Connectivity of
Wireless Ad hoc Networks
Dr. Salman Durrani
School of Engineering,
College of Engineering and Computer Science,
The Australian National University,
Canberra, Australia.
http://engnet.anu.edu.au/DEpeople/Salman.Durrani/
Dec. 2009
1
Overview
• Introduction
• Research Trends in Wireless Communications
• Open research problems in ad hoc networks
• Connectivity Analysis
• Antenna & System Model
• Analytical framework
• Results & Conclusions
2
Canberra
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ASP Academics
• 8 Academics + 4 NICTA Adjuncts
4
ASP Research Group
•
The Applied Signal Processing Group conducts research
in the following application areas:
1. Physical layer Communications (12 PhD
students)
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Telecommunications including Wireless and Mobile
Communications
Space-Time Signal Processing
2. Signal Processing (9 PhD students)
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•
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Acoustic and Audio Signal Processing
Broadband and Near-field Sensor Arrays and Beamforming
Bio-Signal Processing
3. Applied Information Theory (2 PhD students)
5
My PhD Students
• Xiangyun Zhou (EIPRS Scholarship),
Channel estimation in cellular &
ad hoc networks. (Jan 2008present)
• Ali Nasir (ANU International PhD
Scholarship), Synchronization in
co-operative communication
systems. (June 2009-present)
• Zubair Khalid (EIPRS Scholarship) &
Rimla Javaid (ANU PhD Scholarship),
commencing 2010.
6
Research Trends
• IEEE ICC 2009 in Dresden, Germany:• 3600 paper submissions
• 1046 accepted papers after peer review (29%)
• Selected papers presented in oral sessions.
• On average, 5 to 6 papers being presented in every
session.
• We looked at the number of oral sessions presented for
different research topics in GlobeCom and ICC for last
3 years.
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Research Trends
Source: Internal report by PhD student Ali Nasir.
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Research Trends
• Research topics in steady state or decline ?
Source: Internal report by PhD student Ali Nasir.
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Research Trends
• Research topics in steady state or decline ?
Source: Internal report by PhD student Ali Nasir.
10
Research Trends
• Other Research Topics
Source: Internal report by PhD student Ali Nasir.
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Research Trends: Ad Hoc Networks
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Basic Principles of an Ad hoc Network
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•
•
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Formed by wireless nodes which may be mobile.
No need (necessarily) for any pre-existing infrastructure.
Decentralized operation.
Multi-hop communication.


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Applications: Sensor Networks
• Networks of typically small, battery-powered, wireless
devices .
• Wide range of applications:•
•
•
•
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Environmental monitoring,
Military surveillance
Medical care
Home appliance management
Industrial monitoring
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Applications: VANETS
• Vehicular Ad Hoc Networks comprise vehicle-tovehicle and vehicle-to-infrastructure communications
based on WLAN technologies. (IEEE P1609 WAVE
Standards)
Figure from Lin et. al,
IEEE Comm. Mag, April 2008.
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Applications: Telecomms Networks
Ad hoc
Networking
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Research Challenges in Ad hoc
Networks
• Capacity
• What are the fundamental performance limits (in terms
of reliable data rate) for ad hoc networks?
• Routing
• How do you efficiently select paths in a network along
which to send information?
• Connectivity
• If you select any pair of nodes in an ad hoc network,
what is the probability they connected?
• Co-operation
• 3 node Source, Relay, Destination scenario.
Synchronization
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Connectivity Definitions
• Connectivity from view-point of a single node:• Average Node Degree: Average no. of direct links
that any given node has to other nodes.
• Probability of node isolation: Probability that a
randomly selected node in an ad hoc network has no
connections to any other node.
Average Node degree = 1.8
2
1
1
3
3
2
1
3
2
0
Isolated node
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Connectivity Definitions
• Connectivity from view-point of an entire network:• 1- connectivity: Probability that every node pair in the
network has at least one path connecting them.
• Critical Node density: Node density that yields an
almost surely connected network [P (1-con)=0.99].
• Path Probability: Probability that two randomly
chosen nodes are connected either via a single hop or a
multi-hop path.
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Research Challenges in Modelling
Ad hoc network Connectivity
• Mobility
• Dynamic network topology
• Realistic models for mobility
• Node distribution
• Uniform
• Clustered
• Channel
• Wireless links subject to shadowing and fading
• Interference from simultaneous transmissions elsewhere
• Multiple Antennas
• Adopted in 3GPP (Release 6), IEEE802.11n, IEEE802.20
• How does beamforming affect the connectivity of ad hoc
networks?
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Prior Work
• Closed-form analytical results for connectivity are
available for special case of:• Node locations are Poisson,
• Negligible interference,
• No mobility,
• Channel: Path loss & Shadowing,
• Omni-directional antennas
• Open Research Problem:
21
Overview
• Introduction
• Research Trends in Wireless Communications
• Open research problems in ad hoc networks
• Connectivity Analysis
• Antenna & System Model
• Analytical framework
• Results & Conclusions
22
System Model
• Nodes are distributed in 2D according to Poisson point
process.
• All nodes are equipped with beamforming antennas.
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Antenna Model
• Antenna Model is characterized by associated
antenna power pattern.
• Uniform Linear Array or Uniform Circular Array ?
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Power Pattern Demo (N=8)
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Antenna Model
• UCA configuration is chosen:• It has single main lobe.
• 3 dB beamwidth is constant & independent of main beam
direction.
• For UCA, the directivity G is given by
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Random Beamforming
• Core Idea: Each node randomly selects a main beam
direction without co-ordination with other nodes.
• Advantage:• MAC is un-coordinated.
• Minimal communication overhead and hardware
complexity.
• Disadvantage:• May not be optimal strategy
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Channel Model
• Received Signal Power
Shadowing
Beamforming
Path Loss
• Shadowing affects only the randomness and not the
average value of the channel gain.
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Communication Range
• Two nodes can communicate with each other if their
distance apart is smaller than a given communication
range R.
R
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Effective Coverage Area
• With beamforming, the communication range is
Random variable
• Effective coverage area is
Shadowing factor
Beamforming factor
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Effect of Shadowing
• Shadowing factor:
• Depends on:• path loss a and
• Shadowing log-normal standard deviation s
• Key Insight:- Shadowing reduces the effective
coverage area (for a > 2).
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Effect of Shadowing
shadowing factor
1
0.8
0.6
0.4
2
s=4
s=8
s = 12
3
4
a
5
6
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Effect of Beamforming
• Beamforming factor:
®
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Effect of Beamforming
• Beamforming factor:
• Depends on
• path loss a
• Number of antenna elements in the UCA M
• Does not depend on
• Shadowing log-normal standard deviation s
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Effect of Beamforming
• Beamforming factor values:
• Key Insight:- For a<3, random beamforming
increases the effective coverage area.
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Overview
• Introduction
• Research Trends in Wireless Communications
• Open research problems in ad hoc networks
• Connectivity Analysis
• Antenna & System Model
• Analytical framework
•
Results
• Average Node degree
• Probability of node isolation
• 1-connectivity
• Critical node density
• Path probability
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Conclusions
36
Connectivity Metrics - P(iso)
• Probability of node isolation
Effective coverage Area
• Main Result:• shadowing always increases the probability of node
isolation.
• beamforming, compared to omnidirectional antennas,
reduces the probability of node isolation when a<3.
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Connectivity Metrics - P(iso)
• Verification (effect of shadowing, M=1):Probability of node isolation P(iso)
1
0.8
a=4
a=3
0.6
a = 2.5
0.4
0.2
0 -6
10
s=8, analytical
s=4, analytical
s=0, analytical
s=8, simulation
s=4, simulation
s=0, simulation
10
-5
-4
10
Node density, m-2
10
-3
10
-2
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Connectivity Metrics - P(iso)
• Verification (effect of beamforming, M=1,4 & s = 4 dB):Probability of node isolation P(iso)
1
0.8
a=4
a=3
a = 2.5
0.6
0.4
0.2
0 -6
10
RB, analytical
omni, analytical
RB, simulation
omni, simulation
10
-5
-4
10
10
Node density, m-2
-3
10
-2
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Connectivity Metrics - rc
• Critical node density: node density that yields an
almost surely connected network, that is, the density
at which P (1-con) = 0.99.
• Main Result:• shadowing increases the critical node density.
• rc can be reduced by using beamforming when a<3.
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Connectivity Metrics - rc
• Effect of shadowing
• No of antennas M=1
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Connectivity Metrics - rc
• Effect of beamforming
• No of antennas M=1,4
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Conclusions
• We have presented an analytical model to characterize
the effect of random beamforming on the network
connectivity.
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Publications
• X. Zhou, S. Durrani and H. Jones, "Connectivity
Analysis of Wireless Ad Hoc networks with
Beamforming," IEEE Transactions on Vehicular
Technology, vol. 58, no. 9, pp. 5247-5257, Nov. 2009.
• S. Durrani, X. Zhou and H. Jones, "Connectivity of
Wireless Ad Hoc Networks with Random Beamforming:
An Analytical Approach," Proc. IEEE PIMRC, Cannes,
France, Sep. 15-18, 2008.
• Paper PDFs available at:http://engnet.anu.edu.au/DEpeople/Salman.Durrani/papers.html
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Thank you for your attention
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