In this contribution we consider the Cramer-Rao bound (CRB) for the estimation of the time delay of a noisy linearly modulated signal with random data symbols. In spite of the presence of the nuisance parameters (i.e., the random data symbols), we obtain a closed-form expression of this CRB for arbitrary PSK, QAM or PAM constellations and a bandlimited square-root Nyquist transmit pulse.

We discuss the asymptotic Cramer-Rao bound (CRB) for frequency estimation in the presence of multiplicative noise. To improve numerical stability, covariance matrix tapering is employed when the covariance matrix of the signal is singular at high SNR. It is shown that the periodogram-based CRB is a special case of frequency domain evaluation of the CRB, employing the covariance matrix tapering ...

1 The localization problem is fundamentally important for sensor networks. This paper studies the Cramér-Rao lower bound (CRB) for two kinds of localization based on noisy range measurements. The first is Anchored Localization in which the estimated positions of at least 3 nodes are known in global coordinates. We show some basic invariances of the CRB in this case and derive lower and upper bo...

After providing an extension of the Slepian–Bangs formula for general noncircular complex Gaussian distributions, this paper focuses on the stochastic Cramér–Rao bound (CRB) on direction-of-arrival (DOA) estimation accuracy for noncircular sources. We derive an explicit expression of the CRB for DOA parameters alone in the case of noncircular complex Gaussian sources by two different methods. O...

Computation of the Cramer-Rao bound (CRB) on estimator variance requires the inverse or the pseudo-inverse Fisher information matrix (FIM). Direct matrix inversion can be computationally intractable when the number of unknown parameters is large. In this correspondence, we compare several iterative methods for approximating the CRB using matrix splitting and preconditioned conjugate gradient al...

Computation of the Cramer-Rao bound (CRB) on estimator variance requires the inverse or the pseudo-inverse Fisher information matrix (FIM). Direct matrix inversion can be computationally intractable when the number of unknown parameters is large. In this correspondence, we compare several iterative methods for approximating the CRB using matrix splitting and preconditioned conjugate gradient al...

The goal of this contribution is to characterize the best achievable mean-squared error (MSE) in estimating a sparse deterministic parameter from measurements corrupted by Gaussian noise. To this end, an appropriate definition of bias in the sparse setting is developed, and the constrained Cramér–Rao bound (CRB) is obtained. This bound is shown to equal the CRB of an estimator with knowledge of...

Computation of the Cramer-Rao bound (CRB) on estimator variance requires the inverse or the pseudo-inverse Fisher information matrix (FIM). Direct matrix inversion can be computationally intractable when the number of unknown parameters is large. In this note we compare several iterative methods for approximating the CRB using matrix splitting and preconditioned conjugate gradient algorithms. F...

This paper analyses the estimation process for Finite Rate of Innovation (FRI) signals. The main contribution is the derivation of the well known Cramér-Rao Bound (CRB) for the estimation of signal parameters for a pulse stream. Other publications consider the estimation of the signal instead of its parameters or omit the effect of sampling. In this contribution both effect are considered and a...

Despite an increased interest in complex independent component analysis (ICA) during the last two decades, a closed-form expression for the Cramér-Rao bound (CRB) of the complex ICA problem has not yet been established. In this paper, we fill this gap for the noiseless case and circular sources. The CRB depends on the distributions of the sources only through two characteristic values which can...