Energy efficiency optimization in relay-assisted MIMO systems with statistical CSI

The issue of energy-efficient resource allocation in a single-user relay-assisted MIMO system is considered. For this scenario, a great deal of research has focused on rate maximization or sum power minimization, whereas much fewer results are available when bits/Joule energy efficiency optimization is the goal. Here, the performance metric to optimize is the ratio between the system's achievable rate and the total consumed power. The optimization is carried out with respect to the source and relay precoding matrices, subject to QoS and power constraints. Such an optimization problem is a challenging non-concave problem. Moreover, unlike previous contributions, we consider the case in which only statistical CSI is available for resource allocation purposes, which makes the analysis even more involved. In such a challenging scenario, the tools of fractional programming and alternating maximization are employed to come up with a resource allocation algorithm for energy efficiency maximization. Moreover, a necessary and sufficient condition for the optimality of single-stream transmission is derived.