Asymptotic analysis of scale-invariant cost functions for blind adaptive processing

In this paper, we provide an asymptotic precision analysis of blind adaptive filter coefficients derived from a wide class of scale-invariant cost functions implicitly implemented in a batch processing mode. This analysis is based on a first-order Taylor expansion of the cost functions in the vicinity of their maxima and represents an extension of Donoho´s (1981) classic asymptotic precision analysis to the complex case. Through this analysis we have a means of discriminating among different nonlinear cost functions in the sense of yielding more precise estimates with N finite samples. We also find that cost functions based on very large order statistics tend to have highly desirable convergence properties over a wide range of constellations