Covert Communication Against Multi-Stream Sequential Change-Point Detection

We investigate covert communication in a multi-stream setting where an adversary employs a cumulative sum (CUSUM) detector with a myopic sampling policy (MSP) to monitor multiple candidate streams. Within a sequential change-point detection framework, we characterize performance using metrics such as the average run length to false alarm (ARL2FA) and the average detection delay (ADD). Covertness is defined by ensuring that, at the adversary’s optimal detection threshold, the ratio ADD/γ remains at least 1–ε, where γ denotes the lower bound on ARL2FA. We derive exact expressions for ARL2FA and ADD under MSP and obtain a complete characterization of the ε-covert region of the power parameter θ for Gaussian and BPSK ensembles. We further establish sharp overshoot bounds, showing that the overshoot terms remain of lower order even as the optimal threshold tends to zero. Finally, we compare MSP with the single-stream setting and show that, in the covert regime, the performance gap depends explicitly on the number of monitored streams N. Numerical Fredholm calculations and Monte Carlo simulations validate the theoretical predictions.