In this paper, we propose an efficient soft-output signal detection method for spatially multiplexed multiple-input multiple-output (MIMO) systems. The proposed method is based on the ordered successive interference cancellation (OSIC) algorithm, but it significantly improves the performance of the original OSIC algorithm by solving the error propagation problem. The proposed method combines this enhanced OSIC algorithm with a multiple-channel-ordering technique in a very efficient way. As a result, the log likelihood ratio values can be computed by using a very small set of candidate symbol vectors. The proposed method has been synthesized with a 0.13-${mu}m$ CMOS technology for a $4{ imes}4$ 16-QAM MIMO system. The simulation and implementation results show that the proposed detector provides a very good solution in terms of performance and hardware complexity.