Maximum Likelihood Estimation of Wiener Phase Noise Variance in Coherent Optical Systems

The estimation of laser linewidth or phase noise variance is of great significance for the applications including coherent optical communications, optical fiber sensing, quantum optics, etc., to ensure the detection sensitivity and accuracy. In coherent optical communications, the Wiener phase noise introduced by the non-zero laser linewidth can lead to the rotation of constellations of the transmitted signal, which results in severe signal detection performance degradation. Many algorithms require the prior information of phase noise variance to achieve accurate phase recovery. In this paper, we propose a maximum likelihood (ML) algorithm for the estimation of Wiener phase noise variance or laser linewidth, which is based on the amplitude and phase-form of the noisy received signal model together with the use of the best, linearized, additive observation phase noise (AOPN) model due to additive white Gaussian noise (AWGN). The closed-form expression of ML estimates of carrier phase offset and Wiener phase noise variance is derived. We also verified theoretically that the obtained ML estimate of Wiener phase noise variance is unbiased and close to the actual variance with probability arbitrarily close to 1, as the sample size $N$ tends to infinity. The proposed ML estimator is shown to have accurate estimation performance with low computational complexity.