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In mobile WiMAX systems, uplink collaborative MIMO (multiple input multiple output) performs spatial multiplexing with two PSSs (portable subscriber stations), each with one antenna. As two PSSs transmit collaboratively on the same sub-channel, the overall uplink capacity will be doubled. To perform this interesting technique with high performance, most system venders demand the optimal MLD (maximum-likelihood detection) in the RAS (radio access station). However, the MLD is difficult to implement due to its explosive computational complexity. In this paper, we propose a two-step MIMO decoding scheme which achieves near ML performance with low complexity for CSM (collaborative spatial multiplexing) in uplink mobile WiMAX systems that having an iterative channel decoder using bit LLR (log-likelihood ratio) information. Simulation results show that the proposed scheme has almost the same BLER (block error rate) performance of the MLD with only about 15.75% computational complexity in terms of real multiplication, when both PSSs transmit with 16 QAM (quadrature amplitude modulation) modulation.