This paper shows the benefits of using Complex-Valued Neural Network (CVNN) on classification tasks for non-circular complexvalued datasets. Motivated by radar and especially Synthetic Aperture Radar (SAR) applications, we propose a statistical analysis of fully connected feed-forward neural networks performance in the cases where real and imaginary parts of the data are correlated through the non-circular property. In this context, comparisons between CVNNs and their real-valued equivalent models are conducted, showing that CVNNs provide better performance for multiple types of non-circularity. Notably, CVNNs statistically perform less overfitting, higher accuracy and provide shorter confidence intervals than its equivalent Real-Valued Neural Network (RVNN).
Covariance matrix estimation is a ubiquitous problem in signal processing. In most modern signal processing applications, data are generally modeled by non-Gaussian distributions with covariance matrices exhibiting a particular structure. Taking into account this structure and the non-Gaussian behavior improve drastically the estimation accuracy. In this paper, we consider the estimation of structured scatter matrix for complex elliptically distributed observations, where the assumed model can differ from the actual distribution of the observations. Specifically, we tackle this problem, in a mismatched framework, by proposing a novel estimator, named StructurEd ScAtter Matrix Estimator (SESAME), which is based on a two-step estimation procedure. We conduct theoretical analysis on the unbiasedness and the asymptotic efficiency and Gaussianity of SESAME. In addition, we derive a recursive estimation procedure that iteratively applies the SESAME method, called Recursive-SESAME (R-SESAME), reaching with improved performance at lower sample support the (Mismatched) Cramér-Rao Bound. Furthermore, we show that some special cases of the proposed method allow to retrieve preexisting methods. Finally, numerical results corroborate the theoretical analysis and assess the usefulness of the proposed algorithms.
In statistical signal processing, hybrid parameter estimation refers to the case where the parameters vector to estimate contains both non-random and random parameters. As a contribution to the hybrid estimation framework, we introduce a recursive hybrid Cramér Rao lower bounds for discrete-time Markovian dynamic systems depending on unknown deterministic parameters. Additionnally, the regularity conditions required for its existence and its use are clarified.
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