New results for probability of error performance in MMSE multiuser detection for CDMA

The minimum-mean-square-error (MMSE) linear multiuser detector considers multiple access interference (MAI) and background Gaussian noise asymptotically Gaussian for a large number of users in asynchronous code division multiple access (CDMA) system. For this asymptotic condition, the MMSE detector outperforms the decorrelating detector only if the value of normalized cross-correlation (NCC) for any pair of code sequence is less than or equal to numerically derived upper bounded value. The available results in literature have been derived for two-user case. In this paper, we have presented a general formula to calculate upper bound on NCC for arbitrary number of users under near-far situation. We also propose Chernoff bound on error probability of MMSE multiuser detector. Its proof based on divergence theorem and study of leakage coefficients for more than two users imposes the stringent condition on signal-to-noise ratio of desired user.