A General Optimization Framework for Tackling Distance Constraints in Movable Antenna-Aided Systems

The recently emerged movable antenna (MA) shows great promise in leveraging spatial degrees of freedom to enhance the performance of wireless systems. However, resource allocation in MA-aided systems faces challenges due to the nonconvex and coupled constraints on antenna positions. This paper systematically reveals the challenges posed by the minimum antenna separation distance constraints. Furthermore, we propose a penalty optimization framework for resource allocation under such new constraints for MA-aided systems. Specifically, the proposed framework separates the non-convex and coupled antenna distance constraints from the movable region constraints by introducing auxiliary variables. Subsequently, the resulting problem is efficiently solved by alternating optimization, where the optimization of the original variables resembles that in conventional resource allocation problem while the optimization with respect to the auxiliary variables is achieved in closedform solutions. To illustrate the effectiveness of the proposed framework, we present three case studies: capacity maximization, latency minimization, and regularized zero-forcing precoding. Simulation results demonstrate that the proposed optimization framework consistently outperforms state-of-the-art schemes.