Global CMA error surface characteristics, source statistic effects: polytopes and manifolds

This work focuses on gaining insight to CMA behavior through identification of the global properties of CMA stationary point locations due to source statistics (distributions and temporal correlation). The CMA error function under source correlation effects is viewed as a deformation of the i.i.d. CMA error surface. As deformations are the realm of topology, we look at some of the topological aspects connected with CMA source correlation. Some general characteristics of CMA under i.i.d. source are presented, noting relations to Morse theory, polytopes, and Euler characteristics.