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# The true Cramer-Rao bound for estimating the time delay of a linearly modulated waveform

07/2002;
Source: CiteSeer

ABSTRACT 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.

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ABSTRACT: New Cramer-Rao lower bounds (CRBs) are derived for the estimation of phase offset, and frequency offset, from a block of random BPSK or QPSK symbols at low signal-to-noise (SNR) ratios. These bounds are compared to existing bounds which apply to the unmodulated carrier (or to known PSK symbols), and to the performance of some estimation algorithms
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• ##### Article: On the true and the modified Cramer-Rao bounds for the estimation of a scalar parameter in the presence of nuisance parameters
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ABSTRACT: We consider the Cramer-Rao bound (CRB) for the estimation of a scalar parameter in the presence of nuisance parameters. Whereas this true CRB is hard to evaluate in general, we present a simple analytical expression for its high SNR asymptote, i.e., the asymptotic CRB (ACRB). We show that this ACRB is related to the CRB for the joint estimation of the scalar parameter and the nuisance parameters. Previously, a modified CRB (MCRB) for the estimation of a scalar parameter in the presence of nuisance parameters has been derived. This MCRB is also simple to evaluate and is related to the CRB for the estimation of the scalar parameter assuming that the value of the nuisance parameters is a priori known. We show that the MCRB can be quite loose at high SNR, when the scalar parameter is coupled with the nuisance parameters. In the case of synchronization parameter estimation, we find that the ACRB equals the MCRB, whether or not (some of) the nuisance parameters are a priori known
IEEE Transactions on Communications 12/1998; · 1.75 Impact Factor
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##### Article: Low-SNR limit of the Cramer-Rao bound for estimating the carrier phase and frequency of a PAM, PSK, or QAM waveform
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ABSTRACT: We consider the Cramer-Rao bound (CRB) for the estimation of the carrier phase and frequency of a noisy linearly modulated signal with random data symbols. The observation vector consists of the matched filter output samples taken at the symbol rate, assuming known symbol timing. Because of the presence of the random data, the evaluation of this CRB is quite tedious. Instead, here we derive a simple closed-form expression for the limit of the CRB at low-signal-to-noise ratio (SNR), which holds for arbitrary PAM, PSK, and QAM constellations.
IEEE Communications Letters 06/2001; · 1.16 Impact Factor