Probability of error in MMSE multiuser detection

TLDR

The 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. The study examines the multiple‑access interference at the MMSE detector output under asymptotic conditions of high SNR, large near‑far ratios, and many users. The MAI‑plus‑noise seen by a desired user is approximately Gaussian in many cases, and for two users the divergence from Gaussianity is small while the MMSE detector’s error probability outperforms the decorrelating detector for normalized cross‑correlations up to 0.9659.

Abstract

The 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 (MAI) 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 MAI-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 /spl radic/(2+/spl radic/3)/spl cong/0.9659.