One of the key challenges of the Internet of Things (IoT) is to sustainably power the large number of IoT devices in real-time. In this paper, we consider a wireless power transfer (WPT) scenario between an energy transmitter (ET) capable of retrodirective WPT and an energy receiver (ER) capable of ambient backscatter in the presence of an ambient source (AS). The ER requests WPT by backscattering signals from an AS towards the ET, which then retrodirectively beamforms an energy signal towards the ER. To remove the inherent direct-link ambient interference, we propose a scheme of ambient backscatter training. Specifically, the ER varies the reflection coefficient multiple times while backscattering each ambient symbol according to a certain pattern called the training sequence, whose design criterion we also present. To evaluate the system performance, we derive an analytical expression for the average harvested power at the ER. Our numerical results show that with the proposed scheme, the ER harvests tens of $mu$W of power, without any CSI estimation or active transmission from the ER, which is a significant improvement for low-power and low-cost ambient backscatter devices.
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