Transceiver Optimization for Wireless Powered Time-Division Duplex MU-MIMO Systems: Non-Robust and Robust Designs

Wireless powered communication (WPC) has been considered as one of the key technologies in the Internet of Things (IoT) applications. In this paper, we study a wireless powered time-division duplex (TDD) multiuser multiple-input multiple-output (MU-MIMO) system, where the base station (BS) has its own power supply and all users can harvest radio frequency (RF) energy from the BS. We aim to maximize the users’ information rates by jointly optimizing the duration of users’ time slots and the signal covariance matrices of the BS and users. Different to the commonly used sum rate and max-min rate criteria, the proportional fairness of users’ rates is considered in the objective function. We first study the ideal case with the perfect channel state information (CSI), and show that the non-convex proportionally fair rate optimization problem can be transformed into an equivalent convex optimization problem. Then we consider practical systems with imperfect CSI, where the CSI mismatch follows a Gaussian distribution. A chance-constrained robust system design is proposed for this scenario, where the Bernstein inequality is applied to convert the chance constraints into the convex constraints. Finally, we consider a more general case where only partial knowledge of the CSI mismatch is available. In this case, the conditional value-at-risk (CVaR) method is applied to solve the distributionally robust system rate optimization problem. Simulation results are presented to show the effectiveness of the proposed algorithms.