  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.
