## 1 Introduction  
With the integration and advancement of various communication technologies, high-speed trains (HSTs) are evolving from being information-centric to intelligent systems [1]. HSTs have become the preferred mode of transportation for many due to their speed, efficiency, safety, and quality of service [2]. The continuous increase in users and smart devices within the HST communication system has led to a significant rise in the data demand, resulting in higher energy consumption [3]. To meet the growing data requirements of users, a considerable number of active antennas and devices are added to the HST communication system, leading to higher hardware costs and energy consumption [4]. In the context of the next-generation wireless communication systems for HSTs, the surge in mobile devices and the accompanying data demand drive the need for designing more energy-efficient and eco-friendly communication systems, with energy efficiency being a crucial indicator of a green wireless network [5]. However, when the line-of-sight path between the base station (BS) and the train is blocked, it not only seriously affects the safety of train operation but also disrupts stable data connections for users, leading to a decrease in the energy efficiency of the HST communication system. These challenges prompt the exploration of intelligent techniques that can control the propagation environment while minimizing energy consumption to assist the HST communication system. The intelligent reflecting surface (IRS) is considered a promising technology to enhance spectrum and energy efficiency in next-generation HST communication systems. Additionally, it effectively mitigates the rapid fluctuations in received signal strength caused by the Doppler effect [1]. IRS is considered a revolutionary technology for achieving green communications. Comprising a large number of low-cost passive reflecting elements, IRS forms a planar array that enhances the wireless network's performance by controlling the propagation environment [6]. First, IRS only reflects the received signals without amplification, eliminating the need for radio frequency (RF) chains, leading to lower energy consumption compared to traditional relays [7]. Second, it boasts the characteristics of cost effectiveness, simplicity, and easy deployment, as it can be shaped to fit various surfaces that are deployed alongside railway tracks, train windows, building facades, etc., providing a high degree of flexibility to the communication system [8]. Lastly, its integration does not require changes to be made to existing communication system standards. The aforementioned advantages of IRS have motivated numerous researchers to extensively investigate the problem of energy efficiency maximization in IRS-assisted multiple-input single-output (MISO) communication systems [9]. In [10], the authors proposed a joint optimization method based on the Dinkelbach, fractional programming, and semidefinite relaxation (SDR) algorithms. The simulation results demonstrated that the IRS-assisted system achieved higher energy efficiency than the non-IRS-assisted system. The authors of [11] designed the transmit power allocation and IRS phase shifts, showing that the IRS-assisted system outperformed traditional relay systems in terms of energy efficiency. However, the failure to optimize BS beamforming in this study may lead to performance degradation. The authors of [12] developed an optimization framework that incorporates quadratic transformation, alternating optimization, and the weighted least square error. By using an alternating optimization strategy to decouple optimization variables and employing quadratic transformation and the weighted least square error, the problem was transformed into a convex problem to be solved. The simulation results verified the effectiveness of this optimization framework. The authors of [13] maximized the system energy efficiency by jointly optimizing BS beamforming and IRS phase shifts.