Feedback blind phase synchronization for QAM signals based on circular harmonic decomposition

An algorithm is presented for feedback blind phase synchronization for signals with quadrature amplitude modulation. The algorithm is based on a circular harmonic expansion (CHE) 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. Earlier this approach was presented by authors for feedforward blind phase and frequency estimation. In this paper we present application of CHE of LLF to feedback synchronization. The main point is employing the derivative of LLF approximation by CHE as an error signal for phase recovery loop. Optimization of weighting functions is also presented. Simulation results show that optimal biharmonic method has performance close to decision-directed algorithm and approaches modified Cramer-Rao bound. Advantages of the algorithm are wide acquisition range and no necessity of hard decisions that may be absent in soft-output detectors.