AM/FM signal estimation with micro-segmentation and polynomial fit

Amplitude and phase estimation of AM/FM signals with parametric polynomial representation require the polynomial orders for phase and amplitude to be known. But in reality, they are not known and have to be estimated. A well-known method for estimation is the higher-order ambiguity function (HAF) or its variants. But the HAF method has several reported drawbacks such as error propagation and slowly varying or even constant amplitude assumption. Especially for the long duration time-varying signals like AM/FM signals, which require high orders for the phase and amplitude, computational load is very heavy due to nonlinear optimization involving many variables. This paper utilizes a micro-segmentation approach where the length of segment is selected such that the amplitude and instantaneous frequency (IF) is constant over the segment. With this selection first, the amplitude and phase estimates for each micro-segment are obtained optimally in the LS sense, and then, these estimates are concatenated to obtain the overall amplitude and phase estimates. The initial estimates are not optimal but sufficiently close to the optimal solution for subsequent processing. Therefore, by using the initial estimates, the overall polynomial orders for the amplitude and phase are estimated. Using estimated orders, the initial amplitude and phase functions are fitted to the polynomials to obtain the final signal. The method does not use any multivariable nonlinear optimization and is efficient in the sense that the Z. Deprem (B) · A. E. Çetin · O. Arıkan Department of Electrical and Electronics Engineering, Bilkent University, 06800 Ankara, Turkey e-mail: [email protected] A. E. Çetin e-mail: [email protected] O. Arıkan e-mail: [email protected] MSE performance is close enough to the Cramer–Rao bound. Simulation examples are presented.