Backing off from Infinity: Performance Bounds via Concentration of Spectral Measure for Random MIMO Channels

Yuxin Chen, Andrea J. Goldsmith, Yonina C. Eldar

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


The performance analysis of random vector channels, particularly multiple-input-multiple-output (MIMO) channels, has largely been established in the asymptotic regime of large channel dimensions, due to the analytical intractability of characterizing the exact distribution of the objective performance metrics. This paper exposes a new nonasymptotic framework that allows the characterization of many canonical MIMO system performance metrics to within a narrow interval under finite channel dimensionality, provided that these metrics can be expressed as a separable function of the singular values of the matrix. The effectiveness of our framework is illustrated through two canonical examples. In particular, we characterize the mutual information and power offset of random MIMO channels, as well as the minimum mean squared estimation error of MIMO channel inputs from the channel outputs. Our results lead to simple, informative, and reasonably accurate control of various performance metrics in the finite-dimensional regime, as corroborated by the numerical simulations. Our analysis framework is established via the concentration of spectral measure phenomenon for random matrices uncovered by Guionnet and Zeitouni, which arises in a variety of random matrix ensembles irrespective of the precise distributions of the matrix entries.

Original languageEnglish (US)
Article number6937157
Pages (from-to)366-387
Number of pages22
JournalIEEE Transactions on Information Theory
Issue number1
StatePublished - Jan 1 2015

All Science Journal Classification (ASJC) codes

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


  • MIMO
  • MMSE
  • concentration of spectral measure
  • confidence interval
  • massive MIMO
  • mutual information
  • nonasymptotic analysis
  • random matrix theory


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