Channel estimation for pinching-antenna systems via virtual modular arrays

Pinching antenna systems (PASS) enable flexible array reconfiguration but incur prohibitive pilot overhead due to the large number of candidate pinching positions, making channel state information (CSI) acquisition challenging. To address this issue, this paper proposes a two-stage channel estimation framework leveraging a virtual modular array (VMA) architecture, which decouples the recovery of line-of-sight (LoS) and non-line-of-sight (NLoS) channel components in PASS. In the first stage, the LoS channel is estimated via a coarse-to-fine approach, where geometric localization (GL) and gradient optimization (GO) are employed to recover the hybrid near-far-field channel of VMA-based PASS. Specifically, angle-of-departure estimates are first acquired for each subarray during the GL stage to derive a coarse user position, providing a robust initial value for further estimation. The initial estimate is then refined through the GO method to obtain an accurate user position, thereby enabling the LoS channel reconstruction. Building upon the first-stage LoS channel estimation, the second stage exploits the sparse nature of the NLoS paths to develop a wavenumber-domain orthogonal matching pursuit algorithm applied to grouped virtual subarrays, which recovers the NLoS channel components. Numerical results demonstrate that the proposed method achieves accurate CSI estimation while effectively reducing pilot overhead.