Performance Analysis of Millimeter Wave Wireless Power Transfer with Imperfect Beam Alignment

In this paper, the impact of imperfect beam alignment (IBA) on millimeter wave (mmWave) wireless power transfer (WPT) is investigated. We consider a mmWave WPT network, where the location of the energy transmitters follows a Poisson point process. Instead of the mostly used flat-top antenna model, we adopt the Gaussian antenna model suggested by the 3 rd Generation Partnership Project (3GPP) for better accuracy. Two beam alignment error (BAE) models, i.e., truncated Gaussian and uniform models, are introduced to represent different BAE sources. We derive the probability density functions (PDFs) of the cascaded antenna gain with both BAE models and then provide the approximated PDFs for tractability. With the help of Fox's H function, the analytic expression for the energy coverage probability with nonlinear energy harvesting model is derived. Besides, we deduce a closed-form expression of the average harvested radio frequency (RF) energy. The simulation results verify our theoretical results and demonstrate the performance degradation incurred by BAE. It also shows that in the imperfect beam alignment scenario, the Gaussian antenna model can accurately represent the performance of mmWave WPT networks with actual beam pattern, while the flat-top antenna model cannot always provide accurate performance evaluation.