Finite Difference Algorithm for Polynomial Phase Estimation

Abstract

A new algorithm, the finite difference algorithm, is proposed for single-component polynomial phase signal parameter estimation. The proposed algorithm takes advantage of the framework of the quasi-maximum-likelihood (QML) estimator but estimates the finite difference of the polynomial instead of the derivative. Like the QML algorithm it can operate on high-order polynomial phase signals without sacrificing speed or its noise threshold. The algorithm is computationally simpler than the QML algorithm, but does have a higher noise threshold. We derive a framework for error analysis for phase-based polynomial phase estimation algorithms. This framework can help to analyze the SNR threshold effect as well as the effect of unwrapping errors. We note the equivalence of the finite difference approach with that of fitting a polynomial to an unwrapped signal under certain circumstances. We propose modifications to allow the FD algorithm to operate at lower SNRs. The modifications are magnitude weighting for phase values, phase difference filtering, and iterating the polynomial refinement step. Simulation shows that these modifications can lower the algorithm's SNR threshold by 5 dB, without greatly increasing the computational complexity.