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.