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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)

- 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

- 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

- 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

Code assignment

- Opportunistic Large Array (OLA) [SP’03]
- The relay network is as a filter Delay diversity

- Randomized cooperative access [Sirkeci-Mergen ‘05]
- Diversity

- 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

- 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

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

- 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

- 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

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

- Constraint: Groups of contiguous nodes
- Optimum strategy [Hong, Scaglione ‘06]
- Solution non in closed form

- 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

- 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

- With fixed feedback model
- 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

- 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

- 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…]:

- 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]

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

Receiver Operating Characteristic (ROC)

- The fundamental equations for the network are:
- Note the difference with respect to linear 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

- 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

- Scheduling What data I have = When to transmit
- Complex optimization problems