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COST273, Barcelona, 15-17 January, 2003
Department of Information Engineering
University of Padova, Italy
Mathematical Analysis of Mathematical Analysis of Bluetooth Energy EfficiencyBluetooth Energy Efficiency
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are adapted from (or perhaps identical to) our slides, and put a link to the authors webpage:
www.dei.unipd.it/~zanella
Thanks and enjoy!
A note on the use of these ppt slides:We’re making these slides freely available to all, hoping they might be of use for
researchers and/or students. They’re in PowerPoint form so you can add, modify, and delete slides (including this one) and slide content to suit your needs. In return for use, we
only ask the following:If you use these slides (e.g., in a class, presentations, talks and so on) in substantially
unaltered form, that you mention their source.If you post any slides in substantially unaltered form on a www site, that you note that they
are adapted from (or perhaps identical to) our slides, and put a link to the authors webpage:
www.dei.unipd.it/~zanella
Thanks and enjoy!
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
COST273, Barcelona, 15-17 January, 2003 TD (03)-028
What & Why…What & Why…
Motivations &Purposes
COST273, Barcelona, 15-17 January, 2003 TD (03)-028
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
COST273, Barcelona, 15-17 January, 2003 TD (03)-028
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
COST273, Barcelona, 15-17 January, 2003 TD (03)-028
What standard says…
Bluetooth
reception
mechanism
COST273, Barcelona, 15-17 January, 2003 TD (03)-028
AC HEADaccess 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
COST273, Barcelona, 15-17 January, 2003 TD (03)-028
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
COST273, Barcelona, 15-17 January, 2003 TD (03)-028
AC HEADaccess code packet header payload
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
COST273, Barcelona, 15-17 January, 2003 TD (03)-028
AC HEADaccess code packet header payload
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
COST273, Barcelona, 15-17 January, 2003 TD (03)-028
jjS
jok j
AC
72
000
0 172
1830
2000 113 okHEAD
Conditioned probabilitiesConditioned 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
COST273, Barcelona, 15-17 January, 2003 TD (03)-028
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
COST273, Barcelona, 15-17 January, 2003 TD (03)-028
Mathematical AnalysisMathematical Analysis
System Model
COST273, Barcelona, 15-17 January, 2003 TD (03)-028
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
COST273, Barcelona, 15-17 January, 2003 TD (03)-028
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
COST273, Barcelona, 15-17 January, 2003 TD (03)-028
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 & HEAD does not Packet is not recognized
CRCer: AC & HEAD do check, PAYL does not Packet is recognized but PAYL contains unrecoverable errors
CRCok: AC & HEAD & PAYL do check Packet is successfully received
Furthermore, we introduce the following notation Recognition Error: RECer={ACer or HECer}
Recognition OK: RECok={CRCer or CRCok}
COST273, Barcelona, 15-17 January, 2003 TD (03)-028
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
)(2
SerRECr
)()(3
Mer
Ser RECCRCr
)()(4
Mer
Sok RECCRCr
COST273, Barcelona, 15-17 January, 2003 TD (03)-028
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
COST273, Barcelona, 15-17 January, 2003 TD (03)-028
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
COST273, Barcelona, 15-17 January, 2003 TD (03)-028
System Dynamic: E1
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
)(SerCRC )(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
COST273, Barcelona, 15-17 January, 2003 TD (03)-028
System Dynamic: ESystem Dynamic: E22
Rewards earned in state E2 are given by:
Time spent is E2
Energy consumed by Master
Energy consumed by Slave
Data delivered by Master
Data delivered by Slave
MASTER
SLAVE
Transmission
Reception
)(SerREC
slotTnT )1(2
ACwDwW RXxnTXM )(
2
2/10)(
2 nACwwW RXS
0)(2 MD
0)(2 SD
T2
0w ACwRX
COST273, Barcelona, 15-17 January, 2003 TD (03)-028
System Dynamic: E3
Rewards earned in state E3 are given by:
Time spent is E3
Energy consumed by Master
Energy consumed by Slave
Data delivered by Master
Data delivered by Slave
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
COST273, Barcelona, 15-17 January, 2003 TD (03)-028
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
COST273, Barcelona, 15-17 January, 2003 TD (03)-028
Performance Analysis
Results
COST273, Barcelona, 15-17 January, 2003 TD (03)-028
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
COST273, Barcelona, 15-17 January, 2003 TD (03)-028
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
COST273, Barcelona, 15-17 January, 2003 TD (03)-028
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 lose 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
COST273, Barcelona, 15-17 January, 2003 TD (03)-028
Rayleigh channel: M>S Performance in Rayleigh channels is
drastically reduced! SNRdB<14, G 0
SNRdB<18, DMn & DHn types achieve
similar performance Saturation is achieved for SNRdB>40
Energy efficiency curves resemble
Goodput curves
Curves shape is smoother than for
AWGN
COST273, Barcelona, 15-17 January, 2003 TD (03)-028
Rayleigh 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
COST273, Barcelona, 15-17 January, 2003 TD (03)-028
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
COST273, Barcelona, 15-17 January, 2003 TD (03)-028
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
COST273, Barcelona, 15-17 January, 2003 TD (03)-028
That’s all!
Thanks for you attention!
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