If estimation of linear FM signals corrupted by multiplicative and additive noise: A time-frequency approach

This paper presents a time-frequency approach for the estimation of the instantaneous frequency (IF) of a linear frequency modulated (FM) signal affected by multiplicative and additive white Gaussian noise. Contrary to earlier claims, we show that the Wigner-Ville spectrum (WVS) is optimal in the sense of IF localisation for such signals and its peak is proposed as an IF estimator. We derive an analytical expression for the asymptotic variance for this estimator. Simulation results based on Monte-Carlo realisations illustrate and confirm the validity of the theoretical derivations and analysis.