This chapter develops and extends the general theoretical results, previously published in the chapter "Nonlinear filtering of weak chaotic signals", and presents detailed implementations of a computationally simple, robust (filtering fidelity almost insensitive to changes of the desired input signal properties) and rather precise approach for the filtering of weak signals of different physical nature (biological, seismic, voice, etc.) in presence of white Gaussian noise. The implementations rely on non-linear filtering techniques that in general can be considered as either one-moment or multi-moment, in the sense that they operate with a single sample (instantaneous fashion) or with various adjacent samples (non-instantaneous fashion). Chaotic modeling of the real input signals allows achieving an almost ubiquitous filtering approach with a computationally simple implementation. Application of the linearization strategies (for both one and twomoment filtering) provide, additionally, "invariance" of the processing algorithms to variations on the nature and statistics of the input signals.

The current trend in the statistical analysis of chaos shows certain gaps particularly regarding the engineering applications. This paper, which is a sequel of previous publications from the authors [1-5], develops an application of the cumulant approach to the analysis of the covariance properties of chaotic signals. A general approach for the analysis of two-moment cumulants is considered, particular emphasis is made in the covariance function and the third order cumulant behavior. The cumulant functions of the Lorenz and Chua strange attractors are considered as examples.

No abstract

In this paper it is shown that cyclostationary spectrum sensing for Cognitive Radio networks, applying multiple cyclic frequencies for single user detection can be interpreted (with some assumptions) in terms of optimal incoherent diversity addition for “virtual diversity branches” or SIMO radar. This approach allows proposing, by analogy to diversity combining, suboptimal algorithms which can provide near optimal characteristics for the Neyman-Pearson Test (NPT) for single user detection. The analysis is based on the Generalized Gaussian (Klovsky-Middleton) Channel Model, which allows obtaining the NPT noise immunity characteristics: probability of misdetection error (PM) and probability of false alarm (Pfa) or Receiver Operational Characteristics (ROC) in the most general way. Some quasi-optimum algorithms such as energetic receiver and selection addition algorithm are analyzed and their comparison with the noise immunity properties (ROC) of the optimum approach is provided as well. Finally, the diversity combining approach is applied for the collaborative spectrum sensing and censoring. It is shown how the diversity addition principles are applied for distributed detection algorithms, called hereafter as SIMO radar or distributed SIMO radar, implementing Majority Addition (MA) approach and Weighted Majority Addition (WMA) principle

No abstract