Simultaneous Multi-Modal Covert Communications: Analysis and Optimization

This paper investigates the problem of covert communications in a heterogeneous wireless network where multiple communication modalities are used simultaneously. In this setup, a legitimate transmitter sends confidential data to its receiver by selecting multiple modalities with the goal of maximizing communication covertness against a passive adversary (Willie) while satisfying a transmission rate requirement. We analyze two distinct scenarios for a given observation time by Willie. The two scenarios are: (i) Willie knows the modalities selected by the friendly transmitter, and (ii) Willie is unaware of the selected modalities. We first derive the optimal detector for Willie that minimizes the detection error probability (DEP) in both cases. For the first scenario, we derive an exact expression for the DEP and provide a computationally efficient approximation. For the second scenario, we introduce the DEP expressions in the low-signal-to-noise ratio (SNR) regime at Willie. Building on this analysis, we propose a novel low-complexity modality set selection technique designed to maximize the DEP subject to a rate constraint. Numerical simulations validate the derived analytical expressions and demonstrate that the proposed modality set selection technique achieves near-optimal performance, outperforming benchmark schemes.