Linear Precoder and Decoder Design for Two-Way AF MIMO Relaying System

A relay based wireless network system is basically composed of three nodes, two source nodes which are also destination nodes and the relay node which helps reliable communications between two nodes. The amplify-and-forward (AF) relaying scheme is more convenient to implement than the decode-and-forward (DF) relaying scheme which requires a decoding process at the relay node. In this paper, we design an optimal linear precoder and decoder which minimize the sum of mean squared error (SMSE) when the relay and the destination node have perfect knowledge of the channel state information (CSI) for the forward and the backward channels, respectively. The optimal linear precoder and decoder solutions are obtained by using the proposed iterative algorithm which satisfies the KKT optimality conditions. The average BER performance of the proposed scheme is compared with those of a conventional AF-ZF scheme and AF-MMSE scheme.