Transcript Ingegneria dell'Informazione

Department of Information Engineering
University of Padova, ITALY
Special Interest Group on
NEtworking & Telecommunications
Mathematical Analysis of Bluetooth
Energy Efficiency
Andrea Zanella, Daniele Miorandi, Silvano Pupolin
{andrea.zanella, daniele.miorandi, silvano.pupolin}@dei.unipd.it
WPMC 2003
WPMC 2003, 21-22
October 2003
Yokosuka, Kanagawa (Japan) 21-22 October 2003
Outline of the contents

Motivations & Purposes

Bluetooth reception
mechanism

System Model

Results

Conclusions
WPMC 2003
Yokosuka, Kanagawa (Japan) 21-22 October 2003
What & Why…
Motivations &
Purposes
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Yokosuka, Kanagawa (Japan) 21-22 October 2003
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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Yokosuka, Kanagawa (Japan) 21-22 October 2003
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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Yokosuka, Kanagawa (Japan) 21-22 October 2003
Access Code field
72
54
AC
HEAD
0-2745
PAYL
payload
access code packet header

CRC
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
WPMC 2003
Yokosuka, Kanagawa (Japan) 21-22 October 2003
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
WPMC 2003
Yokosuka, Kanagawa (Japan) 21-22 October 2003
Packet HEADer field
72
54
AC
HEAD
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
WPMC 2003
Yokosuka, Kanagawa (Japan) 21-22 October 2003
Packet PAYLoad field
72
54
AC
HEAD
access code packet header

0-2745
PAYL
CRC
payload
Payload (PAYL)

DH: High capacity unprotected packet types

DM: Medium capacity FEC protected packet types


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(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)
Yokosuka, Kanagawa (Japan) 21-22 October 2003
Conditioned probabilities
AC
72 bits
DHn: Unprotected
2-time bit rep.
(1/3 FEC)
ReceiverCorrelator
Margin (S)
HEAD
DMn: (15,10) Hamming
FEC
PAYLOAD
54 bits
CRC
h=2202745 bits
DHn : PLok  0   1   0 h
0: BER

DMn : PLok  0   15  0 1   0   1   0 

HEADok  0   3 0 1   0   1   0 
2

3 18
 72  j
  0 1   0 72 j
ACok  0  
j
j 0 
S

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
15 h 15
14
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Retransmissions
A
B
B
B
B
B
NAK
MASTER
ACK
G
SLAVE
A
 Automatic
F
X
H
H
B
X
DPCK
DPCK
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 (DUPCK)

Slave filters out duplicate packets by checking their sequence number
 Slave
does 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!
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Mathematical Analysis
System Model
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Hypothesis

Single slave piconet

Saturated links


Unlimited retransmission attempts


Packets are transmitted over and over again until positive
acknowledgement
Static Segmentation & Reassembly policy


Master and slave have always packets waiting for transmission
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
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Packet error probabilities

Let us define the following basic packet reception events

ACer: AC does not check


HECer: AC does check & HEAD does not


Packet is recognized but PAYL contains unrecoverable errors
PRok: AC & HEAD & PAYL do check


Packet is not recognized
CRCer: AC & HEAD do check, PAYL does not


Packet is not recognized
Packet is successfully received
Packets experiment independent error events
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Reception events
Reception
Event Index
Downlink pck
reception events



Uplink pck
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
2U3: downlink packet is correctly
received but uplink packet is not
recognized by the master unit


49: downlink and uplink packets
are not correctly received

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Master will transmit DUPCKs
Master will retransmit useful packets
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Mathematical Model

Normal State (N)


Duplicate State (D)


Master transmits duplicate packets (DUPCKs)
Since error events are disjoint, the state transition probabilities are given by
PDN  Pr  2   Pr 3 

Master transmits packets that have never been
correctly received by the slave
PND  Pr  0   Pr  4   Pr 1   Pr 5 
The steady-state probabilities are, then,
N 
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PND
PND  PDN
D 
PDN
PND  PDN
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Reward Functions

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
T

 jT j
E j E

Performance indexes


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D
( x)


( x)
jDj
W
( x)

E j E
 W
j
( x)
j
E j E
Energy Efficiency: 
D  D  D
  lim
 (S )
(M )
  W  
W W
Goodput: G
D  D
G  lim

  T  
(S )
(S )
(M )
D
(M )
T
Yokosuka, Kanagawa (Japan) 21-22 October 2003
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

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pj = Pr(j)
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Time reward ( T )
Transmission
Reception/Sensing
MASTER
SLAVE
n+m
MASTER
SLAVE
n+1
T  (n  m)1  p8  p9   (n  1) p8  p9 
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Data reward ( D )

Master gains Data reward when


System is in state N
Slave perfectly receives the master packet
D ( M )  L( Dxn )   N   p0  p1  p2  p3 

Slave gains Data reward when


Slave recognizes the master polling
Master perfectly receives the slave packet
D ( S )  L( D ym )   p0  p 4 
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Master energy reward ( W )
Receives entire uplink packet

wRX Dym

Receives only AC field
wRX  AC 
Receives till the first
uncorrected field and senses
till the end of the packet
wRX  AC   wRX HEAD   wSS PAYL 
wRX  AC   wSS HEAD   wSS PAYL 
Always transmits a
downlink packet
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wTX Dxn 
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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!
  

W ( S )  1  p8  p9  wTX D ym  wRX Dxn    D  wRX PAYLxn  
 p8  p9 wRX AC   wSS PAYLxn  p8 wRX HEAD   p9 wSS HEAD 
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Performance Analysis
Results
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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=1418, DMn outperforms DHn
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Master Slave swapping
 

 S  M    M  S 
 M  S 
Swapping Master and Slave role:




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DM5 & DM3 energy efficiency increases up to 15 % for SNR20dB
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
Yokosuka, Kanagawa (Japan) 21-22 October 2003
Master Slave swapping

 
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 S  M    M  S 
 M  S 
Swapping Master and Slave role:

DM5 & DM3 energy efficiency
increases up to 15 % for
SNR20dB

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
Yokosuka, Kanagawa (Japan) 21-22 October 2003
Impact of parameter S
AWGN

Rayleigh
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
WPMC 2003
Yokosuka, Kanagawa (Japan) 21-22 October 2003
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
WPMC 2003
Yokosuka, Kanagawa (Japan) 21-22 October 2003