Contents 1. Introduction
BLUETOOTH is a low-power, open standard for implementing Personal Area Networks (PAN) [1]. It uses a slow hop frequency hopping spread spectrum scheme with 79 1-MHz frequency slots in the 2.4 GHz band (23 in some countries). The master of a Bluetooth piconet coordinates time-division duplex transmissions of up to seven active slaves by alternating between master and slave transmissions in time slots. A Bluetooth device has two major states, standby and connection, and seven substates. Substates are used to incorporate a device as a slave to the piconet and transfer the master's counter/address values. The master collects slaves by entering the inquiry substate to discover neighboring devices. The master device uses the page substate to induct new devices into the piconet as slaves. The Bluetooth standard [1] recommends a device remain in the inquiry substate for 10.24 s. Analytical analysis of the inquiry time probability density function (pdf) shows that 99% of devices can be discovered in 5.12 s over an ideal channel [2]. We simulate this inquiry process and verify the probability distribution with the derived distribution. Additionally, we compare both distributions to an empirical inquiry time probability distribution collected from Bluetooth devices [3]. While the simulation matches the analytical pdf, it is clear the tested Bluetooth devices do not strictly adhere to the specification. We speculate that some implementations have simplified the train change in the inquiry substate to improve performance while maintaining compatibility with devices that adhere to the standard.
