Wireless Networks using

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21 Νοε 2013 (πριν από 3 χρόνια και 6 μήνες)

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Special Topics on Algorithmic
Aspects of Wireless Networking

Donghyun

(David) Kim

Department of Mathematics and Computer Science

North Carolina Central University

1

Topology Abstraction of
Wireless Networks using
Physical Model

Department of Mathematics and Computer Science


North
Carolina Central
University

Donghyun

(David) Kim




September 23, 2011

(Ad
-
hoc) Wireless Networks


Instant deployment



No
wired backbone



No
centralized control



Nodes
may cooperate in routing each other’s data
packets

2

Department of Mathematics and Computer Science


North
Carolina Central
University

Donghyun

(David) Kim




September 23, 2011

Example: Wireless Sensor
Networks


Sensor Node Components


Sensor


Data Processor


Wireless Communication Module



Characteristics


Small Size


Low
-
cost


Low
-
Power


3

Department of Mathematics and Computer Science


North
Carolina Central
University

Donghyun

(David) Kim




September 23, 2011

Example: Wireless Sensor
Networks


cont


4

Wireless Multimedia Sensor Networks

(Image Source:
http://www2.ece.ohio
-
state.edu/~
ekici/res_wmsn.html
)

Department of Mathematics and Computer Science


North
Carolina Central
University

Donghyun

(David) Kim




September 23, 2011

Example: Wireless Sensor
Networks


cont


5

Volcano monitoring

(Image Source
:
http://
fiji.eecs.harvard.edu/Volcano
)

Department of Mathematics and Computer Science


North
Carolina Central
University

Donghyun

(David) Kim




September 23, 2011

Example: Ad
-
hoc Network

6

Vehicular Ad
-
hoc Networks

(Image
Source:
http://
monet.postech.ac.kr/research.html
)

Department of Mathematics and Computer Science


North
Carolina Central
University

Donghyun

(David) Kim




September 23, 2011

Example: Ad
-
hoc Network


cont


7

Military
Ad
-
hoc Network

(Image
Source:
http://
www.atacwireless.com/adhoc.html
)

Department of Mathematics and Computer Science


North
Carolina Central
University

Donghyun

(David) Kim




September 23, 2011

Research Issues


Network Layer


problems
are in routing, mobility of nodes
and power constraints


MAC layer


problems
with
wireless signal
interference and collision handling
protocols
such as TDMA, FDMA,CDMA


Physical layer


problems
in power
control



Convenient to have graph model for the
topology of a wireless network


8

Department of Mathematics and Computer Science


North
Carolina Central
University

Donghyun

(David) Kim




September 23, 2011

Arbitrary Networks


n

nodes are arbitrary
located



Each node has
a fixed communication power



When
does a transmission received
successfully?


Allowing
for two possible models for successful
reception over one hop: The
protocol model

and the
physical
model


9

Department of Mathematics and Computer Science


North
Carolina Central
University

Donghyun

(David) Kim




September 23, 2011

Unit Disk Graph (UDG)

10

Department of Mathematics and Computer Science


North
Carolina Central
University

Donghyun

(David) Kim




September 23, 2011

Unit Disk Graph


cont


11

Department of Mathematics and Computer Science


North
Carolina Central
University

Donghyun

(David) Kim




September 23, 2011

Protocol Model


Let
X
i

denote the location of a node


A transmission is successfully received by
X
j

if:



For every other node
X
k


simultaneously
transmitting



is
the guarding zone specified by the
protocol

12




X
X
Δ


X
X
j
i
j
k





1


r
Δ





1
r

j
x
i
x
k
X


r
Δ



1
l
X
Δ
r
Department of Mathematics and Computer Science


North
Carolina Central
University

Donghyun

(David) Kim




September 23, 2011

Physical
Model


cont



In radio communication, the power
p

to send a
message for a distance
l

can be simplified as



where


is a constant called
path
-
loss
exponent
, and is a constant called the
reference loss
factor
.



In other word, given a signal transmission power


at
the sender, the signal power at the receiver side is
proportional to

13



l
p


5
2




.
l
p
t

t
p
Department of Mathematics and Computer Science


North
Carolina Central
University

Donghyun

(David) Kim




September 23, 2011

Physical
Model


cont



Let


be
a subset of nodes simultaneously
transmitting


Let
P
k

be the power level chosen at node
X
k


Transmission from node
X
i
is
successfully received at
node
X
j

if
:









Also called
signal to interference and noise ratio (SINR)
model.

14



Τ
k
X
k

;
β
X
X
P
N
X
X
P
T
k
i
k
α
j
k
k
α
j
i
i







Department of Mathematics and Computer Science


North
Carolina Central
University

Donghyun

(David) Kim




September 23, 2011

Topology Control in UDG

(under Protocol Interference Model)


What is topology control
?


Given
node location, find a (static) communication graph
with desirable properties


Assume adjustable communication power



Idea: Drop links if
possible by adjusting communication
power


Goal: Reduces energy and
interference!

But
still stay connected and satisfies other properties:


Low node degree


Low static interference


Etc


15

Department of Mathematics and Computer Science


North
Carolina Central
University

Donghyun

(David) Kim




September 23, 2011

Topology Control in UDG


cont



It is a static
problem!


16

Topology

Control

Protocol

Department of Mathematics and Computer Science


North
Carolina Central
University

Donghyun

(David) Kim




September 23, 2011

Topology Control in SINR


A schedule
to
actually realize selected links
(transmission requests), to successfully transmit
message over them

17

Minimum signal
-
to
-
interference ratio

Power level of sender
u

Path
-
loss exponent

Noise

Distance between

two nodes

Received signal power from sender

Received signal power from

all other nodes (=interference)

Department of Mathematics and Computer Science


North
Carolina Central
University

Donghyun

(David) Kim




September 23, 2011

Cross Layer Aspects of Power
Control

18

Physical Layer

MAC Layer

Network Layer

Power Control

Incorporating
Physical Layer
Characteristics

Cross Layer Design

Effect of MAC
-
Layer
Interference

Dynamic Topology
Control w.r.t.
Network Traffic

Network
Capacity


Network
Lifetime


Critical
Power
Analysis

Physical Layer

Incorporating
Physical Layer
Characteristics

19

Topology Control for

Maximizing Network Capacity
Under the Physical Model

Ref
: Yan
Gao
, Jennifer C.
Hou
, and Hoang Nguyen,
“Topology
Control
for Maintaining Network Connectivity and Maximizing Network
Capacity under the Physical
Model,”
INFOCOM 2008
.

Department of Mathematics and Computer Science


North
Carolina Central
University

Donghyun

(David) Kim




September 23, 2011

Capacity of Wireless Network


Not well established concept, but there are several
commonly used definition




A (kind of) conceptual throughput




Definition in this paper


The number of bytes that can be simultaneously
transported by the network




20

Department of Mathematics and Computer Science


North
Carolina Central
University

Donghyun

(David) Kim




September 23, 2011

Overview of Contributions


Show existing graph
-
model
-
based topology control
captures interference inadequately under SINR model


Cause high interference and low network capacity



Spatial Reuse
Maximizer

(
MaxSR
)
, a combination of


A
power control algorithm (T4P)

to
compute a power
assignment that maximizes spatial reuse with a fixed
topology


A
topology control algorithm (P4T)

to
generate a topology
that maximizes spatial reuse with a fixed power assignment



MaxSR

alternatively invokes T4P and P4T alternatively


Converge into a stable status



Via simulation, shows
MaxSR

outperforms competitors by
50%
-

110% in terms of maximizing the network capacity



21

Department of Mathematics and Computer Science


North
Carolina Central
University

Donghyun

(David) Kim




September 23, 2011

Limitations of Graph
-
model
-
based topology control


The node degree does not capture interference
adequately



The interference in the resulting topology may be high,
rendering low network capacity



A wireless link that exists in the communication graph
may not in practice exist under the physical model (due
to the high interference level)

22

Department of Mathematics and Computer Science


North
Carolina Central
University

Donghyun

(David) Kim




September 23, 2011

Notations



: 2
-
d coordinate of a node
v





: the Euclidean distance between two
nodes




: the transmit power of a node




: the transmit power
assignment of all nodes, where

23

)
,
(
y
x
v
)
,
(
j
i
ij
v
v
d
d

j
i
v
v
,
)
(
i
p
t
i
v
)}
(
,
),
(
),
(
{
n
p
p
p
P
t
t
t
t

2
1

|
|
t
P
n

Department of Mathematics and Computer Science


North
Carolina Central
University

Donghyun

(David) Kim




September 23, 2011

Assumptions


Large
-
scale path loss model


To describe how signals attenuate along the transmission
path




The two conditions of successful transmission






Homogenous network


Same
-

maximum communication power
level

24


j
i
t
j
i
r
d
i
p
g
j
i
p
,
,
)
(
)
,
(














j
j
i
t
j
i
j
i
j
i
t
j
i
r
I
N
d
i
p
g
SINR
RX
d
i
p
g
j
i
p
,
,
,
min
,
,
)
(
)
(
)
,
(
max
min
,
,
P
RX

Department of Mathematics and Computer Science


North
Carolina Central
University

Donghyun

(David) Kim




September 23, 2011

Network Graph Model


A link (
i
,
j
) is said to exist if and only if





Only consider
bidirectional links


an edge
exists if and only if





and



The communication graph of a network is represented
by a graph
G

= (
V
,
E
), where
E

is a set of undirected
edges.


Based on the power assignment, a graph is induced.

25

.
)
(
,
min
,
j
i
j
i
t
g
RX
d
i
p



j
i
edge
,
j
i
j
i
t
g
RX
d
i
p
,
min
,
)
(



.
)
(
,
min
,
i
j
i
j
t
g
RX
d
j
p



Department of Mathematics and Computer Science


North
Carolina Central
University

Donghyun

(David) Kim




September 23, 2011

Interference Model


A node is said to be an interfering node for link


if

26

)
,
(
j
i
v
v
V
v
k

.
)
(
)
(
.
,
,









j
k
t
j
i
t
d
k
p
N
d
i
p
NOTE: Very loose


simultaneous transmissions of non interfering
nodes can cause interference.













j
j
i
t
j
i
j
i
j
i
t
j
i
r
I
N
d
i
p
g
SINR
RX
d
i
p
g
j
i
p
,
,
,
min
,
,
)
(
)
(
)
,
(
Department of Mathematics and Computer Science


North
Carolina Central
University

Donghyun

(David) Kim




September 23, 2011

Interference Model


cont



The
interference degree

of a link is defined as
the number of interfering nodes for .



Let denote the set of containing all
interfering nodes of , then the
interference
degree



A link with a high interference degree


multiple nodes can interfere with its transmission activity,
causing channel competition and/or collision.


Undesirable since both channel competition and collision
degrade the network capacity


Hence, interference degree is a better index than the
node degree in quantifying the interference





27

)
,
(
j
i
v
v
)
,
(
ˆ
j
i
I
v
v
V
)
,
(
j
i
v
v
V
v

)
,
(
j
i
v
v
.
|
)
,
(
ˆ
|
)
,
(
j
i
I
j
i
I
v
v
V
v
v
D


Department of Mathematics and Computer Science


North
Carolina Central
University

Donghyun

(David) Kim




September 23, 2011

Interference Link Graph


A link
interference graph
represents the
interference


of a link
as , where



, and is the set of



edges such that

28

)
,
(
j
i
v
v
))
,
(
),
,
(
(
j
i
I
j
i
I
I
v
v
E
v
v
V
G
}
{
}
{
)
,
(
ˆ
)
,
(
j
i
j
i
I
j
i
I
v
v
v
v
V
v
v
V



)
(
,
j
i
I
link
E
}.
{
\
)
,
(
),
,
(
)
,
(
j
j
i
I
j
i
I
j
v
v
v
V
w
v
v
E
v
w


j
v
i
v
1
w
2
w
3
w
4
w
j
v
i
v
2
w
3
w
Department of Mathematics and Computer Science


North
Carolina Central
University

Donghyun

(David) Kim




September 23, 2011

Interference Degree vs. Node
Degree

29


Interference degree does not necessarily related to
the node degree.

Department of Mathematics and Computer Science


North
Carolina Central
University

Donghyun

(David) Kim




September 23, 2011

Result 1


Given a communication topology, is it possible to find a
power assignment such that the communication graph
of the topology is identical to the physical
-
model
-
based interference graph?



Based on the simulation result, it is not likely to find
power assignments to a topology induced by graph
-
mode
-
based topology control to represent the
corresponding interference graph.

30

Department of Mathematics and Computer Science


North
Carolina Central
University

Donghyun

(David) Kim




September 23, 2011

Topology Control To Maximize
Spatial Reuse


T4P: compute a power assignment that
maximizes spatial reuse with a fixed
topology



P4T: generate a topology that maximizes spatial reuse
with a fixed power assignment



MaxSR
: A novel algorithm to maximize spatial reuse
and improve network
capacity by repeatedly executing
T4P and P4T

31

Department of Mathematics and Computer Science


North
Carolina Central
University

Donghyun

(David) Kim




September 23, 2011

Topology Power Assignment:
T4P


T4P





Hard SINR requirement can be softened by the
sigmoid function






After set
b



𝛽
, a

sequential

quadratic programming
method [12, 13] can be used to solve this softened
problem.

32

)
,
(
)
(
)
(
.
,
,
j
i
d
k
p
N
d
i
p
k
j
k
t
j
i
t















β
i,j
β
β
i,j
β
j
i
I
k
k
k
)
(
,
)
(
,
))
,
(
(

0

1

max
min
)
(
))
(
(
P
P
P
i,j
β
I
t
T
i,j
link
i,j
k
k







to

subject

minimize
)
(
)
(
b
x
a
e
x
sig




1
1
))
(
(
))
(
(
)
(
i,j
β
sig
i,j
β
I
k
T
i,j
link
i,j
k
k






minimize
Department of Mathematics and Computer Science


North
Carolina Central
University

Donghyun

(David) Kim




September 23, 2011

Topology Control To Maximize
Spatial Reuse


cont



T4P: compute a power assignment that maximizes
spatial reuse with a fixed topology



P4T: generate a topology that maximizes
spatial reuse with a fixed power
assignment



MaxSR
: A novel algorithm to maximize spatial reuse
and improve network capacity by repeatedly executing
T4P and P4T


33

Department of Mathematics and Computer Science


North
Carolina Central
University

Donghyun

(David) Kim




September 23, 2011

Power Assignment to Topology:
P4T


To generate an optimal connected topology given a
fixed power assignment



Similar to the minimum spanning tree algorithm


Differ in that this finds the spanning tree that gives
minimal interference degree



Outline (like Prim’s algorithm)


Given a power assignment, for each link, compute its
interference degree


Sort the edge in the non
-
decreasing order of interference
degree


Add each edge one by one until all nodes are connected

34

Department of Mathematics and Computer Science


North
Carolina Central
University

Donghyun

(David) Kim




September 23, 2011

Topology Control To Maximize
Spatial Reuse


cont



T4P: compute a power assignment that maximizes
spatial reuse with a fixed topology



P4T: generate a topology that maximizes spatial reuse
with a fixed power assignment



MaxSR
: A novel algorithm to maximize
spatial reuse and improve network
capacity by repeatedly executing T4P and
P4T


35

Department of Mathematics and Computer Science


North
Carolina Central
University

Donghyun

(David) Kim




September 23, 2011

Spatial Reuse
Maximizer

(
MaxSR
)



: power level of nodes (optimized by T4P)



T

: topology of nodes (optimized by P4T)











Theorem:
MaxSR

converges to an optimal point



36

t
P
Department of Mathematics and Computer Science


North
Carolina Central
University

Donghyun

(David) Kim




September 23, 2011

Discussion


SINR model with loose interference model





vs




Construction of static topology in dynamic SINR model



37

)
,
(
)
(
)
(
.
,
,
j
i
d
k
p
N
d
i
p
k
j
k
t
j
i
t









)
,
(
)
(
)
(
,
.
,
,
j
i
d
k
p
N
d
i
p
k
T
k
i
k
j
k
t
j
i
t