Antenna Elements' Trajectory Optimization for Throughput Maximization in Continuous-Trajectory Fluid Antenna-Aided Wireless Communications

Fluid antenna (FA) systems offer novel spatial degrees of freedom (DoFs) with the potential for significant performance gains. Compared to existing works focusing solely on optimizing FA positions at discrete time instants, we introduce the concept of continuous-trajectory fluid antenna (CTFA), which explicitly considers the antenna element's movement trajectory across continuous time intervals and incorporates the inherent kinematic constraints present in practical FA implementations. Accordingly, we formulate the total throughput maximization problem in CTFA-aided wireless communication systems, addressing the joint optimization of continuous antenna trajectories in conjunction with the transmit covariance matrices under kinematic constraints. To effectively solve this non-convex problem with highly coupled optimization variables, we develop an iterative algorithm based on block coordinate descent (BCD) and majorization-minimization (MM) principles with the aid of the weighted minimum mean square error (WMMSE) method. Finally, numerical results are presented to validate the efficacy of the proposed algorithms and to quantify the substantial total throughput advantages afforded by the conceived CTFA-aided system compared to conventional fixed-position antenna (FPA) benchmarks and alternative approaches employing simplified trajectories.