Scaling Laws for Homogeneous Sensor Networks

Sensor networks typically observe noisy versions of the desired data, and their goal is to inform an interested party. In our sensor network scenario, Bs sources are simultaneously observed by M sensors. More precisely, in every time slot, each sensor observes a certain noisy combination of the Bs sources. All these observations have to be communicated in a suitable form to a central data collection point whose goal is to learn the underlying Bs sources at the highest possible fidelity. For the case where all involved distributions are Gaussian, we show that the best possible scaling behavior of the distortion at the data collection point is like 1/M . Then, we discuss the power-bandwidth trade-offs that permit to achieve this optimal distortion scaling law.