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Topology Abstraction of Wireless Networks using Physical Model. Special Topics on Algorithmic Aspects of Wireless Networking. Donghyun (David) Kim Department of Mathematics and Computer Science North Carolina Central University. Instant deployment No wired backbone No centralized control - PowerPoint PPT Presentation
1
Special Topics on Algorithmic As-pects of Wireless Networking
Donghyun (David) KimDepartment of Mathematics and Computer ScienceNorth Carolina Central University
Topology Abstraction of Wireless Networks using Physical Model
2Department of Mathematics and Computer Science North Carolina Central UniversityDonghyun (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
3Department of Mathematics and Computer Science North Carolina Central UniversityDonghyun (David) Kim September 23, 2011
Example: Wireless Sensor Net-works• Sensor Node Components
• Sensor• Data Processor• Wireless Communication Module
• Characteristics• Small Size• Low-cost• Low-Power
4Department of Mathematics and Computer Science North Carolina Central UniversityDonghyun (David) Kim September 23, 2011
Example: Wireless Sensor Net-works – cont’
Wireless Multimedia Sensor Networks(Image Source: http://www2.ece.ohio-state.edu/~ekici/res_wmsn.html)
5Department of Mathematics and Computer Science North Carolina Central UniversityDonghyun (David) Kim September 23, 2011
Example: Wireless Sensor Net-works – cont’
Volcano monitoring(Image Source: http://fiji.eecs.harvard.edu/Volcano)
6Department of Mathematics and Computer Science North Carolina Central UniversityDonghyun (David) Kim September 23, 2011
Example: Ad-hoc Network
Vehicular Ad-hoc Networks(Image Source: http://monet.postech.ac.kr/research.html)
7Department of Mathematics and Computer Science North Carolina Central UniversityDonghyun (David) Kim September 23, 2011
Example: Ad-hoc Network – cont’
Military Ad-hoc Network(Image Source: http://www.atacwireless.com/adhoc.html)
8Department of Mathematics and Computer Science North Carolina Central UniversityDonghyun (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 inter-
ference and collision handling proto-cols such as TDMA, FDMA,CDMA
• Physical layer• problems in power control
• Convenient to have graph model for the topology of a wireless network
9Department of Mathematics and Computer Science North Carolina Central UniversityDonghyun (David) Kim September 23, 2011
Arbitrary Networks• n nodes are arbitrary located
• Each node has a fixed communication power
• When does a transmission received success-fully? • Allowing for two possible models for successful
reception over one hop: The protocol model and the physical model
10Department of Mathematics and Computer Science North Carolina Central UniversityDonghyun (David) Kim September 23, 2011
Unit Disk Graph (UDG)
11Department of Mathematics and Computer Science North Carolina Central UniversityDonghyun (David) Kim September 23, 2011
Unit Disk Graph – cont’
12Department of Mathematics and Computer Science North Carolina Central UniversityDonghyun (David) Kim September 23, 2011
Protocol Model• Let Xi denote the location of a node• A transmission is successfully received by Xj if:
• For every other node Xk simultaneously transmitting • is the guarding zone specified by the protocol
XXΔ XX jijk 1
r Δ 1 r
jx
ixkX
r Δ 1
lX
Δ
r
13Department of Mathematics and Computer Science North Carolina Central UniversityDonghyun (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
lp 52
.lpt
tp
14Department of Mathematics and Computer Science North Carolina Central UniversityDonghyun (David) Kim September 23, 2011
Physical Model – cont’• Let be a subset of nodes simultaneously trans-
mitting• Let Pk be the power level chosen at node Xk
• Transmission from node Xi is successfully received at node Xj if:
• Also called signal to interference and noise ratio (S-INR) model.
ΤkX k ;
β
XX
PN
XX
P
Tkik α
jk
k
α
ji
i
15Department of Mathematics and Computer Science North Carolina Central UniversityDonghyun (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 communica-tion power• Goal: Reduces energy and interference!
But still stay connected and satisfies other properties:• Low node degree• Low static interference• Etc…
16Department of Mathematics and Computer Science North Carolina Central UniversityDonghyun (David) Kim September 23, 2011
Topology Control in UDG – cont’• It is a static problem!
TopologyControl Protocol
17Department of Mathematics and Computer Science North Carolina Central UniversityDonghyun (David) Kim September 23, 2011
Topology Control in SINR• A schedule to actually realize selected links
(transmission requests), to successfully transmit message over them
Minimum signal-to-interference ratio
Power level of sender u Path-loss
exponentNoise
Distance betweentwo nodes
Received signal power from sender
Received signal power from all other nodes (=interference)
18Department of Mathematics and Computer Science North Carolina Central UniversityDonghyun (David) Kim September 23, 2011
Cross Layer Aspects of Power Control
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 ModelRef: Yan Gao, Jennifer C. Hou, and Hoang Nguyen, “Topology Control for Maintaining Network Connectivity and Maximizing Network Ca-pacity under the Physical Model,” INFOCOM 2008.
20Department of Mathematics and Computer Science North Carolina Central UniversityDonghyun (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 simultane-
ously transported by the network
21Department of Mathematics and Computer Science North Carolina Central UniversityDonghyun (David) Kim September 23, 2011
Overview of Contributions• Show existing graph-model-based topology control cap-
tures 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 as-
signment 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
22Department of Mathematics and Computer Science North Carolina Central UniversityDonghyun (David) Kim September 23, 2011
Limitations of Graph-model-based topology control• The node degree does not capture interfer-
ence 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 phys-ical model (due to the high interference level)
23Department of Mathematics and Computer Science North Carolina Central UniversityDonghyun (David) Kim September 23, 2011
Notations• : 2-d coordinate of a node v
• : the Euclidean distance be-tween two nodes
• : the transmit power of a node
• : the transmit power assignment of all nodes, where
),( yxv
),( jiij vvdd ji vv ,
)(ipt iv
)}(,),(),({ npppP tttt 21|| tPn
24Department of Mathematics and Computer Science North Carolina Central UniversityDonghyun (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 communica-
tion power level
ji
tjir d
ipgjip
,
, )(),(
j
jitjiji
ji
tjir
INdipg
SINR
RXd
ipgjip
,,,
min,
,
)(
)(),(
maxmin ,, PRX
25Department of Mathematics and Computer Science North Carolina Central UniversityDonghyun (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 repre-sented by a graph G = (V, E), where E is a set of undirected edges.
• Based on the power assignment, a graph is in-duced.
.)(,
min,
ji
jit g
RXdip
jiedge ,
ji
jit g
RXdip
,
min,)(
.)(,
min,
ij
ijt g
RXdjp
26Department of Mathematics and Computer Science North Carolina Central UniversityDonghyun (David) Kim September 23, 2011
Interference Model• A node is said to be an interfering
node for link if
),( ji vvVvk
.)(
)(.
,
,
jkt
jit
dkpNdip
NOTE: Very loose – simultaneous transmissions of non interfering nodes can cause interference.
j
jitjiji
ji
tjir
INdipg
SINR
RXd
ipgjip
,,,
min,
,
)(
)(),(
27Department of Mathematics and Computer Science North Carolina Central UniversityDonghyun (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 inter-ference degree
• A link with a high interference degree• multiple nodes can interfere with its transmission
activity, causing channel competition and/or colli-sion.
• 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
),( ji vv
),(ˆjiI vvV
),( ji vv
Vv),( ji vv.|),(ˆ|),( jiIjiI vvVvvD
28Department of Mathematics and Computer Science North Carolina Central UniversityDonghyun (David) Kim September 23, 2011
Interference Link Graph• A link interference graph represents the in-
terference of a link as , where
, and is the set of edges such that
),( ji vv )),(),,(( jiIjiII vvEvvVG
}{}{),(ˆ),( jijiIjiI vvvvVvvV )( , jiI linkE
}.{\),(),,(),( jjiIjiIj vvvVwvvEvw
jviv
1w 2w
3w 4wjv
iv
2w
3w
29Department of Mathematics and Computer Science North Carolina Central UniversityDonghyun (David) Kim September 23, 2011
Interference Degree vs. Node Degree• Interference degree does not necessarily re-
lated to the node degree.
30Department of Mathematics and Computer Science North Carolina Central UniversityDonghyun (David) Kim September 23, 2011
Result 1• Given a communication topology, is it possi-
ble to find a power assignment such that the communication graph of the topology is iden-tical to the physical-model-based interference graph?
• Based on the simulation result, it is not likely to find power assignments to a topology in-duced by graph-mode-based topology control to represent the corresponding interference graph.
31Department of Mathematics and Computer Science North Carolina Central UniversityDonghyun (David) Kim September 23, 2011
Topology Control To Maximize Spatial Reuse• T4P: compute a power assign-
ment that maximizes spatial re-use with a fixed topology
• P4T: generate a topology that maximizes spa-tial reuse with a fixed power assignment
• MaxSR: A novel algorithm to maximize spatial reuse and improve network capacity by re-peatedly executing T4P and P4T
32Department of Mathematics and Computer Science North Carolina Central UniversityDonghyun (David) Kim September 23, 2011
Topology Power Assignment: T4P• T4P
• Hard SINR requirement can be softened by the sigmoid function
• After set b , a sequential quadratic program-ming method [12, 13] can be used to solve this softened problem.
),()(
)(.
,
, jidkpN
dipk
jkt
jit
βi,jββi,jβ
jiIk
kk )(,
)(,)),(( 0
1
maxmin
)(
))((
PPP
i,jβI
t
Ti,jlink i,jkk
to subject
minimize
)()( bxaexsig
11
))(())(()(
i,jβsigi,jβI kTi,jlink i,jk
k
minimize
33Department of Mathematics and Computer Science North Carolina Central UniversityDonghyun (David) Kim September 23, 2011
Topology Control To Maximize Spatial Reuse – cont’• T4P: compute a power assignment that max-
imizes 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 re-peatedly executing T4P and P4T
34Department of Mathematics and Computer Science North Carolina Central UniversityDonghyun (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 algo-rithm• 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, com-
pute its interference degree• Sort the edge in the non-decreasing order of in-
terference degree• Add each edge one by one until all nodes are
connected
35Department of Mathematics and Computer Science North Carolina Central UniversityDonghyun (David) Kim September 23, 2011
Topology Control To Maximize Spatial Reuse – cont’• T4P: compute a power assignment that max-
imizes spatial reuse with a fixed topology
• P4T: generate a topology that maximizes spa-tial reuse with a fixed power assignment
• MaxSR: A novel algorithm to maximize spatial reuse and im-prove network capacity by re-peatedly executing T4P and P4T
36Department of Mathematics and Computer Science North Carolina Central UniversityDonghyun (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
tP
37Department of Mathematics and Computer Science North Carolina Central UniversityDonghyun (David) Kim September 23, 2011
Discussion• SINR model with loose interference model
vs
• Construction of static topology in dynamic SINR model
),()(
)(.
,
, jidkpN
dipk
jkt
jit
),()(
)(
,.
,
, jidkpN
dipk
Tkik jkt
jit