Characterization of the regions of convergence of CMA adapted blind fractionally spaced equalizer

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.