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In this paper, we propose a joint transceiver design for single-carrierfrequency-domain equalization (SC-FDE) based multiple-input multiple-output(MIMO) relay systems. To this end, we first derive the optimal minimummean-squared error linear and decision-feedback frequency-domain equalizationfilters at the destination along with the corresponding error covariancematrices at the output of the equalizer. Subsequently, we formulate the sourceand relay precoding matrix design problem as the minimization of a family ofSchur-convex and Schur-concave functions of the mean-squared errors at theoutput of the equalizer under separate power constraints for the source and therelay. By exploiting properties of the error covariance matrix and results frommajorization theory, we derive the optimal structures of the source and relayprecoding matrices, which allows us to transform the matrix optimizationproblem into a scalar power optimization problem. Adopting a highsignal-to-noise ratio approximation for the objective function, we obtain theglobal optimal solution for the power allocation variables. Simulation resultsillustrate the excellent performance of the proposed system and its superioritycompared to conventional orthogonal frequency-division multiplexing based MIMOrelay systems.

Transceiver Design For SC-FDE Based MIMO Relay Systems