LAUSR

This paper investigates the optimal energy beamforming and time assignment in radio frequency (RF) energy harvesting (EH) wireless powered sensor networks for smart cities, where sensor nodes (SNs) first harvest energy from a sink node, and then transmit their collected data to the sink node via time-division-multiple-access (TDMA) manner by using the harvested energy. In order to achieve green system design, we formulate a problem to minimize the energy requirement of the sink node to support transmission between the sink node and the SNs under data amount constraint and EH constraint. For practical design, the energy consumed by circuit and information processing is also considered. Since the problem is non-convex, we use semidefinite relaxation (SDR) method to relax it into a convex optimization problem and then solve it efficiently. We theoretically prove that when the number of SNs are not greater than two, the relaxed problem guarantees rank-one constraint and when the number of SNs exceeds two, our obtained results are very close to the optimal ones. Simulation results show that when the data amount is relatively small, the energy consumed by circuit and information processing affects the system performance greatly, but for a relatively large data amount, the energy requirement of the sink node on its own signal processing is affected very limited and the system energy requirement is dominated by the transmit power consumption at the SNs. Furthermore, we also discuss the effects of the other parameters on the system performance, which provide some useful insights in future smart city planning.