  A reconfigurable intelligent surface (RIS) is a two-dimensional surface of
engineered material whose properties are reconfigurable rather than static [4].
For example, the scattering, absorption, reflection, and diffraction properties
can be changed with time and controlled by software. In principle, the surface
can be used to synthesize an arbitrarily-shaped object of the same size, when
it comes to how electromagnetic waves interact with it [5].
  The long-term vision of the RIS technology is to create smart radio
environments [9], where the wireless propagation conditions are co-engineered
with the physical-layer signaling, and investigate how to utilize this new
capability. The common protocol stack consists of seven layers and wireless
technology is chiefly focused on the first three layers (physical, link, and
network) [10]. An RIS operates at what can be referred to as Layer 0, where the
traditional design issue is the antennas of the transmitter/receivers; one can
think of RIS as extending the antenna design towards the environment, commonly
seen as uncontrollable and decided by "nature". This approach can profoundly
change the wireless design beyond 5G.
  This article provides a tutorial on the fundamental properties of the RIS
technology from a signal processing perspective, to complement the recent
surveys of electromagnetic and hardware aspects [4], [7], communication theory
[11], and localization [8]. We will provide the formulas and derivations that
are required to understand and analyze RIS-aided systems, and exemplify how
they can be utilized for improved communication, localization, and sensing. We
will also elaborate on the fundamentally new possibilities enabled by Layer 0
engineering and electromagnetic phenomena that remain to be modeled and
utilized for improved signal processing.
