In this paper, a multiple-input multiple-output detection structure called soft information acceleration (SIA) is proposed, which is suitable for simplifying the two-stage subspace marginalization with interference suppression (SUMIS) into one stage. The proposed one-stage method outperforms the conventional two-stage SUMIS when the subspace size is large enough. The performance advantage of the proposed SUMIS-SIA mainly results from the average number of soft information updates being equal to the ’subspace size,’ instead of only once during the two-stage SUMIS detection. Thus, the SUMIS-SIA achieves a better trade-off between performance and complexity. To further reduce the complexity, a channel-shortening method based on subspace suppression is proposed. Simulation results show that the proposed channel-shortening one-stage method also outperforms SUMIS, which benefits from SIA.