On the true Cramér-Rao lower bound for data-ided carrier-hase-ndependent frequency offset and symbol timing estimation

Authors:
Gonçalo N. Tavares;Luis M. Tavares;Antonio Petrolino
Affiliations:
Department of Electrical and Computer Engineering, Instituto Superior Técnico, Instituto de Engenharia de Sistemas e Computadores - Investigação e Desenvolvimento, Lisbon, Portugal;Department of Engineering, Escola Superior de Tecnologia e Gestão, Beja, Portugal and INESC-ID, Lisbon, Portugal;INESC-D, Lisbon, Portugal
Venue:
IEEE Transactions on Communications
Year:
2010

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Abstract

In this letter we present new and simple closed form expressions for the true Cramér-Rao lower bound (CRB) for data-aided (DA) joint and individual carrier frequency offset and symbol timing estimation from a linearly modulated waveform transmitted over an AWGN channel. The bounds are derived under a carrier-phase-independent (CPI) estimation strategy wherein the carrier phase is viewed as a nuisance parameter and assumed to have a worst-case noninformative uniform distribution over [-π, π]. The computation of these CRBs requires only a single numerical integration. In addition, computationally simpler yet highly accurate asymptotic lower bounds are presented. As particularizations, new bounds for individual CPI frequency estimation with known symbol timing from M-PSK and continuous wave (CW) signals are also reported.