Low-complexity sorted QR decomposition for MIMO systems based on pairwise column symmetrization

This paper presents a low-complexity preprocessing algorithm for multiple-input multiple-output communication systems. The proposed algorithm performs the sorted QR decomposition 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. The reduction rate of the computational complexity by the proposed algorithm is 50% for any MIMO configuration.