Resource Efficiency Optimization for Robust Beamforming in Multi-Beam Satellite Communications

The tradeoff between energy efficiency (EE) and spectral efficiency (SE) provides a new perspective for the transmit design in satellite communications (SATCOM), i.e., one can jointly optimize the system EE and SE of the SATCOM system. In addition, jointly considering that it is challenging to obtain accurate channel state information at the transmitter, we study the tradeoff between EE and SE for the robust beamforming in multi-beam SATCOM in this paper. Specifically, with the quality of service and total power constraints taken into account, we study the robust beamforming aimed at maximizing the resource efficiency, which is defined as the weighted sum of the system EE and SE, to achieve the tradeoff between EE and SE with more flexibility. For this problem, we first approximate the ergodic user rate and ergodic signal-to-interference-plus-noise ratio, both with closed forms. Then, the semidefinite relaxation is applied to tackle the optimization of beamforming vectors via relaxing the rank constraints. To handle the sum of fractions involved in the optimization objective, a nested iterative algorithm exploiting the quadratic transformation and majorization-minimization method is proposed. Finally, the eigenvalue decomposition is utilized to obtain the beamformers. Simulation results indicate the effectivity of our proposed algorithm in achieving the EE-SE tradeoff and illustrate the superiority of the robust approach compared with the conventional baselines.