Search

Consider a two-dimensional domain S ⊆ ℜ2 containing two sets of nodes from two statistically independent uniform Poisson point processes with constant densities pL and pNL. The first point process identifies the distribution of a set of nodes having information about their positions, hereafter denoted as L-nodes (localised-nodes), whereas the other is used to model the spatial distribution of nodes that need to localise themselves, hereafter denoted as NL-nodes (not localised-nodes). For simplicity, both kinds of nodes are equipped with the same kind of transceiver, and communicate over a channel affected by shadow fading. As a first goal, the authors derive the probability that a randomly chosen NL-node over S gets localised as a function of a variety of parameters. Then, the authors derive the probability that the whole network of NL-nodes over S gets localised. As with many other random graph properties, the localisation probability is a monotone graph property showing thresholds. In this work, the authors derive both finite (when the number of nodes in the bounded domain is finite and does not grow) and asymptotic thresholds for the localisation probability. In connection with the asymptotic thresholds, the authors show the presence of asymptotic thresholds on the network localisation probability in two different scenarios. The first refers to dense networks, which arise when the domain S is bounded and the densities of the two kinds of nodes tend to grow unboundedly. The second kind of thresholds manifest themselves when the considered domain increases but the number of nodes grow in such a way that the L-node density remains constant throughout the investigated domain. In this scenario, what matters is the minimum value of the maximum transmission range averaged over the fading process, denoted as dmax, above which the network of NL-nodes almost surely gets asymptotically localised. [ABSTRACT FROM AUTHOR]

This study is concerned with the problem of designing computationally efficient generalised comb (GC) filters. Basically, GC filters are anti-aliasing filters that guarantee superior performance in terms of selectivity and quantisation noise rejection compared to classical comb filters, when used as decimation filters in multistage architectures. Upon employing a partial polyphase (PP) architecture proposed in a companion study, the authors develop a sensitivity analysis in order to investigate the effects of the coefficients' quantisation on the frequency response of the designed filters. The authors show that the sensitivity of the filter response to errors in the coefficients is dependent on the particular split of the decimation factor between the two sub-filters constituting the PP architecture. The sensitivity analysis is then used for developing a fixed-point implementation of a sample filter from the class of GC filters, used as reference filter throughout the study. Finally, the authors present computer simulations in order to evaluate the performance of the designed fixed-point filters. [ABSTRACT FROM AUTHOR]

Cascaded-integrator-comb (CIC) filters are efficient anti-aliasing rate-conversion filters widely used for ΣΔ AID converters. High-order structures, attempting to increase the noise rejection within the folding bands, have the drawback of inserting multiple zeros in the same positions and increasing the edge-band attenuation. A combination of sharpened and CIC filters is proposed in the paper, with the goal of increasing the rejection of the LA quantisation noise around the folding bands and reducing the pass-band drop of the designed decimation filters with respect to classic CIC structures. Design criteria, leading to optimised structures, and comparisons are given with respect to both classical and modified CIC filters. [ABSTRACT FROM AUTHOR]