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Session:Distributed Digital Signal Processing for Sensor Networking
Time:Thursday, May 20, 11:00 - 11:15
Presentation: Special Session Lecture
Topic: Special Sessions: Distributed Digital Signal Processing for Sensor Networking
Authors: Animesh Kumar; University of California, Berkeley 
 Prakash Ishwar; University of California, Berkeley 
 Kannan Ramchandran; University of California, Berkeley 
Abstract: Distributed sampling and reconstruction of a physical field using an array of sensors is a problem of increasing interest in environmental monitoring applications of sensor networks. This work addresses the related sampling framework in the context of both bandlimited and non-bandlimited sensor fields. We show, using a dither-based scheme, that it is possible to reconstructnon-bandlimited fields with a reconstruction accuracy that depends on the available bitrate $R$ and the spectral decay characteristics of the sensor field -- we study exponentially decaying spectra as an illustration. For bandlimited fields $f(t)$, the maximum pointwise error $D_f$ decays as $D_f \sim 2^{-a_1 R}$, i.e. exponentially with rate $R$. For the non-bandlimited case, we show that for fields $u(t)$ with exponentially decaying spectral tails, i.e., $|U(\omega)| \sim e^{-a|\omega|} $, the maximum pointwise error $D_{u}$ decays as $ D_{u} \sim e^{-a_2\sqrt{R}}(1+o(R)) $ with spatial bit rate $R$ bits/meter. We also show that it is possible to trade off the number of sensors with their precision, while maintaining a similar reconstruction accuracy -- a phenomenon that may be dubbed as a {\it ``bit-conservation''} principle underlying the sampling framework.

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