Path Loss Modelling for High Speed Rail in 5G Communication System

A new path loss model for high-speed rail (HSR) in the 5G communication system is constructed in this paper. The model is identified to obtain an accurate mathematical representation of path loss multipath propagation in line of sight of HSR scenarios. The grey box modelling utilization of Generalized Reduced Gradient (GRG) and Genetic algorithm (GA) is applied to find the unknown parameters of the constructed path loss model since some uncertainties in obtaining the corresponded parameters are unavoidable to be collected in the field. Both algorithms achieve excellent results in finding the unknown parameter values with RMSE and MAPE evaluation which are converging finally to 2.779 and 1.701 %. The visualization of fitting plots is also presented, and GA provides a better-adjusted agreement with the measurement dataset of HSR. Accordingly, the constructed path loss model is successfully validated since it is capable of following the dynamic characteristic of the original HSR path loss measurement. The path loss model can then be utilized for the future dense deployment of HSR infrastructures for the 5G communication network.

Generalized reduced gradient algorithm; Genetic algorithm; Grey-box modelling; Parameter estimation; Path loss model

    High-speed rail (HSR) refers to passenger rail systems utilizing a specialized rolling stock integrated system in the dedicated tracks. The deployment of FRCMS (Future Railway Communication System) is expected to fulfill the significantly increased demand for railway signaling systems. Some major communication functions in FRMCS are strictly related to railway operations with safety implications for the critical applications of the similar 5G technologies as radio communication cellular systems (Monserrat et al., 2020).  Over the last decades, many researchers have been focusing on wireless communication technology that will be applied to HSR to ensure data transmission in the 5G framework (Suryanegara, 2018). A satisfying investigation of millimetre-wave propagation characteristics for HSR on field measurement in viaduct and tunnel scenarios has yielded the reliability of wireless transmission (Park et al., 2020).

    The train backbone wireless networking is implemented based on  point-to-point links devices, and the study of path loss in multipath propagation of HSR is stepping into new challenges when dealing with  large-scale fading and shadowing. This types of propagation are the most likely  to occur in railway scenarios. Since practically, HSR runs over 300 km/hr, it suffers from severe fading, vehicle penetration losses (VPL) and unavoidable Doppler effect. Accordingly, it is important to understand a chosen path loss model that can be utilized in line of sight of HSR propagation for a 5G communication system. At the same time, still  revealing the stability of parameter, accuracy, and functionality of the limited measurement dataset.
    It brings out some new challenges in obtaining some path loss parameters value in the field because of the combination of high velocity and spectrum allocation, particularly for the future 5G-HSR wireless system level. Those uncertainties parameters issues are almost existed not only in 5G cellular systems but also in the 5G-HSR scenario therefore a path loss parameterization scheme related to HSR environment scenarios from surrounding physical factors to the model variables must accommodate causal functions of associated 5G-HSR particularly, in line-of-sight variables which in this study, a new path loss model for 5G-HSR is constructed. The accuracy is validated by using a different approach of grey box modelling to yield a comprehensive knowledge of path loss for 5G-HSR that allows network designers to plan the most optimal infrastructures for HSR.
    Furthermore, the major limitation of the existing research is based on particular scenarios, whether empirical or deterministic models. (He et al., 2018) was motivated to observe the path loss model using key parameters such as coherence time, polarization ratios, and Doppler shifts. A simulation was demonstrated based on channel measurement for HSR communications in a 5G Millimeter-Wave Band. As the future 5G technology requires many supporting technologies such as base station infrastructures and fiber optics to be laid on the tracks (Suryanegara, 2016), a local standard emerges as another solution to mainstream technologies. It led to another challenge for a requirement of an accurate path loss that can be utilized world-widely.
    The early studies of the path loss model are majorly conducted in cellular networks. The models are derived from electromagnetic propagation theory (MacCartney et al., 2013), which are not very accurate but easy to implement. Therefore, some correction mechanisms must be constructed in a definite environment to achieve desired accuracy results. (Phillips et al., 2013) investigated additional parameters such as carrier frequency, distance, transmitter, receiver heights and carrier frequency for these cellular path loss models. The research yielded a more accurate path loss model for a 5G cellular network. Accordingly, a prior knowledge or an explicit measurement must be combined for a special path loss model for 5G-HSR (Zhong et al., 2021).
    Several studies concerning 5G coverage path loss prediction were evaluated in recent years with the development of promising stochastic path loss models with the combination of antenna configuration and beamforming in cellular networks (Sousa et al., 2021). Other researchers introduced some key parameters of a line-of-sight characteristics (Sun et al., 2015). This work provided important key parameters of large-scale path loss scenarios and shadow fading for the future 5G communication system in urban macro cellular. The comparison was presented as well at the frequency of 2, 10, 18, and 28 Ghz in Aalborg, Denmark.  Other works in realizing 5G stochastic path loss models were studied by (Rappaport et al., 2017) by investigating large-scale path loss models in wireless communication channels such as mm-MAGIC, NYUSIM, and 3GPP TR38,901. The study concluded that additional random variables in a path loss model must account for supplementary fading due to scattering and multipath effects, which are dominant but difficult to obtain in most stochastic path loss models.
     One of the revolutionary technologies to develop a critical signaling 5G-HSR is millimeter wave technology. It is accessible to a massive capacity and bandwidth in frequency bands above 24 GHz. Since millimeter-wave suffers from higher propagation loss, MIMO directional antenna is widely accepted for designing a wireless communication system. However, 5G-HSR employs different characteristics from traditional cellular scenarios. Some specific characteristics in the 5G-HSR propagation environment, such as line of sight dominance, Doppler shift, high velocity, and multiple scenarios, must be carefully considered to obtain the optimal design and performance (Zhang et al., 2018). These considerations were related to diversity effects and the Doppler shift. Tuned free space path loss model was analyzed, and in this term a path loss model for HSR was estimated theoretically by gaining its diversity effect and Doppler shift performed by Maximal Ratio Combining (MRC) scheme (Roy & Fortier, 2004).
    The capability of machine learning in analyzing the existing system performance to be more accurate is undoubtedly more resourceful for performing prediction tasks.   It has been conducted several times by performing various training and testing on path loss datasets where an estimated model contains necessary predictions to be compared with the actual dataset. It produced the best prediction model for path loss, majorly in the cellular environment. In a single scenario, a requirement of evenly distributed data must be sufficient to be fed to the model for given prediction accuracy. However, the process becomes more complicated when incremental learning algorithms are involved because of gradual model constructions are performed without retraining accomplishment (Zhang et al., 2019).
    The path loss models utilized in most existing research do not contemplate physical factors. In accordance with it, this work investigates an alternative approach to achieving an accurate path loss model for 5G-HSR. A grey box modelling is initiated as the mathematical representation of the path loss model for HSR in 5G communication system. The provision of grey box modelling implementation with appropriate algorithms will allow an optimal or almost optimal model that adjusts to the given path loss measurement. The idea is to find the global minimum cost function in a search space direction. The objective is to minimize the mean square error between the prediction dataset from the optimized model with the real measurement established in the field of study (?eho? & Havlena, 2011).
    The utilization of grey box modelling to obtain mathematical representation had been investigated to find the unknown parameters for AMPS (Automated People Mover System) train by using the Generalized Reduced Gradient Method (Suryana et al., 2020). A near-optimal solution was also achieved by maximizing the sum-rate capacity of a dynamic beam strategy to fulfill the critical quality of high-speed rail requirements through a problem decomposition using GA (Gao et al., 2018). Garah et al. (2016) investigated the Genetic Algorithm (GA) to produce a near-optimal solution for the GSM path loss model. The comparison has yielded a good agreement with the measurement result of the SUI model, COST-231 empirical path loss model, and COST-231 Hata.
    Numerous path loss predictions in 5G scopes with different methods have been analyzed mostly for the case of cellular networks with recent contributions of machine learning implementation (Wu et al., 2010). However, to the best of author’s knowledge, a grey box modelling approach to validate path loss models for 5G-HSR has not been found in any literatures because not only unavoidable measurement difficulties to be taken in the field but also a comprehensive knowledge about causative relationship between path loss parameters must be well constructed.
      For a typical deployment of HSR wireless communication infrastructures, the line of Sight (LOS) scenario is usually referred to minimize radio waves reflection after traveling over a large area (Kanhere & Rapapport, 2021). The terminal equipment in HSR can add signal interferences either constructively or destructively. Random and rapid fluctuations in the received amplitude on a running HSR will cause a situation where signals spread in the frequency domain. It leads to one of the measurement difficulties, which copes with the path loss value. This parameter denotes a close-in measurement or a free space assumption from the transmitter where the signal starts to attenuate (Vahidi., 2021). The values of fading under HSR scenario is perhaps the most difficult parameter to achieve because of multipath propagation in a high mobility environment; consequently, an alternative solution must be considered for this parameter. The performance of wireless system transmission under increased mobility of high-speed rail is dependent on sub-carrier signal frequency shift and Orthogonal frequency division multiplexing [OFDM] due to Doppler Effect. This parameter explains a functional relationship with distance, and when the millimeter -Wave is taken into account for data transmission, a higher Doppler effect will be emerged (Xiong et al., 2021).
        In this study, the investigation of GRG and GA for a grey box model identification is utilized to find some missing parameters value of the constructed path loss model for HSR in a 5G communication network. In this regard, the error between the output of the optimized path loss model and path loss original measurement data will be considered as objective functions with the visualization of fitting plots. The rest of the paper is organized as follows. The grey box model is introduced in Section 2. The optimization method and the constructed path loss model for 5G-HSR are investigated in Section 3. Section 4 displayed the simulation results, and finally, the paper is concluded in Section 5.

As the significance of 5G wireless network planning continues to grow, so will the requirements for better methods of measuring wireless signal propagation and modelling   a path loss prediction for high speed rail.  This paper gives a broad overview of approaches given in a grey box modelling to validate a newly constructed path loss model in the 5G communication system for HSR. The grey box modelling with the application of GRG and GA has shown excellent results in finding the unknown parameters value of the newly constructed path loss model with satisfying results of RMSE convergence approximately to 2.779 and MAPE value 1.701 %, respectively. The results revealed that the new path loss model is successfully validated. The framework in this study had shown that the created path loss model had a good adjusted agreement with the dynamic characteristic of the original path loss measurement which GA ultimately achieves. In future works, many possible directions in this area with promising great impacts in high-speed rail crucial applications are widely open for investigation. Comparative validation techniques and measurement-based approaches are required, so the validated path loss model can be utilized to design the future dense wireless communication infrastructures for high-speed rail in a 5G communication network.

        The Indonesian Ministry of Research partially funds this research, Technology and Higher Education under WCU Program managed by Institute Technology Bandung and Institute Technology Bandung Research Program 2022. The authors would also like to acknowledge BJTU, Beijing, China, for providing dataset measurement of a running bullet train.

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