Ferkans — Interactive Telecom Tutor

One RIS Is Not Enough

Single-panel RIS solves a specific deployment problem: redirect a BS's signal around a blockage to reach one or a few users. For wide-area coverage — an entire street, a dense urban block, a multi-floor building — a single panel is not enough. Deployments in 6G will use multiple RIS panels, spatially distributed, cooperatively configured. This section formalizes the multi-RIS model and highlights how the optimization framework generalizes.

The golden thread continues to apply: each RIS panel programs its own slice of the propagation environment, and the joint optimization coordinates them. Panels can even cascade (signal bounces from panel 1 to panel 2 before reaching UE) — but this introduces new mathematical structure we treat in Section 12.2.

Multi-RIS

A deployment with $M$ RIS panels that jointly serve a set of users. Panels can be parallel (each bouncing BS signal independently to UEs, Section 12.1), cascaded (double-RIS, Section 12.2), or integrated with distributed APs (cell-free, Section 12.3).

Double-RIS

A deployment with two RIS panels in cascade: signal bounces BS → panel 1 → panel 2 → UE. Essential for extreme blockage geometries where no single panel sees both endpoints. SNR scales as $N_1^2 N_2^2$ at the cost of four-hop path loss.

Related: Multi-RIS, Path Loss

Definition:
Multi-RIS Downlink System Model

Consider a BS with $N_t$ antennas serving $K$ single-antenna users via $M$ RIS panels. Panel $m$ has $N_m$ elements and phase-shift matrix $\boldsymbol{\Phi}_m$ . Define:

$\mathbf{H}_{1,m} \in \mathbb{C}^{N_m \times N_t}$ : BS-to-panel- $m$ channel.
$\mathbf{h}_{2,km} \in \mathbb{C}^{N_m}$ : panel- $m$ -to-user- $k$ channel.
$\mathbf{h}_{d,k} \in \mathbb{C}^{N_t}$ : direct BS-to-user- $k$ channel.

Assuming parallel (no inter-panel cascading for now), the effective channel at user $k$ is

$\mathbf{h}_{k,\text{eff}}^H = \mathbf{h}_{d,k}^H + \sum_{m=1}^M \mathbf{h}_{2,km}^H \boldsymbol{\Phi}_m \mathbf{H}_{1,m}.$

Each panel contributes one cascaded path; the contributions add coherently if the phases are aligned across panels.

Note the sum over $m$ . Multi-RIS superposes multiple cascaded paths — a form of spatial diversity. The effective channel has more gain potential than a single panel of the same total element count (because panels can be at different geometric positions, avoiding shadowing and accessing different scattering paths).

,

Theorem: Coherent Multi-RIS SNR Gain

Under coherent alignment across all $M$ panels with symmetric geometries (all panels at similar BS-to-UE distances), the coherent SNR scaling is

$\text{SNR}^{\text{multi-RIS}} \approx M^2 N^2 \alpha^2 \beta^2 P_t / \sigma^2$

where $\alpha, \beta$ are per-hop amplitudes and $N$ is the per-panel element count. Compared with a single panel of $MN$ elements (if that were a valid deployment), multi-RIS gives the same coherent gain — but with geometric diversity (panels at different positions access different scattering paths). Under heterogeneous geometry, some panels serve better than others, giving even better aggregate performance via smart per-panel weighting.

Under coherent phase alignment across all panels, the cascaded signals add constructively. With $M$ panels of $N$ elements each, total $MN$ elements combined. The coherent-sum SNR scales as $(MN)^2$ — linear in $M$ squared, quadratic in $N$ .

Proof

Coherent sum

Each panel contributes $\mathbf{h}_{2,km}^H \boldsymbol{\Phi}_m \mathbf{H}_{1,m} \mathbf{v}$ . With coherent phases, these are all aligned: the sum amplitude is $\sum_m |(\mathbf{h}_{2,km}^H \boldsymbol{\Phi}_m \mathbf{H}_{1,m} \mathbf{v})| \sim M \cdot N \alpha \beta$ .

Squared

SNR $\propto (MN \alpha \beta)^2 = M^2 N^2 \alpha^2 \beta^2$ .

Heterogeneity

If per-panel path losses differ, replace $\alpha \beta$ with panel-specific $\alpha_m \beta_m$ and sum contributions. Under optimal power allocation, worst panels contribute nothing; best panels dominate. Total gain bounded by the sum of per-panel gains. $\blacksquare$

Multi-RIS Urban Deployment — A multi-RIS network: a BS serves a dense urban area with three RIS panels mounted on different building facades. Each panel has its own phase-shift matrix $\boldsymbol{\Phi}_m$ ; the BS optimizes all three jointly. Users in the street canyon see contributions from multiple panels, giving spatial diversity and improved coverage.

What Multi-Panel Actually Buys

Relative to a single large RIS panel of $MN$ elements, multi- RIS offers:

Geometric diversity: panels at different positions see different scattering environments. Robust to localized blockage.
Coverage extension: panels on different facades reach different UE groups (angular diversity).
Distributed deployment: easier to install multiple smaller panels than one huge panel.
Scalability: can add panels incrementally as traffic grows.

Relative to a single RIS, multi-RIS offers:

Graceful degradation: failure of one panel doesn't kill the link.
Multi-user coverage: each panel can specialize in serving a subset of users.
Aperture scaling: $M \cdot N$ total elements instead of just $N$ .

The multi-panel architecture is the default for 6G deployments in dense environments.

Single RIS vs. Multi-RIS Coverage

Compare the coverage map (SNR heatmap) of a single RIS panel vs. $M = 3$ distributed panels with the same total element count. Multi-RIS shows more uniform coverage and better blockage resilience.

Parameters

Total RIS elements

MN

384

Number of panels

M

3

Carrier frequency (GHz)28

Coverage area side (m)150

AO for Multi-RIS Joint Optimization

Complexity:

O(T \cdot (T_{\text{WMMSE}} K N_t^{3} + M C_{\text{passive}}))

where

M

passive updates per iteration

Input: channels

\{\mathbf{H}_{1,m}, \mathbf{h}_{2,km}, \mathbf{h}_{d,k}\}

, power

P_t

.

Output:

(\mathbf{W}^\star, \{\boldsymbol{\Phi}_m^\star\})

.

1. Initialize

\boldsymbol{\Phi}_m^{(0)}

for all

m

(e.g., all ones).

2. Repeat

t = 0, 1, \ldots

:

3.

\quad

Compute aggregate effective channels

\mathbf{h}_{k,\text{eff}}

(summing contributions from all panels).

4.

\quad

Active update (WMMSE):

\mathbf{W}^{(t+1)}

.

5.

\quad

For each panel

m = 1, \ldots, M

:

6.

\quad\quad

Fix

\{\boldsymbol{\Phi}_{m'}\}_{m' \neq m}

; update

\boldsymbol{\Phi}_m^{(t+1)}

via Chapter 6 algorithms (element-wise or manifold).

7.

\quad

Check convergence:

|R^{(t+1)} - R^{(t)}| < \epsilon

.

8. return

(\mathbf{W}, \{\boldsymbol{\Phi}_m\})

.

The key addition over single-RIS AO: $M$ passive updates per iteration instead of 1. Each panel is updated holding the others fixed — a sequential BCD within the outer AO. Monotone convergence preserved.

Key Takeaway

Multi-RIS is the natural extension for wide-area coverage. The AO framework generalizes cleanly: $M$ passive-update subproblems per iteration, each solved by Chapter 6 algorithms. The real design question is not the algorithm — it's the deployment: where to put the panels, and how to allocate users to panels. Section 12.4 addresses this.

Common Mistake: Inter-Panel Coherence Requires Synchronized Control

Mistake:

"Multi-RIS just adds SNR contributions from each panel — deploy a few panels and expect coherent combining."

Correction:

Coherent combining across panels requires phase-aligned control: each panel must apply phases that are tuned to the same BS signal reference. Independent panels without synchronized control yield only incoherent summing (factor $M$ in power, not $M^2$ ). The controller must distribute a common time and phase reference to all panels. At mmWave, $\sim$ ns-level time synchronization is needed. Without it, multi-RIS degrades to SNR combining of $M$ independent paths — helpful but far from the $M^2$ coherent ideal.

Multi-RIS System Model