Distributed Signal Processing for Sensor Networks

Transcription

1 GTTI Rome meeting June 07 Distributed Signal Processing for Sensor Networks Martin Vetterli, EPFL and UC Berkeley joint work with T. Ajdler, G. Barrenetxea, H. Dubois-Ferriere, I. Jovanovic, R. Konsbruck, O. Roy, T. Schmid, L. Sbaiz, E.Telatar, M.Parlange (EPFL), P.L.Dragotti (Imperial), M.Gastpar (UCBerkeley) Spring 2007 Work done within the Swiss NSF National Center on Mobile Information and Communication Systems Audiovisual Communications Laboratory

2 Outline 1. Introduction The Center on Mobile Information and Communication Systems Wireless sensor networks: from one to one to many to many 2. The structure of distributed signals and sampling Sensor networks as sampling devices Distributed image processing: The plenoptic function Spatial sound processing: The plenacoustic function 3. Distributed source coding Source coding, Slepian-Wolf and Wyner-Ziv Distributed KLT Distributed R(D) for sounds fields 4. On the interaction of source and channel coding to separate or not to separate... The world is analog, why go digital? Gaussian sensor networks 5. Environmental monitoring Environmental monitoring for scientific purposes and sensor tomography SensorScope: Intelligent building and environmental monitoring 6. Conclusions Spring

3 Acknowledgements To the organizers, the ACCESS- DLS Seminar Series Swiss and US NSF, our good friends and sponsors The National Competence Center on Research Mobile Information and Communication Systems (MICS) K.Ramchandran and his group at UC Berkeley, for sharing pioneering work on distributed source coding Colleagues at EPFL and ETHZ involved in MICS - J.P.Hubaux, for pushing ad hoc ntws - M.Grossglauser, for making things move - E.Telatar, for wisdom and figures! - J.Bovay, for NCCR matters Spring

4 1.1 Introduction The Swiss National Competence Center on Research (NCCR) Mobile Information and Communication Systems (MICS) Goal: study fundamental and applied questions raised by new generation mobile communication/information services, based on self-organisation. Cross-layer investigation: mathematical issues (statistical physics based analysis, information and communication theory) to networking, signal processing, security, distributed systems, software architecture, DB etc Examples: ad-hoc networks, sensor networks, peer-to-peer systems Network of researchers: - EPFL, ETHZ, CSEM, UNI-BE,L,SG,ZH, 30 profs, 70 PhD students - 5 clusters, ranging from circuits to applications Budget: - 8 MSfr/Year (6 M$/Y-> 7 M$/Y) - 10 years horizon Note: similar to a US-NSF Engineering Research Center Spring

5 The NCCR MICS Network University Basel: Computer Science Department CSEM, Swiss Center for Electronics and Microtechnology University of Applied Sciences Western Switzerland University Bern: Institute of Informatics and Applied Mathematics ETHZ: Electrical Engineering and Computer Science Departments EPFL: Schools of Computer and Communication Sciences (Leading House), Engineering and Architecture & Environment University Lausanne: Ecole des Hautes Etudes Commerciales University Lugano: Computer Science Department Spring

6 From centralized to self-organized (1/2) 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 ; ) Spring

7 From centralized to self-organized (2/2) Why not ad-hoc everywhere? - fully multihop solution - sensor networks - Mesh networks - peer-to-peer communications Current practice -> hybrid solution: multihop access to backbone Spring

8 Some capacity question.. Gupta/Kumar showed that there might be a capacity problem! the total capacity does not scale well with the number of users it depends on the traffic matrix the question is hard! N points (users) O(N) transmissions from left to right over O( N ) transmission links mean 1 O( N) capacity per attempted transmission O(N) users O(N) users Cut set ~ N Very active research area - random matrix theory - sophisticated bounding methods Spring

9 Some fundamental principle Percolation Theory as a Fundamental Concept sub-critical (r slightly < r c ) super-critical (r slightly > r c ) p r c r It percolates through connectivity, capacity, P2P, gossip, etc Spring

10 1.2 The view of the world: Wireless sensor networks! 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 multiterminal 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

11 The Change of Paradigm Old view: one source, one channel, one receiver (Shannon 1948) Source Channel Receiver Next view: distributed sources, many sensors/sources, distributed communication medium, many receivers! sources channels receivers Note: many questions are open! Spring

12 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

13 The swiss version of homeland security (cont.): Avalanche and Landslide Analysis through Sensor Networks (E.Charbon and C.Ancey, EPFL) Approach Sensor network moving within natural event Goals Gain insight into currently unknown phenomena Model and validate novel sensor network paradigms Miniaturize 10GHz UWB local positioning system Gain experience in distributed warning and monitoring systems Spring

14 Environmental Monitoring: Technological Paradigm Change Orders of magnitude less cost for sensing: 100K$ $ Orders of magnitude of difference in price, size and power! We expect this will have a tidal effect on what is monitored how it is monitored what is understood and there are Berkeley motes to save the world! (and many other platforms of the sort) Spring

15 Outline 1. Introduction 2. The structure of distributed signals and sampling Sensor networks as sampling devices Distributed image processing: The plenoptic function Spatial sound processing: The plenacoustic function 3. Distributed source coding 4. On the interaction of source and channel coding 5. Environmental monitoring 6. Conclusions Spring

16 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 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

17 2.1 Sampling the real world We consider 2 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 Light fields wave equation for light or ray tracing plenoptic function and its sampling Sound fields wave equation for sounds plenacoustic function and its sampling Spring

18 2.2 The Plenoptic Function [Adelson[ Adelson] 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

19 Examples 3D 3D 2D 4D 5D [Stanford multi-camera array] [Imperial College multi-camera array] Spring

20 On Plenoptic Sampling [Shum et al] Model Epipolar geometry points become lines slope depends on depth of field Plenoptic function a collection of lines (modulo covering/uncovering) slopes bounded by (min, max) depth Fourier transform...a pie slice... can be sampled Spring

21 Fourier transform (approx.) and after sampling in space ω s ω s ω t ω t Examples of recent results 1. Bandlimited walls/fcts [DoMMV:04] Plenoptic function not BL unless linear wall. 2. Plenoptic function of finite complexity objects [Maravic et al] For certain simple scenes (collection of Diracs), the plenoptic function can be sampled exactly Spring

22 2.3 The Plenacoustic Function [Ajdler[ Ajdler] 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 MIT1020 mics LCAV 8 LS, moving mics Spring

23 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 cancellation Spring

24 Examples: PAF in free fields in a room for a certain 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

25 Plenacoustic function in Fourier domain (approx.): ω:: temporal frequency Φ: spatial frequency Sampled Version: Thus: Spatio-temporal soundfield can be reconstructed up to ω 0 Spring

26 Computed and Measured Plenacoustic Functions Almost bandlimited! Measurement includes noise and temperature fluctuations Spring

27 Example of plenacoustic function on circle This is relevant for HRTF - Measurements - Interpolation Spring

28 HRTF set up and measurement HRTF from KEMAR, every 5 degrees for 44.1 KHz - Personalized audio systems - Efficient aquisition Spring

29 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

30 Some generalizations Sampling patterns Other geometries Spring

31 Some generalizations: The EM case Electromagnetic waves and UWB Wave equation 3 to 6 GHz temp. frequency And a triangle! Spring

32 The EM case and TV channels Assume a movement model Spring

33 On sampling and representation We saw a few examples: Plenoptic function and light fields Plenacoustic function and sound fields It is a general phenomena Heat equation Electromagnetic fields Diffusion processes 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

34 Outline 1. Introduction 2. The structure of distributed signals and sampling 3. Distributed source coding Introduction Source coding, sampling, and Slepian-Wolf Distributed KLT Distributed rate-distortion function for acoustic fields 4. On the interaction of source and channel coding 5. Environmental monitoring 6. Conclusions Spring

35 3.1 Correlated source coding and transmission Dense sources = correlated sources physical world (e.g. landscape, room) degrees of freedom limited denser sampling: more correlated sources Background: Slepian- Wolf (lossless correlated source coding with binning) Wyner-Ziv (source coding with side information) Implications on communications such results are starting to be used... many open problems (general lossy case is still an open problem...) separation might not be the way... are there limiting results? Below, specific results: Distributed compression: a distributed Karhunen-Loeve transform Distributed rate-distortion for acoustic fields based on plenacoustic function Spring

36 Slepian-Wold (1973 ) Given X, Y i.i.d with p(x,y) Then: encode separately, decode jointly, without coders communicating Achievable rate region R 1 H(X/Y) R 2 H(Y/X) R 1 + R 2 H(X,Y) R 2 H(Y) H(Y/X) H(X/Y) H(X) R 1 For many sources. rather complex (binning) Lossy case: mostly open! Example of result: SW based data gathering [CristescuBV:03] Spring

37 The distributed Karhunen-Loeve Transform (DKLT) [Gastpar-Dragotti-RoyV] The Karhunen-Loeve transform (KLT) is a key part of source compression. For example JPEG, MPEG, MP3 all use some version of KLT (DCT, wavelets, filter banks) this is the workhorse of source compression! Assume a correlated vector source, zero mean, autocorrelation best M < N subspace approximation is given by the projection onto the M eigenvectors of RX with largest eigenvalues best compression (Gaussian case) is waterpouring over the eigenvalues in the eigenspace X 1 X 2 X 3 KLT Q Y 1 Y 2 Y 3 Y 4 Approximation Compression X N Spring

38 What about a distributed scenario? Distributed sensors measure correlated data What is the best way to separately compress this source by L local compressors, for a joint decoder? This answers (in part) a distributed source coding problem The problem of the distributed KLT addresses: non-linear approximation (NLA) rate-distortion behavior Spring

39 The plenacoustic function as a model, Konsbruck (1/3) Stationary spatio-temporal source on a line, measured by a microphone array Greens function FT essentially supported on a triangle! Spring

40 The plenacoustic function as a model (2/3) Quincunx sampling lattice Spring

41 The plenacoustic function as a model (3/3) Distributed rate-distortion functions Centralized Quincunx sampling based Rectangular sampling based Thus: the distributed R(D) is determined for this case! Spring

42 On distributed source coding Three cases seen: Data gathering with Slepian-Wolf Distributed versions of the KLT Distributed rate-distortion for acoustic fields These are difficult problems... lossy distributed compression partly open high rate case: Q + SW low rate case: more 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... Spring

43 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

44 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

45 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) R 2 log 2 3 H(Y) Source Y X 1/3 1/3 0 1/3 C 2 1 Channel binary erasure multiaccess H(Y/X) H(X/Y) H(X) log 2 3 R 1 1 C 1 No intersection, but communication possible! Spring

46 To code or not to code [GastparRV[ GastparRV:03]: Uncoded transmission for lossy source-channel communication It is well known that a Gaussian source over a AWGN channel can be sent as is, achieving optimal performance easy way to achieve best performance (no delay...) The parameters of source-channel coding are: source distribution: source distortion or error measure: channel conditional distribution: channel input cost function: The art is measure matching! D(R): channel has to look like the test channel to the source C(P): source has to look like a capacity achiev. distrib. to the channel in the Gaussian case, it all matches up! (MSE, power, densities) Spring

47 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 W 1 U 1 F 1 X 1 W 2 U 2 F 2 X 2 Z Source S Y G S W M U M F M X M Question: distributed source compression and MIMO transmission or uncoded transmission? Spring

48 Example: Gaussian Source, Gaussian Noise Performance (cst or poly. growing power shared among sensors): with uncoded transmission: with separation: Exponential suboptimality! Condition for optimality: measure matching! Can be generalized to many sources Spring

49 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

50 On going work on analog sensor networks Multiple sources L sources, L channel usages sources to sensors matrix A Multiple sources and sinks sensors to sinks matrix B Physical process: degrees of freedom, sampling Robustness to fading, synch loss (Rician fading) Spring

51 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 - wind tomography monitoring for intelligent buildings - SensorScope 6. Conclusions Spring

52 5. The case for environmental monitoring (MICS applications) 5.1 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 University of Basel canopy sensing and actuating Example: UCLA CENS. environmental monitoring Spring

53 Sensor networks and tomography [Jovanovic[ Jovanovic] Scaling laws...usually negative Gupta and Kumar, capacity per user: The tomographic factor N sensing points indirect measurements (integral measures), order number of reconstructed points: 6 sensing pts 12 measurements modalities for measurement - time of flight - absorption Spring

54 An example: Wind Tomography [Sbaiz] The sensor network is a distributed measurement device N sensors lead to a sampling of the field of interest in N points Is there a way to get more information out of N measurement points? Idea: tomography, with scaling law: N measurement points reconstructed values acoustic anemometer measurement field Spring

55 Traditional Tomography and Flow Tomography receivers: measurement is integral along straight line Source (e.g. X-ray) => Radon transform Wind tomography: The path integral is part of the unknowns receivers: measurement influenced by unknown path Source Acoustic measurement delay (time of flight) direction of arrival Spring

56 Results Simulation: Lagrange triangle tesselation. 16 stations, maximum wind speed 380 Km/h Current status: initial experimental platform with ultrasound joint wind and temperature measurement (v ~ ) investigate a 96 terminal, ultrasound set up for temperature imaging Spring

57 Results Measurements: Experimental set up 1m ring with 10 sources, 10 receivers, 40KHz sine pulse, 2KHz BW, 96 KHz sampling Current status: Time delay 10^(-8) leads to 0.01 Kelvin precision Noise problems. 0.5 Kelvin Non-linearity problems Spring

58 5.2 The SensorScope Project [Barrenetxea[ Barrenetxea, Dubois-Ferriere Ferriere] What are we trying to accomplish? (G. Barrenetxea, H.Dubois-Ferriere, T.Schmid) 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 collects fun platform and testbed Spring

59 Welcome to the new building! Spring

60 The network today Spring

61 The next step: SensorScope II and III [w. M.Parlange Parlange] Next step: SensorScope II and III collaboration with EFLUM (Laboratory of Environmental Fluid Mechanics and Hydrology) objective: gather environmental data for modeling of energy fluxes at earthatmosphere boundary two large-scale outdoor sensor networking deployments: EPFL campus and alpine glacier 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

62 The core of SensorScope: WeatherStation WeatherStation centered around Tinynode (lowest-power sensor node) solar energy subsystem: energy autonomous water proof housing seven external sensors measuring: temperature (ambient and surface) humidity wind speed and direction soil moisture solar radiation precipitation Solar energy system First Prototype WeatherStation Spring

63 WeatherStation Deployments SensorScope II (Summer 2006) 110 WeatherStations on EPFL campus SensorScope III (Winter ) N WeatherStations on Glacier de la Plaine Morte, Valais (CH) Spring

64 WeatherStation Deployment and Web Interface Objective: Relevant datasets with clear documentation All data on-line: Anybody can compute/analyze with Spring

65 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

66 Thank you for your attention! the plenoptic function from my window. Questions? Spring

67 References On the NCCR-MICS: all papers on line On sensor networks and separation 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 On sampling M. Vetterli, P. Marziliano, T. Blu. Sampling signals with finite rate of innovation. IEEE Tr. on SP, Jun T. Ajdler, L. Sbaiz and M. Vetterli, The plenacoustic function and its sampling, IEEE Transactions on Signal Processing, Oct T. Ajdler, L. Sbaiz, A. Ridolfi and M. Vetterli, On a stochastic version of the plenacoustic function, ICASSP06. Correlated 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

68 References Uncoded transmission, relays, and sensor networks 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 Flow Tomography I.Jovanovic, L.Sbaiz, M.Vetterli, Acoustic Flow Tomography, ICASSP06. SensorScope See Spring