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QR-decomposition with M-algorithm (QRDM) achieves quasi-ML performance in multiple-input multiple output (MIMO) multiplexing systems. Nevertheless, QRDM performs avoidable computations because of its systematic search strategy and its unawareness of the channel and noise conditions. Another drawback is that QRDM has a sequential nature which limits the capabilities of pipelining. In this paper, we propose semi-ML adaptive parallel QRDM (APQRDM) and iterative QRDM (AIQRDM) algorithms based on set grouping. Using the set grouping, the tree-search stage of QRDM algorithm is divided into partial detection phases (PDP). Therefore, when the tree search stage of QRDM is divided into 4 PDPs, the APQRDM latency is one fourth of that of the QRDM, and the hardware requirements of AIQRDM is approximately one fourth of that of QRDM. Moreover, simulation results show that in 4 Ã 4 system and at Eb/No of 14 dB, APQRDM decreases the average computational complexity to approximately 43% of that of the conventional QRDM. Also, at Eb/No of 0 dB, AIQRDM reduces the computational complexity to about 54% and the average number of metric comparisons to approximately 10% of those required by the conventional QRDM and AQRDM.