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Mathematical Problems in Engineering
Volume 2017, Article ID 5164681, 8 pages
Research Article

Linear Precoding Scheme Design for MIMO Two-Way Relay Systems with Imperfect Channel State Information

College of Electronic and Information Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, China

Correspondence should be addressed to Xiao-min Chen; nc.ude.aaun@204mxnehc

Received 16 November 2016; Revised 16 February 2017; Accepted 1 March 2017; Published 12 April 2017

Academic Editor: Nazrul Islam

Copyright © 2017 Xiao-min Chen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The aim of this paper is to investigate a linear precoding scheme design for a multiple-input multiple-output two-way relay system with imperfect channel state information. The scheme design is simplified as an optimal problem with precoding matrix variables, which is deduced with the maximum power constraint at the relay station based on the minimum mean square error criterion. With channel feedback delay at both ends of the channel and the channel estimation errors being taken into account, we propose a matrix decomposition scheme and a joint iterative scheme to minimize the average sum mean square error. The matrix decomposition method is used to derive the closed form of the relay matrix, and the joint iterative algorithm is used to optimize the precoding matrix and the processing matrix. According to numerical simulation results, the matrix decomposition scheme reduces the system bit error rate (BER) effectively and the joint iterative scheme achieves the best performance of BER against existing methods.