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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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Anna scaglione cornell university ipam workshop january 2007 joint work with yao win hong now faculty at nthu ta

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

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

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)


Anna scaglione cornell university ipam workshop january 2007 joint work with yao win hong now faculty at nthu ta

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


Beyond collision cooperative links

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

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

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

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

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

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

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


Case study discrete binary markov field

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

Performance

  • Constraint: Groups of contiguous nodes

    • Optimum strategy [Hong, Scaglione ‘06]

    • Solution non in closed form


Continuum sources

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

Multi-level crossing

  • Comparison between number of queries and rate distortion function

  • Example: Gaussian

Number of queries used


Challenges

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

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)


Parallel processing average consensus problems

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

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

Decentralized decision fusion

  • Conditionally independent data

  • Convergence to sync.  convergence to decision

  • Note - scalability

Receiver Operating Characteristic (ROC)


Pco model in a nutshell

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

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

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

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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