Anna Scaglione Cornell University IPAM Workshop – January 2007 Joint work with:

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 (can’t listen if transmitting)

4. 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

5. 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

6. 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

7. 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

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 ‘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

12. 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]

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. 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…]:

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)

21. 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 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

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