Polynomial-phase estimation, phase unwrapping and the nearest lattice point problem
Asilomar'09 Proceedings of the 43rd Asilomar conference on Signals, systems and computers
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We model complex signals by approximating the phase and the logarithm of the time-varying amplitude of the signal as a finite order polynomial. We refer to a signal that has this form as an exponential polynomial signal (EPS). We derive an iterative maximum-likelihood (ML) estimation algorithm to estimate the unknown parameters of the EPS model. The initialization of the ML algorithm can be performed by using the result of a related paper. A statistical analysis of the ML algorithm is performed using a finite-order Taylor expansion of the mean squared error (MSE) of the estimate about the variance of the additive noise. This perturbation analysis gives a method of predicting the MSE of the estimate for any choice of the signal parameters. The MSE from the perturbation analysis is compared with the MSE from a Monte Carlo simulation and the Cramer-Rao Bound (CRB). The CRB for this model is also derived