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MotivationOur Results/Contribution
Summary
Effects of Correlated Shadowing: Connectivity,Localization, and RF Tomography
Neal Patwari Piyush Agrawal
Sensing and Processing Across Networks LabDepartment of Electrical and Computer Engineering
University of Utah, USA
International Conference on Information Processing inSensor Networks, 2008
Patwari, Agrawal Effects of Correlated Shadowing
MotivationOur Results/Contribution
Summary
Outline
1 MotivationCurrent Fading Models for WSN are LackingNetwork Shadowing (NeSh) Model
2 Our Results/ContributionConnectivity of Multi-hop NetworksSensor Cooperative LocalizationRF Tomographic Imaging
Patwari, Agrawal Effects of Correlated Shadowing
MotivationOur Results/Contribution
Summary
Current Fading Models for WSN are LackingNetwork Shadowing (NeSh) Model
Outline
1 MotivationCurrent Fading Models for WSN are LackingNetwork Shadowing (NeSh) Model
2 Our Results/ContributionConnectivity of Multi-hop NetworksSensor Cooperative LocalizationRF Tomographic Imaging
Patwari, Agrawal Effects of Correlated Shadowing
MotivationOur Results/Contribution
Summary
Current Fading Models for WSN are LackingNetwork Shadowing (NeSh) Model
Intuition: Fading Models Defy Physical Reality
Measured (a) from [Newport07], compared to three models
NeSh ModelMeasuredLevelSignal
Circular CoverageModel
(a) (c)(b) (d)i.i.d. Fading
Model
1 Coverage is not circular: Random with environment2 Fading is not i.i.d.: Spatial correlations exist
Patwari, Agrawal Effects of Correlated Shadowing
MotivationOur Results/Contribution
Summary
Current Fading Models for WSN are LackingNetwork Shadowing (NeSh) Model
Models all Fit Generic Path Loss and Fading Model
Link (i, j) is disconnected if Pi,j < Pthr.Pi,j: measured received power at node j transmitted bynode i (dBm),
Pi,j = P̄(di,j) − Xi,j − Yi,j
P̄(di,j): ensemble mean dBm received power at distancedi,j between i and j,Xi,j: shadowing loss in dB,Yi,j: other fading losses in dB.
Patwari, Agrawal Effects of Correlated Shadowing
MotivationOur Results/Contribution
Summary
Current Fading Models for WSN are LackingNetwork Shadowing (NeSh) Model
Fading in Circular Coverage and i.i.d. Fading Models
Circular Coverage Model:
Zero fading: Xi,j = Yi,j = 0.At distance dthr, Pi,j < Pthr, link disconnected.
i.i.d. Fading Model:
Total fading Zi,j = Xi,j + Yi,j, where {Zi,j}i,j aremutually independent.Problem: Links to neighboring points arecompletely different.
Patwari, Agrawal Effects of Correlated Shadowing
MotivationOur Results/Contribution
Summary
Current Fading Models for WSN are LackingNetwork Shadowing (NeSh) Model
Related Research on Correlated Shadowing Model
1 Temporal correlations for MANETs [Newport07] [Wang06]2 Exponentially-decaying covariance across space
[Gudmundson91]3 Comparison: NeSh allows links without a common node:
(a)
C
D
A
(b)
C
D
A
B
Patwari, Agrawal Effects of Correlated Shadowing
MotivationOur Results/Contribution
Summary
Current Fading Models for WSN are LackingNetwork Shadowing (NeSh) Model
Outline
1 MotivationCurrent Fading Models for WSN are LackingNetwork Shadowing (NeSh) Model
2 Our Results/ContributionConnectivity of Multi-hop NetworksSensor Cooperative LocalizationRF Tomographic Imaging
Patwari, Agrawal Effects of Correlated Shadowing
MotivationOur Results/Contribution
Summary
Current Fading Models for WSN are LackingNetwork Shadowing (NeSh) Model
Shadowing Field is the Random Environment
Start w/ random shadowing field p(x)
xi
xj
xk
xl
link a link b
shadowing field ( )p x
Assumptions about p(x):Isotropic, zero-mean GaussianCovariance:E
[p(xi)p(xj)
]=
σ2X
δ e−‖xj−xi‖
δ
δ: Distance constant
Assumption: Xa = normalized line integral of p(x),
Xa ,1
‖xj − xi‖1/2
∫ xj
xi
p(y)dy.
Patwari, Agrawal Effects of Correlated Shadowing
MotivationOur Results/Contribution
Summary
Current Fading Models for WSN are LackingNetwork Shadowing (NeSh) Model
NeSh is 2nd-Order Version of Existing Models
The model agrees in distribution with existing models[Rappaport]:
1 Gaussian (in dB),2 Zero-mean,3 Variance σ2
X constant vs. path length.
NeSh also causes E [XaXb] > 0 for ‘close’ links a, b.Assumes no correlation in small-scale fading {Yi,j}.
Patwari, Agrawal Effects of Correlated Shadowing
MotivationOur Results/Contribution
Summary
Current Fading Models for WSN are LackingNetwork Shadowing (NeSh) Model
Experimental Evidence
NeSh model verified in [Agrawal08]Experiment-based indoor measurements of 15 WSNsA random environment was created for each WSNBetter agreement than model of [Gudmundson91]Estimated parameters: σ2
X/σ2dB = 0.29 and δ = 21 cm
Patwari, Agrawal Effects of Correlated Shadowing
MotivationOur Results/Contribution
Summary
Current Fading Models for WSN are LackingNetwork Shadowing (NeSh) Model
NeSh Model Has Limitations
Statistical: Not site-specific, not solution to Maxwell’s EqnsLimited tests: Not tested for multi-floor, outdoor (terrain)Not needed when environments are homogenous
Patwari, Agrawal Effects of Correlated Shadowing
MotivationOur Results/Contribution
Summary
Connectivity of Multi-hop NetworksSensor Cooperative LocalizationRF Tomographic Imaging
Outline
1 MotivationCurrent Fading Models for WSN are LackingNetwork Shadowing (NeSh) Model
2 Our Results/ContributionConnectivity of Multi-hop NetworksSensor Cooperative LocalizationRF Tomographic Imaging
Patwari, Agrawal Effects of Correlated Shadowing
MotivationOur Results/Contribution
Summary
Connectivity of Multi-hop NetworksSensor Cooperative LocalizationRF Tomographic Imaging
Connectivity Research: Circular and i.i.d. Models
Standard assumption: Circular coverage modelUsing i.i.d. fading model [Hekmat06], [Bettstetter05]:Increasing fading → Higher graph connectivity!Intuition: Partially, artifact of i.i.d. model
Patwari, Agrawal Effects of Correlated Shadowing
MotivationOur Results/Contribution
Summary
Connectivity of Multi-hop NetworksSensor Cooperative LocalizationRF Tomographic Imaging
Simulation Examples
(a)
1 m
1m
1 3
1
3
(b)
1.5 m
1.5
m
Simulate two networks with same density: 1 node / m2
Patwari, Agrawal Effects of Correlated Shadowing
MotivationOur Results/Contribution
Summary
Connectivity of Multi-hop NetworksSensor Cooperative LocalizationRF Tomographic Imaging
Using NeSh to Generate Network Connectivity
For a given geometry of sensors, determine connectivity:1 Generate vector of [Pi,j]i,j as multivariate Gaussian with
NeSh model2 Any link (i, j) is connected if Pi,j > Pthr
3 Determine whether or not the graph is connected
Patwari, Agrawal Effects of Correlated Shadowing
MotivationOur Results/Contribution
Summary
Connectivity of Multi-hop NetworksSensor Cooperative LocalizationRF Tomographic Imaging
Results Show i.i.d. Fading Model is Optimistic
For correlated shadowing vs. i.i.d. model:Const. range: P[disconnected] up 230% (4x4), 380% (8x2)Const. connectivity: Need higher transmit powerModel disconnect highest in narrow deployments
Patwari, Agrawal Effects of Correlated Shadowing
MotivationOur Results/Contribution
Summary
Connectivity of Multi-hop NetworksSensor Cooperative LocalizationRF Tomographic Imaging
Outline
1 MotivationCurrent Fading Models for WSN are LackingNetwork Shadowing (NeSh) Model
2 Our Results/ContributionConnectivity of Multi-hop NetworksSensor Cooperative LocalizationRF Tomographic Imaging
Patwari, Agrawal Effects of Correlated Shadowing
MotivationOur Results/Contribution
Summary
Connectivity of Multi-hop NetworksSensor Cooperative LocalizationRF Tomographic Imaging
Correlation Changes Common Assumption
Lower bounds on location variance, MSETo date: Assume link measurements are i.i.d.Pro: simplification. Con: inaccurate for RSSQuestion: Will correlations increase or decrease errors?
Patwari, Agrawal Effects of Correlated Shadowing
MotivationOur Results/Contribution
Summary
Connectivity of Multi-hop NetworksSensor Cooperative LocalizationRF Tomographic Imaging
Localization Formulation Details
Estimate: Coordinates of unknown-location nodes,
θ = [x1, . . . , xn, y1, . . . , yn]T ,
Given: Some nodes n + 1, . . . , N have known coordinatesGiven: Measurements Pi,j between pairs (i, j) ∈ E
Patwari, Agrawal Effects of Correlated Shadowing
MotivationOur Results/Contribution
Summary
Connectivity of Multi-hop NetworksSensor Cooperative LocalizationRF Tomographic Imaging
Lower Bound on Variance: Analysis Setup
Cramér-Rao lower bound (CRLB) on covariance matrix Cθ
of unbiased estimators of θ,
Cθ > F−1 = [Fµ + FC]−1
Total Fisher information F is sum of Fisher information1 from the mean loss on individual links, Fµ2 from the shadowing covariance between links, FC
Also consider bound using only mean term: C∗θ > F−1
µ
Patwari, Agrawal Effects of Correlated Shadowing
MotivationOur Results/Contribution
Summary
Connectivity of Multi-hop NetworksSensor Cooperative LocalizationRF Tomographic Imaging
Lower Bound on Variance: Numerical Results
16 node (·) random network, 4 with known coordinate (x)Bound on 1-σ covariance ellipse – smaller is better
(a) (b)
(a) i.i.d.: (- - - -),NeSh: (—–)(b) i.i.d.: (- - - -),NeSh mean termonly: (—–)
Average std. dev. bound: (a) Down 4%, (b) Up 14%.
Patwari, Agrawal Effects of Correlated Shadowing
MotivationOur Results/Contribution
Summary
Connectivity of Multi-hop NetworksSensor Cooperative LocalizationRF Tomographic Imaging
Intuition Gained: Use pair-wise data
In NeSh model:Diminished localization from individual Pi,j meas’tsIncreased localization from pairs (Pi,j, Pk,l)
Overall, location errors could be slightly reduced (4%).Algorithms should use Pi,∗ and Pj,∗ to infer distance di,j
(e.g.: RF fingerprinting, statistical learning methods)
Patwari, Agrawal Effects of Correlated Shadowing
MotivationOur Results/Contribution
Summary
Connectivity of Multi-hop NetworksSensor Cooperative LocalizationRF Tomographic Imaging
Outline
1 MotivationCurrent Fading Models for WSN are LackingNetwork Shadowing (NeSh) Model
2 Our Results/ContributionConnectivity of Multi-hop NetworksSensor Cooperative LocalizationRF Tomographic Imaging
Patwari, Agrawal Effects of Correlated Shadowing
MotivationOur Results/Contribution
Summary
Connectivity of Multi-hop NetworksSensor Cooperative LocalizationRF Tomographic Imaging
Correlation Enables Inference About Environment
Shadowing Field � Link Losses
5 7
18 19 20 2114 15 16 17
1
2
3
4
5 6 7 8 9 10 11 12 13
Imaging would not be possible in i.i.d. fadingThis work: imaging of environment change
Patwari, Agrawal Effects of Correlated Shadowing
MotivationOur Results/Contribution
Summary
Connectivity of Multi-hop NetworksSensor Cooperative LocalizationRF Tomographic Imaging
Method Overview
Change in shadowing field: M-pixel image vector p
xik
xjk
y
y
m
n
link k
Change in link loss, ν, vector from each link (ik, jk)
A linear combo of pixels m in between xik and xjk
Patwari, Agrawal Effects of Correlated Shadowing
MotivationOur Results/Contribution
Summary
Connectivity of Multi-hop NetworksSensor Cooperative LocalizationRF Tomographic Imaging
Imaging is Inverse Problem in Linear Model
Overall linear model with noise n:
ν = Ap + n
Measure ν, solve for p. Least squares:
p̂ = Πν, where Π = RAT (ARAT + σ2
KIK)−1
R: Covariance in shadowing field (NeSh)σ2
KIK : Diagonal regularization termΠ: Projection matrix, calculated once
Patwari, Agrawal Effects of Correlated Shadowing
MotivationOur Results/Contribution
Summary
Connectivity of Multi-hop NetworksSensor Cooperative LocalizationRF Tomographic Imaging
Experiment: Person Moving in Room
N
SW
Sensor
StoppingPosition
Door
WalkingPath
Key SENE
NW
SW
Environment: Empty 5m x 5m roomSensors: Crossbow Mica2, 915 MHzProtocol: Each broadcasts packet every 0.5 secMovement: Person walks in, 1 min. in each corner
Patwari, Agrawal Effects of Correlated Shadowing
MotivationOur Results/Contribution
Summary
Connectivity of Multi-hop NetworksSensor Cooperative LocalizationRF Tomographic Imaging
Imaging Algorithm: Three Steps
1 Calculate change in path loss from past average2 Calculate tomographic image via LS3 Increase image contrast
Patwari, Agrawal Effects of Correlated Shadowing
MotivationOur Results/Contribution
Summary
Connectivity of Multi-hop NetworksSensor Cooperative LocalizationRF Tomographic Imaging
Experiment Results: Location Seen in Image19:02:23, NE corner
19:03:23, NW corner
19:01:23, SE corner
19:00:23, SW corner
19:04:23, empty room
Patwari, Agrawal Effects of Correlated Shadowing
MotivationOur Results/Contribution
Summary
Summary
Shadowing is correlated: Use correlated model (NeSh)Effects: Degrade connectivity, impact localizationalgorithms, and permit RTI
Future WorkMore experiment-based modeling and RTI developmentDevelopment of link correlation-based loc. algorithms
Patwari, Agrawal Effects of Correlated Shadowing
MotivationOur Results/Contribution
Summary
Questions and Comments
More info on http://span.ece.utah.edu
Patwari, Agrawal Effects of Correlated Shadowing
Appendix For Further Reading
For Further Reading I
M. Gudmundson.Correlation model for shadow fading in mobile radiosystems.IEE Electronics Letters, 27(23):2145 – 2146, 7 Nov. 1991.
M. Youssef, M. Mah, A. Agrawala.Challenges: device-free passive localization for wirelessenvironments.ACM MobiCom, Sept. 2007.
R. Hekmat and P. V. Mieghem.Connectivity in wireless ad-hoc networks with a log-normalradio model.Springer Mobile Networks and Applications, 11:351–360,April 2006.
Patwari, Agrawal Effects of Correlated Shadowing
Appendix For Further Reading
For Further Reading II
C. Bettstetter and C. Hartmann.Connectivity of wireless multihop networks in a shadowfading environment.Wirel. Netw., 11(5):571–579, 2005.
C. Newport, D. Kotz, Y. Yuan, R.S. Gray, J. Liu, C. Elliott.“Experimental Evaluation of Wireless SimulationAssumptions”.Simulation, vol. 83, no. 9, pp. 643-661, 2007.
I P. Agrawal, N. Patwari.Correlated link shadow fading in multi-hop wirelessnetworks.Tech Report arXiv:0804.2708v2, 18 Apr 2008.
Patwari, Agrawal Effects of Correlated Shadowing
Appendix For Further Reading
For Further Reading III
I Z. Wang, E. K. Tameh, A. Nix.Simulating correlated shadowing in mobile multihoprelay/ad-hoc networks.Tech. Rep. IEEE C802.16j-06/060, IEEE 802.16 BroadbandWireless Access Working Group. July 2006.
Patwari, Agrawal Effects of Correlated Shadowing