The Impact of Quasi-equally Spaced Sensor Topologies on Signal Reconstruction

A wireless sensor network with randomly deployed nodes can be used to provide an irregular sampling of a physical field of interest. We assume that a sink node collects the data gathered by the sensors and uses a linear filter for the reconstruction of a bandlimited scalar field defined over a d -dimensional domain. Sensors' locations are assumed to be known at the sink node, up to a certain position error. We then take the mean square error (MSE) of the reconstructed field as performance metric, and evaluate the effect of both uniform and quasi-equally spaced sensor layouts on the quality of the reconstructed field. We define a parameter that provides a measure of the regularity of the sensors deployment, and, through asymptotic analysis, we derive the MSE in the case of different sensor spatial distributions. For two of them, an approximate closed form expression is obtained. We validate our analysis through numerical results, and we show that an excellent match exists between analysis and simulation even for a small number of sensors.