  This letter considers a multi-pair decode-and-forward relay network where a
power-splitting (PS) protocol is adopted at the energy-constrained relay to
provide simultaneous wireless information and energy harvesting (EH). To
achieve higher efficiency of EH, we propose a new PS-based EH architecture at
the relay by incorporating an alternating current (AC) computing logic, which
is employed to directly use the wirelessly harvested AC energy for
computational blocks. Under a nonlinear EH circuit, our goal is to maximize the
fairness of end-to-end rate among user pairs subject to power constraints,
resulting in a nonconvex problem. We propose an iterative algorithm to achieve
a suboptimal and efficient solution to this challenging problem by leveraging
the inner approximation framework. Numerical results demonstrate that the
proposed algorithm outperforms the traditional direct current computing and
other baseline schemes.
