples.

[0032] Step 3: Construct a conditional generative adversarial network model;

[0033] Conditional generative adversarial network models consist of a generator and a discriminator:

[0034] (1) The generator is specifically:

[0035] The generator G selects an image encoder-decoder structure, where the encoder consists of multiple progressively downsampled convolutional blocks up to the bottleneck layer. In the decoder, upsampling is performed layer by layer through multiple upsampled convolutional blocks to gradually restore the original image size, mapping high-dimensional environmental features to the spatial details of the error distribution map.

[0036] Each downsampling convolutional block constituting the encoder includes: a two-dimensional convolutional layer for spatial downsampling; a normalization layer, preferably batch normalization, to accelerate convergence and stabilize gradients; and a nonlinear activation layer, preferably LeakyReLU, to enhance gradient propagation in the negative interval. Optionally, a Dropout layer is added to prevent overfitting.

[0037] Each upsampled convolutional block constituting the decoder includes: a transposed convolutional layer that restores the feature map to a higher resolution; a normalization layer; and a non-linear activation layer, preferably ReLU.

[0038] To allow information flow to bypass bottleneck layers in dimensional information transmission, skip connections are introduced into the generator structure. Specifically, in the generator's... Layer and First Establish skip connections between layers, where This represents the total number of layers in the generator. Each skip connection is used to connect the first... Layer and First All channels of the layer are cascaded to achieve the fusion of features from different layers and enhance information transmission.

[0039] The generator takes a high-dimensional environmental feature image as input. With random noise vector Under the given conditions, learn to generate an error distribution related to the terrain spatial structure. ,Right now The mapping.

[0040] (2) The discriminator is specifically:

[0041] The input to the discriminator D is the error distribution plot of the generator output. Or the actual error distribution map And respectively compared with high-dimensional environmental feature images The channel direction is spliced, that is:

[0042]

[0043]

[0044] It is used to characterize the spatial correspondence between generation error and environmental features.

[0045] The input tensor is progressively downsampled and feature extracted through a multi-layer convolutional network structure, and the output is a discriminant matrix:

[0046] ,

[0047] in and Determined by the total downsampling factor of the network. Each element One of the corresponding input images is of size The local receptive field region (i.e., patch) is defined, and the value of each element represents the similarity score between the generated result and the real sample within that region.

[0048] The discriminator provides discrimination results for multiple local regions of the input image, thereby constraining the local consistency and texture details of the generator output at the spatial level.

[0049] Step four: Perform adversarial training and optimization on the conditional generative adversarial network model;

[0050] The adversarial training process employs a least-squares form adversarial loss function.

[0051] ,

[0052] in, For real input samples, For the corresponding condition information, This represents the statistical expectation value of the discrimination result error calculated based on the input data and its corresponding condition information. This represents the statistical expectation of the discrimination result error calculated from the input data and its generator output.

[0053] Based on this loss function, the discriminator D aims to maximize the loss to distinguish between real and fake samples; the generator G, on the other hand, aims to minimize the loss so that the discriminator cannot distinguish between real and fake samples. Therefore, the generator and discriminator form an adversarial optimization relationship, and their optimization objectives are uniformly expressed as:

[0054] ,

[0055] In the task scenario of this invention, while focusing on the statistical shape of the error distribution, the controllability of numerical accuracy is ensured. The L1 constraint term for the output error is defined as follows: , If the norm is L1, then the ultimate goal of the conditional generative adversarial network is:

[0056]

[0057] in, The weighting coefficient represents the importance of numerical precision.

[0058] The specific process of adversarial training and optimization is as follows: after weight initialization, an alternating iterative strategy is used to update parameters.

[0059] First, fix the generator parameters and update only the discriminator. Then, input real sample pairs... With generated sample pairs The discriminator calculates the discrimination loss, calculates the gradient of the discriminator parameters and updates them so that the output approaches 1 for real samples and approaches 0 for generated samples.

[0060] Then, with the discriminator parameters fixed, only the generator is updated. The terrain feature map is then... Input generator, output prediction error distribution The discriminator receives the generated sample pairs. The generator calculates a loss function based on the discriminator's output, including a generator adversarial loss term. and precision constraints The loss gradient is backpropagated to the generator network and the weights are updated, so that the output error distribution gradually approximates the true error characteristics under the terrain conditions.

[0061] Furthermore, during training, the Adam optimization algorithm is used as the gradient update strategy, employing mini-batch stochastic gradient descent with a learning rate set to 1×10⁻⁶. -4 The momentum parameters are chosen as β1=0.5 and β2=0.999.

[0062] As training iterates, the discriminator's output gradually approaches 1 on real samples and approaches 0 on generated samples, indicating that its discriminative ability is continuously improving; at the same time, the distance between the generator's output error distribution and the real error is continuously decreasing. As the error decreases, the adversarial loss tends to reach equilibrium. When the generator can generate pseudo-samples that are difficult for the discriminator to distinguish, the adversarial training reaches a relatively stable state, and the model converges.

[0063] Step 5: Use the trained cGAN output to correct the empirical formula or deep learning prediction model.

[0064] The path loss results output by the empirical model are compared with the error correction map generated by cGAN to perform compensation calculations:

[0065]

[0066] in The corrected path loss prediction results are shown below. To generate an error map, thereby obtaining a continuous path loss distribution map or signal strength map in geospatial space.

[0067] The advantages and beneficial effects of this invention are as follows:

[0068] This invention establishes a Conditional Generative Adversarial Network (cGAN) model to learn the nonlinear mapping relationship between geographic features and propagation errors. This model utilizes a conditional constraint mechanism to conditionally generate the error distribution under the guidance of terrain feature information, thereby obtaining channel modeling results that combine physical consistency and terrain relevance. This effectively assists in optimizing traditional path loss models or deep learning prediction models, and provides reliable data support for wireless propagation modeling and related model research in data-scarce or complex environments. Attached Figure Description

[0069] Figure 1 This is a flowchart of the wireless channel error distribution modeling method based on the fusion of empirical formulas and conditional generative adversarial networks of the present invention;

[0070] Figure 2 This is a schematic diagram of the error distribution modeling framework of conditional generative adversarial networks in this invention;

[0071] Figure 3 This is a schematic diagram of the generator structure of cGAN in this invention;

[0072] Figure 4 This is a schematic diagram of the PatchGAN discriminator structure of cGAN in this invention. Detailed Implementation

[0073] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments.

[0074] Generative Adversarial Networks (GANs) possess the ability to model complex probability distributions and generate samples with the same statistical properties as real samples. This invention introduces terrain features, physical error constraints, and a conditional generative adversarial mechanism. Environmental features such as terrain and buildings are used as conditional inputs to a conditional generative adversarial network (cGAN), and adversarial training is performed using real propagation error data. This allows the model to learn the nonlinear mapping relationship between geographical features and propagation errors. The model can generate spatial error distributions that simultaneously possess physical consistency and terrain relevance.

[0075] A wireless channel error distribution modeling method based on the fusion of empirical formulas and generative models, the process is as follows: Figure 1 As shown, it includes the following steps:

[0076] Step 1: Sample Data Collection and Dataset Construction

[0077] First, sample data is collected, including two-dimensional images containing terrain or feature information and a set of electromagnetic parameters. and the measured path loss from the transmitter to each receiver location .

[0078] The set of electromagnetic parameters includes, but is not limited to, transmit power, transmit frequency, transmit antenna height, receive antenna height, and climatic conditions. This set of parameters characterizes the electromagnetic properties of the propagation environment and is a necessary input condition for calculating the theoretical path loss.

[0079] Secondly, for each measuring point Based on the selected empirical formula model, including but not limited to COST-231 and ITU-R P.1546, the electromagnetic parameter set is... Substituting the values ​​into the calculation yields the theoretical path loss:

[0080]

[0081] In the formula, Let be the horizontal distance between the transmitter and the i-th receiver. These are the heights of the transmitting antenna and the receiving antenna, respectively.

[0082] Therefore, the propagation error term between the theoretical model and the measured results is defined as:

[0083]

[0084] This definition quantifies the nonlinear effects caused by complex terrain, building obstruction, multipath effects and other factors that are difficult to account for by empirical formulas in signal propagation in the form of residuals, providing a mapping basis between geographical environment and error distribution for the generative network.

[0085] The specific process of constructing the dataset is as follows:

[0086] After comprehensively considering the signal frequency band and propagation scale, the terrain image is rasterized at a suitable fixed resolution.

[0087] The rasterization process refers to rasterizing the image into multiple raster units, each corresponding to different spatial coordinates. Each raster unit is treated as a pixel, and the terrain height at its center is taken as the pixel's numerical value, thus forming a complete terrain feature image. .

[0088] The aforementioned propagation error term By mapping the corresponding measurement point coordinates to the pixel coordinate system of the rasterized terrain image, a mapping with the terrain feature image is obtained. One-to-one correspondence of the true error distribution map This can be used to construct paired samples for training a generative adversarial network. .

[0089] Step 2: Data Preprocessing

[0090] After constructing the sample data, to ensure consistency in spatial scale, projected coordinates, and numerical range of the input data, a feature extraction module based on a convolutional neural network (CNN) is built. The input data is processed through multiple layers of convolution, pooling, and activation functions to output a high-dimensional environmental feature vector. Specifically, this includes the following steps:

[0091] First, the terrain feature image Corresponding error distribution plot Perform geometric matching and projection unification. Project all data onto the same reference coordinate system and ensure that the terrain image and the error image are spatially aligned at the pixel level.

[0092] Next, the matched images are sized. A segmentation and slicing method is used to crop the large image into several smaller blocks of fixed size. In this embodiment, the model input size is set to 256×256 pixels, but this invention is not limited to this size and can be adjusted appropriately according to the application scenario and hardware resources.

[0093] Subsequently, to reduce channel redundancy, Converted to single-channel grayscale image, the resulting grayscale terrain feature image Error distribution plot Both can be represented in two-dimensional matrix form. ,in Considering the differences in terrain feature distribution and error distribution characteristics, it is necessary to first remove extreme outlier samples, and then perform normalization to obtain a high-dimensional environmental feature map and a true error map, specifically:

[0094] = , =

[0095] in and It is the global extremum calculated over all samples.

[0096] In addition, data augmentation methods such as random rotation and flipping can be used to expand the training sample set to enhance the model's generalization ability and robustness.

[0097] This high-dimensional environmental feature vector is used to characterize the spatial structural characteristics of the wireless propagation environment, such as terrain undulation, building distribution, and occlusion effect, and provides conditional information for the generative model.

[0098] During feature extraction, the image layer preserves the texture and morphological structure of the terrain, containing physical feature information of the signal propagation environment, providing accurate conditional input for the subsequent error generation model.

[0099] Step 3: Construct the Conditional Generative Adversarial Network (cGAN) model

[0100] like Figure 2 As shown, the processed terrain feature image The generator part of the conditional generative adversarial network (cGAN) is used to pass conditional information to describe the spatial structure characteristics of the wireless signal propagation environment; cGAN learns the conditional distribution. An error distribution map is generated, whose statistical structure is consistent with the environmental context and whose numerical variations conform to the characteristics of an empirical model for wireless signal propagation. In this implementation, the conditional generative network model for image-to-image transformation can be selected from, but is not limited to, the Pix2Pix framework.

[0101] 1) Generator Structure: In embodiments of the present invention, the generator G can be selected from a suitable image encoding-decoding structure, such as U-Net. Specifically, as follows... Figure 3 As shown. This structure is suitable for image generation tasks with precise spatial correspondences, ensuring that local details are preserved while maintaining global continuity during the generation process. The generator takes the observed image as input. With random noise vector Under the given conditions, learn to generate an error distribution related to the terrain spatial structure. ,Right now The mapping is as follows: The encoder consists of multiple progressively downsampled convolutional blocks, up to a bottleneck layer with a very small dimension. In the decoder, multiple upsampled convolutional blocks are used to upsample layer by layer, gradually restoring the original image size and mapping the deep terrain features to the spatial details of the error distribution map.

[0102] Each downsampling convolutional block constituting the encoder includes: a two-dimensional convolutional layer for spatial downsampling; a normalization layer, preferably batch normalization, to accelerate convergence and stabilize gradients; and a nonlinear activation layer, preferably LeakyReLU, to enhance gradient propagation in the negative interval. Optionally, a Dropout layer is added to prevent overfitting.

[0103] Each upsampled convolutional block constituting the decoder includes: a transposed convolutional layer that restores the feature map to a higher resolution; a normalization layer; and a non-linear activation layer, preferably ReLU.

[0104] To allow information flow to bypass bottlenecks in dimensional information transmission, this invention introduces skip connections into the generator structure. Specifically, in the generator's... Layer and First Establish skip connections between layers, where This represents the total number of layers in the generator. Each skip connection is used to connect the first... Layer and First All channels of the layer are cascaded to achieve the fusion of features from different layers and enhance information transmission.

[0105] By incorporating terrain conditions into the generator, the generative network can spatially perceive environmental factors such as terrain morphology and building density, establishing a one-to-one mapping between error generation and geographic structure. Furthermore, the difference between measured path loss and empirical formula predictions is used as the training objective, enabling the generator to learn terrain environmental errors that empirical models cannot explain, rather than directly fitting path loss values.

[0106] 2) Discriminator Structure: The discriminator can be selected from PatchGAN or other similar structures, such as... Figure 4 As shown in the figure, the input to the discriminator is the error distribution diagram of the generator's output. Or the actual error distribution map And respectively compared with the corresponding terrain feature images The channel direction is spliced, that is:

[0107]

[0108]

[0109] Such that at any spatial location The concatenated tensor simultaneously contains error information and corresponding environmental feature information, thus establishing a spatial correspondence between the two for subsequent discrimination and learning. The concatenated tensor undergoes progressive downsampling and feature extraction via a multi-layer convolutional network structure, outputting a discrimination matrix.

[0110] ,

[0111] in and Determined by the total downsampling factor of the network. Each element One of the corresponding input images is of size The local receptive field region (i.e., patch) is defined, and the value of each element represents the similarity score between the generated result and the real sample within that region.

[0112] In the task scenario of this invention, each pixel value of the error distribution map has a clear physical meaning, representing the difference between the measured path loss and the path loss predicted by the empirical formula at that geographical location. The PatchGAN discriminator no longer outputs a single global true / false label, but instead provides discrimination results for multiple local regions of the input image, thereby constraining the local consistency and texture details of the generator output at the spatial level. Through this local discrimination mechanism, the model can effectively capture spatial features such as terrain structure changes and building density differences, achieving more fine-grained error distribution determination.

[0113] Step 4: Adversarial Training and Optimization of the Network Model

[0114] The adversarial training process employs a least-squares form adversarial loss function.

[0115] ,

[0116] in, For real input samples, For the corresponding condition information, This represents the statistical expectation value of the discrimination result error calculated based on the input data and its corresponding condition information. This represents the statistical expectation of the discrimination result error calculated from the input data and its generator output.

[0117] This loss function mitigates the gradient vanishing problem when the discriminator is too strong, making the conditional generation process more stable. The discriminator D aims to maximize this loss to better distinguish between real and fake samples, while the generator G aims to minimize this loss so that the discriminator cannot differentiate between them. Therefore, the generator and discriminator form an adversarial optimization relationship, and their optimization objective can be uniformly expressed as:

[0118] ,

[0119] In the task scenario of this invention, while focusing on the statistical form of the error distribution, it is also necessary to ensure the controllability of numerical accuracy. Therefore, the L1 constraint term for the output error is defined as follows: The ultimate goal of conditional generative adversarial networks is:

[0120]

[0121] in, The weighting coefficient represents the importance of numerical precision.

[0122] The specific process of adversarial training and optimization is as follows: after weight initialization, an alternating iterative strategy is used to update parameters.

[0123] First, fix the generator parameters and update only the discriminator. Then, input real sample pairs... With generated sample pairs The discriminator calculates the discrimination loss, calculates the gradient of the discriminator parameters and updates them so that the output approaches 1 for real samples and approaches 0 for generated samples.

[0124] Then, with the discriminator parameters fixed, only the generator is updated. The terrain feature map is then... Input generator, output prediction error distribution The discriminator receives the generated sample pairs. The generator calculates a loss function based on the discriminator's output, including a generator adversarial loss term. and precision constraints The loss gradient is backpropagated to the generator network and the weights are updated, so that the output error distribution gradually approximates the true error characteristics under the terrain conditions.

[0125] Furthermore, the Adam optimization algorithm is used as the gradient update strategy during training, with a learning rate set to 1×10⁻⁶. -4 The momentum parameters were chosen as β1=0.5 and β2=0.999. To prevent overfitting and oscillations in the model, mini-batch stochastic gradient descent was used for training, with each batch containing 4 to 16 samples.

[0126] As training iterates, the discriminator's output gradually approaches 1 on real samples and approaches 0 on generated samples, indicating that its discriminative ability is continuously improving; at the same time, the distance between the generator's output error distribution and the real error is continuously decreasing. As the error decreases, the adversarial loss tends to reach equilibrium. When the generator can generate pseudo-samples that are difficult for the discriminator to distinguish, the adversarial training reaches a relatively stable state, and the model converges.

[0127] Step 5: Analyze the path loss results output by the empirical model. Compensation calculations are performed using the error correction map generated by the trained cGAN:

[0128]

[0129] in The corrected path loss prediction results are shown below. To generate an error map, thereby obtaining a continuous path loss distribution map or signal strength map in geospatial space.

[0130] Therefore, this generative model can serve as a supplementary and corrective module to empirical formulas or deep learning prediction models under complex terrain conditions, generating reliable data in scenarios where data is scarce or the environment is complex.

Claims

1. A wireless channel error distribution modeling method based on the fusion of empirical formula and conditional generative adversarial network, characterized in that, The method comprises the following steps: Step one, collect sample data and build dataset , including topographic feature images and real error distribution maps corresponding thereto ; Step two, construct a feature extraction module based on convolutional neural network, and extract features from the constructed data set to obtain high-dimensional environment feature map and real error map ; Step three, constructing a conditional generative adversarial network model; The conditional generative adversarial network model comprises a generator and a discriminator: (1) The generator learns to generate a mapping from the high-dimensional environment feature image to a random noise vector under the condition that the error distribution related to the terrain spatial structure is learned , that is . The discriminator is specifically as follows: The input of the discriminator is the error distribution map of the generator output or the real error distribution map , and is spliced with the channel direction of the high-dimensional environment feature image , that is: to characterize a spatial correspondence between the generation error and the environmental feature; The input tensor is gradually down-sampled and features are extracted through a multi-layer convolutional network structure, and a discrimination matrix is outputted: , wherein with The total downsampling factor of the network determines, each element in the matrix corresponding to a local receptive field region of size of the input image, the value of each element represents the similarity score of the generated result in this region with the true sample; The discriminator gives a discrimination result for each local area of the input image, thereby constraining the local consistency and texture details of the output of the generator in a spatial level; Step four, constructing an objective function, and adopting an alternating iteration strategy to perform adversarial training and optimization on the conditional generative adversarial network model; In the adversarial training process, an adversarial loss function in a least square form is adopted: ， wherein, is a real input sample, is corresponding condition information, denotes a statistical expectation value of a discrimination result error calculated based on the input data and its corresponding condition information, denotes a statistical expectation value of a discrimination result error calculated by the input data and its generator output; Based on the loss function, the discriminator D aims to maximize the loss to distinguish true and false samples; the generator G expects the loss to be minimum, so that the discriminator cannot distinguish true and false; therefore, the generator and the discriminator constitute an adversarial optimization relationship, and the optimization objective is uniformly expressed as: , The L1 constraint term of the output error is defined as: , is the L1 norm; then the final goal of the conditional generative adversarial network is: wherein are weight coefficients, indicating the importance of numerical accuracy; Step five, outputting the cGAN result after training to correct an empirical formula or a deep learning prediction model, and obtaining a continuous path loss distribution map or a signal strength map in a geographical space; Compensating calculation is performed on the path loss result outputted by the empirical model and the error correction map generated by the cGAN: wherein is the corrected path loss prediction result, is the generation error map.

2. The method of modeling wireless channel error distribution according to claim 1, wherein, The construction process of the data set is specifically as follows: The two-dimensional image containing the terrain data is rasterized at a fixed resolution, each raster representing a spatial coordinate point, and the raster unit is regarded as a pixel point, and the pixel value is the terrain height or shielding feature of the center point, to form a complete terrain feature image ; The theoretical path loss of each measuring point is calculated by substituting the electromagnetic parameters into the selected empirical formula model, and the propagation error term is constructed by subtracting the measured result; mapping the propagation error terms into the pixel coordinate system of the rasterized terrain image according to their corresponding measurement point coordinate positions, resulting in a terrain feature image one-to-one real error distribution map , thereby constituting a dataset .

3. The method of claim 1, wherein, The process of feature extraction is specifically as follows: First, the terrain feature image with the corresponding error distribution map geometric matching and projection unification; Then, the matched images are cut into small blocks of a fixed size in a segmentation and slicing manner. Finally, the terrain feature image is converted into a single-channel grayscale image, and the grayscale terrain feature image and the error distribution image are both expressed in the form of a two-dimensional matrix , where , and respectively represent the pixel values of the image height and width; the grayscale terrain feature image and the error distribution image are pruned of extreme abnormal samples, and then normalized to obtain a high-dimensional environment feature image and a real error image, specifically: = ， = wherein and is the global extreme value calculated for all samples.

4. The method of modeling wireless channel error distribution of claim 1, wherein, The generator selects an image encoding-decoding structure, wherein the encoder is composed of multiple progressive down-sampling convolution blocks until a bottleneck layer; in the decoder, multiple up-sampling convolution blocks are used for layer-by-layer up-sampling, the original image size is gradually restored, and high-dimensional environmental features are mapped to the spatial details of the error distribution map.

5. The method of modeling wireless channel error distribution of claim 4, wherein, Each down-sampling convolution block of the encoder comprises: a two-dimensional convolution layer for realizing spatial down-sampling; a normalization layer, preferably batch normalization, for accelerating convergence and stabilizing gradient; and a nonlinear activation layer, preferably LeakyReLU, for enhancing negative interval gradient transmission; optionally, a Dropout layer is added to prevent overfitting.

6. The method of modeling wireless channel error distribution of claim 4, wherein, Each up-sampling convolution block of the decoder comprises: a transposed convolution layer for restoring the feature map to a higher resolution; a normalization layer; and a nonlinear activation layer, preferably ReLU.

7. The method of modeling wireless channel error distribution of claim 4, wherein, The bottleneck layer introduces a skip connection in the generator structure, specifically, a skip connection is established between the first layer and the last layer of the generator, where denotes the total number of layers of the generator; each skip connection is used to cascade all channels of the first layer and the last layer, so as to realize fusion of different layer features and enhancement of information transmission.

8. The method of modeling wireless channel error distribution of claim 1, wherein, The specific process of the adversarial training and optimization is as follows: First, fix the generator parameters, only update the discriminator; by inputting real sample pairs and generated sample pairs , the discriminator calculates the discrimination loss, takes the gradient of the discriminator parameters and updates them so that the output tends to 1 for real samples and 0 for generated samples; Then, fix the discriminator parameters and only update the generator; input the terrain feature map to the generator and output the predicted error distribution ; the discriminator receives the generated sample pair and outputs its authenticity score; The generator calculates a loss function according to the output result of the discriminator, including a generator adversarial loss term and a precision constraint term ; the loss gradient is reversely transmitted to the generator network and the weights are updated, so that the output error distribution gradually approximates the real error characteristics under the terrain condition; As the training iteration proceeds, the output of the discriminator gradually approaches 1 on real samples and 0 on generated samples, indicating that its ability to distinguish is constantly enhanced; at the same time, the error distribution of the generator output is constantly reduced from the distance of the real error, The error is constantly decreasing, and the adversarial loss is tending to balance; when the generator can generate pseudo samples that are difficult for the discriminator to distinguish, the adversarial training reaches a relatively stable state, and the model converges.

9. The method of modeling wireless channel error distribution of claim 8, wherein, In the training process, the Adam optimization algorithm is adopted as a gradient update strategy, and a small batch stochastic gradient descent is adopted.

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