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.< >