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Radio waves carry both energy and information simultaneously. Nevertheless, radio-frequency (RF) transmissions of these quantities have traditionally been treated separately. Currently, the community is experiencing a paradigm shift in wireless network design, namely, unifying wireless transmission of information and power so as to make the best use of the RF spectrum and radiation as well as the network infrastructure for the dual purpose of communicating and energizing. In this paper, we review and discuss recent progress in laying the foundations of the envisioned dual purpose networks by establishing a signal theory and design for wireless information and power transmission (WIPT) and identifying the fundamental tradeoff between conveying information and power wirelessly. We start with an overview of WIPT challenges and technologies, namely, simultaneous WIPT (SWIPT), wirelessly powered …