Ray Tracing Calibration Based on Local Phase Error Estimates for Rail Transit Wireless Channel Modeling

Ray tracing (RT) has become an important method for train-to-ground (T2G) wireless channel modeling due to its physical interpretability. In rail transit scenarios, RT suffers from modeling errors that arise due to environmental reconstruction and uncertainties in electromagnetic parameters, as well as dynamic phase errors caused by coherent multi-path superposition that is further triggered by such modeling errors. Phase errors significantly affect both the calibration accuracy and prediction precision of RT. Therefore, this paper proposes an intelligent RT calibration method based on local phase errors. The method builds a phase error distribution model and uses constraints from limited measurements to explicitly estimate and correct phase errors in RT-generated channel responses. Firstly, the method applies the Variational Expectation–Maximization (VEM) algorithm to optimize the phase error model, where the expectation step derives an approximate posterior distribution and the maximization step updates parameters conditioned on this posterior. Secondly, experiments are conducted using differentiable RT implemented in the Sionna library, which explicitly provides gradients of environmental and link parameters with respect to channel frequency responses, enabling end-to-end calibration. Finally, experimental results show that in railway scenarios, compared with calibration methods based on phase error-oblivious and uniform phase error, the proposed approach achieves average gains of about 10 dB at SNR = 0 dB and 20 dB at SNR = 30 dB.