Characterization of the Regions of Convergence of CMA Adapted Blind
Fractionally Spaced Equalizer
W. Chung and C.R. Johnson, Jr.
Abstract
The constant modulus algorithm (CMA) is an effective and
popular scheme for blind adaptive equalization. Delineation
of
the regions of convergence of this multimodal algorithm has
remained as an unresolved problem in spite of its
significance
with regard to CMA initialization strategies. In this paper
we
present a qualitative analysis of convergence regions of the
fractionally spaced CMA (FS-CMA) equalizer based on a new
geometrical understanding of the constant modulus cost
function. We characterize the location and volume of the
convergence regions of local minima, and associate the
volume
of the convergence regions with their MSE performance. The
convergence regions of the local minima with low noise gain
expand near the origin, while those of the local minima with
high noise gain shrink. This explains partly the robustness
of
FS-CMA and the MSE optimization achieved by the widely used
center spike initialization with constrained magnitude.
