<p>By leveraging the collaborative capabilities of low Earth orbit (LEO) satellites, the LEO satellite-based Internet of Things (LEO-SIoT) provides users with global coverage, low power consumption, and flexible deployment, making it a key trend in the future development of the Internet of Things (IoT). However, it also faces significant challenges in communication performance, such as link loss, collisions, and jitter.This study investigates the grant-free access scenario in LEO-SIoT and develops a terminal-to-satellite communication link model. Taking into account critical factors such as packet size, transmission load, acknowledgment timeout, and collisions, this study derives key performance metrics, including collision probability, system capacity, and transmission delay. Based on the derived model, the communication performance optimization problem is formulated, and a novel ant colony optimization algorithm, termed SAT-IACO (Satellite IoT Adapted Ant Colony Optimization), is proposed to obtain high-quality solutions. To validate the effectiveness of the proposed approach, both software-based simulation experiments and hardware-in-the-loop (HIL) tests are conducted using software-defined radio (SDR) technology. The SAT-IACO algorithm is comprehensively compared with several classical and widely adopted heuristic optimization algorithms to demonstrate its advantages in optimizing communication performance. Results from the simulation and hardware-in-the-loop tests confirm that the proposed model and algorithm are both sound and efficient, providing robust theoretical support and practical validation for the engineering applications of LEO-SIoT.</p>