Based on the compressed sensing technique, the carrier frequency offset (CFO) is estimated in this paper. For the traditional maximum likelihood (ML)-based CFO estimation, we first confirm the CFO estimation metrics are compressible. Then the coarse CFO estimation is implemented by referencing compressive sampling matching pursuit (CoSaMP) algorithm, and a metric characteristic-based CoSaMP (MCB-CoSaMP) algorithm is proposed. According to the estimated value of coarse CFO estimation, the equivalent likelihood function is interpolated to search the frequency value of fine CFO estimation. The analysis and simulation results show that the sampling rate can be reduced. Compared to the classical CoSaMP algorithm, the better mean squared error (MSE) performance can be obtained when the proposed MCB-CoSaMP is employed for coarse CFO estimation.
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