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Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (http://multimedia.ece.uic.edu/) University of Illinois at Chicago

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Page 1: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks

Ashfaq A. KhokharMultimedia Systems Lab(http://multimedia.ece.uic.edu/)

University of Illinois at Chicago

Page 2: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

Wireless Sensor Networks

• A large number of sensor nodes with limited capability of computation, communication and sensing.

• Nodes collaborate with each other through a wireless channel to accomplish an assigned task.

Page 3: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

Sample Sensor Nodes

Modern Sensor Nodes

UC Berkeley: COTS Dust

UC Berkeley: COTS DustUC Berkeley: Smart Dust

UCLA: WINS Rockwell: WINS JPL: Sensor Webs

Courtesy UC Berkley

Page 4: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

Features of WSN

Traffic rate is generally low– typical communication frequency is in seconds or minutes.

Sensor nodes are battery powered– recharging is usually unavailable – energy is an extremely expensive resource

Sensor nodes in the network coordinate with each other to implement a certain function,

– traffic is not random as in mobile ad hoc networks.

Page 5: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

Motivation

Wireless Sensor Networks is one of the top 10 Technologies that will change the World in 21st Century

According to MIT Technology Review

Pervasive computing environments are increasing

Abundance of defense, scientific, and commercial applications

Page 6: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

Wireless Medium Popularity

Phenomenal growth in – Mobile Communications– Internet/Intranet, E-Commerce– Use of Laptops, Palmtops, and PDAs

New High Bit Rate Wireless Services– Intranet/Internet– Multimedia: Integrated Voice, Data, Video– High quality voice and Videoconferencing

New Technology means new products/services– Revenue opportunities

Page 7: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

Market Estimation

WSN: $150 Million in 2003, $7 Billion estimated in 2010 (ON World)

Mobility infrastructure market expected to grow from $25.7 Billion in 2004 to $34.8 Billion in 2008 (Dell’Oro Group)

Today more wireless connections than wired lines

Page 8: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

Typical WSN Applications

Environment monitoring Habitat monitoring

Office securityTransportation

Industrial monitoring

Fire detection

Page 9: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

Challenges in Wireless Sensor Networks

Software Systems– Computing– Control– Databases– Fusion– Knowledge Extraction

Networking and Communication– Routing, Data Gathering, Data Dissemination

Hardware:– VLSI integration– Architectures– Deployment

Signal and Systems– Signal processing– Classification

Devices– Sensor technologies

User Interfaces and Development Environment

Page 10: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

Research at Multimedia Systems Lab

Software Systems– Power-Time Efficient Algorithms

Networking

– MAC layer – Routing Layer Protocols

Signals and Systems– Field Estimation– Localization– Classification

Page 11: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

Collaborative Computing over Sensor Networks

Sensors are smart:– processing, storage and communication capabilities

Exploit these resources and communicate with sink only when necessary

– Similar arguments hold for computing among sinks Develop distributed algorithms which are power-time

efficient:– Power-time product is comparable to sequential counter-

part Contradicting goals:

– Exploit distributed computing resources– Avoid redundant computations

Page 12: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

Example: Conventional Distributed FFT

0 1 2 3 4 5 6 7

0 1 2 3 4 5 6 7

x2 x3

x2 + w x3 x2 - w x3

0 1 2 3 4 5 6 7

0 1 2 3 4 5 6 7

Page 13: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

Unbalanced Power-Aware FFT: (Ramesh et al -- Milcom 2003)

0 1 2 3 4 5 6 7

0 1 2 3 4 5 6 7

x2 w*x3

x2 + w x3 x2 - w x3

0 1 2 3 4 5 6 7

0 1 2 3 4 5 6 7

31 5 7

2 3 6 7

4 5 6 7

Page 14: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

0 1 2 3 4 5 6 7

0 1 2 3 4 5 6 7

x2 w*x3

x2 + w x3 x2 - w x3

0 1 2 3 4 5 6 7

x3

31 5 7

2 3 6 7

8 110

312

514

7

8 9 2 312

13

6 7

x2 w*x3

x2 + w x3 x2 - w x3

8 910

11

12

13

14

15

x3

11

913

15

10

11

14

15

415

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610 2

12

4 8 0

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212

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5 9 1

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15

14 6

12

11

13

914

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8

Inverse-Shuffle Complement Permutation

Power–Time Efficient Distributed 1-d FFT Algorithm

Page 15: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Sensors

Prop

osed

/Con

vent

iona

l Normalized Radio Cost

The ratio of total number of send/receives in the proposed and conventional 64-Sensored FFT algorithm

RESULTS RESULTS [SenSys04, AICSS 2006][SenSys04, AICSS 2006]

•The Actual communication cost improvement based on our experiments result is 36%.

•Theoretical cost improvement is 42%.

•The discrepancy arises from packet dropping due to collisions.

Page 16: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

0

200

400

600

800

1000

1200

8 16 32 64Number of Sensors

En

erg

y(m

J)

Proposed

Original

RESULTSRESULTS

Energy consumption of the FFT computation as the number of sensors increased

•Approximately 20% energy cost reduction for N=32 and 64.

•The energy improvement is due to reduction in the FFT computation time, as sensors are all on during the computation.

•Except for the network of 8, the overhead of id shuffle phase is justified from the overall savings.

Page 17: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

RESULTSRESULTS

The number of packets transmitted at each time-interval during the conventional and proposed FFT computation over a 64-sensor network sensor networks

Conventional FFT Proposed FFT

•The Congested intervals are reduced significantly.

•Packet collision probability is reduced.

•MAC protocols can shut down the radio circuitry aggressively.

Page 18: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

Example: Classification

Apriori determination of categories

Train for each category– Expose to sample

measurements– Compute Mean (i,j) &

Covariance (i,j) Test

– Classifier Algorithms– Develop false positives,

beliefs, etc Deploy

– Identify detected object w.r.t. categories

?

Page 19: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

Classifier Algorithms

Traditional Signal Processing (SP) algorithms Maximum Likelihood (ML) [Li & et. el. 2002; Duarte & Hu, 2003] k Nearest Neighbor (kNN) [Li & et. el. 2002; Duarte & Hu, 2003]

– Pro: used extensively for its known accuracy– Con: computationally intensive

Novel WSN classifiers Sub-optimal Classifiers [Kotecha & et. el. 2005] Influence fields [Arora & et. el. 2004] Differentiated Surveillance [Yan & et. el. 2003]

– Pro: simpler computationally– Con: novice, accuracy?

Our Goal: adapt existing SP algorithms for efficient classification in sensornets

Page 20: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

What’s the Problem?

Events are f × d matricesf – modalities/features sensedd – temporal processing dimensions

Typically f 50 & d 512 Mean is f × d and is f × f matrices

-1 is also f × f Large matrix computations for every detected event

– Matrix multiplication Inverse computation !

– Unstable– Expensive

Page 21: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

Power Consumption Comparison [HiPC 2006]

Power consumption comparison of MAP with Jacobi (MAP-J) and MAP with LU (MAP-L)

0

2

4

6

8

10

10 20 30 40 50 60 70 80 90 100

features

log

of

po

wer

co

nsu

mp

tio

n

MAP-J

MAP-L

d = 512

Page 22: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

Communication Protocols

A fresher look was needed Energy efficiency and network life time as the

main goal– MAC Layer– Network Layer: Geographical Routing– Application Layer: Data Collection

Page 23: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

Geographic Routing in WSN

Geographic routing:– Greedy forwarding: At each hop, data packet is relayed by a neighbor which

is geographically closer to the destination than the packet holder in terms of Euclidean distance

– Communication void(hole): a network area where greedy forwarding fails to locate the next hop node in a packet holder’s neighborhood

– Some strategies must be used to handle the void to guarantee the packet delivery if a real path exist

Page 24: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

Existing Geographic Routing Protocols

Beacon-based(state-based): PGSR…. Neighbor information collection: periodical beacon messages exchanged

among neighbor nodes Next hop node is chosen from the neighbor table by the packet holder Right/left hand rule based on planar graph is used to handle void High communication overhead due to the beacon messages

Beacon-free(state-free): IGF, PSGP, SIF… No neighbor information maintained in each node Next hop node is chosen based on a competition, which is triggered by a packet

holder, among the packet holder’s neighbors Right/left hand rule or increasing transmission power methods are used to

handle the void:

Page 25: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

Motivation for Void Handling

Right/left-hand rule is impractical since it’s hard to build planar graph in beacon-free geographic routing protocols

Increasing transmission power is not energy efficient

History of void handling should be maintained and used for future data delivery

Page 26: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

Proposed Contention-based Geographic Routing Protocol (CGR-D)

Beacon-free A depth first search (DFS) method is used to locate the next hop node

at each hop An integrated cost function which combines forwarding area

determination, void handling and load balancing is defined as the metric used in DFS method

Each node maintains a local variable (void cost) which is an indication whether a node is in or close to a void area

The void cost is updated per sink basis and periodically reset to 0

Page 27: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

Cost Function

If a node C is closer to the sink D than the current packet holder F:f (d, E, r, H) = [* (1-d/R) + * (1-E/E0) + *r + K*(1+H)]*T0 (1)

Otherwise:f (d, E, r, H) = [* (1-d/R) + * (2-E/E0) + *(1+r) + K*(1+H)]*T0 (2)

Whered = dist(F, D) – dist(C, D) dist(x,y)means distance between x and yH = voidCost(C) - voidCost(F) voidCost(x) is the void cost value of

node xR is radio rangeE is the remaining energy of node CE0 is the initial energy

r is a random number between [0,1]+ + = 1 and , , > 0K, T0 are system parameters

Page 28: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

Data Delivery Example for CGR-D

Page 29: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

Performance Evaluation

Page 30: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

General Data Gathering

Data gathering problem:

Sensing data and transmitting data to a sink. Clustering based solution:

LEACH is a typical one.

Nodes organized into clusters.

Head collects data and transmits aggregated data to the sink.

Sink

Page 31: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

Mobility of Sensor Nodes

The nearest cluster head may change especially in a high-mobility scenario.

Keeping transmitting to the old cluster head consumes more energy.

Sink

Page 32: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

Our Solution: Low-energy Dynamic Cluster Selection (LEDCS) Protocol [VTC 06]

As in LEACH, time is divided into rounds and at the beginning of each round, each node i determines whether it is a cluster head in the current round with a predefined probability.

Introduce a contention period at the beginning of each time frame.

Nodes may join the new cluster head during this contention period.

If a node is a cluster head in the current round, it broadcasts this info across the network which also includes its own moving direction and velocity in the current round.

Page 33: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

Our Solution: Low-energy Dynamic Cluster Selection (LEDCS) Protocol

Page 34: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

Simulation Results

Percentage of Percentage of contention contention period period considering considering different different velocity of velocity of sensor nodes.sensor nodes.

1000 sensors in a 400m x 400m area1000 sensors in a 400m x 400m area

Page 35: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

Simulation Results

Total number Total number of data packets of data packets received by the received by the sink sink considering considering different different velocity of velocity of sensor nodes.sensor nodes.

Up to 80% Up to 80% higherhigher

Page 36: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

Simulation Results

Total number of data rounds

Page 37: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

Data Gathering in Event Driven Applications [INSS 07]

Bursty traffic in event driven applications.

Sink

Page 38: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

Estimation of Traffic Load

Estimate the current traffic load at the beginning of each round.

Based on the estimated value, set up mathematical model and determine optimal number of cluster heads to minimize the total energy consumption.

the total energy consumption vs.

optimal number of cluster heads

Page 39: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

Comparison of Total Energy Consumption

Test case 1 Test case 2

Page 40: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

Data Collection via Cross-Layer Optimization

Sink

Sensor nodes

Data Collection:●A major class of sensor network application●Generally a spanning tree is used for data collection over a sensor network

Problems:● Congestion is major performance bottleneck.

Goals:●To increase data delivery ratio with simpler MAC protocols●To mitigate congestion in the network especially near the sink node●To increase bandwidth utilization

Page 41: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

●SMAC like contention based MAC protocols are simpler and do not require tight synchronization.

BA

C

Question: In data collection applications is it absolutely necessary for a node to communicate every one of its hop neighbors?

-Not if we can find route to sink!

AB

C

Sink

-Node B does not have to communicate with C, so it can stop following C's schedule

active

active

activeactive

sleep

sleep

sleep sleep

MOTIVATION

Page 42: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

Single Data Collection Tree

•Single Data Collection Tree

•Multihop communication

•Single spanning tree is constructed and nodes forward their readings to their parents

•Major performance bottlenecks:

• Heavy congestion near the sink node.

• High competition for the wireless medium.

• High delays due to medium access

Page 43: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

Phase 1: Construct 2 different trees Phase 2 : Activate each tree at different times

Multiple Data Collection Trees

Multiple Data Collection Trees

•Construct more than 1 collection tree•Active trees at different times than the others•Data collection is possible without communicating with all the neighbors•Routing protocol should find the set of neighbors necessary to communicate with sink. •Decreasing the number of active nodes will mitigate congestion and increase delivery ratio.

Page 44: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

sleep active

active sleep

sleep

1 Duty Cycle

activeSingle data collection tree:

Advantage: Simple tree construction

Disadvantages:●Network is highly congested near sink●Bandwidth is not fully utilized●High collision probability

Single vs. Multiple Data Collection Trees

Multiple Data Collection Trees

Advantages:

•Increased bandwidth utilization

•Mitigated Congestion

•Energy consumption not increased

•Less nodes are active

Disadvantage: More complex tree construction

Page 45: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

Delivery Ratio- 10% SMAC

0.15

0.25

0.35

0.45

0.55

0.65

0.75

0.85

1 2 3 4 5 6 7 8 9

Num ber Of Trees

SMAC 50

SMAC 100

SMAC 200

Simulation Results

Page 46: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

Delivery Ratio Regular Grid

0

0.2

0.4

0.6

0.8

1

1.2

1 2 3 4 5 6

Number Of Trees

50

100150

200

Simulation Results

Page 47: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

Energy Consum ption

650

670

690

710

730

750

770

790

810

1 2 3 4 5 6 7 8 9

Num ber of Trees

Jou

les

SMAC 50

SMAC 100

Simulation Results

Page 48: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

Data Gathering in Vehicular Networks

Stationary Internet Gateways (IGWs) along the highway which provide interfaces connecting vehicles to the Internet, a gateway communicate with vehicles out of its transmission range via multi-hop communications

Traditional 802.11 MAC solution: Multi-hopping scheme suffers from low throughput

and starvation of packets originating from vehicles far away from gateways due to high collision

Page 49: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

Example: CVIA Protocol

1. Divide the line between gateways into segments , length of segments is equal to the transmission range of a vehicle

2. Assign TDMA slots for each segments such that only segments out of

transmission range will transmit in the same time slot– collision free

3. In the figure S1,3,5,7 transmit in a time slot and s2,4,6,8 transmit in the next

time slot

Page 50: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

CVIA Protocol

Four phases in each time slot:1) Temporary Router Selection phase: inbound and outbound

temporary routers elected for each segments2) Inbound router transmits collected data to outbound router3) Outbound router collects data within its segment4) Outbound router transmits data to the neighboring inbound

router

Page 51: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

Problems

Inter- and Intra-segment contention leads to higher packet losses

The time length of a slot for local data gathering phase is uniform, leading to transmission delays

Solutions:– ???

Page 52: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

Distortion Analysis in Sensing Field Measuring Spatial-temporal Correlated Data

Example of field measuring Gaussian correlated data.

Consider the real-time data gathering problem in a field that data is both spatial and temporal correlated.

Sink will do real-time data reconstruction for the whole field.

Page 53: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

How many nodes should be put into the field to minimize the total distortion?

Number of nodes increases:

Spatial distortion decreases while temporal distortion increases.

An optimal number of nodes exists to minimize the total distortion.

Page 54: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

Randomly deployed single-hop sensor networks

Nodes randomly deployed in the field following Poisson distribution.

1. One-dimensional case

2. Two-dimensional caseUse Voroni Cell partitions to achieve minimal distortion within each cell

TDMA protocol used for data collection

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Possible applications: nodes on the human body to measure some physical parameters like temperature, humidity; in the machine to check the condition of the machine.
Page 55: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

Randomly deployed one-hop sensor networks

1. An optimal number of nodes always exist to minimize the total distortion D.

2. when correlation intensity α is fixed and time scaling constant βT is increased, the optimal value of n that minimizes the total distortion D decreases.

bear
when number of nodes n increases, distortion first decreases due to the reduced spatial distortion; then it increases due to the increased temporal distortion caused by increasing time delay.
bear
This is because when βT increases, the time correlation in the field becomes weaker implying less time slack available in the data collection phase. Therefore, overall data collection traffic should be decreased, i.e. less number of nodes be deployed to reduce the total distortion.
Page 56: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

Fixed topology for multi-hop sensor networks

We assume that each node has a limited transmission range R

A TDMA-based transmission algorithm is designed for collision-free data transmission from nodes to the sink.

bear
One-dimensional grid network case
bear
Two-dimensional wheel-based network case
Page 57: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

An Example 1D Transmission Schedule

Page 58: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

Total distortion varies with different coefficients (one-dimensional case)

Page 59: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

Total distortion varies with different coefficients (two-dimensional case)

a) α=0.1,βT=0.001 b) α=0.1,βT=0.002 c)α=0.1,βT=0.005

d) α=0.02,βT=0.002 e) α=0.05,βT=0.001 f) α=0.05,βT=0.002

Page 60: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

Analysis for both cases

The total distortion experiences a sudden drop for every increase of five in number of nodes (one-dimensional case) or number of rings (two-dimensional case).

With the increase of correlation coefficients α and βT, for a given number of nodes, the total distortion will increase due to the weaker correlation of the field.

bear
each five increase causes an increase of or the time frame length. This leads to a decrease of total distortion which is actually an averaged value over each time frame.
Page 61: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

Minimum number of nodes required given a certain distortion constraint

Correlation Coefficients Distortion constraint

Minimum number of nodes

α=1, βT=0.2 12 35

α=1, βT=0.002 4 6

α=1, βT=0.002 1.5 14

α=0.5, βT=0.02 4 5

α=0.5, βT=0.002 1.5 7

α=0.5, βT=0.002 1 14

α=0.2, βT=0.002 1.5 5

α=0.2, βT=0.002 1 6

Correlation Coefficients Distortion constraint

Minimum number of nodes n*k(n, k)

α=0.1, βT=0.005 120 50(10,5)

α=0.1, βT=0.002 60 90(18,5)

α=0.1, βT=0.001 40 120(24,5)

α=0.1, βT=0.001 120 45(9,5)

α=0.05, βT=0.005 120 35(7,5)

α=0.05, βT=0.002 40 70(14,5)

α=0.02, βT=0.002 60 30(6,5)

α=0.02, βT=0.002 40 35(7,5)

One-dimensional grid network case Two-dimensional wheel-based network case

bear
we observe that when one variable of the correlation pair (α,βT) increases, the correlation of the field becomes weaker and generally we need more nodes for a given distortion constraint.
Page 62: Design of Energy Efficient Computations and Protocols for Wireless Sensor Networks Ashfaq A. Khokhar Multimedia Systems Lab (

Other Problems Under Investigation

Localization Synchronization Upper layer communication protocols Data fusion Knowledge extraction