Multi-Beam Cooperative Time-Varying Directional Modulation for Secure Satellite Downlink Transmission to UAV Swarms

Satellite downlinks reliably connect remote unmanned aerial vehicle (UAV) swarms, but broad coverage exposes information-bearing signals to unauthorized receivers. This paper proposes a multi-beam cooperative time-varying directional modulation (TVDM) framework for secure satellite downlinks. Two asymmetrically partitioned subarrays form cooperative beams whose pointing states and beam-dependent symbol mappings are randomly updated at the symbol rate, thereby introducing controlled randomness for physical-layer security. In each interval, the source symbol is mapped to two transmit symbols whose superposition remains in the correct phase-shift-keying decision region at legitimate UAVs, while the equivalent constellation varies at unauthorized locations. A relaxed transparent-transmission constraint based on constructive decision-region margins enables conventional detection without instantaneous TVDM-state estimation. Mutual information (MI) defines the pointwise multi-UAV secrecy capacity (SC), main-lobe insecure area, and sidelobe leakage. A mixed discrete–continuous problem jointly optimizes the trajectory radius, relative pointing phase, mapping parameters, and subarray partition to reduce insecure coverage and sidelobe leakage. A block alternating algorithm combines Monte Carlo MI evaluation, projected Armijo updates, and finite partition search to coordinate continuous and discrete variables. Simulations using representative low-Earth-orbit satellite parameters show that the proposed design reduces the central insecure-interval length by 82.7% relative to conventional beamforming.