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In this paper, the authors investigate maximum mutual information design for multi-hop Amplify-and-Forward (AF) Multiple-Input Multiple-Output (MIMO) relaying systems with imperfect channel state information, i.e., Gaussian distributed channel estimation errors. The robust design is formulated as a matrix-variate optimization problem. Exploiting the elegant properties of majorization theory and matrix-variate functions, the optimal structures of the forwarding matrices at the relays and pre-coding matrix at the source are derived. Based on the derived structures, a water-filling solution is proposed to solve the remaining unknown variables.
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