Optimum Sensor Density in Distortion-Tolerant Wireless Sensor Networks

The optimum sensor node density for one- and two-dimensional (1-D and 2-D) wireless sensor networks (WSNs) with spatial source correlation is studied in this paper. The WSN attempts to reconstruct a spatially correlated signal field by collecting the location-dependent measurements from the distributed sensor nodes. The WSN is designed to minimize the mean square error (MSE) distortion between the original and the reconstructed signals under the constraint of a fixed power per unit area. The impacts of node density and spatial data correlation on the network performance are investigated for both small networks with finite number of nodes, and large networks with infinite area, infinite number of nodes, but finite node density through asymptotic analysis. The interactions among the various network parameters and their impacts on the system performance are quantitatively identified with exact analytical expressions, many of which are in closed-forms. The results provide guidelines on the design of practical WSNs.