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

The recently emerged movable antenna (MA) shows great potential in leveraging spatial degrees of freedom for enhancing the performance of wireless systems. However, resource allocation in MA-aided systems faces unique challenges due to the non-convex and coupled constraints on antenna positions. This paper systematically reveals the challenges brought by the minimum MA separation constraints, and proposes a penalty framework for resource allocation under such new constraints in MA-aided systems. By introducing auxiliary variables, the proposed framework separates the non-convex and coupled antenna distance constraints from the movable region constraint. This enables the resulting problem be 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 closed-form 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.