Maximum likelihood estimation of signal amplitude and noise variance from complex valued data

Abstract

Complex valued data may be obtained by means of acquisition systems such as magnetic resonance imaging (MRI) or digital communication systems. If the signal amplitude is to be estimated from these (inevitably noise corrupted) complex data, one has two options. Either the signal amplitude is directly estimated from the complex valued data set, or, the complex data is first transformed into a magnitude data set after which the signal amplitude is estimated. Similarly, the noise variance can be estimated from both data sets.This paper addresses the question whether it is better to use complex valued data or magnitude data for the estimation of these parameters using the maximum likelihood method. As a performance criterion, the mean-squared error (MSE) is used.