Optimization and Analysis of Wireless Powered Multi-Antenna Two-Way Relaying Systems

We consider a wireless powered two-way relaying system consisting of two energy constrained single antenna sources and one multi-antenna relay with constant power supply. The time division protocol is adopted, where the relay first acts as the energy source and employs energy beamforming to charge the two sources, and then switches its role as a relay to help forward the information to the sources. To maintain user fairness, we aim to maximize the minimum rate of two sources, by jointly optimizing the energy beamforming vector, time splitting factor and relay transformation matrix. To further reduce the complexity of the optimal algorithm, we propose an alternating optimization method, where closed-form expressions for the energy beamforming and time splitting factor are obtained. To gain more insights, we propose a simple suboptimal design and analyze the outage probability and the average rate when the relay applies simple energy beamforming and transformation matrix. The analysis shows that the system can achieve a diversity order of <inline-formula> <tex-math notation="LaTeX">$\frac {N}{3}$ </tex-math></inline-formula> for a system with a relay of <inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> antennas. Numerical results show that the performance of the proposed low-complexity alternating optimization method approaches the optimal algorithm over the entire SNR range, but has a significantly low complexity, and the proposed suboptimal design can also achieves a decent performance especially in small <inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> regime.