Spatial field estimation through wireless sensor networks under bandwidth constraints

We consider an environmental monitoring application where a scalar field (e.g., atmospheric pressure) is to be sensed by randomly distributed nodes. Each node takes a sample of a l-dimensional signal in its position and sends it to a collector entity through a wireless link. The latter performs signal reconstruction based on the received samples. Because of total bandwidth constraints, the transmission rate per node is limited. Hence, sensors are supposed to reduce the amount of information to be sent through quantization of the measurements. On the one hand, an increased amount of nodes deployed results in a more accurate sampling of the signal. On the other hand, it forces each sensor to perform looser quantization to cope with the smaller fraction of bandwidth allocated. From the theory of random sampling and by accounting for quantization, we compute the mean square error (MSE) in the reconstruction of the original signal. We then show the existence of an optimal deployment density that trades off between quantization error and aliasing error due to random sampling.