  Reconfigurable intelligent surfaces (RISs), which enable tunable anomalous
reflection, have appeared as a promising method to enhance wireless systems. In
this paper, we propose to use an RIS as a spatial equalizer to address the
well-known multi-path fading phenomenon. By introducing some controllable paths
artificially against the multi-path fading through the RIS, we can perform
equalization during the transmission process instead of at the receiver, and
thus all the users can share the same equalizer. Unlike the beamforming
application of the RIS, which aims to maximize the received energy at
receivers, the objective of the equalization application is to reduce the
inter-symbol interference (ISI), which makes phase shifts at the RIS different.
To this end, we formulate the phase shift optimization problem and propose an
iterative algorithm to solve it. Simulation results show that the multi-path
fading effect can be eliminated effectively compared to benchmark schemes.
