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Signal-to-Noise Ratio (SNR) is an important parameter in Turbo soft decoding. In this paper a blind SNR estimator for digital modulated signals in the complex additive white Gaussian noise (AWGN) channel is proposed. The algorithm uses the eigenvalues of the covariance of the received signal. And the eigenvalues are estimated via an iterative subspace tracking algorithm, known as the Projection Approximation Subspace Tracking (PASTd) algorithm. The orthonormality of the estimated eigenvectors is guaranteed by the use of the Gram-Schmidt method. Computer simulations are performed for 2/4/8PSK signals when the true SNR is in the range from 3dB to 25dB. Compared with the eigenvalue decomposition (ED)-based method, the proposed algorithm can achieve a comparable estimation but with a significantly reduced computational complexity.