Anders Ahlen

Somayeh Salimi, Subhrakanti Dey, Anders Ahlen

In this paper, we investigate the role of a physical watermarking signal in quickest detection of a deception attack in a scalar linear control system where the sensor measurements can be replaced by an arbitrary stationary signal generated by an attacker. By adding a random watermarking signal to the control action, the controller designs a sequential test based on a Cumulative Sum (CUSUM) method that accumulates the log-likelihood ratio of the joint distribution of the residue and the watermarking signal (under attack) and the joint distribution of the innovations and the watermarking signal under no attack. As the average detection delay in such tests is asymptotically (as the false alarm rate goes to zero) upper bounded by a quantity inversely proportional to the Kullback-Leibler divergence(KLD) measure between the two joint distributions mentioned above, we analyze the effect of the watermarking signal variance on the above KLD. We also analyze the increase in the LQG control cost due to the watermarking signal, and show that there is a tradeoff between quick detection of attacks and the penalty in the control cost. It is shown that by considering a sequential detection test based on the joint distributions of residue/innovations and the watermarking signal, as opposed to the distributions of the residue/innovations only, we can achieve a higher KLD, thus resulting in a reduced average detection delay. Numerical results are provided to support our claims.

Abbas Arghavani, Subhrakanti Dey, Anders Ahlen

This paper investigates covert wireless communication with a Fusion Center (FC) that aggregates raw energy measurements from multiple Wardens via soft fusion. Extending our prior work on power-threshold randomization, we consider a stronger adversarial model in which FC randomizes both the number of active Wardens W and the detection threshold t, while Alice and a friendly Jammer jointly randomize their transmit powers under an outage constraint at Bob. We derive a closed-form expression for FC's optimal soft-fusion threshold and show that it is independent of the number of active Wardens. Thus, strategic uncertainty in the sensing infrastructure provides no meaningful detection advantage for FC under soft fusion. We further establish a robustness theorem showing that, even under arbitrary FC randomization over (W,t), Alice and Jammer can maintain outage-feasible communication at Bob while preserving covertness with high probability, provided their power ranges are sufficiently large. This reveals a structural limitation of soft fusion. A game-theoretic formulation characterizes the Nash equilibrium mixed strategies of both sides, accounting for deployment costs and detection-pressure parameters. Analytical and numerical results show that: 1) soft fusion is largely insensitive to the number of Wardens; 2) even semi-strategic finite-support geometric randomization of W performs comparably to the full game-theoretic equilibrium; and 3) the covertness-reliability tradeoff remains nearly invariant across a wide range of FC deployment costs and strategy parameters. These findings exemplify a Red Queen effect, in which FC incurs increasing operational costs for only marginal gains in detection performance, and highlight the need for alternative detection architectures.