  Although reconfigurable intelligent surfaces (RISs) can improve the
performance of wireless networks by smartly reconfiguring the radio
environment, existing passive RISs face two key challenges, i.e., double-fading
attenuation and dependence on grid/battery. To address these challenges, this
paper proposes a new RIS architecture, called multi-functional RIS (MF-RIS).
Different from conventional reflecting-only RIS, the proposed MF-RIS is capable
of supporting multiple functions with one surface, including signal reflection,
amplification, and energy harvesting. As such, our MF-RIS is able to overcome
the double-fading attenuation by harvesting energy from incident signals.
Through theoretical analysis, we derive the achievable capacity of an
MF-RIS-aided communication network. Compared to the capacity achieved by the
existing self-sustainable RIS, we derive the number of reflective elements
required for MF-RIS to outperform self-sustainable RIS. To realize a
self-sustainable communication system, we investigate the use of MF-RIS in
improving the sum-rate of multi-user wireless networks. Specifically, we solve
a non-convex optimization problem by jointly designing the transmit beamforming
and MF-RIS coefficients. As an extension, we investigate a resource allocation
problem in a practical scenario with imperfect channel state information. By
approximating the semi-infinite constraints with the S-procedure and the
general sign-definiteness, we propose a robust beamforming scheme to combat the
inevitable channel estimation errors. Finally, numerical results show that: 1)
compared to the self-sustainable RIS, MF-RIS can strike a better balance
between energy self-sustainability and throughput improvement; and 2) unlike
reflecting-only RIS which can be deployed near the transmitter or receiver,
MF-RIS should be deployed closer to the transmitter for higher spectrum
efficiency.
