Linear precoding via conic optimization for fixed MIMO receivers

Ami Wiesel*, Yonina C. Eldar, Shlomo Shamai

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

813 Scopus citations


In this paper, the problem of designing linear precoders for fixed multiple-input-multiple-output (MIMO) receivers is considered. Two different design criteria are considered. In the first, the transmitted power is minimized subject to signal-to-interference-plus-noise-ratio (SINR) constraints. In the second, the worst case SINR is maximized subject to a power constraint. It is shown that both problems can be solved using standard conic optimization packages. In addition, conditions are developed for the optimal precoder for both of these problems, and two simple fixed-point iterations are proposed to find the solutions that satisfy these conditions. The relation to the well-known uplink-downlink duality in the context of joint transmit beamforming and power control is also explored. The proposed precoder design is general, and as a special case, it solves the transmit rank-one beamforming problem. Simulation results in a multiuser system show that the resulting precoders can significantly outperform existing linear precoders.

Original languageAmerican English
Pages (from-to)161-176
Number of pages16
JournalIEEE Transactions on Signal Processing
Issue number1
StatePublished - Jan 2006
Externally publishedYes

Bibliographical note

Funding Information:
Manuscript received July 4, 2004; revised February 1, 2005. This work was supported by the EU 6th framework programme, via the NEWCOM network of excellence, and by the ISRAEL SCIENCE FOUNDATION founded by the Israel Academy of Sciences and Humanities. Conference versions of this paper were presented in IEEE International Zurich Seminar (IZS-2004), Zurich, Switzerland, February 18–20, 2004, and IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP-2004), Montreal, QC, Canada, March 17–21, 2004. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Helmut Boelcskei.


  • Linear precoding
  • Multiple-input-multiple-output (MIMO) systems
  • Optimization methods


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