Energy efficiency (EE) is becoming an important performance indicator for ensuring both the economical and environmental sustainability of the next generation of communication networks. Equally, cooperative communication is an effective way of improving communication system performances. In this paper, we propose a near-optimal energy-efficient joint resource allocation algorithm for multi-hop multiple-input-multiple-output (MIMO) amplify-and-forward (AF) systems. We first show how to simplify the multivariate unconstrained EE-based problem, based on the fact that this problem has a unique optimal solution, and then solve it by means of a low-complexity algorithm. We compare our approach with classic optimization tools in terms of energy efficiency as well as complexity, and results indicate the near-optimality and low-complexity of our approach. As an application, we use our approach to compare the EE of multi-hop MIMO-AF with MIMO systems and our results show that the former outperforms the latter mainly when the direct link quality is poor
