Aiming at the issues that practical interleaver-division multiple-access（IDMA） systems do not cover the high-speed transfer in next generational wireless cellular telecommunication

the probability data association（PDA） algorithm was applied to IDMA higher-order modulated systems.Meanwhile

the reasonable approximate Log-MAP algorithm was adopted to chip by chip iterative multi-user detection（MUD）based on PDA to reduce the MUD complexity of QAM-IDMA systems.Simulation results show that the bit error rate performance of Max-Log-MAP algorithm approaches that of Log-MAP algorithm by increasing the number of the Turbo iterations.