Computationally efficient Maximum Likelihood phase acquisition for QAM constellations

In this paper a blind computationally efficient Maximum Likelihood (ML) phase offset estimator for QAM constellations is introduced. The estimator is based on the computation of a weighted phase histogram named Constellation Phase Signature (CPS). The CPS is defined as the phase-dependent distribution of the received signal modulus after the application of a non-linear transformation. Here we show how the CPS can be exploited to derive a sub-optimal Maximum Likelihood (ML) estimator that approaches the CRLB for medium-high SNR. Specifically, the values of the measured CPS can be recognized as frequencies of recurrence of the received samples phases. Stemming on this observation, the CPS values can be regarded as a multinomial distributed random variable for which we are able to conduct the maximization of the likelihood function. The theoretical analysis of the estimator performance is carried out in close form. The theoretical estimator performance is compared with those of state-of-art estimators and of the Cramer-Rao lower bound (CRLB). The performance improvement is clearly appreciated, since, at medium to high SNR, the herein described estimator approaches the Cramer-Rao lower bound on all constellations.