A central limit theorem for the SINR at the LMMSE estimator output for large-dimensional signals

Abla Kammoun*, Malika Kharouf, Walid Hachem, Jamal Najim

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

42 Scopus citations


This paper is devoted to the performance study of the linear minimum mean squared error (LMMSE) estimator for multidimensional signals in the large-dimension regime. Such an estimator is frequently encountered in wireless communications and in array processing, and the signal-to-interference-plus-noise ratio (SINR) at its output is a popular performance index. The SINR can be modeled as a random quadratic form which can be studied with the help of large random matrix theory, if one assumes that the dimension of the received and transmitted signals go to infinity at the same pace. This paper considers the asymptotic behavior of the SINR for a wide class of multidimensional signal models that includes general multiple-antenna as well as spread-spectrum transmission models. The expression of the deterministic approximation of the SINR in the large-dimension regime is recalled and the SINR fluctuations around this deterministic approximation are studied. These fluctuations are shown to converge in distribution to the Gaussian law in the large-dimension regime, and their variance is shown to decrease as the inverse of the signal dimension.

Original languageEnglish (US)
Pages (from-to)5048-5063
Number of pages16
JournalIEEE Transactions on Information Theory
Issue number11
StatePublished - 2009
Externally publishedYes


  • Antenna arrays
  • Central limit theorem
  • Code-division multiple access (CDMA)
  • Linear minimum mean squared error (LMMSE)
  • Martingales
  • Multiple-carrier (MC)-CDMA
  • Multiple-input multiple-output (MIMO)
  • Random matrix theory

ASJC Scopus subject areas

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


Dive into the research topics of 'A central limit theorem for the SINR at the LMMSE estimator output for large-dimensional signals'. Together they form a unique fingerprint.

Cite this