Maximum mutual information design for amplify-and-forward multi-hop MIMO relaying systems under channel uncertainties

In this paper, we investigate maximum mutual information design for multi-hop amplify-and-forward (AF) multiple-input multiple-out (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 precoding matrix at the source are derived. Based on the derived structures, a water-filling solution is proposed to solve the remaining unknown variables.