  In this paper, the theoretical sustainable capacity of wireless networks with
radio frequency (RF) energy harvesting is analytically studied. Specifically,
we consider a large scale wireless network where base stations (BSs) and low
power wireless devices are deployed by homogeneous Poisson point process (PPP)
with different spatial densities. Wireless devices exploit the downlink
transmissions from the BSs for either information delivery or energy
harvesting. Generally, a BS schedules downlink transmission to wireless
devices. The scheduled device receives the data information while other devices
harvest energy from the downlink signals. The data information can be
successfully received by the scheduled device only if the device has sufficient
energy for data processing, i.e., the harvested energy is larger than a
threshold. Given the densities of BSs and users, we apply stochastic geometry
to analyze the expected number of users per cell and the successful information
delivery probability of a wireless device, based on which the total network
throughput can be derived. It is shown that the maximum network throughput per
cell can be achieved under the optimal density of BSs. Extensive simulations
validate the analysis.
