Ferkans — Interactive Telecom Tutor

What Is Channel Aging?

Channel aging refers to the decorrelation of the cascaded channel $\mathbf{h}_{\text{eff}}$ between the time of channel estimation and the time of RIS configuration application. With a coherence time $T_c$ (typically $10$ ms for pedestrian, $1$ ms for vehicular at 28 GHz) and control-loop latency $\tau_{\text{RIS}}$ , the RIS is using a "stale" $\boldsymbol{\Phi}$ by the time the signal arrives. The SNR degrades with $(\tau_{\text{RIS}}/T_c)^2$ at first order.

Definition:
Aging Efficiency

Let $\rho(\tau)$ be the autocorrelation of the cascaded channel $\mathbf{h}_{\text{eff}}(t)$ at lag $\tau$ . The aging efficiency is $\eta_{\text{age}}(\tau) = |\rho(\tau)|^2$ For a Jakes / Clarke model at Doppler $\nu_D$ : $\rho(\tau) = J_0(2\pi \nu_D \tau)$ (Bessel function), giving $\eta_{\text{age}}(\tau) = J_0^2(2\pi \nu_D \tau)$ . Typical values:

$\tau = 1$ ms, $\nu_D = 10$ Hz (pedestrian): $\eta_{\text{age}} = 0.998$
$\tau = 1$ ms, $\nu_D = 100$ Hz (walking at 28 GHz): $\eta = 0.85$
$\tau = 1$ ms, $\nu_D = 1$ kHz (vehicular at 28 GHz): $\eta = 0.03$

Theorem: Aging SNR Loss

With control-loop latency $\tau_{\text{RIS}}$ , the expected SNR achieved by the RIS is reduced by factor $\eta_{\text{age}}$ : $\mathbb{E}[\text{SNR}_{\text{RIS}}(t + \tau_{\text{RIS}})] = \eta_{\text{age}}(\tau_{\text{RIS}}) \cdot N^2 \cdot \text{SNR}.$ For $\nu_D \tau_{\text{RIS}} \ll 1$ (small Doppler × latency): $\eta_{\text{age}} \approx 1 - (\pi \nu_D \tau_{\text{RIS}})^2$ .

Proof

Channel model

At time $t$ , the RIS is configured with $\boldsymbol{\Phi}$ optimal for $\mathbf{h}_{\text{eff}}(t)$ . At time $t + \tau$ , the actual cascaded channel is $\mathbf{h}_{\text{eff}}(t + \tau)$ , correlated with $\mathbf{h}_{\text{eff}}(t)$ with coefficient $\rho(\tau)$ .

Combining loss

The coherent combining at time $t + \tau$ is proportional to $|\langle \boldsymbol{\Phi}(t), \mathbf{h}_{\text{eff}}(t+\tau) \rangle|^2 \approx |\rho(\tau)|^2 \cdot N^2$ (taking expectation over random fade realizations). $\eta_{\text{age}} = |\rho(\tau)|^2$ . $\blacksquare$

Example: Aging Budget for 28 GHz Vehicular

A 28 GHz 5G vehicular system (relative velocity $30$ m/s, Doppler $\nu_D = v f_c / c = 30 \cdot 28 \times 10^9 / 3 \times 10^8 = 2800$ Hz). What's the maximum allowed control-loop latency $\tau_{\text{RIS}}$ to keep $\eta_{\text{age}} \geq 0.9$ ( $-0.46$ dB loss)?

Solution

Aging formula

$\eta_{\text{age}} \approx 1 - (\pi \nu_D \tau)^2 \geq 0.9$ → $(\pi \nu_D \tau)^2 \leq 0.1$ → $\pi \nu_D \tau \leq 0.316$ . $\tau \leq 0.316/(\pi \cdot 2800) = 36 \; \mu s$ .

Feasibility

$36 \mu s$ is at the edge of feasibility — requires a high-speed RIS controller with $< 10 \mu s$ phase-update latency and $< 20 \mu s$ signal-propagation delay. Standard RIS controllers (1 kHz = 1 ms) are too slow by $30\times$ .

Commercial implications

Vehicular RIS deployment requires a different control-plane architecture: either sub-carrier-level low-latency control, or predictive algorithms that pre-compute $\boldsymbol{\Phi}$ for anticipated UE positions. This is an open research area.

The RIS Control Plane

A RIS control architecture has three layers, each with its latency budget:

Physical: phase-shifter settling time ( $< 1 \mu s$ for PIN/varactor, $< 100$ ns for MEMS).
Controller: FPGA command latency ( $\sim 10 \mu s$ ).
Backhaul: BS-to-RIS Ethernet or fiber link ( $100 \mu s$ – $10$ ms depending on deployment).

The backhaul typically dominates. Future proposals put the RIS controller co-located with the BS DU (distributed unit), reducing end-to-end latency to $< 100 \mu s$ . This is standardization work in progress.

Aging Efficiency vs. Control-Loop Latency

Plot $\eta_{\text{age}}(\tau)$ vs. $\tau$ for several Doppler rates. Identify the critical latency threshold where $\eta_{\text{age}}$ falls below 0.9 (acceptable).

Parameters

UE velocity (m/s)5

Carrier (GHz)28

Max latency (ms)10

Predictive RIS Control

Complexity: O(L · N)

Input: channel estimates ĥ(t-1), ĥ(t), UE position

trajectory model

Output: predicted Φ(t + L · T_c)

1. Extrapolate channel to future instants using Kalman

(or deep-learning predictor)

2. Compute ĥ_pred(t + l · T_c) for l = 1, ..., L

3. For each l:

4. θ_l = arg_max_{θ} |ĥ_pred(t + l·T_c)^H Φ(θ) h_bs|

5. end for

6. Stream θ_l to RIS controller at time t + l·T_c

7. return prediction sequence

🚨Critical Engineering Note

Vehicular RIS: Open Problem

At vehicular speeds (30 m/s, 28 GHz), the coherence time is $\sim 100 \mu s$ . With typical $\tau_{\text{RIS}} = 1$ ms, $\eta_{\text{age}} < 0.01$ — complete decorrelation. Three research directions:

Sub-carrier-latency controllers: physical RIS reconfiguration in $< 50 \mu s$ . Under development in industry labs (Samsung, NTT Docomo).
Predictive control: ML-based channel extrapolation. Accuracy limited by predictable vs. random channel components.
Spatial-frequency tradeoff: use RIS only for the slow-varying components (angular spread) while fast variations are handled by active BS beamforming. This is the current best-practice compromise.

RIS Channel Aging and Control-Loop Design