Gain control free near efficient phase acquisition for QAM constelations

This paper introduces a novel, not data aided, phase offset estimator for quadrature amplitude modulated (QAM) signals. Contrarily to near-efficient existing phase acquisition techniques, this estimator does not require a preliminary gain adjustment stage while its accuracy preserves the slope of Cramér–Rao bound for medium-high signal-to-noise ratio (SNR) ranges, where it typically outperforms existing blind estimators, with significant improvement for dense and crossQAMconstellations. Moreover, it needs only a very rough estimate of the SNR. Like other gain-control- free blind phase-offset estimators, it measures the amount of the cyclic shift by which the (four-folded) phase probability density function (pdf) is rotated under an unknown phase-offset. Estimation of the phase-offset-induced cyclic shift is conducted first by measuring the received data phase pdf by a canonical phase histogram procedure, then by estimating the phase-offset-induced cyclic shift through a cyclic cross correlation-based procedure between the measured phase histogram and a reference phase pdf evaluated within the zero phase-offset hypothesis. Actually, the estimation procedure is presented in a generalized version that considers a tomographic projection of the bidimensional (magnitude/ phase) pdf of suitable nonlinear transformations of the received data. The tomographic projection performs a magnitude weighing on the pdf, and this, in turn, results in an improved overall estimation accuracy, as shown by theoretical analysis and numerical simulations here performed to assess the estimator performance.