Prerequisites & Notation

Before You Begin

Multi-RIS deployments extend the single-panel architecture to networks of coordinated RIS panels. This chapter adds two new dimensions: (1) the double-RIS cascaded channel (signal bounces through two panels in series), and (2) integration with cell-free massive MIMO (distributed access points plus distributed RIS panels). Both build on the single-RIS machinery of Chapters 5-11.

Single-panel RIS optimization (Chapters 5-11)(Review ch05)
Self-check: Recall the joint active-passive AO framework and its complexity.
Cell-free massive MIMO (MIMO Ch. 11-12)(Review ch11)
Self-check: What is the key architectural difference between cell-free and conventional cellular networks?
Distributed beamforming and cooperation(Review ch12)
Self-check: For distributed APs with front-haul backhaul, what are the coherent-cooperation constraints?
Stochastic geometry for network analysis (Telecom Ch. 21)(Review ch21)
Self-check: Given a PPP with density $\lambda$ , what is the expected number of APs within radius $r$ ?
Pilot allocation and reuse (MIMO Ch. 3)(Review ch03)
Self-check: Why is pilot contamination a bigger problem in cell-free than in cellular?

Notation for This Chapter

Multi-RIS notation builds on single-RIS symbols with a panel index $m = 1, \ldots, M$ .

Symbol	Meaning	Introduced
$M$	Number of RIS panels (multi-panel deployment)	s01
$N_m$	Number of elements on panel $m$	s01
$\boldsymbol{\Phi}_m$	Phase-shift matrix of panel $m$	s01
$\mathbf{H}_{1,m}$	BS-to-panel- $m$ channel, $N_m \times N_t$	s01
$\mathbf{h}_{2,km}$	Panel- $m$ -to-user- $k$ channel, $N_m \times 1$	s01
$\mathbf{F}_{mn}$	Inter-panel channel from panel $m$ to panel $n$ (double-RIS)	s02
$\mathcal{A}$	Set of cooperating APs (cell-free)	s03
$\lambda_\text{RIS}$	Spatial density of RIS panels in a stochastic-geometry model	s04

← Ch 11 Multi-RIS System Model