Optimal precoders and power splitting factors in multiuser multiple‐input multiple‐output cognitive decode‐and‐forward relay systems with wireless energy harvesting

Abstract

SummaryThis paper considers an underlay cognitive radio (CR) wireless network with the assistance of a two‐hop decode‐and‐forward (DF) relay node. Different from the conventional CR relay networks, in this paper, the relay node using power‐splitting (PS) techniques harvests wireless energy transmitted from the secondary base station (SBS) and, then, uses its harvested energy to forward the received signals to multiple secondary receive users (SRUs). Due to the highly mutual dependence of the transmission strategies at nodes on the system performance, the optimal design of signal processing at transceivers to efficiently handle the interference and energy constraints is crucial. This paper studies the jointly optimal design of the precoders, PS factors to maximize the minimum user rate under the transmit power, harvested energy, and interference power constraints. Owing to the nonlinearly and mutually coupled design matrix variables in both objective function and constraints, the joint design of the precoders and PS factors for the concerned problem is mathematically challenging. To tackle these difficulties, we devise the appropriate surrogate functions to recast the nonconvex optimization problem into the convex one. By using the minorization–maximization framework, an efficient iterative algorithm with provable convergence is developed by solving the convex optimization problem in each iteration. Numerical results are provided to evaluate the achievable user rate performance of the considered system and investigate the effects of the interference power thresholds at the primary receive users and the number of antennas at the SBS and the relay on the minimum achievable user rate.