Signal Reconstruction in Sensor Networks with Flat and Clustered Topologies

We apply signal processing techniques to the study of wireless sensor networks, whose nodes are deployed over a planar region for environmental monitoring. We address the problem of reconstructing the phenomenon of interest at a sink node, from the samples gathered by the sensors, and we evaluate the system performance in presence of both a flat and a clustered network topology. When the sensors are grouped into (possibly overlapping) clusters, the data collected within each cluster are compressed by the cluster head and sent to the sink node. By representing the compressed data through the Fourier coefficients of the field spectrum, we analyze both the case where the sensor positions are known to the sink, and the case where they are available at the cluster head only. We show that clustering significantly reduces the energy expenditure due to data transmission with respect to the case of a flat network topology, and, most importantly, we derive the possible degradation of the quality of the reconstructed field due to compression.