  We investigate the long-term scheduling and power control scheme for a
wirelessly powered cell-free Internet of Things (IoT) network which consists of
distributed access points (APs) and large number of sensors. In each time slot,
a subset of sensors are scheduled for uplink data transmission or downlink
power transfer. Through asymptotic analysis, we obtain closedform expressions
for the harvested energy and the achievable rates that are independent of
random pilots. Then, using these expressions, we formulate a long-term
scheduling and power control problem to maximize the minimum time average
achievable rate among all sensors, while maintaining the battery state of each
sensor higher than a predefined minimum level. Using Lyapunov optimization, the
transmission mode, the active sensor set, and the power control coefficients
for each time slot are jointly determined. Finally, simulation results validate
the accuracy of our derived closed-form expressions and reveal that the minimum
time average achievable rate is boosted significantly by the proposed scheme
compare with the simple greedy transmission scheme.
