Chaotic phenomena in adaptive blind equalisers

The authors investigate the occurrence of chaotic phenomena in blind equalisers adapted by the constant modulus algorithm (CMA). It is shown that periodic and chaotic behaviour may take place during the update of the coefficients of the equaliser, for certain values of the adaptation step size, in both deterministic and stochastic versions of the algorithm. To study the stochastic CMA, an original theoretical framework is proposed, founded on a Markov chain-based modelling of the algorithm. The results reveal important features of the most useful technique for non-supervised equalisation. As far as is known, such convergence issues have not been properly explored in previous work.