A Fast and Simple Algorithm for Computing MLE of the Amplitude Density Function Parameters

Over the last decades, the family of
$\alpha$
-stable distributions has proven to be useful for a variety of applications in telecommunication systems. Particularly, in the case of radar applications, finding a fast and accurate estimation method for the amplitude density function parameters appears to be of great significance. In this work, the maximum likelihood estimator (MLE) is proposed for parameters of the amplitude's distribution. To this end, the amplitude data are
projected
onto the horizontal and vertical axes using two simple transformations. It will be shown that the
projected
data will follow a zero-location symmetric
$\alpha$
-stable distribution for which MLE can be computed quite fast. The averages of the computed MLEs based on the two
projections
are considered as estimator of parameters of the amplitude's distribution. Performance of the proposed
projection
method is demonstrated through simulation study and analysis of two real radar datasets.