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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.

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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
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)

Distributed Source








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



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:


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





1 1 0 ……. 1





Wireless Medium

Case study – Discrete binary Markov Field
  • Tree-splitting strategy upper-bound [Hong, Scaglione ‘04]
  • 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

  • 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





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
  • 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