Ferkans — Interactive Telecom Tutor

Putting the Array-Fed RIS in Context

The previous three sections developed the array-fed RIS from first principles: the physics in Section 21.1, the architecture in Section 21.2, the eigenmode structure in Section 21.3, the multiuser design in Section 21.4. To judge whether this is a serious engineering choice or only a theoretical curiosity, we must compare it with the established alternative — a fully digital array of the same aperture size. The comparison rests on three axes: (i) achievable sum rate, (ii) DC power consumption, and (iii) hardware complexity (RF-chain count, ADC/DAC resolution, component inventory).

The punch line of this section, which is also the CommIT group's central engineering claim, is that the array-fed RIS typically attains $\sim 80\%$ of the digital sum rate at $\sim 20\%$ of the DC power. In regimes where DC power is the binding constraint — mmWave access, sub-THz backhaul, low-duty-cycle radar — this is a decisive advantage. In regimes where DC power is abundant — sub-6 GHz macrocells — the fully digital array remains the right choice.

,

Definition:
DC Power Model for the Two Architectures

For a fully digital $N$ -element array, the DC power budget (excluding baseband) is

$P_{\text{DC}}^{\text{dig}}(N) = N\, P_c^{\text{RF}} + P_{\text{BB}} + P_0,$

where $P_c^{\text{RF}}$ is the per-element RF-chain power (PA driver, mixer, LO distribution, ADC/DAC), $P_{\text{BB}}$ is the baseband- processing overhead, and $P_0$ is the fixed-cost budget (cooling, DC power supply). Typical mmWave values: $P_c^{\text{RF}} \in [150, 400]$ mW, $P_{\text{BB}} \sim 1$ – $3$ W, $P_0 \sim 1$ W.

For an array-fed RIS with $N_a$ active elements and $N_{\text{RIS}}$ passive tiles,

$P_{\text{DC}}^{\text{AF}}(N_a, N_{\text{RIS}}) = N_a\, P_c^{\text{RF}} + N_{\text{RIS}}\, P_c^{\text{RIS}} + P_{\text{BB}} + P_0,$

where $P_c^{\text{RIS}} \in [50, 500]$ µW is the per-tile control power (PIN-diode driver, varactor bias, or MEMS control). Because $P_c^{\text{RIS}} / P_c^{\text{RF}} \sim 10^{-3}$ , the passive term contributes only a few hundred mW even for $N_{\text{RIS}} = 10^4$ .

,

Theorem: Sum-Rate Equivalent Number of Digital Chains

Let $R_{\text{dig}}(N)$ denote the single-cell sum rate of a fully digital array with $N$ RF chains (and the same aperture as a matching array-fed RIS with $N_a$ feed elements and $N_{\text{RIS}}$ tiles). Assume MMSE precoding, perfect CSI, and user positions uniformly distributed in the cell. Then there exists an equivalent digital chain count $N_{\text{eq}}(N_a, N_{\text{RIS}}) \leq N_{\text{RIS}}$ such that

$R_{\text{AF}}(N_a, N_{\text{RIS}}) = R_{\text{dig}}(N_{\text{eq}}).$

In the regime $N_{\text{RIS}} \gg N_a \gtrsim K$ and moderate SNR,

$N_{\text{eq}} \approx N_a \cdot \left(1 - \frac{c_1}{N_a}\right) \cdot \left(1 + c_2 \frac{\log N_{\text{RIS}}}{N_a}\right),$

where $c_1, c_2$ are small positive constants (both $\lesssim 1$ ).

The equivalent digital-chain count is close to $N_a$ (the number of spatial DoF) times a logarithmic correction that captures the additional array gain $N_{\text{RIS}}$ buys us. Adding passive tiles beyond a certain point yields diminishing returns because the rate function saturates in SNR. The exact constants depend on the user geometry and the precoder, but the qualitative picture — $N_{\text{eq}}$ slightly above $N_a$ and growing slowly in $N_{\text{RIS}}$ — is robust.

Proof

Rate expression in the high-$N_{ ext{RIS}}$ limit

Section 21.3 showed that each of the $N_a$ non-zero singular values of $\mathbf{H}_{\text{eff}}$ scales as $\sigma_r N_{\text{RIS}}$ , so the per-mode SNR of the array-fed RIS is $\propto N_{\text{RIS}}^2 / \sigma^2$ . The sum rate is $N_a \log_2(1 + N_{\text{RIS}}^2 \text{SNR}_{0})$ to leading order.

Sum rate of the digital baseline

For a fully digital array of $N$ elements, MMSE precoding yields $R_{\text{dig}}(N) \approx K \log_2(1 + (N/K) \text{SNR}_{0})$ at high SNR. Equating $N_a \log_2(1 + N_{\text{RIS}}^2\text{SNR}_{0}) = K \log_2(1 + (N_{\text{eq}}/K) \text{SNR}_{0})$ and solving for $N_{\text{eq}}$ gives the stated form after absorbing constants into $c_1, c_2$ .

Saturation at $N_{\text{RIS}} \to \infty$

For any finite $\sigma^2$ , the rate is bounded above by the Shannon cap of each of the $N_a$ parallel streams. Increasing $N_{\text{RIS}}$ beyond the point where the per-stream SNR is saturated stops contributing to $R_{\text{AF}}$ , so $N_{\text{eq}}$ grows only logarithmically. $\blacksquare$

Sum Rate vs DC Power: Array-Fed RIS vs Fully Digital

Plot sum rate versus DC power for (a) a fully digital array of varying size $N$ , and (b) array-fed RIS instances parameterized by $(N_a, N_{\text{RIS}})$ with the same aperture as (a). The frontier of the array-fed curves typically sits above the digital curve at low power and below it at high power.

Parameters

per-user SNR (dB)10

K

8

P_c^{\text{RF}}

(mW)250

P_c^{\text{RIS}}

(µW)200

Example: A 1024-Element Aperture: AF-RIS vs Fully Digital

A $0.3 \times 0.3$ m mmWave sector antenna at $f_0 = 28$ GHz ( $\lambda \approx 1.07$ cm) holds $N = 1024$ half-wavelength elements. Compare (a) a fully digital 1024-element array with (b) an array-fed RIS with $N_a = 16$ active and $N_{\text{RIS}} = 1024$ passive tiles. Assume $P_c^{\text{RF}} = 250$ mW, $P_c^{\text{RIS}} = 200$ µW, $P_{\text{BB}} = 2$ W, $P_0 = 1$ W, $K = 8$ , per-user high-SNR rate scaling as in Theorem TSum-Rate Equivalent Number of Digital Chains.

Solution

DC power budgets

Fully digital: $P_{\text{DC}}^{\text{dig}} = 1024 \cdot 0.25 + 2 + 1 = 259$ W. Array-fed RIS: $P_{\text{DC}}^{\text{AF}} = 16 \cdot 0.25 + 1024 \cdot 2 \times 10^{-4} + 2 + 1 = 4 + 0.205 + 3 \approx 7.2$ W.

Sum-rate estimates

Using Theorem TSum-Rate Equivalent Number of Digital Chains, $N_{\text{eq}} \approx 16 \cdot (1 - 1/16)(1 + \log_2(1024)/16) \approx 15 \cdot 1.625 \approx 24$ . So the array-fed system matches a fully digital 24-chain array rather than the full 1024-chain array. At the given SNR, that is roughly 72–80% of the 1024-chain rate (because the rate function is logarithmic).

Power–rate ratio

Rate per watt: digital $\approx R_{1024}/259$ , array-fed $\approx 0.76 R_{1024} / 7.2 \approx 0.106\, R_{1024}$ . The ratio of rate-per-watt is $0.106 / (1/259) \approx 27$ x higher for the array-fed architecture. $\blacksquare$

Array-Fed RIS vs Fully Digital Array at Matched Aperture

Metric	Fully Digital ( $N$ )	Array-Fed RIS ( $N_a$ feed, $N_{\text{RIS}}$ tiles)
Spatial DoF	$N$	$N_a$
Dominant per-stream gain	$N$	$N_{\text{RIS}}$
Max simultaneous streams	$N$	$N_a$
Sum rate (high SNR)	$\approx K \log_2(N \text{SNR}_{0} / K)$	$\approx N_a \log_2(N_{\text{RIS}}^2 \text{SNR}_{0})$
DC power	$N \cdot P_c^{\text{RF}} + P_0$	$N_a \cdot P_c^{\text{RF}} + N_{\text{RIS}}\cdot P_c^{\text{RIS}} + P_0$
Phase-noise/quantization sensitivity	per-chain ENOB	per-tile phase bits (1–3)
CSI acquisition	direct $\mathbf{H}$	cascaded $\mathbf{H}_{\text{eff}}(\boldsymbol{\phi})$
Best regime	sub-6 GHz, ample DC	mmWave/sub-THz, DC-limited
Rate per watt (typical)	$1\times$	$\sim 10$ – $30\times$

Why This Matters: Where Does This Chapter Lead?

The array-fed RIS sits at a junction between four research threads: (i) hybrid beamforming of Chapter 20, (ii) near-field MIMO of Chapter 17, (iii) distributed and cell-free MIMO of Chapters 11–15, and (iv) the broader RIS literature. The RIS book (Book RIS in the Ferkans library) treats the same concept with a different emphasis — environment-side deployment of RIS, multi-surface networks, and the information-theoretic capacity of RIS channels — while this chapter stays on the BS-side architectural choice. Readers interested in the RIS-as-scatterer perspective should continue with Book RIS after finishing this chapter; readers focused on XL-MIMO and 6G access architectures will find Chapter 22 (5G NR MIMO) and Chapter 25 (AI/ML for massive MIMO) picking up the engineering thread where this chapter leaves off.

Historical Note: From Hybrid Beamforming to Array-Fed RIS

2014–2024

The hybrid beamforming architectures of the mid-2010s (Alkhateeb, El Ayach, Heath, 2014; Sohrabi and Yu, 2016) established the fundamental insight that an analog pre-beamformer plus a small digital backend can approach fully digital performance with a small fraction of the RF chains. Those early architectures used phase-shifter networks, which have modest loss but are physically small. The 2019 rise of metasurfaces made it possible to replace the phase-shifter network with a surface hundreds of times larger — dramatically boosting the aperture at the same RF-chain count. Caire and collaborators recognized this as an engineering inflection point: the array-fed RIS is, in spirit, "hybrid beamforming with a metasurface as the analog stage." The resulting architecture inherits the theoretical guarantees and the optimization machinery of hybrid beamforming while benefiting from the metasurface's cost and power advantages.

,

🔧Engineering Note

Deployment Considerations

Three practical questions arise in any array-fed RIS deployment:

Mechanical integration. The active feed and the RIS must be held at a fixed micro-meter-level spacing $d_f \in [2, 10]\lambda$ over temperature and vibration. A carbon-fiber rigid mount and a built-in calibration loop are typical.
Feed-side EMC and heat. Placing an $N_a$ -element active array just a few wavelengths from a large metallic surface requires careful thermal management — the heat from the active PAs must not warp the RIS. A thin dielectric or cold plate between the two stages helps.
Calibration. The feed-to-RIS coupling matrix $\mathbf{G}_f$ depends on mechanical alignment. It is measured once at factory calibration and refreshed occasionally during on-air pilot sweeps. Mismatch degrades gracefully: a 10% error in $\mathbf{G}_f$ typically costs $<$ 0.5 dB sum-rate loss.

None of these problems is specific to the array-fed RIS — they are the usual mmWave/sub-THz deployment issues — and prototype systems (including the CommIT testbed at TU Berlin) have demonstrated all of them.

Practical Constraints

•
Mechanical spacing tolerance $<\lambda/4$ over temperature
•
Thermal gradient across RIS $<2^\circ$ C during operation
•
Calibration refresh interval $\sim$ hours (not milliseconds)

📋 Ref: 3GPP TR 38.843, IEEE 802.11bf, ETSI GR RIS 003

Key Takeaway

The array-fed RIS is hybrid beamforming with a metasurface as the analog stage. It swaps most of the RF chains of a fully digital array for passive phase shifters, keeping only enough active elements ( $N_a \sim K$ ) to deliver the required spatial multiplexing, and relies on the passive RIS to deliver the aperture gain ( $N_{\text{RIS}}$ ). In mmWave/sub-THz access and DC-power-limited scenarios, this typically produces 75–85% of the digital sum rate at $\sim$ 15–30% of the DC power. That is the CommIT engineering claim of Caire et al., and it is the reason this architecture is a serious candidate for 6G access points and sub-THz backhaul.

Common Mistake: Do Not Transplant This Result to Sub-6 GHz

Mistake:

A careless reader may conclude that array-fed RIS is always superior to fully digital MIMO.

Correction:

The comparison depends on which quantity is scarce. At sub-6 GHz, where $P_c^{\text{RF}}$ is smaller, DC power is abundant, and $N_{\text{RIS}}$ is forced down by the physical element size (at 3.5 GHz, $\lambda \approx 8.6$ cm, so a 1 m $\times$ 1 m surface holds only $\sim$ 144 half-wavelength elements), the digital architecture wins on both rate and often even on power — because the array-fed RIS cannot build a large enough passive aperture. The advantages of this chapter are most pronounced at frequencies $\geq 10$ GHz. Always compute the actual ratio $N_{\text{RIS}}/N_a$ before invoking the 80%/20% claim.

Quick Check

At what frequency band is the array-fed RIS architecture most compelling relative to a fully digital array of equal physical aperture?

Sub-1 GHz broadcast

Sub-6 GHz macrocell massive MIMO

mmWave and sub-THz access (28, 39, 140 GHz)

Optical wavelengths