Estimation of the frequency of sinusoidal signals in Laplace noise

Accurate estimation of the frequency of sinusoidal signals from noisy observations is an important problem in signal processing applications such as radar, sonar, and telecommunications. In this paper, we study the problem under the assumption of non-Gaussian noise in general and Laplace noise in particular. We prove that the Laplace maximum likelihood estimator is able to attain the asymptotic Cramer-Rao lower bound under the Laplace assumption which is one half of the Cramer-Rao lower bound in the Gaussian case. This provides the possibility of improving the currently most efficient methods such as nonlinear least-squares and periodogram maximization in non-Gaussian cases. We propose a computational procedure that overcomes the difficulty of local extrema in the likelihood function when computing the maximum likelihood estimator. We also provide some simulation results to validate the proposed approach.