How Much Training is Required for Channel Estimation in Fluid Antenna System?

Recently, fluid antenna system (FAS) exploiting flexible-location antennas within a given space has emerged as a key enabler for next-generation wireless communications and Internet-of-Things (IoT). In FAS, acquisition of precise channel state information (CSI) for all possible switchable locations, referred to as ports, is necessary, but demanding. Affirmatively, recent studies have revealed that by virtue of high spatial correlation among a number of ports, the CSI for all the ports can be acquired by estimating the CSI only for a small subset of the ports. However, an important and fundamental question still remains unanswered yet: then how much training is exactly required to estimate the CSI for all the ports in FAS? In this paper, we aim to rigorously answer this nontrivial question by developing a new channel estimation technique for FAS based on a latent domain representation of the CSI for the ports and by jointly optimizing training overhead, training sequences, and port switching. Our thorough analysis newly reveals that the training overhead required for estimating the CSI for all the ports is always less than the rank of spatial channel correlation matrix for all the ports and is increasing with signal-to-noise ratio (SNR). To alleviate the computational burden of the optimal solution, we also propose a low-complexity, yet near-optimal, solution for training design and port switching. Extensive simulation results confirm that in a practical situation with a large number of ports in a small size, the training overhead required for accurate CSI acquisition in FAS is within at most 10% of the number of ports at modest SNR, and the FAS outperforms the conventional fixed antenna system in terms of both the channel estimation accuracy and training overhead.