Multidimensional Polynomial Phase Estimation

TL;DR

This paper introduces a versatile, efficient multidimensional polynomial phase estimator capable of handling arbitrary degrees and dimensions, with strong performance across various SNR levels due to its compact algorithm and phase unwrapping functionalities.

Contribution

It presents a novel, linear-complexity estimator for multidimensional polynomial phase signals that surpasses existing methods in flexibility and efficiency.

Findings

Linear computational complexity in the number of observations

Effective at high SNRs with enhanced low/medium SNR performance

Handles arbitrary dimensions and polynomial degrees

Abstract

An estimation method is presented for polynomial phase signals, i.e., those adopting the form of a complex exponential whose phase is polynomial in its indices. Transcending the scope of existing techniques, the proposed estimator can handle an arbitrary number of dimensions and an arbitrary set of polynomial degrees along each dimension; the only requirement is that the number of observations per dimension exceeds the highest degree thereon. Embodied by a highly compact sequential algorithm, this estimator exhibits a strictly linear computational complexity in the number of observations, and is efficient at high signal-to-noise ratios (SNRs). To reinforce the performance at low and medium SNRs, where any phase estimator is bound to be hampered by the inherent ambiguity caused by phase wrappings, suitable functionalities are incorporated and shown to be highly effective.