Joint Shape-Position Optimization Enhanced 2D DOA Estimation in Movable Antenna Systems

Movable Antenna (MA) technology is emerging as a promising advancement with the potential to significantly enhance the performance of future wireless communication and sensing systems. In this paper, we address two-dimensional (2D) direction of arrival (DOA) estimation via joint shape-position optimization. Specifically, we formulate an optimization problem aimed at minimizing the Cramér-Rao Bound (CRB) based on a 2D DOA estimation model for MA systems. To tackle the highly non-convex nature of this CRB minimization, we investigate the spatial utilization of the movable region (MR) under minimum antenna spacing constraints. By demonstrating that an equilateral triangle yields the minimum overlap area, we strategically design an equilateral triangular MR. This specific geometric configuration enables the exploitation of structural symmetry to simplify the geometric constraints, which effectively reduces the complexity of solving the optimization problem. Subsequently, we derive the optimal MA positions by selecting the candidate locations farthest from the centroid of MR. The results demonstrate that the proposed joint shape-position optimization substantially enhances 2D DOA estimation performance.