A wavelet analysis of the Rosenblatt process: chaos expansion and estimation of the self-similarity parameter

By using chaos expansion into multiple stochastic integrals, we make a wavelet analysis of two self-similar stochastic processes: the fractional Brownian motion and the Rosenblatt process. We study the asymptotic behavior of the statistic based on the wavelet coefficients of these processes. Basically, when applied to a non-Gaussian process (such as the Rosenblatt process) this statistic satisfies a non-central limit theorem even when we increase the number of vanishing moments of the wavelet function. We apply our limit theorems to construct estimators for the self-similarity index and we illustrate our results by simulations

A general adaptive algorithm for nonGaussian source separation without any constraint

This paper deals with the blind source separation. The task consists in separating some independent and linearly mixed signals called sources. After some general remarks, the model is recalled and our approach based on the Maximum-Likelihood principle and on the higher-order statistics (HOS) is introduced. The main stages of the calculation are presented leading to the criterion of the separation based on a sum of squared cumulants of the sources at the fourth order. The second part is devoted to the adaptive implementation which is in opposition to the block treatment. The procedure using the gradient calculus is described. Some results obtained in simulations are shown, they correspond to the case of a mixture of two real valued sources. Finally, an example of a possible integration in a communications system based on multidimensional beamformers is briefly shown. But some tests on real data should be carried out beforehand.Peer ReviewedPostprint (published version

Automatic Modulation Classification Using Cyclic Features via Compressed Sensing

Cognitive Radios (CRs) are designed to operate with minimal interference to the Primary User (PU), the incumbent to a radio spectrum band. To ensure that the interference generated does not exceed a specific level, an estimate of the Signal to Interference plus Noise Ratio (SINR) for the PU’s channel is required. This can be accomplished through determining the modulation scheme in use, as it is directly correlated with the SINR. To this end, an Automatic Modulation Classification (AMC) scheme is developed via cyclic feature detection that is successful even with signal bandwidths that exceed the sampling rate of the CR. In order to accomplish this, Compressed Sensing (CS) is applied, allowing for reconstruction, even with very few samples. The use of CS in spectrum sensing and interpretation is becoming necessary for a growing number of scenarios where the radio spectrum band of interest cannot be fully measured, such as low cost sensor networks, or high bandwidth radio localization services. In order to be able to classify a wide range of modulation types, cumulants were chosen as the feature to use. They are robust to noise and provide adequate discrimination between different types of modulation, even those that are fairly similar, such as 16-QAM and 64-QAM. By fusing cumulants and CS, a novel method of classification was developed which inherited the noise resilience of cumulants, and the low sample requirements of CS. Comparisons are drawn between the proposed method and existing ones, both in terms of accuracy and resource usages. The proposed method is shown to perform similarly when many samples are gathered, and shows improvement over existing methods at lower sample counts. It also uses less resources, and is able to produce an estimate faster than the current systems