Feedforward Data-Aided Phase Noise Estimation from a DCT Basis Expansion

This contribution deals with phase noise estimation from pilot symbols. The phase noise process is approximated by an expansion of discrete cosine transform (DCT) basis functions containing only a few terms.We propose a feedforward algorithm that estimates the DCT coefficients without requiring detailed knowledge about the phase noise statistics. We demonstrate that the resulting (linearized) mean-square phase 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. We investigate the effect of the symbol sequence length, the pilot symbol positions, the number of pilot symbols, and the number of estimated DCT coefficients on the estimation accuracy and on the corresponding bit error rate (BER). We propose a pilot symbol configuration allowing to estimate any number of DCT coefficients not exceeding the number of pilot symbols, providing a considerable performance improvement as compared to other pilot symbol configurations. For large block sizes, the DCT-based estimation algorithm substantially outperforms algorithms that estimate only the time-average or the linear trend of the carrier phase.