A new algorithm for the estimation of the frequency of a complex exponential in additive Gaussian noise

The letter presents a new algorithm for the precise estimation of the frequency of a complex exponential signal in additive, complex, white Gaussian noise. The discrete Fourier transform (DFT)-based algorithm performs a frequency interpolation on the results of an N point complex fast Fourier transform. For large N and large signal to noise ratio, the frequency estimation error variance obtained is 0.063 dB above the Cramer-Rao bound. The algorithm has low computational complexity and is well suited for real time digital signal processing applications, including communications, radar and sonar.     

Iterative frequency estimation by interpolation on Fourier coefficients

The estimation of the frequency of a complex exponential is a problem that is relevant to a large number of fields. In this paper, we propose and analyze two new frequency estimators that interpolate on the Fourier coefficients of the received signal samples. The estimators are shown to achieve identical asymptotic performances. They are asymptotically unbiased and normally distributed with a variance that is only 1.0147 times the asymptotic Crame/spl acute/r-Rao bound (ACRB) uniformly over the frequency estimation range.