Mobility Increases the Capacity of Adhoc Wireless Networks

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Mobility Increases the Capacity of Ad-hoc
Wireless Networks

• InfoCom 2001
• Matthias Grossglauser
• ATT Labs-Research
• David Tse
• Department of EECS University of California
  Berkeley CA

Chun-Ta, Yu Graduate Institute Information
Management Dept. National Taiwan University
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Outline

• Introduction
• Model
• Result
• Fixed Nodes
• Mobile Nodes Without Relaying
• Mobile Nodes With Relaying
• Conclusion

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Introduction

• The capacity of ad-hoc wireless networks is
  constrained by the mutual interference of
  concurrent transmission between nodes
• A fundamental characteristic of mobile wireless
  networks is the time variation of the channel
  strength of the underlying communication links

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Introduction (cont.)

• DiversityTo improve performance by having
  several independent signal paths between the
  transmitter and the receiver
• Time (interleaving of coded bits) TDM
• Frequency (combining of multipaths in CDMA
  system) FDM
• Space (multiple antennas)
• Multiuser diversity Knopp and Humblet
• Schedule at any one time only the user with the
  best channel to the basestation

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Introduction (cont.)

• Long-range direct communication limitation comes
  from excessive interference caused
• Traditional fixed node communication through
  relays,most communication occurs between nearest
  neighbor at distance of order
• Fixed ad-hoc throughput per S-D pair decreases
  approximately like , n is node numbers
• n?8, ? 0

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Introduction (cont.)

• Mobility Model show that the average long-term
  throughput per S-D pair can be kept constant even
  as the number of nodes per unit area n increases
• Disadvantage although long-term throughput is
  averaged over the time-scale of node
  mobility,delays of that order will be incurred

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Mobility Model

• To overcome the performance limitation
• First solution To transmit only when the source
  and destination nodes are close together at
  distances of order
• however,the fraction of time two nodes are
  nearest neighbors is too small,of the order
• Improved solution
• Each source node to distribute its packets to as
  many different nodes as possible
• These nodes then serve as mobile relay node and
  whenever they get close to the destination,they
  hand the packet off to the final destination
• Each packet goes through at most one relay node

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Mobility Model (cont.)

• Advantage
• There are many different relay node,the
  probability that at least one is close to the
  destination is significant
• Each packet go through at most one relays
  node,hence the throughput can be kept high
• Disadvantage
• Delay increase
• Unexpected receiving time

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SIR Inequalities

• is the transmit power of node i
• is the channel gain from node i
  to node j
• is the signal-to-interference ratio
  (SIR) requirement for successful
  communication
• is the background noise power
• is the processing gain of the system

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Channel Gain

• is node is position at time
• is a parameter greater than 2

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Models

• Fixed Nodes Model
• Mobile Nodes Without Relaying Model
• Mobile Nodes With Relaying Model

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Fixed Nodes Model

• Theorem 3.1 (by Gupta and Kumar)
• There exists constants c and c such that
• is a long term throughput

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Mobile Nodes Without Relaying Model

• Only letting source transmit directly to
  destinations
• Improve the capacity by not relaying at all
• Per O-D pair throughput can not achieve to O(1)

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Lemma 3.2 implication

• Lemma 3.2 shows that the number of simultaneous
  long-range communication is limited by
  interference
• Since the distance between the source and
  destination is O(1) most of the time,this
  limitation in turn puts a bound on the
  performance of any strategy which uses only
  direct communication

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Theorem 3.3 implication

• Theorem 3.3 says that without relaying,the
  achievable throughput per S-D pair goes to zero
  at least as fast as
• Thus,throughput can achieve O(1)

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Theorem 3.3 Proof
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Theorem 3.3 Proof (cont.)
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Theorem 3.3 Proof (cont.)
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Theorem 3.3 Proof (cont.)
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Theorem 3.3 Proof (cont.)
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Theorem 3.3 Proof (cont.)
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Mobile Nodes With Relaying Model

• Why a packet only need one times to be relayed?
• Node location process are independent
• The Probability for an arbitrary node to be
  scheduled to receive a packet from a source S is
  equal for all nodes and independent of S
• As no packet is transmitted more than twice,the
  achievable total throughput is O(n)

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• Where is a sender-receiver pair which the
  interference generated by the other senders is
  sufficiently small that transmission is possible

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Theorem 3.4 Proof

• Definition
• is the random positions of the
  senders in S
• is the positions of nodes in the
  receiver set R
• is the received power from sender node I at
  receiver node r(1)

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Theorem 3.4 Proof (cont.)

• The total interference at node r(1) is given by
• The SIR for the transmission from sender 1 at
  receiver r(1) is given by

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Theorem 3.4 Proof (cont.)

• When n ?8
• ,
• Condition on for some u in the open
  disk

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Theorem 3.4 Proof (cont.)

• Condition on ,the random variable
  are i.i.d.
• By standard result on the asymptotic distribution
  of extremum of i.i.d. random variable,the
  extremum of i.i.d. random
  variables whose cdf

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Theorem 3.4 Proof (cont.)

• Where is given by
  
• The asymptotic distribution of
  conditional on depends only on the
  tail of the distribution of the and is given
  by

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Theorem 3.4 Proof (cont.)
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Theorem 3.4 Proof (cont.)

• Conditional on and ,as
  the asymptotic distribution of
  conditional on ,we have

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Theorem 3.4 Proof (cont.)

• Combine this last fact with (11) and (12),we get
  the result on the probability of successful
  transmission from node 1 to node r(1)

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Theorem 3.4 Proof (cont.)

• The expected number of feasible sender-receiver
  pairs is
• Proof complete

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Two Phase Scheme

• Phase 1 scheduling of packet transmissions from
  sources to relays (or the final destination)
• Phase 2 scheduling of packet transmissions from
  relays (or the source) to final destination
• 2 phase are interleaved in the even
  time-slots,phase 1 is run in the odd
  time-slots,phase 2 is run

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• The largest possible throughput is c

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Theorem 3.5 Proof

• Policy only depends on node locations and
  node locations are i.i.d.
• Long-term throughput between any two nodes is
  equal to the probability that these two nodes are
  selected by
• According to Theorem 3.4,this probability is O(1
  / n)

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Theorem 3.5 Proof (cont.)

• For a given S-D pair,there is one direct route
  and n-2 two-hop routes which go through one relay
  node R
• The throughput over the direct route is O(1/n)
• For each two-hop route,we can consider the relay
  node R as a single server queue,arrival rate and
  service rate is the same,O(1/n) by Theorem 3.4
• Sum over the throughputs of all the n-1 nodes,it
  imply that the total average throughput per S-D
  pair is O(1)

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Numerical Result

• N 1000,? 0.41,Simulation

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Throughput Simulation
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Conclusion

• Results show that direct communication between
  sources and destinations is not sufficient to
  exploit this diversity,because they are too far
  apart most of time
• Throughput of single relay node is O(1),better
  than fixed node with O( ) relay node

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Conclusion (cont.)

• In practice,every node can get close to any
  other node may not hold,or the delay to wait for
  such events to happen may be too long
• The result in this paper may used in
  delay-insensitive data application,e.g. email
  and database synchronization