Chapter Summary

Chapter Summary

Key Points

• 1.

  Multi-RIS generalizes the single-panel paradigm. $M$ distributed panels, each with phase-shift matrix $\boldsymbol{\Phi}_m$, coherently combine contributions at user locations. Effective channel: $\mathbf{h}_{k,\text{eff}}^H = \mathbf{h}_{d,k}^H + \sum_m \mathbf{h}_{2,km}^H \boldsymbol{\Phi}_m \mathbf{H}_{1,m}$. Under coherent alignment across panels, coherent SNR scales as $M^2 N^2$ — geometric diversity plus coherent gain.

• 2.

  Double-RIS uses inter-panel bouncing. Signal flows BS → panel 1 → panel 2 → UE. Four-hop path loss is severe, but the coherent gain is $N_1^2 N_2^2$ — quartic in $N$. Essential for extreme blockage scenarios (tunnels, L-shaped geometry) where single-panel RIS fails geometrically.

• 3.

  RIS-aided cell-free massive MIMO. Distributed APs + RIS panels + central coordination. Per-user rate scales as $\log_2(P_t\,(L N_t + M N^2))$, combining active-aperture (AP count) with passive-aperture (RIS coherent combining). 6G architectural foundation.

• 4.

  CommIT hierarchical scheduling (Caire & Atzeni 2024). Decouples a nominally $O((LMK)^3)$ joint optimization into parallel sub-problems via macro- (user-cluster assignment) and micro- (within-cluster optimization) scheduling. Reduces computation from hours to milliseconds for 6G-scale deployments.

• 5.

  Deployment optimization: where to put panels. Heuristics (shadow boundaries, geographic diversity, proximity to endpoints) suffice for $M \leq 5$ panels per cell. Beyond that, stochastic-geometry PPP analysis and ML-based deployment are practical tools. Typical urban density: $\sim 2$-$5$ panels per km² for $> 95\%$ coverage.