How to Diagonalize a MIMO Channel with Arbitrary Transmit Covariance?

Liang Liu, Rui Zhang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

1 Citation (Scopus)


Multiple-input multiple-output (MIMO) or multi-Antenna communication is a key technique to achieve high spectral efficiency in wireless systems. For the point-To-point MIMO channel, it is a well-known result that the channel singular value decomposition (SVD) based linear precoding and decoding achieves the channel capacity, which also diagonalizes the MIMO channel into parallel single-input single-output sub-channels for independent encoding and decoding. However, in multi-user MIMO systems, the optimal transmit covariance of each MIMO link is generally not its channel SVD based as a result of the control and balance of the co-channel interference among users. Thus, it remains unknown whether the linear precoding/decoding strategy is still able to achieve the capacity of each MIMO link and yet diagonalize its MIMO channel, with a given set of optimal transmit covariance of all users. This letter solves this open problem by providing a closed-form capacity-Achieving linear precoder/decoder design that diagonalizes a MIMO channel with arbitrary transmit covariance. Numerical examples are also provided to validate the proposed solution in various multi-user MIMO systems.

Original languageEnglish
Article number7460188
Pages (from-to)352-355
Number of pages4
JournalIEEE Wireless Communications Letters
Issue number4
Publication statusPublished - Aug 2016
Externally publishedYes


  • channel capacity
  • channel diagonalization
  • MIMO
  • precoding

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering


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