  In this paper, we develop energy-efficient schemes for multi-user
multiple-input single-output (MISO) broadcast channels (BCs), assisted by
reconfigurable intelligent surfaces (RISs). To this end, we consider three
architectures of RIS: locally passive diagonal (LP-D), globally passive
diagonal (GP-D), and globally passive beyond diagonal (GP-BD). In a globally
passive RIS, the power of the output signal of the RIS is not greater than its
input power, but some RIS elements can amplify the signal. In a locally passive
RIS, every element cannot amplify the incident signal. We show that these RIS
architectures can substantially improve energy efficiency (EE) if the static
power of the RIS elements is not too high. Moreover, GP-BD RIS, which has a
higher complexity and static power than LP-D RIS and GP-D RIS, provides better
spectral efficiency, but its EE performance highly depends on the static power
consumption and may be worse than its diagonal counterparts.
