Power and Frequency Band Allocation Mechanisms for WPT System with Logarithmic-Based Nonlinear Energy Harvesting Model

Wireless power transmission (WPT) is expected to play a crucial role in supporting the perpetual operations of Internet of Things (IoT) devices, thereby contributing significantly to IoT services. However, the development of efficient power allocation algorithms has remained a longstanding challenge. This paper addresses the aforementioned challenge by proposing a novel strategy, called energy poverty-based device selection (EPDS), in conjunction with energy beamforming, where orthogonal frequency bands are allocated to energy harvesting IoT devices (EHIs). To solve two power allocation problems, a logarithmic-based nonlinear energy harvesting model (NEHM) is introduced. The first problem tackled is the total received power maximization (TRPM), which is initially presented and, then, solved optimally in closed-form by incorporating Karush-Kuhn-Tucker (KKT) conditions with the modified water-filling algorithm. The second problem formulated is the common received power maximization (CRPM), which takes into account energy fairness considerations. To assess the proposed algorithms and gain insights into the effects of mobility, the mobility of EHIs is modeled as a one-dimensional random walk. Extensive numerical results are provided to validate the advantages of the proposed algorithms. Both the TRPM and CRPM algorithms exhibit exceptional performance in terms of total and minimum received energy, respectively. Furthermore, in comparison to round-robin scheduling, the EPDS demonstrates superior performance in terms of minimum received energy. This paper highlights the impact of the proposed energy harvesting (EH) model, demonstrating 12.68% and 3.69% higher values than the linear model for the minimum and total received energy, respectively.