Energy Efficient Beamforming Schemes for Satellite-Aerial-Terrestrial Networks

In this paper, we investigate energy efficient transmission for a satellite-aerial-terrestrial network (SATN), where a multi-antenna unmanned aerial vehicle (UAV) is employed as a relay to assist the satellite signal delivery. By considering total power constraint (TPC) or per-antenna power constraint (PPC) at the UAV, we first formulate an optimization problem to maximize the energy efficiency of the SATN, which is defined as ratio of the ergodic capacity to the total power consumption for communication at UAV. Then, by jointly exploiting array signal processing with the Dinkelbach's method, two new beamforming (BF) schemes, namely, TPC-BF and PPC-BF are proposed to solve the non-convex energy efficiency maximization problem. The main advantage of our method is that only angular information-based channel state information is used to obtain BF weight vectors so that a low implementation complexity is achieved. Furthermore, by assuming that the satellite-UAV link undergoes correlated Shadowed-Rician fading while the UAV-terminal link experiences correlated Rician fading, closed-form expressions for the statistics of the equivalent output signal-to-noise ratio are derived and, thus energy efficiency for the considered SATN with BF schemes is analytically presented. Finally, simulation results corroborate the derived expressions and confirm the effectiveness of the proposed BF schemes.