Output MAI distributions of linear MMSE multiuser receivers in DS-CDMA systems

Multiple-access interference (MAI) in a code-division multiple-access (CDMA ) system plays an important role in performance analysis and characterizati on of fundamental system limits. In this paper, we study the behavior of th e output MAI of the minimum mean-square error (MMSE) receiver employed in t he uplink of a direct-sequence (DS)-CDMA system. We focus on imperfect powe r-controlled systems with random spreading, and establish that in a synchro nous system 1) the output MAI of the MMSE receiver is asymptotically Gaussi an, and 2) for almost every realization of the signatures and received powe rs, the conditional distribution of the output MAI converges weakly to the same Gaussian distribution as in the unconditional case. We also extend our study to asynchronous systems and establish the Gaussian nature of the out put interference. These results indicate that in a large system the output interference is approximately Gaussian, and the performance of the MMSE rec eiver is robust to the randomness of the signatures and received powers. Th e Gaussianity justifies the use of single-user Gaussian codes for CDMA syst ems with Linear MMSE receivers, and implies that from the viewpoints of det ection and channel capacity, signal-to-interference ratio (SIR) is the key parameter that governs the performance of the MMSE receiver in a CDMA syste m.