Anna Scaglione

1
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)

2
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

3
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 (cant listen if
  transmitting)

4

• 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

5
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
6
Randomized cooperation

• Code assignment
• Opportunistic Large Array (OLA) SP03
• The relay network is as a filter ?Delay diversity
• Randomized cooperative access Sirkeci-Mergen
  05
• Diversity

7
How much diversity do we need?

• Asymptotic analysis of cooperative broadcast
  Sirkeci Mergen Scaglione IT 06
• With the least diversity (L1) 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
8
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

9
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
10
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
11
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 98A. D. Santis
  et al. IT01
• Sensor access problem
• Type based Multiple Access (TBMA)
• Independently A.Sayeed and G.Mergen L.Tong, 04

12
Case study Discrete binary Markov Field

• Tree-splitting strategy upper-bound Hong,
  Scaglione 04

13
Performance

• Constraint Groups of contiguous nodes
• Optimum strategy Hong, Scaglione 06
• Solution non in closed form

14
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

15
Multi-level crossing

• Comparison between number of queries and rate
  distortion function
• Example Gaussian

Number of queries used
16
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

17
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)

18
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

19
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

20
Decentralized decision fusion

• Conditionally independent data
• Convergence to sync. ? convergence to decision
• Note - scalability

Receiver Operating Characteristic (ROC)
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PCO model in a nutshell

• The fundamental equations for the network are
• Note the difference with respect to linear
  consensus

22
PCO type system for asynchronous average consensus

• Ideal transmit coupling signal, starting at
  common time t0
• 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

23
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

24
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