Optimal Tx-BF for MIMO SC-FDE Systems

Transmit beamforming (Tx-BF) for multiple-input multiple-output (MIMO) channels is an effective means to improve system performance. In frequency-selective channels, Tx-BF can be implemented in combination with single-carrier frequency-domain equalization (SC-FDE) to combat inter-symbol interference. In this paper, we consider the optimal design of the Tx-BF matrix for a MIMO SC-FDE system employing a linear minimum mean square error (MSE) receiver. We formulate the Tx-BF optimization problem as the minimization of a general function of the stream MSEs, subject to a transmit power constraint. The optimal structure of the Tx-BF matrix is obtained in closed form and an efficient algorithm is proposed for computing the optimal power allocation. Our simulation results validate the excellent performance of the proposed scheme in terms of uncoded bit-error rate and achievable bit rate.