  This paper investigates a fog computing-assisted multi-user simultaneous
wireless information and power transfer (SWIPT) network, where multiple sensors
with power splitting (PS) receiver architectures receive information and
harvest energy from a hybrid access point (HAP), and then process the received
data by using local computing mode or fog offloading mode. For such a system,
an optimization problem is formulated to minimize the sensors' required energy
while guaranteeing their required information transmissions and processing
rates by jointly optimizing the multi-user scheduling, the time assignment, the
sensors' transmit powers and the PS ratios. Since the problem is a mixed
integer programming (MIP) problem and cannot be solved with existing solution
methods, we solve it by applying problem decomposition, variable substitutions
and theoretical analysis. For a scheduled sensor, the closed-form and
semi-closedform solutions to achieve its minimal required energy are derived,
and then an efficient multi-user scheduling scheme is presented, which can
achieve the suboptimal user scheduling with low computational complexity.
Numerical results demonstrate our obtained theoretical results, which show that
for each sensor, when it is located close to the HAP or the fog server (FS),
the fog offloading mode is the better choice; otherwise, the local computing
mode should be selected. The system performances in a frame-by-frame manner are
also simulated, which show that using the energy stored in the batteries and
that harvested from the signals transmitted by previous scheduled sensors can
further decrease the total required energy of the sensors.
