How Can LLM Agents Become Wireless Communication Algorithm Engineers?

Wireless communication relies on effective algorithms, yet discovering high-performing algorithms remains challenging. The design space is large, while end-to-end feedback provides limited information about which components should be changed. Moreover, coupled components can change each other's utility as the algorithm evolves, making earlier feedback outdated. We benchmark current LLM-based wireless algorithm discovery agents across four wireless algorithm design tasks and find an important limitation in their search behavior. Existing agents can explore new designs and improve performance through experimentation, but they tend to accumulate and tune algorithm components rather than question whether previously accepted components are still necessary. We find that effective wireless algorithm discovery therefore requires not only exploring new structures, but also proactively and strategically challenging the current design by removing, replacing, or simplifying inherited components to test whether they still contribute to performance. To enable this behavior, we propose Breathe, a wireless algorithm discovery framework that explicitly coordinates when an agent should explore new designs and when it should challenge the current algorithm structure. Across all wireless algorithm design tasks, Breathe consistently improves over the state-of-the-art agent system under the same experimental budget, achieving a task-level macro-average performance improvement of 20.35%.