Minimum BER Transceiver Design for SC-FDE Based MIMO DF Relay Systems

In this paper, we consider minimum bit-error rate (BER) transceiver design for multiple-input multiple-output (MIMO) decode-and-forward (DF) relay systems employing single-carrier transmission with frequency-domain equalization (SC-FDE). The problem is formulated as the minimization of the end to-end (e2e) BER subject to a joint source and relay transmit power constraint. Since the e2e-BER is highly non-convex in terms of the complex matrix optimization variables, solving the optimization problem directly is challenging. By resorting to an upper bound on the e2e-BER and by assuming an optimal sum power budget splitting for the source and relay, we show that the problem can be reduced to the optimization of two equivalent point-to-point MIMO systems. This enables us to derive the optimal eigen-structure of the precoders and the matrix optimization problem simplifies into a convex power allocation problem involving real scalar variables. Primal decomposition is further applied to solve the resulting convex problem in a layered manner, where closed-form solutions are obtained for the inner subproblems. Simulation results are provided to confirm the BER performance of the proposed transceiver design for SC-FDE based MIMO DF relay systems.