An Analytical Study of Wireless Error Models for Bluetooth Networks Hao-Hsiang Hung and Ling-Jyh Chen Academia Sinica

Motivation and Goal packet loss caused by burst errors limits wireless network throughput –co-channel interference dominates a great part wireless error model can provide insights into the behavior of wireless transmissions –help designing more effective schemes!! our goal is to investigate the error model of Bluetooth networks –operate in the crowded unlicensed frequency band –lack analytical studies of its frequency hopping mechanisms

Quick Review on Bluetooth operate in the 2.4GHz ISM frequency band implement ARQ, CRC, and FEC to ensure link reliability employ the Frequency Hopping Spread Spectrum (FHSS) –79 channels, 1MHz of bandwidth for each –f = k; k = 0 ~ 78 –the hopping kernel determines the frequency hopping sequence

Hopping Kernel ordinary one –random sequence of frequency Bluetooth Interference Aware Scheduling (BIAS) [14] –Frequency Usage Table adaptive Frequency Hopping (AFH) [15] –BIAS-like approach –Included in the Bluetooth Spec v1.2

Ordinary Hopping Kernel Channel # segment segment 2 segment ……

Analysis a two-state Gilbert-Elliot model is used to capture the behavior of channel errors –state transition probabilities: P gg, P gb, P gb, P bb –stationary probability for good state: P g = –stationary probability for bad state: P b = Bad P gb P bb P bg P gg Good

Analysis for Ordinary Hopping Kernel Channel 1 Channel 2channel 79 …… the distribution of the hopping sequence is uniform Good Bad Good Bad Good Bad

Analysis for Ordinary Hopping Kernel Channel 1 Channel 2channel 79 …… combine together Good Bad Good Bad Good Bad

Since… the probability of the hopped channels in the good state: 79 channels are independent, apply Bayes’ Theorem Pgg’ = Pbg ’ = Pg ’ Pgb ’ = Pbb ’ = Pb ’ where Pgg ’, Pbg ’, Pgb ’, and Pbb ’ are the transition probabilities

Error Model for Ordinary Hopping Kernel further reduce to this… Bad Good

Adaptive Frequency Hopping (AFH) Channel # used unused

Parameters Definition N good represents the number of used channels 2 operating modes: Mode L: N good >= N min Mode H: N good < N min

Mode L number of used channels is larger than N min behavior: –AFH uniformly map unused channels to the used channels the probability that the channels will be in the good state: where we define

Mode H number of used channels is less than N min behavior: –hopping sequence is divided into R g consecutive good slots & R b consecutive bad slots [5] –R g + R b > N min –All used channels are mapped into good slots, and all unused channels are mapped into bad slots the probability that the channels will be in the good state:

Evaluation Evaluate our error models using Markov Chain Monte Carlo method (20,000 runs for each channel configuration) Bluetooth Frequency Hopping Selection Kernel [9] in Matlab environment is used for simulation Three scenarios: –Homogeneous channels –Semi-homogeneous channels (two groups) –Heterogeneous channels

Homogeneous Channels Pgg = 0.8, varying Pbg

Semi-Homogeneous Channels Pgg = 0.8; Pbb = 0.5 for the first group and 0.9 for the other

Heterogeneous Channels Randomly select Pgg and Pbb in the range [P min gg, 1] and [P min bb, 1]

Heterogeneous Channels

Conclusion We proposed 2 wireless error models for Bluetooth networks when the ordinary hopping kernel and the AFH kernel is implemented. The evaluation results shows that our error models are precise in homogeneous, semi-homogeneous, and heterogeneous channel scenarios. The reduced models provide simple and representative wireless error models for FHSS- based Bluetooth networks.

Thank You!