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Signal-to-noise ratio (SNR) estimators of linear modulation schemes usually operate at one sample per symbol at the matched filter output. In this paper we propose a new method for estimating the SNR in the complex additive white Gaussian noise (AWGN) channel that operates directly on the oversampled cyclostationary signal at the matched filter input. Exploiting cyclostationarity proves to be advantageous due to the fact that a signal-free Euclidean noise subspace can be identified such that only second order moments of the received waveform need to be computed. The proposed method is nondata-aided (NDA), as well as constellation and phase independent, and only requires prior timing synchronization to fully exploit the cyclostationarity property. The estimator can also be applied to nonconstant modulus constellations without requiring any tuning, which is a feature not found in existing approaches. Implementation aspects and simpler suboptimal solutions are also provided.