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Proactive Eavesdropping via Jamming for Rate Maximization over Rayleigh Fading Channels
Jie Xu, Lingjie Duan, Rui Zhang
TL;DR
The paper studies legitimate eavesdropping of suspicious wireless links, where rate control and fading can limit the monitor’s decoding success. It proposes full-duplex proactive jamming with optimized power control and reports higher average eavesdropping rates than passive and constant-power alternatives, especially when the monitor is far away.
Problem
The paper addresses how a legitimate monitor can eavesdrop suspicious wireless communications when fading, distance, and the suspicious transmitter’s target-outage rate constrain successful decoding.
Method
The paper uses full-duplex proactive eavesdropping, optimizing the monitor’s jamming power to moderate the suspicious communication rate and maximize average eavesdropping rate.
Results
Optimized proactive jamming outperforms passive eavesdropping and constant-power jamming, with especially significant gains when the monitor is far from the suspicious transmitter and receiver.
Takeaways & Limitations
Jamming with optimized power control improves legitimate-surveillance eavesdropping performance over conventional passive eavesdropping in the studied Rayleigh-fading setting.
Abstract
from arXiv · showhide
Instead of against eavesdropping, this letter proposes a new paradigm in wireless security by studying how a legitimate monitor (e.g., government agencies) efficiently eavesdrops a suspicious wireless communication link. The suspicious transmitter controls its communication rate over Rayleigh fading channels to maintain a target outage probability at the receiver, and the legitimate monitor can successfully eavesdrop only when its achievable rate is no smaller than the suspicious communication rate. We propose a proactive eavesdropping via jamming approach to maximize the average eavesdropping rate, where the legitimate monitor sends jamming signals with optimized power control to moderate the suspicious communication rate.
I. INTRODUCTION
The letter reframes wireless security around legitimate surveillance of suspicious links, using proactive full-duplex jamming to improve eavesdropping under fading and rate uncertainty.
- I. INTRODUCTION: The paper shifts wireless-security research from preventing conventional eavesdropping attacks toward legitimate surveillance of suspicious wireless communications.The motivation includes monitoring suspicious links that may support criminal or terrorist activity.
- I. INTRODUCTION: A legitimate monitor eavesdrops a point-to-point suspicious link over Rayleigh fading, but succeeds only when its achievable rate reaches the suspicious communication rate.The suspicious transmitter controls its rate to maintain a target receiver outage probability.
- I. INTRODUCTION: Proactive eavesdropping via jamming uses a full-duplex monitor to moderate the suspicious communication rate and facilitate simultaneous eavesdropping.The monitor optimizes its jamming power to maximize average eavesdropping rate.
- I. INTRODUCTION: The optimized jamming approach outperforms passive eavesdropping and constant-power jamming in numerical results.The comparison is reported for average eavesdropping rate.
II. SYSTEM MODEL AND PROBLEM FORMULATION
The system model describes Rayleigh-fading suspicious and eavesdropping links with a full-duplex monitor, then formulates jamming-power optimization for average eavesdropping rate under a target suspicious-link outage.
- II. SYSTEM MODEL AND PROBLEM FORMULATION: The monitor has separate receiving and jamming antennas, while the suspicious transmitter and receiver each use a single antenna.The channels are block-fading and frequency-nonselective.
- II. SYSTEM MODEL AND PROBLEM FORMULATION: The three channel power gains are independent exponential variables under Rayleigh fading, with the monitor knowing g1 instantaneously but only distribution information for g0 and g2.The monitor therefore has perfect knowledge of the eavesdropping channel and channel distribution information for the suspicious and jamming links.
- II. SYSTEM MODEL AND PROBLEM FORMULATION: The suspicious transmitter uses a fixed rate R, and decoding succeeds at either receiver when its achievable rate is at least R.Otherwise, the corresponding receiver declares an outage.
- II. SYSTEM MODEL AND PROBLEM FORMULATION: Average eavesdropping rate is defined as the suspicious communication rate multiplied by the legitimate monitor’s eavesdropping non-outage probability.This is the average rate correctly decoded over a long time.
- II. SYSTEM MODEL AND PROBLEM FORMULATION: The monitor chooses jamming power Q to maximize average eavesdropping rate while the suspicious transmitter adjusts R to maintain a fixed target outage probability.Increasing Q lowers R but can improve the monitor’s non-outage probability, creating a power-control trade-off.
III. OPTIMAL JAMMING FOR PROACTIVE EAVESDROPPING
The paper transforms optimal jamming-power selection into a single-variable optimization over the suspicious communication rate, then derives a closed-form optimum. The optimal rate is characterized by unimodality, and the corresponding jamming power is clipped to the allowable range.
- The optimization is reformulated over R using the one-to-one relationship between suspicious communication rate and jamming power, with ψ−1 providing the inverse mapping.
- The jamming-power function ψ(R) decreases with R, so lowering the suspicious communication rate requires stronger jamming.
- The optimal suspicious communication rate R* maximizes the average eavesdropping rate because the objective increases up to R* and decreases afterward.
- The optimal jamming power is Qopt = min(max(0, ψ(R*)), Qmax), mapping the optimal suspicious rate to a feasible jamming level.
- When R* is at least the zero-jamming suspicious rate, no jamming is optimal; otherwise, positive jamming reduces the suspicious rate to R* when permitted by Qmax.
IV. NUMERICAL RESULTS
Numerical results show that optimized jamming improves eavesdropping performance, especially when the legitimate monitor is far from the suspicious link, while excessive constant-power jamming can reduce performance.
- Effect of jamming power: As jamming power increases, the suspicious communication rate decreases while the eavesdropping non-outage probability increases.The simulation uses average eavesdropping and jamming channel gains of 0.1.
- Effect of jamming power: The average eavesdropping rate first increases and then decreases with jamming power, reaching its maximum at the optimal power Qopt.This behavior agrees with Lemma 3.2 and Theorem 3.1.
- Performance comparison: The optimal-jamming scheme outperforms passive eavesdropping and constant-power jamming, particularly when average channel gains are below −15 dB.Passive eavesdropping is nearly ineffective in this regime, whereas both proactive schemes achieve significant gains.
- Performance comparison: As channel gains increase, passive and optimal-jamming rates increase, whereas constant-power jamming produces a rate that first increases and then decreases.For gains above −5 dB, passive and optimal-jamming schemes achieve identical average eavesdropping rates.
V. CONCLUSION
The letter introduces legitimate surveillance through proactive eavesdropping via jamming and derives closed-form optimal power control for Rayleigh fading channels. The optimized approach significantly improves average eavesdropping rate over passive eavesdropping, especially for distant monitors.
- V. CONCLUSION: The proposed approach uses optimized jamming power to improve the legitimate monitor’s average eavesdropping rate.The legitimate monitor jams the suspicious link while operating in full-duplex mode.
- V. CONCLUSION: The optimal jamming power is obtained in closed form for Rayleigh fading channels.
- V. CONCLUSION: Optimized proactive eavesdropping significantly outperforms passive eavesdropping, especially when the monitor is far from the suspicious transmitter and receiver.
A. Proof of Lemma 3.1
The proof derives the distribution needed to characterize the suspicious-link outage probability under jamming, then substitutes that result into the target-outage constraint to obtain the jamming-power expression.
- A. Proof of Lemma 3.1: The proof proceeds by combining the preceding outage expressions to obtain p_out^0.
- A. Proof of Lemma 3.1: The proof models Z as the difference between two scaled exponential variables, X1 = g0P and X2 = g2(2^R−1)Q.The exponential rates are transformed according to the transmit and jamming powers.
- A. Proof of Lemma 3.1: Substituting the derived outage expression into the constraint p_out^0 = δ yields the closed-form relation in (8).
B. Proof of Lemma 3.2
The proof rewrites the optimization in terms of x = 2^R−1 and establishes that the resulting objective rises before a unique stationary point and falls afterward.
- B. Proof of Lemma 3.2: The original objective is reparameterized using x = 2^R−1 and R = log2(1+x).
- B. Proof of Lemma 3.2: The transformed objective φ(x) increases on [0, x*] and decreases on (x*, +∞), where x* = 2^R*−1.
- B. Proof of Lemma 3.2: Setting φ′(x) = 0 identifies the optimizer x* = 2^R*−1 and the corresponding rate R* given in (11).