Compound time‐frequency domain method for estimating parameters of uniform‐sampling polynomial‐phase signals on the entire identifiable region

Abstract

Parameter estimation of polynomial-phase signals (PPSs) observed in additive white Gaussian noise (AWGN) is addressed. Most of the existing estimators cannot work on a fully identifiable region. Using the algebraic number theory, McKilliam et al. proposed a least squares unwrapping (LSU) estimator, which can operate on the entire identifiable region. However, its computational load may be large, especially when the number of samples is large. In this study, the authors first extend the amplitude-weighted phase-based estimator (AWPE) for sinusoidal and chirp signals to PPSs and derive a time domain maximum likelihood estimator. The performance is analysed and compared with the Cramer–Rao lower bound (CRLB). Then, the authors propose an iterative compound time-frequency domain parameter estimation method, which includes a coarse estimation step and a fine estimation step conducted by the discrete polynomial phase transform and AWPE estimator, respectively. Monte–Carlo simulations show that the proposed method can work on the entire identifiable region and that it outperforms the existing state-of-the-art estimators. Its computational complexity is considerably lower than that of the LSU estimator, while its threshold signal-to-noise ratio is a few decibels higher than that of the LSU estimator.