Time-Varying Channel Estimation via Sparsity Exploitation for Fluid Antenna-Assisted Systems

Abstract

While fluid antennas (FAs) offer a new degree of freedom for wireless communication systems, the corresponding channel estimation problem is more difficult than in conventional fixed-position antenna systems. This is because an FA can only sample a small portion of the full-array spatial observation at each time slot, rather than capturing the complete array observation simultaneously. The difficulty is further compounded in time-varying channels. This paper investigates time-varying channel estimation for a multi-port FA-assisted system with a single radio frequency chain. A structured repeated port-activation strategy is designed to transform sequential single-port pilot observations into a virtual two-dimensional spatial-Doppler line-spectrum model, based on which ambiguity-free activation conditions are derived. For high-accuracy gridless recovery, a decoupled atomic norm minimization (DANM) estimator is developed by replacing the high-dimensional two-level Toeplitz structure with two low-dimensional one-level Toeplitz matrices. To reduce the computational burden, an alternating direction method of multipliers (ADMM)-based implementation, termed DANM-ADMM, is further developed with problem-structured iterative updates. In addition, a decoupled orthogonal matching pursuit (DOMP) algorithm is proposed as a low-complexity dictionary-based alternative, enabling high-resolution one-dimensional searches without constructing a prohibitive full two-dimensional dictionary. An equivalent-to-physical parameter recovery procedure is also developed to reconstruct the global time-varying FA channel over all ports and time slots. Simulation results demonstrate that DANM and DANM-ADMM achieve performance close to the Cramér–Rao bound, whereas the DOMP algorithm attains a favorable complexity–accuracy trade-off.