  In this paper, we consider a multiple-input multiple-output wireless powered
communication network (MIMO-WPCN), where multiple users harvest energy from a
dedicated power station in order to be able to transmit their information
signals to an information receiving station. Employing a practical non-linear
energy harvesting (EH) model, we propose a joint time allocation and power
control scheme, which takes into account the uncertainty regarding the channel
state information (CSI) and provides robustness against imperfect CSI
knowledge. In particular, we formulate two non-convex optimization problems for
different objectives, namely system sum throughput maximization and
maximization of the minimum individual throughput across all wireless powered
users. To overcome the non-convexity, we apply several transformations along
with a one-dimensional search to obtain an efficient resource allocation
algorithm. Numerical results reveal that a significant performance gain can be
achieved when the resource allocation is designed based on the adopted
non-linear EH model instead of the conventional linear EH model. Besides,
unlike a non-robust baseline scheme designed for perfect CSI, the proposed
resource allocation schemes are shown to be robust against imperfect CSI
knowledge.
