Single tone parameter estimation from discrete-time observations

TLDR

The paper discusses estimating the parameters of a single‑frequency complex tone from a limited number of noisy discrete‑time observations. The authors derive Cramér‑Rao bounds and maximum‑likelihood estimation algorithms, exploiting the link to the discrete Fourier transform to produce practical methods, and analyze the threshold effect of one algorithm. The study proves properties of the ML estimators, analyzes the threshold effect of one algorithm with simulation comparison, and confirms additional aspects through further simulations.

Abstract

Estimation of the parameters of a single-frequency complex tone from a finite number of noisy discrete-time observations is discussed. The appropriate Cramér-Rao bounds and maximum-likelihood (MI.) estimation algorithms are derived. Some properties of the ML estimators are proved. The relationship of ML estimation to the discrete Fourier transform is exploited to obtain practical algorithms. The threshold effect of one algorithm is analyzed and compared to simulation results. Other simulation results verify other aspects of the analysis.