Scaling laws of sampled data and many-to-one capacity of sensor networks on closed surfaces

Abstract

In this paper, we study the feasibility of sensing a bandlim-ited random field on a closed surface using a dense sensor network of inexpensive sensor nodes. The goal is to periodically gather quantized samples from the field and communicate it to a central collector, where this data is used to reconstruct the field. We show that under an arbitrary irregular placement of sensors that is uniformly discrete, the field can be reconstructed with a pointwise distortion of O(1/Nwhen the sensors are equipped with logN-bit quantizers.This irregular sampling result allows us, using a recent result in over sampled AID conversion, to trade-off one logN-bit sensor to N one-bit sensors, and still obtain a pointwise distortion ofO(jf). The total data generated in the network also remains O(logTV).We then study the capacity of the many-to-one wireless network through which the sensor nodes communicate their data to a central collector. We find that, upto a constant, the capacity has the same scaing law in the number of nodes as the total data rate of the network. Hence such a network for both sensing and communicating is indeed feasible.