Fair Scheduling of Wireless Power Transfer to Nonlinear Energy Harvesters

The performances of two wireless power transfer (WPT) scheduling schemes,
time sharing
(TS) and
spatial multiplexing
(SM), in terms of provisioning fairness among energy receivers (ERs), are studied and compared while taking into account the nonlinearity of the harvesting circuits. In the network, the multiple-antenna energy transmitter attempts to maximize the harvested energy by the ER which has accumulated the minimum amount of energy among all single-antenna ERs during the WPT block—hence the
max-min
fairness criterion. Two network scenarios are studied: homogeneous, where similar channel coefficients are assumed for all the well-apart ERs, and heterogeneous, where the said coefficients can take arbitrary values. For WPT in single-band or multi-band, we analytically prove that the optimal scheduling policy in the homogeneous scenario is to allocate each ER the
full transmit power
with uniform distribution of charging times among ERs, rather than to allocate the
full power transfer block
with uniform distribution of the power among ERs. Generalization of the network to the heterogeneous scenario aims to find the optimal beamforming vectors for the SM scheme and the optimal time sharing vector for the TS scheme. We form the max-min fairness optimization problems for both scheduling techniques, in single- and multi-band WPT scenarios. The problems, which are nonlinear and non-convex, are solved through exhaustive search algorithms. It is proven that the TS scheduling outperforms the SM one in terms of max-min fairness as a result of taking into account the inherent non-linearity of the harvesting devices.