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.

The linear minimum-mean-square error (LMMSE) estimator is herein derived to estimate phase-noise of Levy statistics (including Wiener phase-noise) and of arbitrarily large magnitude. This estimator may be pre-set to any latency and any number of tabs. This estimator depends only on the signal-to-(additive)-noise ratio and the phase-noise variance, but requires no matrix-inversion.