Ferkans — Interactive Telecom Tutor

Reshape the Channel to Deny the Eavesdropper

Physical-layer security is the information-theoretic foundation: if Bob's channel is better than Eve's, we can achieve positive secrecy rate — information transfer that Eve cannot decode even with infinite computing power. The key resource is the channel difference between Bob and Eve.

Without the RIS, the channel difference is determined by geometry (Bob close, Eve far) and luck (fading diversity). With the RIS, we can engineer the channel difference: focus coherently on Bob, null coherently at Eve. The RIS is a physical-layer security knob that didn't exist in classical systems.

The golden thread: the RIS programs the channel — here, it programs the channel difference. Secrecy is the output of this programming.

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Definition:
RIS-Aided Wiretap Channel

Consider Alice (BS) with $N_t$ antennas transmitting a signal $s$ to Bob. Eve (eavesdropper) listens from a nearby position. Both Bob and Eve receive signal via the same BS transmission, propagating through:

Direct path (blocked or weak).
RIS reflected path (shaped by $\boldsymbol{\Phi}$ ).

The received signals are

$y_B = \mathbf{h}_B^H(\boldsymbol{\Phi}) \mathbf{v}\,s + w_B, \qquad y_E = \mathbf{h}_E^H(\boldsymbol{\Phi}) \mathbf{v}\,s + w_E,$

where $w_B, w_E$ are independent AWGN. The secrecy capacity of this degraded broadcast channel is

$C_s(\boldsymbol{\Phi}) = \left[\log_2\!\left(1 + \frac{|\mathbf{h}_B^H \mathbf{v}|^2}{\sigma^2}\right) - \log_2\!\left(1 + \frac{|\mathbf{h}_E^H \mathbf{v}|^2}{\sigma^2_{E}}\right)\right]^+,$

where $[x]^+ = \max(0, x)$ . The RIS phase matrix $\boldsymbol{\Phi}$ appears in both $\mathbf{h}_B$ and $\mathbf{h}_E$ — tuning it affects both channels.

The secrecy capacity is always non-negative: if Bob's channel is worse than Eve's, no secrecy is possible and $C_s = 0$ . The critical observation: the RIS can reverse the default channel ordering — even if Bob is far and Eve is close, a well-tuned $\boldsymbol{\Phi}$ can make Bob's effective channel stronger.

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Theorem: RIS Secrecy Gain Over Direct Channel

Under optimal RIS phases focused on Bob and nulled at Eve (achievable when Bob and Eve are at different angles with adequate separation):

$\text{SNR}_{B} \approx N^2 \alpha^2 \beta_B^2 P_t/\sigma^2,$

$\text{SNR}_{E} \approx \alpha^2 \beta_E^2 P_t/\sigma^2_{E}$

(no coherent combining at Eve; only direct contribution).

Secrecy capacity:

$C_s \geq \log_2(1 + N^2 \alpha^2 \beta_B^2 P_t/\sigma^2) - \log_2(1 + \alpha^2 \beta_E^2 P_t/\sigma^2_{E}).$

At high SNR: $C_s \approx 2\log_2 N + O(1)$ — the secrecy capacity grows logarithmically in $N$ (similar to comm rate but bounded by $2\log_2 N$ , not $\log_2 N$ ). For $N = 256$ : secrecy capacity increases by $\sim 16$ bits/s/Hz over no-RIS.

The RIS can steer the reflected beam toward Bob and away from Eve. The reflected-path SNR at Bob is $N^2 \alpha^2 \beta_B^2$ ; at Eve, under ideal nulling, the reflected-path SNR is $\sim 1$ (uncorrelated with the Bob-focused beam). The secrecy rate benefits from this double-sided manipulation.

Proof

Bob's coherent gain

Optimal $\boldsymbol{\Phi}$ produces $N^2$ coherent power at Bob.

Eve's null

For Eve at different angle, the RIS-induced phase pattern destructively interferes at Eve's direction: $\sim 1$ (no coherent gain).

Secrecy rate

Subtract Eve's rate from Bob's: $R_s = \log_2(1 + N^2 \cdot \ldots) - \log_2(1 + 1 \cdot \ldots) \approx 2\log_2 N$ at high SNR. $\blacksquare$

Key Takeaway

RIS enables $2\log_2 N$ -bit secrecy gain. By focusing on Bob and nulling at Eve, the RIS dramatically widens the channel difference. For $N = 256$ : secrecy rate grows by $\sim 16$ bits/s/Hz over a no-RIS baseline — enough to protect high-rate services even when Eve is physically closer than Bob.

RIS-Aided Wiretap Channel — Alice (BS) transmits through a RIS. The RIS focuses coherently toward Bob (legitimate) while nulling at Eve (eavesdropper). Even if Eve is physically closer to the BS, the RIS-shaped channel favors Bob, enabling positive secrecy capacity.

Example: Coffee-Shop Secrecy

Alice is a 5G BS. Bob is a legitimate user 50 m away. Eve is at the coffee shop 10 m away, between Alice and Bob. Direct-path secrecy is negative (Eve closer = better channel). A RIS panel is deployed to restore secrecy.

Solution

Without RIS

$\text{SNR}_{B} = P_t \cdot (1/50)^2 / \sigma^2 \propto 4 \times 10^{-4}$ . $\text{SNR}_{E} = P_t \cdot (1/10)^2 / \sigma^2 \propto 10^{-2}$ . Eve has 14 dB more SNR than Bob. Secrecy capacity = 0.

With RIS

RIS on the building wall at 20 m from Alice, 30 m from Bob. Focus on Bob: $\text{SNR}_{B}^{\text{RIS}} \propto N^2 \cdot (1/20)^2 \cdot (1/30)^2 / \sigma^2$ . $= N^2 / (6 \times 10^5) / \sigma^2$ . For $N = 256$ : $N^2/6 \times 10^5 = 0.11$ , so $\text{SNR}_{B}^{\text{RIS}} \propto 0.11/\sigma^2$ . Null at Eve: $\text{SNR}_{E}^{\text{RIS}} \ll$ direct Eve SNR.

Restored secrecy

With RIS, $\text{SNR}_{B} > \text{SNR}_{E}$ for the first time. Secrecy capacity becomes positive; 5G service over RIS can be secured against the closer eavesdropper. $\blacksquare$

Secrecy Rate vs. Eavesdropper Position

Move the eavesdropper around the coverage area and observe the secrecy rate. With RIS, secrecy is achievable over a wider region than without. Change $N$ to see the secure area expand.

Parameters

RIS elements

N

128

BS antennas

N_t

8

Bob distance from BS (m)50

Carrier frequency (GHz)28

The CSI-on-Eve Problem

Designing the optimal $\boldsymbol{\Phi}$ requires knowing Eve's channel $\mathbf{h}_E$ . Eve is uncooperative: she doesn't transmit pilots. Her channel must be estimated from side information (geography, traffic patterns) or modeled as uncertain (robust optimization, Section 15.4).

When Eve's channel is truly unknown:

Worst-case design: assume Eve has the best possible channel; optimize for secrecy against worst-case Eve.
Stochastic design: assume Eve's channel is drawn from a distribution; optimize expected secrecy.
Artificial noise (Section 15.3): inject noise in direction orthogonal to Bob — degrades all non-Bob channels uniformly. Doesn't require knowing Eve's channel.

Common Mistake: Don't Assume Perfect Eve CSI

Mistake:

"Measure Eve's channel like a legitimate user; apply standard RIS optimization."

Correction:

Eve is adversarial and silent. Her channel cannot be pilot- estimated. Assuming perfect Eve CSI is an unrealistic simplification that overestimates secrecy capacity. In practice: use worst-case or stochastic design (Section 15.4), or use artificial noise (Section 15.3) to sidestep the need for Eve CSI. Papers claiming perfect-Eve-CSI secrecy gains should be read as upper bounds, not deployable guarantees.

⚠️Engineering Note

Attack Models for RIS Secrecy

Understanding Eve's capabilities is foundational:

Passive eavesdropper: listens without transmitting. Channel unknown to Alice. Most common attack model.
Active attacker: transmits interference + listens. Can spoof pilot signals to confuse channel estimation.
Co-located with Bob: very difficult; requires physical security. RIS cannot distinguish.
Moving Eve: adversary follows Bob. Time-varying uncertainty; robust design needed.

Each attack model leads to different optimization problems. This chapter focuses on passive Eve with uncertain channel — the most common and tractable case.

Practical Constraints

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Typical Eve position uncertainty: $\sim 10$ m standard deviation (urban).
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Pilot-spoofing attacks are a known failure mode — use authentication + challenge-response.
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For high-security applications (government, military): combine RIS + crypto + physical security.

The RIS-Aided Wiretap Channel