Robust Tomlinson-Harashima source and linear relay precoders design in amplify-and-forward MIMO relay systems

Fan Shuo Tseng*, Min Yao Chang, Wen-Rong Wu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


Existing transceiver designs in amplify-and-forward (AF) multiple-input-multiple-output (MIMO) relay systems often assume the availability of perfect channel state informations (CSIs). Robust designs for imperfect CSI have less been considered. In this paper, we propose a robust nonlinear transceiver design for the system with a Tomlinson-Harashima precoder (THP), a linear relay precoder, and a minimum-mean-squared-error (MMSE) receiver. Since two precoders and imperfect CSIs are involved, the robust transceiver design is difficult. To overcome the difficulty, we first propose cascading an additional unitary precoder after the THP. The unitary precoder can not only simplify the optimization but also improve the performance of the MMSE receiver. We then adopt the primal decomposition dividing the original optimization problem into a subproblem and a master problem. With our formulation, the subproblem can be solved and the two-precoder problem can be transferred to a single relay precoder problem. The master problem, however, is not solvable. We then propose a lower bound for the objective function and transfer the master problem into a convex optimization problem. A closed-form solution can then be obtained by the Karush-Kuhn-Tucker (KKT) conditions. Simulations show that the proposed transceiver can significantly outperform existing linear transceivers with perfect or imperfect CSIs.

Original languageEnglish
Article number6175086
Pages (from-to)1124-1137
Number of pages14
JournalIEEE Transactions on Communications
Issue number4
StatePublished - 1 Apr 2012


  • Amplify-and-forward (AF)
  • channel state information (CSI)
  • joint source/relay precoders
  • Karuch-Kuhn-Tucker (KKT) conditions
  • minimum-mean-squared-error (MMSE)
  • multiple-input multiple-output (MIMO)
  • primal decomposition approach
  • robust transceiver design
  • Tomlinson Harashima precoding (THP)


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