An Analytical Study of Wireless An Analytical Study of Wireless Error Models for Bluetooth Error Models for Bluetooth

NetworksNetworks

Hao-Hsiang Hung and Ling-Jyh ChenHao-Hsiang Hung and Ling-Jyh ChenAcademia SinicaAcademia Sinica

Motivation and GoalMotivation 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 Quick Review on BluetoothBluetooth

• 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

Hopping KernelHopping 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 KernelOrdinary Hopping Kernel

1 2 30 63 64 78 0 1 2 3 76 77 78Channel #

segment 1

0 321

segment 2

segment 3

3332 31 34 6465

……

AnalysisAnalysis

• 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 =

Bad

Pgb

Pbb

Pbg

Pgg

Good

PPP

gbbb

bb

+−−

11

PPP

gbbb

gb

+−

−

1

1

Analysis for Ordinary Analysis for Ordinary Hopping KernelHopping Kernel

Channel 1Channel 2 channel 79

……

……

……

79

1

79

1

the distribution of the hopping sequence is uniform

79

1

Good

Bad

Pgg

)1(

Pgb

)1(

Pbg

)1(

Pbb

)1(

Pbg

)2(

Good

Bad

Pgg

)2(

Pgb

)2(

Pbb

)2(

Good

Bad

Pgg

)3(

Pgb

)3(

Pbg

)3(

Pbb

)3(

Analysis for Ordinary Analysis for Ordinary Hopping KernelHopping Kernel

Channel 1

Channel 2 channel 79

……

……

……

combine together

Good

Bad

79

)1(

Pg

Good

Bad

Good

Bad

79

)1(

Pb

79

)1(

Pg

79

)1(

Pb

79

)79(

Pb

79

)79(

Pb

79

)2(

Pb

79

)2(

Pg79

)79(

Pg

79

)79(

Pb

Since…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

∑=

=79

1

)(

79

1'

i

i

gg PP

Error Model for Ordinary Error Model for Ordinary Hopping KernelHopping Kernel

further reduce to this…

Bad

Good

79

...)79()2()1(

PPP ggg+++

79

...)79()2()1(

PPP bbb+++

79

...)79()2()1(

PPP bbb+++

79

...)79()2()1(

PPP ggg+++

Adaptive Frequency Adaptive Frequency Hopping (AFH)Hopping (AFH)

1 2 30 76 77 78

Channel #

73 74 7571 725 6 74

used

unused

Parameters DefinitionParameters Definition

• Ngood represents the number of used channels

• 2 operating modes:• Mode L: Ngood >= Nmin

• Mode H: Ngood < Nmin

Mode LMode 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

Mode HMode 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:

EvaluationEvaluation

• 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 ChannelsHomogeneous Channels

• Pgg = 0.8 , varying Pbg

Semi-Homogeneous Semi-Homogeneous ChannelsChannels

• Pgg = 0.8; Pbb = 0.5 for the first group and 0.9 for the other

Heterogeneous ChannelsHeterogeneous Channels

• Randomly select Pgg and Pbb in the range [Pmin

gg, 1] and [Pminbb, 1]

Heterogeneous ChannelsHeterogeneous Channels

ConclusionConclusion• 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!Thank You!