Power efficient algorithms for wireless charging under phase shift in the vector model

Recent technological advances in the domain of Wireless Power Transfer (WPT) have enabled the employment of previously unrealistic methods for power management in wireless systems. At the same time, some of the classical scalar models have proved incapable of capturing the multi-dimensional aspects of WPT that are similar to the superposition of wave functions. In this work, we consider the vector model which is by now a widely accepted model for WPT and its validity has been confirmed experimentally in the literature. Under the vector model, we study the problem of power maximization in a wireless network consisting of wireless chargers. We take the state of the art one step further by assuming that chargers can use phase-shifting to adjust their output in order to improve the total power provided by the network of chargers at selected points in the network area. Even though the technology for phase-shifting already exists, researchers have only recently tried to study it from an algorithmic perspective and algorithmic solutions are nearly inexistent. In this paper, we provide a rigorous formulation for the problem of power maximization as a semi-definite program with rank constraints and we present efficient centralized and distributed solutions, and also heuristics where only local information is available.