Widely Linear Estimation of Oscillator Phase Noise with Rank Reduction

In this paper, we present a novel algorithm for oscillator phase noise estimation using two key properties of the phase noise process in digital baseband: reduced-dimensional characteristics when expanded with Karhunen-Loeve basis functions and statistical improperness of the phase noise coefficients paving the way for the optimality of widely-linear (WL) estimators. The proposed methods are designed to take full- advantage of the second-order statistics, rank-deficient models and has an attractive trade- off between performance and complexity. To compute rank-reduced WL Wiener filter for highly compressed estimation, two methods are derived and analyzed using either data or parameter subspace reduction. Numerical experiments are presented for practically relevant phase noise distributions and they demonstrate the applicability of the proposed methods. They show that WL estimator can achieve up to 5 dB improvement over the best strictly linear estimator, with the maximum achieved in complexity-favorable low-rank conditions.