Joint optimization for one and two-way MIMO AF multiple-relay systems

Kyoung Jae Lee, Hakjea Sung, Eunsung Park, Inkyu Lee

Research output: Contribution to journalArticlepeer-review

182 Citations (Scopus)


This paper considers both one-way and two-way relaying systems with multiple relays between two terminal nodes where all nodes have multiple-input multiple-output (MIMO) antennas. We propose a unified algorithm which computes the optimal linear transceivers jointly at the source node and the relay nodes for amplify-and-forward (AF) protocols. First, optimization designs based on the sum-rate and the mean-square error (MSE) criteria are formulated for the two-way AF relaying channel. Due to non-convexity of the given problems, the proposed schemes iteratively identify local-optimal source and relay filters by deriving the gradients of the cost functions for a gradient descent algorithm. Then, the proposed algorithm can optimize a one-way multiple relay system as a special case of the two-way channel. Finally, we prove the global optimality of the maximum sum-rate scheme under an asymptotically large antenna assumption. From simulation results, it is confirmed that the proposed methods yield the near optimum result for the MIMO multiple relay channel even with a moderate number of antennas. Consequently, we show that the proposed algorithm outperforms conventional schemes in terms of the sum-rate and the error performance for both one-way and two-way protocols.

Original languageEnglish
Article number5610977
Pages (from-to)3671-3681
Number of pages11
JournalIEEE Transactions on Wireless Communications
Issue number12
Publication statusPublished - 2010 Dec

Bibliographical note

Funding Information:
This research was supported in part by Seoul R&BD Program (ST090852) and in part by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (No. 2010-0017909). The materials in this paper were presented in part at the IEEE VTC, Barcelona, Spain, April 2009 and at the IEEE VTC, Anchorage, USA, September 2009.


  • Amplify-and-forward (AF) relaying
  • maximum sum-rate
  • minimum mean-square error (MMSE)
  • multiple relays
  • multiple-input multiple-output (MIMO)
  • two-way protocol

ASJC Scopus subject areas

  • Computer Science Applications
  • Electrical and Electronic Engineering
  • Applied Mathematics


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