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ICOM 6505: Wireless Networks Wireless Ad Hoc Networks

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Wireless Ad Hoc Networks - By Dr. Kejie Lu. Department of Electronic and Computer Engineering ... The performance of wireless ad hoc networks is very difficult ... – PowerPoint PPT presentation

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Title: ICOM 6505: Wireless Networks Wireless Ad Hoc Networks


1
ICOM 6505 Wireless Networks- Wireless Ad Hoc
Networks -
  • By Dr. Kejie Lu
  • Department of Electronic and Computer Engineering
  • Spring 2008

2
Outline
  • Capacity analysis

3
References
  • 1 P. Gupta and P. R. Kumar, The capacity of
    wireless networks, IEEE Transaction on
    Information Theory, vol. 46, No. 2, pp. 388-404,
    2000
  • 2 M. Franceschetti, O. Dousse, D. Tse, and P.
    Thiran, Closing the gap in the capacity of
    wireless networks via percolation theory, IEEE
    Transaction on Information Theory, Vol. 53, No.
    3, pp. 1009-1018, 2007
  • 3 J. Liu, D. Goeckel, and D. Towsley, Bounds
    on the gain of network coding and broadcasting in
    wireless networks, in Proc. IEEE Infocom, 2007
  • 4 Kejie Lu, Shengli Fu, and Yi Qian, "Capacity
    of Random Wireless Networks Impact of
    Physical-layer Network Coding," to appear, IEEE
    ICC 2008, Beijing, China, May 2008

4
Motivation
  • The performance of wireless ad hoc networks is
    very difficult to analyze
  • Layers
  • Physical
  • Antenna
  • Interference
  • MAC
  • Scheduling
  • Network
  • Topology control
  • Routing
  • Transport
  • Others
  • Traffic pattern
  • Infrastructure
  • Mobility
  • Etc.

5
Performance Metrics
  • Throughput capacity
  • The total data rate that can be supported
  • Distance may also be considered
  • Delay

6
Notations
  • Big O
  • Used mainly in two areas
  • In mathematics for asymptotic behavior
  • We will use this in the capacity analysis
  • In computer science for computational complexity
  • Definition
  • f(x) O(g(x)) when x tends to infinity if and
    only if
  • There exist x0gt0 and Mgt0 such that
  • f(x) lt Mg(x) for xgt x0
  • Example
  • 3x3-6x29x O(x3)

7
Notations
  • f(x) O(g(x))
  • g(x) is the asymptotic upper bound of f(x)
  • f(x) ?(g(x))
  • g(x) is the asymptotic lower bound of f(x)
  • f(x) ?(g(x))
  • g(x) is the asymptotic tight bound of f(x)

8
Network Model
  • Scaling scenario
  • Model 1 (Dense network) n nodes are located in a
    unit area and n goes to infinity
  • Model 2 (Extended network) The density of nodes
    is fixed but the area of network goes to infinity
  • Randomness scenario
  • Arbitrary network the placement of nodes and the
    traffic pattern can be determined
  • Random network nodes are randomly located and
    the traffic pattern is random

9
Network Model
  • Dimension
  • Two-dimension
  • The most common one
  • One-dimension
  • In 3 and 4
  • Three-dimension
  • In 3

10
Transmission Model
  • Protocol model
  • Suppose Xi is the location of node i
  • Each node transmit with fixed rate W
  • At a certain time epoch, node i is transmitting
    to node j
  • For arbitrary network, the location of all
    transmitting nodes shall be
  • For random network, the location of transmitting
    nodes shall be

Impact of interference
Transmission range
11
Transmission Model
  • Physical model
  • Suppose Xi is the location of node i, Pi be the
    transmission power of node i
  • Let TXk be the set of nodes that are
    transmitting at a certain time epoch
  • Node i is transmitting to node j
  • The location of all transmitters shall be

12
Main Results Arbitrary Network
  • 2-D Arbitrary network
  • In 1, the authors proved that the capacity of
    arbitrary network scales with
  • In 2, the authors shown that the same bound is
    feasible for the physical model, with certain
    constraints

13
Main Results Random Network
  • 2-D random networks
  • In 1, the authors proved that the per node
    capacity for random wireless network is
  • However, the authors in 2 proved that the above
    bound is not correct and they shown that the
    bound is still

14
Main Results Network Coding
  • In 3, the authors considered the same scenarios
    used in 1-2, but they consider network coding
  • They proved that network coding does not change
    the scaling law
  • For 1-D network, they proved that the per node
    throughput is

15
Main Results Physical-Layer Network Coding
  • In our recent study 4, we prove that
    physical-layer network coding can improve the
    capacity of wireless network, but cannot change
    the scaling law
  • Specifically, we proved that, if ?lt2, then the
    per node throughput can be
  • The interesting point is that is the impact of
    interference is removed

16
Network Coding
Node
A
R
B
Wireless links
(b) Transmission Schedule
(a) Network Scenario
17
Proofs
  • 2-D arbitrary networks
  • 2-D random networks
  • 1-D random networks

18
Capacity of 2-D Arbitrary Networks
  • Upper bound
  • Protocol model
  • Physical model
  • Lower bound

19
Upper Bound for the Protocol Model
  • Suppose each node can send data to one
    destination at rate ?
  • The transmission data rate is Wgt ?
  • Then for a certain long duration T, we have
  • Total number of bits delivered is ?nT
  • Let b be a bit and its hop distance is h(b)
  • Because at each time instance there are at most
    n/2 transmissions, we have

20
Upper Bound for the Protocol Model
  • If L is the average distance between source and
    destination, we also have
  • Here r is the transmission distance

21
Upper Bound for the Protocol Model
  • Now consider the transmission distance
  • Below is a simple scenario, in which node i is
    transmitting to node j, while node k is
    transmitting to node j
  • According to the protocol model, we have

22
Upper Bound for the Protocol Model
  • Similarly, we have
  • Combining the above two inequalities, we have
  • But what does that mean?

23
Upper Bound for the Protocol Model
  • Answer for each transmission, there is a region,
    in which there are no other receivers

kl
kl?/2
24
Upper Bound for the Protocol Model
  • Remember we are considering a unit area, which
    means the summation of the area of each
    transmission at the same time shall be less than
    1
  • Taking into account the boundary effect, we have
  • Note that 1/W is the duration for transmitting
    one bit
  • Let 1/W be the duration of a slot, then we have
    WT slots

25
Upper Bound for the Protocol Model
  • The previous inequality can be rewritten as
  • Since function f(x)x2 is convex, we have
  • And then

For example, (a/2b/2)2 lt (a2b2)/2
26
Upper Bound for the Protocol Model
  • And finally,

27
Upper Bound for the Physical Model
28
Upper Bound for the Physical Model
  • Summing all transmitter-receiver pairs, we have
  • Summing for all bits, we have

29
Upper Bound for the Physical Model
  • If xgt0, x? is convex
  • So we can use the same technique to prove that

30
Upper Bound for the Physical Model
  • A special case, when is bounded
  • Consider again the following scenario
  • We have

31
Upper Bound for the Physical Model
  • Then we have
  • So the upper bound for the physical model is the
    same as the upper bound for the protocol model

32
Lower Bound for the Protocol Model
  • Constructive lower bound
  • Lattice

Transmitter
Receiver
r
2?r
33
Capacity of 2-D Random Networks
  • Communication range
  • Connectivity
  • Minimum cut

34
Communication Range
  • Protocol model
  • Range must be at least in the order of
    sqrt(logn/n) for the dense network
  • Physical model
  • Range can be in the order of sqrt(1/n) for the
    dense network

35
Minimum Cut
  • The upper bound of the cut capacity is
    proportional to W/r

36
Capacity of 1-D Networks
  • Main results
  • Traditional transmission scheme
  • Network coding scheme
  • Physical network coding scheme

37
Schedule for Network Coding
?2-
38
Schedule for Physical Layer Network Coding
?2-
39
Discussion
  • How can we improve the performance?
  • Existing approaches
  • Directional antenna
  • Hybrid network
  • Add base stations
  • Mobility
  • Not suitable for delay-required traffic
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