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A new accurate estimation algorithm of frequency and phase suited for low signal-noise ratio (SNR) environment is proposed here. Coarse estimation of frequency and phase is acquired from the peak frequency of the received signal. New interpolation technique and modified formula are made to get fine and unbiased estimation. Simulations indicate that, accurate results close to the Cramer-Rao bound (CRB) within a wide frequency offset range are achieved by using this algorithm.