Multi-Connection to the Sky: Energy-Efficient Beamforming for Multi-Satellite Uplink Transmission with Lens Antenna Array

With the ever-increasing densification of low Earth orbit constellations, lens antenna array has become an attractive option for ground terminals to simultaneously connect to multiple satellites with improved coverage under insufficient energy supply. To this end, an optimization problem is formulated for maximizing the energy efficiency (EE) of the system by respecting the uplink transmit power budget and the quality-of-service (QoS) constraints. This problem has a discrete non-concave objective function and is solved with reduced computational complexity using zero forcing-based precoding and problem decomposition. The proposed algorithm iterates between the following three steps. In the first step, zero forcing-based fully-digital precoder is first optimized under a fixed number of RF chains by adopting Dinkelbach's algorithm. Then, a hybrid analog-digital precoding based on analog beam selection and baseband digital precoding is designed to approximate the optimal fully-digital precoder under Euclidean distance criteria. On this basis, simulated annealing algorithm (SAA) is applied to further optimize the number of required RF chains with the aim of reducing total energy cost. Simulation results demonstrate that the proposed design achieves an improved performance in EE comparing with existing schemes with fixed number of RF chains by up to 15%.