Identification of improper processes by variable tap-length complex-valued adaptive filters

Variable tap-length is introduced into complex-valued adaptive filters in order to provide an additional degree of freedom, enhance tracking ability, and provide data-adaptive optimal modelling. This is achieved by extending the fractional tap-length (FT) algorithm from the real domain ℝ and by accounting for some special properties of the complex domain ℂ. For generality, the augmented least mean square (ACLMS) and augmented complex nonlinear gradient descent (ACNGD) are equipped with the variable tap-length in order to cater for both the second order circular and noncircular signals. Simulations on model order selection and the identification of the noncircular nature of complex data support the approach.