Internet-of-Things (IoT) networks are expected to support the wireless connection of massive energy limited IoT nodes. The emerging wireless powered backscatter communications (WPBC) enable IoT nodes to harvest energy from the incident radio frequency signals transmitted by a power beacon (PB) to support their circuit operation, but the energy consumption of the PB (a potentially high cost borne by the network operator) has not been sufficiently studied for WPBC. In this paper, we aim to minimize the energy consumption of the PB while satisfying the throughput requirement per IoT node by jointly optimizing the time division multiple access (TDMA) time slot duration and backscatter reflection coefficient of each IoT node and the PB transmit power per time slot. As the formulated joint optimization problem is non-convex, we transform it into a convex problem by using auxiliary variables, then employ the Lagrange dual method to obtain the optimal solutions. To reduce the implementation complexity required for adjusting the PB's transmit power every time slot, we keep the PB transmit power constant in each time block and solve the corresponding PB energy consumption minimization problem by using auxiliary variables, the block coordinated decent method and the successive convex approximation technique. Based on the above solutions, two iterative algorithms are proposed for the dynamic PB transmit power scheme and the static PB transmit power scheme. The simulation results show that the dynamic PB transmit power scheme and the static PB transmit power scheme both achieve a lower PB energy consumption than the benchmark schemes, and the former achieves the lowest PB energy consumption.
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