Modeling and Analysis of Wireless Power Transfer in Heterogeneous Cellular Networks

In this paper, we model and analyze the downlink (DL) wireless power transfer and uplink (UL) information transmission of K-tier heterogeneous cellular networks (HCNs) with randomly located base stations (BSs) and mobile terminals (MTs). In the DL and UL, each energy-constrained MT pairs up with its corresponding BS, which provides the maximum received power at the MT. Due to the densely located BSs and universal frequency reuse between all tiers in HCNs, the typical MT is allowed to harvest energy from the serving BS by direct beamforming as well as from the other interfering BSs. Equipped with large storage battery, the typical MT utilizes the harvested energy to provide constant transmit power for the UL information transmission. Stochastic geometry is used to model and evaluate the intrinsic relationship between the energy harvested from the BSs in the DL and the information transmission performance in the UL. To well evaluate the system performance, we first derive exact expressions for the maximum transmit power at MT, the UL outage probability, and the UL average ergodic rate per MT. As the number of BS antennas goes to infinity, we further derive asymptotic expressions for the maximum transmit power at MT, the UL outage probability, and the UL average ergodic rate per MT. Our results show that the UL outage probability per MT first decreases and then increases with increasing the time allocation factor (the fraction of time allocated to the DL), and the UL outage probability, and the UL average ergodic rate per MT, can be largely improved by using the massive antenna arrays at the BSs.