Rail transit intelligent ray tracing channel modeling method based on local phase error calibration

Abstract

The embodiment of the invention provides a rail transit intelligent ray tracing channel modeling method based on local phase error calibration, and aims to solve the problem of inaccurate channel modeling caused by environment modeling errors and dynamic phase distortion in a traditional ray tracing technology in a high-speed dense rail transit scene. The method comprises the following steps: firstly, constructing an intelligent railway communication system three-dimensional geometric model comprising a transmitting end and a receiving end, generating multipath parameters by using ray tracing simulation, and establishing a deterministic frequency response model based on the multipath parameters; secondly, an independent and identically distributed von Mises phase error # imgabs0 # is superposed in the deterministic model, and a random channel model is formed; and finally, optimizing a material electromagnetic parameter vector by using an actually measured data set, minimizing the difference between ray tracing prediction and actually measured data, and improving the generalization ability of the model at an unknown position.

Description

Technical Field

[0001] The present invention belongs to the fields of communication technology, channel modeling, etc., and particularly relates to a rail transit intelligent ray-tracing channel modeling method based on local phase error calibration. Background Art

[0002] With the development of intelligent rail transit systems towards high speed and high density, high-reliability vehicle-ground communication has become the core support for ensuring operation safety and efficiency. In this context, the accuracy of wireless channel models directly determines the key parameters of communication system design, such as modulation methods, error correction coding thresholds, and resource allocation strategies. However, the unique electromagnetic propagation characteristics of the rail transit environment, including strong multipath effects in confined spaces, non-stationarity caused by high-speed movement, and waveguide characteristics of tunnel / elevated structures, make it difficult for traditional methods based on statistical modeling or empirical path loss to meet the requirements of 5G-R and next-generation communication systems.

[0003] Ray Tracing (RT) technology has become the preferred solution to solve this problem due to its physical interpretability based on the first principles of electromagnetics. By simulating the interaction between rays and the environment (such as reflection, diffraction, and scattering), ray tracing can extract high-resolution spatial channel characteristics. However, the practical application of ray tracing in rail transit scenarios still faces bottlenecks. First, environmental modeling errors significantly affect the accuracy of ray tracing. In a closed environment (such as the wall inside a tunnel), the lack of accurate prior knowledge of material properties (such as dielectric constant) leads to deviations in the calculation of the initial ray path. Second, dynamic phase distortion becomes more serious in the case of high-speed train movement. The coupling effect of the Doppler effect and phase noise brought by non-stationary motion makes the traditional power domain calibration method relying on Received Signal Strength (RSS) fail. It should be noted that in the millimeter-wave band, due to the shortening of the wavelength, the influence of phase error on the channel impulse response is amplified, and the existing energy superposition model based on the Friis transmission equation has shown theoretical inadaptability. The existence of these problems makes it more difficult for traditional ray tracing technology to effectively meet the requirements of vehicle-ground wireless channel modeling in rail transit systems.

[0004] Traditional RT channel model calibration methods usually assume that all path phase predictions are completely accurate and directly construct the channel frequency response based on the deterministic parameters output by RT (such as complex amplitude, time delay, angle). Such models achieve efficient simulation by simplifying the calculation process (such as ignoring the phase error term) and are applicable to static or low-dynamic scenarios. However, in complex environments such as actual high-speed railways, due to scene geometric deviations (errors in dimensions and positions) and uncertainties in material electromagnetic parameters (such as dielectric constant measurement errors), there will be significant deviations between the path phases predicted by RT and the actual channel response. This deviation will be dynamically amplified in high-speed mobile scenarios, resulting in phase mismatch between the model output and the measured data, thereby affecting key performance indicators such as channel capacity estimation and beamforming design. In addition, such models cannot characterize the random phase fluctuation characteristics of multipath interference in the real channel, resulting in overly idealized simulation results and making it difficult to support the design and optimization of highly reliable communication systems.

[0005] To address the deficiencies of the deterministic model, some improved methods introduce the assumption of uniform phase error, that is, assume that the phase errors of all paths follow a uniform distribution within the interval [−π, π) (corresponding to the limit case of κ→0 in the von Mises distribution) to cover the phase randomness in the worst-case scenario. This method partially alleviates the phase sensitivity problem of the deterministic model through statistical means such as Monte Carlo simulation. However, the uniform distribution assumption is too conservative and ignores the possible direction concentration of actual errors (such as errors distributed around the mean), resulting in calibration results deviating from the statistical characteristics of the real scenario. In addition, this method cannot dynamically adjust the error distribution parameters (such as the concentration parameter κ) in a data-driven manner, limiting the generalization ability of the model to multiple scenarios. In high-dynamic scenarios such as high-speed railways, the uniform distribution model also requires a large number of samples to cover the randomness, resulting in a significant reduction in computational efficiency and difficulty in capturing the phase time correlation caused by Doppler frequency shift, leading to insufficient dynamic channel prediction accuracy.

[0006] In summary, in ray tracing (RT) channel modeling, the core role of the calibration process is to optimize model parameters through data-driven methods to fit the difference between simulation predictions and real channel responses. Existing calibration techniques that ignore phase errors directly use RT outputs as deterministic channel models. Although this simplifies the calculation process, it cannot characterize the statistical properties of random phase fluctuations in the actual channel. The uniform phase error calibration method, although introducing phase randomness through statistical means, assumes that the error follows a uniform distribution (i.e., the worst-case assumption), ignoring the possible direction concentration of actual errors (such as errors distributed around the mean). Neither of these two methods combines measured data to dynamically adjust the error distribution parameters, nor do they jointly optimize material properties, resulting in the calibrated model being difficult to adapt to dynamic environmental changes and unable to achieve high-precision channel prediction at unknown locations. Therefore, there is an urgent need for a calibration framework that integrates phase error modeling and data-driven parameter optimization to improve the generalization ability and reliability of RT models in complex scenarios. Summary of the Invention

[0007] Aiming at the problems existing in the prior art, the present invention provides a method for intelligent ray tracing channel modeling of rail transit based on local phase error calibration, aiming to solve the problem of inaccurate channel modeling caused by environmental modeling errors and dynamic phase distortion in traditional ray tracing techniques in high-speed and dense rail transit scenarios. First, a three-dimensional geometric model of an intelligent railway communication system including a transmitter and a receiver is constructed, and ray tracing simulation is used to generate multipath parameters, and a deterministic frequency response model is established based on the multipath parameters. Secondly, a local phase error term is superimposed on the deterministic model, and the phase error of each path is modeled as an independent and identically distributed von Mises distribution , forming a random channel model; finally, the electromagnetic parameter vector of the material is optimized using the measured data set to minimize the difference between ray tracing predictions and measured data, and improve the generalization ability of the model at unknown locations.

[0008] The technical solution of the present invention: A method for intelligent ray tracing channel modeling of rail transit based on local phase error calibration, comprising the following steps: Step 1: Construct a three-dimensional geometric model of an intelligent railway communication system including a transmitter and a receiver, use ray tracing simulation to generate multipath parameters, and establish a deterministic frequency response model based on the multipath parameters; Step 2: Superimpose a local phase error term on the deterministic model, and model the phase error of each path as an independent and identically distributed von Mises distribution , and its concentration parameter can be adjusted to match the actual error distribution; Step 3: Optimize the electromagnetic parameter vector of the material using the measured data set to minimize the difference between the ray tracing prediction and the measured data, and improve the generalization ability of the model at unknown locations.

[0009] The specific description is as follows: In Step 1, the construction process of the deterministic frequency response model is specifically as follows: Step 1.1 In the intelligent railway scenario, the positions of the transmitter (Tx, ground station) and the receiver (Rx, high-speed train) are located in the three-dimensional Cartesian coordinate system and . The transmitter and the receiver are respectively equipped with and antenna arrays. The signal transmission between the vehicle and the ground occurs in a frequency band with a bandwidth of , where is the highest frequency of the signal, is the lowest frequency of the signal, and the center frequency of the carrier wave is .

[0010] Step 1.2 Through the path calculated by ray tracing, the simulation model models the channel according to the scene geometric features, the positions of the transmitter and the receiver , and the material property vector .

[0011] Among them, the scene geometric features include the spatial path and height difference structure of one or more railway tracks, and also include platform, tunnel, slope, building facade structure objects, which are used to simulate reflection, occlusion and scattering effects. Each structure has clear spatial position, boundary contour and height information.

[0012] The material property vector includes: permittivity, conductivity, permeability, scattering coefficient and cross-polarization cancellation.

[0013] The ray tracing method (RT) maps the input information (i.e., the scene geometric features, the positions of the transmitter and the receiver, and the material property vector ) to feasible propagation path parameters. The path parameters include complex amplitude, propagation delay, departure angle and arrival angle. The path characteristics generated by RT are represented by the function Among them, the input coordinates and the material parameters are mapped to the parameters of paths. Each propagation path is composed of a complex amplitude , a delay s, a pair of departure angles and a pair of arrival angles as described below.

[0014] Among them, including the elevation angle from the perspective of the transmitter , and the azimuth angle . including the elevation angle at the receiver and the azimuth angle .

[0015] The multipath parameters generated by ray tracing in Step 1.3 , are used to reconstruct the frequency response at each subcarrier frequency for each path. Specifically, the channel frequency response of a single path is expressed as Among them, is the complex amplitude of the path, is the time delay of the path, and are the antenna steering vectors at the receiving end and the transmitting end respectively, is the Kronecker product, is the conjugate of the transmitting antenna steering vector.

[0016] The contributions of all paths on all subcarriers are accumulated to obtain the frequency response model of the entire system: Among them, is the phase contribution jointly determined by the time delay, the departure angle, and the arrival angle: is the projection in the frequency domain of the delay of the subcarrier frequency phase related to the propagation time delay , is a vector representing the phase shift of this path p on different subcarriers: The frequency response model of the entire system obtained above does not consider: there are slight differences between the geometry and material characteristics of the scenario assumed in the ray tracing simulation and the actual physical system, resulting in errors in the phase prediction of the radio wave propagation path.

[0017] In Step 2, a local phase error term is superimposed in the deterministic model, specifically: To compensate for the error, a phase error term is introduced, and this error follows the von Mises distribution , where the mean is 0 and the concentration parameter of the global prior von Mises distribution .

[0018] Superimpose the local phase error for each path , after the phase error is introduced, the channel model becomes: are independent and identically distributed phase error terms where, represents the zero-order modified Bessel function and is used for normalization.

[0019] It should be noted that when defining the probability density of this distribution, the general variable represents any concentration, and may be used for the posterior distribution (such as ) or the prior (such as ) in actual use. When , , the model degenerates into a deterministic model that ignores the phase error; when , the model degenerates into a channel model that adopts a uniform phase distribution.

[0020] To further enhance the adaptability of the channel model to the propagation characteristics of complex environments, the phase error vector of each path is modeled as follows: where, is the phase error vector of each path and follows the von Mises distribution.

[0021] After integrating the phase error into the deterministic model, the overall stochastic channel model is obtained as: where, represents the deterministic part composed of the amplitudes of all paths and the antenna steering vectors.

[0022] In step 3, according to the measured data set , minimize the difference between the ray tracing simulation data and the measured data. The specific process is as follows: Step 3.1 Obtain a training set containing N channel frequency response observation data: where, are the coordinates of the receiver and the transmitter The measured channel frequency response at. The calibration objective is to adjust the electromagnetic material parameters such that the channel simulation result at the known position is consistent with the measured data The difference is minimal and has good generalization at unknown positions. and has good generalization at unknown positions.

[0023] Step 3.2 In the phase error-aware calibration scheme, the channel observation is modeled as a noise observation based on the phase error-aware model, expressed as where is a noise vector composed of a complex Gaussian distribution and is a random phase vector used to represent the phase error. The phase error is independent and identically distributed and follows the von Mises distribution with being the prior concentration parameter.

[0024] To solve the likelihood function of the observation , the joint distribution of the phase error for each path is marginalized to obtain: Furthermore, by minimizing the negative logarithm of the marginal likelihood logarithm with respect to the material parameter , the parameter calibration of the RT model is achieved: Step 3.3 Since the marginal posterior is not integrable, variational inference is used to approximate the marginal likelihood. A variational distribution is defined, denoted as , where and are the mean parameter and the concentration parameter, respectively. The variational distribution describes the phase error estimation corresponding to all paths , and this distribution is expressed as The variational expectation-maximization algorithm approximately solves the problem by minimizing the variational free energy. Its free energy function is expressed as. By minimizing the variational free energy, the phase error distribution of each sample is updated, that is, the mean phase and the concentration of the path are updated, and the posterior approximation distribution is updated: The free energy is specifically expressed as: where is the Bessel ratio, is the Bessel ratio vector, denotes constructing a diagonal matrix for the vector.

[0025] Step 3.4: Use the variational expectation maximization algorithm to solve for the calibrated parameters ; Among them, in the expectation step, fix the material parameters , update the phase error estimate for each data point by minimizing the variational free energy, and update the phase mean for each path where denotes taking the phase of the complex vector element by element; is a column vector of dimension where all elements are 1, and together with constitute the prior part, introducing a unified prior term for each path component; the symbol i represents the current iteration index, used to identify the parameter estimate value in the i-th round of the variational expectation maximization algorithm.

[0026] Update the concentration parameter for each path In the maximization step, given the updated phase error parameter , update the material parameter by minimizing the variational free energy Update the concentration parameter of the prior .

[0027] Step 3.5 After final calibration, the phase error-aware channel frequency response model (applicable to any location ) can be expressed as: where denotes the path structure matrix (including delay, angle, path gain, etc.) constructed using the final calibrated material electromagnetic parameters ; denotes the mean phase error of each path estimated through variational inference.

[0028] The beneficial effects of the present invention are as follows: By adopting the von Mises distribution to probabilistically model multipath phase errors, the present invention significantly improves the accuracy and robustness of ray tracing channel calibration. By explicitly modeling phase uncertainty, the systematic bias of traditional phase-ignoring calibration is avoided, and statistical modeling is performed on the phase uncertainty of each path. The phase perturbation of independent sampling for each path is modeled as , realizing the modeling of local phase errors, introducing a variational concentration parameter to achieve adaptive error compensation for ray tracing simulation, maintaining stable performance in a high-noise environment, and providing a more reliable channel modeling tool. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 It is a schematic diagram of the processing steps of the method of the present invention; Figure 2 It is a schematic diagram of the calibration process of the intelligent ray tracing simulator of the present invention; Figure 3 It is a schematic diagram for explaining the definition of the angle path parameters of the example scenario and the planar antenna array proposed by the present invention; Figure 4 It is a schematic diagram of the change of the calibration error of the present invention with the signal-to-noise ratio (normalized dielectric constant error); Figure 5 It is a schematic diagram of the change of the calibration error of the present invention with the signal-to-noise ratio (normalized conductivity error); Figure 6 It is a schematic diagram of the change of the calibration error of the present invention with the signal-to-noise ratio (normalized received power error). DETAILED DESCRIPTION OF THE EMBODIMENTS

[0030] The technical solutions provided by the present application will be further described below in conjunction with specific embodiments and their accompanying drawings. In combination with the following description, the advantages and features of the present application will become clearer.

[0031] An intelligent rail transit ray tracing channel modeling method based on local phase error calibration includes the following steps: (such as Figure 1 ) Step 1: Construct a three-dimensional geometric model of an intelligent railway communication system including a transmitter and a receiver, generate multipath parameters using ray tracing simulation, and establish a deterministic frequency response model based on the multipath parameters; Step 2: Superimpose independent and identically distributed von Mises phase errors in the deterministic model to form a random channel model, and its concentration parameter can be adjusted to match the actual error distribution; Step 3: Optimize the electromagnetic parameter vector of the material using the measured data set to minimize the difference between the ray tracing prediction and the measured data, and improve the generalization ability of the model at unknown positions.

[0032] The schematic diagram of the calibration process of the intelligent ray tracing simulator of the present invention is as follows Figure 2 .

[0033] The specific steps are as follows: Step 1: Combine the three-dimensional geometric model of the intelligent railway communication system and establish a deterministic frequency response model based on ray tracing simulation Step (11) In the intelligent railway scenario, the transmitting end (Tx) and the receiving end (Rx) are located at positions in the three-dimensional Cartesian coordinate system and , representing the ground station and the high-speed train. The transmitting end and the receiving end are respectively equipped with and antenna arrays. The signal transmission between the vehicle and the ground occurs in a frequency band with a bandwidth of , and the center frequency of the carrier wave is .

[0034] Step (12) According to the paths calculated by ray tracing, the simulation model is based on the scene geometry, the positions of the transmitting end and the receiving end , and the material property vector to model the channel.

[0035] Among them, the material property vector includes parameters such as dielectric constant, conductivity, permeability, scattering coefficient, and cross-polarization cancellation.

[0036] RT maps these input information to feasible propagation path parameters. The path parameters include complex amplitude, propagation delay, departure angle, and arrival angle, and its function is expressed as Among them, the input coordinates and the material parameters are mapped to the parameters of the path. Each propagation path is described by the complex amplitude , delay s, a pair of departure angles and a pair of arrival angles .

[0037] Among them, includes the elevation angle seen from the perspective of the transmitter, and the azimuth angle , contains the elevation angle and the azimuth angle at the receiver, as shown in Figure 3 .

[0038] Step (13) The multipath parameters generated by ray tracing , reconstruct the frequency response of each path at each sub - carrier frequency. Specifically, the channel frequency response of each path is expressed as where is the complex amplitude of the path, is the time delay of the path, and are the antenna steering vectors at the receiver and transmitter respectively, is the Kronecker product, is the conjugate of the transmit - antenna steering vector.

[0039] Accumulate the contributions of all paths on all sub - carriers to obtain the frequency - response model of the entire system: where is the phase contribution determined jointly by the time delay, angle of departure, and angle of arrival: while is the contribution of the sub - carrier frequency phase related to the propagation time delay : Step 2: There are small differences between the geometry and material characteristics of the scenario assumed by the ray - tracing simulation and the actual physical system, resulting in errors in the prediction of the phase of the radio - wave propagation path. To compensate for the errors, introduce the phase - error term , which follows the von Mises distribution , where the mean is 0 and the concentration parameter .

[0040] After introducing the phase error, the channel model becomes: where is an independent and identically - distributed phase - error term that satisfies the von Mises distribution. Obtain the phase - error vector and the phase - factor error vector .

[0041] After incorporating the phase error into the deterministic model, the resulting stochastic model is: where is matrix, representing the deterministic part composed of the amplitudes of all paths and the antenna steering vectors.

[0042] Step 3: Minimize the difference between the ray tracing prediction and the measured data. Step (31) Obtain a training set containing N channel frequency response observation data: Among them, each observation data is the channel frequency response at the coordinates of the receiver and the transmitter . The calibration objective is to make the channel simulation result at the known position more consistent with the measured data by adjusting the electromagnetic material parameters , and it can be extended to a new position .

[0043] In step (32), in the phase error-aware calibration scheme, the channel observation is modeled as a noise observation based on the phase error-aware model, expressed as Among them, is a noise vector composed of a complex Gaussian distribution , is a random phase vector used to represent the phase error. The phase error is independent and identically distributed and follows the von Mises distribution , is the prior concentration parameter.

[0044] According to the data set , estimate the maximum likelihood solution of the ray tracing simulation parameter : In step (33), since the integral is difficult to calculate analytically, variational inference is used to approximate the marginal likelihood, and a variational distribution is defined, denoted as , where and are the mean parameter and the concentration parameter respectively. The mean represents the nominal estimated value of the phase error, and the concentration parameter quantifies the uncertainty of this estimated value. The variational distribution describes the phase error estimation corresponding to all paths , and this distribution is expressed as The variational expectation-maximization algorithm approximately solves the problem by minimizing the variational free energy, and its free energy function is expressed as The free energy is specifically expressed as: Among them, is the Bessel ratio, is the Bessel ratio vector, represents constructing a diagonal matrix for the vector.

[0045] Step (34) adopts the variational expectation-maximization algorithm to solve the calibrated parameters ; Among them, in the expectation step, the material parameters are fixed, and the phase error estimate of each data point is updated by minimizing the variational free energy, and the phase mean of each path is updated Among them, represents taking the phase of the complex vector element by element; is a column vector with a dimension of , where all elements are 1, and together with it constitutes the prior part, introducing a unified prior term for each path component; Update the concentration parameter of each path In the maximization step, given the updated phase error parameter , the material parameters are updated by minimizing the variational free energy Update the concentration parameter of the prior .

[0046] Step (35) After final calibration, the phase error-aware channel frequency response model (applicable to any position ) can be expressed as: Among them, represents the path structure matrix (including delay, angle, path gain, etc.) constructed using the finally calibrated material electromagnetic parameters ; represents the mean of the phase error of each path estimated by variational inference.

[0047] Channel modeling is completed.

[0048] Use a Linux server to build a simulation environment and conduct a comparative performance verification of the method of the present invention and typical methods. The comparative methods include: calibration based on local phase error, calibration based on ignoring phase error, and calibration based on average phase error.

[0049] During the calibration process, assume that the true material parameters are unknown and perform calibration through known observation data . . By modeling and simulating the paths of the receiver and transmitter, the goal is to estimate electromagnetic material parameters using different calibration methods. The final calibration effect is evaluated by the following indicators: normalized dielectric constant error, ; normalized conductivity error, ; and normalized received power error, , where is the total power received at position by all propagation paths estimated using the ray tracing model and calibration parameters .

[0050] Adopt the normalized dielectric constant error, normalized conductivity error, and normalized received power error as evaluation indicators to quantitatively evaluate the performance of various calibration methods under different signal-to-noise ratio conditions, such as Figure 4 , Figure 5 and Figure 6 . Among them: Normalized dielectric constant error, ; Normalized conductivity error, ; Normalized received power error, , which reflects the accuracy of the calibration parameters in predicting the received power at each position.

[0051] The experimental results show that the calibration based on local phase error is significantly better than other methods in all indicators. Specifically, Figure 4 and Figure 5 show that the calibration based on local phase error maintains the lowest dielectric constant and conductivity estimation errors throughout the range of SNR from 0 dB to 30 dB, indicating its obvious advantages in parameter identification accuracy and anti-interference ability. Figure 6Further, it is shown that in the received power prediction task, calibration based on local phase error brings about a performance improvement of approximately 10 dB compared to the calibration method based on uniform phase error at SNR = 0 dB, and this improvement can reach 20 dB at SNR = 30 dB, and its performance continues to enhance as SNR increases. In contrast, the calibration method based on ignoring phase error fails to converge to the true parameters at all SNR levels, resulting in a significant deviation of its power prediction from the true value; although the calibration based on uniform phase error shows improvement at high SNR, its overall prediction ability is still inferior to that based on local phase error. It should be noted that the shaded area in the figure represents the range between the first and third quartiles (Q1–Q3), reflecting the degree of dispersion of the results of each algorithm in multiple independent experiments. The narrower the shade, the more concentrated and stable the algorithm output results are among different trials. It can be observed that the calibration method based on local phase error has the smallest interquartile range under all SNR conditions, indicating that its estimation results have both high precision and good robustness; while the distribution of the calibration method based on ignoring phase error is extremely dispersed, further confirming its characteristic of prediction failure in the presence of phase perturbations. In summary, the calibration method based on local phase error proposed in this paper is superior to the existing ray-tracing calibration methods in terms of accuracy, stability, and generalization ability by introducing a path-level phase uncertainty modeling mechanism.

[0052] As described above, the above are only preferred examples of the present invention, and the scope of the rights claimed by the present invention is not limited thereto. The present invention has many other embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art can make various corresponding changes and deformations according to the present invention, but these changes and deformations should all fall within the protection scope of the appended claims of the present invention.

Claims

1. An intelligent ray tracing channel modeling method for rail transit based on local phase error calibration, characterized in that It includes the following steps: Step 1: Construct a three-dimensional geometric model of an intelligent railway communication system including a transmitter and a receiver, generate multipath parameters using ray tracing simulation, and establish a deterministic frequency response model based on the multipath parameters; Step 2: Superimpose local phase error terms in the deterministic model and model the phase error of each path as an independent and identically distributed von Mises distribution , whose concentration parameter is adjustable to match the actual error distribution; Step 3: Optimize the electromagnetic parameter vector of the material using the measured data set to minimize the difference between the ray tracing prediction and the measured data, and improve the generalization ability of the model at unknown locations.

2. The method according to claim 1, wherein Step 1 includes the following steps: Step 1.1 In the intelligent railway scenario, the transmitter Tx and the receiver Rx are located at positions in a three-dimensional Cartesian coordinate system and ; The transmitter and the receiver are respectively equipped with and antenna arrays; The signal transmission between the vehicle and the ground occurs in a frequency band with a bandwidth of , where is the highest frequency of the signal, is the lowest frequency of the signal, and the center frequency of the carrier wave is ; Step 1.2 calculates the path through ray tracing, and the simulation model models the channel according to the scene geometric characteristics, the positions of the transmitter and the receiver , as well as the material property vector ; The ray tracing method maps the input information into feasible propagation path parameters. The path parameters include complex amplitude, propagation delay, departure angle, and arrival angle. The path characteristics generated by RT are represented by a function as Among them, the input coordinates and material parameters are mapped to the parameters of the paths, and each propagation path is described by a complex amplitude , a delay s, a pair of departure angles and a pair of arrival angles ; Among them, including the elevation angle as seen from the transmitter , and the azimuth angle , containing the elevation angle at the receiver and the azimuth angle ; Multipath parameters generated by ray tracing in Step 1.3 , and the frequency response of each path at each subcarrier frequency is reconstructed; specifically, the channel frequency response of a single path is expressed as wherein, is the complex amplitude of the path, is the time delay of the path, and are the antenna steering vectors of the receiving end and the transmitting end respectively, is the Kronecker product, is the conjugate of the transmitting antenna steering vector; Accumulate the contributions of all paths on all subcarriers to obtain the frequency response model of the entire system: Among them, is the phase contribution jointly determined by the time delay, the departure angle, and the arrival angle: For the projection in the frequency domain of the delay of the subcarrier frequency phase related to the propagation delay is a vector representing the phase shift of this path p on different subcarriers: ​ 。 3. The method according to claim 2, wherein In Step 1.2, The geometric features of the scenario include the spatial paths, height differences of one or more railway tracks, and also include platforms, tunnels, slopes, building facade structures, etc., which are used to simulate reflection, occlusion, and scattering effects. Each structure has clear spatial position, boundary contour, and height information; The material property vector includes: permittivity, conductivity, permeability, scattering coefficient, and cross-polarization cancellation.

4. The method according to claim 1, wherein In step 2, to compensate for the error, a phase error term is introduced , and this error follows a von Mises distribution , where the mean is 0 and the concentration parameter ; After introducing the phase error, the channel model becomes: Among them, are independent and identically distributed phase error terms, satisfying the von Mises distribution; the phase error vector and the phase factor error vector are obtained; After incorporating the phase error into the deterministic model, the resulting stochastic model is: Among them, is a matrix, representing the deterministic part composed of the amplitudes of all paths and the antenna steering vectors.

5. The method according to claim 1, wherein Step 3 includes the following steps: Step 3.1 Obtain a training set containing N channel frequency response observation data: Among them, is the measured channel frequency response at the coordinates of the receiving and transmitting ends ; the calibration objective is to adjust the electromagnetic material parameters such that the channel simulation results at the known location have the smallest difference from the measured data and have good generalization on the unknown location . Step 3.2 In the phase error perception calibration scheme, the channel observation is modeled as a noise observation based on the phase error perception model, expressed as Among them, is a noise vector composed of a complex Gaussian distribution ; is a random phase vector used to represent the phase error; the phase error is independent and identically distributed and follows the von Mises distribution , is the prior concentration parameter; To solve for the likelihood function of the observation and marginalize the joint distribution of the phase error distributions for each path's phase error we obtain: Minimize the negative logarithm of this marginal likelihood value with respect to the material parameters to achieve parameter calibration of the RT model: Step 3.3 Due to the intractability of the marginal posterior , variational inference is adopted to approximate the marginal likelihood, and a variational distribution is defined, denoted as , where and are the mean parameter and the concentration parameter respectively; the variational distribution describes the phase error estimates corresponding to all paths , and this distribution is expressed as The variational expectation-maximization algorithm approximately solves problems by minimizing the variational free energy, and its free energy function is expressed as follows. By minimizing the variational free energy, the phase error distribution of each sample is updated, that is, the mean phase of the path and concentration are updated, and the posterior approximation distribution is updated as follows: The free energy is specifically expressed as: Among them, is the Bessel ratio, is the Bessel ratio vector, denotes constructing a diagonal matrix for the vector; Step 3.4 Use the variational expectation-maximization algorithm to solve for the calibrated parameters ; Among them, in the expectation step, the material parameters are fixed , and the phase error estimate of each data point is updated by minimizing the variational free energy, and the phase mean of each path is updated Among them, represents taking the phase of each element of a complex vector element-wise; is a column vector of dimension where all elements are 1, and together with constitutes the prior part, introducing a unified prior term for each path component; the symbol i represents the current iteration number index, used to identify the parameter estimation value in the i-th round of the variational expectation-maximization algorithm; Update the lumped parameters of each path In the maximization step, given the updated phase error parameter , the material parameters are updated by minimizing the variational free energy Update the concentration parameter of the prior When the maximum number of iterations is reached or convergence occurs, output the final estimated parameters ; Step 3.5 After final calibration, the phase error-aware channel frequency response model is expressed as: Among them, represents the path structure matrix constructed using the finally calibrated electromagnetic parameters of the material; represents the mean phase error of each path estimated by variational inference.​

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