Influence of pilot symbol configuration on 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 DCT basis functions containing only a few terms. We propose an algorithm that estimates the DCT coefficients without requiring detailed knowledge about the phase noise statistics. 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 pilot symbol placement scheme, the number of pilot symbols and the number of estimated DCT coefficients. Choosing the pilot symbol positions such that the DCT basis functions are orthogonal and choosing the pilot symbol ratio such that the phase estimation is accurate while minimizing the overhead energy loss leads to considerable performance improvement as compared to other pilot symbol configurations.