SIM-Assisted Channel Estimation

• SIM-assisted channel estimation is a technique that uses stacked intelligent metasurfaces to directly manipulate electromagnetic fields for accurate channel state acquisition.
• It employs subspace-based estimators and leverages the high-dimensional SIM architecture to minimize training overhead and improve CSI accuracy.
• This method is pivotal for enhancing massive MIMO and holographic MIMO systems, enabling high-capacity precoding and interference shaping.

A stacked intelligent metasurface (SIM) is an advanced electromagnetic structure comprising multiple layers of programmable metasurfaces, where each layer consists of a planar array of passive meta-atoms whose local phase shifts can be dynamically controlled. SIMs enable direct wave-domain manipulation of impinging electromagnetic fields, supporting functionalities such as high-capacity precoding, combining, and interference shaping for massive MIMO and holographic MIMO (HMIMO) wireless systems. SIM-assisted channel estimation refers to the class of methodologies and protocols for acquiring accurate channel state information (CSI) in networks empowered by one or more SIMs, where the unique SIM architecture and its multi-layered, high-dimensional structure are explicitly harnessed to reduce training overhead and improve estimation accuracy.

1. SIM Architecture and Channel Model

A generic SIM-enabled system consists of the following entities:

• A base station (BS) with $M$ antennas (possibly with far fewer $M$ RF-chains than the total number $N$ of meta-atoms per SIM layer).
• One or more SIMs, each with $L$ layers, each layer having $N$ variable-phase meta-atoms operating at subwavelength spacing.
• $K$ single-antenna (or multi-antenna) users.

The end-to-end SIM transfer matrix is constructed as a product of inter-layer coupling matrices and diagonal phase-shift matrices: $$F = \Phi_L W_L \cdots \Phi_1 W_1 \in \mathbb{C}^{N\times N}$$ with phase-shift matrices per layer

$$\Phi_\ell = \operatorname{diag}(e^{j\phi^l_1},\ldots,e^{j\phi^l_N})$$

and inter-layer, or layer-to-antenna, propagation matrices $W_\ell$ determined by the free-space Green's function specific to the SIM geometry (Papazafeiropoulos et al., 18 Feb 2025, Yao et al., 2024, Nadeem et al., 2023). The user-to-final-layer channel vectors $\mathbf{h}_k$ typically have spatial correlations due to dense packing of meta-atoms, and may exhibit Rician fading: $M$0 with $M$1 (Papazafeiropoulos et al., 18 Feb 2025).

2. SIM-Assisted Channel Estimation Protocols

2.1 Subspace-Based Estimators

Due to the property that $M$2 (number of meta-atoms typically much larger than antennas or users), observations of the SIM-preprocessed uplink pilots over multiple blocks are inherently rank-deficient, allowing for sub