End-to-End Channel Capacity Of A Wireless Sensor Network Under Reachback

1
End-to-End Channel Capacity Of A Wireless Sensor
Network Under Reachback

• Presented by Shirish Karande _at_ CISS 2006,
  Princeton, NJ
• For
• Muhammad U. Ilyas Hayder Radha

2
Objectives

• To determine an expression for the end-to-end
  channel capacity between a sensor and the base
  station of a 2-level hierarchy, Wireless Sensor
  Network employing Slepian-Wolf coding.
• To determine the effects of cluster sizes on
  end-to-end capacity.

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Outline

• Network Model
• Wireless Networking Standards for WSNs
• End-to-End Channel
• Notation
• Cluster Communication Capacity
• Overlay Network Communication Capacity
• End-to-End Capacity
• Results

4
Tesselated Wireless Sensor Networks

• Gupta Kumar studied the scalability of a
  wireless networks with randomly chosen source
  destination pairs.
• They offer two solutions
• Design smaller networks
• Localize communication by clustering nodes.
• Assumptions
• Network has a 2-level hierarchy.
• (Intra-)cluster communication between nodes and
  clusterhead (CLH) is 1-hop and proceeds at one
  frequency.
• Different clusters may or may not use different
  frequencies.
• ON communication proceeds at one frequency.

__________________________________________________
________________ P. Gupta, and P. R. Kumar,
The Capacity of Wireless Networks, IEEE
Transactions on Information Theory, Vol. 46, No.
2, March 2000.
5
Cluster Communication

• Slepian-Wolf Coding for WSNs
• Basic Idea
• Sensors transmit readings to CLH one after the
  other.
• Successive transmissions in a round will take
  fewer bits (figure).
• Total number of bits transmitted will approach
  joint entropy.
• Assumption
• Loss of the k-th transmission causes inability of
  receiver to reconstruct all following
  transmissions k1 to n.
• MAC protocol may be CSMA-CA or TDMA
• __________________________________________________
  _
• D. Marco, and D. L. Neuhoff, Reliability vs.
  Efficiency in Distributed Source Coding for
  Field-Gathering Sensor Networks, IEEE
  International Conference on Information
  Processing in Sensor Networks (IPSN04),
  Berkeley, CA, 2004.

6
Overlay Network Communication

• In the Overlay Network (ON), communication
  between CLHs and the BS proceeds over multihop
  routes (figure).
• We are assuming use of a shortest path routing
  protocol that subsequently results a tree
  topology for the routes to BS (figure).
• Transmissions in the ON are on one frequency,
  i.e.
• Higher traffic volume near the base station gives
  rise to the reachback problem.
• MAC protocol may be CSMA-CA or TDMA

__________________________________________________
________________ J. Barros, S. D. Servetto, On
the Capacity of the Reachback Channel in Wireless
Sensor Networks, IEEE Workshop on Multimedia
Signal Processing, December 2002.
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IEEE 802 LAN/MAN Standards Committee
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Wireless Networking Standards
802.15.4 802.11b Bluetooth
Frequencies 868 - 868.6 MHz 902 - 928 MHz 2.4 - 2.4835 GHz 2.4 - 2.4835 GHz 2.4 -2.4835 GHz
MAC type 1.TDMA in beacon- mode 2. CSMA/CA in beaconless-mode 1.CSMA/CA in DCF 2. Polling in PCF Polling
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End-to-End Channel Model
Bit Error Rate Packet Error Rate (end-to-end)
Bit Error Rate Packet Error Rate (1 hop)
Bit Error Rate
Pathloss Model
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Notation

• Is the total number of sensors.
• Is the total number of clusters.
• Is the number of sensors in cluster i.
• Is the i-th clusters j-th node.
• Is the clusterhead (CLH) of cluster i.
• Is the frequency used for cluster
• communication in the i-th cluster.

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Notation
Is a function returning the spatial distance
between i-th clusters j-th node and k-th
clusters l-th node. Is the probability of nk(l)
transmitting at the same time as ni(j) Is a
function that returns the frequency at which
the node provided as argument is communicating.

• Is the indicator function returning
• 1 when the two nodes in the argument are
  communicating at the same frequency and there is
  a potential for interference.
• 0 when the two nodes in the argument are
  communicating at different frequencies and there
  is NO potential for interference.

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Cluster Communication Channel Capacity
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Pathloss Model

• We are considering the pathloss (PL) model in the
  IEEE 802.15.4a Channel Model - final report
  published by the IEEE 802.15.4a channel modeling
  subgroup that was subsequently adopted for all
  further work on this standard.
• Separate channel models for
• 100-900 MHz (indoor office)
• 1000 MHz (narrowband)
• 2 6 GHz (short range Body Area Networks)
• 2 10 GHz (indoor residential, indoor office,
  industrial, outdoor, open outdoor)
• All 3 wireless networking standards being
  considered fall in the 2.4 2.4835 GHz freq
  range.
• Most envisioned WSN applications are expected to
  operate in environments considered for 2 10 GHz
  PL model.
• __________________________________________________
  _______
• Andreas F. Molisch, Kannan Balakrishnan,
  Chia-Chin Chong, Shahriar Emami, Andrew Fort,
  Johan Karedal, Juergen Kunisch, Hans Schantz,
  Ulrich Schuster, Kai Siwiak, IEEE 802.15.4a
  channel model - final report, 2004.

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2 10 GHz Pathloss Model

• Provides the received signal power at the i-th
  clusters j-th node of a transmission from the
  k-th clusters l-th node

is the transmitter signal power after
amplification is the transmitter antenna
efficiency is the receiver antenna efficiency
These are assumed constant for all nodes in a
WSN of homogeneous devices.
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Pathloss Model

• The pathloss model is accompanied with sets of
  values for its environmental parameters for the
  different environments mentioned previously.
• However, some reference parameters remain
  constant across all environments, these are
• Reference frequency
• Reference distance
• Based on these parameters we can determine the
  different remaining model paramters

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Physical Layer Model

• For the Physical Layer Channel Model we assume an
  Additive White Gaussian Noise (AWGN) channel that
  is characterized by the Signal-to-Interference
  Noise-Ratio (SINR) at the receiver.

is the ambient noise power due to co-located
communication networks operating in
same frequency spectrum, or devices (e.g.
microwave ovens). Is the signal power of the
transmitted signal at the receiver Is the signal
power of interfering nodes at the receiver
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Physical Layer Model

• To obtain the SINR of the signal transmitted by
  the i-th clusters j-th node at its CLH (i.e. CLH
  of cluster i), we substitute the pathloss model
  in the power terms of the SINR equation.

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Physical Layer Model

• If,

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Bit Error Rate

• Next, from our knowledge of a Physical Layer
  model we compute a Bit Error Rate (BER). We use
  the Lognormal Shadow Fading Model.
• If,
• Then,
  
• ______________________________________________
• T.S. Rappaport, Wireless Communications
  Principles and Practice, 2nd ed, Pearson
  Education, Singapore, 2002.

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Packet Error Rate

• Recall Failure of ni(0) to receive k-th
  transmission from a sensor in a round results in
  an inability to reconstruct/ a complete loss of
  all subsequent transmissions k1 to Ni.
• Hence,
• 
  
• Is the number of header bits.
• _______________________________________________

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Overlay Network Communication Channel Capacity
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Options in Overlay Network

• We are considering two options for the way CLHs
  communicate their packets to the Base Station.
• Option 1 No recoding, simple forwarding of
  downstream packets and transmission of own
  packets.
• Option 2 Additional compression of own packet
  based on received downstream packets.
• ________________________________________
• Downstream farther away from base station
• Upstream closer to base station

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Pathloss Model (ON)

• Remains similar to the one derived for the
  cluster-level communication,
• Is a function that returns the upstream
  neighbor of ni(0).
• Is a function that returns the set of all
  downstream neighbors of ni(0).
• If,

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1-Hop Bit Error Rate (ON)

• Similar to cluster-level BER model, the BER of
  the channel between ni(0) and its upstream
  neighbor is,

• The expressions obtained up to this point hold
  true for ONs irrespective of whether or not CLHs
  are doing Slepian-Wolf recoding on their own
  packets based on packets received from downstream
  CLHs.

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CLH-to-Base Station Bit Error Rate

• The BER of the channel formed between a CLH and
  the base station can be treated as a cascade of
  BSCs.
• The BER is defined by a recursive expression
  which models the channel as two BSCs (i) a BSC
  between the CLH and its upstream neighbor, and
  (ii) another BSC between the upstream neighbor
  and the Base station.

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1-Hop Packet Error Rate

• Is the packet error rate for the link between
  nk(0) and
• R1?(nk(0) for a packet originated at ni(0).

For an ON without Slepian-Wolf coding.
For an ON with Slepian-Wolf coding.
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CLH-to-Base Station Packet Error Rate

• Is the end-to-end packet error model for the
  channel between CLH
• ni(0) and the base station.
• Is a function that returns the set of all
  downstream neighbors of ni(0).
• 
  
  
  

__________________________________________________
_________________________
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Sensor-to-Base Station Channel Capacity
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Sensor-to-Base Station/ End-to-End BER PER

• Is the packet error rate for the channel from
  ni(j) to ni(0) to base station.
• 
  
• Is the packet error rate for the channel from
  ni(j) to ni(0) to base station.
• 
  
  
  
• 
  

__________________________________________________
_______________________
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Results

• Physical layout and routing topology of a
  wireless sensor network consisting of 50 sensors
  in a square shaped plane of size 10 x 10.
• Configured with 5 CLHs.
• Base station is located at coordintate (0,0).
• We assume an IEEE 802.15.4 frame structure.

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End-to-End Channel Capacity and Probability
Figure 1 - Bit and packet error probability of
the end-to-end channel. Figure 2 Bit and
packet level capacity of the end-to-end channel.
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Effect of Clustering on Capacity
Figure 1 - Bit and packet error probability of
the end-to-end channel with varying number of
clusterheads. Figure 2 - Bit and packet level
capacity of the end-to-end channel with varying
number of clusterheads.
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Thank You!

• ???

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References

• P. Gupta, and P. R. Kumar, The Capacity of
  Wireless Networks, IEEE Transactions on
  Information Theory, Vol. 46, No. 2, March 2000.
• J. Barros, S. D. Servetto, On the Capacity of
  the Reachback Channel in Wireless Sensor
  Networks, IEEE Workshop on Multimedia Signal
  Processing, December 2002.
• IEEE P802.15.4/D18, Draft Standard Low Rate
  Wireless Personal Area Networks, February 2003.
• Soo Young Shin, Hong Seong Park, Sunhyun Choi,
  Wook Hyun Kwon, "Packet Error Rate Analysis of
  IEEE 802.15.4 under IEEE 802.11b Interference,"
  3rd International Conference on Wired/ Wireless
  Internet Communications 2005 (WWIC'05), Xanthi,
  Greece, May 11-13, 2005.
• Andreas F. Molisch, Kannan Balakrishnan,
  Chia-Chin Chong, Shahriar Emami, Andrew Fort,
  Johan Karedal, Juergen Kunisch, Hans Schantz,
  Ulrich Schuster, Kai Siwiak, IEEE 802.15.4a
  channel model - final report, 2004.
• D. Marco, and D. L. Neuhoff, Reliability vs.
  Efficiency in Distributed Source Coding for
  Field-Gathering Sensor Networks, IEEE
  International Conference on Information
  Processing in Sensor Networks (IPSN04),
  Berkeley, CA, 2004.
• T.S. Rappaport, Wireless Communications
  Principles and Practice, 2nd ed, Pearson
  Education, Singapore, 2002.