Performance of Linear Field Reconstruction Techniques with Noise and Uncertain Sensor Locations

We consider a wireless sensor network, sampling a bandlimited field, described by a limited number of harmonics. Sensor nodes are irregularly deployed over the area of interest or subject to random motion; in addition sensors measurements are affected by noise. Our goal is to obtain a high quality reconstruction of the field, with the mean square error (MSE) of the estimate as performance metric. In particular, we analytically derive the performance of several reconstruction/estimation techniques based on linear filtering. For each technique, we obtain the MSE, as well as its asymptotic expression in the case where the field number of harmonics and the number of sensors grow to infinity, while their ratio is kept constant. Through numerical simulations, we show the validity of the asymptotic analysis, even for a small number of sensors. We provide some novel guidelines for the design of sensor networks when many parameters, such as field bandwidth, number of sensors, reconstruction quality, sensor motion characteristics, and noise level of the measures, have to be traded off

Upper Bounds to the Performance of Cooperative Traffic Relaying in Wireless Linear Networks

Wireless networks with linear topology, where nodes generate their own traffic and relay other nodes' traffic, have attracted increasing attention. Indeed, they well represent sensor networks monitoring paths or streets, as well as multihop networks for videosurveillance of roads or vehicular traffic. We study the performance limits of such network systems when (i) the nodes' transmissions can reach receivers farther than one-hop distance from the sender, (ii) the transmitters cooperate in the data delivery, and (iii) interference due to concurrent transmissions is taken into account. By adopting an information-theoretic approach, we derive analytical bounds to the achievable data rate in both the cases where the nodes have full-duplex and half-duplex radios. The expressions we provide are mathematically tractable and allow the analysis of multihop networks with a large number of nodes. Our analysis highlights that increasing the number of coop- erating transmitters beyond two leads to a very limited gain in the achievable data rate. Also, for half-duplex radios, it indicates the existence of dominant network states, which have a major influence on the bound. It follows that efficient, yet simple, communication strategies can be designed by considering at most two cooperating transmitters and by letting half-duplex nodes operate according to the aforementioned dominant state