1 Dynamic Wireless Information and Power Transfer Optimization Scheme for Nano-Empowered Vehicular Networks Li Feng, Amjad Ali, Muddesar Iqbal, Farman Ali, Imran Raza, Muhammad Hameed Saddiqui, Muhammad Shafiq, and Syed Asad Hussain Abstract—In this paper, we investigate the wireless power transfer and energy-efficiency (EE) optimization problem for nano-centric vehicular networks operating over the terahertz band. The in- body nano-sensors harvest energy from a power station via radio-frequency signal and then use the harvested energy to transmit data to the sink node. By considering the properties of terahertz band (i.e., sensitivity to distance and frequency over the communication path), we adopt the Brownian motion model to develop a time-variant terahertz channel model and to describe the mobility of the nano-sensors. Thus, based on the channel model and energy resources, we further develop a long-term EE optimization problem. The EE optimization is further converted into a series of energy-efficient resource allocation problems over the time slots via equivalent transformation method. The resource allocation problem for each timeslot, which is formulated as a mixed integer nonlinear programming (MINLP), is solved based on the particle swarm optimization (PSO) method. In addition, a dynamic PSO-based EE optimization (DPEEO) algorithm is developed to obtain the sub-optimal solution for the EE optimization problem. By exploiting the special structure of the reformulated problem, an improved DPEEO algorithm, is presented which can handle the problem’s constraints quite well, decreases the research space, and greatly reduces the length of the convergence time. Simulation results validate the theoretical analysis of our system. Key words: nano-communications vehicular networks, wireless power transfer, energy-efficiency optimization, terahertz band I. INTRODUCTION In the present era of advance technology, vehicles are get- ting more efficient, sophisticated, faster than the past. More- over, with the significant advancements in nanotechnology, nanotechnology-empowered sensors over terahertz band are L. Feng is with the School of Computer Science and Communication En- gineering, Jiangsu University, 301 Xuefu Road, Zhenjiang, 212013, Jiangsu, China. (Email: fenglixidian@gmail). A. Ali, I.Raza, and S.A. Hussain are with the Department of Computer Science COMSATS University Islamabad, Lahore Campus, Pakistan. (Email: amjad.ali@cuilahore.edu.pk M. Iqbal is with the Division of Computer Science and Informatics, London South Bank University, London SE1 0AA, UK. M. H. Saddiqui is with the College of Computer and Information Sciences, Jouf University, Sakaka, Saudi Arabia F. Ali is with the Department of Software, Sejong University, Seoul, South Korea M. Shafiq is with the Department of Information and Communication Engineering, Yeungnam University, Gyeongsan 38541, South Korea. This project is funded by MSCA-RISE-Marie-Sklodowska-Curie Research and Innovation Staff Exchange (RISE) scheme under the project SONNET (Self-OrganizatioN towards reduced cost and eNergy per bit for future Emerging radio Technologies) with grant agreement no. H2020-MSCA-RISE- 2016-73454 expected to bring a wide range of applications in vehicular networks from the comfort to entertainment [1]. From 0.1 THz - 10 THz wireless spectrum is reserved for terahertz com- munication which has great capability to support extremely high bandwidths communication. However, some constraints, such as frequency selective path-loss and noise may lead fluctuations in terahertz channel capacity [2]. Besides, due to their physical dimensions, nano-sensors implanted in vehicles are always limited by the requirement for a battery. Therefore, wireless power transfer (WPT) technology over the air inter- face is introduced as a viable solution to solve the problem of battery and network lifetime [3]. Energy efficiency (EE) optimization has become a vital design objective in green vehicular communications. Despite the nu- merous advantages of nano-centric vehicular communications over terahertz band, there are still many challenges being faced in energy efficient transmissions using nano-sensors which requires innovative techniques to be develop. Thus, due to the fact that a nano-sensor’s energy resource will change with its energy harvesting and consumption processes, first we need to build a dynamic equation to describe the time-varying energy resources. Secondly, since the channel character varies with the frequency and distance on the communication path, a comprehensive mathematical model is required to portray the time-variant channels of the terahertz band for vehic- ular networks. Thirdly, considering the time-varying energy resources and channels, a dynamic EE optimization problem shall be addressed to improve the vehicular network perfor- mance. Besides, owing to the complex channel property of the terahertz band, the problem built is non-convex, which is difficult to solve. Some efficient mathematic methods are needed to obtain the problem’s sub-optimal solutions. There- fore, in this paper, we propose a dynamic wireless information and power transfer scheme to maximize the long-term EE by jointly considering the time-varying energy resources and the channels for nanotechnology-empowered vehicular networks using terahertz band. In our paper, we employ Brownian motion to describe the mobility of a nano-sensor and build a time-variant terahertz channel model, due to the fact that terahertz communications is sensitive to distance and frequency over the communication path. Meanwhile, based on the power transfer and energy con- sumption processes, we build a stochastic equation to model the dynamic energy resource of the nano-sensor. Consider- ing nano-sensors’ dynamic channel information and energy