Design of energy-efficient precoders in MIMO cognitive two-way relay network

This paper addresses the energy efficiency (EE) maximization problem for a multi-input multi-output cognitive two-way relay network. The secondary system, comprises of a two-way amplify-and-forward (AF) relay and two transceivers, co-exists with the licensed primary user (PU). The secondary transceivers communicate through the two-way AF relay. We jointly design the precoders for the secondary transceivers and the AF relay with the aim to maximize the EE while satisfying the transmit power constraints at the secondary transceivers and the relay, quality-of-service constraints at the secondary transceivers, and interference constraints at the PU. The resulting maximization problem is a non-convex fractional programming problem with three unknown precoder matrices. This problem is first simplified and converted into a vector valued problem using singular value decomposition. Further, the tools of iterative optimization scheme and the fractional programming theory are employed to solve the simplified problem. The computational complexity and convergence behaviour of the proposed solution are analysed. Numerical results are presented to illustrate the effectiveness of the proposed design in terms of the achievable EE and the probability of feasibility.