Vector precoding for Gaussian MIMO broadcast channels: Impact of replica symmetry breaking

Benjamin M. Zaidel, Ralf R. Müller, Aris L. Moustakas, Rodrigo De Miguel

Research output: Contribution to journalArticlepeer-review


The "replica method" of statistical physics is employed for the large-system analysis of vector precoding for the Gaussian multiple-input multiple-output broadcast channel. The transmitter comprises a linear front-end combined with nonlinear precoding, minimizing transmit energy by means of input alphabet relaxation. For the common discrete lattice-based relaxation, the problem violates replica symmetry and a replica symmetry breaking (RSB) ansatz is taken. The limiting empirical distribution of the precoder's output and the limiting transmit energy are derived for one-step RSB. Particularizing to a "zero-forcing" (ZF) linear front-end, a decoupling result is derived. For discrete lattice-based relaxations, the impact of RSB is demonstrated for the transmit energy. The spectral efficiencies of the aforementioned precoding methods are compared to linear ZF and Tomlinson-Harashima precoding (THP). Focusing on quaternary phase shift-keying (QPSK), significant performance gains of both lattice and convex relaxations are revealed for medium to high signal-to-noise ratios (SNRs) when compared to linear ZF precoding. THP is shown to be outperformed as well. Comparing certain lattice-based relaxations for QPSK against a convex counterpart, the latter is found to be superior for low and high SNRs but slightly inferior for medium SNRs in terms of spectral efficiency.

Original languageEnglish
Article number6157078
Pages (from-to)1413-1440
Number of pages28
JournalIEEE Transactions on Information Theory
Issue number3
StatePublished - Mar 2012
Externally publishedYes


  • Antenna arrays
  • R-transform
  • broadcast channel
  • decoupling principle
  • lattice
  • multiple-input multiple-output
  • precoding
  • replica method
  • zero-forcing (ZF)

All Science Journal Classification (ASJC) codes

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


Dive into the research topics of 'Vector precoding for Gaussian MIMO broadcast channels: Impact of replica symmetry breaking'. Together they form a unique fingerprint.

Cite this