The structure of the probability space associated with a general point process, when regarded as a counting process, is reviewed using the coincidence formalism. The rest of the paper is devoted to the class of regular point processes for which all coincidence probabilities admit densities. It is shown that their distribution is completely specified by the system of coincidence densities. The specification formalism is stressed for ‘completely’ regular point processes. A construction theorem gives a characterization of the system of coincidence densities of such a process. It permits the study of most models of point processes. New results on the photon process, a particular type of conditioned Poisson process, are derived. New examples are exhibited, including the Gauss-Poisson process and the ‘fermion’ process that is suitable whenever the points are repulsive.
This paper presents a novel unsupervised (blind) adaptive decision feedback equalizer (DFE). It can be thought of as the cascade of four devices, whose main components are a purely recursive filter (R) and a transversal filter (T): Its major feature is the ability to deal with severe quickly timevarying channels, unlike the conventional adaptive DFE. This result is obtained by allowing the new equalizer to modify, in a reversible way, both its structure and its adaptation according to some measure of performance such as the mean-square error (MSE). In the starting mode, R comes first and whitens its own output by means of a prediction principle, while T removes the remaining intersymbol interference (ISI) thanks to the Godard (or Shalvi-Weinstein) algorithm. In the tracking mode the equalizer becomes the classical DFE controlled by the decision-directed (DD) least-mean-square (LMS) algorithm. With the same computational complexity, the new unsupervised equalizer exhibits the same convergence speed, steady-state MSE, and bit-error rate (BER) as the trained conventional DFE, but it requires no training. It has been implemented on a digital signal processor (DSP) and tested on underwater communications signals-its performances are really convincing.
SUMMARYThis paper is concerned with the problem of separating independent non-Gaussian sources. This is done by adaptively maximizing a contrast function based on fourth-order cumulants of the (mixed) observations. The first class of solutions involves a first stage where the signal vector is adaptively whitened. In order to implement in the second stage the proper separating task, new contrast functions are proposed, especially when all the source kurtosises have the same sign. These contrasts involve only self-cumulants of the outputs. The second class of solutions requires a single separating stage. However, the associated contrasts involve cross-cumulants in addition to self-cumulants. They essentially apply to correlated vectors with normalized powers (rather than to white vectors). The resulting adaptive one-stage and twostage systems achieve satisfactory separation performance independently of the statistics of sources and of the kind of linear mixture.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.