Minimizing Movement Delay for Movable Antennas via Trajectory Optimization

Movable antennas (MAs) have received increasing attention in wireless communications due to their capability of antenna position adjustment to reconfigure wireless channels. However, moving MAs results in non-negligible delay, which may decrease the effective data transmission time. To reduce the movement delay, we study in this paper a new MA trajectory optimization problem. In particular, given the desired destination positions of multiple MAs, we aim to jointly optimize their associations with the initial MA positions and the trajectories for moving them from their respective initial to destination positions within a given two-dimensional (2D) region, such that the delay of antenna movement is minimized, subject to the inter-MA minimum distance constraints in the movement. However, this problem is a continuous-time mixed-integer linear programming (MILP) problem that is challenging to solve. To tackle this challenge, we propose a two-stage optimization framework that sequentially optimizes the MAs' position associations and trajectories, respectively. First, we relax the inter-MA distance constraints and optimally solve the resulted delay minimization problem. Next, we check if the obtained MA association and trajectory solutions satisfy the inter-MA distance constraints. If not satisfied, we then employ a successive convex approximation (SCA) algorithm to adjust the MAs' trajectories until they satisfy the given constraints. Simulation results are provided to show the effectiveness of our proposed trajectory optimization method in reducing the movement delay as well as draw useful insights.