Ferkans — Interactive Telecom Tutor

What Do We Actually Measure?

A RIS measurement campaign has two goals: (i) validate the cascaded channel model for the specific panel under test, and (ii) extract the calibration coefficients needed to run the phase-shift control algorithm correctly. The second goal is the bottleneck: even a $1°$ per-element phase error, consistently biased, degrades the coherent combining by 5–10 dB for $N > 256$ .

Definition:
Over-the-Air (OTA) Testing

OTA testing characterizes a RIS panel by transmitting and receiving radio waves through a controlled propagation environment (chamber or free space), rather than through VNA cables. The measured quantity is typically the received power at the UE antenna for a fixed BS transmit power and a programmed $\boldsymbol{\Phi}$ . The reference quantity is either (i) the received power with the RIS off (reflecting as a metal plate), or (ii) the received power with $\boldsymbol{\Phi} = \mathbf{I}$ (uniform phase).

Theorem: Gain Relative to Metallic Reference

Let $P_{\text{on}}$ be the received power with the RIS programmed to the optimal beamforming phases, and let $P_{\text{mp}}$ be the received power with the RIS replaced by a flat metal plate of equal area (specular-reflection reference). Then the RIS beamforming gain is $G_{\text{BF}} = \frac{P_{\text{on}}}{P_{\text{mp}}} = N^2 \cdot \frac{|\Gamma|^2 \eta_{\text{cal}}}{\rho_{\text{mp}}^2}$ where $\Gamma$ is the per-element reflection coefficient magnitude, $\eta_{\text{cal}}$ is the calibration efficiency, and $\rho_{\text{mp}}$ is the reflection coefficient of the metal plate ( $\approx 1$ ).

Proof

Specular reference

With a flat metal plate, the received amplitude equals the sum of $N$ unit-amplitude phase-random reflections — the free-space signal picks up $\sim 1$ specular reflection from the plate. We approximate $P_{\text{mp}} \approx (\wl/(4\pi (d_1 + d_2)))^2 \cdot \rho_{\text{mp}}^2 P_t$ .

Optimal RIS

With coherent combining across all $N$ elements, $P_{\text{on}} \approx (\wl/(4\pi d_1))^2 (\wl/(4\pi d_2))^2 \cdot N^2 |\Gamma|^2 \eta_{\text{cal}} P_t$ .

Ratio

Dividing: $\frac{P_{\text{on}}}{P_{\text{mp}}} = N^2 \cdot \frac{|\Gamma|^2 \eta_{\text{cal}}}{\rho_{\text{mp}}^2} \cdot \frac{(d_1 + d_2)^2}{(d_1 d_2)^2/(\wl/4\pi)^2}$ . The geometry factor collapses to unity when $d_1 = d_2$ , and in general depends on the specific placement. $\blacksquare$

Anechoic Chamber OTA Setup — Anechoic chamber at TU Berlin for RIS characterization. BS horn (left, 28 GHz) illuminates the RIS panel (center, on rotation stage) which reflects toward the receive horn (right). Multipath suppression: $> 20$ dB absorber isolation.

Codebook Characterization

Continuous-phase characterization (sweep $\theta_n$ over $[0, 2\pi)$ for each element) takes $N \cdot K$ measurements for $K$ phase samples — impractical for $N > 100$ . Instead, most campaigns use a codebook: a precomputed set of $M$ phase patterns (beams, nulls, random). This reduces the measurement time to $M$ patterns (with $M \ll 2^{Nb}$ ), at the cost of losing the ability to optimize for specific UE positions.

OTA Codebook Characterization

Complexity: O(M)

Input: codebook { θ^(1), θ^(2), ..., θ^(M) }, TX/RX positions

Output: measured gain matrix G ∈ R^{M × K} (K receive positions)

1. Fix BS antenna position, power P_TX

2. for m = 1, ..., M:

3. Load θ^(m) onto the RIS panel

4. for k = 1, ..., K:

5. Move RX to position k

6. Wait for settling (~10 ms)

7. Record received power P_rx[m,k]

8. end for

9. end for

10. Subtract reference (RIS-off) measurements to get gain G

11. return G

Example: Measurement Time for N = 128 RIS

A 128-element RIS at 5.8 GHz is characterized using a codebook of $M = 1024$ beams (sweeping azimuth at $\Delta\phi = 0.35°$ resolution). Each measurement takes 50 ms (VNA sweep + settling). Total measurement time?

Solution

Calculation

$T = M \cdot t_{\text{meas}} = 1024 \cdot 50 = 51200$ ms $= 51.2$ seconds per receive position.

Scaling

If $K = 20$ receive positions are needed, the total campaign takes $\sim 17$ minutes — manageable in one session. Compare to continuous-phase: $128 \times K_{\text{phase}}$ samples × 50 ms = many hours. Codebook characterization is the only practical option for $N > 100$ . $\blacksquare$

Rate vs. Phase Error Standard Deviation

Plot how the achievable rate with a RIS degrades as the per-element phase error standard deviation $\sigma_\phi$ grows. At $\sigma_\phi = 0°$ (perfect calibration): full $N^2$ gain. At $\sigma_\phi \to \infty$ : random phases, gain $\to N$ . Move the slider to see how sensitive the gain is.

Parameters

RIS elements

N

256

Transmit SNR (dB)10

Carrier frequency (GHz)28

⚠️Engineering Note

Field Trial Best Practices

Moving from chamber to field trial introduces three confounders: (i) time-varying multipath from pedestrians/vehicles, averaged via 100+ trial repetitions, (ii) temperature drift of PIN-diode capacitances, requiring re-calibration every $\sim 30$ min, and (iii) polarization mismatch if the panel axis is not carefully aligned to the reference horn. Published field trials (NTT Docomo 2021) reported 17 dB gain at 300 m LOS range — lower than chamber measurements, but still convincingly useful for coverage fill-in.

Measurement Setup and OTA Testing