Optimal blind biharmonic feedforward phase offset estimation for QAM signals

An algorithm is presented for blind phase offset estimation for signals with quadrature amplitude modulation. The algorithm is based on a circular harmonic expansion of log-likelihood function (LLF). Retaining one or two most significant terms in this series gives a harmonic or biharmonic circular decomposition of the LLF, this approach leads to notable improvement of the estimation quality comparing to known versions of popular “4^th power” phase estimation algorithm. In this paper we present improvement for harmonic and biharmonic phase offset estimation algorithms by optimization of weighting functions. Simulation results show that it gives much better performance in comparison with original algorithms based on Fourier series truncation. As a result, harmonic method is similar to optimal nonlinear least-squares algorithm, while biharmonic method approaches Cramer-Rao lower bound.