Ferkans — Interactive Telecom Tutor

Jamming Eve Without Knowing Her Channel

The secrecy rate formulation of Section 15.2 assumes Eve's channel is known. In reality, it's usually not. Artificial noise (AN) is a classical remedy: transmit additional signal components orthogonal to Bob's channel, which jam Eve without harming Bob. Adding a RIS multiplies the power of AN: the RIS can shape the noise to reach Eve-specific directions.

Definition:
Artificial Noise Signal Model

In addition to Bob's data signal $\mathbf{v}\,s$ , Alice transmits artificial noise $\mathbf{z}$ along directions orthogonal to Bob's effective channel:

$\mathbf{x}(t) = \mathbf{v}\,s(t) + \mathbf{A}\,\mathbf{z}(t),$

where $\mathbf{A}$ is a matrix projecting onto the null space of $\mathbf{h}_B$ (i.e., $\mathbf{h}_B^H \mathbf{A} = \mathbf{0}$ ).

Bob's received signal: $y_B = \mathbf{h}_B^H \mathbf{v}\,s + w_B$ — no AN contribution. Eve's received signal: $y_E = \mathbf{h}_E^H \mathbf{v}\,s + \mathbf{h}_E^H \mathbf{A}\,\mathbf{z} + w_E$ — AN adds to Eve's noise.

With $\mathbf{z} \sim \mathcal{CN}$ of power $P_z$ : Eve's effective noise is $\mathbf{h}_E^H \mathbf{A}\,\mathbf{z}$ plus local noise.

The crucial property: AN leaks to Eve but not to Bob, because it lies in Bob's null space. Eve's SINR is reduced without affecting Bob's SINR. This enables secrecy even without knowing Eve's channel — the AN is a "blanket jammer" in the non-Bob directions.

,

Theorem: Artificial Noise Enables Secrecy Without Eve CSI

Under random Eve channel and an AN design with $\mathbf{A}$ in Bob's null space:

$R_s^{\text{AN}} = \log_2\!\left(1 + \frac{|\mathbf{h}_B^H \mathbf{v}|^2}{\sigma^2}\right) - \mathbb{E}_{\mathbf{h}_E}\!\left[\log_2\!\left(1 + \frac{|\mathbf{h}_E^H \mathbf{v}|^2}{\|\mathbf{h}_E^H \mathbf{A}\|^2 P_z + \sigma^2_{E}}\right)\right].$

By choosing $P_z$ appropriately, positive $R_s^{\text{AN}}$ is achievable on average over Eve's channel realization. This does not require knowing Eve's specific channel — only assuming she's a "generic eavesdropper."

With AN, Eve's effective noise is $\|\mathbf{h}_E^H \mathbf{A}\|^2 P_z$ (a quadratic in Eve's channel through AN). For a random Eve direction, this is on average a large fraction of the AN power. Bob sees no AN. Hence Eve's SINR is degraded while Bob's is not.

RIS Amplifies AN Power Where It's Needed

Without a RIS, AN propagates as an ordinary wave — it fills space broadly. With a RIS, the AN can be focused away from Bob and amplified coherently in non-Bob directions:

AN focusing: $\boldsymbol{\Phi}$ configures a secondary beam for AN, orthogonal to Bob's beam. The coherent gain $N^2$ boosts AN power where Eve might be.
Bob's null preserved: simultaneously, the primary beam (Bob's) retains its coherent $N^2$ gain. Two beams from one panel — achievable because the RIS has $N$ DoF.
Effective jamming: Eve sees AN with $N^2$ power boost; Bob sees none. Secrecy rate grows accordingly.

The RIS-AN combination is a powerful physical-layer security primitive: it achieves secrecy without Eve CSI, resilient to her mobility, and scales favorably with $N$ .

RIS + Artificial Noise Joint Optimization

Complexity: Similar to AO for secrecy;

\sim 20

-

40

ms per update for

N = 128

Input: Bob's channel

\mathbf{h}_B

, power budget

P_t

, AN fraction

\alpha

.

Output:

(\mathbf{v}, \boldsymbol{\Phi}, \mathbf{A})

.

1. Signal power split:

P_s = (1-\alpha) P_t

for data,

P_z = \alpha P_t

for AN.

2. Initialize

\boldsymbol{\Phi}^{(0)}

matched to Bob.

3. Repeat

t = 0, 1, \ldots

:

4.

\quad

Update Bob's effective channel

\mathbf{h}_B^{(t)}

.

5.

\quad

Active update:

\mathbf{v}^{(t+1)} = \sqrt{P_s} \mathbf{h}_B / \|\mathbf{h}_B\|

(matched filter).

6.

\quad

Compute $\mathbf{A}$ : orthonormal basis of null space of

\mathbf{h}_B

, scaled to

\sqrt{P_z}

.

7.

\quad

Passive update: maximize

\mathbb{E}[\text{secrecy rate}]

over

|\phi_n|=1

. Use Ch. 6 methods.

8.

\quad

Check convergence.

9. return

(\mathbf{v}, \boldsymbol{\Phi}, \mathbf{A})

.

The algorithm does not require knowing Eve's channel. It optimizes for an average over Eve's uncertainty. Practical $\alpha$ (power allocation to AN): $0.3$ - $0.5$ is typical.

AN Power Tradeoff: Secrecy vs. Data Rate

Sweep the fraction $\alpha$ of power allocated to AN. Low $\alpha$ : high Bob rate, low jamming. High $\alpha$ : low Bob rate, high jamming. Optimal in the middle. RIS + AN gives a strictly better tradeoff than no-RIS AN.

Parameters

RIS elements

N

64

BS antennas

N_t

8

Transmit SNR (dB)15

Example: RIS + AN Hybrid Secrecy Strategy

A RIS-aided secrecy system with $N = 128, N_t = 4$ . Eve's location is unknown (anywhere within 100 m). Power budget $P_t = 30$ dBm. How to divide between data and AN?

Solution

Pure-data

All power for data, no AN. $R_B = \log_2(1 + 10^3) \sim 10$ bits/s/Hz. $R_E$ random; Eve might have comparable rate at high-SNR locations. Secrecy uncertain.

Pure-AN (trivial case)

All power for AN. $R_B = 0$ (no data). Not useful.

Optimal split

$\alpha^\star \sim 0.4$ : 60% data, 40% AN. $R_B^\star \sim 8$ bits/s/Hz (slight penalty from shared power). Eve's SNR degraded by factor $\sim 10$ (from 40% AN in her null space). Secrecy rate: $\sim 6$ - $7$ bits/s/Hz, robust to Eve location.

Comparison

No-RIS AN: $\sim 3$ bits/s/Hz secrecy. RIS + AN: $6$ - $7$ bits/s/Hz. RIS doubles the secrecy throughput by shaping both Bob's gain and the AN distribution. $\blacksquare$

Common Mistake: Don't Overlook the AN Rate Penalty

Mistake:

"AN is free — add it to all transmissions for security."

Correction:

AN uses transmit power that would otherwise serve the data signal. Bob's rate is reduced by $\sim \log_2(1 - \alpha)$ for AN fraction $\alpha$ (small at low $\alpha$ , substantial at high $\alpha$ ). Use AN selectively: for security-critical transmissions, not for best-effort data. The AN vs. data tradeoff is an operational policy choice, not a one-size-fits-all.

Artificial Noise via RIS