Movable-Signals and Movable Antennas for Multiuser Covert Communications

Abstract

This paper studies a cognitive-radio downlink for multiuser covert communications, where a secondary transmitter must serve multiple legitimate users while remaining difficult to detect by a passive warden and operating only within spectrum holes identified by CR sensing. We propose a dual-domain reconfiguration framework that combines movable antennas (MA) and Movable-Signals (MS). MA offers wavelength-scale spatial reconfiguration of the transmit array, whereas MS performs blockwise carrier-state selection inside an admissible narrow hole so as to rephase multipath components through their delay differences. Under radiometric detection with noise-power uncertainty, we adopt the standard quadratic warden-power constraint as a tractable sufficient surrogate for the covertness requirement. We formulate a covert weighted sum-rate maximization problem subject to transmit-power, MA rail-geometry, and CR-feasible MS probing constraints. To explain why joint MA–MS reconfiguration is useful, we establish three analytical results: 1) MS is ineffective in frequency-flat links; 2) stringent covertness induces a soft-null bottleneck dominated by the warden channel; and 3) in frequency-selective links, MS reshapes warden–user alignment as a trigonometric polynomial in the carrier, which yields an existence condition for de-alignment carriers inside a finite CR hole and a probing-resolution guideline linked to delay spread. These results motivate a solver structure matched to the covert beamforming, MA-position, and MS-probing blocks. Based on this analysis, we develop a BSUM/MM algorithm that alternates among closed-form WMMSE auxiliary updates, a CVX-free nested dual search for beamforming under power and covertness quadratic constraints, shadow-price weighted MA updates with rail-feasible projection, and nested MS probing over CR holes. Numerical results in a representative geometric multipath covert channel show that the proposed joint design consistently outperforms fixed, MA-only, and MS-only baselines, especially when covertness is stringent, the rail length is limited, or exploitable differential delays are visible within the probed hole. The results also verify the predicted diminishing return with probing budget and the finite-probing effect that appears when a fixed carrier set is used under a large delay spread.