Time Modulation-Based Multi-User Covert Communication

Multi-antenna-based covert communication techniques exploit spatial degrees of freedom to improve transmission efficiency under covertness constraints, but this generally comes at the cost of increased hardware complexity and power consumption. To this end, time-modulated arrays (TMA) enable multi-user covert communication with a single radio-frequency (RF) chain, providing a promising solution for low-complexity and energy-efficient covert communication. However, the infinite-order harmonics generated by time modulation spread signal energy over the entire spectrum, allowing the warden to enhance detection capability via cross-band observations, which aggravates signal leakage toward unintended directions. This paper develops a binary hypothesis testing model from the perspective of the warden based on infinite-order harmonic characteristics, to characterize the statistical properties and power distribution of harmonic-induced leakage. Furthermore, since the Kullback–Leibler (KL) divergence is intractable under infinite-order harmonic conditions, a computable upper bound is derived to enable covert constraint analysis. Considering the strong coupling among system parameters, an optimization problem is formulated to maximize the minimum covert transmission rate, and a genetic algorithm (GA) is employed for the joint design of time modulation, power allocation, and spatial phase. Simulation results demonstrate that the proposed scheme effectively suppresses signal leakage and improves covert transmission performance.