On Minimalism and Scale in Sensor Networks
Upamanyu Madhow
ECE Department
University of California, Santa Barbara
Funding Sources
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Why sensor networks?
• Sensors have been around for a long time
– Why are we so interested in sensor networks?
• Role of networking
– Can we usefully exploit data from lots of sensors?
– A whole greater than the sum of its parts?
• Why lots of sensors?
– Large areas to be covered, small sensing range
• Many big picture issues for theorists to ponder
– How does scale improve information?
– How do we communicate with a million sensors?
– How can inter-sensor collaboration help?
– How can we engineer trust in wireless sensor networks?
Big picture questions lead to new ideas
• How to gather information from 100,000 sensors?
– Imaging sensor nets
• How do we scale surveillance and tracking?
– Tracking with binary proximity sensors
– Large-scale camera networks
• Can sensors act like a distributed antenna array?
– Practical algorithms for distributed transmit beamforming
Today’s focus: minimalism and scale
• Scaling to a very large number of sensors
– Minimalism in sensor capability and deployment requirements
– Imaging sensor nets
Bharath Ananthasubramaniam, Munkyo Seo, Prof. Mark Rodwell
• Scaling in energy
– Collaboration with minimal inter-sensor communication
– Distributed transmit beamforming with feedback control
Raghu Mudumbai, Ben Wild, Prof. Joao Hespanha, Prof. Kannan Ramchandran
• Scaling in sensor cost/functionality
– Minimalism in sensor output: yes or no
– Tracking with binary proximity sensors
Nisheeth Srivastava, Raghu Mudumbai, Jaspreet Singh, Rajesh Kumar, Prof. Subhash Suri
Imaging Sensor Nets
collector: satellite
base station on UAV
vast numbers of
low-complexity "dumb" pixels
sensor + RF transducer + antenna.
Sensor field
Sensor field
Field of simple, low-power sensors dispersed across field of view
Cast on ground from truck, plane, or satellite
Sensor as pixels (“dumb dust”)
Collector-driven data collection: Sensors electronically reflect, with data modulation, beacon
from collector (“virtual radar”)
Sensor-driven data collection: Sensors transmit at will, sensor location and data estimated by
collaboration among a network of collectors
Minimal functionality: no GPS, no inter-sensor networking
Lifetime of year on watch cell battery
Sophisticated collectors
Radar and image processing, multiuser data demodulation
Joint localization and data collection
Range varies from 100m to 100 km
Active versus “passive” sensors, collector characteristics
Prototype with stationary collector

R
transmitted spread-spectrum carrier
with short correllation length
data from pixel
received spead-spectrum carrier
with modulation
Millimeter wave carrier frequencies
Narrow beam with moderate size collector antenna
Small sensor form factor
Key challenges
Low-power, low-cost sensor ICs: mm-wave in CMOS
Collector signal processing
Inducing a radar geometry
Beacon with location code
Active sensor reflects beacon
Collector
Sensor field with
active sensors and inactive sensors
Basic Link Diagram
Dcoll ,TX
f down
f down
Dsens, RX
DOWN-LINK
Freq. shift to filter out
ground return
f PRBS PRBS
f delta  f down  f up
BPSK modulation
f up
DATA
Dcoll, RX
UP-LINK
Jointly detect
DATA and DELAY
Collector
Dsens,TX
Sensor
Zeroth order Link Budget
75 GHz carrier
Collector with 1 meter diameter antenna, 100 mW transmit antenna
100 Kbps using QPSK/BPSK at BER of 10-9
300 m range for semi-passive sensor
Down-link
Up-link
Eb
1





 PTX Dcoll ,TX  down  Dsens, RX Gsens Dsens,TX
N0
 2kTFB 
 4r 
2
 up 

 4r 
 Dcoll , RX


2
Eb
1
 4
N0
r
100 km range for active sensor with 5 mW transmit power
 Eb 


1
 down 


N 

 2kTF B 
 Pcoll ,TX Dcoll ,TX  4r  Dsens, RX


sens
 0  down


Eb
1
 2
N0
r
 Eb 


 up
1






P
D
sens
,
TX
sens
,
TX
 4r
N 
 2kTF B 

coll
 0  up


Eb
1
 2
N0
r
2
2


 Dcoll , RX

Downlink
Uplink
(bottleneck)
Collector Imaging Algorithm
: location code
: beam pattern
Localization for large sensor density
• Single Sensor Algorithm + SIC – works well
25 sensors
100 sensors
Brassboard concept validation
Ongoing research and open issues
• Hardware
– Sensor IC design
– Collector system integration
• Algorithms
– Alleviating inter-sensor interference
– Collaboration among collectors
• Data compression and representation
– Collector-driven data collection
– Sensor-driven data collection
• Integration of transceiver with sensing
– Well-defined interfaces for mm wave motes
Distributed Transmit Beamforming
• Distributed beamforming can increase range or cut power
– Rec’d power = (A + A + …+A)2 = N2 A2 if phases line up
– Rec’d power = N A2 if phases don’t line up (+ fading)
• Can use low frequencies for better propagation
– Large “antenna” using natural spatial distribution of nodes
• Diversity
• BUT: RF-level sync is hard!
f
ej 1
f
ej 2
Sync can be achieved using RX feedback!
SNR
feedback
Receiver
Feedback Control Mechanism
• Initially the carrier phases are unknown
• Each timeslot, the transmitters try a random phase correction
•Keep the corrections that increase SNR, discard the others
• Carrier phases become more and more aligned
• Phase coherence achieved in time linear in number of nodes
Typical phase evolution
(10 nodes)
Concept experimentally verified
by Ben Wild (UC Berkeley)
Towards an analytical model
• Empirical observation: convergence is highly predictable
Net effect of phase perturbations
x2
α.y[n]
What can we say about the distributions of x1 and x2?
(without knowing all the individual transmitter phases)
x1
Key idea: statistical approach
• Received signal proportional to
jf i [ n ]
e

–Infinitely many possible fi[n] for any given y[n]
i
• Analogy with statistical physics
–Given total energy i.e. temperature
• What is the energy of each atom?
• More interesting: how many atoms have a energy, E
– Concept of Macrostates
– Distribution of energy is fixed
– Maxwell-Boltzmann distribution
– Density ~ exp(-E/kT)
The “exp-cosine” distribution
• Initially fi[0] is uniform in (-π, π]
• The phases fi[n] get more and more clustered
• Given | i cos fi | NE[cos f ]  y[n] , what is the distribution of fi[n]?
– “Typical” distribution closest in KL distance to uniform

– The Conditional Limit Theorem
The “exp-cosine” distribution
f (f)  exp(  cos f)/I0 ()
I1( )
E[cos f ] 
 y[n]/N
I 0 ( )
Exp-cosine matches simulations
1
Probability density
N = 500 transmitters
0.5
0
-4
-3
-2
-1
0
1
2
3
4
Phase Angles in radians
Can now predict trajectory, optimize convergence rate, and prove scalability
Accurate prediction of trajectory
Optimize phase perturbation
•Optimize pdf for δi at each iteration
• restrict to uniform pdf: δi~uniform[-δ0,+δ0]
• Choose δ0 to maximize E(Δy[n]), given y[n]
200 transmitters
Fixed uniform distribution vs. uniform distribution optimized at each slot
Scalability and Convergence
Phase perturbation not optimized
o o
Uniform over (-2 ,2 )
Phase perturbation optimized
Scalable: Convergence is linear in the number of nodes N
(provably so for optimized phase perturbations)
Ongoing research and open issues
• Detailed understanding of time variations
– Trade off tracking versus misadjustment
• Protocols leveraging distributed beamforming
• Generalization to other distributed control tasks?
Tracking with binary sensors
• Minimalistic model appropriate for microsensors
– Sensor says target present or absent
– Appropriate for large-scale deployments
• How well can we track with a network of binary sensors?
– Fundamental limits
– Minimal path descriptions
– Efficient geometric algorithms
The Geometry of Binary Sensing
Target Path
Sensor Outputs
Localization patches
Localization arcs
Results
• Attainable resolution ~ 1/(sensor density*sensing range)
• Spatial low pass filtering
– Can track only “lowpass” version of the path
• OccamTrack algorithm
– Minimal piecewise linear representations
– Velocity estimates for “lowpass” version
• Robustness to sensing range variation
– Particle filter + Geometric clean-up
• Multiple targets
– Many possible explanations for snapshot of sensor readings
– Temporal evolution can be exploited by particle filter
How a trajectory is localized
Max patch size at least 1/(density*range) for any deployment
Patch size of the order of 1/(density*range) for Poisson deployment
Resolution
theorems
Minimal representation: OccamTrack
Greedy algorithm for piecewise linear representation:
Draw lines stabbing localization arcs that are as long as possible
Spatial Lowpass Filtering
Cannot capture rapid variations
Can only reconstruct “lowpass” version of path
Justifies simple piecewise linear representation
Velocity estimation and minimal representation
Which path should we use to estimate (lowpass version of) velocity?
We can be off by a factor of two!
A simple formula: dv/v = dL/L
Proposition: If piecewise linear approx works well, then velocity estimate is accurate.
Simulation Results
Weighted Centroid Output
(Kim et al, IPSN 2005)
OccamTrack Output
OccamTrack
Velocity Estimate
Fundamental Resolution Limits
Theoretical resolution attained by both regular and random deployment
Handling non-ideal sensing
Not detected
Experiment with acoustic sensor
?
Detected
Low pass filter
observations
A simple model
Acoustic sensors are unreliable & unpredictable
Localization patch = intersection of outer circles with complements of inner circles
Particle filtering algorithm provides robust performance
Geometric clean-up provides minimal description
Experiments with acoustic sensors
Non-ideal sensor
response
OccamTrack
Particle Filter
OccamTrack
with ideal sensing
Particle Filter +
Geometric
Multiple Targets: what does a snapshot tell us?
Significant ambiguity regarding how many targets and where they are
Can get a minimal explanation for sensor readings: greedy algorithm
But how do we piece together snapshots?
Particle filters work!
Simulation results with non-ideal sensing
Experiments with passive IR sensors
Ongoing research and open issues
• Signal processing framework
– Spatial lowpass filtering
– “Multiuser interference” due to multiple targets
• Multimodal sensing
– Enhancement of binary model
– Bayesian frameworks for combining sensor observations
• Distributed realizations
A Big Picture
• What is needed for sensor networks to be a success?
– Two or three successful big applications
• What can theorists do?
– Thought experiments based on application scenarios
– Ask the big picture questions
– Follow up with logical answers
– Collaborate with builders and experimentalists
• Example big picture questions
– How best to use sensor correlations?
– How to provide wire-like guarantees?
– What are good architectures for nextgen surveillance and
tracking?
– What are good models for distributed sensing & actuation?