Joint blind estimation of carrier phase and frequency offset for QAM signals using circular harmonic decomposition

An algorithm is presented for joint blind estimation of carrier phase and frequency offset for signals with quadrature amplitude modulation (QAM). 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 approximation of the LLF, this approach leads to notable improvement of the estimation quality comparing to known versions of popular 4^th power frequency estimation algorithm. Computer simulation results are presented for 32-QAM constellation; they justify the advantages of the suggested method. It is also shown that the simplified implementation of the algorithm with SNR-independent weighting functions does not lead to any notable performance loss.