Diffusion-Based Frequency Hopping for Collision Mitigation in Dense Bluetooth Networks

This paper challenges the conventional wisdom of using uniform random resource selection for collision resolution in distributed scheduling, particularly in wireless protocols. Bluetooth, being one such technology, is analyzed through its frequency hopping mechanism to explore for a better alternative in random access MAC (medium access control). Using diffusion theory, we characterize Bluetooth's original frequency hopping as exhibiting maximum diffusivity, which correlates with unnecessarily high collision rates and a short mean first encounter time (MFET) between nodes. MFET, defined as the expected time until two independent hopping sequences first collide on the same channel, serves as an intuitive metric for evaluating collision likelihood. This insight leads to the proposal of a new collision avoidance mechanism with reduced diffusivity, effectively increasing MFET while maintaining efficient spectrum utilization. Our analysis and simulation results demonstrate that it can significantly lower packet collisions, outperforming existing techniques such as adaptive frequency hopping. The results are further corroborated by a real-life prototype implementation that closely replicates the predicted performance. The proposed diffusion-based MAC, by explicitly targeting longer MFETs, is expected to better handle dense Bluetooth environments, which are becoming increasingly common.