Beamforming is a key enabling technology for centimeter-wave Gigantic MIMO (G-MIMO) systems, using antenna arrays to generate wide beams for cell-wide broadcasting or narrow beams for data transmission. This paper presents a novel \emph{beam shaping technology} for designing environment-aware broadcast beams (i.e., beams for common control information delivery, as in 5G SSB). As a case study, we shape a \emph{prostrate beam} in the vertical plane to approximate uniform electromagnetic power distribution across the ground, thereby enhancing broadcast coverage quality. We first propose a geometric broadcasting model that, through coordinate transformation, relates base station height, beam spread, maximum service distance, and downtilt angle. Building on this model and the signal propagation model, we formulate the beam shaping problem as a non-convex optimization problem that aims to maximize ground-level coverage. To solve it, we develop a generalized optimization framework. We reformulate the problem into a matrix representation, equivalently transforming it into a target pursuit optimization (TPO) problem. Using variable substitution, the objective is convexified into a quadratically constrained quadratic program, and the non-convex rank constraint is handled via successive convex approximation, decomposing the problem into iteratively solved subproblems. We provide complexity and convergence analyses for the proposed algorithm. Numerical simulations confirm that the optimization effectively shapes the intended beam pattern and that the proposed prostrate beam yields significant performance gains, including substantially extended coverage distance, over conventional wide-beam benchmarks.

翻译：暂无翻译