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Space division multiplexing (SDM)/orthogonal frequency division multiplexing (OFDM) systems transmit different data using the same frequency, so it is necessary to separate the simultaneously received signals in the receiver. Previous studies have shown that maximum likelihood detection (MLD) provides the best bit error rate (BER) performance. However, the complexity of MLD exponentially increases with the constellation size and the number of transmit antenna branches. Therefore, it is impractical to use a full MLD without reducing its computational complexity, because it would be prohibitively large for implementation. Recently, the use of QR decomposition with an M-algorithm (QRD-M) has been proposed to reduce the system complexity while maintaining the performance of the system. However, the QRD-M performance depends on the number of surviving symbol replica candidates. When QRD-M is used with a small number of surviving symbol replica candidates, the performance declines, but when there is a large number of surviving symbol replica candidates and the transmitter antenna branches, QRD-M requires a large memory to maintain their branch metrics, and a long latency time is also required. To reduce these problems, in this paper, we propose a parallel detection algorithm using multiple QR decompositions with permuted channel matrices for SDM/OFDM systems.