Time Synchronization and Distributed Modulation in Large-Scale Sensor Networks Sergio D. Servetto School of Electrical and Computer Engineering Cornell University http://cn.ece.cornell.edu/ RPI Workshop 4/29/04.
Acknowledgements Ron Dabora (PhD Candidate - ECE), An-swol Hu (PhD Candidate - ECE), Megan A. Owen (PhD Candidate - Applied Math), Christina Peraki (PhD Candidate - ECE), Lav R. Varshney (Undergraduate student - ECE), Mingbo Zhao (PhD Candidate - ECE). NSF, for awards CCR-0238271(CAREER), CCR-0330059(SENSORS). ANR-0325556(ITR).
The Sensor Reachback Problem Informal Description Goal: establish a two-way link between the sensors and an external node. Applications: disaster relief, disaster causing, environmental monitoring, data collection under health hazards, etc. Focus of this talk: the uplink.
The Sensor Reachback Problem Main Challenges For the uplink in reachback: Under what (information-theoretic) conditions can we communicate a distributed source from the sensor array to the external node? J. Barros, S. D. Servetto. The Sensor Reachback Problem. Submitted to the IEEE Trans. Inform. Theory, November 2003. How do transmitters synchronize access to the common channel? How do transmitters modulate information for communication with the external node? How do we implement all these things in real life? Focus of this talk: time synchronization and distributed modulation.
Outline Limits of Sums of Randomly Shifted Pulses. The Problem of Time Synchronization. The Problem of Distributed Modulation. Experimental Work in Progress. Summary and Conclusions.
Outline Limits of Sums of Randomly Shifted Pulses. The Problem of Time Synchronization. The Problem of Distributed Modulation. Experimental Work in Progress. Summary and Conclusions.
Limits of Sums of Randomly Shifted Pulses Consider an extreme case: all nodes want to communicate a common message over a single multiple access channel. The signals at the output of an asynchronous, analog, unfaded, power constrained, bandwidth unconstrained Gaussian MAC have the form: where is a constant, is Gaussian noise. is a vector of random delays, and Any communication task involves computing some we say about its statistics, for different choices of?... so, what can
Limits of Sums of Randomly Shifted Pulses Example: take a linear functional! an independent random vector, and #" $ "(e.g., a matched filter), %large. Then: &10 54 * & & -, +. & / 2 3 / )(' all independent by the CLT. How can we detect a signal based on these observations? A hypothesis test for different variances 6Crude, low performance. Estimate delays as in multipath 6Not feasible with %large. Optimal multiuser detection 6NP-Hard, intractable with %large. With correlated delays however, we could control the distribution of...
& Limits of Sums of Randomly Shifted Pulses Our take on this problem: Define a distributed estimation problem (each node computes an estimate of its own same thing), so that the shape of correlations due to all nodes estimating the can be controlled. 1.5 p(t) 1.5 N=400 1 1 0.5 0.5 amplitude 0 amplitude 0 0.5 0.5 1 1 1.5 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 time 1.5 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 time
& : 9 : & 9 : & 9 If & Limits of Sums of Randomly Shifted Pulses is continuous (except for at most a countable but not dense number of points), and bounded, then is continuous. Complete characterization of the roots Exact characterizations of the sets 8 7 8 <;, 8. <=. 1.5 p(t) 1.5 N=400 1 1 0.5 0.5 amplitude 0 amplitude 0 0.5 0.5 1 1 1.5 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 time 1.5 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 time A. Hu, S. D. Servetto. Algorithmic Aspects of the Time Synchronization Problem in Dense Sensor Network. To appear in ACM/Kluwer Journal on Mobile Networks and Applications (MONET) Special Issue on Wireless Sensor Networks, with selected (and revised) papers from ACM WSNA 2003. Invited Paper. A. Hu, S. D. Servetto. Synchronization in Large-Scale Communication Networks. Submitted for publication.
Outline Limits of Sums of Randomly Shifted Pulses. The Problem of Time Synchronization. The Problem of Distributed Modulation. Experimental Work in Progress. Summary and Conclusions.
> %Random placement of > Time Synchronization: Problem Setup local oscillator. nodes on a unit square, each equipped with a An arbitrary node ( node 1 ) has an operational counter increments at integer values of (tick at each period)., that Goal: define at each node such that they all tick at the same time. Node 1 Operational Counter node 1 Node i Operational Counter node i
D F? ; D BAreceive packet and set operation counter; Time Synchronization: Distributed Estimation TimeSync (observation length @) observe pulse arrival time; if (first observed pulse) while (pulse arrived) Cor more arrival times in memory) Cmost recent and discard all other arrival times; use last Carrivals to estimate next pulse time transmit scaled pulse A if ( B ; A keep only observe pulse arrival time; B ; E ; HGDat time E ; ;
7 I ; A Simple Idea for Global Time Synchronization For a period 9, define estimates such that 8 : : 8 & I JK 9 Then 7 provides a clock that can be heard simultaneously by all nodes. A. Hu, S. D. Servetto. Asymptotically Optimal Time Synchronization in Dense Sensor Networks. In Proc. ACM WSNA, 2003. 0.6 Aggregate Waveform at Node i 0.4 0.2 amplitude 0 0.2 0.4 0.6 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 time
Asymptotically Optimal Time Synchronization N nodes in unit area node 1 R2 nodes R3 nodes R4 nodes Rk nodes
Performance for Finite Networks Performance metric: sum (over nodes) of squared errors with node 1. 0.5 0.45 m=10 m=15 m=20 ASD vs. Time (density=400) 0.4 Average Squared Distance (ASD) 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 0 50 100 150 Time
Performance for Finite Networks Feedback Control 0.5 0.45 m=10 m=15 m=20 ASD vs. Time (density=400) 0.5 0.45 m=10 m=15 m=20 ASD vs. Time (density=400) 0.4 0.4 Average Squared Distance (ASD) 0.35 0.3 0.25 0.2 0.15 Average Squared Distance (ASD) 0.35 0.3 0.25 0.2 0.15 0.1 0.1 0.05 0.05 0 0 50 100 150 Time 0.02 ASD vs. Time (density=400) 0 0 50 100 150 Time 0.018 0.016 Average Squared Distance (ASD) 0.014 0.012 0.01 0.008 0.006 0.004 0.002 m=10 m=15 m=20 0 0 50 100 150 Time
Outline Limits of Sums of Randomly Shifted Pulses. The Problem of Time Synchronization. The Problem of Distributed Modulation. Experimental Work in Progress. Summary and Conclusions.
M NO T : : 7 & 9 8 M NO L @ 9 P @ S 8 : 9 I L P JQ R M M A Simple Idea for Distributed Modulation Distributed carrier waves: given a sequence of bits nodes), a symbol time I, and a repetition factor 8 I U L, make NO (known at all if if M M Then provides an encoding of the bits 7 L M to a far receiver. A. Hu, S. D. Servetto. dfsk: Distributed FSK Modulation in Dense Sensor Networks. In Proc. IEEE ICC, 2004. 1.5 One Transition in (0,1) 1.5 Three Transitions in (0,1) 1.5 Reachback Communication Waveform 1 1 1 0.5 0.5 0.5 amplitude 0 amplitude 0 amplitude 0 0.5 0.5 0.5 1 1 1 1.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 time 1.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 time 1.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 time
Another Simple Idea for Modulation: Radar Signals One possible way to actually implement this uplink: Trick a standard radar receiver into believing that signals generated by the sensor array are the reflections of a transmitted pulse then encode information into different reflectivity maps.
System Architecture of a Radar-Based Uplink Key idea: Partition the sensor array into cohorts, then encode information into artificially generated delays among cohorts.
Performance of a Radar-Based Uplink 10 0 10 1 Bit Error Rate / Probability of Error 10 2 10 3 10 4 5 0 5 10 15 20 25 30 35 40 45 Output SNR (db)
Outline Limits of Sums of Randomly Shifted Pulses. The Problem of Time Synchronization. The Problem of Distributed Modulation. Experimental Work in Progress. Summary and Conclusions.
Experimental Work in Progress Acoustic Fields Setting up a microphone/speaker array to map/reproduce acoustic fields: Array with 256 microphones purchased last Monday (April 26th), and currently looking into getting an array with 256 speakers. Hopefully operational by end of May. Simulate distributed MIMO tx/rx using acoustics only.
Experimental Work in Progress Electrostatic Fields Testing some timesync algorithms on the Pushpin platform: Work in collaboration with Prof. Joe Paradiso (Media Lab MIT).
Outline Limits of Sums of Randomly Shifted Pulses. The Problem of Time Synchronization. The Problem of Distributed Modulation. Experimental Work in Progress. Summary and Conclusions.
Summary Proved that scaled sums of randomly shifted pulses, if the random shifts are properly correlated, have some interesting deterministic properties. Set up distributed estimation problems to correlate these shifts, leading to solutions for time syncronization and distributed modulation. Discussed how to implement the uplink in a backward compatible way: Take a standard radar receiver. Feed its output to a standard demodulator. Program the sensors to encode information into radar reflections. Discussed experimental work in progress, dealing with acoustic and with electrostatic fields.
Conclusions Two observations: At its origin, computing was done on big mainframes. But mainframes lost the cost/performance evolution race to smaller networked PCs. Radio design principles today are still conceptually similar to those of a mainframe: improve performance by adding complexity to a centralized system no such thing as a massively distributed radio exists (yet). Main conclusions: Massively distributed communication systems appear to be feasible. Some most interesting research questions in information theory arise when dealing with distributed sources, channels, and transceivers.
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