An Analytical Study of Wireless Error Models for Bluetooth Networks

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

2. 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

3. 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= 2402 + k; k = 0 ~ 78 • the hopping kernel determines the frequency hopping sequence

4. 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

5. Ordinary Hopping Kernel Channel # 1 0 2 3 63 64 78 0 1 2 3 76 77 78 segment 1 segment 2 segment 3 33 32 31 34 64 65 0 …… 3 2 1

6. Analysis • a two-state Gilbert-Elliot model is used to capture the behavior of channel errors • state transition probabilities: Pgg, Pgb, Pgb, Pbb • stationary probability for good state: Pg = • stationary probability for bad state: Pb = Pgg Good Pgb Pbg Bad Pbb

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

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

9. 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

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

11. Adaptive Frequency Hopping (AFH) Channel # 1 5 0 2 3 4 6 7 71 72 73 74 75 76 77 78 used unused

12. Parameters Definition • Ngoodrepresents the number of used channels • 2 operating modes: • Mode L: Ngood >= Nmin • Mode H: Ngood < Nmin

13. Mode L • number of used channels is larger than Nmin • behavior: • AFH uniformly map unused channels to the used channels • the probability that the channels will be in the good state: where we define

14. Mode H • number of used channels is less than Nmin • behavior: • hopping sequence is divided into Rg consecutive good slots & Rb consecutive bad slots [5] • Rg + Rb > Nmin • 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:

15. 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

16. Homogeneous Channels • Pgg = 0.8 , varying Pbg

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

18. Heterogeneous Channels • Randomly select Pgg and Pbb in the range [Pmingg, 1] and [Pminbb, 1]

19. Heterogeneous Channels

20. 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.

21. Thank You!