Power Allocation Optimization for Energy-Efficient Massive MIMO Aided Multi-Pair Decode-and-Forward Relay Systems

We investigate power allocation optimization for global energy efficiency (GEE) maximization in the massive multiple-input multiple-output technique aided multi-pair one-way decode-and-forward relay systems. Assuming that the minimum mean-square error channel estimator and zero-forcing transceivers are employed at the relay, we first derive an accurate closed-form expression of the GEE of this complex system. Based on our analytical results, a non-convex power allocation optimization problem with the objective of GEE maximization is formulated under specific quality-of-service (QoS) and transmit power constraints. To solve this challenging problem, the successive convex approximation technique is invoked to transform the original optimization problem into a concave fractional programming problem, which is then efficiently solved by Dinkelbach's method and by the Charnes-Cooper transformation-based method. In addition, as a special case, the GEE maximization problem under the assumption of using the equal power allocation strategy at both the source users and the relay is also considered. Simulation results demonstrate the accuracy of our analytical results and the effectiveness of the proposed algorithms. Furthermore, the impact of several important system parameters (i.e., the QoS constraint, the transmit power constraints at both the source users and the relay, as well as the quality of channel estimation) on the maximum GEE achieved by the proposed algorithms is also illustrated.