In this paper, we investigate the diversity-multiplexing tradeoff (DMT) of the multiple-antenna (MIMO) static half-duplex relay channel. A general expression is derived for the DMT upper bound, which can be achieved by a compress-and-forward protocol at the relay, under certain assumptions. The DMT expression is given as the solution of a minimization problem in general, and an explicit expression is found when the relay channel is symmetric in terms of number of antennas, i.e., the source and the destination have n antennas each, and the relay has m antennas. It is observed that the static half-duplex DMT matches the full-duplex DMT when the relay has a single antenna, and is strictly below the full-duplex DMT when the relay has multiple antennas. Besides, the derivation of the upper bound involves a new asymptotic study of spherical integrals (that is, integrals with respect to the Haar measure on the unitary groupU(n)), which is a topic of mathematical interest in itself.

In this work, we investigate the diversity-multiplexing tradeoff (DMT) of the multiple-antenna (MIMO) static half-duplex relay channel. The relay channel is assumed to be symmetric in terms of number of antennas, i.e. the source and the destination have n antennas each, and the relay has m antennas. A general expression is derived for the DMT upper bound, which can be achieved by a compress-and-forward protocol at the relay, under certain assumptions. It is observed that the static half-duplex DMT matches the full-duplex DMT when the relay has a single antenna, and is strictly below the full-duplex DMT when the relay has multiple antennas.

The rate region achievable by two transmitter-receiver pairs who wish to communicate over a Gaussian interference channel has been the subject of intense study over the last decades. Recently, the high SNR capacity region of this channel has been completely characterized in a work by Etkin, Tse and Wang (2007). In this paper, we study the effect of adding random fading into the picture, as well as multiple antennas at the transmitters and the receivers. Under the fast fading assumption, we recover a result of the same type as that obtained in the above mentioned paper. Under the slow fading assumption, we obtain an upper bound on the maximally achievable diversity order for a given target rate pair, which we conjecture to be tight.

It is shown that distributions arising in Renyi-Tsallis maximum entropy setting are related to the generalized Pareto distributions (GPD) that are widely used for modeling the tails of distributions. The relevance of such modelization, as well as the ubiquity of GPD in practical situations follows from Balkema-De Haan-Pickands theorem on the distribution of excesses (over a high threshold). We provide an entropic view of this result, by showing that the distribution of a suitably normalized excess variable converges to the solution of a maximum Tsallis entropy, which is the GPD. This result resembles the entropic approach to the central limit theorem; however, the convergence in entropy proved here is weaker than the convergence in supremum norm given by Pickandspsila theorem.

In this paper we are interested in n-dimensional uniform distributions on a triangle and a sphere. We show that their marginal distributions are maximizers of Renyi entropy under a constraint of variance and expectation in the respective cases of the sphere and of the triangle. Moreover, using an example, we show that a distribution on a triangle with (uniform) maximum entropy marginals may have an arbitrary small entropy. As a last result, we address the asymptotic behavior of these results and provide a link to the de Finetti theorem

In this paper, we provide a detailed geometric characterization of multivariate distributions that maximize Renyi entropy under covariance constraint. These distributions are shown to be marginals of the uniform distribution on the hypersphere for q > 1, and conditional distributions of projections of this uniform distribution in the case q > 1. This construction allows to build a natural convolution of random type for which these distributions are stable

In this paper we revisit the Bialynicki-Birula & Mycielski uncertainty principle (I. Bialynicki-Birula and J. Mycielski, 1975) and the associated cases of equality. This Shannon entropic version of the well-known Heisenberg inequality can be used when dealing with variables that admit no variance. In this paper, we extend this uncertainty principle to Renyi entropies. We recall that in both cases, equality occurs only for Gaussian random variables. However, we show that in the particular n-dimensional Laplace case, the bound is asymptotically attained as n grows. We also show numerically that this effect exists for Cauchy variables whatever the Renyi entropy considered, extending the results of S. Abe and A.K. Rajagopal (2001), These two cases are interesting since they show that this asymptotic behavior cannot be considered as a "Gaussianization" of the variable when the dimension increases, so that the effect is rather "dimensional"

We present an estimator of the entropy of a signal. The basic idea is to adopt a model of the probability law, in the form of an AR spectrum. Then, the law parameters can be estimated from the data. We examine the statistical behavior of our estimates of laws and entropy. Finally, we give several examples of applications: an adaptive version of our entropy estimator is applied to detection of law changes, blind deconvolution and sources separation.

In this paper, we address the problem of the separation of convolutive mixtures in the case where the non-Gaussian source signals are not necessarily filtered versions of i.i.d. sequences. In this context, we show that the contrast functions, used in the linear process source case, still allow to separate the sources by a deflation approach. Some particular properties of higher order cumulants based contrast functions are also given.

We consider the problem of blind separation of causal minimum phase convolutive mixtures of two sources. We study in detail the so-called decorrelation approach. It consists in finding a causal minimum phase filter which, driven by the observations, produces decorrelated outputs. It is well established that this approach allows one to separate the sources if the mixing filter is a non-static FIR filter. We show that this result is no longer true in the IIR case. We establish that there exists infinitely many causal minimum phase filters producing decorrelated outputs and provide a parameterisation of these filters. This clearly shows that the decorrelation approach is, in practice, non-robust. In order to overcome this drawback, we propose an alternative approach based on a linear prediction scheme, which, as the decorrelation approach, uses essentially the second order statistics of the observations.

The problem of adapting linear and nonlinear recursive filters through a gradient-based optimization procedure is considered. The rigorous application of this technique implies a time-growing computation load. Recently, a method for estimating the weight updates was introduced, leading to a new class of algorithms. The convergence properties of these algorithms, when applied to a linear and then a nonlinear recursive filter, are exhibited through a dynamical analysis of the adaptation process. Since the general analysis is very difficult, the case of a first-order filter with a constant input is considered. Significant results are obtained in this particular application.>