Error analysis of frequency estimation algorithm based on frequency offset correction

The principle of the frequency estimation algorithm based on frequency offset correction was presented. The computation formula of the frequency estimation's standard deviation of a complex sinusoidal signal in white Gauss noise was obtained. The value of parameter m was optimized when the data length was N, The algorithm can reach the minimum standard deviation when m was the integer closest to N/3. The Monte Carlo simulation results demonstrate that the algorithm based on frequency offset correction as the integer m is closest to N/3 has lower standard deviation than the interpolation method with Hanning window and the phase difference method, while retaining a flat profile in the frequency range away from the fast Fourier transforms(FFT) discrete spectral line. The m-optimized algorithm's standard deviation is less and closer to the Cramer-Rao lower bound(CRLB) than the one as m is the integer closest to N/2 when signal noise ratio(SNR) is higher.