Department of Information Engineering University of Padova, ITALY

WPMC 2003 Yokosuka, Kanagawa (Japan) 21-22 October 2003

Department of Information EngineeringUniversity of Padova, ITALY

Mathematical Analysis of Bluetooth Mathematical Analysis of Bluetooth

Energy EfficiencyEnergy Efficiency

{andrea.zanella, daniele.miorandi, silvano.pupolin}@dei.unipd.it

Andrea Zanella, Daniele Miorandi, Silvano Pupolin

WPMC 2003, 21-22 October 2003

Special Interest Group on NEtworking & Telecommunications


Outline of the contents

Motivations & Purposes

Bluetooth reception

mechanism

System Model

Results

Conclusions


What & Why…

Motivations &Purposes


Motivations Bluetooth was designed to be integrated in portable battery driven

electronic devices

Energy Saving is a key issue!Energy Saving is a key issue!

Bluetooth Baseband aims to achieve high energy efficiency:

Units periodically scan radio channel for valid packets

Scanning takes just the time for a valid packet to be recognized

Units that are not addressed by any valid packet are active for less

than 10% of the time


Aims of the work Although reception mechanism is well defined, many

aspects still need to be investigated:

What’s the energy efficiency achieved by multi-slot packets?

What’s the role plaid by the receiver-correlator margin parameter?

What’s the amount of energy drained by Master and Slave units?

Our aim is to provide answers to such questions! How?

Capture system dynamic by means of a FSMC

Define appropriate reward functions (Data, Energy, Time)

Resort to renewal reward analysis to compute system performance


What standard says…

Bluetooth

reception

mechanism


AC HEADaccess code packet header payload

72 54 0-2745

CRC

Access Code field

Access Code (AC) AC field is used for synchronization and piconet identification

All packet exchanged in a piconet have same AC

Bluetooth receiver correlates the incoming bit stream against the expected

synchronization word:

AC is recognized if correlator output exceeds a given threshold

AC does check HEAD is received

AC does NOT check reception stops and pck is immediately discarded

PAYL


Receiver-Correlator Margin S: Receiver–correlator margin

Determines the selectivity of the

receiver with respect to packets

containing errors

Low S strong selectivity

risk of dropping packets that could

be successfully recovered

High S weak selectivity

risk of receiving an entire packet

that contains unrecoverable errors



72 54 0-2745

CRC

Packet HEADer field

Packet Header (HEAD)

Contains:

Destination address

Packet type

ARQN flags: used for piggy-backing ACK information

Header checksum field (HEC): used to check HEAD integrity

HEC does check PAYL is received

HEC does NOT check reception stops and pck is immediately

discarded

PAYL



72 54 0-2745

CRC

Packet PAYLoad field

Payload (PAYL)

DH: High capacity unprotected packet types

DM: Medium capacity FEC protected packet types

(15,10) Hamming code

CRC field is used to check PAYL integrity:

CRC does check positive acknowledged is return (piggy-back)

CRC does NOT check negative acknowledged is return (piggy-back)

PAYL


jjS

jok j

AC

72

000

0 172

1830

2000 113 okHEAD

Conditioned probabilities

AC HEAD PAYLOAD72 bits 54 bits h=2202745 bits

CRC

Receiver- Correlator Margin (S)

2-time bit rep. (1/3 FEC)

DHn: Unprotected

DMn: (15,10) Hamming FEC

1515

014

000

00

1115:DMn

1:DHnh

ok

hok

PL

PL

00: BER: BER


RetransmissionsMASTER

SLAVE

A B B BB

G F H

NAK

ACK

Automatic Retransmission Query (ARQ): Each data packet is transmitted and retransmitted until positive acknowledge

is returned by the destinationNegative acknowledgement is implicitly assumed!

Errors on return packet determine transmission of duplicate packets (DUPCK) Slave filters out duplicate packets by checking their sequence number

Slave does never never transmit DUPCKs! Slave can transmit when it receives a Master packet Master packet piggy-backs the ACK/NACK for previous Slave transmission Slave retransmits only when needed!

H

B

A X B X DPCK DPCK


Mathematical Analysis

System Model


Hypothesis Single slave piconet Saturated links

Master and slave have always packets waiting for transmission

Unlimited retransmission attempts Packets are transmitted over and over again until positive

acknowledgement

Static Segmentation & Reassembly policy Unique packet type per connection

Sensing capability Nodes can to sense the channel to identify the end of ongoing

transmissions Nodes always wait for idle channel before attempting new transmissions


Packet error probabilities Let us define the following basic packet reception events

ACer: AC does not check

Packet is not recognized

HECer: AC does check & HEAD does not

Packet is not recognized

CRCer: AC & HEAD do check, PAYL does not

Packet is recognized but PAYL contains unrecoverable errors

PRok: AC & HEAD & PAYL do check

Packet is successfully received

Packets experiment independent error events


Reception events

0: both downlink and uplink packet are correctly received

1: downlink packet is correctly received, uplink packet is received but with errors in the PAYL field

2U3: downlink packet is correctly received but uplink packet is not recognized by the master unit Master will transmit DUPCKs DUPCKs

49: downlink and uplink packets are not correctly received Master will retransmit useful packetsuseful packets

Reception Event Index

Downlink pck reception events

Uplink pck reception events


Mathematical Model Normal State (N)

Master transmits packets that have never been

correctly received by the slave

Duplicate State (D) Master transmits duplicate packets (DUPCKs)

32 PrPr DNP 5140 PrPrPrPr NDP

DNND

NDN PP

P

The steady-state probabilities are, then,

Since error events are disjoint, the state transition probabilities are given by

DNND

DND PP

P


Reward Functions

EjE

xjj

xDD )()(

For each state j we define the following reward functions

Tj= Average amount of time spent in state j

Dj(x)= Average amount of data delivered by unit x{M,S}

Wj(x)= Average amount of energy consumed by unit x{M,S}

The average amount of reward earned in state j is given by

EjE

xjj

xWW )()(

EjE

jjTT

Performance indexes Energy Efficiency: Energy Efficiency:

Goodput: G T

DD

T

DG

MS )()(

lim

)()(

)()(

limMS

MS

WW

DD

W

D


Notations

Let us introduce some notation:

Dxn (Dym) downlink (uplink) packet type, n=1,3,5

L(Dxn) = PAYL length (bit) for Dxn packet type

wTX(X) / wRX(X)/ wss(X)= amount of power consumed by

transmitting/ receiving/ sensing the packet field X

pj = Pr(j)


Time reward ( T )

9898 )1(1)( ppnppmnT

MASTER

SLAVE

Transmission Reception/Sensing

n+m

n+1

MASTER

SLAVE


Data reward ( D )

Master gains Data reward when System is in state N Slave perfectly receives the master packet

Slave gains Data reward when Slave recognizes the master polling Master perfectly receives the slave packet

40)( )( ppDLD ym

S

3210)( )( ppppDLD Nxn

M


Master energy reward ( W )Receives entire uplink packet

Receives till the first uncorrected field and senses

till the end of the packet

Receives only AC field

PAYLwHEADwACw SSRXRX

ACwRX

ymRX Dw

Always transmits a downlink packet xnTX Dw

PAYLwHEADwACw SSSSRX


Slave energy reward ( W )

Slave’ energy reward resembles mater’ one except that, in D state, Slave does not listen for the PAYL field of recognized downlink packet since it has been already correctly received!

HEADwpHEADwpPAYLwACwpp

PAYLwDwDwppW

SSRXxnSSRX

xnRXDxnRXymTXS

9898

98)( 1


Performance Analysis

Results


Energy Efficiency

Downlink traffic only (M>S) and S=0 Energy efficiency gets worse in Rayleigh channels DH5 outperform other packet formats for almost every SNR value

For SNRdB=1418, DMn outperforms DHn


Master Slave swapping

Swapping Master and Slave role: DM5 & DM3 energy efficiency increases up to 15 % for SNR20dB Unprotected pck types show slightly reduced performance gain Performance gain drastically reduces for increasing values of the Rice factor K For AWGN channels, master slave swapping does not lead to any significant

performance improvement

SM

SMMS


Master Slave swapping

SM

SMMS

Swapping Master and Slave role: DM5 & DM3 energy efficiency

increases up to 15 % for SNR20dB

Unprotected pck types show slightly reduced performance gain

Performance gain drastically reduces for increasing values of the Rice factor K

For AWGN channels, master slave swapping does not lead to any significant performance improvement


Impact of parameter S

The receiver correlator margin S has strong impact on system performance AWGN: improves with S, in particular for low SNR values Rayleigh: gets worse with S, except for low SNR values

Relaxing AC selectivity is convenient, since G gain is much higher than loss

Impact of S, however, rapidly reduces for SNRdB>15

AWGNAWGN RayleighRayleigh


Conclusions

Main Contribution

mathematical framework for performance evaluation of Bluetooth piconets

Results

In case of asymmetric connections, Slave to Master configuration yields

better performance in terms of both Goodput and Energy Efficiency

Slave never transmits DUPCK

Parameter S may significantly impact on performance

Short and Protected packet types improve performance with S

Long and Unprotected packet types show less dependence on this parameter

Results may be exploited to design energy–efficient scheduling

algorithms for Bluetooth piconets

Department of Information Engineering University of Padova, ITALY

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