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We derive Cramer-Rao lower bounds (CRLBs) for the estimation of signal-to-noise ratio (SNR) of binary phase-shift keying (BPSK) and quaternary phase-shift keying (QPSK) modulated signals. The received signal is corrupted by additive white Gaussian noise (AWGN). The lower bounds are derived for non-data-aided estimation where the transmitted symbols are unknown at the receiver. The bounds are compared to those for data-aided estimations (known symbols at the receiver). It is shown that at low SNR there is a significant difference between the bounds for non-data-aided and data-aided estimations.