  Over the last decades, the family of $\alpha$-stale distributions has proven
to be useful for modelling in telecommunication systems. Particularly, in the
case of radar applications, finding a fast and accurate estimation for the
amplitude density function parameters appears to be very important. In this
work, the maximum likelihood estimator (MLE) is proposed for parameters of the
amplitude distribution. To do this, the amplitude data are \emph{projected} on
the horizontal and vertical axes using two simple transformations. It is proved
that the \emph{projected} data follow a zero-location symmetric $\alpha$-stale
distribution for which the MLE can be computed quite fast. The average of
computed MLEs based on two \emph{projections} is considered as estimator for
parameters of the amplitude distribution. Performance of the proposed
\emph{projection} method is demonstrated through simulation study and analysis
of two sets of real radar data.
