Maximum likelihood scale parameter estimation: An application to gain estimation for QAM constellations

In this paper we address the problem of scale parameter estimation, introducing a reduced complexity Maximum Likelihood (ML) estimation procedure. The estimator stems from the observation that, when the estimandum acts as a shift parameter on a multinomially distributed statistic, direct maximization of the likelihood function can be conducted by an efficient DFT based procedure. A suitable exponential warping of the observation's domain is known to transform a scale parameter problem into a shift estimation problem, thus allowing the afore mentioned reduced complexity ML estimation for shift parameter to be applied also in scale parameter estimation problems. As a case study, we analyze a gain estimator for general QAM constellations. Simulation results and theoretical performance analysis show that the herein presented estimator outperforms selected state of the art high order moments estimator, approaching the Cramér-Rao Lower Bound (CRLB) for a wide range of SNR.