Vector precoding for wireless MIMO systems and its replica analysis

Ralf R. Müller, Dongning Guo, Aris L. Moustakas

Research output: Contribution to journalArticlepeer-review

75 Scopus citations


This paper studies a nonlinear vector precoding scheme which inverts the wireless multiple-input multiple-output (MIMO) channel at the transmitter so that simple symbol-by-symbol detection can be used in lieu of sophisticated multiuser detection at the receiver. In particular, the transmit energy is minimized by relaxing the transmitted symbols to a larger alphabet for precoding, which preserves the minimum signaling distance. The so-called replica method is used to analyze the average energy savings with random MIMO channels in the large-system limit. It is found that significant gains can be achieved with complex-valued alphabets. The analysis applies to a very general class of MIMO channels, where the statistics of the channel matrix enter the result via the R-transform of the asymptotic empirical distribution of its eigenvalues. Moreover, we introduce polynomial-complexity precoding schemes for binary and quadrature phase-shift keying in complex channels by using convex rather than discrete relaxed alphabets. In case the number of transmit antennas is more than twice the number of receive antennas, we show that a convex precoding scheme, despite its polynomial complexity, outperforms NP-hard precoding using the popular Tomlinson-Harashima signaling.

Original languageEnglish (US)
Article number4481377
Pages (from-to)530-539
Number of pages10
JournalIEEE Journal on Selected Areas in Communications
Issue number3
StatePublished - Apr 2008


  • Multiple antennas
  • Multiple-input multiple-output (MIMO) systems
  • R-transform
  • Random matrices
  • Replica method
  • Spatial equalization
  • Tomlinson-Harashima precoding

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Electrical and Electronic Engineering


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