Probability of error in MMSE multiuser detection

Performance analysis of the minimum-mean-square-error (MMSE) linear multiuser detector is considered in an environment of nonorthogonal signaling and additive white Gaussian noise, In particular, the behavior of the multiple-access interference (MAT) at the output of the MMSE detector is examined under various asymptotic conditions, including: large signal-to-noise ratio; large near-far ratios; and large numbers of users, These results suggest that the MAT-plus-noise contending with the demodulation of a desired user is approximately Gaussian in many cases of interest, For the particular case of two users, it is shown that the maximum divergence between the output MAI-plus-noise and a Gaussian distribution having the same mean and variance is quite small in most cases of interest. It is further proved in this two-user case that the probability of error of the MMSE detector is better than that of the decorrelating linear detector for all values of normalized crosscorrelations not greater than 1/2 root 2 + root 3 congruent to 0.9659.