Fading-Resilient Super-Orthogonal Space-Time Signal Sets: Can Good Constellations Survive in Fading?

In this correspondence, first-tier indirect (direct) discernible constellation expansions are defined for generalized orthogonal designs. The expanded signal constellation, leading to so-called super-orthogonal codes, allows the achievement of coding gains in addition to diversity gains enabled by orthogonal designs. Conditions that allow the shape of an expanded multidimensional constellation to be preserved at the channel output, on an instantaneous basis, are derived. It is further shown that, for such constellations, the channel alters neither the relative distances nor the angles between signal points in the expanded signal constellation.Comment: 10 pages, 0 figures, 2 tables, uses IEEEtran.cls, submitted to IEEE Transactions on Information Theor

Le Cam spacings theorem in dimension two

The definition of spacings associated to a sequence of random variables is extended to the case of random vectors in [0,1]^2. Beirlant & al. (1991) give an alternative proof of the Le Cam (1958) theorem concerning asymptotic normality of additive functions of uniform spacings in [0,1]. I adapt their technique to the two-dimensional case, leading the way to new directions in the domain of Complete Spatial Randomness (CSR) testing

Efficient Evaluation of Multidimensional Time-Varying Density Forecasts with an Application to Risk Management

We propose two simple evaluation methods for time varying density forecasts of continuous higher dimensional random variables. Both methods are based on the probability integral transformation for unidimensional forecasts. The first method tests multinormal densities and relies on the rotation of the coordinate system. The advantage of the second method is not only its applicability to any continuous distribution but also the evaluation of the forecast accuracy in specific regions of its domain as defined by the user’s interest. We show that the latter property is particularly useful for evaluating a multidimensional generalization of the Value at Risk. In simulations and in an empirical study, we examine the performance of both tests.Multivariate Density Forecast Evaluation, Probability Integral Transformation, Multidimensional Value at Risk, Monte Carlo Simulations