OceanWhisper: A Covert Communication Scheme for Time-Varying Underwater Acoustic Channels

The extreme variability of time-varying underwater acoustic (UWA) channels poses fundamental barriers to reliability and undetectability in covert communication. In this paper, we propose a covert communication scheme for UWA channels, called OceanWhisper. The OceanWhisper scheme is novel in two aspects. First, to address signal distortions caused by non-uniform hydrophone array (NHA) geometry and motion-induced Doppler spread, we propose an NHA-based Atomic Norm Minimization (ANM) algorithm, coined as NHA-ANM, to estimate unknown parameters of time-varying UWA channels. NHA-ANM constructs a joint delay-Doppler atomic set and develops a prolate spheroidal wave function (PSWF)-integrated semidefinite programming (SDP) framework, which builds closed convex conical hulls with Hermitian kernel matrices in delay-Doppler domains to achieve accurate estimation of channel parameters. Second, by translating instantaneous channel gains into equivalent log-likelihood-ratio (LLR) variances, we propose a gain-to-LLR-based code construction algorithm that embeds these variances into polar recursion, which attains rate adaptation and covertness without additional complexity. Furthermore, a cryptographic message tag computed over the message and the channel-dependent information-bit index sequence using a shared secret key is embedded into the polar code information set within the encoding and decoding process. This design tightly integrates channel estimation with reliable decoding while simultaneously supporting communication integrity and authentication. Comprehensive theory and experiments on realistic UWA datasets under diverse fading conditions demonstrate the reliability and covertness of OceanWhisper.