Investigating a Physically Based Signal Power Model for Robust … · TOSSIM 2.0.1 (2007) •...
Transcript of Investigating a Physically Based Signal Power Model for Robust … · TOSSIM 2.0.1 (2007) •...
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Investigating a PhysicallyBased Signal Power Model
for Robust Low Power Wireless Link Simulation
Philip [email protected]
Computer Systems
Laboratory
Stanford University
Department of
Computer Science
Cornell University
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Outline
• Introduction
• Phase correction and signal extrapolation
• Validation and Evaluation
• Conclusion
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Low Power Wireless Link Performance Is Poor
• Protocols for sensor networks are carefully designed and heavily simulated
• Packet yield in real deployments is low:
– Volcano Study: 68% [ESWN 05]
– Great Duck Island: 58% [SenSys 04]
– Redwood Study: 40% [SenSys 05]
– Potato Agriculture Study: 2% [WPDRTS 06]
• Low packet yield leads to loss of information from networks
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Wireless Link Simulation
• Analytical Models
– For example, Path Loss and Shadowing Model [ICEE 06]
– Many assume packet reception independence
• Empirical Models
– Packet receptions and losses are not temporally independent
– Noise+Interference modeled using CPM [IPSN 07]
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TOSSIM 2.0.1 (2007)
• Closest Fit Pattern Matching (CPM):
– (1) Preprocess an experimental noise trace:
– (2) Take k values from experiment; then sample PMF:
• Signal power given by constant link gain value.
k = History size = 2
HyungJune Lee, Alberto Cerpa, and Philip Levis, "Improving Wireless Simulation Through Noise Modeling." In Proceedings of the IPSN, 2007.
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Reasons for Packet Reception Correlation
• Noise+Interference in environment is correlated
• Signal Power of successive packets is also correlated
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Physically Modeling Signal Power
• Idea: Collect a signal power trace and use CPM to model signal power.
• Collecting power traces is more complex than collecting noise traces, since:
– Signal power is a property of a pair of nodes in the network
– Signal power can only be approximated by sampling the RSSI register, which actually reports signal+noise, where wave phases are considered
– If a packet is lost in transmission, then even the RSSI estimate is not possible.
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Contributions
• We suggest solutions to major challenges in modeling signal power:
– Correcting for phase
– Two algorithms for extrapolating from lossy traces: Average Value and Expected Value
• Our algorithms improve simulation substantially:
– PRR simulated to within 22% absolute difference
– Methods reduce KW distance of simulations by 66% compared to current approaches
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Outline
• Introduction
• Phase correction and signal extrapolation
• Validation and Evaluation
• Conclusion
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Converting RSSI Readings to Signal Power
• Phase assumption used to correct RSSI reading:
– In phase signal power and noise
– Out of phase signal power and noise
– Neutral phase: assumes net phases cancel out
• These assumptions are simplifications to reality.
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Algorithm for FillingIn Lossy Signal Power Links
• Two algorithms suggested:
– Fill in average value for all missing values
– Compute expected distribution of missing signal power values over the whole trace and then sample the distribution
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Average Value FillingIn Algorithm
Lossy Signal Power (dBm) =
82 ?? ?? 87 85 ?? 86 82 ?? 81 ??
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Average Value FillingIn Algorithm
Lossy Signal Power (dBm) =
82 ?? ?? 87 85 ?? 86 82 ?? 81 ??
Average Signal Power(Rounded to Integer) (dBm) =
84
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Average Value FillingIn Algorithm
Lossy Signal Power (dBm) =
82 ?? ?? 87 85 ?? 86 82 ?? 81 ??
FilledIn Signal Power (dBm) =
82 84 84 87 85 84 86 82 84 81 84
Average Signal Power(Rounded to Integer) (dBm) =
84
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Expected Value PMF FillingIn Algorithm
Average Noise (dBm) = 90 Lossy Signal Power (dBm) =
82 ?? ?? 87 85 ?? 86 82 ?? 81 ??
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Expected Value PMF FillingIn Algorithm
Average Noise (dBm) = 90 Lossy Signal Power (dBm) =
82 ?? ?? 87 85 ?? 86 82 ?? 81 ??
SNR (dB) = 8 3 5 4 98
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Expected Value PMF FillingIn Algorithm
Average Noise (dBm) = 90 Lossy Signal Power (dBm) =
82 ?? ?? 87 85 ?? 86 82 ?? 81 ??
SNR (dB) = 8 3 5 4 98
PacketReceptionRate (PRR) =
0.99 0.1 0.4 0.2 10.99
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Expected Value PMF FillingIn Algorithm (continued)
PacketReceptionRate (PRR) =
0.99 0.1 0.4 0.2 10.99
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Expected Value PMF FillingIn Algorithm (continued)
PacketReceptionRate (PRR) =
0.99 0.1 0.4 0.2 10.99
1/PRR 1
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Expected Value PMF FillingIn Algorithm (continued)
PacketReceptionRate (PRR) =
0.99 0.1 0.4 0.2 10.99
1/PRR 1
0 9 1.5 4 00
Expected Number of Packets Missed =
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Expected Value PMF FillingIn Algorithm (continued)
PacketReceptionRate (PRR) =
0.99 0.1 0.4 0.2 10.99
1/PRR 1Expected Number of Packets Missed =
0 9 1.5 4 00
82 87 85 86 8182Signal power values (dBm) =
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Expected Value PMF FillingIn Algorithm (continued)
Expected Packets PMF =
87 86 85 82 810
100
Signal Power (dBm)
% o
f Mis
sed
Pac
kets
Expected Number of Packets Missed =
0 9 1.5 4 00
82 87 85 86 8182Signal power values (dBm) =
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Expected Value PMF FillingIn Algorithm (continued)
FilledIn Signal Power (dBm) =
82 87 86 87 85 87 86 82 87 81 85
Expected Packets PMF =
87 86 85 82 810
100
Signal Power (dBm)
% o
f Mis
sed
Pac
kets
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Outline
• Introduction
• Phase correction and signal extrapolation
• Validation and Evaluation
• Conclusion
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Validation
• Goal is to correctly simulate a particular link between to nodes
• It is possible to use experiments to validate this simulation method
• Conducted packet delivery experiments at 4 Hz for 12 hours at various locations on the Cornell University Campus.
• 4 Hz frequency chosen as a baseline: future work will investigate different collection frequencies and the impacts on the results.
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Experiment Locations
http://www.parking.cornell.edu/pdf/Stu_combo_2006.pdf
Duffield Hall
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Evaluation Criteria
• Packet Reception Rate (PRR)
– First order parameter, difficult to get right in general wireless simulators
• KantorovichWasserstein (KW) distance on Conditional Packet Delivery Functions (CPDFs)
– Rigorous measure of the similarity between two distributions, which places more emphasis on rare rather than common case
– Captures packet burstiness at the level of individual packets.
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0.426 0.591 0.672 0.7550.000.050.100.150.200.250.300.350.400.450.50
In PhaseNo CorrectionOut of PhaseTOSSIM 2.0.2
Experimental PRR
|Exp
erim
enta
l PR
R
Sim
ulat
ed P
RR
|PRR for Expected Value PMF
Algorithm• Maximum absolute error bounded by 22%.
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0.426 0.591 0.672 0.7550.000.050.100.150.200.250.300.350.400.450.50
In PhaseNo CorrectionOut of PhaseTOSSIM 2.0.2
Experimental PRR
|Exp
erim
enta
l PR
R
Sim
ulat
ed P
RR
|PRR for Average Value Algorithm
• Maximum absolute error bounded by 28%.
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Conditional Packet Delivery Function (CPDF)
• Considers the conditional packet reception rate (CPRR) after streams of |x| consecutive receptions for x < 0 or x consecutive failures for x > 0.
• KantarovichWasserstien Distance measures differences between distributions, including CPDFs.
5 0 50
0.20.40.60.8
1
x
CP
RR
Successes Faliures No Data
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50 40 30 20 10 0 100.000.200.400.600.801.00
x
CP
RR
50 40 30 20 10 0 100.000.200.400.600.801.00
x
CP
RR
CPDF: PRR = 82.5%
Real Signal
Power
Log Normal
Shadowing Model
KW Distance = 0.10Successes Failures
Successes Failures
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50 40 30 20 10 0 100.000.200.400.600.801.00
x
CP
RR
50 40 30 20 10 0 100.000.200.400.600.801.00
x
CP
RR
CPDF: PRR = 82.5%
Real Signal
Power
TOSSIM
2.0.2
KW Distance = 0.09Successes Failures
Successes Failures
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50 40 30 20 10 0 100.000.200.400.600.801.00
x
CP
RR
50 40 30 20 10 0 100.000.200.400.600.801.00
x
CP
RR
CPDF: PRR = 82.5%
Real Signal
Power
CPM+Expected
Value PMF
KW Distance = 0.03Successes Failures
Successes Failures
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CPDF: PRR = 58.5%
40 30 20 10 0 100.000.200.400.600.801.00
x
CP
RR
40 30 20 10 0 100.000.200.400.600.801.00
x
CP
RR
Real Signal
Power
Log Normal
Shadowing Model
KW Distance = 0.20Successes Failures
Successes Failures
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40 30 20 10 0 100.000.200.400.600.801.00
x
CP
RR
CPDF: PRR = 58.5%
Real Signal
Power
TOSSIM
2.0.2
KW Distance = 0.21
40 30 20 10 0 100.000.200.400.600.801.00
x
CP
RR
Successes Failures
Successes Failures
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40 30 20 10 0 100.000.200.400.600.801.00
x
CP
RR
CPDF: PRR = 58.5%
Real Signal
Power
CPM+Expected
Value PMF
KW Distance = 0.06
40 30 20 10 0 100.000.200.400.600.801.00
x
CP
RR
Successes Failures
Successes Failures
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Outline
• Introduction
• Phase correction and signal extrapolation
• Validation and Evaluation
• Conclusion
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Conclusions and Future Work
• KW distance < 0.1 for our experiments (substantially reduced as compared to current methods)
• PRR estimated to within 22% (typically to 10%)
• As expected, different assumptions work more effectively for different experiments.
• Future work: Development of an automated optimization layer to predict the most reasonable assumptions for a given environment.
• Future work: Investigate a signal power model that considers burstiness at many time scales, not just that of an individual packet.
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CPM Model for Trace Histories
• Scan noise trace, keeping a history of size k.
• For each signature of k prior noise readings, construct the probability distribution for the next reading.
HyungJune Lee, Alberto Cerpa, and Philip Levis, "Improving Wireless Simulation Through Noise Modeling." In Proceedings of the IPSN, 2007.
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CPM Model for Trace Histories
• Scan noise trace, keeping a history of size k.
• For each signature of k prior noise readings, construct the probability distribution for the next reading.
HyungJune Lee, Alberto Cerpa, and Philip Levis, "Improving Wireless Simulation Through Noise Modeling." In Proceedings of the IPSN, 2007.
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CPM Sampling Demo
HyungJune Lee, Alberto Cerpa, and Philip Levis, "Improving Wireless Simulation Through Noise Modeling." In Proceedings of the IPSN, 2007.
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CPM Sampling Demo
HyungJune Lee, Alberto Cerpa, and Philip Levis, "Improving Wireless Simulation Through Noise Modeling." In Proceedings of the IPSN, 2007.
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CPM Sampling Demo
HyungJune Lee, Alberto Cerpa, and Philip Levis, "Improving Wireless Simulation Through Noise Modeling." In Proceedings of the IPSN, 2007.
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CPM Sampling Demo
HyungJune Lee, Alberto Cerpa, and Philip Levis, "Improving Wireless Simulation Through Noise Modeling." In Proceedings of the IPSN, 2007.
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CPM Sampling Demo
HyungJune Lee, Alberto Cerpa, and Philip Levis, "Improving Wireless Simulation Through Noise Modeling." In Proceedings of the IPSN, 2007.
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CPM Sampling Result
• Modeled trace is not the same as the experimental trace:
• This increases the randomness of simulation output and thus decreases the predictability of the simulation.
• This allows for substantial representative simulation.
HyungJune Lee, Alberto Cerpa, and Philip Levis, "Improving Wireless Simulation Through Noise Modeling." In Proceedings of the IPSN, 2007.