Asymptotic performance bounds of joint channel estimation and multiuser detection in frequency-selective fading DS-CDMA channels

We derive asymptotic upper bounds of the performance of a one-shot MMSE multiuser detector (MUD) and an optimal MUD in frequency-selective fading DS-CDMA channels with imperfect CSI at the receiver, using the replica method. We find that the performance bound of the one-shot MMSE MUD is indistinguishable from the performance of the one-shot LMMSE MUD analyzed by Evans and Tse when signal-to-noise ratio is high and the system load is small, and that the performance gap between the optimal MUD and the one-shot LMMSE MUD is also small on the same conditions.