special topics on algorithmic aspects of wireless networking

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


Example: Wireless Sensor Net-works• Sensor Node Components

• Sensor• Data Processor• Wireless Communication Module

• Characteristics• Small Size• Low-cost• Low-Power


Example: Wireless Sensor Net-works – cont’

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

http://www2.ece.ohio-state.edu/~ekici/res_wmsn.html

http://www2.ece.ohio-state.edu/~ekici/res_wmsn.html


Example: Wireless Sensor Net-works – cont’

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

http://fiji.eecs.harvard.edu/Volcano

http://fiji.eecs.harvard.edu/Volcano


Example: Ad-hoc Network

Vehicular Ad-hoc Networks(Image Source: http://monet.postech.ac.kr/research.html)

http://monet.postech.ac.kr/research.html

http://monet.postech.ac.kr/research.html


Example: Ad-hoc Network – cont’

Military Ad-hoc Network(Image Source: http://www.atacwireless.com/adhoc.html)

http://www.atacwireless.com/adhoc.html

http://www.atacwireless.com/adhoc.html


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


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


Unit Disk Graph (UDG)


Unit Disk Graph – cont’


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


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


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


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…


Topology Control in UDG – cont’• It is a static problem!

TopologyControl Protocol


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)


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.


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


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


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)


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


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


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


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,

,

)(

)(),(


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


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


Interference Degree vs. Node Degree• Interference degree does not necessarily re-

lated to the node degree.


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.


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


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


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


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


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


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


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

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