Replica analysis of general multiuser detection in MIMO DS-CDMA channels with imperfect CSI

We consider impacts of channel estimation errors on performance of general multiuser detectors in MIMO DS-CDMA channels. We evaluate their performance in terms of asymptotic spectral efficiency, which is obtained via decoupling structure, by using the replica method. Numerical results imply that the performance of LMMSE detection is very close to that of MMSE detection for small system loads. Furthermore, we find that the spectral efficiency of MMSE detection grows discontinuously with the length of pilot sequences for large system loads, and that the critical length is close to the optimal length. While it is indistinguishable from that of LMMSE detection for short pilot sequences, the gap between the two is significantly large if the length of pilot sequences is longer than the critical length.