Fast maximum likelihood scale parameter estimation from histogram measurements

In this letter, we address the problem of estimating a parameter acting as a scale factor on the observations probability density function (pdf), i.e. a scale parameter. Histogram based Maximum Likelihood (ML) estimation of a scale parameter requires the evaluation of a discrete scale correlation. We show how ML estimation can be implemented by means of a computationally efficient Discrete Fourier Transform based procedure, when geometric histogram sampling is adopted. As a case study, we analyze a gain estimator for general QAM constellations. Simulation results and theoretical performance analysis show that the presented ML estimator outperforms selected state of the art estimators, approaching the Cramér-Rao Lower Bound (CRLB) for a wide range of SNR.