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arXiv · 1807.08505

The Semiparametric Cram\'er-Rao Bound for Complex Elliptically Symmetric Distributions

Stefano Fortunati·Fulvio Gini·Maria S. Greco·Abdelhak M. Zoubir
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Abstract

This letter aims at extending the Constrained Semiparametric Cramer-Rao Bound (CSCRB) for the joint estimation of mean vector and scatter matrix of Real Elliptically Symmetric (RES) distributions to Complex Elliptically Symmetric (CES) distributions. A closed form expression for the complex CSCRB (CCSCRB) is derived by exploiting the so-called \textit{Wirtinger} or $\mathbb{C}\mathbb{R}$-\textit{calculus}. Finally, the CCSCRB for the estimation of the complex mean vector and scatter matrix of a set of complex $t$-distributed random vectors is provided as an example of application.

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Stefano Fortunati, Fulvio Gini, Maria S. Greco, Abdelhak M. Zoubir. 2018-07-23. The Semiparametric Cram\'er-Rao Bound for Complex Elliptically Symmetric Distributions. https://arxiv.org/abs/1807.08505

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