Euclidean-Division-Based Low-Complexity Precise Analytical Approach of BLE-Like Neighbor Discovery Latency

Neighbor discovery is the procedure to establish a first contact between two wireless devices. For duty-cycled low-power devices, energy consumption is closely related to neighbor discovery latency. Actually, in recent protocols, such as Bluetooth low energy (BLE) or ANT+, neighbor discovery latency is determined by the parameters used by the devices, such as advertising interval, scan window, scan interval, and so on. A fundamental problem of the BLE-like protocol is that the exact relation between parameters and discovery latency has not been fully analyzed. In this article, we propose a Euclidean-division-based low-complexity precise analytical approach that can derive the mathematical expressions of both worst-case latency and average latency for any parameter groups. It is confirmed by simulation results that our solution can make highly accurate predictions about the value of latencies. Simulation results also show that the proposed solution has an extremely low complexity. Moreover, we derive the lower bound of latency for given duty cycles, which provides useful guidelines for the choice of energy-efficient parameter groups for BLE.