mathematical analysis of bluetooth energy efficiency

COST273, Barcelona, 15-17 January, 2003

Department of Information Engineering

University of Padova, Italy

Mathematical Analysis Mathematical Analysis of Bluetooth Energy of Bluetooth Energy

EfficiencyEfficiency

{zanella, pupolin}@dei.unipd.it

Andrea Zanella, Silvano Pupolin

COST273 Barcelona, 15-17 January 2003

COST273, Barcelona, 15-17 January, 2003 TD (03)-028

Outline of the contentsOutline of the contents

Motivations & Purposes Bluetooth reception

mechanism System Model Results Conclusions


What & Why…What & Why…

Motivations &Purposes


MotivationsMotivations

Bluetooth was designed to be integrated in portable battery driven electronic devices

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 workAims 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…What standard says…

Bluetooth

reception

mechanism


AC HECaccess code packet header payload

72 54 0-2745

CRC

Access Code fieldAccess 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 Receiver-Correlator Margin 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 fieldPacket 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 fieldPacket 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 okHEC

Conditioned probabilitiesConditioned probabilities

AC HEC 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


RetransmissionsRetransmissions

MASTER

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 destination Negative acknowledgement is implicitly assumed!

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

Slave never transmits duplicate packets! 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 AnalysisMathematical Analysis

System Model


Mathematical ModelMathematical Model

System dynamic can be modelled by means of a discrete time

independent process {en} with state space E

Each state corresponds to a specific system behaviour

For each state Ej E, we define the following reward functions

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

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

Tj= Average amount of time spent in state Ej

Denoting by j the probability of event Ej, the average amount of

reward earned in state Ej is given by:

EjE

xjj

xDD )()(

EjE

xjj

xWW )()(

EjE

jjTT


System DynamicSystem Dynamic

We need to determine: State space E

System behaviour in each Ej E

System dynamic depends on the packet

reception events that occur at Slave and

Master units

Let us first focus on events that may occur

during the reception of a single packet


Packet reception eventsPacket reception events

Let us define the following basic packet reception events ACer: AC does not check

Packet is not recognized

HECer: AC does check & HEC does not Packet is not recognized

CRCer: AC & HEC do check, CRC does not Packet is recognized but PAYL contains unrecoverable errors

CRCok: AC & HEC & CRC do check Packet is successfully received

Furthermore, we introduce the following notation Recognition Error: RECer={ACer or HECer}

Recognition OK: RECok={CRCer or CRCok}


Basic reception events Basic reception events (1)(1)

Looking at the reception status of both the downlink (master to slave) and uplink (slave to master) packets, we can identify four basic reception events

r1: both downlink and uplink packet are recognized by the slave and master unit, respectively

r2: downlink packet is not recognized by the slave unit (uplink packet is not returned)

r3: downlink packet is recognized by the slave unit, but PAYL is not correct, uplink packet is not recognized by the master unit

r4: downlink packet is successfully received by the slave unit, uplink packet is not recognized by the master unit

)()(1

Mok

Sok RECRECr

)(2S

erRECr

)()(3

Mer

Ser RECCRCr

)()(4

Mer

Sok RECCRCr


Basic reception events Basic reception events (2)(2)

Note that,

Basic events are disjoint:

Their probabilities adds to one:

The occurrence of each basic event determines a

specific system dynamic for a given number of steps

We define a state Ei to each basic event ri: ri Ei

State Ei collects the system dynamic after the occurrence of

the basic event ri

ji rrjiji ,,4,3,2,1,

1)Pr(4

1

i

ir


NotationsNotations

Let us introduce some notation:

Dxn= downlink (Master to Slave) packet type, n=1,3,5

Dym= uplink (Slave to Master) packet type, m=1,3,5

L(Dxn) = number of data bits carried by the Dxn packet type

wTX(X)= amount of power consumed by transmitting packet field

X

wRX(X)= amount of power consumed by receiving packet field X

w0= average amount of power consumed by the receiving unit in

case the incoming packet is not recognized, i.e., RECer occurs: ererRXRX RECHECHEADwACww Pr0


System Dynamic: ESystem Dynamic: E11

Rewards earned in state E1 are given by:

Time spent is E1

Energy consumed by Master

Energy consumed by Slave

Data delivered by Master

Data delivered by Slave

MASTER

SLAVE

Transmission

Reception

)(SokREC )(M

okREC

slotTmnT )(1

ymRXxnTXM DwDwW )(

1

ymTXxnRXS DwDwW )(1

)()()(1 Pr S

okS

okxnM RECCRCDLD

)()()(1 Pr M

okM

okymS RECCRCDLD

T1

xnRX Dw ymTX Dw




Time spent is E2





MASTER

SLAVE

Transmission

Reception

)(SerREC

slotTnT )1(2

ACwDwW RXxnTXM )(2

20)(

2 nACwwW RXS

0)(2 MD

0)(2 SD

T2

0w ACwRX




Time spent is E3





MASTER

SLAVE

Transmission

Reception

)(SokREC )(M

erREC

slotTznT 1)1(3

zACwwzDwW RXxnTXM 0)(

3 1

mnRXymTXxnRXS iACwDwDwW ,)(

3

0)(3 MD

0)(3 SD

T3

11 nmz

otherwise0

;1,1

;3,5,2

, mn

mn

i mn



T4

State E4 is entered when r4 event occurs:

Downlink packet is perfectly received, while uplink packet is not recognized

Master keeps retransmitting duplicate pcks until a return pck is recognized

Slave listens only for AC and HEAD fields of duplicate packets and returns an

uplink packet for each duplicate packet it recognizes

State E4 is left when r1 event occurs:

Both downlink and uplink packets are recognized by the respective units


Performance AnalysisPerformance Analysis

Results


Performance IndexesPerformance Indexes

From the renewal reward analysis, we can evaluate the following performance indexes Goodput: G

Amount of data successfully delivered per unit of time

Energy Efficiency: Amount of data successfully delivered per unit of energy

consumed

T

DD

T

DG

MS )()(

lim

)()(

)()(

limMS

MS

WW

DD

W

D


AWGN channel: M>SAWGN channel: M>S Asymmetric connection: M>S

Data flows from Master to Slave

SNRdB<14, G 0

SNRdB=1418, DMn outperforms DHn

SNRdB>18, DHn achieves better G

Energy efficiency curves resemble

Goodput curves

However, performance gap between

Dx5 and Dx3 pck types is reduced


AWGN channel: S>MAWGN channel: S>M Asymmetric connection: S>M

Data flows from Slave to Master

Swapping Master and Slave role: DM5 & DM3 Goodput increases up to 15 % Other pck types do not improve, but

neither loose performance…

Energy efficiency improvement for

DM5 & Dm3 pcks is up to 22 %

However, for greater SNR values,

performance improvement is lower…

SMG

MSGG

SM

MS


Rayleigh channel: M>SRayleigh channel: M>S Performance in Rayleigh channels is

drastically reduced! SNRdB<14, G 0

SNRdB<18, DMn & DHn types achieve

similar performance SNRdB>18, DH5 achieves higher G

Energy efficiency curves resemble

Goodput curves

Curves shape is smoother than for

AWGN


Rayleigh channel: S>MRayleigh channel: S>M For Rayleigh fading channel, S>M

configuration is much better performing than M>S configuration, for almost all the packet types

DM5 & DM3 Goodput increases up to 55 % DH5 & DH3 Goodput increases up to 15 %

All the packet types improve energy

efficiency performance For DM5 & DM3, Δ up to 88 %!!!

For DH5 & DH3, Δ up to 20 %

SMG

MSGG

SM

MS


Impact of parameter SImpact of parameter S

The receiver correlator margin S has strong impact on system performance G improves for high S values (from 30% up to 230% for SNRdB=15) improves for DMn and DH1 types slightly decreases for DH5 & DH3 types (less 6 % performance loss)

Relaxing AC selectivity is convenient, since G gain is much higher than loss Impact of S, however, rapidly reduces for SNRdB>15


ConclusionsConclusions

Average traffic rate shows a tradeoff between different packet types Unprotected and long types yield better Goodput for SNR> 18

For lower SNR, better performance are achieved by short and protected

formats

Performance gap between protected and unprotected formats is drastically

reduced in fading channels

Slave to Master configuration yields performance improvement in terms

of both Goodput and Energy Efficiency Server (slave) never retransmits pcks that were already received by the

client (master)

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 algorithms for the

piconet management


That’s all!That’s all!

Thanks for you attention!

mathematical analysis of bluetooth energy efficiency

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