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Orthogonal space division multiplexing (OSDM) can be achieved by utilizing multiple antennas at the base station (BS) and all mobile stations (MS) (or multi-user MIMO) jointly. Recently, two iterative methods have been proposed to obtain the antenna weighting for realizing OSDM in the downlink (Kai-Kit Wong et al., IEEE Trans. Wireless Commun.; Zhengang Pan et al., IEEE Trans. Wireless Commun.). However, both suffer from high complexity if the number of BS antennas or users involved is large, as the computational complexity grows with the fourth power of the number of users. By allowing the signal streams for a user to be non-orthogonal, we propose a semi-OSDM system for complexity reduction. In the semi-OSDM system, the signals of multiple users are still orthogonal, but for each user, the multiple signaling streams are made triangular instead so that a simple backward substitution with symbol cancellation can be performed to maintain an accurate signal detection. Remarkably, the antenna weighting for semi-OSDM can be expressed in a closed form. Simulation results show that semi-OSDM has mild performance degradation, but it requires much lower computational complexity (by an order of magnitude) when compared with existing OSDM systems.