We introduce a symbol by symbol, soft-input soft-output (SISO) multiuser detector for frequency selective multiple-input multiple-output (MIMO) channels. The basic principle of this algorithm is to extract a posteriori probabilities (APPs) of all interfering symbols at each symbol interval and then feed these updated APPs as a priori probabilities (apPs) for joint APP extraction in the next symbol interval. Unlike nearoptimal block oriented sphere decoding (SD) and soft decision equalization (SDE), the computational complexity of this updating APP (UA) algorithm is linear in the number of symbols but the exponential computational load of optimal joint APP extraction makes the basic UA impractical. To decrease computations we replace the optimal joint APP extractor by a groupwise SISO multiuser detector with a soft sphere decoding core. The resulting reduced complexity updating APP (RCUA) equalizer is flexible in different situations and outperforms the traditional sub-optimal MMSE-DFE without increasing the computational costs substantially
