It is proved that when the transmit- ted signals are PSK modulated,the optimal maximum likelihood detection algorithm under perfect or imperfect channel estimation is equivalent to the conventional zero-forcing detection algorithm.

Based on the combination of modified iterative QR decomposition (ZFCD#*2MIQRD) and maximum likelihood (ML) detection, the paper represents a new combined detection algorithm which obtains transmission sign vectors,n_T evaluations, by ZFCD#*2MIQRD, and then searches for the optimized adjudgment vector for n_T evaluation vectors by ML detection algorithm.