Robust Energy-Efficient Hybrid Beamforming Design for Massive MIMO LEO Satellite Communication Systems

In low earth orbit (LEO) satellite communication systems, the limited energy supply capacity and the difficulty in obtaining channel state information (CSI) are the practical challenges. Motivated by this, we focus on the design of robust hybrid beamforming to maximize the energy efficiency of LEO satellite communication systems. Assuming that the LEO satellite transmitter adopts the massive multi-input multi-output (MIMO) technology, considering the CSI errors caused by propagation delay and Doppler shift, under the constraints of transmit power and quality of service (QoS), a robust energy-efficient hybrid beamforming scheme is proposed. Since that there are no explicit expressions for the ergodic user rate and the ergodic signal-to-interference-plus-noise ratio, the approximate values with closed-form expressions are adopted. Then, we invoke the semidefinite programming (SDP) algorithm to transform the nonconvex quadratic constrained quadratic programming (QCQP) problem equivalently, and an inner and outer nested iterative algorithm combining quadratic transformation fractional programming (QTFP) and concave convex process (CCCP) is utilized to transfer a nonconvex problem into a convex problem. Meanwhile, we adopt a penalty function algorithm to solve the rank-one constraint in semidefinite programming algorithm. Finally, we invoke the normal form distance minimization (NFDM) algorithm and the alternating optimization (AltOpt) algorithm to jointly solve the digital beamforming matrix and analog beamforming matrix in hybrid beamformer. Numerical results validate that our proposed robust approach significantly outperforms the conventional one.