The Maximum-SNR Optimal Weighting Matrix for a Class of Amplify-and-Forward MIMO Relaying Assisted Orthogonal Space Time Block Coded Transmission

The optimal weighting matrix design at the relay node for the V-BLAST based amplify-and-forward (AF) MIMO relay transmission scheme has been intensively investigated in literature. However, there are few papers considering the optimal design of the weighting matrix at the relay node for orthogonal space time block codes (OSTBCs) based AF MIMO relay transmission scheme. In this paper, the maximum-SNR weighting matrix at the relay node is designed for the OSTBC based AF MIMO relay scheme, so that for the first time we can quantify the SNR gain by optimizing the weighting matrix at the relay node for the OSTBC based AF MIMO relay scheme. Specifically, the canonical form of the optimal linear weighting matrix is derived by exploiting matrix inequality theory and majorization theory. Furthermore, we propose a simulation based Gamma approximation method for diversity order analysis. The simulation results show that the proposed optimal weighting matrix significantly outperforms the traditional scalar-gain weighting matrix for the OSTBC based AF MIMO relay scheme.