Global convergence and mixing parameter selection in the cross-correlation constant modulus algorithm for the multi-user environment

Surface topography of the mixed cross-correlation and constant modulus algorithm (CC-CMA) is undertaken to provide a suitable range for the mixing parameter to avoid ill-convergence. Previous work indicated that the mixing parameter k should be chosen to be greater than 4/3, but this result was based upon an assumption of perfect equalisation of previous equaliser outputs. The authors relax this perfect equalisation assumption and obtain a tighter bound for the mixing parameter in the case of a two-user system as well as a multi-user system. In a two-user transmission scheme, they suggest that the value of k should be chosen as 4. It is shown that for a multi-user system the cross-correlation of the soft decision of the previous equaliser output may result in ill-convergence and a hybrid equalisation method, which employs a hard decision on the equaliser output in the cross-correlation term of the CC-CMA algorithm after a start-up period is therefore proposed. Simulation studies are included to support the results