GRETSI 2009
Signal Processing and
Communications for Sensor Networks
Martin Vetterli, EPFL and UC Berkeley
joint work with T. Ajdler, G. Barrenetxea, H. Dubois-Ferriere, F.Ingelrest, M. Kolundzija,
R. Konsbruck, Y. Lu, O. Roy, T. Schmid, L. Sbaiz, E.Telatar, M.Parlange (EPFL),
P.L.Dragotti (Imperial), M.Gastpar (UCBerkeley)
Support: Swiss NSF National Center on Mobile Information and Communication Systems
http://www.mics.org
Audiovisual Communications
Laboratory
Acknowledgements
• To the organizers!
• Swiss and US NSF, our good friends and sponsors
• The National Competence Center on Research
‘’Mobile Information and Communication Systems’’ (MICS)
• The SwissExperiment, a large scale environmental monitoring effort
in the Swiss Alps
• K.Ramchandran and his group at UC Berkeley,
for sharing pioneering work on distributed source coding
• Colleagues at EPFL and ETHZ involved in MICS
- M.Grossglauser, for making things move
- E.Telatar, for wisdom and figures!
- J.Bovay, for NCCR matters
Spring 2009 - 2
Outline
1. Introduction
Wireless sensor networks
From “one to one” to “many to many”, or from Shannon to now!
2. The structure of distributed signals and their sampling
Sensor networks as sampling devices of the real world
Distributed image processing: The plenoptic function
Spatial sound processing: The plenacoustic function
Acquiring the diffusion equation: trade spatial for temporal super-resolution
3. Distributed source coding
Source coding, Slepian-Wolf and Wyner-Ziv
Distributed R(D) for sounds fields
4. On the interaction of source and channel coding
To separate or not to separate... That is the question!
The world is analog, why go digital? Gaussian sensor networks
5. Environmental monitoring
Environmental monitoring for scientific purposes and sensor tomography
SensorScope: Real life environmental monitoringin the Swiss Alps
6. Conclusions
Spring 2009 - 3
From centralized to “self-organized”
• Classic solutions (e.g. GSM, UMTS):
characterized by heavy fixed infrastructures
• Evolution of wireless communication
equipment: computational power , size ,
price , ~ transmit power
• 110 Billion US$ for UMTS licenses: is there
another way?
Ad-hoc networking solution:
- multihop, collaborative
- reinvented many times
- self-organization cute but tricky ; )
Current practice
-> hybrid solution: multihop access to backbone
-> Sensor Networks
Spring 2009 - 4
The Change of Paradigm
Old view:
one source, one channel, one receiver (Shannon 1948)
Source
Channel
Receiver
Current view:
distributed sources, many sensors/sources,
distributed communication medium, many receivers!
sources
channels
receivers
Note: still many questions open!
Spring 2009 - 5
Wireless Sensor Networks as Signal Processing Devices
Signals exist everywhere...they just need to be sensed!
– distributed signal acquisition: many cameras, microphones etc
– these signals are not independent: more sensors, more correlation
– there can be some substantial structure in the data,
due to the physics of the processes involved
Computation is cheap
– local computation
– complex algorithms to retrieve data are possible
Communication is everywhere
– this is the archetypical multi-terminal challenge
– mobile ad hoc networks, dense, self-organized sensor networks are built
– the cost of mobile communications is still the main constraint
Cross-disciplinarity
– fundamental bounds (what can be sensed?)
– algorithms (what is feasible?)
– systems (what and how to build?)
Spring 2009 - 6
The swiss version of homeland security :)
Distributed sensor network for avalanche monitoring:
Method: drop sensors, self-organized triangulation, monitoring
of location/distance changes, download when critical situation
Challenges: extreme low power, high precision,
asleep most of the time, when waking up, quick download
... and all self-organized!
Legacy technology: build a chalet, see if it stands after 50 years!
Spring 2009 - 7
Outline
1. Introduction
2. The structure of distributed signals and their sampling
Sensor networks as sampling devices of the real world
PDEs are the name of the game
Temporal sampling is easy….
Spatial sampling without filtering!
Distributed image processing: The plenoptic function
Handle with care: not bandlimited!
Spatial sound processing: The plenacoustic function
Non-separable, but essentially bandlimited
Sampling theorem, interpolation, and applications
Acquiring the diffusion equation
Trade spatial for temporal super-resolution
Applications
3. Distributed source coding
4. On the interaction of source and channel coding
5. Environmental monitoring
6. Conclusions
Spring 2009 - 8
2. The Structure of Distributed Signals and Sampling
A sensor network is a distributed sampling device
Physical phenomena
– distributed signals are governed by laws of physics
– partial differential equation at work: heat and wave equation…
– spatio-temporal distribution: evolution over time and space
Sampling
– regular/irregular, density
– in time: easy
– in space: no filtering before sampling
– spatial aliasing is key phenomena
Note: here we assume that we are interested by the ‘’true’’ phenomena,
decision/control: can be different!
Spring 2009 - 9
2. The Structure of Distributed Signals and Sampling
Analog signals:
Different dimensions have physical meanings (e.g. space and time).
The analog signals are governed by certain physical law.
sound field:
wave equation
pollution plume:
diffusion equation
plenoptic field:
ray model (far field);
wave equation (near field)
Spring 2009 - 10
2. Sampling versus sampling physics (1/4)
1. Classic sampling
– Key: Spaces V, W, bijection f(t)  fk
2. Spatio-temporal sampling
t
– Temporal filtering easy
– No spatial filtering possible!
x
Spring 2009 - 11
2. Sampling versus sampling physics (2/4)
3. Sampling physics
– Space V can be partly parametric (e.g. point source, FRI, sparse)
– PDE is given by the physics of the problem
– No spatial filtering in (t,x) but PDE does spatial filtering for us!
Goals
– From samples find field
– From samples find sources
Spring 2009 - 12
2. Challenges of sampling physics (3/4)
Sampling physical fields given by PDEs and driven by sources
Good news:
• PDEs are known, and well understood
• PDE often regularize the problem (e.g. spatial smoothing)
• Some sources are in subspaces
Challenges:
•
•
•
•
•
•
•
Inhomogeneous dimensions: t and x are indeed different
Cost of sampling in x much higher than in t
Multidimensional sampling, possible non-separable
Regular sampling in time, regular/irregular in space
Sources are in manifolds
Aliasing and undersampling, especially in space, are a real problem
Some events are not bandlimited, and will never be
Spring 2009 - 13
2. Challenges of sampling physics (4/4)
Key physical phenomenas:
The wave equation:
• In far field: ray tracing is a good approximation
The diffusion or heat equation:
Navier-Stokes (turbulence):
• When averaged: diffusion or heat equation
Random walks:
• When averaged: diffusion or heat equation
Spring 2009 - 14
2. Sampling the real world
We consider 3 ‘’real’’ cases, and follow:
–
–
–
–
what is the physical phenomena
what can be said on the ‘’discretization” in time and space
is there a sampling theorem
what is the structure of the sampled signal
1. Light fields
– wave equation for near field
– ray tracing for far field
– plenoptic function and its sampling
2. Sound fields
– wave equation for sounds
– plenacoustic function and its sampling
3. Diffusion fields
– heat equation
– diffusion equation and sampling
Spring 2009 - 15
2.1 The Plenoptic Function [Adelson91]
Multiple camera systems
– physical world (e.g. landscape, room)
– distributed signal acquisition
– possible images: plenoptic function, 7-dim!
Background:
– pinhole camera & epipolar geometry
– multidimensional sampling
Implications on communications
– camera sources are correlated in a particular way
– limits on number on ‘’independent’’ cameras
– different BW requirements at different locations
Spring 2009 - 16
Examples
3D
3D
2D
4D
[Stanford multi-camera array]
5D
[Imperial College multi-camera array]
Spring 2009 - 17
2.2 The Plenacoustic Function [AjdlerSV:06]
Multiple microphones/loudspeakers
– physical world (e.g. free field, room)
– distributed signal acquisition of sound with “many” microphones
– sound rendering with many loudspeakers (wavefield synthesis)
This is for real!
–
–
–
–
sound recording
special effects
movie theaters (wavefield synthesis)
MP3 surround etc
Wave equation:
– Source: BL in time, sparse in space
– PDE: essentially BL in (time,space)
MIT1020 mics
Spring 2009 - 18
Plenacoustic function and its sampling
Setup
Questions:
– Sample with “few” microphones and hear any location?
– Solve the wave equation? In general, it is much simpler to sample the
plenacoustic function
– Dual question also of interest for synthesis (moving sources)
– Implication on acoustic localization problems
– Application for acoustic echo cancellation
Spring 2009 - 19
Examples:
PAF in free field and in a room for a given point source
•
•
•
We plot: p(x,t), that is, the spatio-temporal impulse response
The key question for sampling is:
, that is, the Fourier transform
A precise characterization of
for large and
will allow sampling
and reconstruction error analysis
Spring 2009 - 20
Plenacoustic function in Fourier domain (approx.):
:: temporal frequency
: spatial frequency
Sampled Version:
Thus: Spatio-temporal soundfield
can be reconstructed up to 0
Spring 2009 - 21
Computed and Measured Plenacoustic Functions
•
•
Almost bandlimited!
Measurement includes noise and temperature fluctuations
Spring 2009 - 22
A sampling theorem for the plenacoustic function
Theorem [ASV:06]:
•
•
•
Assume a max temporal frequency
Pick a spatial sampling frequency
Spatio-temporal signal interpolated from samples taken at
Argument:
•
•
•
Take a cut through PAF
Use exp. decay away from central triangle to bound aliasing
Improvement using quincunx lattice
Spring 2009 - 23
Plenacoustic function: Application
Application to wavefield synthesis [M. Kolundzija:09]:
•
•
Sound field reconstruction
Wide space equalization
Spring 2009 - 24
Some generalizations: The EM case
Electromagnetic waves and UWB
• Wave equation
• 3 to 6 GHz temp. frequency
• And a triangle!
Spring 2009 - 25
The heat equation and diffusion processes
The diffusion-advection process (Fick’s law):
where a,b: wind, s: unknown source
Model for: temperature, chemical plumes, smoke from forest fires,
radioactive materials ...
Example: heat diffusion in time and frequency
Spring 2009 - 26
A sampling theory for diffusion processes [Y.Lu:08-09]
Model: diffusion of unknown instantaneous sources
(e.g. sudden release of pollutants)
Goal: sample the field using a sensor network, and
estimate
and
.
Assumptions:
is a Poisson process, with average time
is (approximately) bandlimited, with bandwidth
Problem Statement:
What is the minimum total sampling density? (At least
)
What is the trade-off between spatial and temporal sampling rates?
Spring 2009 - 27
A sampling theory for diffusion processes [Y.Lu:08-09]
Spring 2009 - 28
The heat equation and diffusion processes
Theorem: Sampling a homogeneous diffusion process with Nyquist density fs:
temporal
samples
achievable
unachievable
condition number
spatial
density
We have to place the sensors at the right locations!
Spring 2009 - 29
On sampling and representation of distributed signals
We saw a few examples:
– Plenoptic function and light fields
– Plenacoustic function and sound fields
– Heat equation and diffusion processes
It is a general phenomena
– Random walks and the heat equation
– Electromagnetic fields and wave equation
– Diffusion processes and averages of turbulence
This has implications on:
– Sampling: where, how many sensors, how much information is to be sensed
– Gap between simple (separate) and joint coding
– Spatio-temporal waterpouring
Spring 2009 - 30
Outline
1. Introduction
2. The structure of distributed signals and sampling
3. Distributed source coding
Introduction
Source coding, sampling, and Slepian-Wolf
Distributed rate-distortion function for acoustic fields
4. On the interaction of source and channel coding
5. Environmental monitoring
6. Conclusions
Spring 2009 - 31
Correlated source coding and transmission
Dense sources = correlated sources
– physical world (e.g. landscape, room)
– degrees of freedom ‘’limited’’
– denser sampling: sources are more correlated
Background:
– Slepian- Wolf (lossless correlated source coding with binning)
– Wyner-Ziv (lossy source coding with side information)
Implications on communications
– such results are starting to be used...
– many open problems (e.g. general lossy case is still an open problem...)
– separation might not be the way... are there limiting results?
Below, specific results:
– Distributed rate-distortion for acoustic fields based on plenacoustic
function
– Also: Distributed compression: a distributed Karhunen-Loeve transform
Optimal data gathering using Slepian-Wolf
Spring 2009 - 32
Slepian-Wolf (1973…)
Given
– X, Y i.i.d with p(x,y)
X
Then: encode separately, decode jointly,
without coders communicating
Achievable rate region
– R1 ¸ H(X/Y)
– R2 ¸ H(Y/X)
– R1 + R2 ¸ H(X,Y)
R
Y
R2
H(Y)
H(Y/X)
H(X/Y)
H(X)
R1
• For many sources…. rather complex (binning)
• Lossy case: mostly open!
• Example of result: SW based data gathering [CristescuBV:03]
Spring 2009 - 33
The plenacoustic function as a model, Konsbruck (1/4)
Stationary spatio-temporal source on a line, measured by a microphone array
Greens’ function
– Fourier Transform essentially supported on a triangle!
Spring 2009 - 34
The plenacoustic function as a model (2/4)
Quincunx sampling lattice
Spring 2009 - 35
The plenacoustic function as a model (3/4)
Quincunx sampling lattice
Key insight: discrete spatio-temporal process is white!
Spring 2009 - 36
The plenacoustic function as a model (4/4)
Distributed rate-distortion functions for white sound field
– Centralized
– Quincunx sampling based
– Rectangular sampling based
– Thus: the distributed R(D) is determined for this case!
– For white source, some loss
Spring 2009 - 37
On distributed source coding…
Three cases studied:
– Data gathering with Slepian-Wolf (Cristescu et al)
– Distributed versions of the KLT (Gastpar, Dragotti et al)
– Distributed rate-distortion for acoustic fields (above)
These are difficult problems....
– lossy distributed compression partly open
– high rate case: Quantization + Slepian-Wolf
– low rate case: mostly open
In many case
– Strong interaction of “source” and ‘’channel’’
– Large gains possible
but we are only seeing the beginning of fully taking advantage
of the sources structures and the communication medium...
The leads us to revisit the separation principle!
Spring 2009 - 38
Outline
1. Introduction
2. The structure of distributed signals and sampling
3. Distributed source coding
4. On the interaction of source and channel coding
To separate or not to separate...
The world is analog, why go digital?
To code or not to code...
Gaussian sensor networks
5. Environmental monitoring
6. Conclusions
Spring 2009 - 39
4. On the interaction of source and channel coding
Going digital is tightly linked to the separation principle:
– in the point to point case, separation allows to use
“bits” as a universal currency
– but this is a miracle! (or a lucky coincidence)
There is no reason that in multipoint source-channel transmission
the same currency will hold (M.Gastpar)
Multi-source, multi-sink case:
– correlated source coding
– uncoded transmission can be optimal
– source-channel coding for sensor networks
Spring 2009 - 40
4.1 To separate or not to separate…
In point to point, if R < C, all is well in Shannon land. In multipoint
communication, things are trickier (or more interesting)
Famous textbook counter example (e.g. Cover-Thomas)
R2
C2
Source
Channel
Y
binary erasure multiaccess
log2 3
1/3
1/3
0
1/3
X
H(Y)
1
H(Y/X)
H(X/Y)
H(X)
log2 3
R1
1
C1
No intersection, but communication possible!
Spring 2009 - 41
Sensor networks and source channel coding
[GastparV:03/04]
Consider the problem of sensing
– one source of analog information but many sensors
– reconstruct an estimate at the base station
Model: The CEO problem [Berger et al], Gaussian case
W1
U1
W2
Source
U2
F1
F2
X1
X2
S
Z
Y
G
S
WM
UM
FM
XM
Question: distributed source compression and MIMO transmission or
uncoded transmission?
Spring 2009 - 42
Example: Gaussian Source, Gaussian Noise
Performance (growing power shared among sensors):
– with uncoded transmission:
– with separation:
Exponential suboptimality!
Condition for optimality: measure matching!
– Can be generalized to many sources
Spring 2009 - 43
It is the best one can do:
Communication between sensors does not help as M grows!
Intriguing remark:
– by going to ‘’bits’’, MSE went from 1/M to 1/Log(M)
– ‘’bits’’ might not be a good idea for distributed sensing and
communications
If not ‘’bits’’, what is information in networks? [Gastpar:02]
Spring 2009 - 44
Outline
1. Introduction
2. The structure of distributed signals and sampling
3. Distributed source coding
4. On the interaction of source and channel coding
5. Environmental monitoring
Monitoring for scientific purposes
Environmental monitoring
The SensorScope project
The CommonSense project
6. Conclusions
Spring 2009 - 45
Environmental Monitoring: Technological Paradigm Change
Today, one of the primary limitations in environmental research is the lack
of simultaneous high-density spatial and temporal observations
Monitoring for scientific purposes
– “create” a new instrument for critical data
– most current acquisitions are undersampled
– verification of theory, simulations
Environmental data
– unstable terrain, glaciers
– watershed monitoring
– pollutant monitoring, forest monitoring
Orders of magnitude of difference
– price
– size
– power
We expect this will have a transformational effect on
– what is monitored
1K$ “each”
– how it is monitored
– what is understood
100K$
Spring 2009 - 46
The SensorScope Project (2005-…)
Team: G. Barrenetxea, H.Dubois-Ferriere,T.Schmid,F.Ingelrest,
G.Schaeffer + M. Parlange & EFLUM
http://sensorscope.epfl.ch
What are we trying to accomplish?
SensorScope:




distributed sensing instrument
relevant datasets with clear documentation
all data on-line, real-time
anybody can compute/analyze with
Sensor nodes:
 many possible platforms inc. low power
(Berkeley motes, tinynode, tmote)
 many types of sensing (e.g. cyclops)
First Step: SensorScope I




a few dozen nodes
self-organized network up for 9 months
large dataset collected
fun platform and testbed
Spring 2009 - 47
SensorScope II [w. M.Parlange]
SensorScope II
 collaboration with EFLUM (Laboratory of Environmental Fluid Mechanics and
Hydrology)
 10 real-world deployments from build to high mountain environments
 hundreds of Megabytes of sensing data publicly available
Genepi Rock glacier, 2600 m
Genepi Rock glacier, your computer
 very interesting theoretical (physics) and practical problems!
 we need reliable and meaningful data!
Improved networking
 packet combining, routing without routes
 more power efficient platforms (tinynodes)
Data analysis
 signals are far from....Gaussian!
Spring 2009 - 48
The core of SensorScope: WeatherStation
WeatherStation
 Centered around Tinynode (lowest-power sensor node, with medium range)
 Solar energy subsystem: Energy autonomous
 Sensors are daisy-chained to a single connector: No limit on the type and
number of sensors
 Automatic sensor recognition: No configuration required
 Local storage: SD card (2 GB)
 GPS & GPRS module
 Fast and easy installation on all types of terrain:
Spring 2009 - 49
SensorScope Front End
Features:
 Centralized data access and
administration
 Real-time monitoring
 Data visualization and download
 Network health and battery status
 Organize stations into sets
 Set up alerts for out-of-range conditions
 Security and account management
 User friendly
Spring 2009 - 50
Network architecture
 Sensor network with ad hoc data gathering protocols (10 to 100’s)
 Basestation with available wide area communication (e.g. GPRS)
 Web server with data online
Spring 2009 - 51
Networking
Ad Hoc Networking:




We use a custom communication stack:
Keep it as simple as possible (robustness)
Works by overhearing (minimizes traffic)
Written for TinyOS 2.x
Main features:

Routing tables are updated dynamically
(allows to add/remove stations)
 Radio duty-cycle < 10%
(low energy consumption)
 Stations are synchronized
(all “on” at the same time, consistent time stamps)
 Shortest path routing with random selection (among the “shortest path high
quality link neighbours”)
Spring 2009 - 52
Networking: Random, biased selection of next hop
Spring 2009 - 53
Power is the basic problem!
Power usage in a Tinynode
(a) Off
(b) Listening
(c)-(g) various sending power
 Communications is power hungry
 Careful management of power
 Power gathering (e.g. solar panels)
 Energy efficient protocols for data gathering and GPRS connection
Spring 2009 - 54
From Theory to Practice!
All the tools are there (in theory):
Routing algorithms, data correlation, time synchronization,
But ...
Make theory work in practice is hard ...
The Theory …
The Practice…
Spring 2009 - 55
Application Example: Risk Analysis
Real problem: land slides, infrastructure damage etc:
Understanding the changing environment, effects of warming, loss of
permafrost etc
Spring 2009 - 56
Application Example: Genepi
Location: Rock glacier above Martini (VS)
Spring 2009 - 57
Spring 2009 - 58
A day in the life of Genepi!


Fully autonomous camera, GPRS based,
Onboard image processing, Open platform, Linux based
Spring 2009 - 59
Results from Genepi
Spring 2009 - 60
6. Conclusions
There are some good questions on the interaction of
–
–
–
–
–
physics of the process: space of possible values
sensing: analog/digital
representation & compression: local/global
transmission: separate/joint
decoding & reconstruction: applications
From joint source-channel coding to source-channel communication
– This goes back to Shannon’s original question,
but multi-source multi-point communication is hard...
On-going basic questions:
– are there some fundamental bounds on certain data sets?
– are there practical schemes to approach the bounds?
– what is observable and what is not?
Applications:
– environmental monitoring has many interesting,
high impact questions
– technology amazingly mature
– datasets very far from ‘’usual’’ models
Spring 2009 - 61
Thank you for your attention! Questions?
“Would you like to see the top on Google Earth?”
© New Yorker
Spring 2009 - 62
References
•
On sampling
– M. Vetterli, P. Marziliano, T. Blu. Sampling signals with finite rate of innovation.
IEEE Tr. on SP, Jun. 2002.
– T. Ajdler, L. Sbaiz and M. Vetterli, The plenacoustic function and its
sampling, IEEE Transactions on Signal Processing, Oct. 2006.
– T. Blu, P.L. Dragotti, M. Vetterli, P. Marziliano and L. Coulot, Sparse Sampling of
Signal Innovations, IEEE Signal Processing Magazine, Vol. 25, Nr. 2, 2008.
– M.N. Do, D.Marchand-Maillet, M. Vetterli, On the Bandwidth of the Plenoptic
Function, IEEE Tr.IP, submitted, 2008.
– Y.M. Lu and M. Vetterli, Spatial Super-Resolution of a Diffusion Field by
Temporal Oversampling in Sensor Networks, IEEE ICASSP 2009.
•
Correlated distributed source coding
– R.Cristescu, B.Beferull and M.Vetterli, Correlated data gathering, Infocom2004.
– M. Gastpar, P. L. Dragotti, and M. Vetterli. The distributed Karhunen-Loeve
transform. IEEE Tr. on IT, Dec. 06.
– R.Konsbruck, E.Telatar, M.Vetterli, The distributed rate-distortion function of
sounds fields, ICASSP06.
Spring 2009 - 63
References
•
On sensor networks, separation uncoded transmission
– M.Gastpar, M.Vetterli, PL Dragotti, Sensing reality and communicating bits: A
dangerous liaison - Is digital communication sufficient for sensor networks? IEEE
Signal Processing Mag.,July 2006
– M. Gastpar, B. Rimoldi, M. Vetterli. To code or not to code: lossy source-channel
communication revisited, IEEE Tr. on IT, 2003
– M.Gastpar, M..Vetterli, The capacity of large Gaussian relay networks, IEEE Tr
on IT, March 2005.
•
SensorScope
– See http://sensorscope.epfl.ch
– G. Barrenetxea, F. Ingelrest, G. Schaefer and M. Vetterli,The Hitchhiker's Guide
to Successful Wireless Sensor Network Deployments.,. ACM SenSys2008.
– F. Ingelrest, G. Barrenetxea, G. Schaefer, M. Vetterli, O. Couach and M.
Parlange, SensorScope: Application Specific Sensor Network for Environmental
Monitoring, to appear in ACM Transactions on Sensor Networks.
Spring 2009 - 64