Probability of error in MMSE multiuser detection

H. Vincent Poor, Sergio Verdu

Research output: Contribution to journalArticlepeer-review

662 Scopus citations


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 + √2 +√3 ≅ 0.9659.

Original languageEnglish (US)
Pages (from-to)858-871
Number of pages14
JournalIEEE Transactions on Information Theory
Issue number3
StatePublished - 1997

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


  • Asymptotic normality
  • Decorrelating detector. MMSE detection
  • Divergence
  • Multiuser detection
  • Probability of error


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