Power splitting (PS) based simultaneous wireless information and power transfer (SWIPT) is considered in a multiuser multiple-input-single-output broadcast scenario. Specifically, we focus on jointly configuring the transmit beamforming vectors and receive PS ratios to minimize the total transmit energy of the base station under the user-specific latency and energy harvesting (EH) requirements. The battery depletion phenomenon is avoided by preemptively incorporating information regarding the receivers' battery state and EH fluctuations into the resource allocation design. The resulting time-average sum-power minimization problem is temporally correlated, nonconvex (including mutually coupled latency-battery queue dynamics), and in general intractable. We use the Lyapunov optimization framework and derive a dynamic control algorithm to transform the original problem into a sequence of per-time-slot deterministic and independent subproblems. The latter are then solved via two alternative approaches: i) semidefinite relaxation combined with fractional programming, and ii) successive convex approximation. Furthermore, we design a low-complexity closedform iterative algorithm exploiting the Karush-Kuhn-Tucker optimality conditions for a specific scenario with delay bounded batteryless receivers. Numerical results provide insights on the robustness of the proposed designs to realize an energy-efficient SWIPT system while ensuring latency and EH requirements in a time dynamic network.
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