Asymptotically optimum multiuser decision feedback detection

The optimum decision feedback multiuser detection rule was obtained in Varanasi (1997) for the joint detection of K simultaneously transmitting users in a synchronous Gaussian correlated waveform multiple access (CWMA) channel. The measure of optimality considered there was the asymptotic symmetric (worst-case over users) effective energy. The resulting optimum decision feedback detector (ODFD) is characterized by a feedforward-feedback matrix pair and requires K additions and K multiplications per user after matched filtering for its implementation. In this paper, it is shown that in addition to its optimality in asymptotic symmetric effective energy, the ODFD can, under certain conditions, achieve optimum asymptotic effective energy for every user, thereby matching the asymptotic efficiency performance of the exponentially complex maximum likelihood detector for all users simultaneously. In proving this result, it is not assumed that interference cancellation is perfect