Asymptotic minimum bit error rate property of maximum-likelihood multiuser detection

In multiuser detection, the maximum-likelihood (ML) joint detection method is optimal in the sense that it maximizes the probability of correctly detecting all user symbols. However, it is not known whether the ML detector achieves the minimum bit error rate (BER) for each individual user although the ML detector often exhibits superior BER performance in practice. We prove that under high signal-to-noise ratios, the ML detector approaches the minimum BER.