On distributed sampling of bandlimited and non-bandlimited sensor fields
Kumar, A.
Ishwar, P.
Ramchandran, K.
Dept. of Electr. Eng., California Univ., Berkeley, CA, USA;
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. We show, using a dither-based scheme, that it is possible to reconstruct non-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 Df decays as Df ∼ 2-a1R, 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(ω)|∼e-a|ω|, the maximum pointwise error Du decays as Du∼e-a2√R(1+o(R)) with spatial bit rate R bits/metre. 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 "bit-conservation" principle underlying the sampling framework.
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