Fisher information matrix, Rao test, and Wald test for complex-valued signals and their applications

The Fisher information matrix (FIM) is an important tool in signal processing. In this paper, we investigate the FIM with respect to the complex-valued quantities, and show its application in signal processing, such as the design of the Rao and Wald tests, and the derivation of the Cramér–Rao bound...

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Published in:Signal processing 2014-01, Vol.94, p.1-5
Main Authors: Liu, Weijian, Wang, Yongliang, Xie, Wenchong
Format: Article
Language:English
Subjects:
Applied sciences
Complex-valued signal
Cramer-Rao bounds
Cramér–Rao bound
Derivation
Detection, estimation, filtering, equalization, prediction
Estimates
Exact sciences and technology
Fisher information matrix
Information, signal and communications theory
Rao test
Signal and communications theory
Signal processing
Signal, noise
Telecommunications and information theory
Wald test
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Wang, Yongliang
Xie, Wenchong
description The Fisher information matrix (FIM) is an important tool in signal processing. In this paper, we investigate the FIM with respect to the complex-valued quantities, and show its application in signal processing, such as the design of the Rao and Wald tests, and the derivation of the Cramér–Rao bound for the unbiased estimate. Some examples are also given. •We show some important features of the FIM with respect to complex-valued signals.•The Rao and Wald tests for complex-valued signals are given.•We present the CRB of unbiased estimates involved complex FIM.•Several examples about their application are also given.
doi_str_mv 10.1016/j.sigpro.2013.06.032
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subjects Applied sciences
Complex-valued signal
Cramer-Rao bounds
Cramér–Rao bound
Derivation
Detection, estimation, filtering, equalization, prediction
Estimates
Exact sciences and technology
Fisher information matrix
Information, signal and communications theory
Rao test
Signal and communications theory
Signal processing
Signal, noise
Telecommunications and information theory
Wald test
title Fisher information matrix, Rao test, and Wald test for complex-valued signals and their applications
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