Parameter estimation for sinusoidal signals with deterministic amplitude modulation

The problem of estimating the phase and frequency of an amplitude modulated sinusoidal signal is well-known. Estimators and corresponding performance bounds both for noise-like modulating functions and for purely deterministic modulating functions of different parametric models, i.e. polynomial or auto-regressive, are available in the literature. In this paper, we consider the case of known and unknown deterministic modulating functions with unspecified model. It will be shown that the asymptotic Cramèr-Rao lower bounds (ACRBs) for known and unknown modulating functions are equal. Some similarities to the case of multiplicative noise are shown. Furthermore, the variance and bias of the standard discrete Fourier transform (DFT)-based estimators in case of deterministic amplitude modulation are discussed, and maximum likelihood estimators (MLEs) in case of known modulating functions are derived.