Ferkans — Interactive Telecom Tutor

Active RIS vs. the Classical AF Relay

Active RIS and AF relays both amplify reflected signals. What's the difference? An AF relay is a single amplifier+antenna combo that receives on one antenna (or array) and retransmits on another. An active RIS is a distributed array of $N$ small amplifiers, each coupled to a sub-wavelength reflecting element. The distributed architecture enables coherent combining across elements — the same $N^2$ scaling that passive RIS enjoys, now with amplification. Active RIS is morally a "distributed amplify-and-forward relay" with phase control, and it inherits advantages of both.

Definition:
AF Relay Reference Model

A half-duplex AF relay has a single $N_R$ -antenna aperture and an amplifier of gain $g$ . In the receive phase, signal at the relay: $\mathbf{y}_R = \mathbf{h}_1 s + \mathbf{w}_R$ ( $\mathbf{w}_R$ is relay noise). In the transmit phase, the relay re-emits $g\mathbf{y}_R$ through its transmit antenna. Signal at the UE: $y = g(\mathbf{h}_2^H \mathbf{h}_1 s + \mathbf{h}_2^H \mathbf{w}_R) + w$ .

Under half-duplex operation, the relay spends 1/2 the time receiving and 1/2 transmitting → rate loss factor of 2 (3 dB in rate). Active RIS is full-duplex (no receive phase needed), avoiding this penalty.

Theorem: Active RIS Beats AF Relay by $N/2$ (Full-Duplex Factor)

Compare active RIS (with $N$ elements, per-element amplifier gain $g_n^2 = P_{\text{RIS}}/N$ , total amplifier power $P_{\text{RIS}}$ ) with an AF relay (single amplifier, gain $g^2 = P_{\text{relay}}$ , same total power $P_{\text{relay}} = P_{\text{RIS}}$ ) under:

Symmetric BS-RIS and RIS-UE channels.
Matched-phase active RIS (coherent alignment).
Same per-element amplifier noise figure.

Active RIS SNR = $2N \cdot$ AF relay SNR (factor of 2 from full- duplex, factor of $N$ from coherent combining across $N$ elements vs. 1 relay).

At $N = 256$ : active RIS beats the equivalent-power AF relay by $27\text{ dB}$ . This is the decisive advantage.

Per-element amplifier gain is similar ( $\sim 20$ dB) in both active RIS and AF relays. The active RIS has $N$ elements combining coherently, giving an extra $N^2$ signal factor minus noise sharing $\sqrt{N}$ (since noise adds independently per element), for net $\sqrt{N}^2 = N$ SNR boost over a single amplifier. Plus the half-duplex factor of 2: active RIS wins by $2N$ in SNR compared to an AF relay with similar total amplifier power.

Proof

Signal

Active RIS coherent signal: $N^2 \bar{g}^2 \alpha^2 \beta^2$ where $\bar{g}^2 = P_{\text{RIS}}/(N \text{signal power at element})$ . AF relay signal: $g^2 \alpha^2 \beta^2$ . Ratio: $N^2 \bar{g}^2 / g^2 = N^2 \cdot (P_{\text{RIS}}/N)/P_{\text{relay}} = N$ assuming $P_{\text{RIS}} = P_{\text{relay}}$ .

Noise

Active RIS amplified noise: $N \bar{g}^2 \beta^2 \sigma^2_{\text{RIS}}$ (noise per element × $N$ elements, incoherent sum). AF relay amplified noise: $g^2 \beta^2 \sigma^2_{\text{relay}}$ . Ratio: $N/(1)$ .

SNR ratio

Signal / noise ratio = $N$ (signal gain) / 1 (noise gain) = $N$ . Plus half-duplex factor of 2 in favor of active RIS (no receive phase). Total: $2N$ . $\blacksquare$

The Relay Has Its Own Advantages

Despite the SNR gap, AF relays still have their niche:

Physical form factor: a small box with a pair of antennas, vs. a planar array. Relay is easier to mount on a pole.
Decode-and-forward (DF) relays can be noise-free by regenerating the signal. Beats active RIS in noise-dominated scenarios (adding baseband processing and latency).
Backhaul integration: relays can be edge compute nodes with wired backhaul; active RIS is signal-only.
Mature hardware: AF relays are off-the-shelf (WiFi range extenders, cellular repeaters); active RIS is research.

For modern deployments focused on link-budget closure, active RIS is the cleaner architectural win. For edge compute and multi-hop networking, relays remain relevant.

Active RIS vs. AF Relay vs. Passive RIS

Plot SNR vs. distance for three architectures: active RIS, AF relay, passive RIS. Active RIS dominates at moderate $N$ ; AF relay is better for very small $N$ ; passive is best when the link budget allows. Change amplifier power to see each regime.

Parameters

RIS elements

N

256

Amplifier total power (dBm)20

Max distance (m)100

Amplifier NF (dB)5

🎓CommIT Contribution(2023)

Practical Active RIS with Limited Amplifier Budget

G. Caire, I. Atzeni — IEEE Trans. Wireless Commun. (preprint)

Caire et al. (2023) address a practical gap in active-RIS theory: real RIS panels have total-power constraints (set by the DC supply and amplifier efficiency), not just per-element gains. They show that the optimal gain allocation is non-uniform: elements with stronger channels should receive more amplifier power. For $K$ -user scenarios, this becomes a joint resource allocation over $N$ elements and $K$ users. The algorithm (hybrid manifold + waterfilling) achieves $\sim 2\text{-3 dB}$ improvement over uniform-gain active RIS at the same total DC power — a substantial win for constrained deployments. This is the CommIT contribution for the active-RIS chapter.

active-rispower-allocationcaire-2023

⚠️Engineering Note

Active RIS Deployment Checklist

A pragmatic deployment guide:

Identify the regime. Compute the passive-active crossover distance $d^\star$ (Section 9.3). If typical UE distances exceed $d^\star$ , go active.
Size the panel. Active RIS is effective at smaller $N$ (256-512) than passive (1024+). Use this to reduce hardware cost.
Budget DC power. Each element needs $\sim 5$ - $20$ mW. For $N = 256$ : $\sim 1$ - $5$ W total. Ensure wired DC supply at the deployment site.
Control cooling. Amplifier heat over a $\sim 0.5\text{-m}^2$ panel needs passive cooling. Thermal management is a first-order design consideration.
Noise-figure optimization. Amplifier NF directly impacts the crossover. Invest in low-NF amplifiers ( $< 3\text{ dB}$ ) if the deployment is marginal.
Fallback to passive. If amplifier noise dominates, the active RIS can operate at low gain (near-passive) and still work. Plan for degraded-mode operation.

Practical Constraints

•
Typical active-RIS panel size: $20 \times 20$ cm (sub-6 GHz), $10 \times 10$ cm (mmWave).
•
Total DC: $\sim 5$ W typical, $\sim 20$ W at aggressive gain.
•
Amplifier MTBF: $\sim 10^5$ hours at moderate bias — longer than typical deployment.
•
Heat dissipation: $\sim 3$ - $10\,\text{W/dm}^2$ .

Quick Check

At mmWave (28 GHz) with $N = 256$ RIS elements and amplifier noise figure 5 dB, the active-passive crossover distance $d^\star$ is:

$\sim 1$ m

$\sim 10$ cm

$\sim 100$ m

$\sim 1$ km

Correction:

\sim 10

cm

$d^\star = \lambda\sqrt{N/\text{NF}} = 0.011 \cdot \sqrt{256/3.16} \approx 0.1$ m. The crossover is extremely short at mmWave — active RIS is essentially always needed.

Common Mistake: Don't Push Amplifier Gain Past Saturation

Mistake:

"Higher $g_{\max}$ means more SNR. Let's crank each amplifier to its max spec."