Secure and Energy-Efficient Precoding for MIMO Two-Way Untrusted Relay Systems

Abstract

This paper focuses on the multiple-input-multiple-output (MIMO) two-way relay system with an untrusted relay and investigates its secure and energy-efficient precoding design issue based on the physical layer security technology. We first provide theoretical modeling for the index of secrecy energy efficiency (SEE) and formulate the optimal precoding design for SEE maximization (SEEM) as a high-dimensional non-convex programming problem. By exploring the techniques like fractional programming, alternate optimization and semi-definite programming, we then develop a hierarchical theoretical framework to solve the SEEM problem and thus to identify the optimal precoding designs for the source and relay. Furthermore, we demonstrate the proposed theoretical framework is also applicable to the problem of precoding design for secrecy sum rate maximization. Finally, with the help of generalized singular value decomposition, we propose a sub-optimal relay precoding design scheme with significantly lower computational complexity. Extensive numerical results provided in the paper indicate that the proposed schemes can remarkably improve the SEE performance in MIMO two-way untrusted relay systems.