This paper concerns the Cramer-Rao lower bound (CRB) for the data-aided (DA) timing and/or phase recovery, i.e., the synchronization parameter acquisition is aided by a training sequence known to the receiver. For the DA parameter estimation, the CRB typically varies with the training sequence. This indicates that different training sequences offer fundamental different performance. In this man...

How accurately can one estimate a deterministic parameter subject to other unknown deterministic model parameters? The most popular answer to this question is given by the Cramér-Rao bound (CRB). The main assumption behind the derivation of the CRB is local unbiased estimation of all model parameters. The foundations of this work rely on doubting this assumption. Each parameter in its turn is t...

In this paper, the problem of carrier frequency offset estimation for frequency-selective channels in a data-aided context is considered. The channel is assumed to be contaminated with an unknown noise and the Cramér-Rao bound (CRB) is used as an estimation accuracy criterion. The minimax approach consists in minimizing the worst-case (maximum) CRB of the frequency offset. Under certain assumpt...

This paper considers the Cramer-Rao lower Bound (CRB) for the source localization problem in the near field. More specifically, we use the exact expression of the delay parameter for the CRB derivation and show how this ‘exact CRB’ can be significantly different from the one given in the literature and based on an approximate time delay expression (usually considered in the Fresnel region). Thi...

The Cramér-Rao bound (CRB) for direction of arrival (DOA) estimation exploiting both auto-correlation and cross-correlation information within multiple frequencies the received array signals is derived. It provides a tighter than existing CRB dual-frequency scenario. For frequencies, it much lower its counterpart, also exists greater number sources, thereby validating that frequency pairs can i...

This contribution considers carrier phase recovery in turbo receivers. We point out that the resulting Cramer-Rao bound (CRB) is close to its high signal-to-noise ratio (SNR) asymptote, even at the typical low operating SNR of turbo systems. We show that ‘code-unaware’ phase estimators are unable to perform closely to the CRB at the normal operating SNR of powerful codes. The advantage of ‘code...

A statistical analysis of differential Doppler estimation is presented that includes the particular features found in aeroacoustic signals from ground vehicles, namely a sum-of-harmonics signal that is randomly scattered by the atmosphere. We use a physics-based statistical model for the scattering to derive the Cramér-Rao bound (CRB) on differential Doppler estimation as a function of the atmo...

This contribution considers the true Cramer-Rao bound CRB related to estimating the carrier phase of a noisy linearly modulated signal in the presence of encoded data symbols. Timing delay and frequency offset are assumed to be known. A general expression and computational method is derived to evaluate the CRB in the presence of codes for which a trellis diagram can be drawn (block codes, trell...

We derive a complex form of the unconstrained and constrained Cramér-Rao lower bound (CRB) of composite real parameters formed by stacking the real and imaginary part of the complex parameters. The derived complex constrained and unconstrained CRB is easy to calculate and possesses similar structure as in the real parameter case but with the real covariance, Jacobian and the Fisher information ...

The problem of design and placing pilot symbols for the estimation of frequency selective random channels is considered. For both SISO and MIMO channels, the Cramér-Rao Bound (CRB) on the mean square error of channel estimators is derived and minimized with respect to the pilot symbols and their placement. It is shown that placing pilot symbols, possibly in multiple clusters, in the middle of t...