Observed (mis)behavior of CMA with periodic sources: assessment and guidelines

In the analysis of adaptive systems without training sequences, often termed "blind", a common assumption is to have a white source to excite the system. However, a condition which arises in practical systems is presented which does nor conform to the white source condition. A periodic symbol sequence at the input can steer the adaptation process to a solution which is not the desired solution. This (mis)behavior does arise when the equalizer is adapted with the constant modulus algorithm (CMA) and the periodic signal is nor constant modulus. The paper explores the conditions which lead to this (mis)behavior.<>