Department of Information Engineering
University of Padova, Italy
Mathematical Analysis of
Bluetooth Energy
Efficiency
Andrea Zanella, Silvano Pupolin
{zanella, pupolin}@dei.unipd.it
COST273 Barcelona, 15-17 January 2003
Outline of the contents


Motivations & Purposes
Bluetooth reception
mechanism

System Model

Results

Conclusions
COST273, Barcelona, 15-17 January, 2003
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What & Why…
Motivations &
Purposes
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Motivations

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
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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
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What standard says…
Bluetooth reception
mechanism
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Access Code field
72
54
AC
HEC
access code packet header

0-2745
PAYL
CRC
payload
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
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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
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Packet HEADer field
72
54
AC
HEC
access code packet header

0-2745
PAYL
CRC
payload
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
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Packet PAYLoad field
72
54
AC
HEC
access code packet header

0-2745
PAYL
CRC
payload
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)
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Conditioned probabilities
AC
72 bits
DHn: Unprotected
2-time bit rep.
(1/3 FEC)
ReceiverCorrelator
Margin (S)
HEC
DMn: (15,10) Hamming
FEC
PAYLOAD
54 bits
CRC
h=2202745 bits
0: BER
DHn : PLok  0   1   0 h

DMn : PLok  0   15  0 1   0 14  1   0 15

HECok  0   3 0 1   0   1   0 
ACok  0  
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2

h 15

3 18
 72  j
  0 1   0 72 j
j
j 0 
S

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Retransmissions
A
B
B
B
B
B
NAK
MASTER
ACK
G
SLAVE
A

F
X
H
H
B
X
DPCK
DPCK
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!
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Mathematical Analysis
System Model
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Mathematical 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:
D
( x)



( x)
D
j j
E j E
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W
( x)


 jW j( x)
E j E
T
 T
j j
E j E
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System 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
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Packet reception events

Let us define the following basic packet reception events

ACer: AC does not check


HECer: AC does check & HEC does not


Packet is recognized but PAYL contains unrecoverable errors
CRCok: AC & HEC & CRC do check


Packet is not recognized
CRCer: AC & HEC do check, CRC does not


Packet is not recognized
Packet is successfully received
Furthermore, we introduce the following notation

Recognition Error: RECer={ACer or HECer}

Recognition OK:
RECok={CRCer or CRCok}
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Basic reception events (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

(S )
(M )
r1  RECok
 RECok

r2: downlink packet is not recognized by the slave unit (uplink packet is not returned)

r2  RECer( S )


r3: downlink packet is recognized by the slave unit, but PAYL is not correct, uplink
packet is not recognized by the master unit

r3  CRCer( S )  RECer( M )



r4: downlink packet is successfully received by the slave unit, uplink packet is not
recognized by the master unit

(S )
r4  CRCok
 RECer( M )
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Basic reception events (2)

Note that,


Basic events are disjoint:
i, j  1,2,3,4, i  j, ri  r j   
Their probabilities adds to one:
4
 Pr( r )  1
i
i 1

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
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Notations

Let us introduce some notation:

Dxn= downlink (Master to Slave) packet type, n=1,3,5

Dym= uplink (Slave to Master) packet type,

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
m=1,3,5
case the incoming packet is not recognized, i.e., RECer occurs:
w0  wRX  AC  wRX HEADPrHECer RECer 
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System Dynamic: E1
MASTER
Transmission
Reception
(S )
RECok
(M )
RECok
SLAVE
T1

wRX Dxn 
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
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
wTX Dym

T1  (n  m)Tslot
 
W1( S )  wRX Dxn   wTX D ym 
W1( M )  wTX Dxn   wRX D ym

Pr CRC
(S )
(S )
D1( M )  LDxn  Pr CRCok
RECok

D1( S )  L D ym
(M )
ok

(M )
RECok

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System Dynamic: E2
MASTER
Transmission
Reception
RECer(S )
SLAVE
wRX  AC 
T2

Rewards earned in state E2 are given by:
w0

Time spent is E2
T2  (n  1)Tslot

Energy consumed by Master
W2( M )  wTX Dxn   wRX  AC

Energy consumed by Slave
W2( S )  w0  wRX  ACn 2

Data delivered by Master
D2( M )  0

Data delivered by Slave
D2( S )  0
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System Dynamic: E3
MASTER
Transmission
Reception
(S )
RECok
RECer(M )
SLAVE
z  m  1 n  1
T3

Rewards earned in state E3 are given by:
T3  (n  1)z  1Tslot
in , m
2, n  5, m  3;

 1, n  m  1;
0 otherwise


Time spent is E3

Energy consumed by Master
W3( M )  wTX Dxn z  1  w0  wRX  AC z

Energy consumed by Slave
W3( S )  wRX Dxn   wTX D ym  wRX  AC   in, m

Data delivered by Master
D3( M )  0

Data delivered by Slave
D3( S )  0
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

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System Dynamic: E4
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
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Performance Analysis
Results
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Performance Indexes

From the renewal reward analysis, we can evaluate the
following performance indexes

Goodput: G

Amount of data successfully delivered per unit of time
D  D
G  lim

  T  

(S )
D
(M )
T
Energy Efficiency: 

Amount of data successfully delivered per unit of energy consumed
D  D  D
  lim
 (S )
(M )
  W  
W W
(S )
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(M )
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AWGN channel: M>S

Asymmetric connection: M>S


Data flows from Master to Slave

SNRdB<14, G  0

SNRdB=1418, 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
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AWGN 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…
GS  M 
G 
GM  S 

Energy efficiency improvement for DM5 &
Dm3 pcks is up to 22 %

 
 S  M 
 M  S 
However, for greater SNR values,
performance improvement is lower…
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Rayleigh 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
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Rayleigh channel: S>M

G 

GS  M 
GM  S 
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 %
 S  M 
 
 M  S 
All the packet types improve energy
efficiency performance

For DM5 & DM3, Δ up to 88 %!!!

For DH5 & DH3, Δ up to 20 %
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Impact 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
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Conclusions

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
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That’s all!
Thanks for you
attention!
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