In this paper we consider iterative techniques for multi-user detection. In the overdetermined case in which signal and noise subspaces exist, polynomial expansion can perhaps most conveniently be applied to a global MMSE ZF linear receiver. In the resulting iteration sections, we then propose to replace the various receiver components by a (possibly non-linear) MMSE variant, by interpreting the signal estimation functionality of each component. The resulting receiver sections, which can also be applied in the underdetermined case, have interpretations in terms of interference cancellation. We shall apply the proposed receiver strategy to the downlink in the FDD mode of UMTS, in which we consider a mobile terminal that also combats explicitly intercell interference.