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.

This paper proposes a symmetrized extrinsic information transfer (S-EXIT) chart analysis for probabilistic shaped (PS) systems to optimize the joint decoding of low-density parity-check (LDPC) codes and constant composition distribution matchers (CCDMs). A major challenge in analyzing PS systems is the non-uniform channel input caused by shaping, which invalidates the all-zero assumption of traditional EXIT charts, coupled with the three-node structure of the joint decoder (variable nodes, check nodes, and shaping nodes) that exceeds the two-decoder framework of conventional EXIT analysis. To resolve these issues, we first prove the symmetry of the joint decoder and introduce a “symmetrized density” transformation to render the channel output symmetric, thereby enabling the extension of EXIT chart analysis to PS systems. We then approximate the EXIT function of the shaping node decoder via polynomial fitting and integrate it with the variable node decoder into a unified model (VSND) for threshold analysis. On one hand, the proposed S-EXIT chart provides a theoretical threshold for the joint decoder, which is crucial for guiding system design. On the other hand, it enables the joint optimization of LDPC code rates and CCDM rates, unlocking additional performance gains. Simulations over additive white Gaussian noise (AWGN) channels demonstrate that short-blocklength CCDMs (e.g., blocklength 20) achieve up to 1.2 dB gain over uniform systems via S-EXIT-based rate optimization. This work addresses the performance limitations of short-blocklength CCDMs in high-speed optical transmissions, offering a practical and efficient analytical tool for PS system design.