Abstract:  A fast QR decomposition algorithm with optimal detection order is proposed in this paper for common used MIMO non-linear detection, including sorted QR decomposition (SQRD), sphere decoding (SD), K-best/QR decomposition and M algorithm (QRM) and so on. Using this algorithm, the receiver does QR decomposition of the channel matrix firstly, determines the best order of detection from the upper triangular matrix:R, and arranges the columns of Raccording to the optimal detection order; then, the receiver does QR decomposition of the rearrangement matrix of Rfor a second time, which is the QR decomposition results with the optimal detection order. Compared with the existing QR decomposition algorithm, getting its detection order according to the diagonal elements’ modulus of R, the proposed fast QR decomposition algorithm can improve detection performance because of its optimal detection order. Simulation results show when bit error rate (BER) equals 10^-3with the antenna configuration being 4*4 and 6*6, the proposed algorithm can save signal to noise ratio (SNR) in 1 dB and 2 dB, respectively. Compared with the existing QR decomposition algorithm, getting its detection order according to signal to interference and noise ratio (SINR), the proposed algorithm can reduce 25% times of complex multiplications and 33% times of complex additions with the same BER performance.