On Minimalism and Scale in Sensor Networks Upamanyu Madhow ECE Department University of California, Santa Barbara Funding Sources

Why sensor networks? Sensors have been around for a long time Why are we so interested in sensor networks? Role of networking Can we usefully exploit data from lots of sensors? A whole greater than the sum of its parts? Why lots of sensors? Large areas to be covered, small sensing range Many big picture issues for theorists to ponder How does scale improve information? How do we communicate with a million sensors? How can inter-sensor collaboration help? How can we engineer trust in wireless sensor networks?

Big picture questions lead to new ideas How to gather information from 100,000 sensors? Imaging sensor nets How do we scale surveillance and tracking? Tracking with binary proximity sensors Large-scale camera networks Can sensors act like a distributed antenna array? Practical algorithms for distributed transmit beamforming

Today’s focus: minimalism and scale Scaling to a very large number of sensors Minimalism in sensor capability and deployment requirements Imaging sensor nets Scaling in energy Collaboration with minimal inter-sensor communication Distributed transmit beamforming with feedback control Scaling in sensor cost/functionality Minimalism in sensor output: yes or no Tracking with binary proximity sensors Bharath Ananthasubramaniam, Munkyo Seo, Prof. Mark Rodwell Raghu Mudumbai, Ben Wild, Prof. Joao Hespanha, Prof. Kannan Ramchandran Nisheeth Srivastava, Raghu Mudumbai, Jaspreet Singh, Rajesh Kumar, Prof. Subhash Suri

Imaging Sensor Nets collector: satellite base station on UAV vast numbers of low-complexity "dumb" pixels sensor + RF transducer + antenna. Sensor field Sensor field Field of simple, low-power sensors dispersed across field of view Cast on ground from truck, plane, or satellite Sensor as pixels (“dumb dust”) Collector-driven data collection: Sensors electronically reflect, with data modulation, beacon from collector (“virtual radar”) Sensor-driven data collection: Sensors transmit at will, sensor location and data estimated by collaboration among a network of collectors Minimal functionality: no GPS, no inter-sensor networking Lifetime of year on watch cell battery Sophisticated collectors Radar and image processing, multiuser data demodulation Joint localization and data collection Range varies from 100m to 100 km Active versus “passive” sensors, collector characteristics

Prototype with stationary collector Millimeter wave carrier frequencies Narrow beam with moderate size collector antenna Small sensor form factor Key challenges Low-power, low-cost sensor ICs: mm-wave in CMOS Collector signal processing

Inducing a radar geometry Beacon with location code Active sensor reflects beacon Collector Sensor field with active sensors and inactive sensors

Basic Link Diagram Sensor Collector DOWN-LINK UP-LINK PRBS DATA Jointly detect DATA and DELAY Collector Sensor BPSK modulation DOWN-LINK UP-LINK Freq. shift to filter out ground return

Zeroth order Link Budget 75 GHz carrier Collector with 1 meter diameter antenna, 100 mW transmit antenna 100 Kbps using QPSK/BPSK at BER of 10-9 300 m range for semi-passive sensor Down-link Up-link 100 km range for active sensor with 5 mW transmit power Downlink Uplink (bottleneck)

Collector Imaging Algorithm : location code : beam pattern

Localization for large sensor density Single Sensor Algorithm + SIC – works well 25 sensors 100 sensors

Brassboard concept validation

Ongoing research and open issues Hardware Sensor IC design Collector system integration Algorithms Alleviating inter-sensor interference Collaboration among collectors Data compression and representation Collector-driven data collection Sensor-driven data collection Integration of transceiver with sensing Well-defined interfaces for mm wave motes

Distributed Transmit Beamforming Distributed beamforming can increase range or cut power Rec’d power = (A + A + …+A)2 = N2 A2 if phases line up Rec’d power = N A2 if phases don’t line up (+ fading) Can use low frequencies for better propagation Large “antenna” using natural spatial distribution of nodes Diversity BUT: RF-level sync is hard! Receiver 1 f j e 2 SNR feedback Sync can be achieved using RX feedback!

Feedback Control Mechanism Initially the carrier phases are unknown Each timeslot, the transmitters try a random phase correction Keep the corrections that increase SNR, discard the others Carrier phases become more and more aligned Phase coherence achieved in time linear in number of nodes Typical phase evolution (10 nodes) Concept experimentally verified by Ben Wild (UC Berkeley)

Towards an analytical model Empirical observation: convergence is highly predictable Net effect of phase perturbations y[n+1] α.y[n] x1 x2 What can we say about the distributions of x1 and x2? (without knowing all the individual transmitter phases)

Key idea: statistical approach Received signal proportional to Infinitely many possible i[n] for any given y[n] Analogy with statistical physics Given total energy i.e. temperature What is the energy of each atom? More interesting: how many atoms have a energy, E Concept of Macrostates Distribution of energy is fixed Maxwell-Boltzmann distribution Density ~ exp(-E/kT)

The “exp-cosine” distribution Initially i[0] is uniform in (-π, π] The phases i[n] get more and more clustered Given , what is the distribution of i[n]? “Typical” distribution closest in KL distance to uniform The Conditional Limit Theorem The “exp-cosine” distribution

Exp-cosine matches simulations N = 500 transmitters Can now predict trajectory, optimize convergence rate, and prove scalability

Accurate prediction of trajectory

Optimize phase perturbation Optimize pdf for δi at each iteration restrict to uniform pdf: δi~uniform[-δ0,+δ0] Choose δ0 to maximize E(Δy[n]), given y[n] 200 transmitters Fixed uniform distribution vs. uniform distribution optimized at each slot

Scalability and Convergence Phase perturbation not optimized Uniform over (-2o,2o) Phase perturbation optimized Scalable: Convergence is linear in the number of nodes N (provably so for optimized phase perturbations)

Ongoing research and open issues Detailed understanding of time variations Trade off tracking versus misadjustment Protocols leveraging distributed beamforming Generalization to other distributed control tasks?

Tracking with binary sensors Minimalistic model appropriate for microsensors Sensor says target present or absent Appropriate for large-scale deployments How well can we track with a network of binary sensors? Fundamental limits Minimal path descriptions Efficient geometric algorithms

The Geometry of Binary Sensing Target Path Localization patches Sensor Outputs Localization arcs

Results Attainable resolution ~ 1/(sensor density*sensing range) Spatial low pass filtering Can track only “lowpass” version of the path OccamTrack algorithm Minimal piecewise linear representations Velocity estimates for “lowpass” version Robustness to sensing range variation Particle filter + Geometric clean-up Multiple targets Many possible explanations for snapshot of sensor readings Temporal evolution can be exploited by particle filter

How a trajectory is localized Max patch size at least 1/(density*range) for any deployment Patch size of the order of 1/(density*range) for Poisson deployment Resolution theorems

Minimal representation: OccamTrack Greedy algorithm for piecewise linear representation: Draw lines stabbing localization arcs that are as long as possible

Spatial Lowpass Filtering Cannot capture rapid variations Can only reconstruct “lowpass” version of path Justifies simple piecewise linear representation

Velocity estimation and minimal representation Which path should we use to estimate (lowpass version of) velocity? We can be off by a factor of two! A simple formula: dv/v = dL/L Proposition: If piecewise linear approx works well, then velocity estimate is accurate.

Simulation Results Weighted Centroid Output OccamTrack Output (Kim et al, IPSN 2005) OccamTrack Output OccamTrack Velocity Estimate

Fundamental Resolution Limits Theoretical resolution attained by both regular and random deployment

Handling non-ideal sensing Not detected Experiment with acoustic sensor ? Detected Low pass filter observations A simple model Acoustic sensors are unreliable & unpredictable Localization patch = intersection of outer circles with complements of inner circles Particle filtering algorithm provides robust performance Geometric clean-up provides minimal description

Experiments with acoustic sensors Non-ideal sensor response Particle Filter OccamTrack OccamTrack with ideal sensing Particle Filter + Geometric

Multiple Targets: what does a snapshot tell us? Significant ambiguity regarding how many targets and where they are Can get a minimal explanation for sensor readings: greedy algorithm But how do we piece together snapshots?

Particle filters work!

Simulation results with non-ideal sensing

Experiments with passive IR sensors

Ongoing research and open issues Signal processing framework Spatial lowpass filtering “Multiuser interference” due to multiple targets Multimodal sensing Enhancement of binary model Bayesian frameworks for combining sensor observations Distributed realizations

A Big Picture What is needed for sensor networks to be a success? Two or three successful big applications What can theorists do? Thought experiments based on application scenarios Ask the big picture questions Follow up with logical answers Collaborate with builders and experimentalists Example big picture questions How best to use sensor correlations? How to provide wire-like guarantees? What are good architectures for nextgen surveillance and tracking? What are good models for distributed sensing & actuation?