Wireless-Powered Two-Way Relaying via a Multi-Antenna Relay with Energy Beamforming

In this paper, we study a wireless-powered two-way relay system, in which both wireless-powered sources exchange information through a multi-antenna relay. Both sources are assumed to have no embedded energy supply and thus first need to harvest energy from the radio frequency signals broadcasted by the relay before exchanging their information via the relay. We aim to maximize the sum throughput of both sources by jointly optimizing the time switching duration, the energy beamforming vector and the precoding matrix at the relay. The formulated problem is non-convex and hard to solve in its original form. Motivated by this, we simplify the problem by reducing the number of variables and by decomposing the precoding matrix into a transmit vector and a receive vector. We then propose bisection search, 1-D search and iterative algorithms to optimize each variable. Numerical results show that our proposed scheme can achieve higher throughput than the conventional scheme without optimization on beamforming vector and precoding matrix at the relay.