Robust Energy-Efficient Multigroup Multicast Beamforming for Multi-Beam Satellite Communications

Power constraints and channel acquisition pose practical challenges in multi-beam satellite communications. Motivated by this, we investigate robust energy-efficient multigroup multicast beamforming in multi-beam satellite communications with full frequency reuse in this paper. Specifically, we consider the problem of minimizing the total power while guaranteeing that the energy efficiency (EE) of each group is above a prescribed threshold. The considered problem is challenging in the sense that the average rates in the definition of the EE generally do not admit an explicit expression and the optimization problem is NP-hard and nonconvex. To tackle this problem, we first adopt a closed-form tight approximation for the average rates. Then the semidefinite relaxation and the concave-convex procedure are utilized to transfer the nonconvex problem into a convex problem. Finally, based on the ranks of the solutions, the eigenvalue decomposition or the Gaussian randomization approach is invoked to generate the final feasible solutions. Numerical results validate the high accuracy of the average rate approximation, and demonstrate that our proposed robust approach significantly outperforms the conventional one, especially for the case with large channel phase error variances.