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The Full CommIT Contribution

Sections 11.1–11.3 covered the architecture, eigenmode analysis, and multi-user mapping of array-fed RIS. Section 11.4 focuses on the CommIT Group's specific algorithmic contribution: the integrated framework combining eigenmode analysis, multi-user scheduling, and fast channel estimation into a single production- ready architecture. This is the capstone of Part III of the book.

🎓CommIT Contribution(2023)

Multiuser Multibeam Array-Fed RIS Architecture

G. Caire, I. Atzeni, A. Pezeshki — IEEE Trans. Signal Process.

The CommIT Group's array-fed RIS framework addresses a central 6G challenge: how to build multi-user mmWave and sub-THz systems with practical hardware cost. The architecture uses a small active array (few RF chains) tightly coupled to a large passive RIS; the near-field geometry gives the BS-RIS channel a rich eigenmode structure that supports multi-stream multi-user operation with only $N_t \sim 8$ - $16$ active antennas.

Key technical contributions:

Near-field DoF characterization: rigorous analysis of how $\text{rank}(\mathbf{H}_1)$ depends on the array-RIS geometry. Provides design rules: $d_{\text{AR}} < d_F^{\text{AR}}/5$ for practical full-rank operation.
Eigenmode-user assignment: Hungarian algorithm matches users to eigenmodes based on the factored channel structure. No outer AO needed once SVD is computed — near-closed-form operation.
Two-timescale CSI: the BS-RIS channel $\mathbf{H}_1$ is geometrically fixed (slow-varying); only the RIS-UE channels $\{\mathbf{h}_{k,2}\}$ need fast estimation (coherence-time granularity). Pilot overhead: $K$ pilots per coherence block, not $N$ .
Hybrid digital-analog integration: the active array uses conventional digital baseband + few RF chains + analog low-complexity phase shifters. Compatible with 5G-NR hybrid beamforming architectures.

Performance: achieves $\sim 85\%$ of fully-digital massive-MIMO sum rate at $\sim 20\%$ of the hardware cost at 28 GHz with $N_t = 8, N = 512, K = 6$ . At sub-THz ( $140$ GHz), the cost advantage grows to $10\times$ since active arrays become exponentially expensive at higher frequencies while passive RIS stays cheap per element.

array-fed-rismmwavesub-thzmulti-usercaire-2023

Theorem: Capacity Scaling of CommIT Array-Fed RIS

Under the CommIT array-fed architecture with $N_t$ active antennas, $N$ passive elements, and $K = N_t$ users optimally assigned to eigenmodes:

$C = K \log_2\!\left(1 + \bar\sigma^2 \cdot \frac{P_t\,N}{K\,\sigma^2}\right) + O(1)\ \text{bits/s/Hz},$

where $\bar\sigma^2$ is the average singular value squared of $\mathbf{H}_1$ (typically $\sim 1$ for well-conditioned near-field). Key scaling:

Linear in $K$ : multi-user multiplexing.
Logarithmic in $N$ : per-user aperture gain (not $N^2$ ).
Logarithmic in $P_t$ : standard rate scaling.

Compared with a single-user passive RIS ( $N^2$ gain), the array- fed RIS distributes the $N^2$ over $K$ users, giving $N$ per user — which in the log is $\log N$ rate.

In the near-field regime with full eigenmode coupling, the array-fed RIS capacity scales as $K \log_2(P_t N / \sigma^2)$ — logarithmic in $N$ per user (from aperture gain), linear in $K$ (multi-user). No factor $N^2$ as in single-user RIS: the rate is spread across $K$ users, so per-user SNR grows as $N$ , not $N^2$ .

Two-Timescale CSI: The Pilot Savings

One of the CommIT framework's most practical advantages is its two-timescale CSI handling:

$\mathbf{H}_1$ (BS-to-RIS): depends on fixed geometry (array and RIS positions are physical); changes only over minutes-to-hours timescale. Estimate once per day; store its SVD.
$\{\mathbf{h}_{k,2}\}$ (RIS-to-UE): depends on user mobility; changes at coherence-time scale (5-50 ms). Estimate every coherence block.

Pilot cost: $K$ pilots per coherence block (one per user, since $\mathbf{H}_1$ is factored out), not $N \gg K$ as in single-RIS systems. For $K = 8, N = 512$ : $64\times$ pilot savings. This makes high- $N$ deployments feasible despite their potentially huge channel-estimation overhead.

Chapter 4's compressed-sensing approaches are still useful — the two-timescale decomposition and CS are complementary, not competing.

CommIT Array-Fed RIS Full Algorithm

Complexity: Offline:

O(N N_t^{2})

one-time. Per-block:

O(K^3 + NK)

assignment + phase compute.

Offline calibration (once):

1. Estimate

\mathbf{H}_1

via full-rank pilot sweep at deployment.

2. Compute SVD:

\mathbf{H}_1 = \mathbf{U}_1 \boldsymbol{\Sigma}_1 \mathbf{V}_1^H

.

3. Store

\mathbf{U}_1, \mathbf{V}_1, \boldsymbol{\Sigma}_1

;

\mathbf{H}_1

is not re-estimated at runtime.

Per-coherence block (runtime):

4. Estimate

\{\mathbf{h}_{k,2}\}_{k=1}^K

via

K

-pilot protocol.

5. Compute eigenmode-user assignment via Hungarian algorithm.

6. Power-allocate across eigenmodes via water-filling.

7. Design active precoder:

\mathbf{W} = \mathbf{V}_1 \text{diag}(\sqrt{p_k})

.

8. Design RIS phases: composite

\boldsymbol{\phi}^\star

from Section 11.3.

9. Transmit data.

The runtime algorithm is extremely fast: no AO outer loop, no SDP, no manifold iterations. Total per-block computation is sub-millisecond for $N_t = 8, K = 8, N = 512$ on a modern CPU. This is the key advantage enabling real-time deployment.

Example: A Deployed CommIT Array-Fed RIS at 28 GHz

A 28-GHz array-fed RIS panel with $N_t = 8, N = 512$ is deployed serving $K = 6$ users. Compare expected rate vs. a fully-digital $N_t = 32$ mMIMO baseline.

Solution

Array-fed RIS rate

Per-user SNR: $\sigma_k^2 \cdot P_t N / (K \sigma^2)$ . With $\sigma_k^2 \sim 0.1$ (realistic), $N = 512, K = 6$ , SNR = 10 dB (base): per-user SNR boost $= 0.1 \cdot 512 / 6 \approx 8.5$ , so per-user SNR = 20 dB. Sum rate: $6 \log_2(1 + 100) \approx 40$ bits/s/Hz.

Fully-digital 32-antenna mMIMO

ZF precoder with 32 antennas and 6 users: per-user SNR = 10 dB * 32/6 ≈ 53 dB ... not physically realistic. Under realistic path loss (attenuated): per-user SNR ≈ 15-20 dB. Sum rate: $6 \log_2(1 + 30\text{-}100) \approx 30\text{-}40$ bits/s/Hz.

Cost

Array-fed: 8 active RF chains + passive RIS $= \sim 20\%$ of 32-RF-chain digital BS cost. mMIMO: 32 active chains, 5× cost. Array-fed delivers comparable rate at 1/5 cost — the architectural win. $\blacksquare$

Quick Check

For an array-fed RIS with $N_t = 8$ active antennas and $N = 512$ passive elements placed at $d_{\text{AR}} = 5\lambda$ (near-field), the rank of $\mathbf{H}_1$ is approximately:

1

8

512

$\sqrt{512}$

Correction:

8

In the near-field regime (d_AR << d_F), the BS-RIS channel is full-rank in the smaller dimension: rank = min(N_t, N_eff) = N_t = 8. This enables multi-stream multiplexing.

⚠️Engineering Note

CommIT Array-Fed RIS: Tradeoffs and Deployment

When to use CommIT array-fed RIS:

mmWave and sub-THz ( $> 20$ GHz): the cost advantage is clearest. Active antennas expensive; passive RIS cheap.
$K \leq N_t$ : multiplexing capacity matches the eigenbeam count. Beyond $K = N_t$ , needs time-sharing.
Fixed / semi-static UE positions: two-timescale CSI works best when $\mathbf{h}_{k,2}$ can be estimated once per slow-update cycle.
High-directivity deployment: indoor, rooftop-level antennas, vehicular applications where the RIS can be placed specifically to illuminate UE zones.

When to use alternative architectures:

Sub-6 GHz: fully-digital massive MIMO is fine; RIS marginal.
Very dense multi-user ( $K \gg 16$ ): array-fed RIS runs out of eigenmodes. Use multi-panel (Chapter 12) or centralized cell-free MIMO.
Highly mobile UEs: the two-timescale CSI advantage erodes.

Practical Constraints

•
Typical mmWave array-fed RIS: $N_t \sim 8, N \sim 256$ - $1024$ .
•
Cost advantage over fully-digital mMIMO: $3$ - $5\times$ at 28 GHz, $10\times$ at 140 GHz.
•
Array-RIS distance: $d_{\text{AR}} \sim$ few cm (mmWave), $\sim$ cm (sub-THz).
•
Pilot budget: $K$ per block (array-fed) vs. $N$ per block (conventional RIS).

Why This Matters: Array-Fed RIS in the 6G Vision

6G targets include $1$ Tbps peak throughput, $\mu$ -second latency, and ubiquitous sub-THz coverage. The CommIT array-fed RIS addresses the cost feasibility: without it, sub-THz deployment demands thousands of active antennas per BS — prohibitive at network scale. With array-fed RIS, sub-THz small cells become economically viable: $N_t = 16$ active + passive RIS panels per building facade = dense, high-capacity 6G hotspots at 10-20% of the naive cost.

ETSI and ITU have begun work on RIS standardization (ETSI GR RIS 001–003, 2023–2024). The CommIT architecture features in several proposals as the architectural baseline for sub-THz RIS deployment. Expect production chipsets in 2026–2027 and ETSI normative specs shortly after.

See full treatment in Cost-Benefit Analysis and Deployment Strategy

The CommIT Array-Fed RIS Framework