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In this paper we focus on blind estimation of the carrier frequency of QPSK modulated data transmission systems. At low SNR, the so-called threshold phenomenon appears. maximum-likelihood (ML) estimation is used to avoid this phenomenon. The ML estimator is based on the fast-Fourier-transform (FFT). As the SNR decreases, the size of the FFT, that is, the implementation complexity of the estimator, must increase to keep the performance. We propose some ML based algorithms that are able to optimize the implementation of the estimator at low SNR. Simulation results show that the proposed algorithms can lower the threshold of the operating SNR more than 4 dB without increasing the size of the FFT. Thus, we reduce the implementation complexity of the frequency estimator.