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A novel non-data-aided SNR estimation technique for BPSK and QPSK modulations in complex additive white Gaussian noise (AWGN) is proposed. It uses the constant amplitude property of in-phase and quadrature components of these modulations to achieve an improved performance. Its complexity is shown to be lower while its accuracy supersedes the popular moments-based estimator, approaching closely to the Cramer-Rao lower bound.