Data driven sensor
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Anna Scaglione Cornell University IPAM Workshop – January 2007 Joint work with: Yao-Win Hong (now faculty at NTHU, Taiwan) PowerPoint PPT Presentation


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Data driven sensor access architectures for sensor networks. Anna Scaglione Cornell University IPAM Workshop – January 2007 Joint work with: Yao-Win Hong (now faculty at NTHU, Taiwan) Birsen Sirkeci Mergen (now PostDoc. at UC Berkeley). Signal Processing in sensor networks.

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Anna Scaglione Cornell University IPAM Workshop – January 2007 Joint work with: Yao-Win Hong (now faculty at NTHU, Taiwan)

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Data driven sensor

access architectures

for sensor networks

Anna Scaglione

Cornell University

IPAM Workshop – January 2007

Joint work with:

Yao-Win Hong (now faculty at NTHU, Taiwan)

Birsen Sirkeci Mergen (now PostDoc. at UC Berkeley)


Signal Processing in sensor networks

  • Distributed solutions allow to overlay virtually any network

    • Multi-terminal Source coding [e.g. Berger, Han, Amari, Ahlswede & Csiszar….], Distributed Detection [e.g. Tsitsiklis…]

  • Data processing & communication are interdependent

  • Optimize cooperative interactions (sequential or iterative) among network nodes


Classical networking bottlenecks

  • Network theory point of view (fixed strategy)

    • Collision model and Multi-hop routing

    • [Gupta-Kumar 00]

      • Protocol model

      • Physical model

    • Scalability: P2P Fusion Center

  • Real physical layer constraints (Net. Info. Theory):

    • Per antenna power constraint

    • Medium is broadcast and linear

    • Half duplex constraint (can’t listen if transmitting)


Distributed Source

Distributed

Transmitter/Receiver

Environment

S1

S2

S3

SN

Wireless Medium

  • Opportunities for sensor networks

    • Cooperative transmission

    • Redundancy of data  signal proc. to reduce traffic

  • Challenges for sensor networks

    • Difficulty in finding bounds and optimal designs

    • Enforcing decentralized cooperation and compression with minimal knowledge of the network state

      • Collection at fusion center and/or parallel computation


Received vector

Space-time code

Cooperative links

Beyond “collision”: Cooperative links

  • Decode and Forward, Amplify and Forward, Space Time Coding (no bandwidth expansion)

    • [Sedonaris, Erkip, Azhang], [Laneman, Wornell, Tse]

  • Opportunity:

    • Earn multi-antenna gains!

  • Challenges:

    • Control overhead for cooperation – Code assignment problem

    • Redundant sensor data *not* identical messages!

    • How can cooperation *emerge*? Sensor Scheduling problem

Common

Message


Randomized cooperation

Code assignment

  • Opportunistic Large Array (OLA) [SP’03]

    • The relay network is as a filter Delay diversity

  • Randomized cooperative access [Sirkeci-Mergen ‘05]

  • Diversity


How much diversity do we need?

  • Asymptotic analysis of cooperative broadcast [Sirkeci Mergen Scaglione IT ‘06]

    • With the least diversity (L=1) the signal flow proceeds much faster on average!

    • Opportunistic a fraction of far away nodes has beam-forming gains

  • Answer: to spread information rapidly diversity small L is best

Probability of being at a certain level at distance r from the source


Data driven access

  • Observation - simple sensor fields should be recoverable from a limited number of attributes

  • Main objective of Data Driven access

    • Force nodes to transmit at unison if their data share a common features

  • Letting sensors having the data attributes use the same channel…

    • Violates the collision model but enables cooperation

    • Half-duplex constraint: Nodes do not hear other nodes that have the same datum  they transmit at unison


The fusion center problem

Sensor scheduling

  • Cooperative queries

  • Group U is asked:

    “Are you in state c?”

  • Level 1= U (Direct response)

  • Level 2,3,…Cooperative response:

Objective:

Minimizing energy and

or number of queries


A simple cooperative access model

  • Boolean answers

    • Energy detector  logic or of all answers

    • The sequence of answers is a code

    • Bounds:

    • First challenge approaching the entropy lower bound

Erasure Model


Background & similar approaches

  • Group testing

    [Dorfman ‘43]

  • For random access

    scheduling [Capetanakis ’79,

    Berger ‘84,Wolf ‘85]

  • Entropy and guessing games

    • [Massey],[E. Arikan et al. IT ‘98][A. D. Santis et al. IT’01]

  • Sensor access problem:

    • Type based Multiple Access (TBMA)

    • Independently A.Sayeed and G.Mergen L.Tong, ’04


Distributed Markov 1/0 Source

a

0

1

b

1 1 0 ……. 1

S1

S2

S3

SN

Wireless Medium

Case study – Discrete binary Markov Field

  • Tree-splitting strategy upper-bound [Hong, Scaglione ‘04]


Performance

  • Constraint: Groups of contiguous nodes

    • Optimum strategy [Hong, Scaglione ‘06]

    • Solution non in closed form


Continuum Sources

  • Nyquist theorem

    • Reconstruction from quantized samples

  • Logan theorem

    • Reconstruction from zero crossing

    • Binary Markov source approximation  Cooperative group queries

  • Precision trade off

    • Bits per Nyquist sample

    • Zero crossing cooperative group tests


Multi-level crossing

  • Comparison between number of queries and rate distortion function

  • Example: Gaussian

Number of queries used


Challenges

  • Optimization of querying strategies

    • With fixed feedback model

      • Noiseless

      • In the presence of noise

  • Optimum query & cooperative answers

    • Note  The answer to the query cannot be based on other nodes data

  • General tight-bounds?

    • What is the penalty due to the decentralized nature of the problem


From fusion center to parallel processing

  • The fusion center architecture examined has feedback in the form of the “Query”

  • The feedback can be computed from the answer, broadcasted through the network cooperatively

  • A method based on near neighbors communications could be preferable

    Agreement protocols: computer science (special case of gossiping) control theory literature (flocking), statistical physics (emergent behavior)


S1

S2

S3

SN

Wireless Medium

Parallel processing: average consensus problems

  • Basic tool for network computation:

    • functions linear synopsis can be computed: ex. vector projections, cond. Indip. likelihood radios……….

  • Linear model [Tsitsiklis, Li-Rus, Olfati-Saber & Murray, Xiao & Boyd…]:


Consensus via synchronization

  • Synchronization is a recurring phenomenon in nature

    • Pulse Coupled Osc. (PCO) model introduced by Peskin

    • Mirollo-Strogatz, Kuramoto  Convergence towards Sync.

  • Oscillatory Neural networks [Hoppensteadt, Izhikevich ‘00] (pattern recognition in the brain) encode the state in the phase variable

  • Proposed for wireless network Sync.Hong, Scaglione ‘03, Lucarelli-Wang ‘04, Mangharam ‘06, Servetto ’06….

  • Our idea: Use also this mechanism in wireless networks as a gossiping algorithm to achieve consensus [Hong, Scaglione ‘04]


Decentralized decision fusion

  • Conditionally independent data

  • Convergence to sync.  convergence to decision

  • Note - scalability

Receiver Operating Characteristic (ROC)


PCO model in a nutshell

  • The fundamental equations for the network are:

  • Note the difference with respect to linear consensus


PCO type system for asynchronous average consensus

  • Ideal transmit coupling signal, starting at common time t=0:

  • Implementing an asynchronous average consensus protocol [Scaglione ITA ‘07] like in [Meyhar et. al ‘07]

    • Each ‘firing’ event triggers a sequence of pair-wise updates of the state variables of all neighbors cyclically

    • Each update decreases the potential function

    • Conditions allow to preserve the sum  if all states are distinct convergence to the average is guaranteed


Why would we use this method?

  • Kill two birds with one stone:

    • MAC problem is solved! It naturally schedules the transmissions: what datum = when to transmit

    • Incorporates the half duplex constraint

      • If I do not hear anybody we all agree….

  • Data driven

    • The scheduling is data and computation driven

  • Cooperative use of the channel: nodes that have the same value cooperate

  • Scalability

    • Spatial redundancy  cooperation non congestion

    • I use less time/bandwidth to average information that has smaller standard deviation irrespective of the network complexity


Conclusions

  • Several ideas on the table for data driven and cooperative access

    • Scheduling  What data I have = When to transmit

      • Deals naturally with the Half duplex constraint

    • The receiver should be able to use collective answers opportunistically

  • Complex optimization problems


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