  In this paper, we study downlink multi-user scheduling for a time-slotted
system with simultaneous wireless information and power transfer. In
particular, in each time slot, a single user is scheduled to receive
information, while the remaining users opportunistically harvest the ambient
radio frequency energy. We devise novel online scheduling schemes in which the
tradeoff between the users' ergodic rates and their average amount of harvested
energy can be controlled. In particular, we modify the well-known maximum
signal-to-noise ratio (SNR) and maximum normalized-SNR (N-SNR) schedulers by
scheduling the user whose SNR/N-SNR has a certain ascending order (selection
order) rather than the maximum one. We refer to these new schemes as
order-based SNR/N-SNR scheduling and show that the lower the selection order,
the higher the average amount of harvested energy in the system at the expense
of a reduced ergodic sum rate. The order-based N-SNR scheduling scheme provides
proportional fairness among the users in terms of both the ergodic achievable
rate and the average harvested energy. Furthermore, we propose an order-based
equal throughput (ET) fair scheduler, which schedules the user having the
minimum moving average throughput out of the users whose N-SNR orders fall into
a given set of allowed orders. We show that this scheme provides the users with
proportionally fair average harvested energies. In this context, we also derive
feasibility conditions for achieving ET with the order-based ET scheduler.
Using the theory of order statistics, the average per-user harvested energy and
ergodic achievable rate of all proposed scheduling schemes are analyzed and
obtained in closed form for independent and non-identically distributed
Rayleigh, Ricean, Nakagami-m, and Weibull fading channels. Our closed-form
analytical results are corroborated by simulations.
