Steepest gradient-based orthogonal precoder for integer-forcing MIMO

Mohammad Nur Hasan, Brian M. Kurkoski, Amin Sakzad, Emanuele Viterbo

Research output: Contribution to journalArticleResearchpeer-review

2 Citations (Scopus)


In this paper, we develop an orthogonal precoding scheme for integer-forcing (IF) linear receivers using the steepest gradient algorithm. Although this scheme can be viewed as a special case of the unitary precoded integer-forcing (UPIF), it has two major advantages. First, the orthogonal precoding outperforms its unitary counterpart in terms of achievable rate, outage probability, and error rate. We verify this advantage via theoretical and numerical analyses. Second, it exhibits lower complexity as the dimension of orthogonal matrices is half that of unitary matrices in the real-valued domain. For finding 'good' orthogonal precoder matrices, we propose an efficient algorithm based on the steepest gradient algorithm that exploits the geometrical properties of orthogonal matrices as a Lie group. The proposed algorithm has low complexity and can be easily applied to an arbitrary MIMO configuration. We also confirm numerically that the proposed orthogonal precoding outperforms UPIF type II in some scenarios and the X-precoder in high-order QAM schemes, e.g., 64- and 256-QAM.

Original languageEnglish
Pages (from-to)942-955
Number of pages14
JournalIEEE Transactions on Wireless Communications
Issue number2
Publication statusPublished - 5 Nov 2019


  • integer-forcing (IF)
  • lattice codes
  • Lie group
  • Multiple-input multiple-output (MIMO)
  • orthogonal precoding
  • steepest gradient

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