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Low-SNR limit of the Cramer-Rao bound for estimating the time delay of a PSK, QAM, or PAM waveform

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2 Author(s)
Steendam, H. ; Dept. of Telecommun. & Inf. Process., Ghent Univ., Belgium ; Moeneclaey, M.

In this letter we consider the Cramer-Rao bound (CRB) for the estimation of the time delay of a noisy linearly modulated signal with random data symbols and random carrier phase. Because of the presence of the nuisance parameters (i.e., data symbols and carrier phase), a closed-form expression of this CRB is very hard to obtain for arbitrary PSK, QAM or PAM constellations and a band-limited transmit pulse. Instead, we derive a simple expression for the limit of the CRB at low signal-to-noise ratio (SNR), which is a relevant benchmark for timing recovery algorithms operating at small E/sub s//N/sub 0/.

Published in:

Communications Letters, IEEE  (Volume:5 ,  Issue: 1 )

Date of Publication:

Jan. 2001

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