  This work tackles the problem of maximizing the achievable rate in a
reconfigurable intelligent surface (RIS)-assisted communication link, by
enforcing conventional maximum power constraints and additional constraints on
the maximum exposure to electromagnetic radiations of the end-users. The RIS
phase shift matrix, the transmit beamforming filter, and the linear receive
filter are jointly optimized, and two provably convergent and low-complexity
algorithms are developed. One algorithm can be applied to general system
setups, but does not guarantee global optimality. The other is shown to be
provably optimal in the special case of isotropic electromagnetic exposure
constraints. The numerical results show that RIS-assisted communications can
ensure high data rate transmissions while guaranteeing users' exposure
constraints to radio frequency emissions.
