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In this paper, a statistically robust precoding scheme for multiple-input multiple-output systems with orthogonal space-time block code over double correlated Rician fading channels of Kronecker correlation structure is presented. We consider only statistical channel state information (CSI) known at the transmitter for the sake of saving feedback overhead. We adopt eigenrepresentation to express the precoder design in terms of unitary matrix and eigenvalues to minimize pairwise error probability (PEP) subject to an average power constraint for the purpose of reducing computation and fast convergence. A closed-form formulation of the PEP bound in terms of eigenvalue decomposition is derived. By introducing new variables for expressing the power constraint, an optimal power allocation algorithm for given unitary matrix and an optimal unitary matrix update procedure are developed. Based on asymptotic analysis, a near-optimal unitary matrix is derived. With this unitary matrix, the precoder design can be reduced to power allocation that can provide near optimal performance. Using the unitary matrix as initialization, the proposed algorithm can reach the optimal solution in a few iterations. Numerical results show that the proposed optimal scheme provides performance better than existing methods and has low computational complexity and fast convergence in comparison with the fixed-point method.
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