Two dimensional frequency estimation by interpolation on Fourier coefficients

In this paper, we propose a computationally simple algorithm for the estimation of the frequencies of a random phase two-dimensional (2-D) complex exponential in additive noise by extending the 1-D estimator developed by Aboutanios and Mulgrew. The procedure of the algorithm is based on a two-stage scheme consisting of a coarse estimator followed by a fine search stage. The separability of the problem implies that the estimator can be applied in each direction. Theoretical analysis shows, however, that the performance of the algorithm converges to the minimum point of the asymptotic variance after two iterations only if the estimation is applied jointly in the two dimensions. As in the 1-D case, this variance is extremely close to the 2-D Cramer-Rao Lower Bound. The simulation results are presented to verify the analysis.