Space-time reconfigurable intelligent surfaces for downlink multiuser transmissions

Amplitude, phase, frequency, and polarization states of electromagnetic (EM) waves can be dynamically manipulated by means of artificially engineered planar materials, composed of sub-wavelength meta-atoms, which are typically referred to as metasurfaces. Until now, researchers in wireless communications have mainly focused their attention on space-domain designs of reconfigurable intelligent surfaces (RISs), where the main concern is to engineer the spatial-phase gradient across the RIS to decouple incidence and reflected/refracted directions. However, such designs do not exploit the temporal dimension. Indeed, additional degrees of freedom for controlling EM waves can be gained by applying a time modulation to the reflection response of the metasurface, thereby attaining the so-called space-time RISs. We develop a general framework where a downlink multiuser transmission over single-input single-output slow fading channels is assisted by a digitally controlled space-time RIS. The conclusions of our analysis in terms of system design guidelines are as follows: (i) if the network utility function is the sum-rate time-averaged network capacity, without any constraint on fair resource allocation, and full CSIT is available, then a temporal modulation of the electronic properties of the RIS is unnecessary; (ii) if partial CSIT is assumed only, a random modulation in both time and space of the reflection coefficients of the RIS meta-atoms allows to achieve a suitable balance between sum-rate time-averaged capacity and user fairness, especially for a sufficiently large number of users; (iii) regardless of the available amount of CSIT, the design of temporal variations across the RIS is instrumental for developing scheduling algorithms aimed at maximizing the network capacity subject to some fairness constraints.