Joint Design of Equalization and Beamforming for Single-Carrier MIMO Transmission Over Millimeter-Wave and Sub-Terahertz Channels

We consider the joint design of time-domain equalization and hybrid transmit and receive beamforming schemes, so as to combat frequency-selective fading and path loss effects in single-carrier (SC) multiple-input multiple-output (MIMO) communications systems. In particular, considering the linear equalization and hybrid beamforming matrices as variables, a minimum mean square error (MMSE) problem to minimize the bit error rate (BER) of SC-MIMO systems is formulated and solved via an accelerated matrix quadratic transform (QT) and manifold optimization. The relationship between mean square error (MSE) minimization via joint MMSE equalization and beamforming, and the minimization of average BER over all data streams is expressed analytically, which together with numerical results confirm that the proposed SC scheme outperforms the SC systems whose linear equalizer and beamformers are designed separately.