Bounds for Estimation of Complex Exponentials in Unknown Colored Noise

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Abstract

We consider the problem of estimating the parameters of complex exponentials in the presence of complex additive Gaussian noise with unknown covariance. Bounds are derived for the accuracy of jointly estimating the parameters of the exponentials and the noise. We first present an exact Cramér-Rao bound (CRB) for this problem and specialize it for the cases of circular Gaussian processes and autoregressive processes. We also derive an approximate expression for the CRB, which is related to the conditional likelihood function. Numerical evaluation of these bounds provides some insights on the effect of various signal and noise parameters on the achievable estimation accuracy.

Original languageEnglish
Pages (from-to)2176-2185
Number of pages10
JournalIEEE Transactions on Signal Processing
Volume43
Issue number9
DOIs
StatePublished - 1 Jan 1995

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