Multidimensional Polynomial Phase Estimation

Heedong Do

doi:10.1109/OJSP.2025.3577503

Multidimensional Polynomial Phase Estimation

2025-01-01

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DOI：10.1109/OJSP.2025.3577503

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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 is efficient at high signal-to-noise ratios (SNRs), exhibiting a computational complexity that is strictly linear in the number of observations and at most quadratic in the number of polynomial terms. 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.

Keywords:

Polynomial phase signal

estimation theory

Cramer-Rao bound

minimum mean-square error

phase wrapping

phase ambiguity

signal reconstruction

circular averaging

Multidimensional Polynomial Phase Estimation

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