Covert Communication with Spatially Heterogeneous User Cooperation Against a Geometry-Aware Warden

Abstract

This paper investigates covert communication in which a single covert user is assisted by multiple spatially distributed non-covert users against a geometry-aware warden. Unlike prior works based on receiver-centric activation, homogeneous channels, or averaged geometry, the proposed framework retains the individual user-to-warden large-scale fading coefficients in both cooperative user activation and the warden's detection analysis. Under the adopted analytical formulation for large-scale user deployments, we establish an on--off activation structure that balances the interference caused at Bob and the interference effectiveness at warden. Based on the resulting aggregate-interference statistics, we derive a closed-form approximation of the detection error probability, the detection threshold that minimizes it, and the minimum number of cooperative users required to satisfy the covert constraint. Then, we reduce the original high-dimensional power-control problem to a one-dimensional piecewise search and develop a low-complexity algorithm that avoids resolution-dependent grid search. The analysis shows that greater warden-side spatial dispersion can reduce the required cooperative users, whereas a larger average user-to-warden distance increases it. Numerical results validate the analysis and show that finite-sample detection approaches the large-sample benchmark, while imperfect user-to-Bob channel estimation mainly reduces the achievable rate through activation errors.