Joint Orthogonal Band and Power Allocation for Energy Fairness in WPT System with Nonlinear Logarithmic Energy Harvesting Model

Wireless power transmission (WPT) is expected to play an important role in the Internet of Things services by providing the perpetual operation of IoT sensors. However, to prolong the IoT network's lifetime, the efficient resource allocation algorithm is required, in particular, the energy fairness issue among IoT sensors has been a critical challenge of the WPT system. In this paper, considering energy fairness as the minimum received energy of all energy poverty IoT sensors (EPISs), we allocate orthogonal frequency bands to several EPISs and transfer the RF power on each orthogonal band, using energy beamforming. Based on the energy poverty, we propose orthogonal frequency bands assignment rule, granting the priority to the EPISs with less received energy. We also formulate two transmission power allocation problems, incorporated the nonlinear logarithm-energy harvesting (EH) model. First, the total received power maximization (TRPM) problem is presented and solved by combining the well-known Karush-Kuhn-Tucker (KKT) conditions with the modified water-filling algorithm. Second, the common received power maximization (CRPM) problem is formulated and the optimal solution is derived using the iterative bisection search method. To apply the bisection search method to the problem, this paper proposes a method of specifying the scope of the solution for the objective function defined by the sum of monotonous functions. In numerical results, assuming the mobility of EPISs by the one-dimensional random walk model, the effectiveness of the mobility of EPISs on the minimum received energy of all EPISs is presented. Finally, the performance of the proposed resource allocation schemes is verified by comparing other resources allocation schemes, such as Round robin and equal power distributionComment: 12 pages, 27 figure