SWIPT using Hybrid ARQ over Time Varying Channels

In this work, we consider a class of wireless powered devices employing Hybrid Automatic Repeat reQuest (HARQ) to ensure reliable end-to-end communications over a time-varying channel. By using Simultaneous Wireless Information and Power Transfer (SWIPT), the perpetually powered transmitter transmits information bearing RF signal to the receiver. The receiver has no power source, and relies on the energy harvested from the received RF blocks from the transmitter. At each incoming RF signal block, the receiver splits the incoming RF signal between the energy harvester and information decoder so that the message is decoded with the least number of re-transmissions. We cast the problem in a Markovian framework, and we show that the optimal policy minimizing the expected number of retransmissions utilizes the incoming RF signal to either exclusively harvest energy or to accumulate mutual information. By doing so, we reduce the problem which is a two dimensional uncountable state Markov chain (MC) into a two dimensional countable state MC and thus, enable a tractable solution for the optimal policy. For independent and identically distributed channels, we also prove that practically simple-to-implement policies such as harvest-first-store-later type of policies are optimal. However, for the case of time-correlated channels, we demonstrate that the statistical knowledge of the channel state may significantly improve the performance when compared to those of the simple-to-implement policies.