Gain control free blind frequency offset estimator for general QAM communication

In this paper we present a novel not data aided gain control free frequency offset estimator for general Quadrature Amplitude Modulated constellations along with its theoretical performance analysis. The estimator is based on applying a tentative frequency offset compensation by means of a nonlinear transformation of the received signal samples and on estimating an accumulation function in different angular windows. For perfect frequency offset compensation, the measurements are suitably clustered and their accumulation, named “Constellation Phase Signature” (CPS), is a function of the window orientation made up by a set of pulses whose locations depend on the constellation. If the constellation is known, the CPS is known, and the estimated frequency offset is the one such that the preliminary frequency compensation of the non linearly transformed signal samples provides the best match between the observed phase histogram and its expected value corresponding to zero frequency offset. The performance analysis is shown to match the numerical simulations for medium to high values of SNR.