Linear minimum‐mean‐squared error estimation of phase noise, which has a symmetric Levy distribution and a possibly large magnitude, from observables at irregular instants

Abstract

This study extends an algorithm, previously proposed by the present authors, for ‘linear minimum-mean-squared error’ estimation of phase noise of (possibly) temporal non-stationarity, large magnitude, ‘non’-identical increments that have a Levy distribution, of which the Wiener distribution represents a special case. This estimator-taps may be pre-set to any number, may be pre-computed offline with no matrix inversion, based on the prior knowledge of only the signal-to-(additive)-noise ratio and the phase-noise's characteristic function. That estimator may be set to various degrees of latency. This is here generalised to allow observables at irregular time-instants (e.g. because of the irregular placement of pilot symbols in the transmitted waveform), under which the phase-noise increments become non-identically distributed. This study handles this more complicated scenario.