摘要：The basic concept of Bluetooth Low Energy (BLE) is short packet transmission and transient connection. It can quickly establish a connection, send data, and quickly disconnect, so that neighbor discovery is frequent and becomes an important issue. In the neighbor discovery which includes advertising and scanning, the BLE specification defines several important parameters. The parameters on the advertiser side include advertising interval, advertising duration, etc. On the scanner side, there are scan interval, scan window, etc. How to configure these parameters for quick neighbor discovery has been troublesome for BLE implementers. Prior analyses on BLE discovery process also showed some disagreements or made some incorrect assumptions. In this paper, we use rigorous probability-theory based derivations to obtain different kinds of successful discovery probabilities. We clarify disagreements in prior works and also provide insights on how to configure parameters for maximizing discovery probability. In particular, we prove that the discovery probabilities on each of the three channels are correlated. We also find that, when the advertising duration is set close to some multiples of the scan interval, an ill-fated synchronization problem will occur. To have a high discovery probability, both scan window and scan interval should be set at a large value, though it might not be good for energy saving.
