Low-Complexity Sorted QR Decomposition for MIMO Systems Based on Pairwise Column Symmetrization

QR decomposition (QRD) is a preprocessing technique for detecting symbols in multiple-input and multiple-output (MIMO) systems, but the computational complexity is prohibitively high when the systems incorporate a large number of antennas. This paper presents a low-complexity sorted QRD (SQRD) algorithm for MIMO systems. The proposed algorithm performs SQRD through orthogonalizations based on the modified Gram-Schmidt process, rearranging the column vectors of a real-valued MIMO channel matrix in such a way that the symmetry between the vectors is maintained. By using the symmetry, the computations required for orthogonalizing one of the two adjacent vectors can be eliminated effectively, which significantly reduces the computational complexity. Theoretical analyses show that the proposed algorithm reduces the computational complexity required for SQRD by 50% for any MIMO configurations, when compared to the conventional algorithm. In addition, the memory requirement to store resultant matrices is 50% of that in the conventional one.