Joint unitary triangularization for MIMO networks

Anatoly Khina*, Yuval Kochman, Uri Errez

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


This paper considers communication networks where individual links can be described as those based on multiple-input multiple-output channels. Unlike orthogonal modulation methods (such as the singular-value decomposition), we allow interference between subchannels, which can be removed by the receivers via successive cancellation. The degrees of freedom earned by this relaxation are used for obtaining a basis, and corresponding decomposition, which are simultaneously good for more than one link. Specifically, we derive necessary and sufficient conditions for shaping the ratio vector of subchannel gains of two broadcast-channel receivers. We then apply this decomposition to two scenarios: First, in digital multicasting we present a practical capacity-achieving scheme which uses only scalar codes and linear processing. Then, we consider the joint source-channel problem of transmitting a Gaussian source over a two-user multiple-input multiple-output channel, where we show the existence of nontrivial cases, where the optimal distortion pair (which for high signal-to-noise ratios (SNRs) equals the optimal point-to-point distortions of the individual users) may be achieved by employing a hybrid digital-analog scheme over the induced equivalent channel. These scenarios demonstrate the advantage of choosing a modulation basis based upon multiple links in the network. Thus, we coin the approach "network modulation".

Original languageAmerican English
Article number6043915
Pages (from-to)326-336
Number of pages11
JournalIEEE Transactions on Signal Processing
Issue number1
StatePublished - Jan 2012
Externally publishedYes

Bibliographical note

Funding Information:
Manuscript received December 20, 2010; revised April 29, 2011 and September 15, 2011; accepted September 17, 2011. Date of publication October 13, 2011; date of current version December 16, 2011. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Xiqi Gao. The work of the Y. Kochman was supported in part by the National Science Foundation by Grant No. CCF-1017772 and by a grant from Hewlett-Packard Laboratories. The work of U. Erez was supported in part by the U.S.—Israel Binational Science Foundation by Grant 2008/455. The material in this paper was presented in part at the 48th Annual Allerton Conference on Communication, Control and Computing, Monticello, IL, September 2010, and ICASSP, Prague, Czech Republic, May 2011.


  • Broadcast channel
  • GDFE
  • GSVD
  • MIMO
  • generalized triangular decomposition (GTD)
  • geometric mean decomposition
  • joint source-channel coding
  • multicasting
  • multiplicative majorization


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