In this paper, we employ a reconfigurable intelligent surface (RIS) to boost the single-carrier frequency-domain equalization (SC-FDE) transmission for both single- and multi-antenna broadband wireless communications. Different from the existing RIS-SC-FDE schemes that use an RIS to harvest cyclic delay diversity with a limited beamforming gain, our advanced schemes unlock the potential of the RIS in passive beamforming to maximize the receive signal-to-noise ratio. Concerning the high complexity issue, a low-complexity minorization-maximization (MM) method, which leads to a closed-form solution in each iteration, is developed for the RIS beamforming optimization problem. Finally, simulation results show that the proposed RIS-SC-FDE with the MM-based beamforming significantly outperforms the existing counterparts in terms of bit error rate.
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