In this paper, we consider parameter estimation of high-order polynomial-phase signals (PPSs). We propose an approach that combines the cubic phase function (CPF) and the highorder ambiguity function (HAF), and is referred to as the hybrid CPF-HAF method. In the proposed method, the phase differentiation is first applied on the observed PPS to produce a cubic phase signal, whose parameters are, in turn, estimated by the CPF. The performance analysis, carried out in the paper, considers up to the tenth-order PPSs, and is supported by numerical examples revealing that the proposed approach outperforms the HAF in terms of the accuracy and signal-to-noise-ratio threshold. Extensions to multicomponent and multidimensional PPSs are also considered, all supported by numerical examples. Specifically, when multicomponent PPSs are considered, the product version of the CPF-HAF outperforms the product HAF (PHAF) that fails to estimate parameters of components whose PPS order exceeds three.Index Terms-Polynomial-phase signals, high-order ambiguity function, cubic phase function, parameter estimation, multicomponent signals, multidimensional signals, non-Gaussian noise.
Flexible, multiple-clock-cycle, hardware design for the quasi maximum likelihood (QML) algorithm core realization for the polynomial phase signals (PPSs) estimation is proposed. The QML algorithm significantly outperforms existing PPS estimators in terms of accuracy. However, its practical applications require efficient software and hardware systems. The main challenges in the proposed hardware development with respect to existing systems for time-frequency analysis are realization of time-frequency (TF) representation based instantaneous frequency (IF) estimator, the polynomial regression, and phase extraction. The developed design is tested on a PPS corrupted by a white Gaussian noise and verified by a field programmable gate array (FPGA) circuit design. All implementation and verification details are provided along with the comparison of the results achieved by hardware and software implementations.
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