Convergence speed analysis is crucial in TBICM-ID-SSD systems in order to tune the number of iterations when considering the practical implementation perspectives. Conducted analysis has demonstrated that omitting two turbo demodulation iterations without decreasing the total number of turbo decoding iterations leads to promising complexity reductions while keeping error rate performance almost unaltered. In the same context, promising results have been recently obtained when considering a feedback loop to the SISO equalizer for MIMO systems. Future work targets the extension of this analysis to other base-band iterative applications and its integration into available hardware prototypes.