On the Implications of the Log-normal Path Loss Model: An Efficient Method to Deploy and Move Sensor...

On the Implications of the Log-normal Path Loss Model:

An Efficient Method to Deploy and Move Sensor Motes

Yin Chen, Andreas Terzis

November 2, 2011

• What to do about the transitional region?– Place motes in the transitional region vs in the connected

region

Transitional region

2

Connected region

Our Proposal

• Occupy the transitional region– Perform random trials to construct links with high PRR– Based on the Log-normal radio model

3

Motivation: Placing Relay Nodes

4

Outline

• Introduce log-normal path loss model

• Discuss pitfalls

• Present the experimental results – reality check

5

Log-normal Path Loss Model

• Received signal strength at a distance is

– , is a Gaussian random variable• Due to artifacts in the environment (occlusions, multipath, etc.)

– Does not consider temporal variation

Power of the transmitted signal

Path loss at distance

Path loss exponent

Random variation

Sender Receiverdistance

6

Three Regions of Radio Links

• As the distance increases, we go through 3

regions– Connected:– Transitional: – Disconnected:

• Observation– The packet reception ratio at any given location is random 7

Connected Region

• In connected region

• PRR is very likely to be

high

• Trying one location will

likely produce good link

Sender Receiver5 meters

8

Transitional Region

• In transitional region

• PRR may or may not be

high

• Trying a few spots should

yield a good link


9

Disconnected Region

• In disconnected region

• PRR is very unlikely to be

high

• Trying multiple spots

seems worthless


10

Outline

• Introduce log-normal path loss model

• Discuss pitfalls

• Present the experimental results – reality check

11

Pitfalls

• Log-normal path loss model is not perfect

• The Gaussian variation in signal strength is a

statistical observation

• Signal strengths at nearby locations are

correlated

12

Reality Check

• Verify log-normal path loss model

• Quantify spatial correlations

• Count number of trials to construct good links

• Investigate temporal variations

13

Experimental Setup

• Devices– TelosB motes– iRobot with an Ebox-3854 running Linux

• Environments– Outdoor parking lot– Lawn– Indoor hallway– Indoor testbed– Two forests

14

Evaluations on the Log-normal Model

• Holds well in all the environments– Example figure for the parking lot

– We can subtract the solid line from the raw RSSI readings• The residual RSSI values are samples of the random variable :

15

Q-Q Plot of the Residual RSSI Values

16

Reality Check





17

Spatial Correlation

• PRR measurements at a parking lot– iRobot moves in a 2-d plane (the ground)– Black cell : PRR below 85%; Gray cell : PRR above 85%

• PRR are correlated• Trying two adjacent locations

flipping two coins

• In all of our experiments, 1 meter is sufficient to remove most correlation

18

Reality Check





19

Number of Trials - Configuration

• Grid sampling– Bernoulli trials

• Number of trials to find a good PRR is

geometrically distributed

distance

1 meter

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Number of Trials - Results• Measure and compute the length of connected region

– Place motes at distances longer than

Parking Lot

Hallway 1 Hallway 2 Office Forest0

0.5

1

1.5

2

2.5

3

3.5

Number of Trials Expected Number of Trials

Park

ing

Lot

Hallw

ay 1

Hallw

ay 2

Office

Fore

st0

0.5

1

1.5

2

2.5

3

3.5

Distance to the Sender (Normalized by lc)

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Number of Trials – Fitting Geometric Distribution

Suggests that 1 meter

ensures independent

trials.

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Connecting Two Motes

Mote A Mote BRelay

TAR: number of trials to connect to A

TBR: number of trials to connect to B

TARB: number of trials to connect to both A and B

Hallway 1 Hallway 2 Parking Lot 1

Parking Lot 2

Parking Lot 3

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

TAR TBRTARB TAR multiplied by TBR

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TARB TAR TBR

Reality Check





24

Temporal Variation

• Box plots of residual RSSI values for two forests

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Conclusion

• Log-normal model fits sensornets

• Signal correlation vanishes at 1 meter separation

• Easy to find good links in the transitional region– Rule of thumb: at twice the length of connected region,

number of trials is less than 5 with high probability

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Application – Placing Relay Nodes

• Number of relay nodes at large scale– Place 120 sensor motes in an area of size 800m by 800m – Run Steiner Tree algorithm to place relay nodes

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Application – Mobile Sensor Networks

• Mobile sink– If the current spot yields low PRR, move 1 meter– Minimize travel distance

• Mobile motes

Signal variation in the space domain

Signal variation in the time domain

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Thank you!Questions?

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On the Implications of the Log-normal Path Loss Model: An Efficient Method to Deploy and Move Sensor...

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