On distributed sampling of bandlimited and non-bandlimited sensor fields

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 D_f decays as D_f ∼ 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 D_u decays as D_u∼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.