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In this letter we present new and simple closed form expressions for the true Cramer-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 [-Â¿, Â¿]. 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.