Structural Limits of Soft Fusion in Multi-Warden Covert Communication

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.