Abstract-In this paper, we discuss three applications of the QR decomposition algorithm to decoding in a number of MultiInput Multi-Output (MIMO) systems. In the first application, we propose a new structure for MIMO Sphere Decoding (SD). We show that the new approach achieves 80% reduction in the overall complexity compared to conventional SD for a 2 × 2 system, and almost 50% reduction for the 4 × 4 and 6 × 6 cases. In the second application, we propose a low complexity Maximum Likelihood Decoding (MLD) algorithm for quasiorthogonal space-time block codes (QOSTBCs). We show that for N = 8 transmit antennas and 16-QAM modulation scheme, the new approach achieves > 97% reduction in the overall complexity compared to conventional MLD, and > 89% reduction compared to the most competitive reported algorithms in the literature. This complexity gain becomes greater when the number of transmit antennas (N ) or the constellation size (L) becomes larger. In the third application, we propose a low complexity Maximum Likelihood Decoding (MLD) algorithm for orthogonal spacetime block codes (OSTBCs) based on the real-valued lattice representation and QR decomposition. For a system employing the well-known Alamouti OSTBC and 16-QAM modulation scheme, the new approach achieves > 87% reduction in the overall complexity compared to conventional MLD. Moreover, we show that for square L-QAM constellations, the proposed algorithm reduces the decoding computational complexity from O(L N/2 ) for conventional MLD to O(L) for systems employing QOSTBCs and from O(L) for conventional MLD to O( √ L) for those employing OSTBCs without sacrificing the performance.