Chapter Summary

Chapter Summary

Key Points

• 1.

  Array-fed RIS architecture: small active array + large passive RIS in near-field coupling. A few active antennas ($N_t \sim 8$-$16$) illuminate a large passive RIS ($N \sim 256$-$2048$) from a short distance ($d_{\text{AR}} \sim$ few $\lambda$). The near- field BS-RIS channel $\mathbf{H}_1$ has rank $\approx N_t$, supporting multi-stream multi-user operation.

• 2.

  Eigenmode analysis is the algorithmic heart. SVD of $\mathbf{H}_1$ yields $r$ orthogonal eigenmodes, each a different RIS-side signature $\mathbf{u}_k$. Each eigenmode can be separately focused toward a distinct user by the RIS phase matrix $\boldsymbol{\Phi}$, giving $r$ near-orthogonal beams.

• 3.

  Multi-user multiplexing via eigenmode assignment. Assign each user $k$ to one eigenmode $\pi(k)$ via Hungarian algorithm. Each user gets aperture gain $N$ and eigenmode coupling $\sigma_k^2$. Per-user SNR scales as $N/K$; sum rate as $K \log_2 N$. Linear multiplexing, logarithmic aperture.

• 4.

  CommIT contribution (Caire et al. 2023). The complete framework: near-field DoF characterization + eigenmode-user assignment + two-timescale CSI (fast $\mathbf{h}_{k,2}$, slow $\mathbf{H}_1$) + hybrid-beamforming integration. Near-closed- form runtime algorithm; sub-millisecond per-coherence-block compute. Production-ready framework.

• 5.

  Economic case for mmWave and sub-THz. Fully-digital massive MIMO is prohibitively expensive at $> 20$ GHz due to active RF chain cost. Array-fed RIS shifts cost from expensive active hardware to cheap passive metasurface, delivering massive-MIMO-like performance at $10$-$20\%$ of the cost. This is the architectural case for 6G.