Modeling of the Data Link Layer in Wireless Sensor Networks

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Modeling of the Data Link Layer in Wireless
Sensor Networks

• Charlie Zhong
• Qualifying Exam
• December 13, 2002

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My Research

• For designers of the data link layer in wireless
  sensor networks
• Who need to do design tradeoffs
• My research provides analytical models
• That help them to understand the data link layer
  quantitatively
• Unlike simulative or experimental approaches
• My models can give them more insight to the
  design of the data link layer in much less time
  and enable them to do design optimization.

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Wireless Sensor Networks
Wireless sensor network is becoming a very
important component of wireless data networks
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The Data Link Layer
routing
Network Layer
Data link Layer
Power control
MAC
Power Management
Link Layer
Error Control
acquisition modulation
Physical Layer
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Problem Statement
Data Link

• Need models
• to study the relationships between design
  metrics and parameters
• to evaluate a design option in the context of
  others

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Existing Work

• Simulative/experimental approaches require long
  run time and provide much less insight
• Analytical approaches
• Most research focus on throughput only
• Recent work on energy analysis
• Ignore the interaction between components
• Only study the impact of a few parameters
• Dont link results to directly controllable
  parameters

References Throughput analysisAbramson (1970),
Roberts (1975) , Kleinrock and Tobagi
(1975). Energy analysis El-Hoiydi (ICC2002),
Schurgers et al. (IEEE Trans. Mob. Comp.
2002). Simulation/experiments Sohrabi et al.
(VTC 99), Pei et al. (Milcom 01), Ye et al.
(Infocom 02).
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Research Goal

• Bring all of the following together in one
  framework
• The models for every component within the data
  link layer
• Interacting with the abstracted models of the
  network layer, physical layer and channel.
• Conduct more comprehensive analysis than any
  existing work
• Use models built to identify
• Important parameters
• What is good/bad for low energy design
• And provide venues for major improvement
• Provide a framework in which to raise and address
  fundamental questions

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Importance of This Research
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Clean Interface
Network Layer
neighbors
Qos
Traffic density
Packet size
Data Link Layer
Power
channels
Radio Data Rate
Physical Layer
Interactions between layers are captured by
parameters.
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Inside the Data Link Layer
Network Layer
NN
pkt_loss
TN
delay
LN

pb
NN
g
Nh
NN
TN
Ebl
pkt_COL
PRAD
Power control
MAC (W,Mbk)
Channel model
Power Management (Ton,T,Tp)
Nch
R
PRX
L
pb
Pr
PTX
EN
pb
Link Layer (M,Mr,Mn,LOHD)
Error Control (n-k)
PT
PI
Pwakeup
EN
Pi
pkt
L
Pkt_BER
h
Nch
tcs
Pwakeup
PI
R
Physical Layer
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Network Traffic Model

• Poisson process model
• TN is the average number of packets per cycle for
  every destination
• Retransmissions are also Poisson distributed
• Valid if the time between retransmissions is
  large and random
• Network model has impact on collision rate
  evaluation
• We are working on creating more realistic network
  models

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MAC Model
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The Link Layer Model
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Error Control and Power Control Models
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Power Management Models
PT
TN
NN
PI
Power Management
Pwakeup
PTX
PRX
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Power Management Models
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PHY model

• TX section
• Power amplifier
• Oscillator
• RX section
• Low noise amplifier
• Envelope detector power gain
• Three modes
• Channel monitoring
• Acquisition
• Receive
• Digital protocol processor

e.g. 3mW(110)/21.15mW
e.g. hPA40
e.g. 0.5mW
e.g. 1.2mW
e.g. 20us
Time needed
e.g. 250uW
e.g. 0.5mW
Impact of the data rate is being modeled
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Channel Models
Independent channel model
For the same average BER, this model results in
higher packet error rate than bursty channel
models
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A Fixed Point Problem
When we put the models together, we get stuck
in a close loop.
f1
Simplified view
pkt
EN
Link
f2
C gt 0
MAC
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Ordered Set

• pkt belongs to 0,1
• This is a real valued closed set
• It is a fully ordered set (algebraic ordering)
  with bottom 0 and top 1.
• It is also a complete ordered set (CPO) since
  every chain Y in it has lowest upper bound V(Y).
• Every non-decreasing sequence xnin 0,1 is
  bounded, so it has limit x in 0,1.
  Additionally, x is its lowest upper bound.

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Function

• f is monotonic
• If x1ltx2, f(x1)ltf(x2)
• f is continuous
• For every chain Y in 0,1, V(f(Y))f(V(Y))
• f is continuous gt

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Banachs Fixed Point Theorem

• If X is a CPO with bottom , and f X-gtX is
  continuous,
• Then f has a least fixed point x and we can find
  x constructively by finding the lowest upper
  bound of the chain
• , f(), f(f(), ..

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Energy Design Metric
Average energy per bit per node
EM is average energy spent on maintenance per
cycle PT/PI is TX/RX power TN is average number
of packets per cycle per node from network NN is
the number of neighborsR is radio data rate
LN/LOH is the length of info/OH bits N is number
of transmissions ti is the node idle time. e.g.
receiver duty cycle when no packet has arrived or
time in carrier sensing.
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Other Design Metrics
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Parameters Used
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Design Metrics
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Design Metrics
Average Power
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Impact of the External Parameters

• Help designers of other layers to understand
• the energy cost of the data link layer
• Enable higher level optimization

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Impact of the External Parameters
Number of Channels
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Impact of the Internal Parameters
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Impact of the Internal Parameters
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Verifying the Models

• Compare with simulation to see the effect of
  inaccurate modeling in the following areas
• Retransmission traffic not Poisson distributed
• Channel not independent between packets
• Interaction between retransmissions and collision
  rate
• Timing issues not considered in the modeling so
  far

Some design metrics are less sensitive to these
inaccuracies than the others.
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Simulation Setup

• OMNET
• 24 nodes
• 2 channels
• 1 hour
• network time
• No any of the
• previous
• assumptions
• CSMA
• Gilbert channel

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Comparison Results
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IEEE802.11 results
Can we handle more complicated designs?
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Conclusion

• Models are built for commonly used MAC/link
  designs
• Fixed point theorem is used to solve the problem
  involved
• Simulations verify the models
• We provided component based models with clean
  interface
• For given constraints and design combinations, we
  can bring individual components together to
  quantify the design metrics of the data link
  layer.

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Publications

• L. C. Zhong and J. M. Rabaey, "Modeling and
  Analysis of the Data Link Layer in Wireless
  Sensor Networks", Submitted to SNPA and ICC2003,
  Anchorage, AK, USA, May 11, 2003.
• M. Kubisch, H. Karl, A. Wolisz, L. C. Zhong and
  J. M. Rabaey,"Distributed algorithms for
  transmission power control in wireless sensor
  neworks" Accepted by IEEE WCNC 2003, New Orleans,
  Lousiana, March 16-20 2003. 
• C. Guo, L. C. Zhong and J. M. Rabaey, "Low Power
  Distributed MAC for Ad Hoc Sensor Radio
  Networks", Proceedings of IEEE GlobeCom 2001, San
  Antonio, November 25-29, 2001
• L. Zhong, J. Rabaey, C. Guo and R. Shah, "Data
  Link Layer Design for Wireless Sensor Networks",
  Proceedings of IEEE MILCOM 2001, vol.1, p. 352-6,
  October 2001.
• L. Zhong, R. Shah, C. Guo and J. Rabaey, "An
  ultra-low power and distributed access protocol
  for broadband wireless sensor networks",
  NetworldInterop IEEE Broadband Wireless Summit,
  Las Vegas, May 2001.

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Ongoing Work

• Study impact of more parameters (Feb. 03)
• Consider other power control and error control
  designs (May 03)
• Evaluate the impact from different network and
  channel models (May 03)
• Export these models to other designers in pico
  radio project to improve their designs in the
  network and physical layers (Jan. 03)

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Potential Routes to Follow
How do I bring my research to the next level?
Optimal parameter value
Design evaluation

• A fixed design
• Fixed external
• parameters values

• Several fixed designs
• Fixed external
• parameters values
• Best combination

Fundamental limit

• Find a fundamental limit independent of
  design
• For given Qos and external parameters values
• What is the lowest energy consumption for any
  design?

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Some Thoughts
1)
or
2) Shannon limit
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Timeline

• Modeling and Analysis May 03
• Optimization September 03
• Thesis Sep. 03 to May 04
• Graduation May 04

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Summary

• I built models for each component in the data
  link layer
• I used fixed point theorem to solve the close
  loop problem when putting these models together
• I used these models to get insight to the
  important design metrics and impact of design
  parameters on them
• My research results are very useful to designers
  in the data link layer as well as other layers
• I introduced a new methodology for design
  evaluation
• Future research can bring even more exciting
  results