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
Connected region
Transitional region
• What to do about the transitional region?
– Place motes in the transitional region vs in the connected region
2
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
distance 𝑑
Sender
Receiver
• Received signal strength
Power of the
transmitted signal
–
at a distance 𝑑 is
Path loss at
distance 𝑑0
Path loss
exponent
Random
variation
, is a Gaussian random variable
• Due to artifacts in the environment (occlusions, multipath, etc.)
– Does not consider temporal variation
6
Three Regions of Radio Links
• As the distance increases, we go through 3 regions
– Connected:
– Transitional:
– Disconnected:
P 𝑃𝑅𝑅 ≥ 85% ≥ 95%
5% < P 𝑃𝑅𝑅 ≥ 85% < 95%
P 𝑃𝑅𝑅 ≥ 85% ≤ 5%
• Observation
– The packet reception ratio at any given location is random
7
Connected Region
Sender
5 meters
Receiver
• In connected region
• PRR is very likely to be high
• Trying one location will
likely produce good link
8
Transitional Region
Sender
15 meters
Receiver
• In transitional region
• PRR may or may not be high
• Trying a few spots should
yield a good link
9
Disconnected Region
Sender
40 meters
Receiver
• 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 𝑋𝜎 :
15
Q-Q Plot of the Residual RSSI Values
16
Reality Check
• Verify log-normal path loss model
• Quantify spatial correlations
• Count number of trials to construct good links
• Investigate temporal variations
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
• Verify log-normal path loss model
• Quantify spatial correlations
• Count number of trials to construct good links
• Investigate temporal variations
19
Number of Trials - Configuration
1 meter
distance 𝑑
• Grid sampling
– Bernoulli trials
• Number of trials to find a good PRR is geometrically
distributed
20
Number of Trials - Results
• Measure and compute the length of connected region 𝑙𝑐
–
Place motes at distances longer than 𝑙𝑐
Number of Trials
Expected Number of Trials
3.5
3
Distance to the Sender (Normalized by lc)
2.5
3.5
2
3
2.5
1.5
2
1
1.5
1
0.5
0.5
0
0
Parking
Lot
Hallway 1 Hallway 2
Office
Forest
21
Number of Trials – Fitting Geometric Distribution
Suggests that 1 meter ensures
independent trials.
22
Connecting Two Motes
Relay
Mote A
Mote B
TAR
TBR
TARB
TAR multiplied by TBR
4.5

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
4
3.5
3
2.5
2
1.5
1
0.5
0
Hallway 1
Hallway 2
Parking Lot
1
Parking Lot
2
Parking Lot
3
TARB ≈ TAR × TBR
23
Reality Check
• Verify log-normal path loss model
• Quantify spatial correlations
• Count number of trials to construct good links
• Investigate temporal variations
24
Temporal Variation
• Box plots of residual RSSI values for two forests
25
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
26
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
27
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
28
Thank you!
Questions?
29