Mathematical Analysis of Bluetooth Energy Efficiency

1
Mathematical Analysis of Bluetooth Energy
Efficiency
Department of Information Engineering University
of Padova, Italy

• Andrea Zanella, Silvano Pupolin

zanella, pupolin_at_dei.unipd.it
COST273 Barcelona, 15-17 January 2003
2
Outline of the contents

• Motivations Purposes
• Bluetooth reception mechanism
• System Model
• Results
• Conclusions

3
What Why
Motivations Purposes
4
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

5
Aims of the work

• Although reception mechanism is well defined,
  many aspects still need to be investigated
• Whats the energy efficiency achieved by
  multi-slot packets?
• Whats the role plaid by the receiver-correlator
  margin parameter?
• Whats 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

6
What standard says
Bluetooth reception mechanism
7
Access Code field
PAYL

• 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

8
Receiver-Correlator Margin

• S Receivercorrelator 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

9
Packet HEADer field
PAYL

• 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

10
Packet PAYLoad field
PAYL

• 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)

11
Conditioned probabilities
DHn Unprotected DMn (15,10) Hamming FEC
2-time bit rep. (1/3 FEC)
Receiver- Correlator Margin (S)
AC
HEC
PAYLOAD
CRC
54 bits
72 bits
h220?2745 bits
?0 BER
12
Retransmissions
NAK
MASTER
ACK
SLAVE
X
A
DPCK
B
X
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!

13
Mathematical Analysis
System Model
14
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

15
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

16
Packet 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 RECerACer or HECer
• Recognition OK RECokCRCer or CRCok

17
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
• 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

18
Basic reception events (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

19
Notations

• Let us introduce some notation
• Dxn downlink (Master to Slave) packet type,
  n1,3,5
• Dym uplink (Slave to Master) packet type,
  m1,3,5
• 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

20
System Dynamic E1
MASTER
Transmission
Reception
SLAVE
T1

• 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

21
System Dynamic E2
MASTER
Transmission
Reception
SLAVE
T2

• 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

22
System Dynamic E3
MASTER
Transmission
Reception
SLAVE
T3

• 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

23
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

24
Performance Analysis
Results
25
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
• Energy Efficiency ?
• Amount of data successfully delivered per unit of
  energy consumed

26
AWGN channel MgtS

• Asymmetric connection MgtS
• Data flows from Master to Slave
• SNRdBlt14, G ? 0
• SNRdB14?18, DMn outperforms DHn
• SNRdBgt18, DHn achieves better G

• Energy efficiency curves resemble Goodput curves
• However, performance gap between Dx5 and Dx3 pck
  types is reduced

27
AWGN channel SgtM

• Asymmetric connection SgtM
• 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

28
Rayleigh channel MgtS

• Performance in Rayleigh channels is drastically
  reduced!
• SNRdBlt14, G ? 0
• SNRdBlt18, DMn DHn types achieve similar
  performance
• SNRdBgt18, DH5 achieves higher G

• Energy efficiency curves resemble Goodput curves
• Curves shape is smoother than for AWGN

29
Rayleigh channel SgtM

• For Rayleigh fading channel, SgtM configuration is
  much better performing than MgtS 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, ?? up to 88 !!!
• For DH5 DH3, ?? up to 20

30
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 SNRdB15)
• ? 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
  SNRdBgt15

31
Conclusions

• Average traffic rate shows a tradeoff between
  different packet types
• Unprotected and long types yield better Goodput
  for SNRgt 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
  energyefficient algorithms for the piconet
  management

32
Thats all!
Thanks for you attention!