## 1 Introduction  
In recent years, vehicular communication has become a very important subject of study among researchers, due to its potential to increase road-safety and reduce traffic congestion [1; 2; 3; 4; 5; 6]. There has been a tremendous amount of effort and investment from the government and private organizations to develop a means for highly efficient communication. To support various emerging applications, \"cellular-connected vehicles\" have been recognized as promising new solutions, by integrating vehicles into the cellular network as the new ground user equipment served by the base stations [7; 8; 9]. Thanks to the superior performance of the Long Term Evolution and the fifth-generation cellular networks, cellular-connected vehicles are expected to obtain significant performance enhancement in terms of all of throughput, coverage and reliability. In fact, the 3 rd Generation Partnership Project (3 GPP)standardization body released a dedicated set of criteria for providing V2X applications in future cellular networks in 2016 [10; 11; 12]. Preliminary field trials have also demonstrated that it is feasible to support the basic communication requirements for V2X with LTE networks [13; 14; 15; 16; 17]. The key issue with cellular-connected vehicle networks is how to prolong their lifetime. As we all know, the majority of vehicles in V2X networks are sensors that are typically powered by batteries with limited energy, resulting in a constrained network life time [18; 19; 20; 21]. Meanwhile, the development of battery energy storage technology is unable to keep pace with the significant growth of energy requirements. Though replacement of batteries can extend their lifetime effectively, it will bring higher costs and is sometimes impossible. Traditionally, the energy collecting unit could harvest plentiful renewable energy from natural resources such as the hydro energy, tide and wind, etc. [22; 23]. However, renewable sources are liable for the limitation caused by an unpredictable climate and change of position. Moreover, it may not be applicable for some application scenarios while harvesting energy from the ambient radio frequency (RF) signals can be controllable. The SWIPT technique exploits different aspects of RF signals, which are signal transmission and power transfer. Therefore, SWIPT technology has attracted great interest from investigators in recent years [24; 25; 26; 27; 28]. Utilizing this technology, the battery-powered vehicular communication devices can collect energy from the RF radios to prolong their network lifetime. For future vehicles with a mass of on-board sensors, the SWIPT technique is more meaningful for continuable communications of these on-board sensors, whose power can be provided from base stations or other vehicles with excess power or grid-connected roadside electrical units. Particularly, the authors in [27] designed the optimal beamforming to balance the information and energy transmission. In [28], the harvested energy and the secrecy channel capacity trade-off problem between the information receiver and energy receivers are considered. However, all of the above works assume that the perfect knowledge of the receivers' CSI is available at the base station. In practice, the CSI obtained by the base station may be imperfect. There are many factors resulting in imperfect CSI, such as the quantization error, the delay error and the limited capacity of feedback channel. Moreover, as is known to all, the performance of the approaches with perfect CSI may become poor due to the fact that these methods may be quite sensitive to channel uncertainties. Supposing imperfect CSI at the base station, there are several valuable works on robust beamforming design for multiuser SWIPT systems [29; 30; 31; 32; 33]. In [29; 30], the authors proposed a secure beamforming optimization algorithm for SWIPT systems, where cooperation jamming and the external helper is considered. [PERSON] et al.