Rate Optimization for Hybrid SC-FDE/OFDM Decode-and-Forward MIMO Relay Systems

In this paper, we consider the rate-optimal transceiver design for a hybrid single-carrier frequency-domain equalization and orthogonal frequency-division multiplexing decode-and-forward (DF) multiple-input-multiple-output (MIMO) relay system. Such hybrid systems can provide a high end-to-end bit rate and a low peak-to-average power ratio at one of the transmitting nodes. Assuming minimum mean-squared-error equalization at the receiving nodes, we optimize the transmit precoding matrices for maximization of the achievable bit rate (ABR) of the system subject to a joint node transmit power constraint. We provide a unified solution for the precoding matrices, which subsumes the solutions for pure single-carrier and pure multicarrier MIMO DF relay systems as special cases. Specifically, the optimal structure of the precoding matrices is obtained by exploiting the relation between our design and conventional point-to-point MIMO transceiver designs. With the optimal precoding structure, the optimization problem reduces to a convex power allocation problem, for which an efficient closed-form solution is derived. Numerical results are provided to confirm the excellent ABR performance of the proposed relaying schemes.