Although Multiple-Input Multiple-Output（MIMO） technology can improve the utilization rate of the spectrum, multi-dimensional signal processing brings great challenges to the detection of MIMO signals. Based on the analysis of various MIMO detection algorithms, the nonlinear QR decomposition algorithm is selected as the research object. In order to obtain a higher performance of detection, the sorted QR decomposition is further studied and the sorting scheme based on the L1-norm is proposed. Using Matlab for performance simulation, the L1-norm sorting strategy and the L2-norm sorting strategy have the same impact on the MIMO system, but the L1-norm sorting strategy reduces the computational complexity. On this basis, the hardware structure of the improved sorted QR decomposition by Givens rotation on FPGA is proposed. Compared with the solution of the L2-norm, the L1-norm strategy reduces at least 29.2% combinational logic resources and 32.4% register resources when calculating a single-column norm in the realization of 4×4 channel matrix decomposition. By comparing the design of the integral structure and similar dimension one, the frequency of the operating clock is significantly improved.