Convex Optimization Strategies for Energy-Efficient Beamforming in Satellite Communications

Abstract

A trend in the design and development of beamforming has emerged as a critical issue in modern satellite communications, particularly with the emergence of low Earth orbit (LEO) satellite constellations. This paper presents a comprehensive system for energy-efficient beamforming optimization that uses convex optimization techniques such as semidefinite programming (SDP), successive convex approximation (SCA), and second-order cone programming (SOCP). The beamforming problem is formulated as a power minimization problem subject to quality-of-service (QoS) constraints, and efficient optimization algorithms are developed to obtain feasible beamforming solutions that converge reliably toward the optimal solution. The proposed rank-one optimization model addresses the non-convexity of the traditional beamforming issue by using tight semidefinite relaxation. The experimental results indicate that the proposed solution can provide 23.4% power savings relative to the traditional methods with the signal-to-interference-plus-noise ratio (SINR) specifications. In the case of LEO satellites with imperfect channel state information (CSI), the robust beamforming approach improves energy efficiency by 18.7%. The analysis of computational complexity demonstrates that the suggested SCA-based algorithm takes 2–10 iterations for the considered LEO satellite scenarios. Since each cycle solves a computationally efficient SOCP subproblem, the overall runtime is significantly less than that of the SDP formulation, making the proposed model appropriate for adaptive beamforming in practical satellite communication systems.