  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 3rd 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 the flat-top antenna model cannot always provide
accurate performance evaluation in the presence of BAE.
