On the Power Transfer Efficiency and Feasibility of Wireless Energy Transfer Using Double IRS

We study feasibility of wireless energy transfer (WET) from a source that is assisted by double intelligent reflecting surfaces (IRSs). To this end, we derive new closed-form analytical expressions for the outage probability (OP) in WET under non-linear energy harvesting (EH) at the user for different channel fading scenarios. We also generalize our outage analysis to a scenario where all links via the direct path and via the cascaded paths along the two IRSs undergo Rician fading. This analysis involves developing a novel statistical model based on Gamma distribution for the sum of product of Rician fading envelopes corresponding to cascaded path. As benchmarks, we derive new closed-form mathematical expressions for the OP in WET for single IRS-assisted configuration and massive multiple input multiple output (MIMO) configuration under non-linear EH at the user. We also study the impact of four communication links between source and user on OP. To this end, we develop two algorithms based on manifold optimization and alternating optimization to design the phase shift matrices at two IRSs, and then obtain OP. Furthermore, we determine the optimal number of IRS elements that minimizes the total power consumption for a given received power, thereby maximizing the power transfer efficiency (PTE) under double IRS-assisted configuration. As a baseline, we also derive the corresponding new closed-form expressions with single IRS-assisted WET and massive MIMO enabled WET. Through our extensive analysis and simulations, we elucidate that double IRSs aided WET 1) provides significant savings of power radiated by the source, and 2) requires fewer IRS elements in comparison to single IRS aided WET or antenna elements in massive MIMO enabled WET while keeping received power and OP fixed at a specific level. Furthermore, double IRSs aided WET provides 10x and 1000x improvement in PTE compared to single IRS and massive MIMO configurations, respectively.