Robust Superimposed Training Designs for MIMO AF Relaying Channels under Total Power Constraint

We investigate how to design the robust training matrix for spatially correlated multiple-input multiple-output (MIMO) amplify-and-forward (AF) relaying channels with imperfect channel covariance matrices, where the unitary-invariant channel covariance error matrices and the colored noise are assumed. Moreover, the superimposed training technology and the total power constraint are both taken into account. In our work, the robust training design for linear minimum mean-squared-error (LMMSE) channel estimation is formulated as a nonconvex problem. In order to effectively solve the considered nonconvex optimization problem, we resort to an upper bound of the performance of the training optimization and then an iterative SDP algorithm is proposed for the training optimization. Finally, numerical simulations demonstrate the excellent advantages of the proposed robust training design for the LMMSE based channel estimation.