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1
Department of Information EngineeringUniversity
of Padova, ITALY
Mathematical Analysis of Bluetooth Energy
Efficiency
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Department of Information EngineeringUniversity
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_at_dei.unipd.it
WPMC 2003, 21-22 October 2003
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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
• Whats the energy efficiency achieved by
  multi-slot packets?
• Whats the role plaid by the receiver-correlator
  margin parameter?
• Whats the best Master and Slave configuration?
• How do we answer such questions?
• 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
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

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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

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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

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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)?

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Retransmissions
NAK
MASTER
ACK
SLAVE
X
A
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 (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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Reception events
Downlink pck reception events
Reception Event Index
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
• Master will transmit DUPCKs
• ?4??9 downlink and uplink packets are not
  correctly received
• Master will retransmit useful packets

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Mathematical Model

• Normal State (N)?
• Master transmits packets that have never been
  correctly received by the slave
• Duplicate State (D)?
• Master transmits duplicate packets (DUPCKs)?

• Since error events are disjoint, the state
  transition probabilities are given by

• The steady-state probabilities are, then,

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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

• Performance indexes
• Energy Efficiency ?
• Goodput G

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Time reward ( T )?
Reception/Sensing
MASTER
SLAVE
nm
MASTER
SLAVE
n1
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Data reward ( D )?

• Master gains Data reward when
• System is in state N
• Slave perfectly receives the master packet
• Slave gains Data reward when
• Slave recognizes the master polling
• Master perfectly receives the slave packet

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Master energy reward ( W )?
Receives entire uplink packet
Receives only AC field
Receives till the first uncorrected field and
senses till the end of the packet
Always transmits a downlink packet
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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!

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Performance Analysis
Results
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Energy Efficiency

• Downlink traffic only (MgtS) and S0
• Energy efficiency gets worse in Rayleigh channels
• DH5 outperform other packet formats for almost
  every SNR value
• For SNRdB14?18, DMn outperforms DHn

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Master Slave swapping

• 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

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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
  SNRdBgt15

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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
• Next steps
• Design energyefficient scheduling algorithms for
  Bluetooth piconets

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Department of Information EngineeringUniversity
of Padova, ITALY
Mathematical Analysis of Bluetooth Energy
Efficiency
Andrea Zanella, Daniele Miorandi, Silvano Pupolin
Questions?
WPMC 2003, 21-22 October 2003
25
Extra Slides
Spare slides
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Conditioned probabilities
DHn Unprotected DMn (15,10) Hamming FEC
2-time bit rep. (1/3 FEC)?
Receiver- Correlator Margin (S)?
AC
HEAD
PAYLOAD
CRC
54 bits
72 bits
h220?2745 bits
?0 BER
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Hypothesis

• Single slave piconet
• Saturated links
• Master and slave have always packets waiting for
  transmission
• Unlimited retransmission attempts
• Packets are transmitted over and over again until
  positive acknowledgement
• Static Segmentation Reassembly policy
• 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
• 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
• PRok AC HEAD PAYL do check
• Packet is successfully received
• Packets experiment independent error events

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Notations

• Let us introduce some notation
• Dxn (Dym) downlink (uplink) packet type, n1,3,5
• ?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
• pj Pr(?j)?

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Master Slave swapping

• 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