  Recent studies have demonstrated that correntropy is an efficient tool for
analyzing higher-order statistical moments in nonGaussian noise environments.
Although correntropy has been used with complex data, no theoretical study was
pursued to elucidate its properties, nor how to best use it for optimization.
This paper presents a probabilistic interpretation for correntropy using
complex-valued data called complex correntropy. A recursive solution for the
maximum complex correntropy criterion (MCCC) is introduced based on a fixed
point solution. This technique is applied to a simple system identification
case study, and the results demonstrate prominent advantages when compared to
the complex recursive least squares (RLS) algorithm. By using such
probabilistic interpretation, correntropy can be applied to solve several
problems involving complex data in a more straightforward way. Keywords:
complex-valued data correntropy, maximum complex correntropy criterion,
fixed-point algorithm.
