  In a heterogeneous cellular network (HetNet) consisting of multiple different
types (tiers) of base stations (BSs), the void cell event in which a BS does
not have any users has been shown to exist due to user-centric BS association
and its probability is dominated by the cell load of each tier. Such a void
cell phenomenon has not been well characterized in the modeling and analytical
framework of simultaneous wireless information and power transmission (SWIPT)
in a HetNet. This paper aims to accurately exploit the fundamental performance
limits of the SWIPT between a BS and its user by modeling the cell-load impact
on the downlink and uplink transmissions of each BS. We first characterize the
power-splitting receiver architecture at a user and analyze the statistical
properties and limits of its harvested power and energy, which reveals how much
of the average energy can be harvested by users and how likely the self-powered
sustainability of users can be achieved. We then derive the downlink and uplink
rates that characterize the cell-load and user association effects and use them
to define the energy efficiency of a user. The optimality of the energy
efficiency is investigated, which maximizes the SWIPT performance of the
receiver architecture for different user association and network deployment
scenarios.
