Iterative soft-decision-directed phase noise estimation from a DCT basis expansion

This contribution deals with estimation and compensation of phase noise in single-carrier digital communications. We present an iterative feedforward soft-decision-directed phase noise estimation algorithm, that is based on approximating the phase noise process by an expansion of DCT basis functions containing only a few terms. An initial estimate of the phase noise is obtained using pilot symbols inserted in the data sequence. The estimate is iteratively improved by exploiting also soft decisions from the data symbols, obtained in a previous iteration. We demonstrate that the resulting (linearized) mean-square estimation error consists of two contributions: a contribution from the additive noise, that equals the Cramer-Rao lower bound, and a noise-independent contribution that results from the phase noise modeling error. Performance can be optimized by a proper selection of the number of DCT coefficients in the expansion of the phase noise. Iterative soft-decision-directed phase noise estimation yields a considerable performance improvement as compared to estimation using only pilot symbols.