Low-SNR limit of the Cramer-Rao bound for estimating the carrier phase and frequency of a PAM, PSK, or QAM waveform

Author

Steendam, Heidi ; Moeneclaey, Marc

Author_Institution

Dept. of Telecommun. & Inf. Process., Ghent Univ., Belgium

Volume

5

Issue

5

fYear

2001

fDate

5/1/2001 12:00:00 AM

Firstpage

218

Lastpage

220

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.

Keywords

AWGN channels; frequency estimation; phase estimation; phase shift keying; pulse amplitude modulation; quadrature amplitude modulation; random processes; AWGN channel; CRB; Cramer-Rao bound; PAM waveform; PSK waveform; QAM waveform; carrier frequency estimation; carrier phase estimation; closed-form expression; low-SNR limit; low-signal-to-noise ratio; matched filter output samples; noisy linearly modulated signal; observation vector; random data; random data symbols; symbol rate; symbol timing; Chirp modulation; Closed-form solution; Frequency estimation; Matched filters; Phase estimation; Phase modulation; Phase noise; Phase shift keying; Quadrature amplitude modulation; Timing;

fLanguage

English

Journal_Title

Communications Letters, IEEE

Publisher

ieee

ISSN

1089-7798

Type

jour

DOI

10.1109/4234.922765

Filename

922765